Author: Астахов И.В.
Tags: тепловые двигатели (кроме паровых машин и паровых турбин) механика
Year: 1971
Text
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nop' 06meH pe.naKItHeil npotI>. H. B. ACTAXOBA
H31{ATEJIbCTBO «.MAllIHHOCTPOEHHE»
MocKBa 1972
y J1K 521.436 -43;' 44
1144
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x 0 B 11. B., T p y COB B. J.1., X a 'I U 51 lj A. C. H .D:!P. .11,1.,
«MilU:IIJHOCTpOcHHe», 1971, 359 CTp. .
. KHMrc paccMoTpCHbI rH pb.D:!JHaMHKa npOI.\CCCOB Bnp :
CKa M pacnbwHBamI!J TO!J,1HBa B .D:H3CJlHX H MCTO.D:bl pac-
'-ICTa 3TIIX !JpOI.\CCCOB .D:.TJSI pa3.'IlI'lHb!X TOIl,1HBHbIX CHCTCl\!.
npHBC;J.CH paC'lCTHO-5iKcncpHMcHTa,1bHbIII MaTcpna.TJ, xapaK-
TCp!J3Y!OIllHH OC06CHHOCTH pa60Tb! TO!J.TJHBHbIX CHCTCM
II BJIIISlHIIC !Jpol.\ccca B!Jpb!CKa Ha pa60'IHH !JpOI.\CCC J1lH3cm!.
PaccMoTpCHbl npIl6J1HLKCHllbIC MeTotJ,bI paC'ICTa TO!JJ1HBHblX
CHCTClII H HCKOTOpbIC ncpcnCKTHBb! IIX pa3BHTHH. ,QaHb!
KJIaccHQJHK8rum TO!J.1f!BHbIX CHCTCM H KpaTlmH 063,OP HC-
KOTOpbJX cOBpeMeHHblx KOHCTPYKII,HH. KHuta npe.D:H83Ha'lCH8
;r,lSl IIH)KCHCPHO-TCXHH'-ICCKIIX II HaY4Hb!X pa601f!ll1KOB.
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Pc 1.\ e H 3. C H T A-P' Te tI; flaYK 10. 4>. ,[I.HTSlKIH"
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pa3pa60TKe TOn.TJ.llBOBnpbICKHBaIDlilJIX CHCTeM nOCBHIll.eHO MH<;fO
pa6OT. ABTOpbI nOCTaBHJ1H nepe c060i1 3a.u.aqy 0606ll1.HTb MaTe-
pHaJ1, OC06eHHO B OTHOllIeHHll MeTO.u.OB paC'IeTa II nOHCKOB B3aHMO-
CBH3H npO eCCOB nO;J:aqll II p3CnbIJ1HBaHllH TOD.'IHBa C pa60'IHM HK-
.10M BHfaTe.'1H C BOCn aMeHeHHeM OT cmaTHH, a 'raKme K.JIaccH<lm-
Ka HH Ton"lHBHbIX CHCTeM. B OCHOBY KHHfH nO,,10meHbl fJIaBHbIM
06pa30M pa60TbI, BbInO.'1HeHHbIe caMHMH 3BTopaMH. BO:lbIlIHHCTBO
H3 HHX nOCBHll1.eHO H3yqeHHID npo eCCOB .no.u.aqfl H pacnbI.1llBaHllH
TOnJ1HB3 B 6bICTPOXO.Z/.HbIX )1.H3eJIJIX Ma.noll II cpe)1.Heii MOll1.HOCTH.
I1cc"1e)1.0BaHHH npOBO)1.H.1HCb B Dp06.1eMHOH .i136opaTopHH TpaHC-
nopTHbIX )1.BHf'aTeJ1eH MA)].I1, a TaKme B HeCKO.'1bKHX HaY'lHO-HC-
c.le;J:OBaTe.'1bCKHX HHCTHTYT3X. BBHlI.Y 06ll1.HOCTH npOTeKaHHH YKa-
3aHHbIX npo eCCOB B .z:r.H;3e.ilHX Bcex THnOB, B rOM QHC.i1e H B . !Oll1.HbIX
TllXOXO;J:HbIX, aBTopbI H3.z:r.eIDTCJI, QTO npe)1.J1afaeMbIH MaTepHaJi MO-
meT 6bITb nO.'1e3eH H cneUHa.1lfCTaM no Ten.10B03HbiM II Cy.z:r.OBbIM
lI.H3e,,1HM.
Ope)1.llCJ10BHe, BBe.z:r.eHHe, f.1. II, 3a llCK.1ID'IeHHeM paCQeTa npo-
XO)1.HO n.10ll1.a;J:H nO;J: KOHYCOM llr.1bI II 3, f.'1. IV, 3a HCK.1JOQeHHeM
9, H'r.7I. VII HanHcaHb 11. B. ACTaXOBbIM; f,,1. 1, 3 fJ1. II, a TaK-
me 9 rJI. IV - A. C. Xa'IHHHOM; f.'1. III - J1. H. fo.'1y6KOBbIM;
f.l13Bbi V II VI, 3 TaK)Ke paCQeT npOXO)1.HOH n.'1Oll1.a.II.Hno)1. KOHYCOM
Hr.lbI B f.1. II - B. H. TpYCOBbIM.
OCHOBHblE YCJlOBHblE 0603HA4EHI-1S1
a - CKOpOCTb paCnpOCTpaHCHH5I BO.TJH .D:aB,lCHHH B TOnJlIIBe;
C.. C... C n - CKOpOCTII .LI.BlliKCHII5I Hr.1bI 1j:J0PCYHKII, HarHCTaTCJlbHOrO j(,1a-
naHa, nJlymKcpa;
C.., C'.. - CKOpOCTII .D:BlliKCIIHH TOnJlHBa Ha nxo.D:C H BbIxo,n:e Ton.1HBO-
npoao.!J.a;
U 11. - CKOpOCTb nOTOKa ra3a;
u"o, U.. n , U.. P - Ha'-la.1bHa5l, TCKYll.\aH 11 KpHTH4CCKaH CKOpOCTII ,n:BIILKCHI151
KanJIII no OTIIOIllCHHJO K ra30BOH cpe.D:e;
ron, ro.. - pa.!J.I1YCbI BnYCKHoro H OTCC4HorO OKOH rH.1b3bI;
d n , d.. - .D:HaMCTpbI n,lYHLKcpa 11 HarHCTaTC.lbHOro K.TJanaHa no pa3-
rpY30'-lnOlllY nOHCKY;
d.. - .D:llaMCTp KaHa.1a B nafHCTaTe,1bHOM Tpy60I1pOBO,n:C;
d u , d x - .D:llaMCTpbI HanpaB.l51JOIll.CH 4aCTII IIr.1bI H 3anopnOH KpOMKI1
lIa CC KOHYCC;
d p .., de - .D:llaMCTpbI Kana.1a B HOCKe paCnbI.TJIITC,lH H con.10Boro OT-
BCpCTI1H;
d.. n - AHaMCTp Kan_111;
d max , dmin - MaKCIIMa.1bHbIi1 H MHHl1l\1a.TJbHbIi1 ,n:llaMCTpbI Kiln.TJH;
F ( t - ) - npHMaH BO.1Ha .ilaB.1CHHH, nO.D:OIllC.ilIllaH K 1j:J0PCYHKC;
I", f ;, f"l - n.10Ill.a.!J.H nOnCpC'-IHOrO ce4eHHH no nOHCKY, nepbHM If nol!.
n05lCKOM llarHCTaTC.1bHoro KJlanaHa;
f u - n.10U.\a.D:b nOnCp qHOrO CCqeHH5I HrJlbl, Ha KOTOpyJO .D:eHCTBY-
JOT ,iJ.aB.1CHH5I P tP H P<JJO;
f 1<, f 0 - TCKYll.\a51 n.10Il.\a;rb npOXO.l<HbIX CC'-ICHIIH no;:!; KOHYCOM Hr.1bI H
OTCe'-lHOrO H.1H BCaCbIBaIOIl.\Cro OKOH rll.lb3bI n.'IYHLKepa;
fo - n,10U.\a.ilb con.10Bb!X OTBCpCTIli1 paCnbl.TJIITc.'1H;
f 11., f.. - n.10U.\a.D:H noncpC4Horo CC4CHHH n.'1YHLKcpa H KaHa.TJa B Ha-
rHCTaTC.TJbHOM Tpy60npOBO,n:c;
fw. - n.10U.\a.D:b Il.\THIj:JTa IIr.1bl 4JOPCYHKH;
h n , he.... - no.1Hb!i1 H aKTHBHbIII XO.!J. n.TJYH>KCpa;
h", h..o - nO.D:"bCM HafHeTaTC.TJbHOro K.TJanaHa no.1Hbli1 H paBHb!i1 abICO-
TC pa3rpYLKaJOIl.\CrO n05lCKa;
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KaMcpbl IllTYI.\Cpa Hacoca AO KaMepbI paCnbI.1HTCJlH;
Lrfj - .!J..TJHHa lj:JaKc,'!a (.:\a.lbIJ060HHOCTb) npn Bnpb!CKe B HenOA-
BIILKHYJO ra30BYJO cpCAy;
in - A.1ItHa npOBo.TJOKII npYLKHHbI;
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M - MaCCa HarHCTaTe.1bHoro K.1analJa H .D:BIILKYIl.\IIXCH C III1M AC-
Ta.lci1;
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n - 4HCJIO 060pOTOB Ky.TJa'-lKOBOro Ba.1a Hacoca;
P Ii' p.. - TCKYll.\He .ll.aB.1CHH5I B Ka ICpC HarHCTaHH5I H 06"bCMC IllTYI.\C-
pa HaCOCa;
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,!\BmKCHH5I HarHCTaTC.lbIlOrO K.lanaHa;
po - OCTaTO'-lHOe ,J,aB.leHlle TOn.1HBa B HarHeTaTCJlbHoit MarH-
CTpa.lll ;
Prf>, P.."o - ,J,aB.leHIIC TOn.1HBa B KaMepe paCnbI.1HTe.1H BbIIllC 3anOpHOrO
KOHyca TCKYll.\Ce H B 1II0MCHT Ha'-l3.TJa ;rBIILKeHHH HrJlbl;
p - TCKYll.\Ce .!J.aBJlCHHC TOn.TJIIBa B 06"bCIIIC IIICJK.l\Y 3anOpHbIM KO-
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II KO.1bllCBbIM npOXO.D:!lbIM CC4eHIICM Y IllTHIj:JTa);
p1f - ;:J:aB.1CHIIC ra3a B 1111J1HH.D:pC .!J.BHraTe.'IfI;
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1\11\ OTBCpCTHflMH B ncpBOM lj:Ja3c BnpbICKa npH «CTyneH'-Ia-
TOM» 3aKOHC no,!\a'JH, 06CCnC'-IHBaeMOe pcrYJlHpOBaHHeM CHC-
TCMbl;
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q1f -I.\IIK.10Ba51 nO.D:a'-la Ton.1HBa;
ql{<P - Ko.1H'-IeCTBO TonJ111Ba, no,'!,aHlloro H3 pacnbl.1HTe.1H K TCKYll.\e-
MY MOMeHTY npOI.\CCca BnpbICKa;
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no.TJHOMY !IOJI:"bCMY nJlYHLKepa;
V - 06"beM lIlTYllcpa Hacoca;
V oc - OCTaTO'-lHbli1 CB060.D:Hblll 06"bCM B HarHCTaTc.'lbHoi1 MamCT-
paJ1H;
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CYHKe;
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60npOBO.D:a H B pacnbI.TJHTC,le 1j:J0PCYHKH;
V"n - 06"beM Kane.'Ib;
W(t) - 06paTHaH Bo.1Ha, nO;J.OIllC):{Illa51 K IllTYllCpy Hacoca;
X -TCKYll.\CC 3Ha'ICIIHC ,!\.lHHbI Tpy60npOBO.D:a;
y, Ymax - TCKYll.\IIi1 H MaKCHMa.TJbHbIH (.D:O ynopa) nO.D:"bCMbI HrJlbl;
Z), Z2. Z3 - paCXO.D:bI Ton.1l1Ba '-ICpC3 3a30pbI B 30JIOT!lHKOBOit '-IaCTH
nJlY!lJKepa, nopIllHCBOH '-IaCTII nJlYHJKepa, MCJK.II.Y HrJlOH H
KopnYCOM pacnbI.1I1TC.151;
- cpe.D:!lIIi1 K031j:Jlj:JHI.\HCHT C:tKHMaCMOCTII Ton.1HBa;
- nO.!J.a'!a Ton,1HBa Ha rpa.D:Yc yraa nOBopOTa Kyaa4Ka;
- npHpall.\CHHC 06"bCMa;
- JKCCTKOCTb nppKH!lbl COOTBCTCTBCHHO HarHCTaTCJlbHoro KJla-
naHa H $OPCYHKII;
6 n , 6" - pa.D:lla.'Ib!lbIH 3a30p COOTBCTCTBeHHO B pacnbl.lI1TC.'IC H Hacoc-
HOIll ,WCIIIC!lTC;
Ec - K031j:Jlj:JHI.\IIeHT C)KaTH5I CTPYH ,!\.1H con.TJOBOrO OTBCPCH!H;
t} - K031j:Jlj:JHI.\HeHT .D:CMnlj:JlJpOBaHHH Ko.'Ie6aHIJi1;
'A' - K031j:Jlj:JHI.\HeHT conpOTHB.1CHIJH C.D:IIHHl.\bl JI:.1HHbI Tpy60npo-
BO.!J.a;
JtT, Jt. - K03<p$HI.\HeHTbI BH3KOCTIJ COOTBCTCTBeHHO TOnJlIJBa IJ ra3a;
J.tUj - K031j:Jlj:JHlllleHT pacxo,!\a TOnJlIJBa '-IepC3 npoXO.D:HYIO ll.\CJlb Me-
JKJI:Y HarHCTaTCJlbHbIM K.1anaHOM H cra Ce.D:JlOM;
- K03<p<PHllHeHT pacxo.D:a TOnJ1llBa COOTBeTCTBCHHO Ha ce'JeHHIJ:
COnJlOBbIX OTBCpCTHM, BCaCb!BalOll.\HX If OTCC'JHbIX OKOH, MeLK-
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B c60pe;
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V T , V" VB - K03lj:JcpHI.\IICHT KHHCMaTII'-IeCKOH 1J5I3KOC1U COOTBeTCTBCHHO
TOnmlBa, ra3a, B03.!J.yxa;
V T' V n- qaCTOTa C06CTIJCHHblX KO.'Ic6aHHi1 COOTBCTCTBCHHO CTO.16i1
LKl!.D:KOCTH IJ TOnnHBOnpOBO;J,C l! npYJKHHbI CPOPCYHKH;
p, p.. PB - n_l0THOCTb COOTBCTCTBeHHO TOn.1l!Ba. ra3a H B03D.yxa;
00. at. 0"2 II T..D:. - cTynCH'-IaTbIe Ij:JYHKUl!H, npHHHMaIOlUlIC COOTBCTCTBCHHO 3Ha-
qeHII5I 0; I H.1H -I B 3aBHCIIMOCTU OT Ha.TJOLKCHHb!X Ha HHX
YC.l0BHH;
aT - K03cpcpUUHCHT nOBcpXHOCTHoro HaTHJKCHH5I TOm!l!Ba;
1:, - BpCl\!5I 3ana3J].bIBaHH5I BOCJ1.11aMeHCHH5I B eel(;
Tn - npO.!J.OJlLKIITC.TJbHOCTb nO.D:aqll TOnJlHBa B eeK;
1', TI - yr.lb! KO!lYCOB CC.D:.1a H Hr.1b!;
\jJ - yro.TJ nOBopOTa Ky.la4KoBoro Ba.'1a Hacoca;
\jJn - npO.!J.omKHTc.TJbHOCTb nob,a'-lll TOnmma IJ 2paiJ;
'PI- yrOJ1 nOBopOTa Ba.1a Hacoca OT MOMCHTa Haq,Wa .!J.BIILKCHIIH
n.'IymKcpa .D:O MOMCIlTa nO_11l0rO ncpCKpbITHH BCaCbIBaIOIUI1X
OKOH;
qJaKm- yroJi nOBopOTa BaJJa Hacoea. COOTI3CTCTBY!OIUHII aKTl!BHOMY
XO.!J.Y n.1YHiKcpa.
BBEAEHHE
Oc06eHHOCTblO .LUI3eJHJ 5lBJ1HeTCH 3aBHCHMOCTb ero TeXHUKO-.3KO-
HOMH4eCKHX nOKa3aTe eH OT KaqeCTBa pa60T H napaMeTpOB Ton-
HBHOH CHCTeMbI. B ,lLH3e,JIe Ton HBO BnpbICKHBaeTCH no.n. BbICOKHM
,lLaB,,'1eHHeM (350-1000 KF/cM 2 H BbIllle) 4epe3 He60J1blllUe OTBep-
CTHH, BCJle.n.CTBHe qero OHO paCnbIJIHBaeTCH HenOCpe,lLCTBeHHO B Ka.
Mepe cropaHliH .n.Bl1raTemJ.. B KaMepe CrOpaHll51 HaXO.lJ.I1TC5I B03.lJ.YX,
CfKaTbIH ,LI,O HeCKO.'1bKI1X ,lLeCHTKOB aTMoccpep U HarpeTbIH B npouecce
OKaTU5I ,LI,O 600-800° C. TOnJ1UBO, BnpbIcHYToe B rOp5I4lIH B03,L1,YX,
HarpeBaeTCH B HeM, BOCnJiaMeH5IeTCH 11 cropaeT. C e,Ll,OBaTe bHO,
KalIeCTBO pa604ero npouecca 6Y,LI,eT 3aBHceTb OT Toro, KaK II KOr,lLa
nO,J,aeTCH Ton.'1I1BO, KaK OHO paCnbIJleHO 11 pacnpe,lLe.'leHO no 06"beMY
KaMepbI cropaHIiH.
TOnJ1IIBHaH CI1CTelVIa, B 06lll.eM C Y4ae COCTOHlll.aH H3 Ton.'1IIB-
HOro Hacoca, HarHeTaTe.'lbHOrO Tpy60npOBO,Ll,a II CPOPCYHKII, OTHOCIIT-
CH K lIUC.'l)" Ba.lli:HeIIlllI1X arperaTOB ,lL1I3e. l lH. YlIIiTbIBaH, 4TO TOI1.'lf!B-
l-IaH CIiCTeMa llrpaeT Ba.lli:I-IYlO pO b B npouecce cMece06pa30BaHlIH,
K Heli npe,Ll,"bHB.1HlOTCH .lli:eCTKUe Tpe60BaHIiH. OHa ,lLomKHa:
1) nO,Ll,aBaTb Ha .UIIKJ1 3alIaHHoe KO.'1IIlIeCTBO TOnJ1IIBa;
2) nO,Ll,aBaTb Ton.'lIiBO B 3a.n.aHHbIH neplIO,Ll, II no onpe.rr.e.'1eHHoMY
3aKOHV.
3) J paCnbI.J1lmaTb Ton.llIBO Ha Kan.'lII, pa3Mep KOTOpbIX n03Bo.'1HJI
6 TaI\ pacnpe,Ll,emlTb I1X no 06"beMY I\aMep cropaHllH, QT06bI HaH-
50.lee paU110HaJ1bHO HCn0J1b30BaJ1CH paoolIliH B03,lLYX;
) 06ecnelIliBaTb lI,LI,eHTlI4HYlO pa60TY Bcex CeI\UHH TOnJIlIBH9H
CHCTeMbI.
BbInOmIeHlIe YKa3aHHbIx Tpe60BaHIIH 3aTpY,lLHHeTCH TeM, QTO:
1) npon:o.IJ.lli:IITe.rIbHocTb nO,lLalIH TOn.'lHBa OlIeHb MaJIa (0,01 celi.
B TIIXOXO,Ll,HbIX ,LI,l13eJIHX II 0,0005 ceK B 6 CTpOXO,lLHbIX ,lLII3eJlHX Ma-
JIOII MOlll.HOCTII);
2) KOJIIIlIeCTBO Ton.IJIIBa, nO,Ll,aBaeMOro Ha UIIKJI, TaK.lli:e OlIeHb
Ma.'1O. B ,LI,1I3eJ1HX 60J1bllIOH MOlllHOCTH Ha HOMHHaJ1bHOM pe}KIIMe
BnphlcKIiBaeTcH HeCKO,,'lbKO rpaMMoB TOnJIIIBa, B 6bICTPOXO,Ll,HbIX ,lL1I-
3eJIHX Ma.'lOH MOlll.HOCTIi - COTbIe ,LI,O.1J1I rpaMMa;
3) ,LI,aBJIeHIIe II CKOpOCTb Bnp cKa TonJ1IIBa, a TaK (e ,lLaBJIeHlIe
II TeMnepaTypa cpe,Ll,bI, B KOTOPYlO no TOnJ1UBO BnpblcKIiBaeTcH,
pe3KO 1I3MeHHlOTCH;
7
4) HeH3BeCTeH 33KOH nO.rI.a'IH TOn.'IHBa, cooTBeTcTBYlOllI.HH KOH-
CTPYKTHBHbIM oc06eHHocTHM H YC.'lOBHHM 3KCnJ1yaTau.HH .rI.H3eJUI, .rI.JUI
KOToporo 3Ta CHCTeMa C03.rI.aeTCH. 3aKoH nO.rI.allH Ton HBa HeH3Be-
CTeH, TaK KaK nOKa OCTaIOTC5I HeBbIHCHeHHbIMH KOJIHlleCTBeHHbIe H
KalleCTBeHHbIe B3aHMOCBH3H MeLK.!'I.Y npou.eccaMH nO.rI.allH Ton HBa,
cMece06pa30BaHHH H cropaljJ1H. 13.,arO.rI.apH pa60TaM COBeTCKHX Y4.e-
HbIX [7, 20, 25, 27, 34, 52, 60, 67, 75 H .rI.p.J MOLKHO TO.lbKO BeCbl\Ia
npH6.1HLKeHHo OL(eHHTb HeKoTopbIe oc06eHHocTH 3aKOHa nOJ,allH Ton-
.'lHBa H Ton.'1HBHOH CHCTeMbI, npoeKTHpyeMoH )J..'lH KOHKpeTHoro .rI.H-
3e H.
He.rI.OCTaTOllHocTb HalllHX 3HaHIffH 0 B3aHMOCBH3H MeLK.rI.Y npoL(ec-
caMH nO.rI.allH Ton.TJHBa, cMece06pa30BaHHH H cropaHHH HB.'IHeTCH
"C.TJeJJ.CTBHeM C OLKHOCTH <pH3HllecKHx HBJ1eHHH H XHl\U14.eCKHX peaK-
II.HH, B03HHKalOllI.HX B U.H.'IHHJJ.pe .ZI.H3eJUI npH nOJJ.rOTOBKe Ton.'IHBa K
Bocn aMeHeHHIO H cropaHHIO. KpoMe Toro, He 0606ll1.eHbI JI.OBO.'IbHO
MHOrOllHCJ1eHHbIe pa60TbI no HCCJJIeJJ.OBaHHIO YKa3aHHbIX npou.eccoB.
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oc06eHHocTeH npoTeKaHHH npou.ecca Bnp cKa Ton HBa H pa6011ero
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TepHcTHKH BnpbIcKa H TOII.'IHBHOH CHCTeMbI. B CBH3H C 3THM YKa-
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(rHJJ.p0JJ.HH3MHlleCKHe MeToJJ.bI).
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npHMeHHlOTCH, TaK KaK norpeWHOCTb HX OlleHb BeJIHKa, HO HMI1 nO.1b-
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MeTO.lI.bI HB''lHlOTCH npH6J1H)KeHHbIMH, a 06.1aCTb HX npHMeI-IeHHH
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TopbIe CTOpOHHHKH TaKI1X MeTO..'l.OB npOTI1BOnOcTaB.'lHlOT I1X cOBpe-
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llaeT, 'ITO MeTOAbI nO;:I.06HH H pa3MepHocTH oc06eHHO 3<p<peKTHBHbI
Ha Halla bHoii: CTa.lI.HH H3YlleHHH CJ10)!{HbIX HBJ1eHHi'I, T. e. KOrJl,a BO-
npoc TeopeTHllecKH elll.e He.lI.OCTaTO'IHO pa3pa60TaH. OAHaKo OFf npe-
Aynpe)J{AaeT KaK 0 HeJl,Oou.eHKe, TaK H 0 nepeou.eHKe B03MO)!{HOCTeII
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COlIeTaHHe TeopmI nO..'l.06HH H pa3MepHocTH C aHa.'lHTHlleCKHM pac-
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MeTOllaM He BepHO.
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BeCbMa TpY;:I.oeMKHMH, a TOIIHOCTb HX HH3KOH. TaK, 3i'IxeJlb6epr H
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CTBe OCHOBHbIX llJIH CHCTeM C HarHeTaTeJ1bHbIMH Tpy6onpOBO.lI.aMH
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BnpbIcKa.
HarHeTaTe 'lbHbIH K"lanaH (plIC. 4)
C MOMeHTa BXOAa pa3rpY)KalOIl..I.ero Il.IWHH.D.pHQeCKOrO nOfiCKa .D.lIa-
MeTpoM d", B HanpaBJIHIOIl..I.YIO I{.1JanaHa pa3rpY)KaeT TorrmmorrpoBoA
OT LI.aBJ'leHHfI, 'ITO crroco6cTByeT 'IeTKoMY OKOH1JaHHIO npoIl.ecca
BnpbICKa H npenHTcTByeT B03HHKHOBeHHIO .D.OnOJIHHTeJIbHbIXBnpbIc-
KOB. B orrpe.n.e.'IeHHbIX YC.TJOBHflX npH pa60Te K.TJarraHa C pa3rpY)KalO-
Il..I.HM rrORCKOM B CHCTeMe MorYT C03AaBaTbCfI cBo6oAHbIe 06"beMbI,
KOTopwe B pfiAe cllY1JaeB He6J'IarOrrpHHTHo B.TJHHlOT Ha npoIl.eCC
BnpbICKa TonJ'IHBa.
Ha pHC. 5 nOKa3(}H HaH60"lee pacnpoCTpaHeHHbrH THn rH.D.paB-
.TJHQeCKH ynpaBJI5IeMOH CPOPCYHl{H 3aKpbITOro THna, HMelOIl..I.eH HrO.1Jb-
QaTbIH 3anopHbIH KJ1anaH C .n.lIcpcpepeHIl.HaJIbHOii n.loIl..I.a.D.KoH. B nOH
CPopcYHKe ,u:aB.1JeHHe Ton.nHBa npH OTKpbITHH Hr.1JbI n.eHCTByeT Ha
14
9
10
PHC. 3. CCKI.\II5J Ton.l!!BHoro
Hacoca C IIICXaHH'-ICCKHlII npM-
BO OM !J 03!JpoBaH!JcM
n.1YH1KepOlll-30JlOTHMKO M:
1 - perYJIUpyroru.aH pellKa:
2 - BTY 1)Ka n..1YH}Kepa; 3-
nollYH.Mep; 4 - ce.lI, T[O HarH€-
T3TeJIbHOrO K 1anaHa; 5 - Ha-
fHeTaTe".'lbHbIH KllarraH; 6
lllTYIjep CeKIjHH; 7 - nPY>KHHa
HarHeraTe.HbHoro f(,,'IanaHa; 8 -
rnecTepHfI: 9 - BTy.HRa c na-
30M; 10 - XBOCTOBHK nJIYH-
>Kepa
.lI,11Q:><}JepeHlJ,lIa.1bHYIO n.'IOIII a.lI,KY, npl1 3aKpblTIIl1 - Ha BCIO n.10-
llla,.lI,b nOnepeqHOro ee CeqeHlIH, BC.1e.lI,CTBIIe qerO .lI,aB.1eHl1e Haqa,la
OTKpbITHH 11 r.1 bI 0I<a3blBaeTCH 60.'Ibll1e .lI,aBJIeHHH HaqaJIa ee 3aKpbI-
TH5JI, qTO He6.'IarOnpHHTHO BJIl1HeT Ha npou.ecc CrOpaHlIH.
flI.lI,paBJIH'leCKH ynpaBJIHeMbIe <}JOPCYHKlI 3aKpbITOrO nIlla, CO-
3.lI,alHHbIe B nOCJ1e.lI,Hee BpeMH .lI,J1H aBTOTpaKTopHbIX .lI,H3eJIeH, OT.'III-
qaOOTCH YMeHbll1eHHbIM, no cpaBHeHHIO C npe)J{HHMH MO.lI,e.'IHMH, YCTa-
HOBOqHbIM ,3,HaMeTpOM (Ha 2-3 .MM), qTO Y"lyqll1aeT YC.10BIIH ox-
{j
a)
6)
PilC. 4. HarHCTaTeJIbHble K.1anaHb!:
fl - rpH6KoBoro TJUIa c pa3rpYLKaIOllJ.HM n05lC-
KOM; 6 - 30ol'lOTHHKOBoro THna; 1 - rOJJOBKa
K.1:anaHa; 2 - pa3rpy alOrn.Hfr nOfiCOK; 3 -
XBOCTOBHK KJ}.anaHa; 4 - ceJJ....lo; 5 - K.nan H;
6 - rrpYJKHHa; 7 - cTonopHoe KO.lIhl{O; 8 -
ynopRa>! rnaii6a; h K - pa3rpY>KalOI.U.Hii xo)],
KJIanaHa
PHC. 5. 4>opcYHKa C paCnb!JlHTCJlCM 3aKpbl-
Toro 'runa:
1 - npY>KIlHa; 2 - IiJTOK; 3 - Kopnyc;
4 - w..e.TJ.eBoi'I q,HJ1bTp; 5 .- pacnbl.1HTeoilb
7
6
5
If
2
J
l,
)'
'+
5
JIa:lK.lI, HIIH <}JOPCYHOK II HanO"lH€HIIH AII3eJ1H. CTH)J{HaH raHKa Kpen-
.'IeJHHH paCnbI.111Te"lH BbIDO.'IHHeTCH 60.'Iee TOHKOCTeHHOH, 6.1arO.n.ap5I
qelMY YMeHbll1aIOTC5I .lI,e<}JOpMau.HH paCnbI.111TeJIH, 06eCneqHBalOTCH
CTa6HJ1bHOCTb 3a30pa B nape Kopnyc - Hr,1a, a TaK)Ke nO,J,BHIKHOCTb
BLJJbI B pa60'leM COCTOHHlIlI.
B TaK Ha3bIBaeMbIX KapaH,J,alIIHbIx <}JopCYHKax YCTaIIOBOLJHbIl!
.lI,II aMeTp COCTaB"lHeT 9,5 .MJl-t (B 06bIqHbIX <}JopcYHKax aBToTpaKTOp-
HbIIX, .lI,113e,1eii 20-25 Jl-1M). 3TH <}JOPCYHKH OTJ1HLJaIOTCH Ma.10H Mac-
COM nO.lI,BH1KHbIX .lI,eTa.rIeH II OTCYTcTBHeM cBep leIIbIx KaHa.10B. Ton-
J1IIBO nO,3,BO,J:J:HTCH K ce.lJ,J1Y II rJI bI LJepe3 3a30p Me)Ii.lI,Y Hr,10i1 H KOp-
nycoM, LJellI .lI,OCTHraeTCH cHMMeTpIfllHoe OX:Ia)K.n.eHHe .lI,eTa.1eH.
Ton.'II1BHaH annapaTypa HenOCpe.lI,CTBeHIIoro ,J:J:eHcTBHH nO.lI,pa3-
.lI,e,.1HeTCH Ha 6"10qHYIO H ceKu.HoHHYIO. Do,!J, 6.'lOQHOH nOHIIMalOT
an napaTYPY, B KOTOpOH HarHeTalOllllIe TOllJUIBO 3JIeMeHTbI Bcex U.H-
1.5
JJHH;J.pOB .ZJ.H3eJJSI. a TaKme npHBO.ZJ. K HHM 06'be.ZJ.HHeHbI B aBTOHOM-
HbIM arperaT - Hacoc BbICOKoro AaB.'1eHHSI. CeKII.HOHHaSl almapa-
Typa BK.'1l0lJaeT HaCOCbI B BHge CeKII.HM (c O.ZJ.HHM H.'1H .'I,BYMH HarHe-
TalOI.l.lHMH 3.neMeHTa!\IH), nO.'I,alOI.l.lHX Ton.1HBO B OT.ZJ.e.'1bHbIe pa60lJHe
II.H.'1HH.ZJ.pbI WIll B IJ.Ba coce.ZJ.HHX II.H.rIHH.n.pa. 4aI.l.le Bcero CeKII.HH naco-
COB He Hl\IelOT CBoero KYJIalJKOBOrO Ba.'1a. Ky.'1alJKOBbIM Ball H TOJI-
KaTe.lb pacnO.'1aralOTCH Henocpe.n.CTBeHlIO B .n.BHraTe.'1e.
Ton.'1HBHaSl annapaTypa C 6JIOlJHbIM HaCOCOM BbICOKoro .ZJ.aB.'1e-
HHH Hcno.'1b3yeTcH Ha MHOrOII.H.'1HHllPOBbIX 6bICTPOXOllHbIX .ZJ.BHraTe-
J1S1X cpaBHHTeJIbHO He60.'lblllHX pa3MepOB. Pa3HOBH.ZJ.HOCTH 6JIOlJHbIX
HaCOCOB - MHoronJIYHmepHbIM Hacoc H Hacoc jpacnpe.n.e.'1HTeJlbHOrO
THna (pHC. 13). KOHCTPYHPYIOTCH OHH no exeMe Haeoc BbiCOKoro
.ZJ.aBJ1eHHSI - Tpy6Ka BbICOKoro .n.aB.leHl-1H - <l>0pcYHKa (annapaTypa
pa3.ZJ.e..leHHoro THna H.1H pa3.ZJ.e.JIeHHaSl TOTIJIHBHaSl annapaTypa).
OCHoBHoe OTJIH He l\Iem.ZJ.Y HHMH B TOM, lJTO B l\IHOron.'1YHmepHOM
Hacoce KOJIWIeCTBO HarHeTalOI.l.lHX ceKII.l1Il paJImo lJHC.'1Y pa60lJHX
U.HJ1HH.ZJ.POB (B OT.n.eJ1bHbIX CJIYlJaHX 60.'lbllle H KpaTHO nOCJ1e.ZJ.HeMY),
B Hacoce pacnpeJJ.e.'1HTe.'1bHOrO nma OJJ.Ha-JJ.Be HlarHeTaIOI.l.lHe CeKlI.HH
06CJ1ymHBaIOT pa60TY lJeTbIpex - BOCbMH pa60lJHX lI.WIHH.n.pOB, no-
JJ.aBaH Ton.'IHBO K <l>opCYHKaM lJepe3 Cnell.HaJ1bH:bIC pacnpeAe.'IHTem-I.
DO.TJbIlIHHCTBO 6.TJOlIHbIX MHOrOnJIYHmepHbIX HaCOCOB HMeeT pH.lume
pacn0J10meHHe CeKlI.HH. HalJaT BbmyeK V-06pa3HbIX TOD.TIHBHbIX Ha-
COCOB C yr.110M pa3Ba.'Ia 75° (<I>HpMa Bosch) H 60° (<I>HpMa
L'Orange) .
B nOC.;leAHIfX IWHCTPYKII.HHX MHoron.'1YHmepHbIx HaCOCOB Yl\leHb-
llIeHO MemceKlI.HOHHOe paCCTOHHIfe H npHMeHeHbI T0.'1KaTe.1H 6e3
perYJIHpOBOlJHblX 60.11TOB. 3TO n03BO.'1If.'10 YMeHJbIlIHTb pa3pbIB B ra-
6apHTHbIX pa3Mepax H l\Iaece MHoron.1YHmepHbIx II pacnpelle.'1H-
Te.'1bHbIX HacoeOB.
PacnpeJJ.eJ1HTeJIbHbIe HacoebI HMelOT MeHbwee lJHC."IO .n.eTa.TJeM,
MeHbllIHe Macey H ra6apHTHbIe pa3MepbI H, KaK npaBH..l0, llellleBJIe
COOTBeTCTBYIOllI.HX l\1Horon.'1YHmepHbIX HaeOCOB. KpOMe TOro, OHH B
npHHlI.Hne MorYT paBHOMepHee nOJJ.aBaTb Ton.'1HIBO no lI.HJIIm.n.paM B
CBH3H C YMeHbllIeHHeM lJHC.la HCTOlJHHKOB, BbI3blBalOlI.J.llX HeOJJ.HHa-
KOBYlO nOll.alJY Ton.'1HBa B OT.n.eJJbHble lI.HJJHH.n.pbI. KaK npaBlf.lIO, B
pacnpeJJ.e.'1HTe.!JbHbIX Haeoeax He npeJJ.YCMOTpeHa B03MomHoeTb pe-
rYJ1HpOBaHHH paBHOMepHOCTII nOJJ.alJH TOnJIHBa no lI.HJJHHJJ.paM. no-
3TOMY He06xoJJ.HMO Yllie npH H3rOTOB.leHHH OOeCnelJHBaTb rHJJ.paB- .
J1HlJeCKOe eJJ.HHo06pa3He .'1HHHH BcaebIBaHHH If HarHeTaHHH. Pac-
npe.ZJ.e.JIfITe.lbHble HaCOCbI yCTynalOT !\rHOrOnJJYHmepHbIM no HeKOTO-
pbIM xapaKTepHCTHKaM H H3HOCOCTOHKOCTH. npHMeHHIOTCH OHH npe-
HMYllI.eCTBeHIIO Ha MaJJOJIHTpamHblX .n.BHraTemHX C pa311eJIeHHbIMH
KaMepa1l-IH eropaHHH, B KOTOpbIX pa3Mep, Macca II CTOHMOCTb Ton.'1HB-
HOM annapaTypbI HrpalOT pellialOI.I.lYIO pOJ1b, a llaB.1eHHe BnpbICKa
cpaBHHTe.'1bHO HeBe.'1HKO.
nOMHMO TOnJJHBHOM annapaTypbI CeKII.HOHHOro THna, CKOHCTPYH-
pOBaHHOM no cxeMe HacOC BbICOKOro .n.aBJJeHH:H - TPy6Ka BbICOKO-
ro .lI.aBJJeHHH - <l>opC_YHKa, npHMeHHeTCH anna parypa, B KOT,()pOM
16
HaCOCHblil 3J1eMeHT H CPOpCYHKa 06'be.LI:HHeHbI B O.LI:HH arperaT-
HaCOC-cpOPCYHKY (CM. pHC. 18-21). 3TO 06ecrre l UJBaeT YMeHbIIIeHHe
06"beMa TOrrJIHBa, HaXO.lI,5I erOC5I B CHCTeMe no.lI, BbICOKHM .LI:aBJIe-
HHe;\I, H rr03BOJI5IeT rro.'IYIJHTb 3HaIJHTe.1bHbIe .lI,aBJIeHH5I BnpblcKa,
6bICTpO B03paCTaIO He npH YBeJIHIJeHHH IJHC,,1a 060POTOB, H HarpY3-
KH, IJTO IIIOrKeT rrO,,'IO:tKHTe.'IbHO B.'IH5ITb Ha pa60TY 6bICTPOXO.lI,HbIX
.lI,H3e.1elI C OTKpbITOH KaMepoH crOpaHH5I. O.n:HoBpeMeHHo OTCYTcTBHe
Tpy6KH BbICOKOro .lI,aBJ1eHH5I npHBo,aHT K TOMY, IJTO Ha npol.{ecc
BnpbICKa He B.'IH5IIOT BOJ1HOBbIe 5IBJIeHHH, Hepe,aKO cy ecTBeHHO H3-
MeH5IIO He .lI,eHCTBHTeJ1bHbIH 3aKOH no,aaIIH, oc06eHHO B 6bICTpOXO.lI.-
HbIX TpaHcrropTHbIX ,aBHraTe.'I5IX, 3Kcrr,,1yaTHpyeMbIx B IIIHpOKOM
.lI,Harra30He CIWPOCTHbIX H HarpY30IJHbIX peMHMOB. n03TOMY Hacoc-
CPOPCYHKH npHMeH5IIOTC5I rrpeHMy ecTBeHHO B 6bICTpOXO.lI,HbIX TpaHC-
rropHbIX .lI,H3eJ15IX C OTKpbITOH KaMepOH crOpaUH5I (.lI,H3e.'IH Cum-
mins, 5IM3-204, 5IM3-206, GMC). PacrrpoCTpaHeHHe Hacoc-cpopcy-
HOK OrpaHHIJHBaeTC5I p5I.lI,OM He.lI,OCTaTKOB: CJ10MHbIM rrpHBo.lI,OM,
TPY.J.HOCTbIO perYJ1HpOBaIU15I yr,,'Ia onepeMeHlI5I BnpblcKa H paBHo-
MepHocTH no,aaIJH no l.{HJIHH,apaM, 60J1bIIIOH CTOHMOCTbIO 06CJ1YMH-
BaHH5I, nOBbIrneHHbIM TerrJ10BbIM pe)KHMOM Hacoca H T. .lI,.
.D.aBJIeHHe ra30B, 3anOJIH5IIO HX pa60IJHM QH.TJHH,ap, BrrepBbIe
6bI.10 rrpe,aaoMeHo HcrrO.'Ib30BaTb rrpocp. B. AprnaYJ10BbIM .D..TJ5I rrpH-
BO.TI.a rr"lYHfKepa Hacoca. TaKoH npHBO.lI, ynpo aeT cHCTeMY H 06ec-
nelIHBaeT HHbIe, IJeM npH )VIexaHHIlecKoM npHBO.lI,e, xapaKTepHcTHKH
BnpbIcKa TOnJ1HBa, a TaKMe HX H3MeHeHHe npH H3MeHeHHH pe)KHMa
pa60TbI .n:BHraTeJ15I. B IJaCTHOCTH, npH ra30BOM npHBo.n:e ,aaB.'IeHHe
BnpbIcKa MaJIO 3aBHCHT OT IJHCJ1a 060pOTOB .LI:H3eJ15I, oc06eHHo rrpH
OTCYTCTBHH Ha,a.n:YBa, TaK KaK OHO onpe,ae.J15IeTC5I, B OCHOBHOM, .lI,aB-
aeHHeM B l.{HJ1HH,ape, COOTHOIIIeHHeM n.'IO a.lI,eH CH,,10Boro rrOprnH5I
H n.1YHMepa H B HeKoTopoM Mepe cYMMapHbIM npOXO.D.HbIM CeIJeHHeM
oTBepcTHH B paCnbIJ1HTeJle. 3aBHcHMoCTb .D.aB.'IeHHH BnpbIcKa OT ,aaB-
J1eHH5I B pa60IJeM l.{HJ1HH.LI:pe npHBO.lI,HT K B03paCTaHHIO .n:aB.TJeHHM
BnpbIcKa npn YBeJ1HIJeHHH HarpY3KH H CTeneHH Ha,a.n:YBa, a TaKMe
06eCneIJHBaeT nOJ1YIJeHHe xapaKTepHcTHK BnpbIcKa, cnoc06cTBYIOI.l.{HX
«M5IrKOH» pa60Te .n:H3eJ15I. nOCJIe.n:Hee CB5I3aHO C TeM, IJTO xapaKTep
H3i\IeHeIIHH .lI,aB:leHHH B QHJ1HH.n:pe .n:H3eJ15I onpe.n:eJI5IeT xapaKTepH-
CTHI<Y BnpbIcKa, 6,,1H3KYIO K «cTyneHIJaToH».
nplIl\IeHeHHe ra30Boro npHBo.n:a CB5I3aHO C p5I.n:OM Tpy.n:HocTeH.
n pH .'II060M KOHCTPYKTHBHOM pemeHHH OCHOBHbIe 3JIeMeHTbI Ton.TJHB-
HOli annapaTypbI C ra30BbIM npHBO.lI,OM OKa3bIBaIOTC5I no.lI, .n:eHCT-
BHeM BbICOKHX TeMnepaTYP, B03HHKaIO HX B pe3YJIbTaTe nepe.lI,aIJH
K HHM Ten.TJa OT rOp5J1IHX ra30B, IJTO CHHMaeT Ha.n:eMHocTb H .lI,0.'l-
rOBelIHOCTb HX pa60TbI, oc06eHHo Hacoc-qJOpCYHKH C ra30BbIM npH-
BO.J.OM, TaK KaK BeCb arperaT paCnOJIOMeH B rO,,10BKe l.{HJ1I1H.n:pa. 3TO
3aTpY.lI,H5IeT OTBO.n: TenJIa. B O.n:HOH H3 KOHCTPYKQHH Hacoca (pHC. 6)
Ha CHJI\.)BOH nopmeHb B03.n:eHcTByeT MaCJIO, Haxo.n:5I eeC5I no.n: .n:aB-
.'leHHeM ra30B H3 pa60IJero QHJ1HH.n:pa. 3THM, B IJaCTHOCTH, cTpe-
M5ITC5I orpa.n:HTb CHJ10BOH l.{HJIHH,ap OT KOHTaKTa C rOp5IIJHMH H XH-
MHIJeCKH aKTHBHbIMH ra3aMH. O.lI,HaKO npH 3TOM B03HHKaeT onac-
2 3aKas 748
17
HOCTb H3MeHeHHH <pH3HKO-XHMWIeCKHX XapaKTepHCTHK laCJ1a rroJJ,
B03.L1.ellCTBHeM BbICOKHX Tel\mepaTYp. I1cnO.'Ib30BaHHe C.'Ie.LI.Hlll.erO
YCTpOHCTBa JJ.OnOJIHHTeJ1bHO YCJ10LKHHeT KOHCTPYKII.H10 HaCOCa H CHH-
)J{aeT HaJJ.efKHOCTb erO pa60TbI.
A
5
B
PHC. 6. Hacoc c ra30BblM npHBOJJ.OM:
A - nO;:I,BOJJ. TOnJIHBa; E -- KaHa.,"], coe-
ll.RHRlOI.ll.HR KaMeIlY CRJlOBOrO TlOpllIHS-1 C
nOJIOCTI:.IO 3; B - nOJIOCTh HaJ{ CIfJIOBblM
noplllHeM; 1 - OKHa BTYJIKH; 2-
o6paTHbirr rnapHKoBblH KlIanaH; 3 - MaC.TJSl-
HaSI KaMepa; 4 _ lllTYllep; 5 - lllTaHra;
6 - BTYJlKa CJIe)],HIl\ero YCTpmic1Ha; 7 -
Kopnyc; 8 - CH.JlOBoit noproeHb: 9 - 30-
.'OTHHI<; 10 - npY>KHHa; /1 - nJlYH>Kep;
12 - TOJlI<aTeJIb; 13 - rafiKa )],m! pery.'Hpo-
BaHliH 38TH1KKH rrpY}f(HHbI
PHC. 7. Hacoc-lj:JopcYIlKa c ra30BblM
npHBO.D: OM :
A - KaHa:l CfTBGj1,a {\x.n:,nKJ3.2.mrn.ef
)Kll;:J.I(OCTlT; E - KaHa,fr ,J,..TJ5I npo){o a
)KH,IJ,KOCTl:I, OX"TIaM.naIometi BTYlIKY CHJIO-
Boro noplllHfI; B - KaHa.'1 A.J"'ISI nO.il.BOJJ.a
ox.1Ja)K;I.alOlllei'1 }l{H.D..KOCTH
B KOHCTPYKII.HH HaCOC-<pOPCYHKH C ra30BbIM npHBO.n.OM, H306pa-
MeHHOll Ha pHC. 7, npeJJ.ycMoTpeHo HHTeHCHBHoe OXJIa:tK:JJ,eHHe CHJIO-
Bora II.HJ1HHJJ:pa.
Hacoc-<pOPCYHKH c ra30BbIM npHBOJJ.OM He nOJ1YLJHJIH llIHpOKoro
pacrrpOCTpaHeHHH, a pa3JJ,eJ1eHHaH annapaTypa C ra30BbIM npHBO-
.n.OM .1Hlllb OrpaHHLJeHHO npHMeH5IeTCH Ha THXOXOJJ:HbIX ,,1,H3e.'IHX
60JIblI1HX pa3MepOB. 06'bHCHHeTCH ::;no, KpOMe OTMeLJeHHOrO BbIIlle,
He6JIarOnpHHTH M xapaKTepOM OKOHQaHHH npOII.eCca Bnp CKa,
18
HHepltHOHHOCTblO npHBO,J,a, a T8K2Ke HeCKOJ1bKO nOBbIllleHHbIMII ra-
6aplITHbIMH pa3MepaMlI H MaCCOM Hacoca [17].
MaJIaH 3aBHCHMOCTb llaBJIeHHH BnpblcKa OT pe2KHMa pa60TbI
llH3eJIH npH6JIIl2KaeT annapaTYPY C ra30BbIM npHBO.ll.OM K aKKYMY-
.TJHTOpHbIM CIiCTeMaM. O.nHaKo B OTJ1H'lHe OT nOC.TJe.nHHX npM anna-
paType C ra30BbIM npHBo.noM BnpblcK ocymeCTBJIHeTCH no.ll. .neHcT-
BHeM 3HeprHll, HenpepbIBHo nOllBO.ll.HMOH OT pa6011ero ltllJIHH.npa no
Mepe pa3BHTHH npoltecca.
Y Hall60JIee pacnpocTpaHeHHbIx CIiCTeM HenOCpe.ll.CTBeHHoro JJ,eM-
CTBIiH C MexaHHlleCKIiM npllBo.noM napaMeTpbI BnpblcK8 cymecTBeH-
HO 3aBHCHT OT pe2KHMa pa60TbI .ll.BllraTeJIH, II BJ111HTb Ha xapaKTep
H3MeHeHHH 3THX napaMeTpoB npH H3MeHeHHH HarpY3KH H llHCoIla
060pOTOB .lI.OBO,,'IbHO CJIOiKHO. B qaCTHOCTH, 3Ha IHTeJIbHOe CHHiKeHHe
llaB.'IeHHH BnpbIcKa H YXYJJ,llleHHe KalleCTBa paCllbIJ1HBaHHH HB.15IIOT-
CH npHllHHaMH HeCTa6HJIbHOH pa60TbI .nM3eJHJ: Ha peiKHMax M3JIbIX
060pOTOB XOJ10CToro xOJJ,a H 6JIH3KHX K HHM peiKHMax. Ha pa60TY
JJ,BHraTeJ1H BJIHHeT TaK)Ke M HepaBHOMepHocTb nOJJ,a4H TOnJIHBa no
OTlleJIbHbIM U.llJIHH.ll.paM npH JJ,03HpoBaHHIl nJIymKepOM-30JIOTHHKOM.
.Q.1H CHCTeM, pa60TalomHx B BeCbMa lllHpOKOM JJ,Hana30He 060pOTOB
H nOJJ,a1.J. (TpaHcnopTHbIX )],1l3eJIeH C BblCOKIiM Ha)]'JJ,YBoM), TPY)],HO
nO)l,06paTb 3J1eMeHTbI, HCKJ1lO11alOmHe HeiKeJIaTeJIbHOe B03.ll.eHcTBHe
BO.1HOBbIX HBJ1eHHM Ha npoltecc BnpblcKa H KaK CJ1e.ll.CTBHe Ha nOKa-
3aTe.1H pa60TbJ llH3eJIH.
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HHH o6ecne IHBaTb 3KOHOMHllHYlO cTa6MJIbHYlO pa60TY )],H3e.'HI Ha
pe)KHMaX Ma.lbIX 060pOTOB H nOJJ,all. B 3THX CHCTeMax B03MOlKHa
TaKn(e peaJ11I3altHH BeCbMa BbiCOKIIX Cpe.ll.HHX )l,aBJIeHUH BnpbIcKa,
nOToMY 'LTO npH p = canst CiKHMaeMOCTb TOnJIIIBa He BJIIIHeT Ha xa-
paKTeplICTHKY BnpbICKa. OOCTOHHCTBO BOJ1HbI .n.aBJIeHIIH B aKKYMY-
.1HTOpHbIX CIICTeMax 06.1epIaeT 60pb6y C HeiKeJIaTeJIbHbIM B03.neH-
CTBHeM BOJ1HOBbIX IlBJ1eHHH Ha npoltecc BnpblcKa. HecoMHeHHbI npe-
HMymecTBa aKKYMYJIHTOpHbIX CHCTeM B CHJIOBbIX YCTaHoBKax co
CB060,TJ,HbIl\H1 noplllHHMH (cBo6oJJ,Ho-noplllHeBblx JJ,BHraTe;r!HX -ROM-
npeccopax H CB060)l,1I0-noplllHeBbIX reHepaTopax ra3a). Pacnpo-
CTpaHeHHlO HeIWTopbIX THnOB aKKYMYJ1HTOpHbIX CMCTeM cnoco6CT-
BYlOT TaK2Ke TPY)l,HOCTll, KOTopbIe B03HllKalOT npH KOHCTpYlIpOBaHHH
H 3KCnJIyaTaltHH TOnJ1HBHOH annapaTypbI HenOCpe.ll.CTBeHHoro JJ,eH-
CTBHH C MeXaHH1.J.eCKHM npHBO.ll.OM .!J.JIH .!J.H3eJIeH 60JIblllHX pa3MepOB
H cpOpClIpOBaHHbIX TenJIOB03HbIX )lH3eJ1eH, r)le 60JIblllHMH OKa3bI-
BalOTCH YCH.1HH B npHBO)l,e (8 T H 60JIee).
Do.ll. aKKYMYJ1HTOpHbIMH CHCTeMaMH nOHHMalOT .ll.OBOJIbHO pa3JIlflI-
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CH TO, 'iTO co6CTBeHi-IO npOlteccy BnpbICKa TOnJ1HBa npe.ll.llleCTBYlOT
npOlteCCbI HaKOnJIeHHH 3HeprHH, HCnOJIb3yeMoH .ll.JIH ocymeCTBJIeHHH
BnpbICKa. TaK, B CJ1YQae npYfImHHoro npHBo.na BnpbICKY npe)l,llle-
CTByeT )l,ecpopMaltHH npYiKHH. OpH nHeBMorH)l,paBJ1H4eCKOM npHBO-
.ll.e BnpbICK ocymeCTBJ15IeTC5I no.ll. )],eHCTBHeM aKKYMYJ1HpOBaHlIOll
3Hepnm OKaTOrO B03.ll.yxa.
2* 19
HaCOCbl c npY)KHHHbIM npHBOJI.OM OrpaHWIeHO npHMeHHIOTCH Ha
JI.H3eJIHX MaJ10M MOIl.{HOCTH H JI.H3eJ1b-KOMnpeCCOpax. 0pY)KHHa B Ta-
KHX npHB01IaX JI.ectJOpMHpyeTcH CneUHaJlbHbIM MeXaHH3MOM. B onpe-
JI.eJ1eHHbIM MOMeHT OHa OCB06o)KJI.aeTCH, T. e. )"CTpaHHeTCH ynop,
npenHTCTBYIOll.\HM ee paCnpHMJ1eHHIO. BnpbICK HJI.eT no)]. .lI.eMCTBHeM
:;meprHH, HaKOnJleHHOH npli JI.ectJopMaUHH npY)KHHbI. B nepBOM npH-
6.11I)KeHHII ,n:aBJleHlIe BnpbICKa, UIIKJlOBaH no,n:a'Ia H np0JI.OJI)KHTe.;lb-
HOCTb BnpblCKa B e,n:llHlluax BpeMeHll He 3aBI1CHT OT 'IIICJla 060pOTOB.
)],aB.leHHe BnpbICKa Ma.10 3aBHCHT OT HarpY3KII. TOnJIHBHble CllCTe-
MbI C npY)KllHHbIM npllBo,n:OM OT.'IH1.JaIOTCH He,n:OCTaT01.JHOM HaJI.e)K-
HOCTblO npll BbICOKOH 1I.IIK.1111.JHOCTll, B5I.'JbIM OKOH l 18HlleM npoueCC8
BnpbICKa, OTHOCIITe.1bHOll rnYMHOCTblO II 38MeTHbIM 38n83,n:bIB8HlleM
yrJl8 H81J.8JI8 BnpbICK8 C YBeJlH1J.eHHeM 1J.HCJI8 060pOTOB. )],Jl51 n8CO-
COB C npY)KIIHHbIM npHBo,n:OM X8p8KTepH8 60J1bIlIaH CKOpOCTb H8pa-
CT8HlIH ,n:aBJ1eHHH B H81J.8J1e BnpbICK8.
npli nHeBMOrII,n:p8BJlll1J.eCKOM npllBo,n:e nJIYH)Kep8 (CM. pHC. 18),
npe,n:JIO)KeHHOM BICERA, TOnJIllBO CJlY)KllT o,n:HOBpeMeHHO cepBO-
)KH,n:KOCTblO. B onpe,n:eJIeHHbIM MOMeHT MeX8HH1J.eCKH HJIH rll,n:p8BJIH-
qeCKll ynp8BJ1HeMbIH 30JIOTHHK OTKpblB8eT ,n:ocTyn Tonmmy, H8XOlJ,H-
ll.\eMYCfl nOA .n:8BJIeHlleM, C03.n:aB8eMbIM cepBOH8COCOM. B K8Mepy
CHJIOBOrO nopllIHH, CBH38HHoro C nJIYH)KepOM, H8rHeT81011IJIM Ton.1H-
BO. )],JIfl no.n:.u.ep)K8HHH nOCTOHHHbIM .n:8BJIeHHfl CepBOn\:f{.n:KOCTH B
neplIO.u. BIlpbICK8 nOJIOCTb, 38nO.'IHeHHaH TOnJIHBOM - CepBO)KII.n:-
KOCTblO, 1J.epe3 .u.HactJparMY CBH3aH8 C B03.u.YllIHbIM aKKYMYJIHTOpOM,
B KOTOpOM Haxo.u.HTC5I B03.u.yX H.1H 830T no.u. ,lJ,aBJIeHHeM, HeCKO.lbKO
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no.u.aLJ:H CepBO)KH.u.KOCTH pacnpe,lJ,eJ1HTe.;leM K.TJ8naH-30JlOTHHK, ,lJ,BH-
raHCb no.u. .u.eMCTBHeM npY)KHHbI, OTKpbIBaeT pa3rpY30LJ:HOe OKHO.
HarHeTalOIl.{HH nJIYH)Kep no,lJ, BJ11I5IHHeM npY./KHHbl 1I.1m ,lJ,aBJleHHH
TOnJIHBa, nO,lJ,aBaeMOro B KaMepy nJIYH./Kepa, ,lJ,BH)KeTCfl K H. M. T.,
nplI'IeM CepBO)KH,lJ,KOCTb nepenycKaeTcH 'Iepe3 pa3rpY301.JHOe OKHO B
TOnJIHBHbIH 6aK. B .3TOM cJ1Y1.Jae xapaKTepHcTHKH BnpbICKa TOnJIHB8
B H3BeCTHOH Mepe He 3aBHCHMbI OT pe)KHMa pa60TbI lI.BHraTe.'IH. TaK
KaK .u.aBJIeHHe B aKKYMYJlflTOpe nO.lI.,lJ,ep)KHBaeTCH nOCTOHHHbIM.
KaK C npY)KHHHLIM, TaK H C nHeBMOrII.lI.paBJIH'IeCKHM npHBO.lI.OM
TOnJIHBHaH annapaTypa MO)KeT 6bITb BblI10JlHeHa no cxeMe Hacoc-
TOnJ1I1BOnpOBO,lJ, - <l>opcYHKa HJ1H B BH.lI.e Hacoc-ctJ0PCYHKH. Hacoc-
<l>0PCYHKH c npY)KHHHbIM npHBO,lJ,OM He HalliJIH eIlle IlIlIpOKoro pac-
npOCTpaHeHIIH, 'ITO 06bHCHHeTCH, B OCHOBHOM, TPy.lI.HOCTHMH pa3Me-
ll.\eHlIH npY)KHHbI nplIeMJIeMbIX xapaKTepHCTHK B .3TOM arperaTe.
CIiCTeMbI C rH,lJ,paBJIlI1.JeCKlIM aKKYMYJI5ITOpOM 06bILJ:HO nO,lJ,p83-
,lJ,eJl5IIOT Ha annapaTYPY C aKKYMy.rI5ITOpOM MaJIOM eMKOCTIi H anna-
paTYPY C aKKYMYJIHTOpOM 60J1bllIOH eMKOCTH. B nepBOM CJ1YLJ:ae
3HeprlIH aKKYMYJ1HPyeTcH .lI.JI5I OCYll.\eCTBJ1eHHH e.lI.HHH'IHoro BnpbICKa
B HaCOCHOH ceKUHH HJIIi B <l>opCYHKe, BO BTOpOM CJIY1.Jae B ClICTeMV
BKJII01.JaeTCH eMKOCTb-aKKYMYJ1HTOp, B KOTOpOH nO,lJ,,lJ,ep)KHBaeTCH
nOCTOHHHoe lIJIlI perYJ1HpyeMoe ,lJ,aB.TJeHHe.
TIpHMepoM aKKYMYJIHTOpHOH CHCTeMbI C aKKYMYJI5ITOpOM Ma.rIOH
20
eMKOCTH CJIpKHT TOnoilHBHaH CHCTeMa C nJIymKepHbiM aKKYMYJIHTO-
pOM. B KafK.'I:OH CeKll.HH TaKofI CHCTeMbi npe.LI:YCMOTpeHbI .'l.Ba nJ1YH-
fKepa (CM. pHC. 24). O.'l:HH H3 HHX HMeeT MeXaHHlJeCKHH npHBo!l: OT
KVoilalJKa HJ1H 3KCll.eHTpHKa lJepe3 pO'!lHKOBbIH TO.1JKaTeJ1b H Ha3bIBaeT-
CH B03BO.ll,HIll.HM. B03BO.'l.HIll.HH nJIYHfKep O.LI:HOBpeMeHHo BbInOJIHHeT
.LI:03HpYJOIll.He CPYHKll.HH. .L1.pyroH mIYJIfKep Ha3bIBaeTCH aKKYMYJIH-
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BO.'l.HIll.erO mIymKepa oTKpbIBaeT HarHeTaJOIll.ee oTBepCTlIe, HalJI1-
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npH .il.BI1fKeHI1H B03BO.LI:HIll.erO n.1JYHfKepa.
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.'l.eoilHeTCH Ha TPH TlIna: C npYfKHHHbIM nplIBO.'l.OM, B03.LI:YllIHbIM npH-
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n pmll.(I1nHaJlbHO B paccMaTpHBaeMoH CHCTeMe KOJIHlJeCTBO nO.il.aBae-
MOll nOpll.lII1 TOnJIHBa He .'l.OJIfKHO 3aBlIceTb OT lJlICJIa 060pOTOB.
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pa npO.'l:OJI.iKHTeoi1bHOCTb BnpbICKa B rpa.LI:ycax yrJ1a nOBopOTa KO.'1eH-
'laTOrO Ba:Ia H3MeHHeTCH nponOpll.I10Ha.1bHO H3MeHeHHlO lJI1c.'la 060-
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npYMHHHOM npHBO,lJ,e TPY.lJ.HO .LI:OCTMfHYTb BbICOKHX .J,aBJIeHHi'I BnpbI-
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,lJ,a n.'lymKepa C nOBbIllleHHeM lJHCJ1a 060pOTOB 06eCnelJHBaeTCH YBe-
.1HlJeHHe .LI:aBoi1eHlIH BnpbICKa H COKpaIll.eHHe ero npO,lJ,OJ1fKHTeJIbHO-
CTH, H3MepeHHoi'I B e;U1HHuaX BpeMeHH. HaCOChI C IWYHMepHbIMH
aKKYMYJIHTOpaMlI HaH60oi1ee rtO.1HO OTBelJaJOT YC.'lOBHHM pa60ThI Ha
CB06o.ll.HO-nOplllHeBhIX reHepaTopax ra3a (Cnrq. K He.'l.OCTaTKaM
HX c.'le,lJ,yeT OTHeCTH OTHOCHTe.1bHYlO C.'lO.iKHOCTb YCTpOHCTBa, OTCYT-
CTBlIe B 60.lblllHHCTBe KOHCTPYKUHH aBTOMaTHlJeCKOrO H3MeHeHHH
HalJacla U OTCelJKH nO.ll.a1IH Ton.1HBa. J1MelOTcH, O,lJ,HaKO, rrpe,lJ,JIOllie-
HHH, cB060.J,HhIe B 3JIa 1 IHTe.'IbHoi1 Mepe OT nOCaC.LI:Hero HC,lJ,OCTaT-
Ka [17, 18].
B aKK)'M)'.1HTOpIIOH CHCTeMe Maoi'lOH eMKOCTH C aKKYMY.1HTOpHOH
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H BcaChIBaHHJJ OT,lJ,e.leHbI O.ll,Ha OT ,lJ,pyroi-i, lJTO nOBhIllIaeT cTa6HJIh-
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lJH Ton.lHBa npH 60.1bllIOM 'lHC.7Je 060pOTOB cnoco6cTByeT TaKfKe
npOTOlJHaH CHCTe la'nHTaHHH TOnJIHBHOrO HaCOca BbICOKoro .LI:aBJ1e-
HHH npH .ll.OCTaT01JHO 3HalJHTeJIhHOM ,lJ,aBJIeHHH nO.ll,KalJKH TOnJIUBa.
npH HarHeTaTe.'lbHOM XO,lJ,e n.'lymKepa Ton.'lUBO aKKYMy.'lHpyeTcH B
cnell.Ua.lbHOM 061>eMe CPOPCYHKU. npH OTCelJKe BnphiCKa no.lJ. .LI:ei'I-
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Hell. BnpbICKa HacTynaeT, Kor.rr.a .rr.aB.1JeHHe B aKKYMYJIHpYJOIll.eM 061>-
21
eMe <POPCYHKll YMeHblllllTC5J J.I.O 3Ha lJ.eHll5J, npll KOTOpOM HrJIa CaJ.I.HT-
C5I Ha MeCTO nOJ.I. J.I.eHCTBHeM npYMHIHbI.
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5IBJI5IeTCfI OTHOCHTeJIbHa5J npOCTOT21 KOHCTPYKIJ.Hll, MaJIa5I 3aBHCH-
MOCTb npO.n:OJ1)KHTe.'IbHOCTH H .n:aB.lIeHHH BnpbICKa OT lJ.HCJ1a 060po-
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3eJIfI XapaKTepllCTllKY BnpbICKa B CBfl3ll C pe3KHM Hap3CT3HHeM JI:aB-
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CYlll.eCTBeH JJ..rJ5J 6bICTPOXOJI:HbIX Ma.JIOpa3MepHbIX J.I.H3eJIeH C OTKpbl-
TOH llJ1ll nOJIypa3JI:eJ1eHHOH KaMepOH CrOpaHllfl. B KOTOpbIX 06lll.a5I
npOJI:OJIMllTeJ1bHOCTb BnpbICKa paBIHa HJIH MeHbllle npOJI:OJIMHTe.'Ib-
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5JB.l5JeTC5J 'Ipe3MepHafl 3aBllCHMOCTb ,lI,aBJ1eHH5J BnpbICKa OT HarpY3KI1
II MaJIa5I cTa6llJIbHOCTb nOpIJ.HH TOmmIBa. fll,ll,paB,fm'leCKlle aKKY.
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JIeHlIeM. Opll IlCnO.TJb30BaHHH <POPCYHOK C MeXaBIl'IeCKIlM npIlBOLLOM,
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51BJ15leTCH TaK)Ke B03l\IOLI\HOCTb OTK.'IIO'IaTb <POPCYHKY npll pa60TaIO-
llI.eM LLBHraTe.'Ie.
2. METOAbl A0311iPOBAHHSI TOnnlliBA
TOnJIHBHa51 annapaTypa MOLKeT KOHcTpynpoBaTbC51 C IlCnOJIb30-
BaHneM pa3JIH'IHbIX npHHIJ:HnOB ,n:03IlpOBaHH5I TOII.'IHBa.
1. .Q03HpOBaHHe nJ1YHLKepOM -30.10THHKOM (Cl\!. pHC. 3) - HaH60-
J1ee npoCToll H pacnpocTpaHeHHbJi.'I MeTO.n: .n:03HpoBafIIlH. B 3TOM
cJ1Y<Jae BO BTy.TJKe nJ1YHLI(epa HMelOTC51 HanO.TJHHTe.TJbHbIe H OTCeqHbIe
'oTBepcTIl51 (qalll.e Bcero Kpyr J1bIe), a Ha TeJIe n.'IYHLKepa BbInO.'IH51eT-
C51 <pacoHHa51 BbITOqKa, CB513aHHa51 C KaMepoll n.'IymKepa na30M IlJIH
cBep.TJeHH51l\UI. Oo.n:a'la TOnJIl1Ba H3MeHHeTC51 nOBopoTOM nJlymKepa
OTHOCHTeabHO HeIIoLLBHLKHOll BTy.rIKH (B03MOLKHO H 06paTHoe pewe-
HHe), '1TO npHBoLLHT K H3MeHeHHIO aKTHBHoro XOLLa IWYHLKepa, T. e.
XOLLa nJ1YHLKepa, npollCXOLL51llI.ero npll nepeKpbITbIX Te.l0M n.1YHLI(epa
oTBepCTH51X BO BTy.TIKe. OJIYHLKep nOBOpaqHBaeTC51 06bIqHO C no-
MOlll.blO pee'IHoro MexaHH3Ma, npH'IeM CeKIJ:HH MorYT 6bITb oTpery-
J1HpOBaHbI Ha OLLHHaJ\OBYIO nOLLaq)'. ()LLHaKo npH 3TOM Tpe6yeTcH
.n:OCTaTOqHO 60.TIbWOH no.'IHbIH XOLL n.'1YHLKepa, TaK KaK 3HaqHTeab-
HaH ero qaCTb 3aTpa'lHBaeTCSI Ha HanO.'IHeHHe H oTce<JKY BnpblcKa.
3TO YC.'IOLKHHeT C03.n:aHHe Ha.n:eLKHoro H H3HOCOCTOllKOro npI1BOLLa
nJ1YHLKepa. B03MOLKHbI BapHaHTbI C npo<pH,lIbHbIMH oTBepcTHSIMH BO
BTy.1Ke (B BHLLe Tpe)To.lbHHKa, napa. T lJ1e.'IOrpaMMa H np.) Il npo-
CTbINIIl CBepJ1eHH$IMIl B nJ1YHLKepe, OLLHaKO OHH pacnpOCTpaHeHHH He
nOJ1Y'lH.'1H. PaCCMaTpHBaeMbIH MeTO.n: .n:03HpOBaHHH 06eCneqHBaeT
npH COOTBeTCTBYlOllI.eM npo<pH,;lHpOBaHHH BbITO'leK Ha n.1YIUKepe
TeOpeTH'leCKH .TJ:1060H xapaKTep H3MeHeHH51 yr,,'Ja OnepeLl{eHH5! BnpbI-
CKa npH If3MeHeHHH HarpY3KH. O,n:HaKO 3TOT MeTOLL 06eCne'IIlBaeT
cpaBHIlTe.nbHO Hlf3KYlO pa60Tocnoc06HOCTb n.'IYHLKepHOH napbI (no
CB5!3aHO C TeM, '1TO OHa BbITIO.'1HHeT OLLHOBpeMeHHO <PYHKIJ:lllf 30JIOT-
HlfKa). .ll.'IH YBeJIH'IeHlfH KOHTaKTHOH nOBepXHOCTlf rO.TJOBKIl n.TJYH-
LKepa Hepe,n:KO npllMeHHIOT KOHCTPYKIJ:HIO (pHC. 8), B KOTOpOll BTO-
pOll <pacoHHbIH na3 C.'1YLl(HT LL.'1H y.TJ:Y'lIlleHHH CMa3EH H ypaBHoBe-
IllHBaIIIlSI 60KOBoro LLaB.TJ:eHlf51, C03,n:aBael\lOrO Ton.TJlfBOM, 3anO.1H5!IO-
llI.Hl\1 KaHaBKH Ha n.'IymKepe.
ECJ11l OTCYTCTBYIOT CneIJ:Ha.'IbHble KoppeKTopbI, npll paccMaTpH-
BaeMOM MeTOLLe .n:03IlpoBaHIl5! nOJIyqaeTCH cpaBHlfTe.lbHo HeOJIaro-
23
npH51THa51 XapaKTeplfCTHKa Ton.'JlfBOnO.LI.a'lH no 060pOTaM. HCK.mO'le-
HHe COCTaB.""I51IQT CHCTeMbl, B KOTOpbIX .n.aB.'JeHHe BnpbICKa H CKOpOCTb
ero HapaCTaHH51 C B03paCT3HHeM 060pOTOB BeJIlfKH (Hacoc-cpOPCYH-
Ka C )J(eCTKlfM MeXaHH'leCKlfM npHBo.n.OM nplf n0J10meHH51X peI"IIUI,
6.'Jlf3KHX K HOMHHaJlbHoMY).
2. l103HpoBaHHe K.'JanaHa!\lH If.'1H 30.10THHKa:\lI1. MeTO..1 pacnpo-
cTpaHeH B TOnJIHBHOH annapaType 60J1bWHX TllXOXO.n.H X ..11l3eJIeH,
r.n.e CTOHMOCTb Ton.I1llBHOH annapaTYP COCTaBJ151eT He3Ha'lHTe.'Jb-
HYIQ .D.0.1IQ OT 06meI'i CTOHMOCTlf .n.H3e.151, If n03ToMY .n.onycKaeTcH
HeKOTopoe Y.D.OpOmaHHe TOnJ1HBHOH anna-
paTypbI, o6eCne'II1BaIQmeH, HanpHMep, no-
BbIllleHHe H3HOCOCTOHKOCTH, Ha..1e)J(HOCTll
pa60TbI H 3KOHOMH'lHOCTH. 113MeHeHHe no-
.a.a'lH Ton.'JHBa TaKme .n.OCTHraeTC51 H3MeHe-
HHeM aKTHBHoro xo.n.a. 3a.n.a'la KOHCTPYK-
THBHO MQ)KeT pewaTbCH .lH60 HCnOJIb30Ba-
HlfeM MeXaHH'leCKH ynpaB.1HeMoro K.'JanaHa,
MOMeHT 3aKp TH51 KOToporo onpe.n.eJI51eT
Ha'la.10 HarHeTaHH51 Ton.1HBa, a l\lOMeHT OT-
KpbITI1H - Ha'laJIO OTCe'lKH no.n.a'lll, .'11160
npHMeHeHlleM MeXaHH'leCKH ynpaB.J15IeMOro
2
1
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I ,
, :1
PHC. 8. nJlYH}KCpHaH napa:
A - HanO"lHllTe..1bHoe OTBepCTHe: J - pery npYlOw.afl
I\po:\'iKa; 2 - oeeaoe CBep.,'leHl1e; 3 - Cnllpa.TIbHblC na3bl;
4 - 3a n.1el.)HKH n.."IYH:iKepa 5 - XBOCTOBHK n..'1YH)I{epa
OTCe'lHorO HJI11 nepenYCKHOro K.1anaHa (Hepe.n.KO npH 3TOM npe.'I.Y-
CMaTpHBaeTCH aBTOMaTH'leCKHH BnYCKHOH KJ1anaH, KOTOpbIH, B 'laCT-
HOCTH, cnoco6cTByeT nOJ1Y'leHHIQ na.n.aIQmeH C B03paCTaHHeM 'l11CJIa
060pOTOB II.HKJIOBOH nO.a.a'lH). B HeKOTOpbIX C.TIYlfaHX YCTaHaB.1HBaIQT
.n.Ba MeXaHH'leCK11 ynpaBJIHeMbIX KJ1anaHa: BnYCKHOH - ,lI,.'J51 ynpaB-
J1eHHH Half3JIOM nO.a.alf11 H nepenYCKHOH - ..1.151 ynpaB.'JeHIIH KOHUO:'.!
HarHeTaHHH TOnJ1HBa. BMeCTO KJ1anaHOB MOmHO HCn0J1b30BaTb 30-
J10THHKOBOe YCTPOHCTBO. BeJ1HlfHHa nOpUHH TOnJ111Ba npH OnI-ICbIBae-
MOM MeTO.n.e perYJ1HpyeTc51 H3MeHeHHeM MOMeHTOB OTKpbITH51 11 3a-
KpbITH51 K.'1anaHOB. Dp11 HCnOJIb30BaH11H 30JIOTHHKOBOrO YCTpOHCTBa
aHa.TIOrHlfHOro 3cpcpeKTa MOmHO .n.OCTHrHYTb H3:'.IeHeHHeM YCTaHOBKH
30.10THHKa. MeTO,lI, ..'J.03HpOBaHH51 n03BO.TI51eT perYJ1HpOBaTb KO.'JH'le-
CTBO nO,'1.aBaeMOrO TOn.'JHBa npH nOCTOHHHOM HalfaJ1e nOna'lH, nOCTO-
HHHOM KOHue H npH nepeMeHHbIX Ha'la.TIe H KOHue nOXl,alfH.
PaCCl\IaTpHBaeMbIH MeTO.a. ,lI,03HpOB3HHH OT.'1Hlf3eTCH OT npe,lI,bI-
,lI,ymero 60JIee BbICOKOH ..10J1rOBelfHOCTbIQ H n.10THOCTbIQ n.'JYH)J(ep-
HOli napbI, a T3K)J(e MeHbWHM XO;J:Ol\l n.'IYH)J(epa. .T1Y'lWHe pe3y.lIbTa-
T 06eCne'lHBaeT B 6NCTpOXO.n.H X KOHCTPYKUHHX ,lI,03HpOBaHHe 30-
J10THHKaMH. K.'IanaHbI H.1H 30JIOTHHK B C11CTeMe BbICOKoro ..'laBJIeHHH
24
YBe:Ul1umaIOT o6"hel\I y nacoca, IITO nOBbIlllaeT HCKaL!."aIOmee BJ1IUl-
HHe CL!.UlMaeMOCTH TOn.''Uma Ha npou.ecc BnpbICI\a, OC06eHHO B CHCTe-
MaX Henocpe.n.CTBeHHoro .n.ei1cTBHH,
3. LI03HpoBaHHe .n.pocce.1HpoBaHHeM Ha BcaCbmaHHH (CM.
pHC. 13). B MamCTpa.1Jb. llepe3 KOTOpyIO HanOJIHHeTCH HarneTaIO-
maH ceKu.HH, BBO.n.HTCH .n.pocce.lb (llame Bcero B BH.n.e 30.TIOTHHKa),
perY.1HpYIOlIJ.HH Hanom-reHHe KaMepbI n.1YHJKepa. B pe3YJIbTaTe B
I1aIJa.le HarHeTaIOlIJ.erO xO.J,a n.1YHJKepa .lI.Byx<pa3HaH CIICTeMa CJKII-
MaeTCf/. B onpeAe.leHHbIH l\IOMeHT npou.ecca 3aKaHIJlIBaeTCH KOH-
.n.eHcau.lIfI napoB Ton.1HBa II HalllIHaeTCH C)KaTlIe Ton.lIIBa. OplI 3TOM
B03HlIKaeT rII.lI.paB.7JIIIJeCKHM Y.ll.ap.
HarHeTaHHe 3aKaWUlBaeTCH B KOHu.e HarHeTaIOmero xo.n.a nJIYH-
JKepa H.llI nplI OTCeIJKe nO.ll.aIJII. OplI HcnO.1b30BaHIIII 3TOro MeTo.n.a
06ecnelllIBaeTcH nepeMeHHoe HallaJIO no.n.aIJH II HeH3MeHHHH ee KO-
Heu.. XapaKTep 1I3MeHeHlIH Haqa.la BnpbIcKa Ton.1HBa nplI 1I3MeHeHlIH
U.HK.l0BOH no.n.aIJII He BCer.ll.a 6.1arOnpHHTeH. TaK, IIpe3MepHO 60.lIb-
lllHM OKa3bIBaeTCII onepeJKeHHe HaqaJIa no.n.aqlI Ha nYCKOBOM pe-
JKIIMe. OpeHMymecTBo MeTO.ll.a .n.03IIpOBaHIIH .n.pocce.'llIpOBaHHeM Ha
BcaCbIBaHHH - na.n.eHlIe U.HK.7JOBOH no.n.aqu TOn.'llIBa nplI YBe.1HqeHIIII
qlICJla 060pOTOB H nOCTOllHHOM nO.l0JKeHIIH .lI.pOcce.7JH, B CBf/3H C qeM
CIICTeMbI C TaKllM MeTo.n.OM .n.03IIpOBaHlIll IIHor.n.a Ha3bIBaIOT caMO-
pery.7JHpYIOlIJ.IIMIICH. CaI'vIOperY.llIpYIOlIJ.aH cnoc06HOCTb 3TlIX CIICTeM,
BnpOqeM, .n.a.1eKa OT COBepllleHCTBa. O.n.HaKO OTMeqeHHOe CBOHCTBO,
HeCOMHeHHO, 06.TIerqaeT pellleHlIe 3a.n.a l IH pery.7JlIpOBaHIIH IIHC.la 060-
pOTOB .lI.BlIraTe.1H B pe3Y.1bTaTe 3HaqlITe.lbHoro caMOBbIpaBHHBaHIIH,
KOTOpbIM 06,;la.n.aeT caM .lI.BHraTe.1b nplI 060py.n.OBaHHII ero TOnJIHB-
HOM CHCTel\IOH paCCMaTplIBae!\lOrO TlIna.
MeTo.'!: .:r.031IpoBaHIIfI .:r.pocce.m1pOBaHlIeM Ha BcaCbIBaHIUI nplIMe-
HHeTCII B o.n.Hon.lymKepHbIX Hacocax II Hacocax pacnpe.n.e.lIITe.1bHo-
fO TlIna. 06"hllCHHeTcH 3TO Tpy.n.HOCTbIO paBHOMepHOfO H3MeHeHlUl
celleHIIH B HeCKO.1JbKIIX 3.1eMeHTax BO BceM IIHTepBa.1e no.n.all. OplI
IICnOJIb30BaHlIlI JKe O.ll.HorO .lI.pOCCeJIH HeMIIHyeMo B.1IIHHlIe pa3J1IIQ-
Horo rH:J:paB.1JIIQeCKOrO conpOTIIB.1JeHIIH MamcTpa.7Jeii, Be.ll.ymlIX OT
.n.pocce.1H K HaCOCHbIM ceKu.Hll l, a TaK.iKe B.1JHflHlIe Ko.1e6aHIIH .n.aB-
JIeHIIH B HanOJIHIITeJIbHOM CIICTeMe, oc06eHHO eCJ11I nOCJIe.n.HHH He
OT.n.e.1JeHa OT OTCeQHoM.
4. LI03HpoBaHlIe nepeMeHHHM XO.n.OM n.1YHJKepa (CM. pHC. 23).
Xo.n. n,;lymKepa MOJKeT 1I3MeHHTbCH nepeMemeHlIeM B oceBOM Ha-
npaB.1eHHH KY.'IaqKOBOrO Ba:la C KOHYCHbIMII KYJIaqKaMH, nepeMeme-
HHeM B pa.n.HaJIbHOM HaUpaBJIeHlI1I cneu.lIaJIbHO cnp0<pIIJIHpoBaHHoH
B BII.n.e KY.laQKa n.laCTIIHbI, a TaKJKe H3MeHeHlIeM 3a30pa B nplIBo.n.e
n.1YHJKepa. 3TOT MeTO,n: Hepau.IlOHa.1bHo nplIMeHHTb oc06eHHO .n..1JH
CHCTeM Henocpe.n.CTBeHHoro .n.eHCTBHH He TOJIbKO B CBH3H C ero KOH-
CTPYKTHBHOM C.7JOfKHOCTbIO, HO H 1I3-3a BH.10ro HaQa,;la H KOHu.a
BnpbIcKa.
5. LIo3HpoBaHI1e nepenycKoM Ha BceM xo.n.e nJrymKepa. OplI 3TOM
B Ton,,1HBHOM Hacoce npe.n.ycMaTpHBaeTcH nepenycKHaH .i1HHHH, no
KOTOpOH TOnJ1HBO H3 KaMepbI nJ1ymKepa MO)!{eT nepenycKaTbCH BO
25
BnYCKHYIO nO.10CTb HaCOCa. B nepenycKImii J1I1HHH YCTaHaB.l11BaeT-
C5I rrepeMeHHOe .n.pOCCeJIHPYIOw.ee CeqeHHe (HanpHMep, B BH.n.e OT-
BepCTH5I, nepeKpbIBael\WrO npoqm.'IbHOH Hr.'loil), H3MeH5IeMOe Bpyq-
HYIO HJIH pery.'I5ITOpOM qHC.lIa 060pOTOB. YMeHbllleHHe Be.1WII1Hbl
IJ.HK.1JOBOll nO.n.aqH .n.OCTHraeTC5I YBe.1HQeHHeM npoxo.n.HOrO CeqeHI15I
B .n.pocce.'Ie. KaMepa rrJIYH1Kepa nOJ1HOCTbIO 3anOJIH5IeTC5I TOnJII1BOM
Qepe3 aBTOl\1aTH'leCKHH BnYCKHoi'I K.'IanaH, HarpyrKeHHbIH JIerKOH
npY)j{HHOiL
PaCCMaTpl1BaeMbIlf MeTO.n. )I.03HpOBaHH5I COXpaH5IeT npO.n.O.1)KH-
Te.'IbHOCTb BnpbICKa, H3MepeHHYIO B rpa.n.ycax, He3aBHCHMO OT KOJIH-
QeCTBa nO.n.aBaeMOrO TOlIJIlfBa. O.n.HaKO MeTO.n. He nOJIYQH.'l pacnpo-
CTpaHeHH5I, TaK KaK C YBe.'lH'leHHeM QHCJIa 060pOTOB .n.BHraTeJIH
pe3KO B03paCTaeT KOJIHQeCTBO no.n.aBaeMoro TOnJIHBa, QTO 3aTpy.n.-
H5IeT perYJIHpOBaHHe qHCJIa 060pOTOB .n.BHraTeJI5I; CJ10)j{HO perYJIH-
pOBaTb paBHOMepHYW nO)I.aQy TOnJIHBa lIO IJ.HJ1HH.n.paM npH MHoro-
n.1JYH1KepHOM Hacoce; .n.OBO.'lbHO BHJIO OKaH'lHBaeTCH npOIJ.eCC
BnpbICKa.
6. LLo3IfpoBaHIfe nJIYH)JiepoM -.n.03aTopOM C nepeMeHHbIM XO.n.OM
(CM, pIfC. 17). Cnoco6 npmvIeHHeTC5I B CHCTeMax pacnpe.n.emne.'Ib-
Horo THna qmpMbI Cummins, onHcaHHe KOTOpbIX 6y.n.eT .n.aHO HmKe.
MeXaHIfQeCKH HJ1If rH.n.paB.1JH'leCKIf npHBO.lIHMbIH .lI03aTOp BbITeCH5IeT
npH .n.BmKeHlIH OT o.n.Horo KpaHHero nOJIO)j{eHH5I K .n.pyroMY onpe.n.e-
JIeHHbIH 06"beM Ton.1JHBa, HaXO,.'l.5IlIJ.erOC5I noJI, HeKoTopbIM nOCT05IH-
HbIM JI,aB.1eHHeM. TonJ1HBo, BbITeCHeHHoe nJ1ymKepoM-.n.o3aTopolVI, no-
.n.aeTC5I 'lepe3 pacnpe.n.eJIHTeJIb K Hacoc-cpopcYHI(aM THna Cummins.
TaK o6eCneQHBaeTC5I nOCTOHHCTBO no.n.a'lH no IJ.HJIHH.n.paM. PerYJI5I-
TOp B03JI,eIIcTByeT Ha MexaHH3M, OrpaHH'lHBaww.HH XOJI, nJIYH1Kepa-
.n.03aTopa, B pe3y.1JbTaTe 'lero H3MeH5IeTC5I Be.1JHQHHa no.n.aBael\IOII
nOpIJ.HIf TOnJ1HBa. MmKHO 01KHJI,aTb nOCTOHHCTBa IJ.HK.l0BOll no.n.a'lH
TOnJIIfBa npH If3MeHeHHH 'lIfCJla 060pOTOB H nOCT05IHHOM XOJI,e nJIYH-
)I(epa-.n. o 3aTopa.
7. KOM6HHupoBalIHoe .n.o3HpoBaHHe. H3BecTHbI pa3.1JH'lHbIe c.1JY-
'laIf KOM6IfHIfpoBaHHoro .n.o3HpOBaHIf5I, HanpHMep, CO'leTaHHe nepe-
lI1eHHOrO xona n.'lYH)!{epa C .n.o3IfpoBaHHeM nocpencTBOM MexaHlilIe-
CKH ynpaBJIHeMOrO nepenycKHoro KJIanaHa, CO'leTaHHe .n.o3HpOBaHI15I
nJIYH)!{epOM-30JIOTHIfKOM If MeXaHIf'leCKH ynpaBJIHeMblMIf KJ1anaHa-
MIi If T. JI,. KOM6HHaIJ.I15I pa3JIIf'lHbIX MeTo.n.OB .n.o3IfpOBaHI15I MO)j{eT
KOMneHcIfpoBaTb He.n.oc-raTKIf Toro IWH HHoro MeTOJI,a. B aKKYMYJIH-
TOpHbIX CHCTeMax C rIfnpaB.1JH'leCKHM aKKYMY.l5ITOpOM 60.'IblilOH
eMKOCTIf HcnoJlb3YWT TaK)Ke c.leJI,ywlllHe MeTo.n.hI .ao3HpOBaHI15I:
A. .lJ.o3HpoBaHHe npOJI,OJI)JmTe.'lbHOCTbW OTKpbITH5I MeXaHH'leCK!I
ynpaBJI5IeMoI-i CPOPCYHKIi HJIli 3.'1eKTpOMexaHwlecKH ynpaB.15leMOH
3J1eKTpOMarHHTHoll CPOPCYHKH. npH MeXaHH'leCKH ynpaB.1J5Iel'vwi%
CPopcYHKe npo.n.o.'l)ImTeJIbHOCTb OTKpbITH5I l\IO)j{eT perYJIHpOBaTbC5I,
HanpHMep, H311leHelmelll 3a30pa B npHBo.n.e HrJIbI. npH nOM Ha pe-
)KIfl\Ie Ma.1J:Oll no.n.a'lH HrJIa 6y.n.eT OTKpbIBaTbCH n03,n:Hee H 3aKpbI-
BaTbCH paHblile (3aKpWTHe 06WQHO npOHCKo,n:HT no,n: eHCTBHeM
npY)j{HHbI). npH 3.'1eKTpOMarHHTHOI{ CPopCYHKe npo.n.o.'I)j{HTe.1bHocTb
26
OTKpbITI1H I1rJIbI 3aBI1CI1T OT BeJII1IJI1HbI 3apHLLa KOHLLeHCaTOpa, pery-
JIHpyeMoro peOCTaTOM. DpI1 HeH3MeHHOH npOAO.1DKHTe.'lbHOCTI1 OT-
KpbITH5I CPOPCYHKH B rpaLLycax yr.rra nOBOpOTa YBe.'lI1IJeHI1e IJI1C.1J3
060pOTOB npHBOLLI1T K YMeHbllleHI1IO l.{HK.'10BOH nOLLaIJH TOn,;lHBa.
B paCCMaTpHBaeMOM MeTO,1J:e LLJIH paBHOMepHOH nOLLalJH Ton.'1HBa
no l.{I1m1HJI,paM BmKHO YMeHblllI1Tb rI1JI,paBJIHIJeeKOe eonpOTHBJIeHI1e
<POPCYHOI , B TOM 'IHC.'le npI1 MI1HHMaJlbHOM nOLL'beMe Hr.'1bI, H o6ec-
neIJHTb paBelICTBO npOXOJI,HbIX CeIJeHHII B paCnbIJIHTe.'1Hx.
D. KOM6HHHpoBaHHoe LL03HpoBaHHe C nepeMeHHwM JI,aB eHHeM
B aKKYMYJIHTope. DpH nOCTOHHHOM LLaBJleHHH B aKKYMYJ1HTope npo-
).I,O.'UKHTeJ1bHOCTb BnpbIcKa IJpe3MepHo cOKpalll.aeTcH npH YMeHbllle-
HHH HarpY3KH. llT06bI H36eLKaTb 3Toro, npHMeHHIOT perYJIHpOBaHHe
(BPYIJHYIO HJIH aBTOMaTHIJeCKH) ).I,aB.rreHHH B aKKYMYJ1HTOpe, npHIJeM
€ro Be.1JWIHHY 06bIIJHO CHHLKalOT npH nepexo).l,e Ha pe)KHMbI Ma.TJbIX
HarpY30K H X0J10CTOrO xona.
B. Ll.03HpoBaHHe K.'1anaHal\IH H 30.'lOTHHKaMI1. LI..'lH aJmYMYJIHTOp-
HWX CHCTeM 3TOT cnoc06 n03HpoBaHHH CBOnHTCH K H3MeHeHHIO
HHTepBa.la BpeMeHH, B TeIJeHHe KOToporo rHnpaB.TIHIJeCKH ynpaB.TIHe-
]viaH CPopcYIIKa OCTaeTCH coe.lU1HemlOH C aKKYMYJ1HTOpOM.
Ha pHC. I nOKa3aHbI MeTOnbI n03HpoBaHHH, Hcno.1Jb3yeMbIe B
pa3Hblx THnax Ton.'lHBHOH annapaTypbI. He CJIenyeT nOHI1MaTb, IJTO
"TO.'lbKO YKa3aHHbIe B K.1JaccmlJI1Kal.{HH cnoco6bI n03I1pOBaHHH MorYT
npHMeHHTbCH. HanpHMep, npH Ton.1HBH0I1 annapaType C npYLKHH-
HbIM npHBonOM nJIYHLKepa n03HpOBaHI-!e MOLKHO OC) meCTBoilHTb He
"TO.'lbKO nepeMeHHbIM XOLLOM nJ1ymKepa, HO H ll.11ymKepOM-30.'lOTHH-
KOM, K.'IanaHaMH II T. JI,. KOHe'lHO, onpeLLe.1JNIHbIe OrpaHHIJeHIIH B
npHMeHeHIIH MeTonOB n0311pOBaHH5I IIMeIOTCH. TaK, enBa .'Ill l.{eJ1e-
co06pa3HO HcnO.1Jb30BaTb n.'IYHLKep-L!.03aTOp C nepeMeHHblM XOL!.OM
npH MHoronJIYHLKepHOM Hacoce. KaK OTI\1eIJa.l0Cb, B :'JTOM CJ1YIJae
HenpHMeHHM MeTOL!. L!.03HpOBaHHH JJ:pOCCeJ1HpOBaHHeM Ha BcaCbIBa-
HHII. HeKOTopbIe H3 npHBeJI,eHHbIX cnoc060B LL03HpOBaHHH He nep-
cneKTHBHbI JJ:JIH OJJ:HOro TlIna TOnJ1HBHOH annapaTypbl, HO MorYT
6bITb HCnOJIb30BaHbI e JJ:pyrHI\I. D03TOI\IY, YIJHTbIBaH nHHaMIIKY pa3-
BIITHH TOnJ111BHbIX CHCTeM II nOHB.leHlle HOBbIX exeM II pellleHHH,
3L!.eCb onllcaHO I\laKCHMaJ1bHOe 'lHCJ10 I\IeTO.lI.OB JJ:03HpOBaHI-IH. He
HCKJIIOIJeHO, 'ITO HenpHMeIUIeMbIe B HaCTOHllI.ee BpeI\IH MeTOLLbI JI,03H-
pOBaHHH MorYT 6bITb HcnO.'lb30BaHbI B 6Y.lI.Ylll.eM.
3. KOHCTPYK4HH
3D,eCb paCCI\latpHBalOTCH HeKOTopbIe HOBbIe KOHCTPYKl.{IlIl, onll-
caHHe KOTOpbIX npllBeneHO B 3apy6ex<HOH .1JWrepaType. JJ..'lH pa360pa
BbI6paHbI BbmYCKaeMbIe Mo.n:e.'Ill H.'UI no.n:rOTOBJIeHHbIe I( BbmYCKY,
a TaKiKe HeKOTopbIe CTapwe XapaI<TepHbIe MOJJ:e.1JH TOn.1lIBHOH anna..
paTypbI B COOTBeTCTBHH e KJIaCCHcpHKal.{HeH (CM. pHC. I).
D pHMepoM TOnJIHBHOH annapaTypbI C 6.'10'IHbIM MHoron.TIymKep-
HbII\I HaCOCOM MOX{eT CJIYX<HTb annapaTypa, pa3pa6oTaHHaH H BbI-
nYCKaeMaH Holley Carburator [83]. Mo.a;e.TJb 3200, pa3pa6OTaHHaH
2Z
:iTOH q:mpMOH, npe.1.Ha3HaGeHa .n.ml 6bICTPOXO)],HbIX )],ll3e:JeH C 'lllC-
JlOM 060pOTOB KOJIeHGaTOrO Ba.'Ia )],0 3000 Ii 60.'Iee, YCTaHaBJ1IiBae-
MbIX Ha aBTOM0611.i'I5IX Cpe)],HeH rpY30nO,J:"beMHOCTli. Ha pliC. 9 H30-
6pa}KeH pa3pe3 O.lI.HOH 113 CeKIJ.IIH Hacoca lVlO.lI.eJlll 3200, Ha pliC. 10-
perymnop GIICJIa 060POTOB, C6 'IOKI1pOBaHHbIH C HaCOCOM BbICOKOro
)],aBJIeHHH. Hacoc 6.'IOtJHbIH BocbMHnJ'IYH}KepHbIH, PH)],HbIH C Heno-
cpe)],cTBeHHbIl\! npHBO.lI.OM n.'IYH}Kepa OT KYJ1atJKOBoro BaJIa tJepe3
pO.1JHKOBbIe TO.'IKaTeJIl1. Ll03HpoBaHlie
06eCneGHBaeTC5I nJIYH}KepOM -30JIOTHll-
KOM npll HaJIH4HH BnycKHoro aBTOM8-
THGeCKOrO KJI8naHa. HatJ8J10 reOMeT-
pHtJecKoH no)],atJH nOCTOHHHO (3a HC-
K.'II04eHHeM nycKoBoro pe}KllMa), KO-
HeIJ. nepeMeHHbIH. Oco6eHHocTll Haeo-
ca CBH3aHbI C llCnOJIb30BaHlleM ero Ha
6bICTPOXO.lI.HbIX TpaHcnopTHbIX .lI.H3e-
.'IHX. B Hacoce npe)],ycl\WTpeH aBTOMa-
T1l4ecKliH BnycKHoH KJIanaH (CM.
pI1c. 9), C.'lY}K8li1.11H .lI.JI5I YMeHbIIleHIIH
KaBliTaIJ.HOHHOH 3p031111 II Y.lI.apHbIX
HarpY30K B lI.1l3eJ'Ie. KJlanaH YJlY4IIl8eT
xapaKTepHcTHKY Ton.1JIIBonO.lI.aGH no
060POT3M, 06ecnetJIlBa5I YBe.'IIlGeHlle
IJ.HK.'lOBOH no)],a'IH npH YMeHbllIeHIIll
4HC.'I3 060pOTOB (pIlC. 11), Dpll 3TOM,
tJTo6bI 1136e)!i3Tb ,J:bIM.TJeH1l5I H3 Ma.'IbIX
060porax, B perYJ'IHTOpe npe)],ycMoT-
peH TOpCHOH 14 (CM. pllC. 10), O.lI.llH
H3 KOHIJ.OB KOToporo CJIYllillT onopoH
pbltJ3ra 5, nepelI.aIOliI.ero lI.BH)J\.eHl1e
OT tJYBCTBllTe:JbHoro 3JIeMeHTa pery-
JI5ITOpa K peHKe TonmIBHoro Hacoca.
YCllJ'IHe rpY30B nepe)],aeTC5I Ha npoTll-
Bono.7IO}KHbIH KOHeIJ. TopclloHa. Do Mepe YBemI4eHHf! 4IIC la ooopo-
TOB II YCU.'ll15I rpY30B TOpCHOH )],e<lJ0pMupyeTcH. ooecne4UBaH nepeMe-
liI.emle pelIKu B HanpaBJlemm YBeJlll4eHllH nOJ1.a4U Ton.'IliBa. LleHCT-
BIle TOpCHOH3 orpaHU411BaeTCH ynopoM 10, paCnOJIO}KeHHbJ;\I B Bepx-
HeH GaCTH pW4ara
Ha Bll,'!, xapaI<TepHCTllKH TOn.'IllBonO.lI.a4H no 060poniM (CM.
pHC. ] 1) B.'IllHIOT llieCTKOCTb TopclloHa II MaKCllM3.1JbH35I ero ,'!,e<lJop-
MaIJ.1l5I. DOJloCTH BcaCbIB3HlUI II OTcetJKH B Hacoce coe)],llHeHb! Y3KHM
KO.'IbIJ.eBbIM npoxo)],oM, tJTO, BH;J.HMO, o6ecnetJIIBaeT 60.'IbruyIO CTa-
611JIbHOCTb HanOJIHeHl!5I KaMepbI n.'IYH}Kepa. DYCK )],H3eJIH 06JIerG3eT-
CH B pe3YJ1bTaTe aBToM3THtJecKoH nO.lI.3tJll ll30WTO'lHOrO Ton:JllBa H
3ana3.I1.bIB3HHH H3'la.'I3 ero BnpbIcKa. DepBoe )],OCTHraeTCH KOHCTPYK-
IJ.HeH perYJIHTopa. npe)],ycM3TpHB3IOliI.eH nepeMelil.eHHe pellKH )],3.'Ib-
rue nOJIO}KeHHH, npn KOTOpOM o6eCne'lHB3eTC5I n0J1H35I nO,1,3'l3. PeH-
K3 B03BpalU3eTcH B pa60tJee nOJI01KeHHe nOCJIe nycKa BlIraTeJI5I.
PHC. 9. CCKI.\IIH Hacoca Ij:Jllplllbl
Hollcy Carburator CO IO.!J.C.'IH
3200
28
3ana3 NBaHHe Haqana BnpNCKa OCTHraeTCH CneUHaJbHO 06pa60'
TaHHbIM na30M Ha rO.'10BKe n.'1)'HLKepa. OpH n)'CKOBO:\I nO.rIOn eHIUI
g
6
5
l;
3
2
PilC. 10. CXCMa perYJ1HTopa, C6.'10KilpOBaHHoro C HaCOCOM:
A - KaMepa, Hcrro,,"Ib3yeM:a51 D.lIH H3MeHeHHf[ a8TSI.iKKH npY)l{HHbI perynHTopa;
1 - 3KcI1.eHTpHKoBbifi flaJ1 L{; 2 - pbIQar pery"rmpoBaHHH no.a.a1.£H npH H3MeHeHHH
TIJ10THOCTH TOnJIHEa; 3 - «pHKcaTop OCll pbI1..J.ara; 4 _ lllTOK perYJIHpOnaHHSJ no-
,:].a'lll npM H3MeHeHHll fl,.,'10'tHOCTH TOUJJHBa; 5 - pbJ11ar pery.rrHTopa; 6 - pbITlar
:MHUII!\laJIbHhlJ: OOOpOTOB XOJIOCTOrO x().LI.a; 7 - KOHTpraHKa; 8 _ BRRT perYJIH-
pOBBHHH J\fHHHManbHbIX Ot)0POTOB XO.nOCToro xo.n:a; 9 - pbJ1lar ynpaBJI€RHH
pery.1HToPOM: 10 - ynop MaKcHMa."bIlOlI nO.1J;a4H; 11 - CTon-pbI4ar; 12 - BHIlT
oCTaHoBKH; 13 - HeperYJIllpyeMbIIt rnop pf>r'lara; /4 - TOpCHOH; 15 _ npY>KHHa
MaKCHMa.""Hbrx 06opoToa; 16 .- onoI)a npY>KHHb'; 17 - IlopweIlb; 18 - npo-
KJIa,lI,Ka A.oUl pery..'1HpOS8Hlt5I M:aKCHM3.,'IbHbIX 060pOTOB XO..1:0CTOrO xo.n.a; 19 _
ynopHblfr nOJI.WHnHHK; 20 Myq,Ta perYJIHTOpa; 21 _ Kyaa'lKOBLllt BaJI; 22 _
rpY3 perYlIRTopa; 23 - nPYLKHHa MHHHManbHhIX 060POTOB XO..'10CTOrO xo,rr,a; 24 _
lliTOK coe.!t.HHeHlul pbIt:lara perYJulTopa c peHKoi'r TOnllHBHoro Hacoca; "'25 _ npy-
>KUHa 6yq,epa XOJIOCToro xo)],a; 26 - I<pblWKa Kopnyca perYJIHTOpa; 27 - JIIDK;
28 - BHUT perYJIHpOBaIlH'I 6yq,epa XO,'OCToro xo)],a; 29 - KopnyC ;r;na<jJparMbl;
30 KpblwKa "opnyca :\naq,parMbl
nnymKepa na3 COBMemaeTC5I C OTCeqHbnI OTBepCTHe:\1. DOOIe nepe-
KpbITH5I :onoro OTBepCTH5I TeJ10M nJIYHLKepa, npOHCXOn:5Ill.(H 1 B pe.
3y.1bTaTe nO 'beM8 nOC.IIe HerO Ha on- ,.,,.,¥qUKI1
pe.J,e.'1eHH)'IO BbICOT)', H8'lHHaeTCH reo- 1/ 60 -r
MeTpHQeCK85I non:8'la. f
npH 06bJlIHbIX nOJIO:iKeHH5IX nnYH- 55
rKepa Ha'IaJIO reOMeTpU<IeCKOH nOn:a'IH
COBrra aeT C .HaQa.'IOM BH}( eHHH
n.11YH:lKepa.
B npIIBO e HaCOC8 rrpen:YCMOTpeH
IJ.eHTpo6eLKHbIH aBTOMal.' onepeLKeHHH
BrrpbICKa. H8COC HMeeT CHCTeM)' Cl\la3-
KH no aB.'1eHHeM, npU<IeM Mac.'IO no-
CTynaeT H3 CHCTeMbI CMa3KH llBHraTe-
nH Qepe3 CBepneHH5I BO r3Ty.rIKax .r[5I CM-a.3KH n.'I)'HLKepHbIx nap. no
MHeHHIO <pHPMbI, 3TO 06eCneQHBaeT B03MOLKHOCTb Hcrronb30B8Tb
l:IaCOc Ha MHorOTorr.'1I!BlibIX llH3e.TIHX, B KOTOpbIX B cn)''Iae npHMeHe-
29
50 2
f200 2000 2800
l/UCIIO o50pomofJ i}fJuzamellR {J HUH
PHC. II. CKopOCTHaH xapaK-
TCpllCTHKa nO.D:a'-lll Tonmma:
1 - oe3 TOpCHOH3; 2 - C rop-
CMOHO'1
HHH C\Ia.l0BH3KHX TOnJIHB l\W;>KeT pe3KO B03paCTH H3HOC nJIYH;>KepHbIX
nap. OTe1.IeCTBeHHbIH OnblT BbIHBI1.'I, O.lI.HaKO, MaJ1YlO 3<p<peKTHBHOCTb
:,HO}J J\OHCTPYKTllBHOll MepbI. Do.lee 3<pcpeKTllBHbJM HB.':IHeTCH HcnO.1b-
30BaHHe KO b eBWX BWT01.IeK Ha .lI.eTa HX n YHx epHOH napw H OT-
BO;J. 113 HHX Ton.1HB3 B MarHCTpa,,1b HH3Koro .lI.aB.leHHH. PerYJ1HTOp
.lI.Byxpe;>KHMHbIH, HO MomeT pa60TaTb 11
KaK BCepemHl\lHbIH. .lJ..!IH 3Toro 3aTH)KKa
np}%HHbJ 15 (CM. pHC. 10) MomeT pery-
.1I1pOBaTbCH nYTeM 113MeHeHHH ;J.aBJIemlH
B03.lI.yxa, nO,lJ,8B8eMoro B J\8Mepy A.
OpHMepOM ceK HoHHOro O.lI.HOn lYH-
n\.epHoro H8coca C MeXaHH1.IeCKHM npIlBO-
.lI.Ol\"I MmKeT eJIymHTb TOnJIHBHblH Hacoe
(pIle. 12), BbwymeHHbIll cpIlpMOH Bryee
Berger [85]. B Hacoc MorYT YCTaHaB.1Il-
1
BaTbCH nJ1YHmepHbIe napbI .lI.llaMeTpOM OT
5 .lI.O 9 )jUI, eKoHcTpYHpoBaHHbIe ;J.J151 pa-
60TbI npll xO.lI.e 7 H 7,5 MM. .lJ.03HpoBaHHe
ocymeCTB.TJHeTCH nJIYH;>KepOM -30J10THll-
2 KOM. PbI1.Iar .lI..':1H nOBopOTa nJ1YHmepa
HMeeT illapOBOH HaKOHelJHHK, '-ITO 06.ler-
qaeT COe.lI.HHeHHe ero C THrOH perYJIHTO-
pa. BTYJIKa n.'lYH}Kepa cpIlKcHpyeTcH OT
nOBopOTa BHHTOM. B Hacoce npHMeHeH
J HarHeTaTe.lbHbIH K.'lanaH THna Atlas,
06eCnelJHBalOmIlH lIeTKoe OKOHlJaHHe
BnpbICKa Ton.1HBa II cTa6H.'lbHOCTb IlHK-
.1]OB no BpeMeml. OpaBIlJIbHOCTb yr.TJoBoi:i
YCTaHOBKH Kopnyca nacoca, a CJIe.lI.OBa-
Te.lbHO, H BTY lKH n.1YH;>Kepa OTHOCIlTe.1b-
HO nJ1YH;>Kepa, CBH3aHHoro C pb!llaroM
ynpaBJ1eHHH nO.lI.a1.IeH. .lI.OCTHraeTCH nOBO-
pOTOM Kopnyca .lI.0 COBna.lI.eHHH MeTOK.
Ha1.Ia.lo reOMeTpH1.IeCKOH nO.lI.a1.IH MmKeT
B He60.'lbillHX npe.lI.e.rrax H3MeHHTbCH TO.1-
mHHoH npOKJIa.lI.KH, YCTaHaBJIHBaeMOH
Me;>K.lI.Y q,JIaH eM Hacoca J1 .lI.BllraTeJIeM.
HacocbI l\IO.lI.e.1J1 DP A q,Hpl\lbI CA V OTHOCHTCH K KaTerOpJ1J1 pac-
npe.I\emne.'lbHbIX HaCOCOB HenOCpe.lI.CTBeHHoro .I\eHCTBllH C MexaHH-
1.IeCKHM npHBOJJ.OM J1 JJ.03J1pOBaHHeM nYTeM .lI.pOcce.'IHpOBaHHH Ha Bca-
CbIBaHHH [82]. HacocbI BbITIycKalOTcH C MeXaHll1.IeCKHM H rH.JpaB.'UJ-
qeCKHM perYJ15ITopoM. Ha pHC. 13, a nOKa3aH Hacoc MO,lI,e.'I1J DPA
C rH.lI.paB.1J11.IeCKHM pery.:1HTopOM. POTOp 9, HecymIJH IIaCOCHbIe H
pacnpe,lI,eJIHTe.1bHbIe <PYHKl{HH, npHBO,lI,HTC5I OT Ba.la 1 c nOMOllIbJO
lll.lH eBoro COelI.HIIeHHH. B nepeJJ.HeH 1.IaCTI1 pOTopa llMeeTC5I o6pa-
60TaHHoe HJIHH,lI,pHqeCKOe oTBepcTHe. B KOTOpOM pacnOJIOmeHbI ,lI,Ba
npoTHBOnOJImKHO JJ.BJ1;>KymHxcH n.:1YInKepa 2. HarHeTalOmI1H XOJJ.
n.'lYH:lli.epoB ocymecTB.15JeTCH npH BpauLeHHH pOTopa B pe3y.'lbTaTe
30
5
"
PIIC. 12. CCI(1.\1I0IIHbli1 Hacoe
MO;J;C.1H AI,lJ,A9 Ij:JIIpMbl
Bryce Bcrgcr;
1 - HarHeTaTeJIbHhrft KJI8IJ3H;
2 - pblqar ynpaMeHHH; J-
npY>KHHa n.oymKepa; 4 - n.nYH-
lKepH8H napa; 5 - BHHl' Bb1-
nycI<a B031J'yxa; 6 - q,nKcnPYlo-
ll.\Hii BHHT
06KaTbIBaHI15I KIIHel'vIaTliIfeCKII CB5J3aHHbIMII C pOTOpOM pO.'IHKOBbIMII
TO KaTe HMII KO bua 3 C BHYTpeHHIIMII Ky aqKOB MII B cTYllaMlI.
CX€Ma Ha pllC. 13, 6 llOHCHH€T llpoueccbI HanOJ1H€HlIH BHYTPll-
n.'lymKepHoH nO OCTlI Hacoca TOllJIHBOM H pacnpeLLeJleHll5J TOnJIHBa
PHC. 13. Hacoc DPA c rn.D:paB.'1H4C-
CKHM pcrYJlHTOpOM: ,
" - 061l\HII BH)],; 6 - cxeMa pa60Tb'; ,
1 - BnycK TOII.ilHBa "3 J:t03HpYIOIJJ;ero ",,,\:
30. OTHHKa; II - no)],a'la TOnJIHBa K 1--
q,opcYHKe; 1 - BaJI npHBo)],a; 2-
BCTpe'mo-)],BHMYIl\HeCH n. YH}j{epbI; 3 -
KOJIb11.O C BHYTpeHHHMH Ky.,'1aQKOBbIMU
BbIcTynaMH .lJ,JlH npHBo.!t.a n...1YH>KepOB;
4 - cepBopery.1HTop yrJIa onepe>KeHHH
BnpblcKa; 5 - nOJJ.KaQHBalOI1l.Hil Hacoc
6 - perYJIHpYIOIl\Hit KJIanaH; - BTY. -
Ka perYJIHpYIOll\ero KJlanaHa; "8 - HefI-
.10HOBbIi1 q,HJIbTp; 9 - POTOP; 10--
rH.D.paBJIHIJeCKaH rOJIOBKa; 11 - )J.03U-
PYlOllI,HH 30.TIOTHUK; 12 - rHJJ,pa B.'1H'le- 2
CKillI perY.U1TOp
8
7
6'
a)
9
!J
no UllJlllHLLpaM. B03BpaTH u XOLL nJlYHMepa llpOllcxoLLIIT nOLL LLeu-
CTBlIeM U.eHTp06e)KHbIX ClI.'I. B Te.'Ie pOTopa llMelOTCH CBepJ1eHIIH,
411C 0 KOTOp X paBHo KOJII4€CTBY llH IIHLLpOB LLII3e H. Bo BTYJ1K€
pOTopa npOCBepJleHO HanOJlHIITeJ1bHOe oTBepcTHe, K KOTOPOMY TOll-
.'IHBO lloCTynaeT nOLL LLaBJ1eHlIeM, pery.'IlIpyeMbIM LL03I1PYlOlLJ.IIM 30-
JIOTHHKOM. KOr,ll,a O,ll,HO 1I3 HanO.HHIITe.1JbHbIX oTsepcTlIu B POTOP€
31
COBMellLeHO C m1TaKJLQHM KaHa.l0M BO BTy.'IKe pOTopa, KaMepa n.'IYH-
fKepOB HanO,,'IHHeTCH Ton.'IHBOM B COOTBeTCTBHH C Be.'IH4HHOfI KOHTpO-
.TIHpyeMoro ,lJ,aB.'IeHHH H 4HCJ'IOM 060pOTOB pOTopa. D pH ,lJ,8.'IbHeHllleM
(nocne HanOJIHeHHH) BpameHHH pOTopa pOJUlKH, 06KaTbIBaH KYJIaLJ-
KOBbIe BbICTynbI, nepeMelll.aIOT nJIYHfKepbl lIaBCTpeLJY O.rUIH ,lJ,pyrOMY.
DpH 3TOM Tonmmo nO,lJ,aeTCH 4epe3 e,lJ,HHCTBeHHoe HarHeTaIOLQee
CBepJIeHHe B pOTope (COBMelll.eHHOe C O.!J,HI1M H3 HarHeTaIOllI.HX CBep-
.'IeHHH BO BTYJ1Ke). 113 nOC.'Ie,lJ,Hero Ton.'II1BO nocTynaeT B O.!J,HH H3
lllTyu.epoB Hacoca, a oTTY.!J,a - K COOTB€TCTBYIOwei\ opcYHKe O.!J,HO-
ro H3 IlH,;lHH,lJ,pOB.
LLo3HpOBaHH€ Ton.'IfIBa O,lJ,HHM 30.'IOTHliKOM, HarHeTaHHe ero
o.!J,HofI napoH n.'IYHfKepoB Ii pacnpe.!J,e.'IeHfle C nOMOlll.bKJ TOLJHO Bbl-
nO.'IHeHHbIX H paCnOJIO:tKeHHblx oTBepCTHH MorYT 06eCneLJHTb paB-
HOMepHocTb UI1KJIOBbIX nO.!J,a4 H I1AeHTH4HOCTb MOMeHTOB HaLJa.'1a no-
JI,aLJI1 TOn.'IHBa no IlHJIHH.LI.paM. O.LI.H8KO .LI.JIH 3Toro He06xo.LI.HMO no.'1-
Hoe rH.LI.paBJIHLJeCKOe e.LI.I1Ho06p83He HarHeTaTe.'IbHbIX OTBepCTHH,
Tpy60npOBO.!J,OB H OPCYHOK. B npOIlecce 3Kcn.'1yaTaIlHH .LI.OCTHrHYToe
e,lJ,HHo06pa3He HapYlllaeTCH. B CBH3H co CKa3aHHbIM HaCOCbI pac-
CMaTpl1BaeMOro THna He BCer.LI.a 06ecne4HBaIOT Tpe6yeMYIO paBHO-
MepHOCTb pa60TbI ,lJ,H3e.'1H.
DO,lJ,Ka1.JI1BaIOllI.l1l1 Hacoc 5 Ko.'10BpaTHoro Tl1na (pl1c. 13, a) pac-
nOJIO:tKeH B 3a,lJ,Hei\ 4aCTl1 Hacoca. Ero pOTOp CBH38H fKeCTKO C pO-
TOpOM Hacoca. Ton.'1HBO nocTynaeT BO BcacbIBaIOmyIO nOJIOCTb Ha-
coca, npOlI,lJ,H '-Iepe3 HalI.'IOHOBblH tPI1.)lbTP TOHKOH 04HCTKH. C HarHe-
TaIOmeH nOJl0CTbIO Hacoca CBH3aII perymlpYIOllI.HH KJ1anaH,
pacrr0J10:tKeHHbIH B KpbIlllKe rrOIJ.Ka4HBaKJllI.erO Hacoca H BbInOmlHIO-
LQHH .!J,Be tPYHKIll1l1: 06ecne4HBaeT rrOJIY1.JeHHe onpe,lJ,eJIeHHOH CBH3H
Me:tK.LI.Y .LI.aB.'IeHl1eM nO.LI.KaLJKH H 1.JHC.'10M 060pOTOB Hacoca, a TaK:tKe
B03MO:tKHOCTb BPY1.JHYKJ npOKa IHBaTb Hacoc npH HenO.LI.BH:tKHbIX .'10-
naCTHX nO.!J,Ka1.JHBaJOLQerO Hacoca.
Y3eJI perYJlHpYIOllI.ero K.l:JanaHa nOKa3aH Ha pHC. l4. Ton.'1HBO
nOCTyrraeT cBepxy H npOXO,lJ,HT BO BcaCbIBaIOLQYIO nOJIOCTb 110.LI.Ka-
1.JHBaIOLQerO Hacoca 4epe3 HaHJIOHOBbIH cpHJIbTp 2 H BepxHee CBep,;'Ie-
HHe A B Kopnyce KJ1anaHa. 4epe3 HH:tKHee CBep.leHHe B Ton.1HBO
no,lJ, .LI.aB.'IeHHeM, C03,lJ,aBaeMbIM nO,lJ,K8LJI1B8IOllI.HM H8COCOM, nOCTY-
naeT BHYTPb BTYJIKH KJIanaHa 11 CTpeMHTCH nO,lJ,HHTb KJIan8H 4, npe-
o.n;OJIeBaH YCfume rrpYJImHbI 3. DpH YBe.'IWIeHlIIl LJHUm 060pOTOB H
,lJ,aBJ1eHHH rrO.!J,Ka1.JKH K.'1arraH 4 nO.LI.HHMaeTCH Ha 60JIblllYIO Be.'I114HHY
11 oTKp BaeT oTBepCTl1e E, 1.Jepe3 KOTopoe TOnJIHBO nepenYCKaeTCH
113 HarHeT810lll.eH BO BcaCbIBaIOLQYIO nO.'10CTb nO.LI.KaLJHBaIOLQero Ha-
coca. 3cp eI(THBHOe npOXO.LI.HOe CeLJeHHe nepenYCI<HOrO OTBepCTI1H
B03paCTaeT C YBeJ1HLJeHHeM LJHCJIa 060pOTOB ,lJ,BHraTeJIH.
f1pH npOKalJKe BPY1.JHYIO TOnJIHBO rrocTyrraeT BHYTPb BTYJIKH K.'1a-
rraHa cBepxy. K.TIanaH no,lJ, n:eHCTBHeM YCH.'IHH OT .LI.aBJIeHHH Ton.'IHBa
rrpeO,lJ,0.1eBaeT YCHJIHe rrpYfKHHbI 5 H npH ,D,BH:tKeHHH BHH3 oTKpbIBaeT
oTBepcTHe r. DPOi'I,lJ,H .:HO oTBepcTHe, TOnJIHBO LJepe3 CBepJIeHHe B
rrocTynaeT B HarHeTaIOllI.YIO nO.'IOCTb nO.rJ:KaLJHBaIOLQerO Hacoca, a OT-
Ty.n;a - B nO.'IOCTb Hacoca BbICOKoro .n;aB.1eHHH.
32
B HaCOCe (CM. pIle. 13, a) IlMeeTCH cepBoperY.1HTOp yr.'1a one-
pe)KeHfIH BnpbICKa (pHe. 15). YBeJII1'leHile YrJla onepellieHf1H BnpbI-
CKa D.OCTHraeTCH npil nOBbIlIIeHilil 4I1C.Tla 060pOTOB BpaIl.leHileM KY-
.TlaIlKOBOrO Ko.'1bua C nOMOlll.blO cneUfla.TlbHoro. MeXaHH31\la. C KV.Tlall-
KOBbIM KO.TJbUOM CBH3aHa' pe3b60EbIM coeD.flHeHfI€N1 uamj:>a -4 co
crpepfllIeCKflM HaKOHeIlHHKOM. Ooc.'Ie,D,HHH BXO,D,flT B oTBepCTile noplII-
HH 5, HaXO.J,5JllI.erOCH no,D, ,D,eHCTBfleM ,D,a.B.'1eHH5J TOnJ1f1Ba I1 YCfl.TIflH
npY)KHH 2, 3. Opfl YBe.'1I1lleHHH
1.J1JU1a 060pOTOB B03paCTaeT YCfI-
.'1f1e 01' ,D,aB.'IeHI15J Ton.'IflBa. Oop-
.meHb nepeMelll.aeTC5J BnpaBo,
nOBOpallflBa5J Kyna4KoBoe KOJ1b-
2
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-,
i
Puc. 14. PcrYJluPY!Oll.\Ul1 K.TJanaH:
/1 - oTBepcTue JJ.JIH no.naqn TOn.,'1HBa K
nO.lJ.Ka1.J:HBalOllleMY Hacoey; E - nepenYCK-.
Hoe OTBepCTHe: B - OTBepCTHe lI.JHi HarHe- t
T8HHH TOrIJU1Ba H3 nO.iJ;KaQHB810Il.{erO HaCGCa
BHYTPb BTYJIKH KJlanaH8; r - OTBepCTHe
,i]JIs.J nOlI,34H Ton.nHB3 B H8COC. MHH.YS\ noJJ,-
K8 l lH.BalOmHfi HaCGC; 1 - nHTalOlli.HH llITY-
L(ep: 2 - Hefr_'0HoBt"fr q,H.1bTp: 3, 5 -.
npY>KHHLI: 4 -- pery.,TJHPYIOllJ,Hf'r I{JIanaH
Puc. 15. ABTOJlaT OnCpC)KCHH5I
Bnpb!CKa:
:1 :.-. pOJIHKOahI/\ TO.1KaTeJIb: 2. 3 - npY>KH-
HbI; 4 - .1I.anQJa; .5 rropUl_eHL
UO B CTOPOHY OnepelKeHI!5I Halla.'1a HarHeTalOllI.ero D.BlIllieHH5I nJIYH-
)KepOB. MaKCIlMa.'IbHa5I nO,D,alla TOnJIflBa HaCOCOM OnpeD.e.'I5IeTC5I npe-
D.eJlbHbIM paCXOlliD.eHHel\l n.'IymKepOB. OOC.'1eD.Hee pery.'1IlpyeTC5I Ha-
60pOM IIJIaCTHH4aTbIX npY)KflH. B HfI)KHIlH JII1CT KOTOpbIX ynlIpalOTC5J
TO.'1KaTe.'IH npli HX paCXmKD.eHHH. PerYJIHpOBaHlie OCYIl.leCTBlI5IeTC5J
BIIHTOM, rrpfl 3aBflH4f1Bamm KOTOpOrO HIllliHHl1 .J1I1CT n.'1aCnlH4aTbIX
npYlliflH BbIl1p5Jl\o!.'I5IeTCH, TeM CaMbiM YBe.'1f14HBaH XOD. nJ1YH)Kep2 [59].
fH,D,paB.'1f14eCKflH pery.TJ5ITOp 12 Hacoca (CM. pflC. 13, a) BJQIio-
llaeT 30.nOTHIIK, Ha KOTOpbIH J],eHcTBYlOT YCH.TIHe 01' J],aB.TJeHflf! nOA-
KallKH Ton.'1HBa fI yCflJ1He npYlliflHbI. Opfl YBem14eHIJfI IlflCJ1a 060po-
TOB B03pacTalOIl.lee yCfI.TIlle 01' J],aBJIeHIlf! TOn.TIfIBa nepeMelll.aeT 30-
JIOTHHK, YMeHblIIaf! npOXOJ],Hoe Ce1leHIfe J],.'1f! Ton.1IfBa, HanpaB.TJf!e-
3 3aKa3 748 33
MOro K Han0J1HHTe.1bHOMY OTBepCTHIQ BTYJIKH pOTOpa. HaT5Ir npy-
)!{HHbJ, Onpe.11e.1JHJOll.\HH HHTepBa.1 pa6mmx 060pOTOB .11BHraTe.15I,
H3MeHHeTCH C nOMOll.\bJO Ba.1HKa pbIlJara ynpaB.'JeHHH, CBH3aHHoro
C ynopoM npY)!{HHbI peelJHbIM MexaHH3MOM. OpH nOBopOTe 30.10T-
HHKa Ha 90° npOTOlJKa Ha 30J10THHKe pa306ll.\aeTC5I C TOnJIHBOnO -
BO.11Hll.\HM KaHa.10M, H .lI.BHraTe.'1b OCTaHaBJIHB8eTCfl. MeX8HH'leClmff
pery.1J5ITOp Hacoca H3MeH5IeT npoxo.lI.Hoe oTBepcTlle ,1I..1JH Ton.'IHBa npH
nOBopoTe 30.10THIlKa no)], AeHcTBHeM YBe.1H'lHBaJOll.\erO YCH.1H}!
rpY30B.
Pnc. 16. Ton.'1I1BHbIi1 !laCGC pacnpc,J,c.TJIITC.lbHoro TlJlla C MCXaHII'-ICCKIDI npHBo.J.oM
n.1YHLKcpa II ;J.o3HpoBaHllcM ;rpoccc.lIIpoBaIlHe:V1 Ha BCaCblBa!lIlH. MO;J.C.lb C Ij:JHpMbI
Standard Screw Co:
J - npHB01J.HOiI Ba.l1; 2 - Kopnyc; 3 - pery.aslTOp onCpeiKeHH.H BnpbtCKa; 4 - rI.aYH}I(ep;
5 - pacnpe.ne.'1I1Te.;1b; 6 - nO.ll.K31.1HBalOllI,Hi1 Hacoe; 7 - KpbllllKa nO.!l.K3'-1HBalOll1.erO Hacoca;
8 - rH.lI.paB.TIH4eCK3H rO,,10BKa H3coca; 9 - perYw'lfiTOp '-lHC '1a OOOpOTOB; 10 - rnecTepHH
O)],HOH H3 nOCJIe)],HHX l\l0.n.H<pHK8IJ.HH HaCOCOB paCCMOTpeHHOrO
Tllna HBJ15IeTCH HaCOC MO.n.eJIH C, OCBOeHHbIH q:mpMOH Standart
Sorew CO. (pHC. 16). B Hacoce HMeeTC5I nOlJ.KalJIlBaJOll.\HH Hacoc KO-
.1JOBpaTHoro THna, KOMnaKTHbIH perYJIHTOp C MeXaHHlJeCKHM IJ.eHTpO-
6e)!{HbIM npeIJ.H3HOHHbIM lJYBCTBHTe.'IbHbIl\l 3J1eMeHTOM, B03.11eHcTBYIO-
ll.\HM Ha Bpall.\alOll.\HHC5I J.W3HPYIOll.\HH 30.10THHK, B KOTOpOM TpeHIle
CBe eHO K l\WHHMYMY, 3JIeKTpOMarHHTHblH K.lanaH npeKpaIl(emUI
nO,1I.a'lH Ton,lIHBa, BK.'1lOlJaeMbIlI B CHCTeMY 3all.\HTbI J.I.H3e.J15I, IJ.eHTpO-
6e)!{HbIH cenapaTOp B03.n.yxa H aBTOM8T onepe)!{emUI BnpbICKa B BlL'I,e
cepBOMexaHH3Ma. Bpall.\alOlll.ero KYJla1JKOBOe KOJ1bIJ.O H npHBO)],HMoro
B lJ.eHCTBHe lJ.aB.1eHHeM Ton.'IHBa [84]. B Hacoce npelJ.YCMOTpeH 06-
lll.HH HarHeTaTeJIbHbIH KJlanaH, pacno.1JO)!{eHHbIH B oceBOM CBepJ1eHHH
pOTopa Hacoca. IhIeeTC5I BnYCKllOH wapHKOBbIH K.1JanaH. POTOp Bpa-
lll.aeTC5I B paCT01JKe rHJ.I.paB.'IH1JeCKOH rOJlOBKH Hacoca, B KOTOpOH
pacnOJIO)!{eHa 60,;lbwaH lJaCTb Y3Jl0B H J.I.eTa.'IefI. OpHBOJ.I.HOii Ba.'I
34
coe.n.lIHHeTcn C pOTOpOM C nOMO hlO BbIcTyna Ha pOTOpe II na3a
B BaJlY. POJlllKOBbIe TOJIKaTeJlH BpalI1.aIOTCH BMeCTe C pOTOpOM, .n.BlI-
rancb B ero na3ax. LlJIHHa Hacoca 178 .MM, Macca 3,5 KZ. Hacoc
npellHa3HaIJeU .n.JlH .n.H3eJIeH c pa60'lHM 061>el\WM I.{HJII-fH.n.pa 110 1,15 .Il
H 'lllCJIOM UH.7Il1H.n.POB He 60Jlee 8.
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Pnc. 17. CxeMa Hacoca:
J - Tpy60npoBo)], nO;I.a411 Ton.1HBa npH nYCKe II XOJJOCTOM xo.ne II nepenYCKe Ton.1l1Ba npH
npeBbllIleHHIf HOMHHa 1:bHOrO 4'HC.,'Ia 060pOTOB; J I - nepenYCK Ton:IHBa npH npeBblllleHHH
HOMHHa.;1blioro YHC..TJa 060pOTOB; 1 ........ Ton.,lHBHbJH 6al\; 2 - JlleCTepeH aThlfi H8COC; 3 _
<pHJIbTp; 4 - nepenYCKHofi KJIafJ8H; 5 - co..TJeHoH;':U-ibJJ1 K.."JanaH; 6 - .n;03:t1PYIOU(HU 110pmeHb;
7 - perY-"lTop C 30_10THIlKOBbIM YCl"pOiiCTBOM; lJ - Ba. ynpaB.leHHH no"a4eii; 9 - pac-
npei\e.JU!Te.lb
<PlIpMa Buchler Corporation BhmycTHJla Hacoc Hydra Meter
llJ1H pa60TbI c H8COC-q:,OPCYHK8MlI TlIn8 Cummins [83]. P8cMaTpH-
BaeMaH ClICTeMa TOnJlllBOnOJ1,a'lH OTHOCHTCH K Hacoc-q)OpcYHKaM C
Henocpe.n.cTBeHHbIM MeXaHH'leCKlIM npHBo.n.oM II .n.o3l1pOBaHlIeM C no-
MO blO n.TJymKepa-.n.o3aTopa.
CxeM8, nOHCI1HIO 8H npl1Hl1.lIll pa60TbI OCHOBHhlX :')JIeMeHTOB H8-
coca, H306p8./KeHa H8 pHC. 17. Ton"mBo lI3 6aKa 1 HanpaB.'1HeTCH
rneCTepeH'laTbIM HaCOCOM 2 B q:,lI.TJbTP 3, B KOTOpOM pacno.TJOMeH
nepenycKHOH KJIanaH 4, oTperYJIlIpOBaHHbIH H8 onpeJ1,eJIeHHOe .n.aB-
JIeHHe. LI.aB.'1eHlIe A03HpOBaHlI5I ,lI,.'15I l.JeTbIpeXTaKTHOrO ,lI,1I3e.'15I C MaK-
CIIMa.'1bHOH 1l.IIK.TIOBOH nO.lJ,al.JeH 200 MM 3 H3 peJKHMe 3000 06/MUH
COCTaBJUleT 24,5 KFjCM 2 . }Ja.TIee TOn,JIHBO nOCTynaeT B co.'1eHOII,lI,HbIH
K.TIanaH 5, c.'1YJKallI.HH AJI5I ,lI,IICTaHUIIOHHoro BbIK.'11OI.JeHH5I rrO,lI,al.JlI,
noc.le Hero HarrpaB.TIHeTC5I l.Jepe3 CBepJ1eHHH B pOTope pery.J15ITOpa
I.JIIC"la 060pOTOB B ,lI,03IIpYlOllI.ee YCTPOHCTBO. Ha pliC. 17 nOKa3aH
,lI,03aTop C rlI,lI,paB.'1lI'IeCKIiM npIIBoJJ:oM. XO.lJ, n.rrYHJKepa-,lI,03aTOpa
orpaHlflleH cnpaBa HenO,lI,BII)jmbIM ynopoM, c.leBa - ,lI,pOCCeJ1bllbIM
BaJIlIKOM, TOLIHee J.I.HOM rrpoqm.'1bHoro na3a, BbInO.IHeHlloro Ha J.I.POC-
ce.TIbHOM Ba.TIIiKe. BOJ.I.IITe.TIb, nOBOpal.J.llBa5I !I.pOcce.lbHbIH Ba.HIIK, 1I3-
MeH5IeT XO!l. n.'lYHIKepa-!I.03aTOpa liTeM caMbIM Be"IHI.JIIHY rropll.1I1i
TOrr.lHBa. MaKCIIMa.lbHaH no)].al.Ja Torr.llIBa orrpe!l.e.l5IeTCH HaII60.lb-
well rJ1y6HHoH rra3a B !I.poCCeJ1bHOM Ba.'1HKe. f1pH 3aMeHe rrOc.:le!l.-
Hero CHCTeMY MOJKHO npHcnoc06HTb A. 5I pa60TbI Ha !I.pyroM ,lI,BH-
raTe.TIe. LI.03aTop !I.BOHHOro !I.eHCTBIIH, T. e. 011 OTIVlepliBaeT H no-
,lI,aeT TOnJIHBO K pacnpe!l.emITeJ1lO npH XO,lI,e n.TJYHJKepa B.leBO H npH
XO,lI,e ero BnpaBO. <PYHKll.HH 3Q.'10THHKa npH nOM OCYllI.eCTB.TI5IeT pO-
TOp pery.TI5ITOpa, KOTOpbIH HMeeT COOTBeTCTBYIOllI.He BbI.TOI.JKH II CBep-
JIeHHH H HanpaB.TI5IeT TOOJIlIBO noli. ,lI,aB.'leHlIeM, C03!1.aBaeMbIM we-
CTepeHl.JaTbIM HaCOCOM, TO B KaMepy cnpaBa 01' OJlYHJKepa-,l1,03aTOpa,
TO B KaMepy C.'leBa 01' Hero.
f10,l1, ,lI,eHCTBI1eM YClIJIH5I 01' ,lI,aB.TIeHI1H TOnmiEa n.'1YH)j t;p- !I.03aTOp
nepeMeWaeTC5I, BbITeCH5I5I TOI.JHO OTMepeHHoe KO.llflIeCTBO Ton.TJHBa.
EC"lH TOnJIlIBO nO!l.aeTC5I C.'1eBa 01' OJlYH)j epa-)].03aTopa, npaBaH Ka-
Mepa ,lI,03aTOpa OKa3bIBaeTC5I C nOMOllI.blO CBepJleHlI5I B Te.'1e pOTopa
perymnopa COe,l1,I'IHeHI-IOH C pacnpe,lI,e,J1HTe.TIeM, l.Jepe3 KOTOpbIll TOI.J-
HO OTMepeHHoe KOJ1lIl.JeCTBO Ton.TIHBa nO!l.aeTCH B COOTBeTCTBYlOUJ,ylO
HaCOC-<pOPCYHKY TII.na Cummins. f10BOpOT pOTopa perYJ15ITOpa Ha
180 0 npHBO!l.HT K TOMY, I.JTO TOnJIHBO !I.J1H rH,lI,ponpHBO!l.a IWYHJKepa-
,lI,03aTOpa nocTynaeT cnpaBa 01' Hero, a JIeBaH KaMepa !I.03aTOpa
OKa3bIBaeTC5I CB5I3aHHOH C nOMOllI.bIO cBep.lJeHI1H B TeJ1e pOTopa pe-
rY,J15ITOpa C pacnpe.LI.emneJlelVl, a 'iepe3 Hero - co c.TIe,lI,YlOllI.eH no
nOp5l,l1,KY pa60TbI .LI.BHraTeJIH HaCOC-<p0PCYHKOH. BCnOJIb30BaHlie
O.LI.HOrO n.1YHfKepa-,lI,03aTopa ,l1,.TJH OTMepHBaHHH TOnJIHBa, nO,l1,aBae-
Moro BO Bce ll.H.TIlIH.lJ,pbI, 5IBJI5IeTCH npeHMYllI.eCTBOM paCCMaTpHBae-
MOH CHCTeMbI Ton.rIHBOnO!l.aI.JH. KaK BH.LI.HO H3 pHC. 17, pacnpe!l.eJ1H-
Te,,1b npocT no KOHcrpYKll.HH, TaK KaK O!l.HO CBepJ1eHHe 06C.'1)")KHBaeT
TPH Hacoc-<popcYHlm. OTMepeHHoe KOJ1H'ieCTBO TOOJIlIBa rrOCTvnaeT
B O.LI.HY H3 Hacoc-<poPCYHOK, TaK KaK n.TIYHJKepbI .LI.BYX .LI.PYrHx' nplI-
)j{aTbi K ce.LI.J1Y pacnbI.llITeJI5I II TOOJIlIBO B HI'IX He nocTynaeT. f1plI
nOBopOTe pOTopa pery.'15ITOpa Ha 180 0 pOTOp pacnpe.LI.em-ne.'15I TaKJKe
nOBOpal.JlIBaeTCH Ha 180 0 II bTMepeHHoe KOJ1Hl.JeCTBO TOnmiEa Ha-
npaBJI5IeTCH B 06llI.YlO nWtaIOllI.ylO MarHcTpa.lb Tpex !I.PYrHX Hacoc-
<POPCYHOK II nOCTynaeT B O!l.HY H3 HHX. TaKHM 06pa30M, Hacoc-<pop-
CYHKH THna Cummins KaK 6bI BbInOJ1HfIlOT caMH l.JaCTb <PYHKll.III1 no
pacnpe,l1,e.'1eHIIIO Ton.'1HBa.
3a KaJK!l.bIH 060POT pOTopa pery.15lTOpa 11 pacnpe.LI.e.'1IITe.15I Ton-
.TIIiBO nO..'l:aeTC5I B !I.Ba 1{II.TIIIH!l.pa. f103TOMY .n..IH rneCTHll.H.TIlIH.n.pOBO-
36
ro lJeTblpeXTaKTHOrO .lI.M3e:UI 'IMC.10 060pOTOB HaCOCa ,'J.O:VKHO B
1,5 pa3a npeBbIlllaTb lJMCJlO 060pOTOB KO.leHlJaTOrO Ba.1a, a .lI.J15I
BOCbl\UiL{I1.1I1H.lI.pOBOrO - B 2 pa.3a.
POTOp pery.1HTopa BbInO.1HHeT He TO.lbKO <PYHKL{I1M 30.10THMKa,
HO M C Y2KMT opraHOM perY MpOBaHMH nO,'J.alJM TOn.1I1Ba B perY.1I1-
pyeMbIx iinana30Hax lJMce.'1 060pO.TOB. OpH npeBbIllleHHH .lI.BMraTe-
J1eM HOMHHac'lbHOrO lJHC.TJa 060pOTOB YCH.1He OT Bpall1.alOll1.HXCH rpy-
30B pery.'15ITOpa, npeOJJ:o.'1eBaH .lI.eMCTBYlOll1.ee C npOTHBono.10:iKHOrO
KOH.U. yelJ.'1He npY:iKMHbI perYJ1HTopa, nepeMell1.aeT pOTOp perymITopa
BnpaBO. DpH :'ITOM 01'Kpb1BaeTCH c.'lHBHaR MarHCTpa.1b, 'lepe3 KOTO-
pylO TQn.1HBO, OTMeplmaeMoe n.'1ymKepoM-A03aTopOM, nepenYCKaeT-
CH BO BcaCLIBalOll1.YlO MarHCTpa.'1b nO.ll.KalJHBalOll1.erO Hacoca, lJeM
JJ:OCTMraeTCH YMeHbllleHHe nO.ll.alJH Ton.'1MBa, a c e,'J.OBaTeJ1bHO, orpa-
HI1lJHBaeTCH .n.a.TJbHeMWee nOBbIllleIme lJHCJla 060pOTOB .lI.BHraTe.'1H.
MHHHMa.!lbHbIe 060POTbI TaK:iKe perY HpYlOTCH C nOMOll1.blO pOTO-
pa perY.'1HTopa. OpM OTKpbITOM .lI.pocce bHOM Ba.TJIiKe nOTOK TOnJIHBa
npoxO,'J.I1T LJepe3 CBep eHI1e B HeM H BO BTy.TJKe 3TorO Ba.'1I1Ka. OpIi
BbIK.TJlOlIeHHOH nO.ll.alle (OAHO M3 KpaMHHX no.TJO:iKeHHM .lI.pOcce.'1bHOrO
Ba.'1HKa) 3TOT nYTb Ton.TJHBa OKa3bIBaeTCH nepeKpLITbIM, TaK KaK
CBep eHMe B JJ:pOCCeJ1bHOM Ba.TJHKe He COBna.ll.aeT C OTBepCTH5IMH B
ero BTy.1Ke. Ton.'1MBO, MHHYH JJ:pOCCeJIbHbIM BaJJIiK, nOCTynaeT no
nepenYCKHOM MarHCTpaJ1H lJepe3 CneL{I1a bHOe OTBepCTHe, OTI{pbITHe
KOToporo KOHTpo.'1HpyeTcH pOTOpOM perYJ15ITOpa,
Hacoc-<poPCYHKH TllIla Cummins, npeJJ.Ha3HalJeHHbIe 11.151 pa60-
TLI C HaCOCOM Hydra Meter, nO.ll.roTaB.1HBalOTCH K npoH3BoACTBY.
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CYHKY npH nOBbIllleHHH 060pOTOB [46]. .
Ha puc. 22, a nOKa3aH pa3pe3 ceKllUOHHoro Ton.'lUBHOrO Hacoca
C ra30BbIM npHBolloM nJ1YHiKepa <PHpMbI Crupp. HarHeTaIOlllUH XOJI.
nJIYHiKepa oCYIl1.eCTB.'lHeTC5I noJI, JI,eHcTBHeM JI,aBJ1eHHH ra30B. no-
C.'IeJI,HHe H3 pa60IJero llHJIHHJI,pa JI,H3eJ1H IJepe3 JI,pOCCeJ1b 5 H lllapH-
KOBbIH KJ1anaH 8 nOCTynaIOT B CI1.'IOBOH llH.'lHHJI.P Hacoca. CHJIOBOH
nopllleHb 10 nOA BJ1H5IHHeM JI,aB.'leHHSI ra30B nepeMeIl1.aeTCH BHH3.
oCYIl1.eCTBJI5I5I HarHeTaIOIl1.HH XOJI, n.1JYHiKepa. TOnJ1HBO nOCTynaeT B
KaMepy nJIYHiKepa IJepe3 BnycKHoH KJ1anaH 15. npH HarHeTaIOIl1.eM
XOJI,e nJ1YIuKepa pbIIJar 13 B TeIJeHl1e HeKoToporo HHTepBaJ1a BpeMe-
Hll YJI,epiKHBaeT KJ1anaH 150TKpblTbIM.
reOMeTpHIJeCKOe HaIJaJIO nOJI.aIJH HacTynaeT B MOMeHT nocallKll
K.'lanaHa 15. KOHel..!. npHxOJI,HTCH Ha MOMeHT nepeKpblTHH nJ1ymKepoM
oTBepcTHSI A. Ton.'IHBO, OCTaBllleeC5I B KaMepe n.'lYHiKepa, CJ1YiKllT
rHJI.paBJ1HIJeCKHM aI\WpTH3aTOpOI\t. BcaCbIBaIOIl1.HH XOJI, nJIYHiKepa
oCYIl1.eCTBJ1HeTCSI npYiKHHoH 2. npH 3aKpbITOM KJ1anaHe 8 nOTOK ra-
30B, BbITeCH5IeMbIX npH JI.BH}KeHHll CHJ10BOrO nOplllH5I BBepx, JI,pOCce-
JIHpyeTC5I npH npOXOiKJI,eHHH IJepe3 JI.pOcce.TJb 5, IJTO npeJI.OTBpaIl1.aeT
YJI,ap noplllHH B BepxHeM nOJIOiKeHHH.
BeJIHIJHHa llHKJ10BOH nOJI,aIJH perYJIHpyeTC5I no BceM llHJIHHJI.paM
OJI,HOBpeMeHHo B pe3YJ1bTaTe H3MeHeHH5I npOJI.O,TJiKHTeJ1bHOCTH OT-
KpbITH5I BcaCbIBaIOIl1.erO KJIanaHa. Eho JI,OCTHraeTCSI nOBopoTOM Ba-
,1IHKa, COeJI,HH5IIOIl1.erO 3KclleHTpHKoBbIe OCH 12 Bcex HaCOCOB JI,H3eJI5I.
nOJI.aIJa TOnJIl1Ba B OTLl.eJ1bHbIe llHJ1HHJI,pbI MOiKeT H3MeH5ITbC5I TOJ1-
Il1.HHOH lllaH6bI 14. Hacoc BbIKJ1IOIJaeTCH npH npeKpaIl1.eHHH nOJI.aIJH
ra3a H3 pa60IJero UHm1HJI.pa AH3eJ151.
<I>opcYHKa, npHMeH5IeMaSl C onHcaHHbIM HaCOCOM (pHC. 22, 6),
HMeeT nHeBMaTHIJeCKOe pa3rpY30IJHOe YCTPOHCTBO, KOTopoe oCJ1a6
.1JHeT 3aTHiKKY npYiKHHbI 26 npH pa60Te JI,H3eJIH Ha MaJ1bIX HarpY3.
Kax H npH nycKe.
B03JI,YX nOCTynaeT B <POPCYHKY no Tpy6Ke 25 H, B03JI,eHcTBYH Ha
nopllleHb 22, nOJI,HHMaeT ero BMeCTe C TOJIKaTeJ1eM 20, oCJ1a6J1S1S1
3aTHiKKY npYiKHHbl 26. B03JI.YX nOJI,aeTCH aBTOMaTllIJeCKH IJepe3 KJIa-
naIl B pacnpeJI,e.'lHTe.TJbHOH Kop06Ke, pacnOJIo}J{eHHoH Ha nocTY
ynpaBJIeHllH.
42
Oc06eHHOCTbIO q>OPCYHKII HBJIHeTCH TaKLKe HaJ1lIlllIe HarHeTa-
TeJ1bHOrO KJIanaHa.
flplIMepOM HaCOCa C npYLKIIHHbIM npIIBO.ll.OM MOLKeT CJ1YLKIITb Ha-
COC q>IIPMI;.>I Hanz-Endrassik (pIIC. 23). BnycK TOnJllIBa npOHCKO.ll.lIT
6)
PHC. 22. CCKI.\110HHa51 Ton.1HBHaH annapaTypa C ra30BbiM npHBo-
.!J.OM n,lymKcpa q>HpMbI Crupp:
a - l.On 1HBHLIli: Macoc; fj - 4>opcYHKa .4 - OTBcpC1He nO.il.31JU TonnH-
B3; [) - OXJla}f{J],3IOlUaH no..1:0CTb; J - nol1}rH>Kep; 2 - npY>KHHa: 3 -
TOJIKaTenb; 4 - lllTYL1.ep nOD,BO.ll.a M3cna; 5 - JI.pOCCeJ1b; 6 - rOlIOBKa;
7 - uITY1.1ep nOJI.BOl\3 ra3a; 8 - ll1apHKOBufi K.TIanaH; 9 - HanpaBJIHIO-
llJ,aR BT)'JlKa; 10 - CHllOBOil nopmeHb; 11 - cyxapb; 12 - 3Kcu,eHTpHKO-
BaR OCb; 13 - pbl1.lar: /4 -- perYlIHpYIOlll,3H ulait6a; 15 - BnycKHoH
KJl3n3H; 16 - HH>KHstH ronOBKa; 17 - HarHeT8Te.,'lbHblfI KaHan; 18 -
BKO)],Hoii llITYl1ep; 19 - Tpy6Ka nO)],Bo)],a TonJIHBa K q,opCYHKe; 20 - TOJI-
1{3Te.rIb; 2/ - npYiKHH3 pa3rpY30'lHOrO nopUlHR; 22 - nopUJeHi. pa3rpy-
304Horo YCTpoitcTBa: 2.3 - OrpaHH1.£HTCJIb xo.na nOplllH5I.; 24 - LlIUntH.lJ.p
nHCBM3THIleCKoro pa3rpY304Horo YCTpoiicTBa; 28 - TpYUK3 n01180.o.a 803-
Ayxa B pa3rPY301.lHOe YCTpoiICTBO; 26 - npY>KHHa <tJOPCYHKIi
iIepe3 K.!JanaH 11, npIILKIIMaIOII.J.IICICH K TOpn.y nJ1YHLKepa npYLKII-
Hon 12, pa60TaIOw.en Ha paCTHiKeHlIe. DplI 3TOM TOnJ1IIBO npOXO.ll.lIT
nO.TJOCTb A, BbITOllKY r, CBep.TJeHIIH B, E II llepe3 KJ1anaH 11 nona-
43
,iJ,aeT B pa60'lYIO nO."10CTb Hacoca. BcaCbIBalOllI.HH XO,iJ, nJIymKepa
npOHCXO,iJ,HT B pe3y.lbTaTe Ha6ermIliH Ky.'1a'IKa 19 Ha npaBbIH KOHeu:
,iJ,Byn.lle'lerO pbIqar.a 18. O.IYH)J{ep 13 npfl 3TOM ynep)J{I1BaeTCH npy-
)J{flHOH 14 B KOHTaKTe C TOJIKaTe.'1eM 16. B cpeAHeH qaCTfI pbIqar
rnapHI1pHO CBH3aH C 060HMOH,
KOTopaH qepe3 TOJIKaTeJ1b 16
nepenaeT nJ1YH)J{epy YCflJIIIe
pa60qeH npY}KflHbI 1. JIeBbIM
n.'1eQOM pbIqar 18 Qepe3 pO.TlHK
3 ynHpaeTcH B TOJIRaTeJIb 4.
Pa60QHH xon HaQflHaeTCH.
KOrna BblcTyn Ha npaBoM KOH-
u:e pbI<Iara 18 COBMellI.aeTCH
co cpe30M Ky.'1a<JKa. Pa60<IfIii
xon npoflCXOnHT non p,eHCTBfI-
eM YCII.'1I1H npenBa pflTe.TlbHO
(npfl BcaCbIBalOllI.eM XOne
n.rIYH)J{epa) C)J{aTOH npY)J{flHbI
1. EyrpepHoe YCTpoikTBO 2
BocnpHHflMaeT o6paTHble yna-
pbI pbI<Jara 18.
TaK KaK nOJlO)J{eHHe cpe3a
Ky.TJa<lKa OTHOCflTe.'1bHO KO.TleH-
QaTOrO BaJIa nfl3eJ1H nOCTOHH-
HO, TO HaQa.'10 reOMeTpflQeC-
KOH nOnaQfl OCTaeTCH HeH3-
MeHHbIM npfl Bcex Be.1m<JflHax
U:HK.iIbBbIX nona</. U,IIKJIOBa5I
nOAaQa perYJ1f1pyeTcH fl3MeHe-
HI1eM BeJ1WlfIHbI xona nJ1YH-
)J{epa nYTeM fl3MeHeHflH KOH-
u:a HarHeTalOllI.erO ero Xona.
JIflHeHHbIH Xon nJIYH)J{epa pe-
rYJIflpyeTcH OnHOBpeMeHHO no
BceM LJ.fI.'1f1HnpaM C nOMOllI.bIO
Ba.TJflKa 6, npOXOnHIl.\ero
CKB03b K.'1HHbH 5. BaJ1f1K ne-
peCTaBJ1HeTCH C nOCTa ynpaB-
.TJeHflH Ton.TJflBHOH PYKOHTI\OH
I1 HaxOllflTCH non KOHTpOJIeM
Bcepe)J{flMHoro perY.IIHTopa. OpH nepeMellI.eHfIfI Ba.'1f1Ka fl3MeHHeTCH
nO.lIO)J{eHfle 11.0 BblCOTe TOJIKaTe.IIH 4. B COOTBeTCTBfIfI C 3TflM fl3Me-
HHeTCH TO<JKa onopbI J1eBOrO KOH.u.a 3 pbJ1J.ara 18. Opfl nOllHHTflH TO.l-
KaTeJIH 4 6YPTHK TO.1JKaTe.TJH 16 npH6J1f1}J{aeTcH K ynopHoH BTy.TlKe.
003TOMY npfl BcaCbIBalOllI.eM xOAe OoTlYH)J{epa npaBbIH KOHe.u. pbI<Jara
18 n03)J{e KacaeTOI KYJIa<JKa H XOJI. nJ1YH}J{epa YMeHbillaeTcH. XO.II,
nJ1ym epa OKaJKeTCH paBHbIM HYJ110 npfl TaKOM nOJ1O}J{eHfIfI TOJ1Ka-
TeJ1H 4, npfl KOTOpOM .oH He KacaeTCH OnOpHOI:O KOH.u.a :} pWlara 18.
g
5
3/
2
PHC. 23. Ton.lI1BHbIi1 HacoC C npY)Kl1!lIlbBI
npI1I30,J,OM nma Hanz-Endrassik:
A - BnYCKHa>f nO.,'10CTb; E - aKCHa T}bHbli'i: Ka-
H2a.3l B \1JYY\-DKep ;.. B - pa.I\ a.nbH() CBe-p.neH\\e
B nJIYH)Kepe; F "- BblTO Ka Ha lI.llYH>Kepe;
1 - pa604a>l npyffiHHa; 2 - 6ycjJep; 3 - _1e-
BLIli KOHeu pl "lara; 4 - To...1KaTeJIb perYllHpylO-
lllero McxaHH3Ma; 5, 7 - J{ ,]HHL5J; 6 - pery-
flHpOB01.IHblt'r na.aHK; 8 - npocTaBKa; 9 - YCTa-
HOBOLJ:HbHI 60J1T; 10 - HarHeTaTeJIbHblfI KJIa-
naH; /1 - nnycKHof'I K"lalIaH; 12 npY>KHH3
BnYCKHoro J:(JIanaHa; 13 - nJIYH)f{ep; 14-
npY>KHHa n.nYH>Kepa; 15 - ynopHaH BTY_1Ka;
/6 - TOJIKaTeJIb; /7 OCL pLIQara; 18-
phPlar; 19 - KY,,'Ia'-lOK
.44
UHK.TIOBaSJ nOJl.alla l(H.'JI:IHJl.pOB pery.'1Hpye1 CJJ H3MeHeIlHeM noc'W-
1KeIlHJI BepxHero KJJI:IHa 7 C nOMOll1.bIO 60J1Ta 9. DpHBoJl. Hacoca oCY-
llI.eCTB.'1HeTCH .lIepe3 npOMe)KYToll-
HYIO nepeJl.allY, COCTOJIWYIO Jl3 na-
pbI WeCTepeH C KOCbIMH 3y6bJIMH.
9Ta nepeJl.alla HCn0J1b3yeTcH A H
H3MeHeHHH yrJ1a Onepe1KeHHH
BnpbICKa TOn.'1HBa B 3aBHCHMOCTH
OT CKOpOCTllOrO pe1KHMa Jl.BHraTe-
.'1H. OepeJl.aTOIlHbLH BaJ1HK 3aKaHIIU-
BaeTCH PYKOHTKOH, BbIBeJl.eHHOH J{
nOCTY ynpaBJ1eHHH. YrOJI onepe)l\.e-
HUH BnpbICKa Ha 3aJl.aHHbIX 06opo-
TaX Jl.BUraTeJ1H <pHKcHpyeTcH CTono-
pOM. CneUHa.'1bHaH nepeAalla, CO-
CTOJIIl(aJI H3 KOHHlIeCKHX weCTepen,
06ecnellHBaeT HeH3MeHHOCTb Ha-
npaB"ieHHH BpaweHHJI Ky allKoB
npB peBepce Jl.H3e.'1H.
Ha CBo60Jl.HO-nopllIHeBbJX reHe-
paTopax ra3a GS-34, BbmYCKaeMblX
qmpMoH Sigma, YCTaHoB.'1eIt 1'on-
.1JHBHbJH Hacoc C nJ1ymKepHbIM aK-
KYMYJIJITOpOM qmpMbI Bryce Ber-
ger [26, 80, 81]. Ha pHC. 24 nOKa3aH
Hacoc Toro llie TBna.
Ha aKKYMy.'1HPYIOWHH n.'1YH1Kep
8 lIepe3 B03J1.YWHbIH nopweHb 7
Jl.eHcTByeT B03.l1.YX, clliaTbIH .lI.O 3a-
lIaHHOrO Jl.aBJ1eHBJI. KpoMe Toro, Ha
n"iYHlliep 8 Jl.eiicTByeT npYfI\.HHa 6.
B03Bo.ll.Hll1.HM nJiYHlliep 11 npHBo-
Jl.HTCH B Jl.BHllieHHe lIepe3 TO.'1Ka-
TeJJb 2 Ky.'1aIlKOBOH waH60H 1, CBH-
3aHHoH C BaJ10M wecTepHH CHHXpO-
HH3HpYIOll1.erO MexaHH3Ma cB060.ll.-
Ho-nopwHeBoro reHepaTopa ra33.
XO.ll. TO.'1KaTeJIH B O.ll.HOM U3 HanpaB-
.'1eHHH orpaHH IeH BH.'1bllaTbiM PbI';
lJarOM 12, npeJl.Ha3Ha leHHbIM Jl.J1JI
perYJIHpOBaHHH UHKJIOBOH nO.ll.allH TOnJIHBa. TOnJ1HBO K Hacocy nOA-
BO.ll.HTCH liepe3 wTyuep 3, Clli8TbJH B03.l1.YX -lIepe3 WTYUep 5. OpH
BcaCblBaIOweM xOJl.e OJ1YHlliepa 11 Jl.aB.'1eHHe Ton.'1HBa B nO.'10CTH 9
aKKYMYJIHTOpa YMeHbwaeTCH, liTO BbI3bIBaeT OTKpbITHe KJIanaHa 10,
"LJepe3 npOXOJl.HOe celieHHe KOToporo Ton.'IHBO H3 c'IHHHH BcaCbIBaHHH
nOCTynaeT B nO.'10CTb 9. Oocne OKOHliaHHJJ HanO.1JHeHHH !WanaH 10
3aKpbIBaeTcH. BeJ1HIIHHa 06"beMa nOJIOCTH 9 onpe.ll.e. I IJIeTCH nO.'10llie-
HHeM pbIliara 12.
5
6
7
PIIC. 24. T orr.1HBllblii nacoc C
rr.1YHLKcPHbIM aKKYMy.15lTO-
pOM:
A - KaHa",'1; Ii - KOJ1bu.eBa
npOTOtIKa; 1 - Ky.1a'-lKOBa51
lUaIf6a; 2 - TO 1:KaTe.rIb; 3-
llIT)'u..ep nO.LI.BO.lI.a TOn "1HBa; 4 -
TpoJIHIfH HarHCT2HIHI Ton. .HBa:
5 - llITyu,ep nOABOi1a B03.D.yxa;
6 - npY>KHHa aKKYMy.rmpYIOlll,erO
nJIYH>Kepa; 7 - B03.D.ywHb111 nop-
UleHb; 8 - aKKYMymipYlOlllHi\
tlJIYHmep; 9 - 2KKYMy..'1JJPYWlU351
no.rIocTb; 10 - nnycKHoi'! K 13naH;
I J - B03BOD,fill1.Hi'r n.;"lYHJKep:
12 - pblGar ynpaBJIeHllfi
45
npH HarHeTaTeJ1bHOM XO.ll.e nJIymKepa 11 TOnJ1HBO B nOJIOCTH 9
CLKMMaeTCH .lI.O -.lI.aBJleHHH, onpe.ll.eJIHeMOrO YCHJ1HeM, .lI.eiicTBYIOI.l.lH:\1
Ha nJ1YHLKep 8 co CTOpOHbI B03.l1.YlIlHoro noplIlHH. Bo BpeMH C)KaTHH
TOnJIHBa o;lUIOspeMeHHo C .lI.BHLKeHHeM n.1YH)J(epa 11 nOAHHMaeTCH
llJJyHLKep 8.' [}PH - 3a.ll.aHHoi'I Be.1H'IHHe nO.ll."beMa n.'1ymKepa 11 ero
KOJIbueBaH npOTOqKa E
BbIXO.ll.HT H3 BTYJ1KH.
BCJIe.ll.CTBHe qero no-
JIOCTb 9 COe.ll.HHHeTCH C
KaHaJIOM A, Be.ll.yruHM K
TpOi'IHHKY 4 Hacoca, KO-
ropbIi'I HarHeTaTe.1JbHbl-
MH Tpy60npOBO.ll.aMH
COe.ll.HHHeTCH C <i:>OPCYH-
KaMH. B MOMeHT, KOr.ll.a
pacxo.ll. TOnJ1HBa, BblTe-
KalOI.l.lerO 'Iepe3 npOTOq-
KY E, npeBbIcHT 06"beM-
HYIO CKOpOCTb BbITeCHe-
HHH TOnJ1HBa n.'1YH)J(e-
pOM 11, n.'1YHLKep 8 H3-
MeHHT HanpaBJIeHHe
.lI.BHLKeHHH H TeM caMbI I
6Y.ll.eT nO.ll..lI.epLKHBaTb
nOCTOHHHbIM .lI.aB.1JeHUe
TOnJIHBa B n0J10CTH 9,
BeJ1HqHHa KOToporo. on-
pe.ll.eJIHeTCH YCHJIHeM,
.lI.ei'IcTBYlOruHM lfa n.1JYH-
)Kep 8 co CTOpOHbI B03-
.lI.YlIlHoro noplIlHH. L!.BH-
LKeHHe nJ1ymKepa 8 npo-
.lI.OJ1)KaeTCH .lI.O MOMeHTa
nOCa.ll.KH ero Ha ynop,
noc.1Je qero Ton.;1HBO no-
.lI.aeTCH K <i:>opcYHKaM
TO.'JbKO B pe3YJIbTaTe
paclIlHpeHHH Ton.1HBa.
H TOnJ1HBa, BbIT CHHeMoro
5
4
.3
2
12
1.3
16
15
14
oj
PHC. 25. Ton.TJHBHa51 annapaTypa C aKKYMy.1H-
PYIOlllCII q,OPCYHKOi\:
a - Hacoc; 6 - q,opcYHKa; .4 - )],pocce. HpYKJII<ee_
OTBepCTlIe; I, 16 - Kopnycbl; 2, 17 - npY>KHHb';
3 - peiIKa; 4 - lllTyltep nepenycKB TOnw1]UBa; 5 -
nHTaJOllI.Hfi nrryu..ep; 6 - HarHeTaTeJ1bHbU1 UlTyu..ep;
7 - yn '10THHTeJIbHOe Ko.nbIJ,O; 8 - BbITeCHHTe 1]b;
9 - BTY :]Ka n.;'1YH.iKepa; 10 - 3y6qaT3H BTYlIKa;
1/ - n.1YH>Kep; 12 - HH>KH>IH Tape. Ka; 13 - TO. -
K8TeJIb; 14 - HanpaBJUIIOllJ,aSl To...'lK3Te.11Si: 15-
COnJIOBaH BCT3BKa: 18 - CTSI>KH3H raHKa; 19 - Ha-
npaBJIfllOlll.aH Hr '1LJ; 20 - HaKHJ1.H3fI rafiKa; 21 -
ynopHa>I rnaii6a; 22 - nrJIa; 23 - TapeJIKa
npY:>KHHbl
0)
CLKaToro B aKKYMYJIHpYIOI.l.lei'I n0J10CTH 9,
n.1JYHLKepOM 11.
Ha pHC. 25 nOKa3aHa TOnJ1HBHaH annapaTypa C aKKYMy.'1HPYIO-
ruei'I <i:>OPCYHKOi'I, npe.ll..1JOLKeHHaH lJ.HHL!.H. 3.l1.eCb HaCOCHaH ceKUHH
npHBO.ll.HTCH OT 3KCUeHTPHKOBOi'I lIlai'I6bI, a BnpbIcK Ton.1JHBa npoHc-
XO.ll.HT nOCJIe OTCeqKH HarHeTaHHH H pa3rpY3KH TOnJIHBOnpOBO.ll.a OT
.lI.aB.1JeHHH [63].
npHMepoM aKKYMYJ1HTOpHOii TOnJIHBHoi'I CHCTeMbI C rH.lI.paBJIHqe-
CKHM aKKYMYJ1HTOpOM 60.1JblIlOi'I eMKOCTH MOLKeT CJ1Y)KHTb Ton.'1HB-
HaH annapaTypa <i:>HpMbI Cooper-Bessemer, YCTaHaB.1JHBaeMaH Ha
46
.l1.H3eJ1JIX (pnc. 26). TOfl.'1IfBHblH H8COC 1 nO.l1.8eT Ton.'1HBO B aKKY-
MymITOp 5. npH onpelI.eJ1eHHO!\I nOJIO)J{emIH lI.03HpYlOllI.erO YCTPOH-
CTBa 7 TOnJ1HBO H3 aKKYMy.TJHTOpa HanpaB,,':meTcH B aBTOMaTH4.ecKYlO
9
16
11-
j{ rpOPOjHKOI'1
KOp/101JblX 4U/lUHiJoo6
1
PHC. 26. CxcMa Ton.TJHBHoi'I annapaTYPbI C fH.D:paBJlH'-IeCKHM aKKYMym!TOpOM
60; bIllOi'I CMKOCTH THna Coopcr Bcsscmcr:
1 - TOnJJHBHbJfi H3COC BblCOKoro lI,aB.,'1eHIUI; 2 - n.TJYH:>Kep; 3 - KOJIeH1.J.3TbIil BaJJHK
Hacoca; 4, 6 - Tpy6onpOBo;r.bI BhlCOKoro JI.aB,aeHHfI; 5 - aKKYMy..1JSITOp; 7 .!J.03HpYIOw.ee
YCTPOHCTBO; 8 .popcYHI<a; 9 - ll1e.leRofl .pH.nbTP; TO - pblQar; 11 - 31<CI.(eHTp"I<OBaH
rO 10BKa; 12 - MaHOMe11P; 13 - Kopnyc pery..'ulTopa .na JIeHHfI; 14 - npY>KHHa KJ1anaHa;
/5 - K..."lanaH c6poca :!aB..'1eHHfI: 16 - To.umTe.rlb
CPOPCYHKY 8. 4HC:1O CeKl1.HH lI.03HpYlOllI.ero YCTpOHCTBa paBHO 'IHCJIY
l1.HJIHHlI.pOB lI.H3eJIH. nOlI.p06HOe onHcaHHe paCCMaTpHBaeMOH TOn-
JIHBHOH CHCT€MbI .l1.aHO B pa60Tax [26, 80].
r 11 a B-a II. TEOP....SI .... METOAbl PACLlUA np0LtECCA
BnPblCKA TOnn....BA B AB....r A fEnSix
C BoCnnAMEHEH....EM or C)f(AT....SI
1. rHAPOAHHAMH'IECKHE OCHOBbl TEOPHH H METOAOB PACIfETA
Ha1160.'Iee 06W.11CI npHIIl.t11ll )],eHCTB11H 11Mee1 TOnJ1I1BHaH C11CTeMa
C HarHeTaTe.'1bIlbIM Tpy60npoBOAOM 11 3aKpbITOH <POPCYHK0I1, KOTO-
pylO B CBH311 C 3T11M 6YAeM C'-I11TaTb OCHOBHbIM 061,eKTOM 11cc.'Ie.rro-
BaHI-lH. D.pyr11e cxeMbI Ton.'I11BHbIX C11CTeM HB.'IHlOTCH '-IaCTHbIM11 CJIY-
'IaHM11 3TOH CIiCTeMbI, '1TO YKa3bIBaeT Ha 06IHHOCTb IiX. npIiHIJ,Ima
)],eHciim5!, a c.'Ie)],oaaTe.'IbHO, Ii Ha 06W.HOCTb -reopeTIi'leCKHX nOJIO-
)KeHI-iH npOIJ,eCca BnpbICKa Ton.'IIiBa.
Bo Bcex CIiCTeMax )],aBJ'IeHIie no)], KOHYCOM 11r.'IbI, a cae)],OBa-
TeJ1bHO, Ii onpe)],e.'IHeMaH 3T11M )],aB.'IeH11eM CIWPOCTb BnpbICKa Ton-
J1IiBa pe3KO Ii3MeH5!lOTC5!, np11'-IeM B nepBOH nO.'IOB11He npOIJ,eCca
BnpbICKa OHM B03paCTalOT 110 MaKCHMa.'IbHOrO 3Ha'leHHH, B KOHIJ,e
BnpbICKa CKOpOCTb )"MeHbiliaeTCH )],0 HYJI5!, a ,naB.'IeH11e -)],0 Be.'I11-
'1HHbI )],:aBJIeHliH cpe)],bI, B KOTOpylO BnpbICK11Ba.eTC5! TOIIJIIiBO. OCO-
6eHHOCTH npOTeKaH11H npOIJ,eCca no)], a'! 11 TOnJIBBa )],alOT OCHOBaH11e
C'-I11TaTb ero KpaTKOBpeMeHHbIM elIIiH11'1HbIM BMny.'IbCOM, KOTOpbIH
B03H11KaeT BO BXOlIHOM Ce'-IeHI-Ili HarHeTaTeJ1I;>HOrO Tpy60npOBo)],a
Bc.'Ie)],CTBIie BbITa.'IKI1BaHI-IH Ton.'IHBa II.'IymKepoM Hacoca H3 06 beMa
KaMepbI HarHeTaH11H. B CBH311 C TeM, '1TO TOnJIliBO - C.tKHlvlaeMaH
)KIi)],KOCTb, BO BXOlIHOM Ce'leH1111 HarHeTaTe.'IbHOrO Tpy60npOBo)],a
B03HIiKaeT HeYCTaHOBIiBilleeCH AB11)KeHHe C)KHMaeMOH )K11)],KOCT11, np11
KOTOpOM, KaK H3BeCTHO, OT Hacoca K <PopCYHKe co CKOpOCTblO 3BYKa
Ii)],eT Ha'la.'IbHa5!, Ii.'IIi KaK ee elIJ,e Ha3bIBalOT - nepB11'1HaH, BOJ1Ha
)],aB.'IeH115!.
OCHOBHbIM <p aKTO p01\1, <pOpM11PYlOlIJ,HM xapaKTep 113MeHemm H
BeaH'-I11HY mvmYJIbCa, HB.'IHeTCH CKOpOCTb )],BH)KeHH5! n.'IYH.tKepa Ton-
JIHBHOrO Hacoca, H.'IH np0<pHJ1b TOn.'I11BHOrO Ky.'Ja'lKa. OAHaKO HeKO-
KOTopbIe <paKTopbI, onpe)],eJI5!lOlIJ,He rpaHH'IHbIe YC.'lOBH5! BO BXO)],HOM
Ce'leHHH Tpy60npOBo)],a, CYlIJ,eCTBeHHO HCKaJJzalOT B03H11KalOw.m1
3)],eCb HMnYJlbC. K. '-IHCJ1Y 3T11X <paKTOpOB OTHOCHTCH: HaJTH'IHe 061,-
eMa B KaMepe HarHeTaHHH H B IllTYIJ,epe Hacoca; )],BH:iKeHHe HarHe-
TaTe.'IbHOrO K.'lanaHa, I\OTOpbIH B Ha'-IaJ1bHbIH MOMeHT pa31,e)],HH5!eT
KaMepy HarHeTaHH5! H 06'beM IllTYIJ,epa Hacoca.; nepeTeKaH11e Ton-
.'lHBa '-Iepe3 BcaCbIBalOlIJ,11e OKHa, KOTopble B 60.'IbIllHHCTBe c.'lY'-IaeB
K Ha'laJ1Y )],BlDKeHHH KaanaHa no.'IHOCTblO ew.e He nepeKpbWHCb.
OpH 60J1bIllOM H3Hoce n.'IYH)KepHOH napbI 3aMeTHO B.'lIHIIOT Ha
HMnYJ1bC YTe'lKH Ton.'lHBa '-Iepe3 3a30p Me)KLI.Y n.1YH)KepOM 11 BTY.'I-
48
KOI1- Ha Be.TJH'UIHY HMnYJ1bCa BJIHHlOT TaKfKe H3HI.J.eCKHe XapaKTe-
pHCTHKH TOnJ1HBa: CfKHMaeMOCTb, BH3KOCTb, nJIoTHOCTb. 3TH napa-
MeTpbI BCJIe,lJ,CTBHe H3MeHelIH5I :LaB.'1eHHH npH BfIpbICKe Ton.'1HBa TaK-
)Ke H3MeHHlOTC5I H TeM caMbIM ,lJ,OnO.'1HHTe.'1bHO HCKa)KaIOT IIa'-la.Tb-
HbIII HMnV.TJbC.
B H8CTOHll1.ee BpeMH npH p8CIleTe npOl(eCC8 nO,lLa'lH TOnJIHBa
YI.J.HTbIB81OTCH TOJ1bKO Te <p8KTOpbI, BJ1HHHHe KQTOPbIX npOHBJUleTC51
H8H6oJ1ee CYll1.eCTBeHIIO. Bo. BpeM51 nepeMelIleIIHH HMny.'1bCa no II8-
rIIeT8TeJIblIOMY Tpy60npOBO.n.y rnepOXOBaTOCTb i1 ynpyrocTb ero CTe-
HOK, rH:Lp8BJ1HI.J.eCKOe conpOTI1BJ1eHHe H .n.pyrHe <p8KTOpbI (MeCTHbIe
CY)KeIU15I, ,lJ,e<peKTbI M8TepH8.'1a H T. ,lL.) TaKfKe 11 CE.8f1, 8 lOT HMnYJ1bC,
npHI.J.eM B HeKOTopbIX C.'1YI.J.8HX 3TH HCKafl,eHHH 3H8 I II1Te.'1bIIbI. B BbI-
XOLl.HOM CeI.J.eHlm 1I8rHeT8Te.'1bHOrO Tpy60npOBO]t8 H8J1H'IIIe 38nopHo-
ro opr8H8 rpOPCYHKH Hero .lLBH:tKeHH5I, 8 T8K)Ke 06"beM pacnbwH-
Te:r51 H pe3KHH nepexo,lJ, OT npoxO.lLHoro ceIleBHH Tpy60npOBO,lJ,8 K
npoxo.n.HbIM CeIleHH5IM p8cnbI.'1HB81OllLHX OTBepCTHH .lLOnOJIHMTe.'1bHO
HCK8)K81OT nO,lJ,OllIe,lJ,IlIHH OT Hacoca MMnYJIbc.
CKa'-lK006pa3HbIH nepeXO,lJ, OT npoxo.n.Horo Ce'-leHM51 HarHeTaTeJIb-
Horo Tpy60npOBo.n.a K npoxO,lJ,HbIM CeI.J.eHHHM pacnbI.'1HBalOllI.MX OT-
BepCTMH TOpM03MT ,lJ,Bf1)KeHMe Tonmma M nOBbIll.IaeT ero .lLaBJ1eHHe -
B03HHKaeT rH,lJ,P8B.'1HI.J.eCKMH Yllap. H8J1HI.J.Me nOCJ1e.lLHerO n03B0J151eT
OIIlICbIBaTb .J.BH:tKeHHe TOnJ1HBa B HarHeTaTeJIbHOM rpy60npOB o .n. e
yp8BHeHH5IMH TeopHH rH,lLpaB.'IH'leCKOro y.n:apa, npe.n:JImKeHHbIMH
H. E. )I(YKOBCKHM [32]. YpaBIIeHH51 TeopfUl fII,lL.paB.'1II'-IeCKoro y,lJ,8pa
BbIBOllHJ1IICb Ha OCHOBe ,lJ,onYllLeIIHH, npMeMJ1eMbIX ,lLJIH YC.'1OBHH Te-
IleHHH BO,lJ,bI B Bo.n.onpOBOAHOH ceTM. Y CJ10BHH ./Ke npOTeKaHH5I npo-
l(eCca BnpbICKa Tonmma CYlll.eCTBeHHO OTJIM'-IalOTC51 OT notJIe.!J.Hl1X,
n03TOMY KOJ1HIleCTBeHHaH Ol(eHKa napaMeTpoa npOl(eCca BnpWCKa
nOTpe6yeT YI.J.eTa .n.onOJ1HllTeJ1bHWX rpaKTopOB, onpe,lJ,eJ15I1OllLHX OCO-
6eHHOCTH npOTeKaHH5I nOIl8'-1H Ton.'1HBa B IlH3e.TJHX. 3TH oc06eHHOCTH
,lJ,0.1)KHbI YIlHTbIBaTbC5I npH COCT8B.;1eHHlJ. YP8BHeHHH rpaHH4HbIX
YC.10BHH, KOTopbIe pellI81OTC5I COBMeCTHO C 06llLHMM yp8BHeHH5IMH
TeopHH rH}J,paBJ1WIecKoro YIl8pa:
o(Ji I op. oC = ___ . op
---at = -p-' ox ' iJx a 2 p iJt (1)
OCHOB/:we OT.'1HIlMe YCJ10BMH BnpbIcKa - nOAaIla 3a l(HKJ1 M8.'10rO
KO.1WIeCTBa TonJ1MB8 npM pe3Ko M3MeH5IlOllLMXC5I BbICOKHX Il8B.'1e-
HMHX. CVlIlecTBeHHoe 3IIalJeHHe HMeeT TO, '-ITO B5I3KOCTb Tonmma H
CKOPOCT ero ,lLBH:tKeHH5I B Tpy60npOBO,lLe 3FfalJfITeJIbHO 60J1bWe B5I3-
KOCTH BOIlbI H CKOpOCTII ee ,lLBHIKeHH5I B BO,lLonpOBO.lI:BdH 'ceTH. B CB5I-
3H C 3THM B03IIHKaeT COMHeHHe B B03MOfKHOCTH npeHe6peraTb B5I3-
KOCTblO TOnJ1HB8 H npelJ,no:raraTb HeH3MeHHOCTb K03rprpHl(I1eHTa
CflUIM8eMOCTH Ton.'1HB8, a c.'1e,lJ,OBaTeJIbHO, M CIWpOCTII p8cnpOCTpa-
HeHM5I B TOnJ1MBe MMny.'1bca. OIlHaKO MHOrO'-lMCJIeHHbIe paCIleTbI npo-
l(eCC8 BnpWCKa TOnJ1MB8 B 6bICTPOXO.lI:HbIX ,lLM3eJ15IX, B KOTOpbIX npM-
MeHHeTCH TOnJ1MBO M8.'10H BH3KOCTH, a .lI:J1lIH8 HarHeT8Te.'1bIIOrO
Tpy60npOBO,lJ,a L 1 M, nOK83bIBalOT, '-ITO B 3TOM cJ1Y'-lae npeHe-
4 3aKa3 748 49
6pe:iKeHlle, HanpHMep, B5J3KOCTblO TOn.'IHBa H JJ,pyrHe ,'J,Onyru.eHI151
npI1eM.'IeMbI, TaK I<aK pe3Y.lbTaTbI paCqeTa Y,'J,OBaeTBopHTe.'IbHO COB-
na.n.alOT C JJ,aHHbIMH onbITa.
EC.1H B ypaBHeHH5JX CHCTeMbI (1) HCKJ1lOqI1Tb BeJ1H HHY p nYTeM
,rrH4J4JepeHl.mpOBaHH5J nepBoro ypaBHeHH5J no t, a BToporo no x, TO
nO':lyqHM BO.'IHOBOe ypaBHeHHe
(PC
ot 2
2 02C
Q-.
ox 2
(2)
npH BWBOJJ,e ypaBHeHHH TeOpHI1 rH)],paBJ1I1qeCKoro y.n.apa
H. E. )KYKOBCKHH He YQI1TbIBaa HepaBHOMepHOCTI1 pacnpe..'J.e':leHI15l
.n.aB,,'IeHH5I H CKOpOCTH no nOnepeqHOMY CeqeHHlO Tpy60npOBo.n.a.
B .n.aJ1bHeHWeM npHMeHeHHe ::nOH TeopHH nOKa3aJIO no.:'IHYlO npH-
eIVIJIeMOCTb npHH5JTOrO npe.n.no.'10:iKeHH5J, TaK KaK .n.aHHbIe paCqeTa,
CJJ,eJ1aHHOrO Ha OCHOBe YKa3aHHOH TeOpHIJ .l1.a:iKe AJ15J Tpy60npOBo.n.OB
.n.HaMeTpOM d r 600 MJ1f, y.n.oBJ1eTBOpHTeJIbHO COBna.n.alOT C OnbIT-
HbIMH. TeM 60.'1ee HeT OCHOBaHHH yqI1TbIBaTb YKa3aHHbIH BbIwe 4JaK-
TOp npH paCqeTe npo ecca no.n.a'IH TOnJ1HBa B .l1.H3e.H5JX, 60"lbIJlIJH-
CTBO TOnJII1BHbIX CHCTeM KOTOpbIX HMelOT .n.I1aMeTp HarHeTaTe.'1bHbIX
Tpy60npoBo)],oB 2-3 J11J11. B CB5J3I1 C 3THM npH pa3pa60TKe MeTo,rra
paCqeTa npo ecca BnpbICKa TOn.'IIma pacnpeIle.'1eHI1e AaB.'IeHI1H H
CKOpOCTH no nOnepeqIwMY CeqeHHlO HarHeTaTe"lbHoro Tpy60npoBo-
.n.a MbI TaK:iKe He yqHTbIBa.'1H. B nOC.'1eAHee BpeM5J 6bIJIH c.n.e.'IaHbI
nOnbITKH yqeCTb npH paC'JeTe npo ecca BnpbICKa YKa3aHHbIH 4JaK-
TOp. COr,,'IaCHO H3.'IO)KeHHOMY 3TH nOnblTKH He.'1b35J npH3HaTb paIJ.HO-
Ha.'IbHbIMH.
YpaBHeHH5J TeopHH rH;J,paBJIHqeCKOrO y,rrapa B OCHOBHOM onHCW-
BalOT xapaKTep .n.BH:iKeHI15J TOn,,'IHBa B HarHeTaTe':lbHOM Tpy60npoBO-
.n.e. I\o.'1HQeCTBeHHoe lKe 3HaQeHHe HMny.'IbCa H xapaKTep ero H3Me-
HeHI151 onpeAe.'15JlOT nYTeM COCTaB"leHH5I ypaBHemfH rpaHHQHhIX H
HaqaJIbHbIX YCJ10BHH B pa3J1HQHbIX CeQeHH5JX Tpy60npOBo.n.a.
B CB5J3H C TeM, qTO .n.aBJ1eHI1e I1 CKOpOCTb Ton.'1HBa pacnpOCTpa-
H51lOTC5J C KOHelIHOH CKOpOCTblO, xapaKTep I1X pacnpe.n.e,,'IeHH51 no
Tpy60npOBO.n.y 3aBHCI1T OT mIHHbI nOC,,'Ie,rrHero. EC.:'IH .l1.JIHHa Tpy60-
npOBo.n.a TaK Be.'IHKa, 'ITO BpeM51 npOXO:iK.l1.eHH51 HMnY,,1bCa OT BXO.n.-
Horo CeQeHI151 )],0 Bwxo.n.Horo paBHO HeCKOJIbKHM pa60qI1M HKJIaM,
TO no Tpy60npOBO.l1.Y 6YIleT nepeMell.I.aTbC51 HeCKOJIbKO I1MnYJIbCOB
(pI1c. 27, a).
B BWXO.l1.HOM CeqeHHH Tpy60npoBolla BCJIellCTBHe pe3Koro H3Me-
HeHI1H npOXO.l1.HOH nJIOll.I.a.l1.I1 I1 HaJIHqH51 llpyrI1x 4JaKTOpOB, B03MY-
ll.I.alOll.I.HX nOTOK, B03HHKalOT OTpa:iKeHHble BOJ1HbI, KOTopbIe I1llYT B
06paTHoM HanpaBJIeHHH OT 4JOPCYHKH K Hacocy. ECJ1H K MOMeHTY
nO.l1.XO.l1.a OTpa:iKeHHOH BOJIHbI K Hacocy nO;J,aqa Ton.'1HBa B Tpy60npo-
BOA He npeKpaTIWaCb, TO 3Ta BO,,'IHa TaK}Ke HCKa3HT Be.'1HqHHY H
xapaKTep npOTeKaHH51 HMnYJIbCa, H.n.yru.ero OT Hacoca K 4JopCYHKe.
n03TOMY, Korlla BpeM51 06pall.I.eHI151 BOJ1HbI llaBJ1eHH51 3Ha l Hne.1JbHO
MeHblJle npo,rrOJI:iKHTeJIbHOCTI1 BnpbICKa, ,rraBJ1eHI1e no .l1.JIHHe HarHe-
50
TaTe bHOro Tpy6onpoBO a pacnpe e HTC TaK, KaK nOKa3aHO Ha
pRC. 27, 6.
npH rH paB HlJeCKOM y ape .u. C.'lO.lKHbIX rpaHRlJHbIX YC OBHH
H e,n:HHHlJHOro HMnYJIbCa I.{eJIeC006pa3Ho perneHHe ypaBHeHHH CHCTe-
MbI (1) 3anHcaTb B <POp Me .z:LaJ1aM6epa:
p-Po=F(t- : )-W (t+ : ); I
(3)
C-C o =-1P[F(t- : )+W (t+ )}
npH nanHcaHHli CHCTeMbI ypaBHeHHH (3) HalJaJIO Koop HHaT
JlPHHHMaJ1H paCnOJIOLKeHHbIM BO BXO,'l,HOM CelJeHHfI Tpy6onpoBo,n:a.
P
K!jCH 2
L CM
0)
L Of
PIIC, 27. XapaKTep HMnYJIbCa .n:aBJICHH5I B Tpy60npOBO.D:ax:
a - ,n}IHHHOM; 6 - KOpOTKOM
BOJe,1.CTBHe KOHelJHOH CKOpOCTH paCnpOCTpaHeHH ,'I,aBJIeHH npo-
uecc MmKHO paCCM8TpflBaTb p83,'1,eJ1bHO SO BXO,'l,HOM CelJeHI1H HarHe-
TaTeJIbHOrO Tpy60npoBO a Y HaCOCa H B BbIXO,1.HOM CeqeHHH y <pOp-
CYHKH. .lJ.JI5I BXO.u.HOfO CelJeHH5I, KOr.u.a X = 0,
PH-PO = F(t) -- W(t);
C T = (F(t) + W(t»).
ap
]
(4)
YCTaHOBJIenO, lJTO lJarn:e Bcero K HalJaJIY HOBorO BnpbICKa ABH-
.lKeHHe TOnJIHBa B Tpy6onpOBO.u.e npeKparn:aeTC , T. e. Co = o. .lJ.JI
BbJXO,'l,HOrO CelJeHHH Tpy6onpoBOlla, KOf,'l,a X = L,
pt/J-Po=F(t- )-W (t+ );
C;=-1P[F(t- )+W(t+ )].
I
(5)
OCHOBHa 3a.u.alJa nIApaB HlJeCKOrO paClJeTa npOll.eCca SnpbI-
CKa - OnpeAeJIHTb KOJIHlJeCTBO TOn.1JHBa, nO.u.aHHOrO B lI.HJIHH.u.p ABH-
raTeJl 3a lI.HKJ1, a TaK}Ke xapaKTep H3MeHeHH CKOpOCTH BnpbICKa
TOnJIHBa, T. e, ero pacnpeAe.1eHHe BO BpeMeHH. HaJ1HlJHe HCKaLKalO-
rn:HX <paKTOpOB YMeHbrnaeT TeOpeTHlJeCKYIO nO,1.aqy TOnJIHBa n.1YH-
LKepOM Hacoca. B CB 3H C 3THM O.u.HOH H3 OCHOBHbIX 3a.u.aQ rHApo-
4* 51
HHaMHqeCKOrO paCqeTa npo ecca BnpWCKa HB HeTCH Onpe eJ1eHHe
eHCTBHTe bHOrO KO WIeCTBa TOnJIHBa, nO.n:aBaeJl.lOrO 3a U:HKa. Pe-
llleHHlO nOli 3a.n:a'IH O lKHbI 6bITb nO qHHeHbI H ypaBHeHI1H rpa-
HHqHbIX YC.1JOBHlI, 'ITO He06xOAHMO yqHTbIBaTb npH HX COCTaBJ1eHHH.
C.'Ie OBaTe.1JbHO, 3TH ypaBHeHHH OJJ}KHbI COCTaBJ1HTbCH TaK, 'IT06bI
MOMHO 6bIJ10 yCTaHoBHTb, KaKaH '1aCTb Tonmma, nO Ollle wero K
paCCMaTpHBaeMOMY Ce'leHHlO HarHeTaTe.1JbHoro Tpy60npoBo a, no-
cTynaeT K pacnbI.1JHBalOI1I.HM OTBepCTHHM H KaKaH '1aCTb OCTaeTCH
H.'IH nepeTeKaeT B pyrHe MeCTa H3-3a B HHHHH HCKaIKalOI.l{HX <)JaK-
TOpOB. IlpH TaIWH nOCTaHOBKe 3a a'lH ypaBHeHHH rpaUH'IHbIX YCJ10-
BHi:j .n:O.'1fKHbI 6bITb ypaBHeHH5IMH 6a.'1aHCa, Y'IHTbIBalOI.l{HMH B pac-
CMaTpHBaeMOM Ce'IeHHH HarHeTaTe bHoro Tpy60npoBo a nocTyn e-
HHe H pacxo TonJ1HBa. YpaBHeHHH BHMeHHH HarHeTaTeJ1bHOrO KJ1a-
naHa, 3aBHCHMOCTH npOXO HOH n.TJOI.l{a H no,cl. nOHCKOM KTJanaIla,
nJ10I.l{a H BcaCbIBalOI.l{HX H OTCe'lHbIX OKOIl 01' )TJIa nOBopOTa Ba.1a
Hacoca TaIUKe O.'DKHbI 6bITb OTHeceHbI K ypaBHeHHHM rpaHWIHbIX
VC,,10BHH, nOTOMY '11'0 6aJ1aHC Ton.TJHBa CVI.l{eCTBeHHO 3aBHCHT 01' xa-
paKTepa H3MeHeHHH nepe'lHCJ1eHHbIX napaMeTpOB. IlpH COCTaB,,'Ie-
HHH ypaBHeHHH rpaHH'IHHX YC OBHH He06xo.n:HMO Y'lHTWBaTb TaKHe
<)JH3H'IeCKHe napaMeTpbI TOnJ1HBa, KaK C)KHMaeMOCTb, n.'IOTHOCTb,
a npH .n: HHHbIX Tpy60npOBo.n:ax - H BH3KOCTb Ton.1HBa.
IlonbITKH onpe.n:e HTb BJ1HHHHe rH paB.TJH'IeCKOrO conpOTHBc'IeHHH
HarHeTaTe bHoro Tpy60npoBo.n:a Ha BOJ1HbI .n:aBJ1eHHH no Cpe.n:HHM
CKOpOCT5IM BHfKeHHH )KH KOCTH HY)KHO C'IHTaTb rrpH6J1H)KeHHbIMH,
rroToMY 'ITO BoaHa pacnpocTpaHHeTcH co CKOpOCTblO OKO,,'10
1200 MIceK, a Torr.'1HBO ABlUKeTC5I co CKOpOCTblO 20-30 MIceK. IlpH
TaKOH CKOpOCTH .n:BH)KeHII51 3a BpeM5I BnpbICKa '1aCTH a TOnJ1HBa,
BbITeCHeHHa51 B Tpy60npOBO.n:, nepeMeCHITC5I TOJ1bRO Ha 10-15 C/n
01' Bxo.n:Horo Ce'leHH5I. IlpH Y'leTe )Ke B5I3KOCTH npllHlIMaeTC5I BO
BHHMaHHe BCR .n:nHHa HarHeTaTenbHoro Tpy60npoBo.n:a, T. e. npHHH-
MaeTC5I, '11'0 CKOpOCTb .n:BH)KeHI15I nOTOKa TOnJ1I1Ba YCTaHoBHBwa5lc5I.
Do.'1bIIlOe B HRHHe Ha npOTeKaHl1e npou:ecca BnpbIcKa OKa3bIBa-
lOT H Ha'laJ1bHbIe YC OBH5I. CoraaCHO CHCTeMe ypaBHeHHH (3) Ha-
I1avlbHbIe YCJ10BI151 onpe.n:e.'151lOTC5I CKOpOCTblO Co H .n:aB.1JeHIIeM po.
B 60.!1bwlIHcTBe caYI1aeB Co = 0, '11'0 H npHHHMaeTC5I B HaI1a.'IbHbIX
YC.'10BH5IX. ,QaB,,'1eHHe Po, KOTopoe Ha3blBaeTC5I OCTaTO'lHbIM, 113Me-
H5IeTC51 B WHpOKHX npe e.'1ax, npHI1eM 113MeHeHHe .n:aB.1eHH5I B 06.'1a-
CTH, Kor.n:a Po > 1 KFlcM 2 , OKa3bIBaeT He oc06eHHO 60.'1bIIlOe B.1JH5I-
HHe. HanpHMep, OIIlH6Ka npH onpe.n:e.'1eHHH po. paBHaR 10-
25 KFjCM2, BHOCHT B paCI1eT HeTO'lHOCTb OK0J10 2-5% B 3aBHCH!\10-
CTH 01' Be.'1HI1HHbI 060eMa CHCTeMbI.' OpH Po < 1 KF/CM 2 B CHCTeMe
o6pa3yeTc5I cB060.n:HbIH 06oeM, He 3anO.1HeHHbIH TOnJIHBOM, KOTO-
pbIH no aHaJIOrHH Ha3bIBalOT OCTaTOI1HbIM. OWH6Ka B onpe e.1JeHHH
Be.'1WIHHbI V oc BHOCHT B paC'IeT 3Ha'lHTe.1bHYIO norpeIIlHOCTb, KOTO-
paH B HeKOTopbIX C.1Y'la51X OCTHraeT 40% H 60.'1ee. O.n:HaKo 1'0'1-
HbIX MeTo.n:OB onpe.n:e.TJeHH5I Be,,1H'II1H Po H V rw DOKa He C03.n:aHO.
IlpH CTaTHI1eCKHX MeTo.n:ax paCiIeTa npHMeH5IeMbIe ypaBHeHH5I
TaIOKe 51B.'I5IlOTC5I ypaBHeHHHMH 6a.'1aHca. LlelICTBIne.'1bHO, ec.'1H
52
npe.n:no.I0m:I1Tb, 1.JTO PH. = Ptjj, TO CI1CTel\lbI ypaBHeHlIH (4) 1I (5)
COCTaBlITb He.'1b3H, 1I Tor.n:a ypaBlIeHI1H rpaHI1 1 lHbIX YC.I0BHH BO
BXO.n:HOM 1I BNXO.n:HOM Ce1.JeHHHX Tpy60npoBo.n:a onpe.n:e HT npoQecc
no.n:a1.JH TOnJIlIBa. OD.HaKO BC.IeD.CTBHe TOro. 1.JTO PH. = Ptjj, ypaBHeHlIH
H3l\1eHHT BH.n: 1I pernaTb HX npHD.eTCH COBMeCTHO .n:.1H BXOD.HOrO H
BbIxo.n:Horo Ce1.JeHHH HarHeTaTe.1bHoro Tpy60npOBOD.a. Ho npH TaKOM
MeTOAe 1JHC.l0 COBMeCTHO pernaeMbIx ypaBHeHHH Mom:eT 6bITb D.a)Ke
60.Ibrne, 1JeM npH rHD.pOD.HHaMlI1JeCKoM. npH1JeM B 06mIx IeTo.n:ax
pernaTb ypaBHeHHH MOm:HO TO.lbKO npH6.1Hi-KeHHo.
HeKoTopbIe aBTopbI, CTpeMHCb 06eCne1JHTb aHaJ1HTH1JeCKOe pe-
rneHlIe ypaBHeHHH CTaTH1JeCKOrO MeTo.n:a paC1JeTa, He Y1.JHTbIBaIOT
1I.pOcce.1HpOBaHHH Ton.IHBa BO BCaCbIBaIOIl.(HX H OTCe1JHbIX OKHax
BTy.IKI1 n.1YH:iKepa, 1I3MeHeHlIH 06"beMa Ka!\IepbI HarHeTaHliH Ton.'1HB-
Horo lIacoca, B.II1HlIliH lIarHeTaTe.'1bHOrO KJlanaHa 11 HrJlbI CPOPCYlIKH
1I .n:p. npI1 TaKHX )],onyu].elIHHX T01JlIOCTb paC1JeTa HenpHeM.;leMa )],.lH
pernelII1H npaKTH1JeCKHX 3a.n:a1J COBpeMeHlIoro .n:H3e.leCTpoeHHH. CTa-
TI1CTI11JeCKHH )Ke MeTo.n: paC1JeTa C nO.'1HbIM Y1JeTOM rpaHH1JHbIX YC.rIO-
BHH HlIOrD.a MO)KeT 6bITb .n:a)Ke CJI0)lmee .n:HHaMH1JeCKoro.
EC.IH B CliCTeMe c03.n:moTcH YC.l0BHH, npH KOTOpbIX PH. = Ptjj, TO
CTaTlI1JeCKI1H MeTO.n: paC1JeTa D.aeT TaKYlO )Ke TOl!HOCTb, KaK 1I ::J.HHa-
Mlf1IeCKHH. n01l.06HbIe YC.l0BlIH B03MO)KHbI, Kor,'J.a:
a) nYTb OT Hacoca 11.0 pacnbI.IHBalOIl.(I1X OTBepCTliH 01JeHb Ma.'l, B
pe3y.rIbTaTe 1Jero Be.llI1JlIHa aMn.1HTy.n:bI BO.IHbI F(t) 6Y.lI.eT lIe3Ha-
1JHTe.'1bHO OT.llI1JaTbCH OT Be.1H1JHlIbI aMll.'IHTY.lI.bI BO.1HbI F(t-;).
B CBH31I C 3THM Be.llf1IHHN aMnJIHTY.n: OTpa)KeHHbIX BO.'lH \\7 (t) H
W (t+ )6YAYT TaKm:e 6.l1I3KlI O,'J.Ha K .n:pyrOH. npaKTH1JeCI{lJ nOk
HOCTblO nO.lI.06HbIe yCJI0BlIH C03,'J.alOTCH B Ton.IlIBHbIX CHCTeMax nIlla
lIacoc - CPopcYlIKa;
6) 1JHCJ10 060pOTOB .lI.BHraTeJ1H MaJIO (nopH.lI.Ka 150 o6/J',1.Wi),
a nYTb OT lIacoca .n:o pacnbI.llIBalOIl.lHX oTBepCn-IH L 1 )11.. Ho .lI.a-
)l{e B 3TlIX YCJ10BHHX npH .n:ByxTaKTHol\l .n:BHraTeJIe BOJIHbI 6Y.lI.YT
npoxo.lI.lITb nYTb L 3a 0,75° yrJla nOBopoTa KOJ1eH1JaToro Ba.Ia (npli
MaKClIMa.rIbHbIX 3Ha1.JeHlIHX n H L), BC.1Je.n:CTBHe 1Jero B O.n:lIH H TOT
)Ke MOMeHT BpeMeHI1 3Ha1JelIHH PH. H ptjj 6y.n:YT pa3.1H1JHbI. .n:.'1H 1Je-
TbIpeXTaKTHoro .n:BHraTeJ1H OTpe30K BpeMeHH COCTaBJIHeT 0,375°
a
yr.Ia nOBopOTa Ba.na Ton.1HBHoro Hacoca. C.leD.OBaTe.'lbHO, B .l106bIX
YCJ10BlIHX CTaTH1JeCKliH MeTO.n: 60.'lee nplIeMJIeM .n:aH 1.JeTbIpexT8KT-
HbIX .n:1I3e.'1eH, 1JeM .n:.1H .n:ByxTaKTHbIX. y!TaK, Bonpoc 0 npHMelIeHHlI
,'J.HHaMlf1IeCKOro H.llI CTaTH1JeCKOrO MeTO.lI.a pernaeTCH B 3aBHCHMO-
CTH OT T01JHOCTH paC1JeTa. ECJ1lI
2[ F(t) -F ( t-:.+ ) 1
F(t) +F( t- )
1 00 8
53
H
2r w( t+ )-Wf(t) 1
100 < 8,
w ( t + ) + W (t)
r.n:e () - Tpe6yeI\1aH TOLJHOCTb paCLJeTa B %, TO 06a MeTO.n:a .n:Q.lUK-
HbI .n:aBaTb npHeI\1.'IeMYIO TOLJHOCTb paCIJeTa H BbI60p MeTO.n:a 6y.n:eT
3aBHCeTb OT CJ10)KHOCTH perneHHH paCLJeTHbIX ypaBHeHHH. npH HC-
nOJIb30BaHHH l.{HQ:>POBbIX BbIIJHC.;lHTe"lbHbIX "'IarnHH YKa3aHHoe 06-
CTOHTeJ1bCTBO He BbI3bIBaeT OC06bIX 3aTpy.n:HeHHH.
npH YIJeTe ru.n:paB.TIHIJeCKOrO conpOTHB.'IeHHH BMeCTO ypaBHeHHH
(1) nOJ1YIJlII\1
ap --L P + 2 P kC=0' 1
ax' iJt '
ac +.....!...-. iJp =0.
ax a 2 p dt
ECJIH nepBoe ypaBHeHHe CHCTeMbI (6) npo.n:IIQ:>Q:>epeHl.{HpOBaTb
no t, a BTopoe, YMHO)KeHHOe Ha alp, no x, TO no.TJ:YLJHM TaK Ha3bIBae-
Moe TeJ1erpaQ:>Hoe ypaBHeHlIe
iJ2C _ . iJ2C _ . iJC =0.
iJx 2 a 2 p iJt 2 a 2 dt
TeJIerpaQ:>Hoe ypaBHeHHe xapaKTepH3yeT BO:IHbI, aMn.'IHTy.n:a KO-
TOpbIX npH HX .n:BH)KeHHH HenpepbIBHo H3MeHHeTCH. YpaBHeHHe (7)
BBH.n:y C.'IO)KHOCTH rpaHHIJHbIX YC.'IOBHH H caMoro ypaBHeHHH pe-
rnaeTCH npH6J1H)KeHHO. CYll1.eCTBYIOT .n:Ba MeTo.n:a perneHHH noro
ypaBHeHHH. no O.n:HOMY H3 3THX MeTo.n:OB [43] nYTeM no.n:CTaHOBOK
iJw -l1 t
p = po - C -; ill = e Y CHCTeMa ypaBHeHHll (6) npHBo.n:HTCH K
dt
BH.n:y
(6)
(7)
(J2y _ . iJy +.J!1: y = 0,
iJx 2 a 2 iJt 2 a 2
r.n:e
k = 'J.Cep .
4d T '
'A - K03Q:>Q:>IIl.{HeHT ru.n:paB"lHIJeCKOrO conpoTHB.'IeHHH.
npH YC.'IOBHH (k 2 _ 0, T. e. eC.;lH npeHe6peraTb B.;lHHHHeM BH3-
a
KOCTH Ha HCKa)KeHHe rrepHo.n:HIJHOCTH, no.'IYLJeHHOe ypaBHeHHe MO)K-
HO pernaTb B BII.n:e
p = Po + e- kt [ F ( t - : ) - W (t + : ) ] ;
I -kt [ ( X ) ( X ) ]
C=--;;pe F t--;; +W t+ _'
I
(8)
54
T. e. npliHUlfnllaJlbHO ypaBHeHHe (8) COBna.n:aeT C cHcTeMoH ypaB-
HeHI-IH (3), OTJIJ11Ia5ICb OT Hee JIHlllb MHomllTe.TJeM e- kt .
10. 5I. <l>OMHH [71] npe.n:.1mKlIJI MeTO.n: pellIeHlISI, KOTOpbIH 3HaqH-
Te.lbHO OTJIHqaeTC5I OT pellleHIi5I BO.'1HOBOrO ypaBHeHlISI, n03ToMY
paccMoTpHM ero B c.le.n:YIoLUeM naparpa4>e.
2. PAC ET npOIlECCA BnPblCKA TOnnHBHOA CHCTEMbi
HEnOCPEACTBEHHOrO AEACTBHSI
C HArHETATEnbHblM TPy&OnpOBOAOM
TaKa5I CHCTeMa nO.1YlIH.la lllHpOKoe pacnpOCTpaHeHHe Ii no KOH-
CTPYKTIIBHOMY 04>opM.TJeHHlO sm.'15IeTC5I HaH60.'1ee 06LUeH (pliC. 28).
I13MeHeHHe YCJ10BHH npoTeKa-
IUl5I npouecca BO BXO.n:HOM H BbIXO.n:-
HON CeqeHH5IX HarHeTaTeJIbHOrO
Tpy60npoBo.n:a B CB5I3H C .n:BI1meHH-
eM HJ1I1 OCTaHOBKOH HarHeTaTe.'1bHO-
ro KJ1anaHa H HrJlbI 4>OPCYHKH, a
TaKMe 3aKpbITHSI H OTKpbITHSI n.'1YH-
)J{epOM BcaCbIBalOI.IJ.lIX H OTCeqHbIX
OKOH BTY.'1KH BbI3bIBaIOT He06xo.n:H-
MOCTb pa3.n:eJISITb npouecc Ha 3Ta-
nbI, QHCJIO KOTOpbIX onpe.n:e.'15IeTC5I
KOHCTpYKUHeH CHCTeMbI H COOTHO-
llIeHHeM pa3MepOB Me)J{.n:y ee 3.'1e-
MeHTaMH. XapaKTep ypaBHeHlIH Ii
MeTO.n: HX COCTaBJIeHlI5I .n:J1SI Bcex
3TanOB o.n:HHaKOBbI, H3MeH5IlOTC5I
TO.lbKO QHC.1I0 ypaBHeHlIH II KOJ1IiQe-
CTBO Q.lIeHOB B HeKOTopbIX H3 HHX.
I Icno.'1b30BaHlIe UH4>POBbIX BbIQHC-
J1HTeJIbHbIX MalllHH BeCbMa 06J1er-
lJaeT paClJeT.
B 06LUeM cJ1YlJae npouecc BO BXO.n:HOM CeQeHHH Tpy60npoBo.n:a
pa3.n:e.'15IeTC5I Ha c.'1e.n:YIOI.IJ.He 3TanbI:
1) OT HaQa.'1a .n:mUKeHH5I nJ1ymKepa .n:o HaQaJIa .n:BHmeHHSI HarHe-
TaTeJ1bHOrO KJ1anaHa;
2) OT HalJaJIa .n:BHmeHH5I K.TJanaHa .n:o nOollHoro nepeKpbITH5I Bca-
CbIBalOI.IJ.HX OKOH;
3) OT nepeKpbITH5I BcaCbIBalOLUHX OKOH.n:O MOMeHTa BbIxo.n:a
pa3rpymalOI.IJ.erO n05ICKa HarHeTaTe.'IbHOrO K.'1anaHa H3 KaHa.na
rHe3.n:a;
4) OT BbIxo.n:a pa3rpymalOLUero n05ICKa H3 KaHaJJa rHe3.n:a .n:o
HaQaJ1a OTKpbITH5I OTCeQHbIX OKOH;
5) OT OTKpbITH5I OTCeQHbIX OKOH .n:o MOMeHTa Bxo.n:a n05ICKa
KoIlanaHa B I\aHa.'1 rHe3.n:a;
6) OT Bxo.n:a pa3rppKalOllIero n05ICKa B KaHa.'I rHe3.n:a .n:o MO-
MeHTa noca.n:KH IwanaHa Ha ce.n:JIO;
P;;V':
PH;
/..
flp ; v"
t
PHC. 28. PaC4CTHa51 cxeMa Ton-
.lHl3Hoii CHCTC!\Ibl Hcnocpc.!J.cTBeH-
HOro .!J.Ci1CTBHH C MCXaHH'-ICCKIIM npH-
BO.D:O!\l !J HafHCTaTC,1bHbIM Tpy60-
rrpoBO.D:o M
55
7) aT .naca.n:KI1 HarHeTaTe,'IbHara K lanaHa Ha ce.a,.la .n:a IOMeHTa
nO.1Hara npeKpallI.eHIHI ,J,BlDKeHIIH Tan.llIBa B HarHeTaTe.lbHaM TPY-
6anp aBa .n: e .
4IIC"lC 3TanaB B BbIxa.a,HaM CeqeHlUl HarHeTaTe.lbHara Tpy6anpa-
Ba.n:a 3aBI1CHT OT Taro, HMeeT J11I Hr.la <PapCYBKH ynap.
[L.1H Bblxa;XHora CeqemIH BarHeTaTe.lbBara Tpy6onpaBa:I,a, Kar.'Ia
xa,J, Hr.lbI arpaHWIeH ynapaM, npau,ecc pa3.n:e.1HeTCH Ha C.le;XYIOllI.He
3TanbI:
f L '
1) aT na;xxa.n:a K <PapcYHKe Ba.'1HbI F (t - -) .n:a Halla.la .n:BH-
, a ,
LKeHIIH IIr.lbl;
2) aT na.n:"beM3 IIr.1bI .n:a MaMeHT3 .n:OCTIILKeBIIH eIO ynap3;
3) aT ;xaCTlI.tKeHIIH IIr.laH ynapa
.n:a BaqaJ1a ee naca.n:KII;
4) aT aTxa.a,a HrJ1bI aT ynopa .n:o
naca.n:KH ee Ba ce.n:.'1a.
3aKaKcaBbIBaBIIe paCnbIJ1l1Te-
"leH CYllI.eCTBeHHa 3aBlIClIT aT xa-
paKTepa npaTeKaHIIH qeTBepTora
3Tana. 5!B.'1eHIIH, B03HIIKaIOllI.lIe B
Tan HBHOH CIICTeMe B qeTBepTaM
3Tane, 6y.n:YT paCCMOTpeHbI .n:aJ1bllle.
DYTeM pa3.n:e.'1eHIIH npou,ecca Ha
3TanbI II caCTaB.'1eHII5I ,l.LJ1H Ka*.n:ara
1I3 HHX ypaBHeHIIH rpaHlIqHHX YC-
PHC. 29. CxeMa nCpCKpblTH5I OKOH ,,'Jo.BHH, B qHC.'1a KaTapbIx BxaLl.5IT
BTYJIKII n.TJymKcpoM Hacoca ypaBHeflHH CnJ1alllHaCTII ABHLKeHIISJ
)JUl.n:KaCTII II ypaBHeHI1H JI.BIUKeHHH
3anapHbIx II .n:pymx apraHaB Tan.lIIBHOH CIICTCMbI, MOfKHa YllecTb
J1l06bIe KaHcTpYKTHBHbIe aco6eHHacTlI Ton.llIBHoro Hacoca 11 <pop-
CYHKII.
Pac eT npou,ecca BO BXOAHOM ce eHHH Tpy6onpoBo.n:a Y Hacoca
(CM. pl1c. 28). OplI paCqeTe Hea6xa.n:lIl'vIO 3HaTb, KaK 113MeHflIOTCH
rpa<plIllecKII nYTb II cKapocTb ,l.LBIILKeHHH n lYHfKepa, 06"beM K3MepbI
HarHeTaHIIH V 1{, npaxalIHafi n.lallI.a,lIb BcaCbIBaIOllI.IIX II aTcellHbIX
OKaH, a TaI(LKe ,lIpyrlIe napaMeTpbI, 1I3MeHeHlIe KOTOpbIX no. yr lY
naBapaTa B3d3 TondHBHara HacaC3 MaLKHa anpeJI.e HTb He3aBHCH-
Ma aT npau,ecca BnpbICKa.
B .1 IO60. i-i MOMeHT BpeMeHH npaxO,lIHaH n.l0llI.3JI.b BcaCbIB3IOllI.I1X
aKaH Kpyr.laH <po.pMbI (pl1c. 29)
,2
f6C=-(2JL-2'1+sin2'1). (9)
2
Yra.'1 v anpe,l.Le.1HeTCH 113 caaTHOllleHH5I
h-h
cas 'I = l- .
,
56
Kar,l.La KO.1HlleCTBa na,l.LaBaeMara TanJ1HBa perYJIHpyeTcH H3Me-
HeHHeM MOMeHTa Ha<Ia.la nO.n:a<JH, T.. e. KOr.n:a BCaCbIBaJOlllHe OKHa
nepeKpbIBalOTC5I KOCOH KpOIVIKoil BbIpe3a, TO
h-h
cosv= 1- sin ".
r
DpH OTKpbITHH OTce<JHbIX OKOH HX npOXOAHa5I n.lOllI.a.lI,b
2 .
to =.!.....- (2.,-sin 2.,). (10)
2
DO.'IblllYIO <JaCTb OKPY:>KHOCTH nOBopoTa BaJIa Ton.i'UIBHoro Haco-
ca n.!IymKep Haxo.n:HTC5I B nOKoe. DpHHu.HnHa.'IbHO cor.laCHO nepBO-
MY 3Tany paC<JeT npou.ecca Bnp CKa He06xo.n:HMO Ha<JHHaTb C MO-
MeHTa Ha<Ja.'Ia .n:BH:>KeHH5I n.!IymKepa. O.n:HaKO B nepBbIe MOMeHTbI
3Toro 3Tana npOXOllHa5I nJ10llI.allb BcaCblBalOllI.HX OKOH ellI.e 01.IeHb
Be.'IHKa, nonOMY Ton.!IHBO, BbITeCH5Iel\lOe n.'IYH:>KepOM, KOTOpbIij npH
CBoeM .n:BH./KeHHH nepeKpbIBaeT BcaCblBalOllI.He OKHa, nepeTeKaeT B
.!IHHHIO BcaCbIBaHH5I 6e3 3aMeTHoro nOBbIllIeHll5I .n:aB.!IeHH5I. YpaBHe-
HHe rpaHH<JHbIX YC.!IOBHH .n:JI5I 3Toro 3Tana
tncn = /-toto V ; V PH-P6C'
(11 )
OTKy.n: a
P" p +[ "ofo; : r
(12)
T. e. C)KHMaeMOCTb
MaHHe.
C:>KHMaeI\IOCTb TOn.!IllBa HY)KHO Y<JHTbIBaTb B 3aBHCHMOCTH OT
IWHKpeTHbIx YC.!IOBUII Ha1.Ia:la pe3Iwro B03paCTaHH5I .n:aB.leHH5I pu.
Do cYllI.eCTBY MOMeHT Ha<Ja.la Y<JeTa C:>KHMaeIVIOCTH Torr.lIlBa 5IB,!I5IeT-
C5I Ha<Ja.'10M pac<JeTa npou.ecca BnpbIcKa TonJ1HBa.
Dpou.ecc BrrpbIcKa paCC1.IHTbIBaeTC5I npH c.le.n:YIOllI.Hx YC.l0BH5IX:
I} ypaBHeHH5I rrpou.ecca pellialOTC5I rrpH6.1I1:>KeHHO MeTOllOM KO-
He1.IHbIX pa3HocTeH. Ka:>K.n:bIH :::;Tan pa3.n:e,i15IeTC5I Ha npOMe:>KYTKH
BpeMeHII !'J..t, npIlHIIMaeMbIe B 60.1blllIlHcTBe CJ1Y1.IaeB paBHbIMH 1 0
yr.'Ia rroBopoTa BaJIa Hacoca. Ho 3Ta Be.!II1<JI1Ha MO:>KeT 113MeH5ITbC5I
B 3aBHCI1MOCTH OT 1.IIIc.!Ia 060POTOB, rrpHH5ITOH T01.IHOCTI1 paC1.IeTa II
llpymx YC.'10BHH;
2) npH pellleHHII nepeMeHHbIe pa3.n:e.15IIOTC51 II ypaBHeHH5I HHTe-
rpHpYlOTC5I n01.I.'1eHHO aHa.1H.TII<JeCKH H.1H npH6,ilH)j{eHHo no Cpe.n:HIIM
Be.'1H<JHHaM IICKOMbIX napaMeTpoB. BBH.n:y Ma.'IOH BeJIH1.IHHbI !1t Cpell-
HHe 3Ha1.IeHH5I onpe.lI,e.15IIOTC5I KaK cpellHee apHcpMeTH<JecKoe 3Ha1.Ie-
HHe HCKOMbIX napaMeTpoB B Ha1.Iaae H B KOHu.e rrpOMe)KYTKa Bpe-
MeHH !1t;
3) HarHeTaTe.lbHbIU K.'IanaH H I1'rJIa CPOPCYHKH
BpeMeHI-I !1t .n:BH:>KYTC5I paBHoMepHo YCKopeHHO [5].
Ton.1HBa B 06"beMe He rrpHHHMaeTC5I BO BHIl-
B npOMe:>KYTKe
Eho ..n:orrYllI.eHHe
57
He BHOCI1T BBI1.n:y M.aJIOH Be.1JHIII1HbI /j,[ 3a!\IeTHOH norpernHOCTI1 B
pe3YJ1bTaT paclleTa;
4) .n:aB.;1eHI15I Ton.;1I1Ba B 06""beMe V: H BO BXO.n:HOM CelleHl1H Ha-
rneTaTe.lJbHOrO Tpy60npoBo.n:a paBHbI;
5) .n:aBoJleHH5I TOnJIHBa B BbIXO.n:HOM CeqeHliH HarHeTaTeJ1bHOrO
Tpy60npoBo.n:a 11 B 06...,eMe V rJj paBHbI;
6) MrHOBeHHbIe 3HaLJeHI15I CKOpOCTI1 HeycTaHoBHBrnerOC5I I1CTe-
LJeHI15I Ton.;lI1Ba onpe.n:eJ15IIOTC5I no <POPMYJIaM YCTaHoBlIBrnerOC5!
.n:BI1MeHI15! iI\H.n:KOCTI1. HanpI1Mep, MrHOBeHHbIe 3HalleHli5! CKOpOCTII
nepeTeKaHH5I TOnJIlIBa llepe3 OKHa BTy.TJKH n.TJYHMepa
C oe = / J! PH-Pec '
npHLJeM p = const. BIHOCI1Ma5! IrIPI1 3TOM ornH6Ka MaJIa H npH perne-
HHH npaKTI111eCKIIX 3a.n:aLJ MO)KeT He npHHHMaTbC5I BO BHI1MaHI1e;
7) He YLJHT BaeTC:H B.TJH5IHI1e 06"beMa KaHaJIa no.n: KOHYCOM I1rJ1bI
Ha npollecc BnpbICI\a BBHAY He3HaLJHTe.TJbHOCTH 3TOH BeJIHLJHHbI. O.n:-
HaKO OHa npI1HHMaeTC5I BO BHiHMaHHe npH paCCMOTpeHI1I1 npHLJHHbI
3arOpaHH5! paCnbJ.1IHB;aIOWHX oTBepcHIII;
8) BBH]],Y OTCYTCTBH5I 3KcnepHMeHTa.1bHbIX .n:aHHbIX He YLJHTbI-
BaeTC5I TpeHHe HarHeTaTeJIbHOFO KJIanaHa B KaHaJIe rHe3]],a, a TaK-
Me HrJ1bI <POPCYHKH JB pacnbI.TJHTeJle. flpH6.1I1MeHHbIII YLJeT 3Toro
<paKTopa MOMeT YBeJIHLJHTb nOFpernHOCTb paCLJeTa;
9) He npI1HHMaIOTC5I BO BHII1MaHHe YTellKH Ton.TJHBa LJepe3 3a30p
MeM.n:y nJ1YHMepOM H BTy.IJKOH. Jl..'I5I HeH3HorneHHOH nJ1YHMepHOH
napbI 3TOT <paKTOp lHe OKa3bIBaeT 3aMeTHoro B,,'IH5IHlUI Ha npou:ecc
BnpbICKa H pa6011HH npou:ecc .lI.H3eJ15I. Hcc.TJelI:OBaTb Me Ton.TJHBHYIO
CHCTeMY C noJ1YHMepH[bIMH napaMH, HMeIOWHl\UI 3a30p .1. > to MKM,
HepaU:HOHa.1bHO.
b1eTO]], nOLJJ1eHHOrO HHTerpnpOBaHH5I H .n:onyweHH5I 0 xapaKTepe
.n:BHMeHH5I HarHeTaTeJIbHOrO KJ1anaHa .n:aIOT B03MOMHOCTb nepeHTH
OT CHCTeMbI .n:H<p<pepeHU:Ha,,'IbHbIX ypaBHeHHH K a.lJre6paHlleCKHM.
flpe.n:J1araeMbIH MeTO.n: perneHH5I CHCTeMbI ypaBHeHHII npou:ecca
BnpbICK3 ,lI,3eT B03MOMHOCTb C ,lI,OCTaTOllHOH ,lI,JI5! np3KTHKH TOLJHO-
CTbIO onpe,lI,eJIlITb Be.IJHIlHHY a rvWJ1HTy.n:bI BO.'IHbI F (t) , H.n:yweH OT
BXO,lI,HOro CeLJeHH5! H,arHeTaTe.'1bHOrO Tpy60npOBo.n:a K 06"beMY V rJj.
CJIYllaII, Kor.n:a IB J1HHHH IHarHeTaHH5! HMeeTC5! OCTaTOLJHOe pa3-
peMeHHe 11 HallaJ10 npou:eCC3 npOTeKaeT HeCKO.'IbKO cneU:H<pHllHO,
paCCMOTpHM OT.n:eoJ'IbHIO.
flpH nepexo.n:e OT o.n:Horo 3Tana K .n:pyrOMY LJHC,,'IO ypaBHeHHH H
KOJIHLJeCTBO LJ.TJeHOB B HeKOTopbIX 113 HHX H3MeH5!IOTC5!, 3 06WHH BI1.n:
11 xapaKTep ypaBHeHI1H COxp aH5!IOTC5I. fl03TOMY u:e.'IeC006pa3HO
oc06eHHOCTH rpaHHllH X YCJ10BI1H paCCMaTpHBaTb Ha O.n:HOM 60JIee
06weM 3Tane, B KOT(()POM Y'lHTbIBaeTC5! MaKCHMaJIbHOe LJI1C.'IO I1CI\a-
JKa!OlllHx <paKTOpOB, a 3aTeM IrIpHBeCTH OCHOBHbIe ypaBHeHH5I H pac-
lleTHbIe <pOpMY,,'IbI OC'TaJ1bHbIX 3TanOB. He OCT3HaB.IJHB35!Cb "PH 3TOM
Ha aHa.'IH3e oco6eHHOCTeH HX IrpaHHllHblX YC,,'IOBHH.
58
B HCC.'1eD.yel\-lOH CHCTeMe HaH6oJ1ee 06IlI.HM HB.'1HeTCH nHTbIH
:/Tan, B KOTOpOM HarHeTaTe.'1bHbIH K.'1anaH nepeMeIlI.aeTCH BHe Ka-
HaJ1a rHe3D.a, npOXOD.HaH n.'10IlI.aD.b OTCeIlHbIX OKOH HenpepbIBHO B03-
paCTaeT, nJ1ymKep np0D.O.l}KaeT nOAaBaTb TOn.'1HBO - B HarHeTaTe.'1b-
HbIH Tpy6onpOBOA.
YpaBl eHIIH npoll.ecca A.'1H 3TH X YC.l0BHll:
aV II dPH = fnCn- lofo'" I 2 V PII-P8C-
dt JI P
f -. /T V ' f dh K .
- Ui I" JI P PH-PH - K----;jf'
, dp -./ 2 V " dh K
aV H ----;jf = IJUj V P _ P,,- PII + fK ----;jf-f TCT ;
M d 2 h K + M",+ fp", = f (PH-P' ) .
dt 2 K K H
(13)
(14)
(15)
YpaBHeHHe (13) onHCbIBaeT MrHOBeHHbIH 6a.'1aHC TonmIBa B Ka-
Mepe HarHeTaHHH Hacoca VI<' DepBbIlI 'lJIeH ypaBHeHHH' xapaKTe-
pH3yeT KO.'1l-JIleCTBO TonmIBa, OCTalOIlI.erOCH B 061>eMe V H B OKaTOM
COCTOHHIUI; BTOpOH - 061>eMHYlO CKOpOCTb BbITa.'1KHBaHHH Ton.'1HBa
nJIYH}KepOM Hacoca, TpeTHH - 061>eMHYlO CKOpOCTb nepeTeKaHIiH
Ton.'1IIBa IIepe3 npOXOD.HYlO n.'10Lll.aD.b OTceIlHbIX OKOH B J1IIHIIlO OT-
Ce'lKH, lJeTBepTbIH - 061>eMHYlO CKOpOCTb nepeTeKaHHH TOll.'UIBa H3
KaMepbl HameTaHHH V H B 061>eM lllTYlI.epa Hacoca V lJepe3 npo-
XOD.HYlO LlI.e.'1b Me}KD.Y KpOl\IKOH pa3rpY}KalOIlI.erO nOHCKa HameTa-
Te.'1bHOrO K.'1anaHa H TOPll.OBOH nOBepxHocTblO nOCaAO'lHOrO KOHyca
3Toro }Ke KJIanaHa, nHTbIH 'l.'1eH onpeD.e.1HeT CIWpOCTb 3an0J1HeHHH
Ton lHBOM 061>eMa, oCBo60}KD.aeMOrO K.lanaHOM npli ero nOAHHTIIII.
a npH onycKaHIIII KJ1anaHa 3TOT 'l.'1eH 6YAeT onpeD.e.'1HTb CKOpOCTb
BbITeCHeHIIH TOnJIIiBa II3 061>eMa lllTYll.epa V B 061>eM V H' Bo Bpe-
MH pacno.l0}KeHIIH pa3rpY}KalOLlI.erO nOHCKa K.:lanaHa BHe KaHa.'1a
rHe3D.a pa60'leH n.J10Lll.aD.bIO KJIanaHa, Ha KOTOPYlO JJ.eIICTBYlOT D.aB-
.'1eHHH PH II P , 6YD.eT HBJ1HTbCH n.'10IlI.aJ],b nOnepe'lHOrO Ce'leHIIH no
era nepbHM. TaKIiM 06pa30M, ypaBHeHIIe (13) nOKa3bIBaeT. CKOJ1b-
KO nJ1YH}Kep BbITeCHII.'1 TonmIBa npli CBoeM. D.BII}KeHIIII II Ha lJTO
H3paCXOAOBaHO 3TO Ton.1IIBO.
YpaBHeHIIe (14) onHCbIBaeT 6a.laHc TOn.'IIlBa A.'1H 06DeMa lllTY-
I.{epa V , KOTOpbIH HenocpeJJ.cTBeHHo conpllKacaeTcH C BXOJJ.HbIM ce-
'leHlleM HarHeTaTe.lbHoro Tpy6onpoBoJJ.a. C.'IeJJ.oBaTe.'1bHO, ypaBHe-
HIIe (14) oAHoBpeMeHHo HB.'1HeTCH H ypaBHeHIIeM 6a.'1aHCa TOn.'1HBa
JJ.J1H BXOAHoro Ce'leHHH Tpy6onpoBoJJ.a. nepBbIH 'l.'1eH norD ypaBHe-
HIIH xapaKTepl:l3yeT IW.:1H'leCTBO Ton.'1HBa, OCTalOIlI.erOCH B 061>eMe
V B C}KaTOM COCTOHHHH, BTOpOH - onpe,LI.e.'IHeT KOJIH'leCTBO Ton-
JIHBa, nocTynalOIlI.erO B 061>eM V lJepe3 npOXO,LI.HOe Ce'leHHe no,LI.
59
pa3rpYLKalOIlllBl nO>ICKOM HarHeTaTeJIbHOrO K.'1anaHa, TpenIiI
nOKa3bIBaeT, KaKOe KO.'1Ii'leCTBO TOnmma BbITeCH5IIOT B 06"beM V
nepb51 K.JlanaHa, 1.JeTBepTbIUI 1.J,,'IeH Onpe,lI,e.rmeT KO.'1H1.JeCTBO TOn.'1IIBa,
nOCTynalOIltero B HameTaTe.TJbHbIH Tpy6onpOBO,lI, 1.Jepe3 ero BXO,lI,Hoe
Ce1.Jemfe f r. YpaBHeHHe (14) nOKa3blBaeT, CKO.'1bKO TOnJ1HBa noCTY-
nH.'IO B 06bel\l V , CKO.1bKO ero OCTa.'10Cb B 3TOM 06"beMe B CLKaTOl\l
COCT05lHHH H CKOJIbKO nocTynHJIO B HarHeTaTeJIbH H Tpy6onpOBO,lI,
Qepe3 BXOllHoe Ce1.JeHHe f r.
M3 paccMoTpeHHH ypaBHeHHH (13) H (14) B TeKaeT nOHHTHe 0
TaK Ha3bIBael\lOM MrHOBeHHOM K03<P<PHlJ,HeHTe nO,lI,a1.JH Ton.'IHB3 B
HarHeT3Te.'IbHbIH Tpy6onpoBoA. TeopeTH1.JecKH B03MOLKHoe KO.JIWle-
CTBO Ton.1HBa xapaKTepH3)7eT 1.J,,1eH fnC n . KO,,1H1.JeCTBO TonmlBa, no-
CTynalOIltero B H3rHeTaTe.'1bHbIH Tpy6onpoBO,lI" xapaKTepH3yeT 1.J.'1eH
frCr. Tor,lI,a MrHOBeHHbIH K03<P<PHlJ,HeHT nOAa1.JH Ton.1HBa ,lI,.'1H BXO,lI,-
HOro Ce1.JeHHH Tpy6onpoBo a
f r e r
'l') li6X=- t - e .
n n
(16)
!\03<P<PHlJ,HeHT '1')... ex - eCTb OTHOllJeHHe OO"bCMHOH CKOpOCTH no-
cTyn.'1CHHH B HarHeTaTeJIbHbIH Tpy6onpo-
BO,lI, K 06"bCMHOH CKOpOCTH BbITeCHeHHH
TonmlBa n,,1YHLKepoM Hacoca.
YpaBHeHHe rpaHH1.JHbIX YC.'10BHH (15) onHCbIBaeT ,lI,BHLKeHHe Ha-
rHeTaTe.1bHoro K.'1anaHa. f1epB i1 1.J,,1eH 3Toro ypaBHeHHH xapaKTe-
pH3yeT CH.'1bI HHeplJ,HH MaCCbI K.'IanaHa H ,lI,BmKYIltHXCH C HHM 1.Ja-
CTeH, BTOpOH - Y1.JHTbIBaeT lJ,eHCTBHe Ha K,,1anaH CHJIbI ynpyrocTH
npYLKHHbI, TpeTHH - CH.'1 HaQa.'1bHOH 3aTH)KKH npYLKHHbI KJlanaHa.
YKa3aHHbIe CHJlbi ypaBHOBellJHBalOTCH CH.10H, onpelJ,eJIHeMoi:i pa3Ho-
CTblO .n.aBJIeHHH (P1i - p,). T3KHM 06P330M, ypaBHeHHe ,lI,BmKeHHH
K.'1anaHa 51B.'1HeTCH ypaBHeHHeM 6a.TJaHCa CHJ1, ,lI,eHcTBYIOIltHX H3 1\..'Ia-
naH, npHQei\1 CH.1a f (P1i - P J CTpeMHTCH OTopBaTb KJIanaH OT
rHe3.lI.a, a OCT3,,1bHbIe CH.'1bI - npH)KaTb ero K noca.n.01.JHOMY KOHYCY.
YpaBHeHHH (13)-(15) II CHCTeMa ypaBHeHHH (4) .lI.OJI)KHbI 6bITb
pemeHbI COBMeCTHO. PaccMoTpHM MeTO.n. peweHHH YKa3aHHbIx yp3B-
HeHHH .n..'1H paC1.JeTa npolJ,ecca BnpbIcK3 6e3 nOMOIltH lJ,H<PPOB X BbI-
1.JHC,,1HTe,,1bH X MallJHH. Cor,,1acHo npHHlJ,Hny n01.J,,'1eHHOrO HHTerpH-
pOBaHHH ypaBHeHHe (13) MOLKHO 3anHcaTb B BI1.lI.e
PH I t
aV llcp S dPfl=fn 5 Cndt- ofocp S V PH-PeC dt-
't, I,
PH
/"2 I. h K
- l4fl4 Cti V p J V PH-P dt-fK 5 dh K ; (17)
I, h
.
60
3,D.eCb
VIi+V'
V Ii Cp = 2 Ii ;
f = tOI + to . f = Ill>' + tUt
o CfJ 2' If{ cp 2'
T. e. H3MeH5IIOllI.HeCSI BeJIHqHHbI rrapaMeTpoB V H, f 0, fUf rrpHHHMa-
IOTCSI Cpe.n:HHMH .n:.1SI paccMaTpHBael\WrO npoMemYTKa BpeMeHH
1 - t l = I1t. Iho6bI yqeCTb H3MeHeHHe K03<p<PHllHeHTOB a, fio, IUf'
HX TaKme Ha3HaqaIOT cpe.n:IUIMH. .n:JJSI paccMaTpHBaeMoro npoMeJl\:YT-
Ka BpeMeHH, npHHHMaSI YG1OBHO .n:aBJIeHHe Ton<1HBa B 3TOM OTpe3Ke
BpervIeHH I1t rrOCTOSIHHbIM H paBHbIM rro BeJlHqHHe ero 3HaqeIUIIO B
Haqa.TIe npoMemYTKa, KOTopoe H3BecTHo. EC.1H rrpHHSITb, qTO yroJI
HaKJIOHa KOHyca ce.n:JIa 45°, 'lTO 6bIBaeT 'Ialll.e Bcero, TO Be.'1H'lHHa
f = (2:rd K + hK)hl( . (18 )
'II 2V2
C .n:ocTaTOqHOH .n:J1SI npaKTHKH TO'lHOCTbID MomHO C'lIITaTb
fut = 2,22d K h",. (19)
BC<1HqHHbI a II K03<P<PIIIJ:HeHToB pacxo.n:a BbI6HpaIOT rro 3KcrrepH-
MeHT3.1JbHbIM 3aBHCHMOCTSIM. HeKoTopbIe I1HTerpa.'1bI ypaBHeIU1SI
(17) orrpe.n:eJ1SIIOTCSI 6e3 OC06bIX 3aTpy.n:neHIIH. HarrpHMep,
nOTOMY 'ITO
P II
aV llcp r dp,,=aV"CP(PH-PIi');
PHI
"n
fn.l Cndt=fn I' dhn=fn(hn-h nl ),
/, hnI
Cndt = dh n ;
h K
f S dh K = f (hK-hKI).
hKI
Tm<HM 06pa30M, npn6.'1HmeHHO He06xo.n:HMO onpe.n:e.1HTb TOJ1b-
KO IIHTerpaJIbi TpeTbero II qeTBepToro 4JIeHOB ypaBHeHHSI (17).
I1HTerpa.1 TpeTbero 'IJ1eHa MOJKHO orrpe.n:e.'1HTb no cpe.n:HeMY 3Ha-
'leHIIIO .n:aB.1eHHSI PH .n:J1SI OTpe3Ka BpeMeHH 111, KOTopoe rrpHHIIMaeM
paBHbIM
PII+PHI
- PH CP;
2
Tor,J,a
t
f 11 2 t/ / PH+P" I _ P \ n . dt =
flo 0 cp 2 BC
. P L
I,
= f 1/ 2 -. /' p"+p,, I
flo 0 cp P V 2
Pec I1t.
81
Dpej.J(lI.e 'IeM nepeHTH K OnpelI.e.leHHIO HHTerpa.'Ia 'IeTBepTOrO
'I.1JeHa, paCCMOTpHM perueHHe ypaBHeHHH (15). 3amuneM 3TO ypaB-
HeHHe B BHlI.e
Mi,,+ ()h,,+ f p" = f (PH-pJ.
EC.'IH npHHHTb, 'ITO B npoMeMYTKe BpeMeHH .1.t KJIanaH lI.BHMeT-
CH paBHoMepHo yCKopeHHO, TO YCKOpeHIIe .J.BIImeHHH K,,'IanaHa
. C,,-C"I
/,,=
!J.t
r.n.e
c= 2(h,,-h"l) C"h
" !J.t
oTKy.n.a
i,,= 2 (h,,-h"l) 2C"1
"'.f2 I1t
Doc.'!e non:CTaHoBKH B BbIpaMeHIIe (15) BMeCTO in ero 3Ha'IeHHH,
a TaK)Ke He6o.Hbllloro npeo6pa30BaHHH nO.ilYQIlM
2Mh,, _ 2Mh,,] _ 2MC"I + h+ _ _'
'2 -' 2 -' t .' Ii. PIC - PH PH
f ,,!J.t t "l1t t ,,11- t"
(20)
1I.1JH
Ahli.+ B = PH-P ,
rn:e
A= --!- '
, 2 I "
f ,,!J.t f"
B=p _ 2Mh"l _ 2MC,,! .
K , 2 "
f ,pt f ,,!J.t
. dC"
/,,= dt'
Hcno.nb3YH 3aBI1CHMOCTb (20), 3anHllIeM HHTerpa.n 'IeTBepToro
q.neHa ypaBHeHHH (13) B Bl1.II.e
t t
fttijf tij cp .. /"i \ 1/ P 11- P dt = fttijf tij cp "II ( 2 f V Ah" + B dt.
V p V p
DpH6J1HmeHHO Be.nH'IUHa
h = h , ( C + j"I!J.t ) I1t
K "II "J 2 '
r.n.e .n..nH npOMemYTKa BpeMeHH I1t
C j"ll1t C
".+-= "cp'
2
62
nO.n.CTBBHB 3HB4eHHe h" B HHTerpaJI 'leTBepToro J1eHa ypaBHe-.
HHH (13), no.'1Y4HM
_t
fl",/u! <p .. I 2 . f V Ah,,+ B dt =
V po.
t,
t
= flU4fU4 'P V : J II A l h,,+ (CK,+ j,, .it ) M J + B dt.
t,
KBK C,,'1e.n.yeT H3 BHa.1H3B nOC.'le.n.Hero BbIpa)KeHHH, OllIH6KB 6y-
)J,eT He3HB4HTe.'1bHOH, eCJ1H 3Ha4eHHe jn npHHHTb paBHbIM Be.1H4HHe
j"l - YCKopeHHlO )J,JIH npe)J,bI)J,YllI.erO OTpe3Ka BpeMeHH !1t. Tor)J,a
HHTerpaJI 'leTBepToro 'l.'1eHa ypaBHeHHH (13) MO)KHO 3BnHCBTb B
BH)J,e
_ t
11",{", tp i/ X V A [hK + (C"l + j,, t ) M] + Bdt =
/.
= flU4fU4 cp V VA l h" + (C"l + j,,;M ) !1t]+ B !1t.
no npH6JIH)KeHHoMY 3HB4eHHlO h" onpe)J,eJ1HeM Bem1'lHHY ('If'
nOn:CTBBHB B ypBBHeHHe (17) BMeCTO HHTerpBJIOB HX 3HB4eHHH.
no.'1Y4HM noc.TIe He6oJ1bllIOrO npe06pa30BBHHH
/lofo -. 12 M /
\I p V PH--!-PHI
aV H cp 2
PII = PHI + fn (hn-h m )
aV H cp
P.,--
/lUjfUj cp .. f 2 p M I
aV p V A[hK+(C/d+ h M fHJ+B-
t (h"-h,,d
aV H cp
(21)
11cnoJ1b3YH cHCTeMY YPBBHeHHH (4), BbIpB3HM CKOpOCTb
BB BO BXO)J,HOM CeqeHHH HBrHeTBTeJIbHOrO Tpy60npoBo B
P 2W (t) Po
C T =-+---.
up ap up
TIO)J,CTBBHB 3HBqeHHe C T B ypBBHeHHe (14), nOCJ1e npH6.'1H)KeH-
Horo nOlJ.1emIOro HHTerpHpoBBHHH .:noro YPBBHeHHH H HeKOTopbIX
npe06pB30BBHHH C HCnOJIb30BaHHeM ypBBHeHHH (20) 6y.n.eM HMeTb
TOnJIH-
B BH)J,e
. N
PH = - +'l'PII'
X
(22)
63
rJ(e
IV = ' + f.lUjfUj cp V t V A [ .h ..L ( C. + J . 'K, t ) M J + B-
PHI aV' Kl, "I . 2
H
f B f hKI
(2\f1(t)-po];
2apaV
f r
AaV aV
f r M f
.X= 1 + +---:-;
2ap:lV AuV"
1jJ= .
x aV "
Pellum COBMeCTHO ypaBHeHl-I5! (21)- (22), nOJIYIIHM KBa.n.paTHoe
ypaBHeHHe
PII+ PHI -2P6C+ fJ' V P" + PIII-2Poc-D = 0,
H3 KOToporo Hal'I.n.eM
,. ! 2
lfp,,+p"I-2PBc= -2+ V 4+ D ,
(23)
r.n.e
D= PHI +P"I+ fn(hn--h m }
1; 1;aV HCp
_ fi'u.fL4cpV M / A[h ..L(C + )M]+B+
1":. v "I I Ki 2
"lh llCp
f 'N f 'h
. K + + -2'
-t- A V V Po,.,
1; X a IICp ;;A sa IICp
1": = 1 + ( . I - \jJ .
'" 'A '
aV"
__ f.lofo V f M
-- -
Y 2 suV" cp
Onpe.n.eJ1HB .n.aBJIeHHe PH' Hal'I.n.eM no ypaBHeHHIO (22) BeJIHqHHY
P , a no ypaBHeHHlO (20) - h", a 3aTeM no qJOpMYJ1e paBlIOMepHo
YCKopeHHoro .n.mUKeHIUI BbIqHCmIM Be.'IHqI-IHY j", Heo6xo.n.HlVIYlO .n.JI5I
pac'!eTa npol(ecca B c.JIe.n.YlO1lI.eM oTpe3Ke BpeMeHH /l.t. Onpe.n.e_1HB
P , H3 nepBoro ypaBHeHH5I CHCTeMbI (4) HaH.n.eM BO.1JHY F(t), a
H3 BTOporO - CKOpOCTb Cr. AMnmny.n.a OTpan-.:eHHOH BOJ1HbI W(t)
64
H3BeCTHa, nOTOMV LJTO OHa 06pa30Ba:laCb Y CPOPCYHIUl paHbllle Ha
. L
OTpe30K BpeMeHH PaCCMOTpHM nOC'Ie..'J,OBaTe:lbHOCTb paCLJeTa
a
no 3TanaM.
n epBblU 3Tan: BcaCbIBaIOll{He OKHa OTKpbITbI, HarHeTaTe.'IbHbIH
I\J1anaH CH,lI.HT Ha ce,lI.J1e. rpaHIflIHbIe YCJIOBH5I H npou.ecc onpe.rr.eJ15I-
IOTC5I ypaBHeHIleM
eN" d;" = tnCn-/lofo V 1""' PH-Pec . (24)
K03cpcpHIl.HeHTbI paCXO,lI.a OKOH BTYJ1KH nJIymKepa onpe,lI.e.'I5IIOTC5I
3KcnepHMeHTac1bHO. Ha pHC. 30 nOKa3aHa 3aBflCHMOCTb K03CPCPHUH-
eHTa pacxo.rr.a LJepe3 BnycKHoe )lBn
OKHO OT LJHCJIa PeHHOJlbJI,Ca. Be-
J1HlJflHa l-Len He3HaLJl1TeJIbHO 3a-
BHCHT OT LJHCJ1a Re B OCHOBHOM /),7
JI,Hana30He npOXO,lJ,HbIX CeLJeHHlI
H MOlKeT 6PITb npHH5ITa nOCT05lH- 0,6
Hoff. npH MeHblllUX 3HaLJeHHHX
0..5
n.'IOma,lJ,eH 3aBHcHMoCTb K03cpcpH- '1'70 3 6 8 10""
UHeHTa paCXO.l1.a OT 'IHCJIa Re
B03paCTaeT, ero Be.'IHLJHHa YMeHb-
lllaeTC5L OJJ.HaKO cpaBHHTe.TJbHPIe
paC4eTPI npouecca nOKa3aJlH,
LJTO B CB5I3H C He60.'1blllHM HH-
repBaJIOM, Ha IWTOpOM K03<pqm-
UHeHT paCXO,lI.a cymecTBeHHO 3a-
BHCI1T OT LJHCJla Re, npeHe6pe)KeHHe 3TOH 3aBHCHMOCTbJO npaKTHLJeC-
KII He B.1HHeT Ha pe3y.TJbTaTbI paCLJeTa.
nac.le HHTerpnpOBaHH5I ypaBHeHH5I (24) II era pellleHH5I nOlIY-
LJlIJ\I paCLJeTHYJO cpapMY.'1Y
1 1,/2
........c
rx-- pc u .....
. --
I
I
2
4
6 Re
PIIC. 30. 3aBI1CHMOCTb K09Ij:J<}JIIlUICH-
Ta pacxo.!J.a '-ICpC3 BnYCKHOC OKHO
flf.TJb3bl Ton.'lHBHOro !Jacoca .D:H3e.151
5lM3-236 OT 'lHCJla Re:
1 - f an 0.18 MM'; 2 - fen
= 2.95 ,fLU 2
l' [111+111-11-2Pec= _l...+ ,/ f:I2 +D.
2 JI 4
BbIpa)KemIe (25) nO,lI.06HO ypaBHeHHIO (23), XOT5I nOCTOHHHbIe
13 H D HMeJOT ,lI.pyrHe 3HaLJeHHH. llJ15I paCCMaTpHBael\IOrO 3Tana
(25)
! ,
[.tofo c pV 2 M
1)= P
Y2 llV" cp
D=2 p + tn{hn-hnr>
1-11 L'
. a." cp
2Pec.
OepBLIH 3Tan npO,lI.OJI)KaeTC5I ,lJ,O HaLJa.la ,lI.BlDKeHII51 HarHeTa-
Te.'1bHOrO K.'lanaHa II onpe;J.e.151eTC5I rpacpHLIeCKH no 3aBHCHMOCTH
.l1.aBJIeHHH PH. OT qi.
5 3aKa3 748
65
.l1aBJIeHHe, npl1 KOTOpOM HalJJIHaeT nO.Ll,HHMaTbCH HarHeTaTe,,'Ib-
HbIH KJlanaH,
f: ( , )
PIII'=t:: Po"t"P".
no ,n:aB.:1eHHlO p.,.. H 3aBI1CHMOCTH p., = f «(f') MO)J{IIO onpelle.'IHTb
MOMeHT HaIla.'Ia no,n:'beMa K.'IanaHa.
BTOp0i1. 3Tan: HarHeTaTe.;lbHbIH K.lanaH Haxo,n:HTCH B JJ,BHn,eHHH,
BC3CbIB31OllI.He OKHa He nepeKpbITbI, p33rpy:tK3lOllI.JIH nOHCOK He Bbl-
me,,'I H3 KaHa.'Ia ce,n:,,'Ia, 06'beMbI V., H V npo,n:o.'I:tKaIOT OCTaBaTbCH
pa3'be,n:HHeHHbIMH. O,n:HaKO no,n:alJa Ton.'IHBa B Tpy60npOBO,lJ, Y:iKe
H3IlaJ13Cb, TaK K3K HarHeTaTe.'IbHbIH K.'IanaH npH .lI.BH)J{eHHI1 6y,n:eT
BbITeCHHTb H3 06'beMa V'; Ton.lIHBO, paBHoe no BeJII1IlHHe 06'beMY,
BblTeCHeHHOMY K.lJ.anaHOM 3a BpeMH J}.t. H3 3TOM 3Tane K.llanan J]}IH
06'beMa V HrpaeT T3KYlO )J{e pO.lb, '1TO H ll.TlymKep .lI.JIH 06'beMa V.,.
YpaBHeHJUI rpaHHIlHbIX YCJIOBHH .lI..'IH ':)Toro 3T3na:
aV II d;/i = fnCn-flofo V V PH-P6C -f" " ;
. dp dh
aV II - = f" -----'5...-t T C T ;
dt dt
M d 2 h" --j-M"+f,,p,,=f,,(PH-P').
H
nOC,,'Ie COBMeCTHoro pemeHJIH ypaBHeHHH rpaHI1IlHbIX
nOJIYIlHM
r ' V 2 .
1, P +p 1 --2 p = -- _-1- D
t'H H 6C 2' 4"
P = N +1JJPH;
Ah,,+B= PH-P ,
r.u.e
!-tofo cpM V 2
B= - p 1JJ= ;
V 2aV/i cp X a VII A
f M f
X=I...!-- T + .
'2ap::tV AaV '
£=I+ f ,,(1-'\1) ;
AaV II cp
D = PH1- :/i + fn(hn-h m ) +
b saV H cp
+ f"B + f"h" I
sAaV H cp saV/i cp
f"N +
sAaV H cp'X
2p#c;
66
(26)
(27)
(28)
(29)
YC.'IOBI1H
(30)
(31 )
(32)
, fTMCTI
N = P,,, --
2aV
f T M (2W(t)- Po]- f,, _ f"h,,} .
2ap.1V: aV"A aV"
BO.'IHY F(t) H CKOpOCTb C T onpe.n:e.1HM no ypaBHeHHHM CHCTe-
MbI (4).
TpeTldi. 3Tan: BcaCbIBaJOlll.He OKHa 3aKpblTbI, K.:lanaH HaXO,'UITCH
B lI,BH:tKeHHII, HO pa3rppKalOllI.HH nOHCOK H3 KaHaJIa rHe3.J.a He
BbIIlIeJI.
'paBHeHHH rpmmqHbIX YC.l0BHH .n:.1H :Horo 3Tana:
aV" dp" =!nCn-fK C ,,; (33)
dt
, dp
aV" - = f"C,,-!TC T , (34)
dt
YpaBHeHHe .n:BH:tKeHl1H l{aanaHa coxpaHHeTcH HeH3MeHHbIM BO
Bcex :JTanax. Ooc.TIe npH6J1I1:tKeHHOrO COBMeCTHoro peIlIeHHH ypaB-
HeHHH nOJIY'fHM, qTO P1I. = D. YpaBHeHHH (31) H (32) CBoero BH.n:a
He H3MeHHIOT.
OOCTOHHHbIe 6y.n:YT HMeTb C,;le.n:YlOlIJ,He 3Ha'feHl1H:
D = + f,,(hn-h nJ } + f"N + f"h"l
aV 'i cp GAuV" cp GIlV II cp
OOCTOHHHble N, X, '1\:', 5 coxpaHHIOT Te :tKe 3HaqeHHH, qTO H BO
BTOpOM 3Tane.
l.f eTBepTblU 3Tan: pa3rpy:tKalOllI.HH nOHCOI{ l{.JlanaHa BbIIlIe.'I H3
KaH3aa rHe3.II:a, B pe3YJIbT3Te 'fero TOnJIHBO CTaao nepeTeKaTb H3
06'beMa V 11. B 06'beM V . YpaBHeHHH 6a.'la HCa TOn J1liBa:
dPII _ V 2 V ' 'dh".
aVII- fnCn- uJ14 - PII-PII -f,,-,
dt p dt
. dP: V "2 j , 'dh"
aV II -=PI"/ 14 -Jf PII-P,,+!,,--fTC T .
& p &
(35)
(36)
YpaBHeHHe lI,BH:tKeHHH HarHeTaTe.'IbHOrO KJIanaHa coxpaHHeTCH
HeH3MeHHbIM. O.n:HaJW K03<pqmI.{HeHTbI A H B He06xo1I.HMO nepeC'fH-
TaTb, TaK KaK nOCJ1e Bwxo.n:a nOHCK3 KJIanaHa H3 KaHaJIa rHC3.II:3
.n:aB.TIeHlIe 1I.elIcTByeT Ha n.Jl0lll.all,b CeqeHHH K.TIanaHa no ero nepl>HM
f . Ooc.'1e npH6.J1H)l{eHHOrO COBMeCTHoro peIlIeHHH ypaBHeHHH (35)
H (36) C .n:onYlll.eHHHMH OTHOCHTe.JIbHO h"" KOTopbIe 6bI.'IH ClI,e.1aHbI
npH peIlIeHHH ypaBHeHHH (13) H (14), IlO.JIyqHM
p,,=D;
. N.
PII=-+'lJJP,,;
'X
Ah,,+B=p,,-p:.
5*
67
T. e. no <POp Me 1:I Bl:I.ay paC'leTHbIe <pOpMy.1JbI ]lJIfI 'leTBepToro ::Hana
nOJIHVCTblO no.ao6Hbl <PopMYJ1aM npeLLbIAYl.I.{l:IX 3TanOB. OLLHaKO no-
CTOHHHbIe ljJleHbI H K03 qJHUHeHTbI ypaBHeHHH 6YLLYT HMeTb CJIeLLY-
lOll.(l:Ie 3HaQeHHSI:
D= ...J-
1; ,
p.uJU{ cp6.t V V
P A [ h" + ( C"I + j l6.t ) M ] + B -
saV" cp 2 .
f N B .
Asx aV Ii cp AsaV" cp ,
. "J ..At]l : . f [ i,At) ]
N=Pnl+ aV V A hKI+(C KI + M +B-
f..MC.. I f..M [2W(t)-Po]- h"l- h B , ; ,n
2a.V 2apa.V aV t! AaV Ii
( 1 . f (l-1j;) .'
'1);= t;= --r-
AaV x AaV"cp
fn(hn-h m } + f h 1
1;aV H cp SUV.r CD
f..6.t
')(=1+
2apaV
t'
, K.
T
AaV
JJJlTblU 3Tan: KJ1anaII LLBH)KeTCSI, ero nOSICOK HaxoLLHTCH BHe Iwa-
naHa rHe3LLa, OTCe'lHbIe OKHa OTKpbIBalOTCH. YpaBHeHl:IH 3Toro 3Ta-
na onHCbIBalOTCH BbIpa)KeHHHMH (13)-(15).
lllecTou 3Tan: rpaHl:I'lHble YC.1JOBl:IH 3Toro 3Tana nO.1JHOCTblO COB-
naLLalOT C YCJ10Bl:IfIMH BToporo 3Tana. Pa3.11:I'lHe 3aK.11O'laeTCH B
TOM, 'ITO BO BTOpOM 3Tane KJ1anaH nOLLHHMaeTCH, B llleCTOl\1 onyc-
KaeTCfl. B CBH3H C .3THM ypaBHeHHH 1:I paC'lenlble <pOpl\IYJlbI BTOpO-
ro 3Tana nO 1HOCTbIO npHMeHHMbI K llleCTOl\IY 3Tany.
CeOb.MOU 3Tan l:IMeeT OTHOllleHHe K BXOLLHOMY 1:I BblXOLLHOMY ce-
lleHHHM Tpy6onpoBOLLa, n03ToMy 6YLLeT paCCMOTpeH LLaJ1bllle. .
PaC'IeT npoQecca B BbIXO.n.HOM Ce'leHIfIf HafHeTaTeJlbHoro Tpy6o
npOBO)J.a y .pOPCYHKIf. TOnJ1HBO, nOCTynalOl.I.{ee B 06"beM OPCYHKM
V ff), pacnpe.rr.e,,'IHeTCH TaK. DpM nOLL"beMe Hr.TIbI 'laCTb TOnJ1MBa BbI-
TeKae-r Qepe3 pacnbI,,1MBaIOl.I.{He OTBepCTHH, LJ.pyraH QaCTb 3anO.1HHeT
06"beM, OCBo6o)KLLaeMbIH Hr:IO}1 npH ee LLBlJ)KeHMH, a 'laCTb OnaeTC5!
B 06"heMe B C)KaTOM COCTOHHl:IH. DpM nocaLLKe l:Ir.'IbI, KorLLa LLaB:re-
HHe yMeHblllaeTC5!, B LLH.1HHLLp LLBHraTe 15! BnpbICI<HBaeTCH Tonm-mo,
nocTym1Blllee B 3TOT nepl:IOLL B 06"beM V!Ii H3 Tpy6onpoBOLLa, a TaK-
)Ke TO!IJIHBO, BblTa.1KIIBaeMoe HL10H npH ee nocaLLKe; Bc.'IeLLCTBHe
68
Yl\IeHbllIeHlIH .n.aBJ1eHHSJ ptjj TOmIHBO B 06"beMe V tjj paCIlIHpSJeTCSJ H
4.aCTb ero BbITa.'IKHBaeTCSJ B Il.H."IHH.n.p .n.BHraTe."ISJ.
flepBblU 3Tan: Hr."Ia He no.n.HHMaeTCSJ, n03TOMY Ton.'IHBO OCTaeT-
CSJ B 06"beMe V tjj B OK aTOM COCTOSJHHH. fpaHIf1IHbIe YCJ10BHSJ 3Toro
3Tana onpeAe."IHIOTCSJ ypaBHeHHeM
dprf> '
a'vq,-=!TC T , (37)
dt
. HHTerpHpySJ 3TO ypaBHeHHe notl.'IeHHO, nOJIyqHM
D'
p..,=-, (38)
'f' X'
fJI,e
f T M C;I
D'=Prf>I+
2aVq,
fTMF(t- )
..l-
i
apaVrf>
f T M
X' = I +
2apaV I/.>
Tpy60npoBO.n.a B CBH3H C TeM, IJTO aMnJIH-
H3BeCTHa, CKOpOCTb C Il.eJIeC006pa3Hee
+ f T M PO
2apaV c/J
B BbIXO.n.HOM CelJeHHH
Ty.n.a BOJIHbI F ( t - )
onpe.n.eJISJTb ypaBHeHHeM
.' 2F (t - ) + Po _ PI/.>
C T =
ap up
rl" BTOpOi1 3Tan: HrJ1a q>OPCYHKH OTXO.n.HT OT ce.!I.J1a, H TOnJ1HBO lJe-
pe3 npOXO.n.Hoe CeIJeHHe Me}K.!I.y KOHYCOM HrJ"IbI H KOHYCOM Ce.!I..Ha
nocTynaeT B KaHa."I paCnbIJ1HBalOIlIHx oTBepcTHll. Doc.TIe Toro KaK
;J:aBJIeHHe B 3TOM KaHaJIe, T. e. .!I.aBJ1eHHe BnpbICKa, CTaHeT p6np >
> Pv" Ton.'IHBO Ha4.HeT nO.n.aBaTbCSJ B Il.HJIHH.!I.p .!I.BHraTeJ1SJ. nplIH-
Il.HnHa.'IbHO Bcer.n.a HMeeTCSJ HeKOTOpbIll npOMefKYTOK BpeMeHH, B
Te'leHHe KOTopOrO HrJ1a nO.ltHHMaeTCSJ, a BnpbICK TOnJIHBa OTCYTCT-
ByeT. DPO.n.o.'I}KHTeJ1bHOCTb 3Toro npOMe}KYTKa 3aBHCHT OT BeJIH4.H-
HbI .!I.aB.leHHSJ HatIaJIa no.n."beMa Hr.'IbI H .!I.aBJ1eHHSJ ra30B B Il.HJIHH.n.pe
,ZI,BHraTeJISJ. 4eM MeHbllIe Ptjjo H 60.'IbllIe Pv" TeM npO.!I.OJI}KHTeJIbHee
3TOT npOMe}KYTOK BpeMeHH. TeOpeTIf1leCKH HrJIa .!I.O.l}KHa no.n.HH-
MaTbCH npH .!I.aBJIeHHH P o, MeHbllIeM Ptjjo, no TO MY 4.TO 3aTH}KKa
npY}KHHbI q>OPCYHKH perYJ1HpyeTCSJ B aTMoc4>epHbIX YC.'IOBHHX, a
TOnJ1HBO BnpbICKlI'BaeTCSJ B Cpe.!I.Y C .npOTHBo.n:aBJIeHHeM. DpOTHBO-
.n:aBJIeHHe ,ZI,ellcTByeT Ha nJ'IOllJ,a.n.b f , onpe.!I.eJ1SJeMYIO noca.n.O'lHbIM
.n:HaMeTpOM KOHyca HrJIbI d xap .
,QaBJIeHHe
f
Pc/Jo = PI/.>o+- Pq'
fu-f
(39)
69
B ..aei1cTBlITe.1bHOCTlI no.a .aeHCTBlIel\! ClIJ1 j1HepI..I.1111 11 TpeHIIH
111".1a nO,.'J,HI1l\IaeTCH npl1 HeCKO,TIbI<O 60.1bllleM ..aaBJleHI1I1.
Bo BTOpOM ,nane ..aaB.1eHI1H 11 CKOpOCTI1 BrlpbICKa TOn.l11Ba pe3-
KO B03paCTalOT. npl1 CAe.1aHHbIX ..aOnYlLI.eHI15IX ypaBHeHI1H rpaHH'I-
HbIX YCJIOBI1H BTOpOrO 3Tana MmKHO 3anl1CaTb B BI1..ae
V dP<I>' .
a q,-=f T C T -l1cfPc-fJ-u,
dt
d 2 y' . f . . (
M' ---;y2+ By = (fu -fu)(prp-pq,oH-- up",. 41)
nepB H J1eH ypaBHeHH5I (40) xapaKTepH3yeT KO H eCTBO TOIl-
J1l1Ba B 06'"beMe V!J), Haxo..a5IlLI.erOCH B OKaTOM COCTOHHIm; BTOPOH-
06'"beMHYlO CKOpOCTb TOn,TII1Ba, nOCTvnalOll1.erO B 06'"beM V!J); Tpe-
THH - ot5'"beMHYlO CKOpOCTb BnpbIcKa TOII.'II1Ba; 'leTBepTbIH - Tpe-
oyeMYlO 06'"beMHYlO CKOpOCTb 3an0J1HeHHH Ton/IHBOM 06'"beMa, OCBO-
omK..aaeMoro npH no..a'"beMe HrJ10H <P0PCYHKH.
nepBbIH J1eH ypaBHeHHH (41) xapaKTepH3yeT CH.1IY fIHepI..I.HII
MaCCbI Hr.1IbI H ..aBRlKYlLl.HXCH C Heii ..aeTa.1IeH; B'fOpOH - CH.1IY LKeCT-
KOCTH CLKaTHH npYLKHHbI Hr,,'IbI; TpeTHH - ..aeilcTBl1e Ha I1rlIY ..aaB-
.'leHI1H P!J) 11 PrjJo; qeTBepTbIH - onpe..ae.1I5IeT ..aeikTBHe Ha Hr.'lY .lI:aB-
J1eHH5I p . 4T06bI COBMeCTHO pelllHTb ypamleHI1H (40) 11 (41),
He06xo..aHMO HaHTH CBH3b MeLK,rry HeH3BeCTHbI!\'111 PrjJ; P ; C c 11 Cu.
3TY CBH3b MOLKHO YCTaHOBI1Tb 113 ypaBHeHI1H Hepa3pbIBHOCTI1 ..aBH-
:tKeHI1H Ton.'lI1Ba B npoxo..aHOM Ce eHI1I1 no,lL KOtIYCOM I1r.TJbI, KOTopoe
MbI I1MeeM npaBo I1CnO.'Ib30BaTb BCJ1e,lLCTBHe npeJIe6pelKeHHH B.1II1H-
Hl1eM 06'"beMa no..a I<OHYCOM I1LTJbI pacnbImne.1H:
fH.CII=fPe'
MrHOBeHHaSI CKOpOCTb BnpbICKa TOnJ1HBa
(40)
(42)
C e =l1e V : V P -P'j;
CKOpOCTb B npOXO,lLHOM CeQeHHI1 no..a KOHYCOM IIr.1IbI
r-
I 2 V .
CH. = 1111 1/ p Prp-PtjJ-
nO,lLCTaBI1B nO.'IyqeHHOe BbIpalKeHI1e ,lL.TJ5I C It B ypaBHeHHe (42),
nO.1IYQHM
, k 2 ( ) (43)
ptjJ-P,. = p",-P,. .
BeJ1I1 HHa k, BXO,lLHIua5I B ypaBHeHl1e (43) .lI..TJ5I MHOrOCOnJ10BOrO
3aKpbITOrO pacnbI.'II1Te.15I, onpe.rr.e,;15IetC5I OTHollleHI1eM npoxo,lLHoro
CeQeHI1H MeLK.n:y 3anOpHbIMI1 KOHycaMI1 Hr.1IbI tI ce,lL.TJa H con.TJOBbIX
()TBepCTHH:
k = !lilt II .
!let e
(44)
70
MHHHMaJ1bHaH n.TJ:Olll.aJ],b f", npo-
XOAHOro Ce'IelUIH MeJKJ],Y KOHycaMH
Hr.'IbI H ceJ],.TJ:a 6YJ],eT COOTBeTCTBO-
BaTb MeCTY nepexoJ],a nOTOKa TOn-
.'IIma B l.leHTpaJIbHblH KaHaJI B HOC-
Ke pacnbIlIHTe.TJ:H (ceIIeHHe II-II
Ha pHC. 31). BeJ1HIIHHa ceIIeHHH Y
3anopHoH KpOMKH (ceIIeHHe I-I Ha
pHC. 31) HBJIHeTCH MHHHMaJ1bHOH
JIHllIb Ha HaIIaJIbHOM YIIacTKe noJ],'b-
eMa HrJIbI. .D.JIH cepHHHbIX paCnbI.TJ:H-
Te.'IeH J],H3eJ1eH 51M3 3TO COOTBeT-
cTByeT BeJIHIIHHe nOJ],'beMa Y MeHb-
llIe 0,005 CM.
.D.JIH pacIIeTa npoxoJ],HOH nJIO- PIIC. 31. CxeMa cepHi1Horo pac-
llI.aJ],H f", no reoMeTpHIIecKHM pa3- nWIIITe.TJ5I J{H3C.TJCi1 51M3
MepaM paCnbIJIHTeJIH (pHC. 31) C
YIIeToM pa3HocTH yrJIOB KOHYCOB ceJ],JIa H HrJIbI MOJKHO HCnOJIb30BaTb
BbIpaJKeHHe [31]
fH = 1t
. 1:\
sm-
2
1:\-T
cos-
4
[ dx-dpK ( 1 1 ) ]
Y+ --- X
2 1: TI
tg- tg-
2 2
jd . T\
X PK- sm 2
T 1 +1:
cos-
4
) ]1.
TI-T
cos-
4
[ + dx- d PK ( I
Y --
2 T
tg-
2
TI
tg-
2
(45)
B. Xeq>KeH npe.n:JIaraeT nOJIb30BaTbCH ynpOtl.leHHbIM ypaBHeHHeM
fll=1tsi n .2L [ y + dx-d pK ( - I )] dPK' (46)
2 2 T 1: 1
tg- tg-
2 2
B pa60Te {6] HCnOJIb3yeTcH ypaBHeHHe, He YIIHTbIBalOlll.ee pa3-
HOCTb KOHYCOB IIrJ1bI II ceJ],JIa:
f . 1: 1 (d I . )
1I=1tSIII 2 P"-2 ysmO \ y.
(47)
PaCIIeT npoxOJ],Horo ceIIeHIIH f", no ypaBHelUIHM (45), (46) II
(47) J],J1H cepIIHHoro paCnbIJIIITelIH J],II3eJIeH 51M3 H306paJKeH Ha
pHC. 32. TaM JKe HaHeceHa 01lIII6Ka B npOl.leHTaX npH paCIIeTe no
cpopMYJ1aM (46) II (47) no CpaBl-IeHIIIO C pacIIeToM no BblpaJKeHHIO
(45). 113 aHaJ1H3a I,PHBbIX BIIJ],HO, 'ITO <l>opMYJIa (46) He npHrOJ],Ha
71
D: lH paCLJeTa BeJ1HLJIIHbI f n,
TaK KaK npH ee HCnOJIb30-
BaHHH no Mepe nOD:oeMa
Hf.TIbI OlllH6Ka B03paCTaeT
H B D:nana30He 0,02 Y
0,04 C,1t COCTaB.1HeT
10-18%. <PopMYJ1a (46)
6bI.'Ia npeD:.'101KeHa ,'LJIH
paCLJeTOB B D:Hana30He l\1a-
.1:JbIX nOD:oeMOB Hf.'lL!.
Opn paCLJeTe no CPOPMY-
Jle (47) olllH6Ka B onpe.rr.e-
.1:JeHHH Be lHLlHHbI f"ll. YMeHb-
waeTCH no Mepe nOAoel\1a
lIr,,'lb!. OAHaKo TO.lbKO npn
TIOAoeMax i/ > 0,035 CAt
oWH6Ka M CTaHOBHTCH
MeHbllIe 5 % . ECJ1H pa3-
HOCTb KOHYCOB HfJ'lbI II ceD:-
la npeBbIllIae1' 1°, TO OllIH6-
Ka npII nOD:CLJeTe no cpopMYJIe (47) B03paCTae1'.
BbIpa)KeHHe (45) MO)KHO HeCKOJlbKO ynpoc1'HTb:
./HCM2 1
q ,1JH%
""--- I -- + -- -+ T- 7.0
--:- -I . .0
I :3 2
I
0,008
I
!
4006
4004
o
qOt
0,03
0,04 !/ CM
D;02
PHC. 32. 3aBHcHMoCTb n,,10ll.{aJJ.H f n OT
nO.D:'beMa HrJlbl y npH paC'-ICTe no 1j:J0PMY-
JlaM:
1 - (45); 2 - (46); 3 - (47)
f . T [ d -d p I I
II = :rt Sin -t- y + x 2 K (
tg-
2
)] X t
I (48)
"[1
tg-
2
x ( d - y cos T+T1 sin ) .
pK 4 2
OOJIYLJaIOmaHCH B 31'01\1 CJIYIJae norpelliHOCTb .1(n He npeBbIlliaeT
1,5%. Ha pHC. 33 nOKa3aHO H3MeHeHHe Ce1!eHHH Me)KD:y 3anopHbIMH
KOHycaMH D:.1:JH pa3.1HLJHbIX nOD:oeMOB HrJ1bI Ha Y1IaC1'Ke 01' d PK D:O d x .
B BblpaLKeHHe (44) D:JIH nOD:CLJeTa BeJ1HLJHHbI k BXOD:HT TaJOKe
K03cpcpHlJ,HeHTbI pacxoD:a ,'LJ'lH CeLJeHHH Me)KD:Y 3anopHbIMH KOHycaMH
H con.'lOBbIX oTBepcTHH. K03cpcpHllHeHT pacxoD:a D:.'lH npOXOD:HOrO
CeIJeHHH
1111=
(49)
.. ( ( fl/ ) 2
V f pK + \;"
nd 2
tD:e fp"/'i = - nOnepeLJHOe CeLJeHIIe II,eHTpa.'lbHOfO KaHa.1:Ja B
4
HOCKe paCnbI.'IHTeJ1H;
n - K03cpcpHII,HeHT conpOTHBJleHHH, OTHeceHHbIH K CIW-
pOCTH B CeLJeHHH II-II (CM. pHC. 31).
72
COOTBeTCTBeHHO A.'1H COn.10BbIX OTBepCTHH npH ec = I K03q,qJH-
qHeHT pacxo.rr.a
lC =
(50)
/ 1 GC-( £C K Y
3H3LJeHHe K03q,q,m.I.HeHTa !lu .rr..1H paCnbIJIHTeJIH, H306pmKeHHOrO
lfa pHe. 31, 6bI.10 onpe.rr.eJ1eHO npo.'1HBKOH Ha CTeH.rr.e nOCTOHHHOH
fH MM2
1,6
1,2
020
o,l; 010
0,05
D Y 0 .d d x
1,4- 1,6 1,8 2,0 2,2 2,4 d MM
Pile. 33. XapaKTcp H3MCHCHH5I CC'ICHIHI lIICLK.AY 3anopHbl1ll1l KO-
HycaMH lWH pa3.'III'-IHbIX nOD."bCMOB ur.lbl. PaCnblnllTC,1b cCplli1-
HbIM }1M3:
d pK 0,12 c.t/; d X 0,26 ct/; T, 60"; T 59"
no.rr.aLJH. )J.1H :OJTOrO 3aMepH.'1H .rr.aBJIeHHH B Kopnyce paCnbIJIHTeJ1H
nepe.rr. 3anOpHbIMH KOHycaMH B l{eHTpa.'1bHOM KaHaJ1e H CeKYHAHbIII
pacxo.rr. TOnJIHBa LJepe3 PH
paCnbIJ1HTeJIb.
Ha P HC. 34 nOKa3aHO
0,8
H3MeHeHHe K03q,q,Hl{HeH-
Ta pacxo.rr.a B 3aBHCHMO- fl.6
CTH OT LJHCJ1a Re .rr.J1}J
pa3JIHLJHbIX no.rr.'beMOB 0,4
Hr J1bI. 0
K03q,q,Hl{HeHT pacxo-
.rr.a !In llJ151 no.rr."beMOB Hr-
JIb! Y > 0,02 CM CTaHO-
BfITC5I 60J1blIJe 0,8. BeJIH-
LJHHa !In, B35ITa5I no KPH-
BbIM Ha puc. 34, MOIKeT
HCn0J1b30BaTbC5I .rr.JIH paCLJeTOB npOl{eCCoB BnpbIcKa. DpH ClleJ1aHHOM
.rr.onY1l.I.eHHH YCKopeHHe .rr.BHLKeHHH HrJ1bI onpe.rr.e.'151eTCH no q,opMYJIe
d 2 y 2(Y-YI) 2C u1
dt2 (M)2 M
5
5
6
7x10 3 R
"
PHC. 34. 3aBHcHMoCTb K031j:Jlj:JUI.\UCHTa pacxo.D:iI
CC'ICHII5I MCLK.AY 3anopHbIMli KOllycaMH paCnbIJlII-
TC.l51 OT 'Hlc.TJa Re:
1 - Y 0,01 c."; 2 - Y 0,02 CM; 3 - Y U,03 c.";
4 - Y 0,04 c,,; 5 - Y 0,05 C<t
(51 )
73
flo.n:CTaBHB BbIpmKeHHe (51) .n:mI BTOpOH npoH3Bo.n:HOH B 3aBH-
CHMOCTb (41), pernaSI 3aTeM ee COBMeCTHO C ypaBHeHHeM (40)
MeTo.n:OM KOHellHbIX pa3HocTeH H nOll.'1eHHOrO HHTerpHpoBaHHSI H
YllHTbIBaSI npH perneHHH 3aBIICHMOCTH, onpe.n:e.'ISIe:\IbIe ypaBHeHHeM
(43), 6y.n:eM Hl\IeTb
/
Z'}/
V Prp+ PcPI -2Pl 1 =
k;p
-)
I + k p +
2 '
r I /
+ V (x' V
'J
k p
'J
I + k p
21":'
...
,
) + - t - P 1 --.lEJL-2 p .
. 'I"::' '" 1"::' " Ii'
... ... a. cp
A;+ B'
P4'.-- , k 2 )
f"-f,, (I--
2
(52)
(53)
rJJ.e
/1cfc M .. I 2
X'= V p
f2 aV 4>
2 k 2 + k7
k cp =
2
f T M C;I
D' = P4>I +
2aV4>
fm M
1;' = 1 + '
2apaV 4>
frMF (t- )
+
apaV 4>
2M'
A'=- , ()"
(L\t)2 T ,
B'= (f - f ' ) _ 2M'y, _ 2M'Cul _ f ' ( 1_ ) P
" II P4'O (M)2 M U I + k2 l{"
+ f T M PO + fUYl ;
2ap aV t/J aV4J
flOJIYlleHHbIe .n:Ba aJIre6paHlleCKHx ypaBHeHHSI C .n:BYMSI HeH3Be-
CTHbIMH MOLKHO pernHTb COBMeCTHO TOJIbKO rpa<pHllecKH. 3a.n:aBaSICb
pa3J1HllHbIMH 3HalleHHSIMH y, HaH.n:eM 3aBHCHMbIe OT 3Toro napa-
MeTpa K03<p<pHllHeHT k H n.'10111alI.b f 1i' flouIe :'!Toro onpe.n:eJIHM y
no ypaBHeHHSIM (44) H (45). 3aTeM B Koop.n:HHaTax ptjj, y nocTpoHM
.lI.Be 3aBHCHMOCTH Ptjj OT y, nOJIYlIeHHbIe no paccMaTpHBaeMbIM ypaB-
HeHHSIM. TOlIKa nepecelleHHSI KpHBbIX lI.aCT HCTHHHbIe 3HalleHHH ptjj
II y. K03<p<pHI.{HeHTbI paCXOlI.a tH H /lc Ha3HallaJOTCSI no 3KcnepH-
MeHTaJIbHbIM .lI.aHHbIM.
74
YpaBHeHHe 6a.'IaHC3 TOfI.'1HB3 J(mI YC.'10BHCI, KorA3 npH nOADeMe
HrJlbI BnpbICK Ton.'1HBa OTC)'TCTB)'eT, a ypaBHeHHe J(BH./KemI5I Hr.'IbI
Jte H3MeH5IeTC5I,
dp</J '
aV</J- =fTCT-fuCu o
dt
(54)
Ooc.TIe npH6.1H)J(eHHoro pellleHH5I ypaBHeHHH rpaHHI.J:HbIX- yCJ10-
B'HH nO.'IYI.J:HM
- - .
P q ,- s' s'aVI/>'
A'y+ B'-(fu-f )p</J = f P'I"
(55)
(56)
Be.'1H'lHHY P MO)J(HO onpe.ne.1JMTb npM COBMeCTHOM
ypaBHeHHH (55) H (56):
D' '" [
T- 'uV
P _ t/J
rjJ-
peweH11H
f PIj-B
A'
]
(57)
fu (fll-f )
IT
'A'uVI/>
r,lJ,e
, f T 81F ( I - L a ) f
f T M C T1 + -'_ TMPO + 'llY' 0
D'=P</JI+ ,
2aV tjJ apaV tjJ 2ap\-' rjJ aV I/>
3Ha'leHH5I OCTa.'IbHbIX K03<p<pH HeHToB OCTaIOTC5I 6es H3MCHeHH5I.
BnpbICK TOnJIHBa H3'lHHaeTC5I, KOr,lJ,a P; > Pv,.
TpeTuii 3Tan: HfJ13 npH)J(aTa K ynopy, rp3HH'lHbIe YC.'IOBH5I on-
pe.!Le.l5IIOTC5I ypaBHeHHeM CnJIOlllHOCTH JJ:BH)J(eHH5I .Tonmm3 B pac-
CM3TpHBaeMoM ce'lemm:
dptjJ' ,I 2"" V '
aVtjJ-=fTCT- tcftCp=fTCT-/lcfc V - P</J-Pljo (58)
& p
r1oc.'Ie npH6ml)J(eHHoro HHTerpHpOBaHH5I ypaBHeHHH (58) n He-
KOTOpbIX 3.'Ire6p3HI.J:eCKHX npeo6pa30 B3HHH no.TIY'lHM
V P</J+p q )I-2PI( = - :i, + 1/ ( ; , r + r + p</JI-2pw (59)
r,lJ,e
f T M C;I
D' = P</JI + 2aV</J
cfcM V V
X' =
V2uVtjJ
' = f T M + 1;
2ap[lV </J
fTMF (t- )
-j-
apaV</J
k 2
AI
1 +k
f T M PO
+
2apaV I/>
75
B paCCMaTplfBae IOM 3Tane BeJWqUHa k;, nOCT05lHHa5l, TaK KaK
Ur,1Ja npH)KaT K yn IJ py .
lJeTBepTblU 3Tan: Hr,1a OnVCKaeTC5I JJ.O l\IO:\leHTa nOCaJJ.KU ee Ha
CeJJ.,10. 06bIqHO n\)U paCqeTe npOll.eCCa BnpbICKa na 3TOM 3Tane
06"beM KaHa,rIa nepe.:{ paCnbl,,1llBaIOllUI!\HI OTBepCTllHMll V 1'1< BBllJJ.Y
ero Ma,1JOH Be 111qIUlI:,I lie VqllTbIBa,l111. Ho B pa60Te [53] 6bIJ10 cJJ.e-
J1aHO npeJJ.no.'IO)KeHI:le, qTO' B KOHlI.e npOll.eCca nOJJ.a'Ill Ton,1HBa npo-
HCXOJJ.llT BbDKlll\1aHll('> Ton.1HBa KaK ll3 3Toro KaHa.1a, TaK II 113 OTHO-
C5IWeHC5I K HeMY qal:'TH o6"be:\Ia no KOHYCOM Hr.1bI (CM. pIlC. 31),
'11V HlJC ICW uOTHUB IOH npHqHHOH 3aKOKCOBbIBaHll51 paCnbJ.TIllBaIO-
mHX OTBepCTllll. J],O.liillHoro 3KcnepHMellTa.:1bHOrO H TeOpeTH'leCIWrO
nOJJ.TBepLKJJ.eH1l51 3Ta Mb1C 1b ewe He nO.'1V4llJ1a. OOnblTKH yqeCTb
B.7!Il51 HIle .3TorO 4J a KTopa Ha npOll.eCC B pbICKa JJ.e 1aJIHCb HeOJJ.HO-
KpaTHO {53]. B CB5I3tI C .3TIlM B.'1ll5llme 3Toro 06"beMa 6YJJ.eT TaIOKe
yqllTbIBaTbC5I II B nPeJJ..'laraeMOM Hll)Ke MeTon.e, npllqel\1 llaB.'1eHlle
TOnJ111Ba B 06"beMe v PK npllMeM paBHbIl\I Be.'lllqllHe p;. YpaBHeHll51
rpaHllqHbIX YC.l0BUG paccMaTpllBae:VIoro .3Tana 3amUlleM B Bun.e
dpt/J . C . ( 2" V ' ' )
av.1> -;It = tr ";,-ft"' } P P,p-ptjJ-(fu -fu C u ;
dp _ -. /2 _; , . -. /2 V ' , ,
aVpK-;jf-rJII V p r P,p-ptjJ- cfc V p fJtjJ-plj-fuCu,
(61 )
(62)
(60)
M d 2 y --' ' .' ,
u dj2-f'. (jy = (fu-fu)(ptjJ-p,po) + tu(PtjJ-P'j)'
OpllMeH5I5I noq.'1el-IHOe uHTerpllpoBaHlle II COBMeCTHO perna51
ypaBHeHll51 (60) II «)2), nO.1yqllM
D' r ( ' 1' )
/F,p= ' -- {:.v f/ [- la-z cv Prf- 6 /y+ff; (63 )
( h' + ) y- fu £ p =N'+x,,1/ ( 1 (fu--:f » ) IfJ4>+H +b'y-
a K 4> V
-X" 1 V b 1y -( fu f ) P,p+ H. (64)
YpaBHeHll51 (63) (64) nOJ1yqeHbI Ha OCHOBe B3aIlMOCB5I3ll Me-
)KJJ.Y Hell3BeCTHbIMll, onpeJJ.eJ151eMOH ypaBHeHlleM (62), KOTOpa51 B
COOTBeTCTBllii co cn.eJIaHHbIMII .zt.onyweHll5lMll 6bIJ1a BbIpa)KeHa B
BllJJ.e
h4J == b y + B
fu-f
PIjJ'
f
76
B npHBel!.eHHbIX ypaBHeHHHX
f T M F (t_.i... )
D' = f T M C;I a fu-f
I + V. + Pqd + V
2u\ ,p apu ,p <J. ,p
tllM . / 2
V P
V 2uV IjJ
. .. f Yl
H=PIjJI+B+PIjJ" N =pIjJI-B+-:
aVp
/2
f.lcfc M 11 -
x'" = P
V2 aV pK
2M'
H' = B+p .; b' =
f (ill) 2
YI;
f r M
=1+
2apn V IjJ
x=
x" =
f.lnMV+
".2 nV pK
fu-f
B = P"'I +Pa+b'YI
f 'P
2M'C UI
f /':,.l
lXJ1H COBMecTHoro peWeHI1H ypaBHeHI1H (63) H (64) I1CnOJlb3yeM
HaH60.llee npneM,;'1eMbIit B pacC\laTpnBaeMOM C,;'1Y4ae rpaqm4ecKHII
MeTOl!.. 3a.'J:aBaHcb HeCKOJlbKI1;.m Be.'1H4HHaIvIH y, onpel!.eJIHM l!..'1H
Ka}/{l!.Oro H3 HHX 3Hal./eHfte n.'1ow:a:UJ {n. 3aTeM no no.1Y4eHHb1M
3HaqeHHHl\I In H3 ypaBHeHHH (63), a TaJOKe H3 ypaBHeHHH (64)
HaHl!.eM cooTBeTcTBYlOW:He Be.'1H4HHbI pg;. lXa,;'1ee nOCTpOIil\I 3aBIi-
CHMOCTH ptjj = f(y), n0J1Y4eHHble no ypaBHemIHM (63) H (64). T04-
Ka nepeCeqeHHH :,JTHX 3aBHcHMocTeH onpel!.e.'1HT HCKOMbIe Be.TJIi'IHHbI
pg; H y. I13.TJOJKeHHbIH MeTOl!. Y4eTa BJIHHHHH Ha npOIxecc BnpbIcKa
o6'bervIa V p» BbITeKaeT H3 o6w:eH TeopHH npou.ecca BrIpbICKa TOrI-
JIHBa H n03ToMY HB.l51eTCH 60,;lee T04HbIM H3 npeJl:,;l.o)J eHHbIx l!.py-
rHI\IH aBTopaMH.
ECJIIi He Y4HTbIBaTb BJ1HHHHe 06"beMa V p » Ha npouecc BnpbICKa,
TO ypaBHeHHH BToporo 3Tana .nommCTblO npW,\1eHHl\1bI ..1.'151 paC4eTa
npouecca B lleTBepTO!\l 3Tane.
I1r.'1a HallHHaeT OTXO.'J:HTb OT ynopa npn .J.aB,;lemIli
(tu-f )Pt/>o+{)'YM-f (1 k )p
p, (' I )
. k;"
fu-f ll I C}
\ I +k;,
(65)
nOCJIe nOcal!.KU Hf,;'1bI Ha cel!..'1o Ha41IHaeTCH nepHOl!. OCTaTOHHbIX
:KOJIe6aHHH l!.aB.TJeHHH. Y CPOPCYHKI1 B nOM nepl1o.n.e, KOTOpbliLNOJK-
77
HO Ha3BaTb n5lTbIl\I 3TanOM, npou.ecc paCC'lHTbIBaeTCH no ypaBHeHH-
HM nepBoro nana. Y Hacoca 3TOT nepHO.ll., KOTOpbIH MbI paHee Ha-
3BaJIH Ce.ll.bMbIM :HanOM, paCCIIHTbIBaeTCH no ypaBHeHHHM BToporo
3Tana. OpH 3TOJ'i;] npou.ecc npOBepHeTCH Ha AOnOJ1HHTeclbHbIe
BnpbICKH, TaK KaK npH paClJeTe 6e3 YlJeTa BH3IWCTH OCTaTOlJHbIe
Ko.1Je6aHlIH 6YlI.YT He3aTyxa101llHMH. Ha 3TO 1 paClJeT npeKpa-
w.aeTCH.
OCTaTO'.IJIOe .lI.aB.1JeHHe B CHCTeMe onpe.ll.e.'IHeTCH npH6.'IH)KeHHO
B 3aBHCHMOCTH OT YCJ10BH1I OKOHlJaHHH npou.ecca BnpbICKa. EC.'IH K
MOMeHTY OKOHlJaHHH nO.ll.alJH Ton.1JHBa HarHeTaTeJ'IbHbIH K.1JanaH ce.'!
Ha rHe3.l1.0, TO, onpelI.eJIHB .lI.aB.1JeHHH P H pifJ, a TaK)J{e ellJ,e .lI.aB.'1e-
HHH B HeCKO.lbKHX CelJeHlIHX Tpy60npOBO..'l,a, HaXO.ll.HM Be.1JWlHHY Po
KaK Cpe.ll.Hee apH<pMeTlJIleClwe:
P + Plr + P2r + ... + Pnr + Pt/J
Po= ,
n+2
(66)
r.ll.e PIr, p2r, ..., pm - .lI.aBJleHHH B pa3.'1HlJHbIX CelJeHHHX HarHeTa-
Te.lbHOrO Tpy6onpOBO.ll.a.
ECJ1H K MOMeHTV nOC8,lI,KH Hr.lbI Ha Ce,lI,JIO HarHeTaTe.'!bHbIH K.la-
naH He ce,,'I H8 rHe3.l1.0, TO, lJTo6bI onpe.ll.e.1HTb BeJIHlJHHY Po, Heo6-
XO.ll.HMO paCClJHTaTb KOJ1HlJeCTBO TOnJ1HBa, OCTaBlllerOCH B CHCTeMe
B C)J{aTOM COCTOHHHH:
v = aVePep,
rlIe PCP - cpelI.Hee ,lI,aBcleHHe Ton"lHBa B .'II1HHI1 HarHeTaHI1H, onpe-
lIe.1HeI\We <pOpMy.1JOH (66). LJ:acTb C)KaTOrO TOnJIHBa nOH.lI.eT Ha 3a-
nO.1HeHHe 06'beMa, oCB060)J{.lI.aeMOrO npH nOCa.ll.Ke HarHeTaTeJlbHblM
I\.'!anaHOM. KOTOpbIiI lIO.,!)J{eH npoHTH ew.e nYTb h K " a OCTaJlbHoe
Ko.:1HIIeCTBO Ton.1HBa onpe.ll.e.TJHT Be.'IWlHHY OCTaTOlJHOrO .lI.aB.'!eHlIH.
Be.'IHlJHHa 3Toro lIaB.1JeHHSI
V-fKhKl ( 67 )
Po = \ 1 .
a e
OpH pa3pe}KeHHH He06xolIHMO BbIlJHC.'IHTb 06'beM, He 3anOJIHeH-
HbI1I Ton.'1HBOM. B 3THX YC.1l0BHHX <popMy.1Ja (66) onpe.ll.emn yC.'IOB-
Hoe OTpnu.aTe.'IbHOe .n.aB.'!eHHe Po. Be.lw.umy OCTaTO'-!HOfO 06'beMa
MO}J{JIO npH6.'ImKeHHO HaHTlI no <popMy.'Ie
V oe = -aVcpo' (68)
Kor,lI,a KJIanaH Ca.ll.HTCH Ha fHe3.l1.0 nOCJle npeKpallJ,eHHH nO.ll.aGH
Ton.'IHBa, a B .'!HHHII HarHeTaHHH C03,lI,aeTCH pa3pe)J{eHHe, TO .lI..'IH
MOMeHTa nOca.ll.KH Hr.TJbI Ha ce.J,.'IO Be.'!WIHHY V vc npH6.'!H)J{emw
MO)J{HO BbI'-!HC.1HTb TaR:
Vne=f"hK+aVCpo. (69)
3Ha'-!eHI15! Po H V vc npH6mI)J{eHHo MO)J{HO onpelIeJ1HTb TaK)J{e no
6aJIaHcy TOfl.1IHBa 3a BeCb npou.ecc BnpbIcKa [5].
78
Pac eT npoL{eCCa nO,lI,aIJH TOnJ1HBa, KOr,lI,a B J1HHHH HarHeTaHHSI
nepe,lI, HalJaJ10M BnpblCKa HMeeTCJI CB060,lI,HMH 061>eM. CB060,'J,HbIe
06"beMbI nOHB.15IlOTCH npH I-JapYllleHHH Cn.'lOlllHOCTlI ABlDKeHHH TOn-
JIlIBa. DbIJIO YCTaHOB.'1eHO (16}, 'ITO 113-3a pa3pbIBOB Cn.l0lllHOCTH B
KOHI.I,e npou.ecca BnpblCKa B CHCTeMe B03HHKalOT OCTaTO'IHbIe 06"be-
MbI, npeHe6peMeHHe KOTOpbIMH BHOCHT B paC4eT nOrpelllHOCTb .n.o
40 % H 60.1ee.
J1. H. [0.ly6I<OB c.n.e.'la.l nepBYlO nOnbITKY 3KcnepHMellTa.lbHO
onpeAe.1HTb Be.'1I1'IHHY V oc JI pacnpe.:re.'leHHe 3Toro 06"be!\la no .1HHHII
HarHeTaHHH.
OpH pac4eTe 6bI.l0 npHHHTo, lJTO cB060.n.Hble 06"bel\lbI cocpe.n.o-
TOlIHBalOTCH B lllTyu.epe Hacoca V'Ii' HarHeTaTe.lbHOM Tpy60npoBo.n.e
V T H paCnbIJ1HTe.1Je q,OPCYHKH V g;, npH'IeM 3TH 06"beMbI pacnpe.n.e-
J1HlOTCfI TaK:
V CH = V OCT _ Vocq,
V' V T - Vq, .
H
(70)
OpH paC'IeTe 6bI.l0 CAe.laHO .Z10nYllleHHe 0 He3Ha'IHTe.!IbHOCTH
B.1JHflHJIH Ha npou.ecc B!1pbICKa B03.n.yxa H napOB TOn.1lIBa, HaXO.Z1H-
lllHXCH B CB060.Z1HbIX 06"bel\Iax, B CBH3H C 'IeM 3TO B.1JHHHlIe He YlJH-
TbIBaJIOCb. )],aB.leHHe B CB060.Z1HblX 06"be1VIaX 6bI:J.0 nplUIHTO paBHbDI
HY.llO.
. OepBbIH 3Tan .110 MOMeHTa HalJa.la nO.Z1"be:VIa HarHeTaTe.'1bHOrO
K.lanaHa coxpaHfleTCH HeH3MeHHbIM. K.'lanaH Ha'IHeT no.n.HlIlVIaTbCH
npH .Z1aBJ1eHHH P'Ii = PH., TaK KaK .Z1aB.'1eHHe Po = O.
BTOpOH ::lTan OT.'1H'IaeTCfI OT COOTBeTCTBYlOlllero 3Tana B c.'1Y'Iae
Po =1= 0 TeM, 'ITO K.lanaH. nO.Z1HHl\IaHCb, He BbITeCHHeT TOnJIHBO B
HarHeTaTeJIbHblH Tpy60npOB0.Z1, a TOnJ1HBO TOJIbKO 3anO:J.HHeT ny-
CTOTbl 06"bel\Ia V .
CJ1e.Z10BaTe.lbHO, B Te'IeHHe HeKOToporo BpeMeHH, nOKa 06"be.M
V oc 'Ii He 3anOJII-IHTCH Ton.'lllBOM, .n.aB.leHHe P = O. B 3THX YCJ10BH-
HX ypaBHeHHH rpaHH'IHbIX YCJIOBHH 6y.n.YT HMeTb c,rre.n.YlOlllHH
BHZ!:
,-
(XVII d;H = fnCn-!lofo 1/ 11 PH-Pec-!"C,,;
d c H = ' t C .
dt T " 10
(71 )
(72)
M d2h" -L "' h .L f - f
dt 2 ,u" I "p" - "PH'
(73)
B ypaBHeHHH (72) nepe.Z1 npoH3Bo.n.HOH dV OCH CTOHT 3HaK «MH-
dt
HYC», TaK KaK 06"beM V oc H yMeHblliaeTcH.
79
OOCJ1e npH6JIH}KeHHOrO perneHlUI ypaBHeHHH paCCMaTpI-lBaeMOrO
3Tana nOJ1YLfIlM
j) , f ( j) ) 2
VPII+PIII-2P.( = -2f+ V 2f +D+P"I-2P.C;
V OC H-VOCI<, = f"(h,,-h,,,);
Ah,,+ B=PII'
(74)
(75)
(76)
B HarneM c.'lYlJae perneHIIe ynpolllaeTCH, nOTOMY lJTO ypaBHeHlle
(76) AaeT HenOCpe.lJ.CTBeHHYIO 3aBliCHMOCTb h g OT PH. HCnO.1Jb3YH
KOTOpylO, MmKHO pernIlTb OCTa.'lbHbIe ypaBHeHIIH. EC.'lH K MOMeHTY
BbIXO.l1.a pa3rpY}KaIOU{erO nOHCRa H3 K.'lanaHa rHe3.l1.a 06'beM V OC H
He 3anOJIHHTCH TOnJIHBOM, TO ypaBHeHHH (71) H (72) H3MeHHTCH
TeM, lJTO B HHX nOHBHTCH lJJ1eH. xapaInepH3YlOlllHll RO.'lHlJeCTBO Ton-
JIHBa, nepeTeRalOLl{erO B 06'beM V lJepe3 ll.'lOma!l,b fUj' T. e. no-
JIYlJHM
aV" " =fnCn-PofoV V P,,-P.c -P,i u ,}/ V p" -f,,C,,;
(77)
dV C.1I (2 Y - ,
dt = p 14 f'l{ P P" --r- f"C". (78)
BH.l1. ypaBHeHl1H (73) He H3MeHlITCH, TO.TIbKO BMeCTO fg B Hero
HV}KHO nO!l,CTaBHTb f ' .
. "
Ooc.'le npIl6.'lmKeHHoro perneHlIH ypaBHeHMI paCCMaTpl1BaeMOro
3Tana no.aY'IHM
'I." , f ( '"I." ) 2
YPII+p"I-2P6C = -2+ V +D+P"I- 2p.,:
V V trlif14.cP A t ' /2 f 2 '
c.,,- oc.I<I= Y2 V p1 PII+P"I- P.c-r-
+ f"PII _ f"B - f 'h .
A .4 " "I>
Ah,,+B =P/i"
(79)
(80)
(81 )
OpH perueHHH ypaBHeHl1li
'lHHe h"" nO!l,C'lHTaHHo[I
perneHHl1 ypaBHeHHH (73);
f.luJ'ijM' / 2
V pj -L
_ Y P" I PHI
V 2
Ma (PH + PHd 3HalJHTe.'IbHO npeBbIrnaeT Be.'lHlJHHY 2PBC' 3TO ,lJ,ony-
llleHl1e He BHOClIT 3aMeTHOH norpernHOCTII B pe3y.'lbTaTbI paClJeTa.
n.'lOllla,rtt f"Uf onpe,lJ,eJIHeTCH no BemI-
npH6;IH.tKeHHO, TaR }Ke KaK npH
B nO.l1.KOpeHHoe BbIpa2KeHHe lJJIeHa
BBe,lJ,eH lJ.'IeH 2Pec. BBI1.l1.Y TOro, lJTO CYM-
so
C.'IeJl,OBaTeJIbHO, KO.1HlJeCTBO TOnJIHBa, nepeTeKalOwerO B 06"b-
eM V lJepe3 nJIOlltaJl,b f14' MOiKHO onpeJl,eJIHTb no <POp MYJIe
I-'-l4flll cp/j,t V 2 .
p V PH + p;;! - 2PBC" Ooc.'Ie 3anO:IHeHIUI 06"beMa V;c Il
1 2
Ton,lHBOM npou.ecc B llITyu.epe Hacoca paCClJHTbIBaeTcSI B COOTBeT-
CTBHH C 3TanaMH no paCCMoT-
peHHbIM <popMYJIaM.
Cor.TIaCHO npHH51TOMY Jl,O-
nyllteHIIIO 0 pacnpeJl,eJ1eHHH
OCTaTOl/HOrO 06"beMa pa3J1,e-
JIHM 06"beM V OC . T lIa m paBHbIx
IJ:aCTeH, HaxoAHlltHXC5I oJl,Ha OT
Jl,pyroH Ha paBHWx paCCTOSI-
HH5IX. Do Mepe nocTynJIeHHH
TomUIBa 3TH 06"beMbI 6YJl,YT
3an0.1HHTbCSI. DpH6JIHiKeHHaH
Kapnma 3anOJIHeHHH OIJ:epeJl,-
Horo CBo6oJl,HOrO 06"beMa,
pacnO.'IOiKeHHOro OT BXOJl,HorO
ce'IelIIiH Ha paCCT051lIHH li, no-
Ka3aHa lIa pHC. 35, CJ1eBa OT
3anOJIH51eMOrO 06"beMa CnJIOllI-
1I0CTb nOTOKa BOCCTalIOBJ1eHa,
11 npou.ecc B 3TOH IJ:aCTH MO-
LKeT pacc'UiTbIBaTbcH no npHBeJl,eHHbIM paHee ypaBHeHH51M.
B CBSI3H C TeM, IJ:TO po = 0 Ii P (li, t) = 0, no.'IYlJHM
C(li, t)= F ( t- ) ;
ap a
teeK
-
--...:::- ::::.-====--
-- '%"% ::::.
-
.:::::-:::::::--
-..:::::- ..::::::--
- ..::::::-
L MI'f
Pile. 35. CxcMa pacnpocTpaHeHI1H BO.1H no
Tpy6onpOBO'!\Y npu Ha.TJWlHH B HCM o6"be-
MOB, HC 3ano.TJHCHHb!X TonmmOM:
CII lOllIHble .1UIHHll - BO.'IHbI no,aa1.J1I F(t); IIlTpH-
XOBble - oTpaMeHHLIe BO;lHbI 117(1)
(82)
Ifl (t + ) = F (t _li. ) .
,a ,a
(83)
Cor.'IaCHO pHC. 35 BHaqa:lC 3an0.1HHCTC5I ncpBbIH 06"bClVI, pacno-
llOLKeHHbIH Ha paccToSIHIiH 1 OT BXOJl,HorO CeT.JeHHH Tpy60npOBOJl,a.
OJl,HOBpeMeHHo C 3an0J1HeHHeM 06"beMa K Hacocy nOJl,XOJl,HT OTpa-
LKeHHbIC BO.11IbI W (t + -;-). 0603HaQHB (.<1 Ii t"I - BpeMSI HaT.JaJ1a II
V DC T 1
OKOHT.JaHII5T 3anO.TIIleHH5T 06"beMa , rJl,e IiHJI,eKC 03Ha'laeT, '1TO
m[
06"beM paCnOJImKeH lIa paccT05THHH 1 OT BXOJl,HOro CeQeHHSI Tpy60-
npoBona, a TaKiKe Y'lHTbIBa5! BbIpaLKeHHe (82), HanHllIeM
I K1
f F ( t--.£.)dt= VOC.T . (84)
ap . a , m
till
6 3aKa3 748
81
YpaBHeHHe (84) JI,aeT B03MmKHOCTb onpeJI,e.iIITb BpeMSI 3anO,'1-
HeHHSI 06'beMa !'1't I = t"I - t >iI. 3anOJIHeHlIe BToporo 06'beMa, pac-
nO.'1mKeHHOro Ha paccToSIHlI1i 21, HalIHHaeTCSI lJepe3 oTpe30K Bpe-
MeHH
t 1l2 = 'tl+
a
noc,,'1e Ha l Ia.1a nOJI,alJH Ton.ilIBa B Tpy60npOBO)]..
.IJ.JISI ::Horo YlJaCTJ{a TaK>Ke cnpaBe)]..iHBO ypaBHeHHe
t
2 f K2 V
----!... . c F ( t - ) dt = ,
ap .1 a m
t H2
oTKy)].a
't2 = t K2 -t H2 .
B CBSI3H C TeM, lJTO F (t--;.)+ F (t- ), nepUO.ll.bI 3anOJIHe-
HHSl 06'beMOB He paBHbI, T. e. 'tI -=1= !l't 2 .
nOC,,'1e)].HHH 06'beM HalJHeT 3anOJiHf!TbCf! 3a BpeMf!
m-I
tllm = 1: Ll'td- :1
Ill=I
nOCJ1e HalIaJIa nO)].alJH TOnJIIiBa B HarHeTaTeJ1bHbIH Tpy60npOBO)]..
.IJ..if! 3Toro YlJaCTKa TaKLKe HanHllleM ypaBHeHIIe
t
2" Km V
f F ( t-:!!!... ) dt= .
aPT v a m
t Hm
06'beM V oc.g; HalJIIHaeT 3anO.'1HSITbCSI lJepe3 oTpe30K BpeMeHH
III L
t ll ",= 'ti+ '
m=I
npHlJeM II )].JIf! 3TOro 06'beMa l\1Q)KHO HanIIcaTb ypaBHeHIIe
tKef;
2f T f F (t- ) dt = V oc .4>,
ap \ a
t 1l 4>
KOTOpoe )].aeT B03MOLKHOCTb OnpeJI,eJIIITb BpeMSI 3anOJIHeHlISI OCTa-
TOlJHOrO 06'beMa V oc.g;.
nOC.'1e TOrO, KaK BCSI CHCTeMa 3anOJIHIITCSI Ton.TIHBOM, paClJeT
npo ecca ,lJ,O.'lLKeH npoH3Bo)].IITbCf! no TeM LKe 4>opMYJIaM, lJTO II npii
po > O. Y 4>OPCYHKII 3TOT nepIIO)]. paClJeTa HalJHeTCf! lJepe3 OTpe30K
BpeMeHII
m
! NtI+ 'tt;b+ '
m=I
82
npH'.J.el\I B nOT J\IOMeHT K 4>opCYHKe nO.lLOH.lLeT BOJ1Ha, 06pa30BaB-
UlaHCH Y Hacoca Ilepe3 OTpe30K BpeMeHl1
m
't.+ 't",
__ I 't'
m=I
nOCJIe HaIlaJ1a no.n.aIlH TOnJ1IiBa B Tpy6onpoBO.lL.
TaKl1M 06pa30M, npH HaJ"mIlHH V oqp n05IB.J15IeTCH .lLonO"lHl1TeJ1b-
HbIH 3Tan, npO.lLOJ1lliHTe.'lbHOCTb KOToporo paBHa BpeMeHH 3anO.'IHe-
HHH TOnJ1HBOM 06"beMa V oc.!p, rpaHH'IHbIe YCJ10BHSI 3Toro 3Tana on-
pe.l1eJISIIOTCSI ypaBHeHHeM
.' dVoc.cp
tTC T = --.
dt
(85)
BBH.lLY npOCTOTbI paCIleTa 3aTpaTbI BpeMeHH Ha YIleT V oc 6Y.lLYT
He3HaIll1Te.lbHbIi\Il1. O.lLHaKO C.l0lliHOCTb B 3TOM C.'IYIlae 3aK.'lIOIlaeTCSI
B TOM, IlTO HaIla"lbHbIe YC,,10Bl1H paCCIlHTbIBaeMoro npou.ecca BnpbIC-
I{a He113BeCTHbI. OpHXO.lLl1TCSI .lLe.laTb HeCKO.'1bKO paCIleTOB: nepBbIH
np0113BOJ.I.l1Tb B npeJ.I.n0J10llieHHH, TO po = 1 KFlcM 2 , HJIH 3aJ.I.aTbCH
HeKoTopbIM 06"beMOM V nc, BTOpOH - npH
V = V oco + Voc,
oc 2
H T. .lL., nOKa V oc = const. OnblT nOKa3bIBaeT, 'ITO J.I.JIH onpeJ.I.e.'IeHH5I
J.I.eHCTBl1Te"lbHbIX HaIlaJ1bHbIX YCJIOBHH HHorJ.I.a He06xoJ.I.HMO npOBe-
CTI:I 5-6 paCIleTOB. C npHMeHeHl1eM U.l14>POBbIX BbI'Il1C.'1l1TeJIbHbIX
MaUlliH BbInOJIHeHl1e 3TOH 3allaIlli 06JIerIlaeTCSI. 00l106HbIM MeTO-
.lLOM MOlliHO onpe.ll.eJ1IITb 11 peaJ1bHOe OCTaTOIlHoe .lLaB.'1eHl1e, KOTO-
pbIM npl1 pacIleTe B 60.'1blIJl1HCTBe c.'1YQaeB 3a.lLaIOTCH npH6JIII-
llieHHO.
Pac eT npOl\ecca BnpbICKa CUCTeM C OTKpbITbIMU «)JopcYHKaMH.
Opl1MeHeHHe OTKpbITbIX 4>OPCYHOK He BHOCHT H3MeHeHHH B MeTOllH-
KY paCIIeTa npOl\eCca Y Hacoca. PaCqeT npOIJ,eCca y 4>OPCYHKH 3Ha-
qIITeJIbHO ynpow.aeTCSI BBH.lLY OTCYTCTBHSI Y nOCJIellHeH 3anopHoro
opraHa, B pe3YJIbTaTe llero lIlIC.'IO 3TanOB cOKpaw.aeTCSI 110 011Horo.
B paCCMaTpliBaeMbIX YCJIOBHHX Ha OCHOBe ClleJIaHHOrO paHee 110ny-
w.eHIISI MOlliHO HanHcaTb ypaBHeHHe 5epHY.'1.1H:
p 2 P ,2
Pcp-Po=- CC+-C T .
2 2
BBHJ.I.Y Toro, IlTO OTKpbITaSI 4>opCYHKa npaKTHIleCKH He HMeeT
06"beMa, BOCnOJIb3yeMcH 3aBHCHMOCTbIO
C _ f T C ; .
c-
cfc
6*
83
oO.lI.CTaBHB .lI.aHHOe 3HaqeHHe C c B ypaBHeHHe BepHYJIJIH H HC-
nOJIb30BaB CHCTeMY ypaBHeHH H (5), nOJIyqHM
C; = - ;' + Vi ( )2 +k'F (t- ). (86)
r.lI.e
0' =
2a f
J.l f; + f
4 f
J.l j + f;.
k'=
oOC.1e onpe.lI.e.TJem!fl C.; H3 BToporo ypaBHeHIffl CHCTeMbI (5) BbI-
qHCJIHM W (t + ). a 3aTeM: Pifi H .lI.pyrne napaMeTpbI npoIJ.ecca
BnpblcKa.
PaC'IeT npoIJ.ecca BnpblcKa C Y eTOM BSl3KOCTil TOnJ1I1Ba. op"
Y'leTe BSl3KOCTH Ton.'lHBa ero .lI.BIUKeHI-Ie B Tpy6onpOBO.lI.e 6Y.lI.eT om-I-
CbIBaTbC5J C .lI.OcTaTOqHOH nOJIHOTOH ypaBHemIeM (7), .lJ.J15J perneHH5I
KOToporo npe.lI.JIO.lli.eJ-IbI .lI.Ba MeTO.lI.a. O.lJ.HO 113 perneHHi'I 3Toro ypaB-
HeHH5J 3anHCbIBaeTC5J B BH.lI.e CHCTeMbJ (8). opeI1MYIl.LeCTBO 3Toro
perneHH5J B TOM, qTO MeTO.lI.HKa paCqeTa npouecca BnpbICKa TOTIJIHBa
npaKTl1qeCKlI nO.'lHOCTbIO COBna.lJ.aeT C 06Il.LeH3BeCTHbIM MeTO.lI.OM
paCqeTa JToro npouecca 6e3 yqeTa B5J3KOCTH. opH 3TOM 06Il.LHOCTb
TeopHH H MeTO.lI.OB paCqeTa BnpblCKa He HapyruaeTC5I. DO.'lee 06Il.LHH
MeTO.lI. paCqeTa BnpbICKa C yqeTOM BH3KOCTII Ton.'lI1Ba npe.lI.JImKeH
10. 51. \POMHHbIM PI]. B OCHOBY ::noro MeTO.lI.a nOJIO.lli.eH cnoco6 pe-
rueHH5J Te.1erpaqmoro ypaBHeHHH, pa3pa6oTaHHbIH A. <1>. raBpHJJO-
BbIM. CYIl.LHOCTb nOCJIe.lJ.HerO cnoco6a 3aK.1IOqaeTCSI B I1CnO.Tlb30Ba-
HlIH H.lI.eH MOH1KY 0 3aMeHe .lI.l1I-p<pepeHUHaJIbHbIX ypaBHeHlI.H C qa-
THbIMH npOH3BO.lI.HbIMlI BToporo nopHLIKa, KOTopbIe .lJ.OJ1.lli.HbI 6bITb
J1HHeHHbIMlI OTHOClITeJIbHO .3TlIX np01I3Bo.lI.HbIX, clIcTeMo I ypaBHeHlIH
B nOJIHbJX .lI.H<p<pepeHIJ.lIaJlax.
oOJIO.lli.HB
ac = V. ac a 2 c a 2 c
ax 'iit=q; ax 2 =r; iJj2= m;
a 2 c
-=5
iJxiJt '
MO.lli.HO nO.TlyqlITb BMeCTO ypaBHeHlIH (7) .lI.Be ClICTeMbI 3KBHBaJIeHT-
HbIX ypaBHeHHH:
dt-'A1dx=O; j
dC-V dx-qdt=O;
2k
dV -'A1dq--qdx=O;
a 2
(87)
fM
dt-'A 2 dx = 0; ]
dC-Vdx-qdt=O;
dV -11.2 dq- q dx = 0,
a 2
(88)
, . 1
f.l(e 1'.1 = -}.2 = -. i+2
a
CIICTeJ\ila ypaBHeHIIH (87) i+1
pernaeTCH npM
t = A1X+C 1 ;
CHCTeM8 yp8BHeHlIll (83)-
npH
t = 'A 2 x+ C 2 ,
r,J,e C I H C 2 -nocToHHHbIe MH-
Terpl1pOBaHHH.
EC.'lM npBHHTb a = const,
TO no.1yQHM npHMOJIHHellHYIO
ceTKY xapaKTepIlCTIiK (pIle.
36). CHcTeMa ypaBHeH115I (79)
pernaeTcH MeTO.l(OM KOHe'lHbIX
pa3HoCTeH, nYTeM 3aMeHbI
.1IH<p<pepeHl.J.Ila.1bHbIX ypaBHe-
>, HMII CIlCTeMOH ypaBHeHIlH
t
t
t-l
.....,
"
><;
j )+1)+2
n-2 n-l n,).
o
')+1, l +2
1 9+1 it-I C.
j
',;
Cj,i+
+2,;+1
Cj+1,i
PIIC. 36. CCTKa xapaKTcpllcTHK TeJJerpal}>-
Horo ypaBHcHHH
C=Vcp-h-i--(q+ q ) t; J
(1 + k!3.t)!3.q = a V - 2kMq;
V = rcp-h+sM.
(89)
PaCqeT npOBO.1IUTCH C IlcnO.TJb30BaHMeM ceTKM xapaKTepHCTHK
(pHC. 36), H8 JWTOPOi'f no OCB a6CI.J.BCC OT.'lO)KeHO X - .Ivuma TPY-
6onpoBo.'l:a, no OCH Opl.J.f1H8T - BpeMH. LLJ1HH8 Tpy6onpOBO.l(8 L
pa3l.J.e.1HeTCH TaK LKe, KaK II nepBO.n; BnpbICKa, H8 n paCqeTHblX yqa-
CTKOB. 3aBl-lCliMOCTb MelKAY .MaCllITa6aMB no OCHM onpe.n;e.TJHeTCH
ypaBHeHMHMH
M = 'Al X; M = A2 X,
n09TOMY xapmnepnCTHKH h] M C 1 HaK.'10HeHbJ no.n. yrJIOM 45° K no-
JlolKMTe.1bHoMY HanpaB.'1eHIlIO OCM x, a xapaKTepIlcTMKB h 2 11 C 2 -
no,L{ Vf.101\1 135°.
r1pIl perneHlH1 CHCTeMbl ypaBHeHllll (89) nOJIyqaeM npHpallI.eHHe
CKOpOCTII /1C B.n;O"lb xapaKTepHcTIiKIl, a ee 3HaqeHIle B KOJlI.J.e
85
HHTepBa.'Ia B TOlIKe j + I; i + I paBHO C j , i + !1C, T. e. no-
JIY'IIIM
C j + I , ;+1 =C nl +!1C;
3.LI:eCb j - HOMep .LI:e.'IeHHH no OCH a6cu.Hcc;
i - HOMep ,'J;e.'IeHHH no OCH Op.LI:HHaT.
PaClIeT ynpOIll,aeTCH, KorAa H3BeCTHbI Be.'1HQHHbI CKOpOCTH C B
BYX CTpOKax ceTKH, nOTOMY lITO H3 BToporo ypaBHeHHH CHCTeMbi
(7) 6y.rreM HMeTb
C j + I , ;+2 = blC j , i+ bIC j + I , i+I -b 2 C j +!, i + b 2 C j + 2 , i+I + b 3 C j , i+"
(89a)
r.rre
kM I I - kM
b I = b 2 = b 3 =
I + kM I + kM I + Mt
ECJ1H H3BeCTHO 3HalIeHHe CKOpOCTH C B nHTH TOlIKax llBYX CTpOK,
TO MO:tKHO onpe.LI:e.'1HTb Be.'IHlIHHY CIWpOCTH B CJIell,YIOIlI,eM npOMe-
:tKYTKe BpeMeHH M (CM. pHC. 36).
npH paclIeTe KOHKpeTHoH Ton.nHBHoH CHCTeIVIbI npou.ecc BnpbIcKa
TaK:tKe pa3l1,e.'1HeTCH Ha nanbI, H CHCTeMbI ypaBHeHHH (87) H (88)
pelllaIOTcH C Y'IeTOM rpaHwIHbIx YC.'10BHH <j)H3HlIecKHx xapaKTepH-
CTHK TommBa, a TaK:tKe COCTOHHHH Cpell,bI, B KOTOPYIO BnpbIcKlmaeT-
CH TOnJIHBO. CpaBHHTeJ1bHOe Hcc.nell,OBaHHe 060HX MeTOll,OB paclIeTa
npH Ton.1HBe OTHOCHTe.1bHO Ma.'lOH BH3KOCTII {72] nOKa3bIBaeT, lITO
paClIeTHbIe BeJ1HlIHHbI napaMeTpOB npou.ecca y <j)OPCYHKII, T. e. BbI-
XOll,HbIe napaMeTpbI npou.ecca, no.'lYlIeHHbIe no 060HM MeTOAaM.
npaKTIIlIeCKII COBnall,aIOT. MaKCHMa.'lbHOe lI,aB.1eHHe B Hacoce, onpe-
lI,e....IeHHoe no MeTOll,Y T. <1>. KY3Heu.OBa, nO,'IyqaeTCH HeCKo.1bKO
MeHbllle, lIeM BeJ1HqHHa .LI:aB.1eHHH, onpe.l1.e.'1eHHOrO no MeTOll,Y
10. 51. <1>oMHHa. Ho eC.'1H HeT OCHOBaHHH COMHeBaTbCH B Hall,e:tKHO-
CTH Ton.1HBHoro Hacoca, TO npou.ecc BnpbICKa C yqeTOM BH3KOCTH
Ton.'lHBa l\IO:tKHO paCClIHTbIBaTb no MeTOll,Y T. <1>. KY3Heu.OBa. 3TOT
MeTOll, HB.'lHeTCH 60JIee npOCTbIM, 1.J.eM MeTOll, 10. 51. <1>oMHHa.
CHCTeMbI c nepeMeHHbIM .LI:HaMeTpOM HarueTaTeJ1bHOrO Tpy60-
npOBO.LI:a H c pa3BeTBJIeHHMM Tpy6onpOBO.LI:OM. npell,no.'lO:tKIIM, lITO
B HarHeTaTeJIbHOM Tpy6onpOBOll,e Ha paCCTOHlIlIII II 01' BXOll,HOrO
CeqeHHH lI,I1aMeTp HarHeTaTe.'1bHOrO Tpy60npOBO.LI:a pe3KO H3MeHHeT-
CH. npH 3TOM HapYlllaeTCH xapaKTep TelIeHIIH H H3MeHHeTCH 3Raqe-
BIle aMnJIHTY.LI: BO.'1R. C.'lell,OBaTe.'1bHO, B 3TOM MeCTe Tpy6onpoBO.LI.a
He06xoll,HMO onpell,eJIHTb HOBYIO Be,'IW-IHHY aMnmnYlI,bI BO.'lHbI, HlI,Y-
IlI,YIO OT MeCTa H3MeHeHIIH lI,HaMeTpa K <j)opCYIme. B MeCTe H3MeHe-
HIIH lI,I1aMeTpa MmKeT B03HIIKHYTb .LI:Ono.'lHHTe.'1bHbIII 06beM. Pac-
CMOTpHM c.'1yqai1, Koma ,LLOnO.'1HHTe.'1bHoro 06'beMa B MeCTe H3Me-
BeHHH .rrIlaMeTpa HeT. npe,LLno.10:tKHM, lITO no celIeHHIO CTbIKa lI,BYX
I1aMeTpOB Tpy60npOBO.LI:a .LI:aB.'IeHHe PT CT He H3MeHHeTCH. Toma
ypaBHeHHe Hepa3pbIBHoCTII B 3TOM CeIJeHIIM 3anI1llIeTCH B BIIlI,e
tTIC;l = fT2 C ;2;
86
3}J,eCb H B nOC le,lJ,YlOllleM I1H,lJ,eKCbI 1, 2 o3HaI.IalOT, LiTO CKOpOCTb,
npOXO,lJ,HbIe n.rIOllla.llH II .llPYrIIe napaMeTpbI OTHOCHTCH K Tpy6onpo-
130,L{aM C pa3HbIMH Cel.JemU!MII.
ECJ1II B nOM ypaBHeHlIH Hepa3pbIBHOCTII CKOpOCTII C;I H C;2
BbIpa3IITb Liepe3 B0.'IHbI ,lJ,aB.'IeHlI5I B COOTBeTCTBIIII C BbIpaLKeHIIHMH
(4) H (5) H 3aTeM pelllIITb 3TH vpaBHeHHH OTHOCHTe.'IbHO BO lH F(t)2
H W (t+ ). TO nOJlYI.JIIM .
F 2 (t)= 2 f r . FI(t- ) + frI-fr2 W2(t); (90)
f rI + f r 2 ' a f rI + f r2
WI ( t+ ) = frI-fr2 F ( t_ )_ 2fr2 W 2 (t); (91)
a f rI +fr2 a I f r, +f r2
3.lleCb Fdt) - Bo:ma, H,L{YlllaH OT ceI.IeHlIH I-I K QJopcYHKe;
FI (t - ) - BO.'IHa, nO,lJ,Ollle,lJ,llla5I K Cel.JeHlHO I-loT HaCOCa;
Wdt) - OTpaLKeHHaH Bo.lHa, nO.llOllle.lllllaH K Ce1.JeHHlO I-I
OT QJopcymm;
WI (t+ ) - OTpa)KeHHaH Bo.lHa, H.llYlllaH OT cel.JemU! I-I K Ha..
cocy.
If <
+----P- ---
u '
(1) 0)
-{]t--
d)
PIIC. 37. CxeMbl pa3BcTB-
.TJCHllblX Tpy60npoBoJJ,oB:
a - c nepeMeHHbIi\I Lt.Ha 1eT-
pOM 6e3 .D.Ono.rmIlTe.;1bHoro
06"beMa (lllTplIXOBa >I .1HHII") :
c JI.onOlIHHTeJtbHbIM 06'beMOM(cnnOllIHaH JIlIHUH); 6 - Ha
)],Be q,OPCYIlKII: 6 - lIa 4eTbIpe q,OPCYIII<H
TOnJIIlBHbIe CHCTeMbI C pa3BeTB.TJeHHbIM TPy6onpOBO,lJ,OM npHMe-
H5IlOTCH B OCHOBHOM 13 .llBilraTemlX C npOTlIl30nO.lOfKHO .llBHLKYlll.HMH-
CH nOplllH5IMH (2LU 00, TIlna 101\1.0 H .llp.). B TaKIlX .llBIIraTe.'IHX
TOnJIIlBO ITO.llaeTCH B UHJIIlH.llp Qepe3 HeCKOJIbKO QJOPCYHOK (,lJ,Be,
TPH, l.JeTbIpe H T. ,L{.). TaK I\al\ yCTaHal3JIHBaTb Ha KaLK,lJ,bIH UH.'IHH.llP
JI.BHraTemI l.JeTbIpeX- H JI.aLKe JI.Byxn.'IYHLKepHbIH HaCOC CJIOLKHO H
rpOM031I.KO. TO O.llHH n.TJYH.lKep nO,lJ,aeT TOn.'IHBO Ha HeCKO.lbKO QJOP-
CYHOK. n03TOMY H npHMeHHIOT pa3BeTBc'IeHHbIH Tpy6onpOBO.ll.
npHHUHITHa.lbHble CXeMbI TOn.'IHBHbIX CHCTeM C pa3BeTBJleHHbIM
Tpy6onpol301I.OM H306paLKeHbI Ha pIlC. 37, a, 6, 8. B 60.'IblllIlHCTl3e
CJIYLiaeB OT Hacoca HJI.eT OJI.HH Ii.'IH ,lJ,l3a HarHeTaTe.lbHbIX Tpy6onpo-
87
BO..'l.a, KOTOpbIe MOrYT pa3BeTB.1HTbCH Ha .LiBa, TpIf HJ1If lJeTbIpe TPY-
60npOBO.Lia. nO.1YlJaeTCH C.l0LKHbIll rHApaB.1HIIeCKIfll K0J1e6aTeJ1bHbIll
KOMIl.leKC, HaCTpOHTb KOTOpbIIi Ha l1..'1.eHTHlJHOCTb pa60TbJ BeCbMa
TPY.LiHO. n03TOMY CTpeMHTCH .LiIfaMeTpbI If .Li.'1HHbI Tpy60npOB0..10B,
H.LiYI.I..{HX 01' HaCOCa .Li0 MeCTa HX pa3BeTB.leHIfH If 01' pa3BeTB.1eHIfll
.Li0 cpOPCYHOK, .Lie.1aTb O,J,IfHaKOBbIl\Ilf. I1HOr.Lia npIfMeH5IIOT Tpy60-
npOBO.LibI pa3Hol'i JJ,.1HHbI H pa3HOrO npOXOJJ,HOrO CelJeHIf5l. npIfHUIfn
paClJeTa TaKIIX TPy60npOBOJJ,OB He H3MeH5IeTC5I, OJJ,HaKO paClJeT CTa-
HOBIfTC5I 60.1ee rpOM03JJ,KIfM H TpYJJ,oeMKIfM. HanpIfMep, eCJ1II 01'
nacoca HJJ,YT JJ,Ba Tpy60npOBOJJ,a C pa3.1H'IHbIMH .LiHaMeTpa llf, Ka)K-
.D.bIH H3 KOTOpbIX HMeeT HarHeTaTe.1bHbIH K.lanaH, TO B 06I.1..{eM 1151-
TOM 3Tane nponecc 6YJJ,e1' onpeJJ,e.l511'bC5I C.leJJ,YIOI.I..{IfMIf ypaBHe-
HIf5lMH:
aV H d: t " =fnCn-J..lofoV V PH-P6c -J..lUJl"I /F V PH-P
f /2 V " f ' C' ., C".
-J..lu; U! 2 1' p PH-P II - KI KI -t K1 K'
v,dP -rC.f -./2V ' f C'
a. H& - KI KT J..l U ! u;1 V P PH -P II - TI T'
a.V: d:; =f 2C: +J..lu;fU; 2 1/ }' P H -P: -!T2 C ;;
dh - ", , ( ' )
M' +l)hK+fKIPK=!KI PH-PH;
1\1" d 2 h K + {)"h" + t ' -., ( " )
dt 2 K K]P K2 -t K2 PH-PH'
1', e. 3..'1.eCb B]\leC1'O 1'pex HMee1'C5I nH1'b ypaBHeHIfll rpaHHlJHbJX YC.10-
Bl1ll. He3aBIfCHMO 01' npOC1'01'bI H lH C.10.lKHOC1'If ypaBHeHIfH npHH-
uIfn paClJe1'a He If3MeH5IeTC5I.
PaCCM01'pHM npouecc B MeCTe pa3Be1'B::reHHH, KorJJ,a B Ce'1eHHH
I-I O1'CYTCTBye1' JJ,ono.'1HH1'eJ1bHbIll 06'beM (CM. pIfC. 37, a).
YpaBHeHHe Hepa3pbIBHoCTH JJ,.151 3THX YC.l0BHM
fT1C TI = !T2 C T2 + fT3 C T3'
HH,3,eKCbI 1, 2, 3 O1'HOCH1'C5I K cooTBe1'c1'BYIOI.I..{HM Tpy60npOBO..'l.aM
(CM. pHC. 37). BbIpa3HB B 31'OM ypaBHeHIfH CKOpOCTH '1epe3 BO.1HbI
.lI.aB.leHHH H npHH5IB, 'ITO no BceMY ce'IeHHIO pa3Be1'B.leHl-I51 .lI.aB.le-
HHe PH CT = const. nOC le HeKOTopbIX npeo6pa30BaHHH no.'1YlJHJ\I
F 2 (t) = 2f T I FI ( t- ) - fT2 + f T3 -f TI W 2 (t)-
f TI + f T2 -t- f T 3 a f T1 + f T2 + f T3
2f T3 W 3 (t); (92)
'fTI+fT2+fT3- .
88
211'1 ( 1 )
F 3 (t) = FI \ t-.....l-
11'1+/1'2+/1'3 ' a J
'1'2 + /1'3 -f TI
W 3 (t) -
'1'1 + f T2 + f T3
2f T2
W 2 (t); t 93 )
f TI + f T2 + f T3
-tVI{t+ ) ' = f T I -,UT2+f T3 ) FI(t- ) -
\ a f TI -;-f T2 + f T3 \ a
2f 2f
1'2 U?2(t) - 1'3. W 3 (t). (94)
f TI + f T2 + t. r3 f TI +f T2 + TT3
MIIHHMaJ1bHO€ pacxo}J{,lL€HH€ M€}J{,lLY aIVID.'IlITY,lLaMH BOJIH F 2 (t)
n F 3 (t) COOTB€TCTBY€T C.'1YlJ.mo, KOr,lLa
fTI = fT2 + fT3; iT2 = fT3;
1 2 = 13 .
EC.1lI }J{€ B M€CT€ pa3BeTB.'I€HHH 6YAeT ,lLOnOc'IHHTe.'IbHbIH 06'beM
(CM. pHC. 37, a), TO ypaBHeHH€ Hepa3pbIBHOCTH ,lLBH}J{€HHH TonclHBa
3anHllJeTCH B BH,lL€
i C 11 dp".CT , . C ...L t " C
1'1 1'1 =a¥cT-,fT2 1'2 I 1'3 1'3-
df
0PHHHB, '-ITO ,lLaB.leHHe B 06'b€M€ V CT paBHO ,lLaB.'IeHHlO PH CT,
npH'-I€M no Ce'-I€HHlO pa3B€TBJ1€HIIH PH CT = const II, HcnO"'Ib3YH CH-
CTeMbI ypaBHeHHH (3), (4), (5), npllIVIeH€HHbIe K paCCMaTpIIBa€!\IO-
MY Ce'-IeHlllO, noc.'Ie npH6.;nDKeHHoro HHTerpHpOBaHHH npIIBe,lLeHHO-
ro BbIllle ypaBHeHIIH H pelll€HHH ero OTHOCHT€.'IbHO WI (t + ) no-
.'lYlJ.HM
- W 1( t ...L ..'2.. ) = ..!!.....
I a. £",
(95)
r,lLe
, 'T! L\t , T2 M, t T3 M , .
£ =-+--r--,apaV cm ,
222
( fTIM f r2 M f r3 j.f ) ( .[1 )
D= ------a p aV FI t-- +
2 2 2 em a
t TI M
+- C ITI +apO',V cm PO-fT2:1tU'/ 2 (t)-
2
froM f T3 M
---=- C IT2 -t 73 W 3 (t)M-- C IT3 .
2 2
89
Tal{ IiaK Be.'lU'lUHa PI (I- ) H3BeCTIla, TO ypaBHeHue (95) 0)1,-
HOBpeMeHHo onpe,'I,e.'1HeT Ii BeJ1II'lIiHY .lI.aB.1emtH PH CT. BO.IHbI .lI.aB-
JIeHHH, H.n;YllI,He K 4JopCYHKaM OT MeCTa pa3BenweHIIH:
PII.cm = Po + F I ( I - il ) - w J 1 + il ) ;
a \ a ,
PH.em = Po + F 2 (/)- \F 2 (t);
PII.em = Po + F 3 (t)- W 3 (t).
BeJIIf'lIiHbI BG.'m W 2 (t) H W 3 (t), npHllle.ll.Ume K pa3BeTBJ1eHHlO
OT COOTBeTCTBYlOllI,HX 4JOPCYHOK, H3BeCTHbI. MeTo.ll. paC'leTa npouec-
ca Y 4JOPCYHOK TaKOH llie, KaK II .n;.1H 06bI'lHOH TOnaIiBHOH CHCTeMbI.
TIPUHI.UW paC'leTa COXpaHHeTCH HeH3MeHHbIM npu HaJIH'lHH .n;ono.'I-
HHTeJIbHOrO 060eMa B MeCTe H3MeHeHHH .lI.HaMeTpa Tpy60npOBO.ll.8
(CM. pHC. 37, a), IBMeHHlOTCH TO 1bKO 3HalJeHHH Sf U D.
Pa3BeTB.'leHHbIe Tpy6onpOBO.ll.bI IlIHpOKO HCrrOJlb3YlOTCH TaKllie B
ra30Typ6uHHbiX .n;BIIraTe:J5JX. Oc06eHHOCTH flI.n;po.n;HHaMIiKH TaKHX
Tpy6onpOBo.n;OB HCCJ1e.ll.OBaHbI la. H. fPH30.n;yt50M [28]. O.n;HaKo He-
nocpe.n;cTBeHHo nepeHocHTb pe3y.'lbTaTbI 3THX pa60T Ha narHeTa-
Te.7JbHbIe Tpy60npOBO.ll.bI .n;H3e.'Ieil HeB03MO'KHO BBH.a:y 60.1bllieH
CJJOflmOCTH rpaHlf'lHbIX yc.rlOBHi'I H HeYCTaHOBHBlllerOCR xapaKTepa
TelJeHlIH. KaK H3BeCTHO, B ra30Typ6HHHbiX .lI.BHraTe.1HX Ton.'IHBO
BrrpblcKHBaeTcH HerrpepblBHo npH rrOCTOHHHOM .n;aBc1eHHH. BElI.lI.Y
TPY.lI.HOCTH pery.'IHpOBaHH5J paBHoMepHocTH nO.ll.alJH TOn 'IHBa Ton-
.TJ.HBHbIMIi CHCTeMaMIi C pa3BeTB,;1eHHbIM Tpy60npOBO.ll.OM H npoTe-
KaHIi5J npouecca no OT.lI.eJ1bHbIM ceKUIIHM Ii 4JopcYHKaM HX npHMeHH-
roT TO.TJbKO B CJ1YlJae Heo6xo.ll.HMOCTH. Ho TaKHe Ton.1IIBHbIe CHCTe-
MbI y.n;06HbI jI,.'H1 3KcnepuMeHTa.1.bHbIX eJIei1, Tali KaK nYTeM
EOHCTPYKTHBHbIX KOM6HHaUHH pa3.1HlJHbIX 3JleMeHTOB CHCTeM MOlli-
HO 3<p<peKTHBHO H3MeHHTb xapaKTepHCTHKY no.a,alJH Ton.1HBa II .lI.a)J{e
06eCne'lHBaTb .ZI,BOHHoil H.'IH «CTyneHlJaTbIH» BnpbICK.
Oco6eHHOCTH paC eTa npoJ..{ecca BnpMCKa TOnJlHBa CHCTeMOH C
lIITHIjJTOBOH IjJOPCYHKOH. B TOnJ1I1BHOH CIICTeMe C lliTH<pTOBOii cpop-
CYHKOH MeTO.ll. paClJeTa rrpouecca Y Hacoca coxpaHHeTCH TeM )Ke, lJTO
II B CHCTeMe C 3aKpbtTOH <popcYHlwi'r. B BbtX0.lJ.HOM celJemm Tpy60-
npoBo.a:a y 4JOPCYHKH npHHJ..{Hn COCTaB.TJeHHH ypaBHeHHH rpaHl1lJHbIX
YC.;10BHH TaIOKe He H3MeH5JeTCH. O.ll.HaKO lJI1C,,'JO 3TanOB Ii Tpy.n;oeM-
KOCTb pellieHIiH ypaBHeHHH 3aBHCHT OT KOHCTPYKUIiI1 lliTIicpTa. Pac-
eT HeCKO,,'IbKO YCJIOIKHHeTC5J BCJIe.ll.CTBHe Toro, 'lTO B EJTOH <P0PCYH-
Ke npOXOlI.HaH n.TJOlll,a.n;b pacnbI"lHBalOllI,erO OTBepCTIiH 33BHCHT OT
nO.ZI,oeMa Hr.'lbI. MeTo.n;IiKa paClJeTa npouecca BnpbtCKa Tonmma CH-
CTeMOH C IlITHcpTOBOH cpOpC)"HKOH HaH60 'Iee nO:IHO II3J10)KeH3
B. f. OKYJ10BbIM.
LL 5J pacnpocTpaHeHHoH B OTelJeCTBeHHOM .ZI,H3eaeCTpoeHIiH KOH-
-nPYKUIiH lliTHcpTa (pHC. 38) B. f. OKY.1.0B pa3.l1.e.'tHeT np0l..{ecc B
BbIXO,nHOM CelJeHIiH HarHeT3TeJIbHOrO Tpy60npOBO.ZI,a Ha c..'Je.ll.YlOllI,He
3TanbI:
90
1) OT H3'13,,'la nOBbIlIleHlUI A3BJ1eHHH 11:0 H3'l3J13 11.BHlKeHl1H
llfJIbI;
2) OT Ha'l3.TJ3 11.BI1lKeHHH Hr.'lbI AO MOMeHT3 BbIXOAa ee UH,,'lHHJJ:-
plI'leCKOH 'laCTH lI3 nepenycKHoro KaHa,,'la Kopnyca paCI1I.IJIHTeJ1H;
3) OT Ha'l3J13 BbIX011.a
UHJIHHnpH'leCKOH 'laCTH
IIr J1bI H3 nepenycKHoro
KaH3JIa Kopnyca p3cn -
.JIHTeJ1H 11.0 11.0CTHlKeHliH
HrJ10H ynopa;
4) OT MOMeHTa 11.0-
CTHlKeHHH HrJIOH ynopa
.Jl.O Ha'l3.TIa ee noca.n;KH;
5) OT H3'la.'Ia .n;BmKe-
HHH Hr JIbI BHH3 .n;o BXO.n;3
UHJ1HH11.pH'leCKOH 'laCTH
ee B nepenycKHoM KaHaJl
Kopnyca paCnbIJ1HTeJIH;
6) OT Ha'laJIa Bxo.n;a UHJIHHnpH'leCKOH 'laC.H RrJI B nepenYCK-
ROll KaHa.l Kopnyca paCnblv'lHTeJIH 11.0 nO.'lHOH ee nOCa;J:KII.
YpaBHeHHH rpaHH'lHbIX YC.TIOBI1H B HaH60.'lee 06rueM BRAe MorYT
ObITb npe.n;CTaB.TIeHbI TaK:
1 dpt/J _ " .
U\ </.' ill - frCr-(f,.-fuj)C,.-rtcfcCc,
d 2 y . ( ' ) ( , ) '
M' dt 2 +6 y= fu-fu (P</.>-P</.,o)+ Iu-fll{ pt/1+fll{p", (97)
bfbl
I : I I
I 0) I 0) I 6) I
e)
PHC. .38. CXCtvta KOHl.\a pacnbI.l!JTC.1H IlITHIj:JTO-
BOI! 1j:J0PCYHKII
(96)
B ypaBHeHHH (96) Be.lIH'lHHa (fu - 't/.!) C u onpe.n;eJI5IeT 06"beM,
()cB06mK.n;aeMbIH Rr.l0lI <POPCYHKH npH no.n;"beMe. BemI'lUHa Fe H3-
JVIeWleTCH B 3aBHCHMOCTH OT nO,,10lKeHHH Hr .1bI, npH'IeM B nepBOM,
BTOpOM H lIleCTOM 3Tanax 3Ta Be,,'lH'lHHa onpe.n;e"lHeTCH Bem1'lHHOH
.3a30pa Me1K.n;y UH"lHH11.pH'leCK0I1 'laCTblO IIr.lbI H CTeHKOH nepenYCK-
Horo KaHa.'la paCnbI.J1HTe"lH.
CBH3b MelK.n;y Be,,1HlIHH3l\1H prfj H P :np YCTaHaB.'lHBaeTCH H3 yc-
.JIOBHH cn:IOlIlHOCTH )].BH)KeHHH TOnJ1HBa B npoxo.n;HOM Ce'leHHII nOr(
yn.'lOTHHTeJ1bHbIM KOH)"COM II r"lbI, a TaIGKe 'lepe3 3a30p MelK.n;y
lUTHCPTOM Hr.JIbI II CTeHlWI1 nepenYCl<Horo KaHaJIa paCnbI.'IHTe.TlH.
COBMeCTHoe pelIleHHe 3TOH CHCTeMbI ypaBHeHHH C ypaBHeHIIHMH CH-
CTeMbI (5) onpe.n;e.1HeT .n;aBJ1eHlIe prfj II no.n;"beM Hr.TJbI Y IWH KalKlJ.OrO
paC'leTHOrO MOMeHTa Bpel\IeHH.
CHcTeMa c HacocaMH pacnpe.n;eJIHTeJIbHOrO THna. B OT.TJH'lIle OT
MHOrOnJIymKepHoro Hacoca pacnpelJ.e.TJIITe.'lbHblll Hacoc IIMeeT O.n;HY
nJIYHlKepHYIO napy, KOTopaH 3a pa60'lIIH 060pOT Ba.TJa lJ.BHraTeJIH
06C.TIYlKHBaeT HeCI<O.TJbKO UH:IHHlJ.POB. Oco6eHHocTb pacnpe11.e.'III-
TeJIbHOrO Hacoca - BbICOKaH UIIK.'lH'lHOCTb, npeBbIlIlalOruaH npH
npO'lIIX paBHbJX YC.10BHHX UUKJI11'lHOCTb l\1HOron.rIYHlKepHoro Hacoca
.BO CTO.lbKO p33, CKO:lbIW UlI.1HH.n;POB 11.BI-fr3Te.TJH o6C.1JYIKHB3eT p3C-
91
npe,J,e"l11Te.lbHblH HaCOC. nplIHlUIll .n.ei'IcTB1I5I paCnpe,lJ,e.lIITe"lbHoro
HaCOCa aHaJIOrIlIleH nplIHlumy .1,eMCTBH5I l\1HOrOnaYHiKepHOrO HaCO-
ca, n03TOMY 06mHe TeOpeTH'leCime nO.'I0}J{eHH5I npou.ecca BnpbICIW
H MeTO,lJ,bI ero paC11eTa MO}J{HO pacnpOCTpaHHTb H Ha CHCTel\lbI C pac-
npe,lJ,eJIHTe,,'IbHbIl\IH HacocaMH. O.n.HaKO cymecTBeHHoe OTJIH11He KOH-
CTPYKI1.HH pacnpe.n:e.1HTe.lbHoro Hacoca BbI3bI8aeT Heo6xo,'I,HMOCTb
yqeTa 1I.OnO.1HHTe.1bHbIX <paKTOpOB, 11TO B HeKOTopbIX c.'IY11a5IX H3!\Ie-
HSleT pa3,lJ,eJIeHI-Ie npou:ecca Ha "JTanbI H BHOCHT HeKOTopbIe H3MeHe-
fIH5I B pell1eHHe AH<p<pepeHU:Ha.'IbHbIX ypaBHeHHH. Bce 3TH H3MeHeHHR.
OTHOC5ITC5I K paCIJ:eTY npou:ecca Y Hacoca.
tH
Pn
V;;P /"
to
I( peey/lfll7lO{JlJ
VnK;PnK/"
V/J;PP'-- ---=-- !be
VIlJ;PIlJ
p
PHC. 39. npllHI.\!HIHa.1bHa51 CXC Ia pacnpC,J.c.lllTc.lbHoro Hacoca pOTOp-
Horo THna
IfJH'"PS
,
/
!i H ; PH
I1/1YHJKep
PaCqeT npou:ecca y <P0PCYHI\I1 He H3MeH5IeTC5I. BBH.Ll.Y BbICOKOH
U:HKJIH11HOCTI1 oe060e 3HaIJ:eHHe B paenpe,n:e.1HTe:1bHoM Haeoee npII-
06peTaIOT JIJIH8J\fHK8 J1.BIUKYIl1.HXCR. 3.'1eMeHTOB H HanOJIHeHHe TOf!.TIH-
BOM KaMepbI HarHeTaHHfl. YJ1.0BJleTBopHTe.lbHoe HanO.'1HeHlle TO IT-
.'IHBOM KaMepbI HarHeTaHH5I B pacnpe,lJ,e,'IHTeol'IbHOM Haeoee eBfl3aHO
co 3Ha11HTe.'IbHbIMH TPYJ1.HOCT5IMH, KOTopbIe B 60:1bll1HHCTBe C.'IY11aeB
nbITaIOTCH pernHTb KOHCTPYKTH8HbIM nYTel\I.
B I{a11eCTBe OCHOBHoro 06'beKTa HCc.1elI.OBaHHfl HaMH BbI6paH
pacnpe,rr,eJJHTe.lbHbIII Hacoc pOTOpHOro THna. 3TOT Hacoc 60JJbrne
.Ll.pyrHx pacnpeJ1.e.1HTe.1bHbIX HaCOCOB OT.1J1I'IaeTC5I OT I1moron.'IYH-
)J{epHoro I-IaeOca, C.'Ie,lJ,OBaTe.'IbHO. eCJIH lI..15I paC11eTa nponecca
BnpbICKa pOTopHoro Hacoca Hcno.lb3yeTC5I MeTO,n, npHHHTbJH ,LI,.'I5I
06bI1.JHbIX n.TYJDKepHbIX HaCOCOB, TO B Hero ):(O.JI)J{HbI 6bITb BHeeeHbI
60JIee cymecTBeHHble H3MeHeml5I. PaCqeTHa5J cxe!\-la Hacoea nOKa-
3aHa Ha pEC, 39. B Hacoce npHMeHeHbI ):(Ba npoTHBOnO,,1o)J{Ho pac-
nO.10}J{eHHbIX n,,1YH}J{epa, C}J{HMaIOIllHe Ton.;1HBO B o6mei1 KaMepe
HarHeTaHI15I. DJJYH}J{epbI pacnO"lOfI{eHbI B pOTope Hacoca H Bpama-
lOTCSl BMeCTe C HH!\I. npH BpameHIUl pOTopa U.eHTpo6e}J{Ha5I CII.'Ia
npH}J{HMaeT D.aYH}J{epbI K BHYTpeHHei'I nOBepxHocTH KY,llalJKOBOH
rnaH6bI. Ha rnaf'r6e I1MelOTCH HeCKO.'IbKO nap npoTHBOnOJJo}J{Ho pac-
nOJIO:iKeHHbIX OJLI1H K ,lJ,pyroMY KYJ1aIJ:KOB, npH11eM 11HCJJO nap paBHo
92
KOlIH'IeCTBY 1.(H.rJlfHlJ,pOB, 06caY))UmaeMbIX HaCOCOM. npH HeKOTOpOM
nOBOpOTe pOTopa nJIYHLKepbl Ha6eralOT Ha KY:Ia'lKIi Ii HaqIiHalOT
C6.'1II)JWTbCR II OKHMaTb Ton.rmBO, HaXOlJ,Rll1.eeCR B KallJepe HarHe-
TaHHR. Oc06eHHOCTb paCClIJaTpflBael\WrO Hacoca - OTCYTCTBHe Me-
XaHH'IeCKOM CBR3H nJ1YHLKepOB C lJ,P)THMH lJ,eTa.'IRMH.
fIpoqm.'1b TOnJIHBHoro Ky.la'lKa pOTopHoro Hacoca cywecTBeHHO
OT.:1:H'.JaeTCH OT npoqm.'IH Ky.TJaqKa n.'I)'H.iKepHOrO Hacoca. Ha pHC. 40
nOKa3aH nYTb n.'1YH)KepOB paccMaTpHBaeMoro Hacoca (KpHBaH 3).
B pe3)'c1bTaTe paCXO.iKlJ,eHHH nJIYH)KepOB nolJ, B.'lHHHHeM U.eHTp06e.iK-
HOM CHJlbl Hacoc (pHC. 40) HMeeT lJ,Ba nepHOlJ,a pa3rpY3KH. fIepBbIH
nepHOlJ, pa3rpY3KH HacTynaeT nOCJle IIJaKCHlIIa.'lbHOrO c6.'lIDKeHlHI
PI1C. 40. PaC'-ICTHO-KHHC-
l\IaTII'-ICCKIIC JlHarpal\ll\lbl
pOTopHoro Hacoca:
1 - BpeMH-CeqeHHR HarHe-
'faTe:lbHoro oKHa 2 - Bpe-
Mf[-CeGeHH£ BcaChlBalOI..U.erO
OKHa; 3 - nYTu nJIYH>K:epoB;
4 - H3MeHeHHSl 06"beM8 9 He
3anO....:lHeHHoro TOnJIHBOM; 5 -
H3MCHeHHe AaBJIeHHH npH
HarHCTaTCJIbHOM xo e nop-
l1lH!!; 6 - H3MeHeHHe CBO()OjJ,-
Horo 06"bCMa BO BpeMH xo a
OTceQKH
PI, VoCH t;H"
Kflc.
60 tJ 15
fOO af
50 0,05
o 0
folofH 3
linloflof
! -J
-----j
fO
{II"
20
o
nJ1YH))(epOB. 3TOT nepHOl{ He3Ha'II1Te.leH no npOlJ,o.'l.iKHTe.:lbHOCTH H
pa3rpY30'lHOllIY XOlJ,Y. fIOC.:le npelJ,BapHTe.1bHOM pa3rpY3KH B Te'le-
HI1e 60.1blIloro yrJla nOBopOTa pOTopa Hacoca nO.:l0.iKeHHe nJI)'H.iKe-
pOB He H3MeHHeTCH, a 3aTelli B COOTBeTCTBHH C npoqmJ1eM TOnJ1HB-
HOro KYJ1a'lI(a n.'IYH.iKepbI l{OmKHbI 6bICTpO paCXOlJ,IITbCH lJ,0 CBoero
HCXOlJ,HOrO n0J10.iKeHI1H. COOTBeTCTBYlOlIJ.erO HaqaJIY pa6oqero I1K-
.lIa. OTCYTCTBHe MeXaHHqeCKOM CBH3H nJ1YH.iKepOB C HX npHBOlJ,aM!J
6J1arOnpI1HTHO CKa3bIBaeTCH Ha YC.'10BHHX pa60TbI pacnpe]J,eJ1I1TeJ1b-
Horo Hacoca. B HeKOTopbIX CJ1YQaHX lJ,.'lH YBe.'lH'IeHHH YCI1J1HH, lJ,eM-
CTBYlOWI1X Ha n,IJYHLKepbI npH 06paTHOM xOlJ,e, Me))(lJ,)' IT,lJYH.iKepallII1
nOMeI.U.alOT npY.iKHHY. Ko.TJHQeCTBO. nOlJ,aBaellfOro TOn.rJlma pery.TJH-
pyeTcH H3MeHeHiIeM npOXOlJ,HOlI IT.'IOllJ.alJ,I1 lJ,03HpYlOlIJ.erO OTBepCTI1H
(lJ,03aTopa) faoa, Qepe3 KOTopoe, a TaK.iKe OKHO fee B TeqeHHe onpe-
l{eJleHHoro yrJla nOBopOTa pOTopa KaMepa HarHeTaHI1R HalTOJ1HHeT-
CH TOlT.'IHBOM. fIpI1 pery.1I1pOBaHI1I1 KO.1WIeCTBa lTOlJ,aBaellIOro Ton-
.'IHBa nYTeM lJ,pOcce.'1HpOBaHHR Ha BcaCbIBaHHH B KaMepe HarHeTa-
HHH BCerlJ,a OCTaeTCH HeKOTopaH qaCTb 06DeMa. He 3alTO,IJHeHHaH
Ton.lHBOIlL Be.nfI'IHHa 3TOlI qaCTH lJ,D.'I)JUW 6bITb H3BeCTHa, TaK KaK
6e3 Hee HeJIb3H onpelJ,e.1HTb MOMeHT HaqaJW C)KaTHH TOlT.IHBa. KaK
93
c"lell.yeT H3 pl1C, 39, lI.mI lI.el\>mqmpoBaHlIH K0J1e6aHl1lI Me.IKlI.Y A03a-
TOpaI\1WI1 BcaCbIBaJOI.l.lI1M OKHOl\l I1MeeTCH 06"beM V p.
B nOC"lell.Hee BpeMH lI.J1H nOBbIWeHI1H paBHoMepHOCTI1 nOll.aqH
Ton HBa no CeKUI1HM B pOTOpH X Hacocax CTa H YCTaHaB I1BaTb
HarHeTaTe.lbHbIe K.lanaHbI. Ha cxeMe pnc. 40 TaKolI K.'IanaH pacno-
J10.IKeH 3a HarHeTaTe.lbHbIM OKHOM. B03MO.IKHbI ABa C.lyqaH pacno-
.IIO.IKeHI1H HaTHeTaTe.lbHoro K.lanaHa B paCCMaTpl1BaeI\WH CHCTeMe:
nepell. OKHOM f >t, Me.IKlI.y OKHOM I" H 06"beMOM V>t. I1HOrll.a HarneTa-
TeJ1bHbIH K.'IanaH He YCTaHaBoillIBaeTCH. OpllHUHll COCTaBJ1eHI1H 11 pe-
rneHI1H ypaBHeHI1H lI.BI1.IKeHI1H Ton.'II1Ba 11 rpaHI1QHbIX ye oBI1H coxpa-
HHeTCH Hel13MeHHbIM II llOA06HbIM npl1HHTOMY npl1 COCTaB.lelIl1l1 It
peWeHl111 ypaBHeHI1H (13)- (15).
PaCCMOTpl1I\I Ha1160.1ee C.l0.IKHbIH C"lYQaH (eM. pHC. 39). TOnJ1HBO
HaQHHaeT nocTynaTb B HarHeTaTe bHbIH Tpy60npoBoll. noe le YMeHb-
WeHI1H n.'IYH.lKepaMI1 06"beMa V>t Ha BeJ1I1QHHY V oc ..". Opl1 npl1H5ITbIX
YC.'IOBI1HX pa3.1I1QaIOTCH Tpl1 npell.BapHTe.JlbHbIX :::lTana, eB5I3aHHbIe c
3anO.'IHellHeM TorWHBOM CB060ll.HbIX 06"beMoB. OepBbIH :)Tan: TOn l1-
BOM 3anO.1HHeTCH 06"beM Voc.>t. YpaBlleHl1e rpaHI1QHbIX ye.'IOBI1H lI.,1JH
3Toro 3Tana
aV
- =2 t "C .
dt n n
B pe3y.1LTaTe peweHlIH 3Toro ypaBHeHI1H no.:'IYQI1M
V ocHI - V OC . H = 2tn(h n -h nI ).
(98)
Ee.ll1 K OIWHQaHI1JO 3anO.'IHeHI1H Ton.!II1BOM 06"beMa Voc.>t OKHa
f>t OTKpbIBaJOTCH, TO HaQHeT 3anO.;lHHTbCH TOnJ1HBOM eBo6oll.HblH
06"beM V ac . n >;. OepHOll. 3anOJ1HeHI1H 06"beMa V oC.n'/< npl1MeM 3a BTO-
pOH npell.BapI1Te.'IbHbIH 3Tan.
YpaBHeHI15I rpaHHIlHbIX ye.'IOBI1H BToporo 3Tana
V dPn 21 C t /2..r- dV nK f .. /2..r-
a n & = n n- II" 11 p t' 1711-& = II "V P t' PI<"
OpH peWeHl111 3TI1X ypaBHeHnH npn6.1JH.lKeHHbIM MeTOll.OM no-
.1JY'II1M
. v 'I\J ,,('1: 2
Pn+PIII=-2+V 4+ D ;
v,,",,_v,, "J.At ff) (- ; +v ;' +0)-
f,ne
(99)
(100)
J.lnfn M · ( 2
'IjJ= V p
Jf 2ctV II . cp
D 2 2fn(hn-hnl)
= P"I+
aV n . c /1
94
B <POPMYJIaX (98)- (100) HYIKHO Y4HTbIBaTb 2f n, TaI( KaK B pac-
cMaTpHBaeMoH CHCTeMe .IlEa n.lymKepa CIKHMalOT Ton.1HBO B O.ll.HOfl
KaMepe HarHeTaHHSL
Bo Bpel\l51 TpeTbero 3Tana, KOTOpbIl1 HacTynaeT nOC.le 3anO.1He-
HH5I Ton.1HBOM 06'belVIa V OC . lI "", Ton.mmo 6V.lI.eT CIKHMaTbCH B 06'beMe
Vn'K .lI.O AaB.'IeHI1H, cooTBeTcTBYlOllI.erO Ha4a.1Y nO.ll.'beMa HarHeTa-
Te.TJbHOrO K.7IanaHa. BBlI.lI.Y Toro, LITO Ha 3TOM 3Tane npOHCXO.ll.HT
TO.TJbKO CIKaTHe TOnJ1HBa B 06'beMe V n,,1, ypaBHeHHSI npou.ecca 3J1e-
MeHTapHbI, II paCCMaTpHB8Tb HX He 6Y.ll.eM. B LIeTBepTO!\I 3Tane Ha-
rHeT8Te.1JbHbIH K.1JanaH Ha1IHHaeT nO.ll.HHMaTbC51 H BblTeCmlTb Ton-
JIHBO H3 06'beM8 V , KOTopoe nOH.lI.eT Ha 38nO.'IHeHHe 06'beMa V' .
oc.1t
HenOCpe.ll.CTBeHHOIO nepeTeK8HHH TOnJ1HB8 H3 06'beM8 V 71), B 06'b-
eM V nOKa He npoHCxO.ll.HT. He OCTaHaBJUlBaHCb Ha 3TOM 3Tane,
paCCMOTpl1M 60.1ee 06IJJ.HH c.TJY4aH, KOr.ll.a 06'beM V c.f/ 6Y.lI.eT 3anO.1-
HSITbCSI Ton.'IHBOM H nOCJIe Ha4a.la nocTyn.neHHSI ero B 06UM V
LIepe3 npoxo.ll.HOe ceLIeUHe K.'IanaHa f"UJ' OporeKaHHe npou.ecca B
3THX YCJ10BH5IX HB.1HeTCSI nHTbIM 3TanOM. PaccMoTpHM ero. YpaBHe-
HHSI rpaUI:I4HbIX YC.TJOBHH .lI..TJSI 3Toro 3Tana
aV ll d :; =2fnCn- JII V VPII-Pn,,;
aV n " d;;" = JH V ; V Pf/-Pn,, -f,P,,-
- ll!fUj V V Pn,,;
dV CH f C 11 /T V -
---;;t-= " "+ li!dll! V p Pn,,;
d 2 h
M" + 6h" + f"p" = fI(Pn,,'
dt 2
(101)
(102)
( 103)
(l 04)
Cor.laCHO pm-lee npHHSITbIM .lI.OnYllI.eHHHM ypaBHeHl:le (104) Mo:;.l(-
HO npe.a:cTaBI1Tb B BH,1I.e
Ah" + B = P n",
(104a)
r.ll.e nOCTOHHHbIe A 1:1 B HMelOT Te IKe 3HaLIeHHSI, LITO H B paCCMOT-
peHHblX CHCTeMax.
PellIHB npH6.TJHIKeHHO ypaBHeHl:le (102), nO.1YLIHM
'I\J r 'l\J2
VPH-Pn."+I1P,,I= -2+1/ 4+ D - Pn ,,'
(lOla)
95
I13 npH6mUKeHHOrO COBMeCTHOrO perueHH5I ypaBHeHHfI (101a),
(102), (104a) nOJI)"'IHM
( fK ) ( 1jJ Y $2
PnK 1 +- =PnKI+b --+ -+D-PnlC+
AaV nK 2 4
Ill,!fu, cpM .. I 2 )
..L f"h" 1 ..L V P II' (102 )
I I - , t PnK ,. PnKI' a
aV nK AaV n " Y2al-nK
PeruaTb ypaBHeHHe (1 02a) npollte rpa£pHlieCKH.
B nplIBe.n,eHHbIx ypaBHeHHHx
D- + .1 , 2fll(h n -h nt )
-PHI . P"IT .'
aVH cp
.1PKi = PHI-Pn"I;
IlHf"M 11
1jJ= P .
JI 2aV h cp ,
IlllfH M .. I 2
b'= V P
J r 2a V nK
BeJIHqlmy fUf onpe.n:eJI5IeM no npH6.'1H2KeHHOMY 3HaQeHHIO h",:
h h , (C ,jK!M ) A t
,,= "I. KlTT!..l.
PeruHB COBMeCTHO ypaBHeHHH (103) H (104a), nOJIyqHM
tuJUj cpM V I f"B
112 J; Pn,,+PnKJ- A ' (103a)
V , V f"p" ,
,- DC.H'=-"
DC.H I A
nOCJIe HanO.'1HeHHH TOnJIHBOM 06'beMa V OC . H ' HaliHHaeTC5I ruec-
TOll .3Tan, BO Bpei\:I5I KOToporo B HarHeTaTeJ1bHbIll Tpy6onpOBO.n, no-
.n:aeTC5I OCHOBHoe JWJlHlieCTBO Ton.'1HBa. fpaHHliHbIe yC.'10BHH :noro
.3Tana:
V dPH - 2' " C f Y 21./ .
a 11-- n n-f.tll H - II P"-P n ,,,
dt p
(105)
Y -
. . dPn" 2 '
aV nlCdi = f.tJII p V PH-Pn"-f,,C,,-f.t,'/U(
v ; V PnK-P ;
(106)
, dp C f / '"2 V '
aV Hdi =f" K + f.tll( II( 1 p PnK-PII-fTCT;
M d 2 h K + bh +f = f ( - ' ) .
K dt 2 ""p" K P nK P II ,
(107)
(108)
96
::na CHCTeMa ypaBHetIHH pernaeTCSI C Y1.IeTOM CHCTeMbi ypaBHeHHH
(4) H C HcnOJlb30BaHHeM .n.onYllI.eHHH, npHH5ITbIX npH perneHHH ypaB-
HeHHH (13)-(15).
npe.n.cTaBHM ypaBHeHHe (108) B BH.n.e
Ah,,+ B=f"(PnK-P )' (l08a)
B pe3y.lbTaTe COBMeCTHoro perneH1UI ypaBHeHHH (108a) H (106)
C ypaBHeHH5IMH CHCTeMbI (4) no.'IY1.IHM B3aHMOCB5I3b Me)K.n.y .n.aBJIe-
HH5IMH P H pm; B BHJJ:e ypaBHeHHSI:
. N' K'
P"=---;-+-;-Pn,,, (107a)
Z X
r.n.e
!-lU,tU,MV :
N'=P 1 + X
Jf2aV
I [ ( iK\M ) ] B f/ 1tW (t)
X 1 A h'd+ C"l +- M -B+ I'1Pl--- .
2 aV" ap:xll"
f/ 1t po f.,.MC"'1 fKhKl.
2apaV 2aV aV '
f.,.M fK.
X' = I + . +----;--,
2ap:xV" AaV II
K'= '
AaV '
I'1P 1 = Pn"I -P I'
PernHM npH6JIH)KeHHO COBMeCTHO ypaBHemUI (105), (107a) H
(108a). B pe3YJIbTaTe HeKOTopbIX npeo6pa30B8HHH nOJIY1.IHM
b' .f ( b' 2 D'
VPII-Pn,,+I'1P"I= -- 2 ,,+1/ _ 2 ,, ) --;;-+PII+I'1PKh (106a)
z t X X
r.n.e
!-l"fllM V 2
b'= p . X"= I + _ k'f"
V2aV nK ' AaV nK AaVn"x'
{KN ' f B f h !-l,ilij cp!1t · I P 2
D'= + - - V X
Ax'a V nK AaV nK aV n " V 2aV nK
X V A [hid +( C"l + jK M ) M J-B+ I'1P"l.
.3aK83748
97
Ec,;'UI ypaBHeHIfe
y\>aBHeHHeM (106£1),
J1yLJIfM
V I P +.1.p ! ...L ( ) 2 - = _ ...L'" l £ + D",
II K I 2x" x" 2 I V 4
( 105) npIf6JJlDKeHHO pewIfTb COB!\IeCTHO C
TO noc e HeKOTOpwX npeo6pa30BaHIfH no-
rD.e
II.fM./ 2
_ rH H V p .
1P - Y2 V .-
a Ii cp
D" = 2fn(h n -h nl ) ...L -L b' ...L ( .!t.- ) 2 + 11 _
V I PHI I 2 ,,, 2 " P"I " .
a II cp X X X
Onpe.l1.e.1HB D.aB.leHHe P", HaH.l1.eM .l1.aB,;leHHe Pn", a 3aTeM Be.'IIf-
lJIfHbI P 11 h". DOLle onpeD.e,;leHHH P , HCnOJIb3Y5I CHcTeMY ypaBHe-
HIfH (4). paCClJlITaeM aI\fIT.1IfTY.l1.Y BO,;lHbI. KOTopaH nOH,lI.eT K <pop-
cYHKe.
OKOHlJamIe weCToro 3Tana onpe..'l.e,lIHeTcH XO.l1.0M nJIymKepoB,
KOTopble, .l1.0CTIfrHYB MaKcHMYMa nO.II.'beMa, HaLJHYT 3aTeM nepeMe-
l.U.aTbCH B o6paTHoM HanpaB.lemm, T. e. HacTynHT npe.II.BapHTC.lb-
HaH pa3rpY3I<a Ton.1HBHoli CHCTeMbI. KOTOPYIO c.le.II.yeT npHHHTb 3£1
Ce.II.bMOH 3Tan. Ha 3TOM 3Tane n.1YH)J{epbI, nepeMel.U.aHCb B 06paT-
I:!OM HanpaB.1eHHH, oCBo6o..'l.HT HeKOTopbIH 06'beM, KOTOpbIi1 6Y.II.eT
3anOJlH5ITbC5I Ton.1HBoM, HaXO.l1.Hl.U.HMCH B CIfCTeMe B OKaTOM COCTO-
HHHH. OO:>TOMY lI..1H 06'beMa V" Ha 3TOM 3Tane ypaBHeHHe rpaHHLJ-
HbIX YC.l0BHH 6Y..'I.eT HIVleTb BHlI.
V dPH f C' t " /2 1 ,
-a lidi= - n n-r-- f!1i Ii . P yPII-PII'"
( 109)
EC.;1H P" < PM' TO B nO.II.KOpeHHOM BbIpaLKeHHH 3HaK nepe..'l. .l1.aB-
lIeHHHMH B BbIpa)J{emm (109) H3MeHHTCH. OCTa.lbHbIe ypaBlIeHIIH
rpaHHlJHbIX YC.'10BHH oCTaHYTcH 6e3 113MeHeHHH. PewalOTcH ypaBHe-
HHH npol{ccca B ceAbMOM 3Tane TaK )J{e, K£1K If B npelI.bID.Yl.U.eM.
BpeMH. B TelJeHHe KOToporo n.lymKepbI HaXO..'l.HTCH B COCTOHHHH
nOKOH, MO)J{HO npHHHTb 3£1 BOCbMOH ::Han npOl{ecca H£1COC£1. Opn
3TOM Ton.'1HBH£1H CHCTeM£1 6YD.eT p£13rppKaTbCH B pe3Y,;lbT£1Te BbI-
TeK£1HIfH paCWHp5lICl.U.erOCH B CHCTeMe Ton.1HBa LJepe3 pacnbI.1HBalO-
l.U.He OTBepCHIH.
Bo BXO.LI.HOM CelJeHHII Tpy6onpOBOlI.£1 y Hacoca .1IIMIITHPYIOl.U.HM
CelJeHIIe 1 6Y..'l.eT 1"Uj, f"Uj, T. e. n.'10l.U.£1D.b l.U.eJIII H£1rHeT£1Te.lbHoro
J{,;lanaHa, KOTOpa5I 3HalJHTeJIbHO MeHbwe npOXOD.HOH nJ10l.U.£1lI.II OK-
Ha. B CBH3H C 3TIfM B.'1HHHIieM Olma f" MO)J{HO npeHe6pe'lb, TaK KaK
npOl{eCC onpelI.eJIHeTC5I npOXOD.HOH nJ10l.U.alI.blO Jl"Uj' f Uf' LJTO D.aeT
OCHOBaHI1e C'lHTaTb pn" = Pu.. a_ 06'beMbI V ll " Ii V" 06pa3YlOT 06l.U.I1H
98
06"beM. OpH 3THX AOnYllJ.eHH5IX ypaBHeHH5I rpaHJ-I<lHbIX YCJ10BHH 3a-
mUIIYTC5I B BH.lI.e
-a(VH+VHK) H =J.LuJU! ]I Jl pH-P ; (110)
aV dPII =II. f ./ 2 -. rp_p' _ f C ( Ill )
dt .", '" V P JI H H T T'
YpaBHeHHe ,!J,BHMeHH5I K.;'lanaHa He H3MeH5IeTC5I. B COOTBeTCTBHH
t npe.lI.bI.lI.YLUHM efO MOMHO 3anHcaTb B BH.lI.e
AhK+B=PH-P , (112)
npWIeM 3HalJ.eHH5I K03cpcpHlI.HeHTOB A H B COXpaH5IlOTC5I TeMH Me,
lJ.TO H B npe.lI.bI.lI.YllJ.HX 3Tanax.
OpH6.JnIMeHHO HHTerpHpY5I npHBe.lI.eHHbIe BbIIlle ypaBHeHH5I H
peIlla5I HX COBMeCTHO, nO:IYlJ.HM
, I ( h' ) ]1 I ( h' ) 2
VAhK+D=-- --b +- - --b +D,
2 z' 4 x'
(113)
f.lI.e
D'=PH1-+- D - B - N ';
, '. f T M PO fTMCTI f T l'1tW(t)
N =P -t-
III 2ap:xV 2aV H ap:x\;
r-
V I 2
!-tulu! cplJ.t '-
b'= P
Y2 .N
!-t",f'Lj cpM ]I
b=
V 2a(V II + V nK )
f T I '1t
X'= 1+
2ap:x V
D = Ah K 1 +- B 1 + B.
OCTaTOlJ.HOe .lI.aB.'IeHHe onpe.lI.e.'meTC5J MOMeHTOM noca.lI.KH HfJIbI
CPOPCYHKH Ha ce.lI.cI0 H I\WMeHTOl\I nO.lHoro nepeKpbITH5J OKHa f n.
HaLJa.lbHbIe YC.l0BH5J noc.1e.lI.YIOLUero BnpbICKa 6Y.lI.YT 60JIee CTa-
6H,}lbHbIMH, KOr.lI.a OKHO fn nO.'1HOCTblO 3aKpbIBaeTC5I .lI.0 HalJ.a.'Ia OC-
HOBHOll pa3rpY3KH CHCTeMbi. B 3TOM CJ1YlJ.ae B ,}lHHHH HarHeTaHH5I 3a
OKHOM fn Be.'IHlJ.HHa Po 6Y;:I.eT no.'10MHTe.iIbHOH, nOTOI\1Y lJ.TO "iTa lJ.aCTb
CHCTeMbl pa3fpYMaeTC5I TO.TlbKO BC.'Ie.lI.CTBHe nO.lI.alJ.H TOnJIlIBa B lI.H-
JIlIH.lI.p .lI.BHraTe.'m. C.'1e.lI.OBaTe:IbHO, .J,aB.leHHe P"H'K He MmKeT 6bITb
MeHbllle .lI.aB.leHfm nOC8.lI.KH Hf,;IbI CPOPCYHKH. llaB.leHHe nOC8;:I.KH
Hr.'IbI npH6.1HllieHHO MOMHO onpe.lI.e:IHTb no C,'Ie.lI.YIOLUeH cpopMYJIe:
{tu-Q P<pc -f PtI
Pnoc = fu .
(114)
7*
99
npHHHB, 'ITO P..1< = pn1<, BeJlH'lHHY .z:r;aBJlCHHH P 'K MO}l{HO BbI'lH-
CJ1HTb H3 COOTHOllIeHmI
, f
P/i = t:PIIK'
Tor.z:r;a OCTaTO'IHOe .n:aB.neHHe B CHCTeMe rrpHO.'IH>KeHHO oy.z:r;eT
paBHO
Pnoc + PH
PO=
2
(115)
ECJ1H OKOH'IaTe.'IbHaH pa3rpY3Ka KaMepbI V H Ha'IHeTCH paHbllle
rr0.1IHOrO nepeKpbITHH OKHa fH' TO B J1HHHH HarHeTaHHH MOrYT o6pa-
30BaTbCH He 3anOJIHeHHbIe TOnJ1HBOM 06'beMbI. B KHHeMaTHKe Ha-
coca >KeJIaTe.'IbHO npe.z:r;YCMOTpeTb, 'IT06bI Ha Bcex paOO'IHX pe>KH-
Max OKHO f H ObIJIO 3aKpbITO B nepHo.z:r;bI, KorAa B KaMepe V H HMe-
IOTCH He 3anOJIHeHHble TOnJ1HBOM OO'beMbI.
nepHO.z:r; pe3KOH pa3rpY3KH OO'beMa V H, B03HHKalOIl.{eH BCJIellCT-
BHe ObICTporo nepeMelll.eHHH n.1YH}I{epOB B Ha'Ia.'IbHOe no.'Io}KeHHe,
oy.z:r;eM C'lHTaTb .n:eBHTbIM 3TanOM npou:ecca. BcaCbIBalOllI.He OKHa
OTKpbIBalOTCH paHbllle npHxo.n:a rrJ1ymKepa B Ha1Ia.TJbHOe nO.'Io)J{e-
HHe, "liTO BbI3BaHO He06xo.z:r;HMOCTblO OOeCne'IHTb npOTeKaHHe paoo-
'lero U:HKJ1a ceKU:HH CHCTeMbI B OrpaHH'IeHHbIH npOMe)J{YTOI{ BpeMe-
HH. C.'Ie.z:r;yeT OTMeTHTb, 'ITO rrpH .z:r;03HpOBaHHH Ton.1HBa .n:pocce.TJH-
pOBaHHeM Ha BcaCbIBaHHH >KeJ1aTeJ1bHO, 'ITOOhI IIHCJIO perYJ1HpYIOIl.{HX
opraHOB ObIJ10 MHHHMaJ1bHbIM (.'IY"lIllIe Bcero O.z:r;HH); Bc1HHHHe .n:py-
rHx cpaKTopOB Ha npou:ecc HanO.'IHeHHH He3Ha'IHTe.'IbHhIM; BO.'IHOBbIe
HBJIeHHH (KoJ1e6aHHe BeJ1H'IHH .z:r;aBc1eHHH H CKOpOCTH) Ha c1HHHH
BcaCbIBaHH5I OTCYTCTBOBaJIH H.'IH 6bI.1H 04eHb Ma.'1bIMH.
B.'IH5IHHe BcaChIBalOllI.erO OKHa Ha npOIlecc Hano.rIHeHHH He3Ha-
IIHTe.'1bHO, nOTOMY 4TO ero npoxo.n:Ha51 nJ10ll.l.a.n:b BO MHoro pa3 npe-
BbIllIaeT npoxo.z:r;HYIO n.10Il.{allb A03aTopa, npJ1IleM rrpoxo.z:r;Ha51 nJIO-
llI.a.z:r;b OKHa fec B03paCTaeT 04eHb 6bICTpO. B CB5I3H C 3THM BJ1H5IHHeM
OKHa fec MO)J{HO npeHe6pe4b. TaI{HM 06pa30M, OKHO fec onpe.z:r;e.'151eT
TO.'IbKO npo.z:r;omKHTe.'IbHOCTb npou:ecca Hano.rIHeHHH. B paCCMaTpH-
BaeMOM Hacoce OTCYTCTByeT pacxo.z:r; OTCe'IHOrO Ton.1HBa H3 .1lmHH
HarHeTaHHH. DJIaro.z:r;apH 3TOMY BO BpeM5I HanOJ1HeHH5I B KaMepy V H
no.z:r;aeTC5I KO.'IH4eCTBO TOnJ1HBa, Heooxo.z:r;HMoe .z:r;J151 3a.z:r;aHHoro pe)J{H-
Ma, T. e. q.... O.z:r;HaKO He.z:r;OCTaTOK TaKoro Hacoca B TOM, 'ITO OH He
OXJ1a>K.z:r;aeTCH OTce4HbIM Ton.'IHBOM, KO.1H4eCTBO KOToporo B nJ1YH-
}l{epHbIX Hacocax r-IHor.n:a B HeCKOJ1bKO pa3 60.'IbllIe, 4eM KO.'IH'Ie-
CTBO q1J.'
EC.'IH npe.n:nOJIO>KHTb, 'ITO .n:aB.'leHHe B OO'beMe V p paBHO .z:r;aB.'le-
HHIO, C03.z:r;aBaeMOMY no.z:r;Ka'lHBaIOIlI.HM HaCOCOM Pll' TO 3a BpeMH
OTKpbITH5I BcaCbIBalOllI.erO OKHa 'Iepe3 .z:r;03aTOp .z:r;0.1)J{HO npoflTH q1J.
TOnJ1HBa, Be.1H'lHHa KOToporo H3BeCTHa. npOlIecc HanO.'IHeHHH npn-
6,/IH}I{eHHO MO)J{HO onHcaTb ypaBHeHHeM
100
;-
qq = fli(iec / -; V P n - Ps,
HJlH
ofiJqJec 11+ V
qu,= 6n
(I 16)
B 9TOM c.1YIJae .n.aBJleHHe HaCbIIlI.eHHbIX napoB Ps B 06'beMe V u
)KeJlaTeJlbHO YIJHTbIBaTb, TaK KaK Be.TIHIJHHa Pn 'laIll.e Bcero He npe-
BbIIlIaeT 2 KFjCM 2 , IJTO Y)Ke CpaBHI1I\W C .n.aBJleHHeM HaCbIIlI.eHHblX
napoB. TaKHM 06pa30M, npH6.TIH)KeHHO perYJ15!Top .n.OJI)KeH 06ecne-
IJHBaTb c.-'Ie.n.YJOIlI.HH 3aKOH H3MeHeHHH npOXO.lJ:HOH nJIOIll.a.n.H .n.03a-
Topa:
flilt o = _ qu,
\Pec t l -%- y Pn- Ps
(117)
l.ho6bI BCJ1e.n.CTBHe 6bIcTporo OTKpbITHH OKHa fec YMeHbIlIHTb
BJ1HHHHe Ha HanOJlHeHHe B03MO)KHbIX K0J1e6aHHH .n.aBJ1eHHH B 06'beMe
V p, rlJ10Ill.a.n.b /lafa .n.OJI)KHa 6bITb KaK MO)KHO MeHbIlIeH, a 06'beM V p
60.!lbIlIHM.
llJIH OKOHIJaHHH paCIJeTa npo ecca nOAaIJfl pOTopHoro Hacoca
onpe.n.eJIHJOT KOJIWleCTBO Ton.TIHBa B 06'beMe V." OCTaJOIlI.erOCH no-
c.TIe OKOHIJaHHH pa60IIero npo ecca. ECJ1H npe,lLnO.l0)KHTb, liTO OKHO
fu 3aKpbIBaeTCH ,lI,O Ha'la.'1a OCHOBHOH pa3rpY3Kfl, KOTopaH HaCTynaeT
npH .lIaB.TIeHHH PHS' TO KOJ1HIJeCTBO TOnJIflBa, H8XO,ll,HIlI.erOCH B o6'be-.
Me V H , .
qocm = (V H mIn + V;as)+(V II mIn + V pa3)aPlI3 = (V H min+ V pa3)(1 + aPII3)'
( 118)
t,ll,e V H min - OQ'beM KaMepbI HarHeTaHHH npH J\taKCHMa.!lbHOM C6J1H-
)KeHlIH n.'1YH)KepOB;
V;aa = 2t nh;aa.
ECJlH npHHHTb, 'lTO 3a BpeMH HanOJ1HeHHH 6 06'beM V H 6Y,ll,eT
nO,ll,aHO TOnJ1HBO, paBHOe qlj.' TO BeJIHIJHHa C6060,ll,HOrO 06'beMa B
KaMepe HarHeTaHHH nepe,ll, HaIJaJIOM XO,ll,a C)KaTHH COCTaBHT
V OC . H = VHmax-qocm-qu,>
( 119)
HJ111
V OC . H = V Hmax -(VHmln+ 2fn h ;aa)(I + aPH3)-flio ::c v. V PH- P S .
lOl
CJ1e.rI:OBaTeJIbHO, BeJIlIlJl1Ha XO.'IOCTOrO xo.n:a n.rIymKepoB
h = V OCH
nx 2fn'
OC06eHHOCTH paC'leTa npou.ecca BnpMCKa TOnJIHBHOH CHCTeMbi
MHOrOTOnJ1HBHOro AH3eJ1S1. Ilp06J1eMa C03,J,aHHH ..'U13e.'1H, pa60TaIO-
llI.ero Ha pa3.'1lIlJHbIX TOn.'lIiBaX, nOJIHOCTblO He peweHa. LlaBHaH
npHlJHHa, onpe,n:e:UllOllI.a51 3a,n:ep)lmy peWeHH5I YKa3aHHOM np06.'1e-
MbI,- pa3.'IWIlIe B <p1I3IIlJeCKHX xapaKTepHCTHKax Ton.'lHB, nplIMeHH-
eMbIX B O.n:HOM ,n:H3eJ1e. Pa3pa60TKa np06.'leMbI MHOrOTOnJ1HBHOrO
,n:H3eJI5I CBH3aHa C peweHHeM BonpOCOB no TorWHBHOM CHCTeMe. 3a-
,n:alla CBOAHTCH K 06eCnelJeHHlO BbICOKoro KalleCTBa pa60Tbl TOnJ1HB-
HOM CHCTeMbI Ha pa3J1HlJHbIX Ton.'lHBax. 113BecTHo, lJTO napaMeTpbI
npou.ecca BnpbICKa lIe.lb3H paCCllHTblBaTb 6e3 YlJeTa <pH3HlJeCKIiX
KOHCTaHT Ton.1HBa, OCHOBHbIMH H3 KOTOpbIX HB.'lHlOTCH CLKHMae-
MOCTb, B5I3KOCTb, n.'lOTHOCTb, nOBepXHOCTHoe HaTHLKeHHe, HcnapHe-
MOCTb fI.'l1i <ppaKL(HOHHbIM COCTaB. B 6bICTPOXO,n:HbIX .n:1I3e.'l5lX MaJIOii
H cpe,n:HeH MOlll.HOCTH, Ton.'lHBHbIe CIiCTeMbI KOTOpbIX 51B.'lHlOTCH OC-
HOBHbIMH 06'beKTaMH Hcc.'le,n:OBaHHH,. OCBeIllaeMbIMH B .n:aHHOH pa-
60Te, np06.'leMa MHorOTonJ1HBHOCTH paCCl'iIaTplmaeTC5I KaK B03MOLK-
HOCTb IIcnO.'1b30BaHII5I B O.n:HOM .n:BlIraTe.'le 6eH3I1Ha, .'lHrpOHHa, Ke-
pOCHHa H ,n:H3e.'lbHOrO TOnJ1HBa. <PH3HlJeCKlie KOHCTaHTbI 3THX Ton-
J1HB, onpe,n:eJ1eHHbIe KaK cpe,n:HHe Be.'lHllHHbI no KaLK.n:OMY TOnJIHBY,
npHBeAeHbI B Ta6.'l. I, B3HTOH H3 pa60TbI npo<p. A. 11. TO.'1CTOBa.
Ta6ilUlja I
cIIH3H'IecKHe KOHCTaHTbI TOnJlHB
HallMeliOBaHHe I fieH3HH I .'IHrpoHH I KepocHH I ,n:lI3eJIbHOe
Ton/IUBO
n.10T!lOCTb npll 20° C 0,72-0,75 0,78-0,80 0,83-0,85 0,86-0,88
KHHCMaTII'-ICCKa51 BH3KOCTb
npH 20° C B CCT 0,65-0,7 0,8-0,85 2,4-2,5 3,5-6,5
4JpaKI.\HOHHb!H COCTaB:
Ha'-la.TJO pa3roHKH B °C 40-50 8Q-110 100-170 180-200
KOIICI.\ pa3roHKH IJ °C 180- 00 210-230 290-310 330-350
113 Ta6JI. 1 CJIe.n:yeT, llTO TOn.'lHBHaH CHCTeMa MHOrOTOnJ1HBHOrO
.n:H3emI ,n:OJ1LKHa pa60TaTb Ha TOnJ1HBaX, BH3KOCTb, n.'lOTHOCTb, a
c.'le.n:OBaTe.'1bHO, H CLKHMaeMOCTb KOTOpbIX CYIlI.eCTBeHHO OT.'IHllalOT-
C5I. BJ1HHHHe pa3J1HllHH npHBe.n:eHHbIX B Ta6JI. 1 <pH3HlJeCKHX KOH-
CTaHT TOnJIHBa npeLK.n:e Bcero OTpaLKaeTCH Ha BeCOBOH npOH3Bo.n:H-
TeJ1bHOCTH I-Jacoca, KOTopaH npH 3a.n:aHHOM nO.'10LKeHHII ero peHKH
,n:OJ1LKHa YMeHbwaTbCH npOnOpL(HOHa.'lbHO YMeHbIlleHHlO nJIOTHOCTH
TOnJ1HBa, T. e. Ha 12-18% npH nepexo,n:e C ,n:U3eJ1bHOrO Ton.'lHBa Ha
6eH3HH. B ,n:eikT1BIITe.'lbHOCTH npOII3Bo.n:HTe.'1bHOCTb YMeHbwaeTcH Ha
102
ew.e 60JlblllYlO Be.'Ul1.JIIH)' BCJ1eACTBHe Toro, 1.JTO C)J(HMaeMOCTb 6eH-
3HHa npHMepHO B 2 pa3a npeBbIlllaeT C)J(HMaeMOCTb )].H3eJ1bHOrO
Ton.'lHBa, a BH3KOCTb 6eH3HHa B 5-6 pa3 MeHbllle BH3KOCTH )].H3eJIb-
Horo Ton.'lHBa. OLl.HaKO TaK KaK Bce )'Ka3aHlibIe Ton.'lHBa OTHOCHT-
CH K Ma.'10BH3KHM. TO B.'lHHHHe EITOH KOHCTaHTbI Ha xapaKTepHCTIIKY
BnpbICKa H npOH3BO)].HTeJ1bHOCTb CHCTeMbI He3Ha1.JHTe.lbHO. BC.1e.LI.CT-
BHe 1.Jero 3THM B.'lHHHIIeM MmKHO npeHe6pe1.Jb.
C)J(HMaeMOCTb Ton.1HBa OKa3bIBaeT 60.'1blllOe B.'1IIHHHe Ha Bce
napaMeTpbI npouecca BnpblCKa II nO.LI.a1.JII Ton.'lHBa. CJlmMaeMOCTb H
n.10TIIOCTb B OCHOBHOM onpeAe.'lHlOT TaK)J(e CKOpOCTb pacnpOCTpa-
HeHHH 3BYKa B TOnJ1HBe, C KOTOpOH Ha1.Ja.'1bHbIH HMnYJIbC nepeMe-
w.aeTCH OT Hacoca K <popC)'HKe.
YMeHbllIeHHe BH3KOCTH npH O)].HOBpeMeHHOM B03paCTaHHII C)J(II-
MaeMOCTII H HcnapHeMOCTH 3aMeTHO YBeJ1H1.JHBaeT HepaBHOMepHOCTb
nO,J,a1.JH TOnJUlBa no ceKUHHM Ton.TJHBHOH CHCTeMbI. OpII1.JHHOH HB-
J1HeTCH TO, 1.JTO npH YMeHbllleHIIH B'H3KOCTH B03paCTaeT B.'1IIHHHe Ha
napaMeTpbI npouecca BnpbICKa Ton.1HBa HeT01.JHOCTII II3rOTOB.'leHIIH
3.'leMeHTOB CHCTeMbI, a nOBbIllleHHaH IIcnapHeMOCTb C03L1.aeT 6.'1aro-
npHHTHbIe YC.'10BH5I )]..'151 06pa30BaHH5I B pa3.'lI11.JlIbIX MeCTax CIICTe-
l\lbI napOBbJX H B03)].YlllHbIX npo6oK.
B CB5I3II C H3.'10)J(eHHbIM TOn.'lHBH)'lO cHcTeMY, npe)].Ha3Ha1.JeHHYlO
LJ:.151 pa60TbI Ha pa3JIH1.JHbIX Tonmmax, B nepBYlO 01.Jepe)].b c.'1e.rr)'eT
paCC1.JHTbIBaTb Ha B03MO)J(HOCTb 06eCne1.JeHH5I y)].oBJleTBopHTe.1bHoro
BnpbIcKa npH pa60Te Ha 6eH3HHe. OnacHocTb o6pa30BaHHH B CH-
CTe:\Ie ra30BbIX np060K 3aCTaB.'151eT Y.LI.e.'l5lTb 60.'lblllOe BIIHMaHHe
Bonpocy HanOJIHeHH5I 6eH3HHoM KaMepbI HarHeTaHH5I Hacoca.
K03<p<pHuHeHT C)J(HMaeMOCTH 6eH3HHa npH YBe.1H1.JeHI1If .rraBJ1e-
HHH OT aTMOc<pepHoro )].0 p = 500 Kr;CM 2 YMeHblllaeTC5I n01.JTH B
2 pa3a [10]. OpeH€6p€)K€HII€ 3THM <paKTopOM MmKeT 3Ha1.JIIT€JIbHO
YB€.lH1.JHTb norpelllHOCTb paC1.JeTa. HanpHMep, )].onyw.eHH5I, c)].e.'1aH-
HbIe npH pellleHHH ypaBHeHHH TeopHH mJJ.paB.1H1.JeCKOrO YJJ.apa, He
npIIMeHHMbI )].JIH 6eH3HHa, nOTOM)' 1.JTO K03<p<PHUHeHTbI YKa3aHHbIX
ypaBHeHHH B CJIY1.Jae npHMeHeHH5I HX K 6eH3HHY HeJIb351 C1.JHTaTb
nOCT05lHHbIMH. C.'le)].OBaTe.'1bHO, npHHUHnHaJ1bHO MeTO)]. paC1.JeTa
npouecca BnpbICKa, OCHOBaHHbIH Ha COBMeCTHOM pellleHHH ypaBHe-
HHH rpaHH1.JHbIX YCJ10BHH C CHCTeMaMH ypaBHeHHH (3). A.'151 6eH3HHa
He npHMeHHM, TaK KaK npH HaJIH1.JHH nepeMeHHbIX K03<p<PHUHeHTOB
pellleHHe CHCTeMbJ ypaBHeHHH (1) )].O.:1)KHO 6bITb OT.'1H'IHbIM OT pe-
llIeHH5I ypaBHeHHH (3). O)].HaKo, Y1.JHTblBa5l. 1.JTO Be.1H1.JHHbI napa-
MeTpoB npouecca BnpbIcKa onpeLJ:eJI5lI0TC5I [[3 ypaBHeHHH rpaHH1.J-
HbIX YC.'10BHH, KOTopble pelllalOTC5I npH6.1H)J(eHHO MeTO)].OM KOHe1.J-
HbIX pa3HOCTeH, npHMeM, 1.JTO H3.'10)J(eHIIbIH MeTO)]. paC1.JeTa npouecca
BnpbICKa npHMeHHM H )]..'1H pa60TbI CHCTeMbI Ha 6eH3HHe, T. e. Kor)].a
He06xo)].HlYIO Y1.JHTblBaTb 3aBHCHMOCTb a = f (p). TeMnepaTYPY Ton-
.'1HBa C1.JHTaeM HeH3MeHHOH. TaKHM 06pa30M, npe)].no.'1araeM, 1.JTO
npH y'IeTe 3aBHCHMOCTH a = f (p) 06eCne1.JHBae-rCH )].OCTaT01.JHa51 )].J151
npaHTHKH T01.JHOCTb H B c.1J)'1.Jae npHMeHeHH5I II3.'l0)J{eHHOrO paHee
MeTo)].a )]..lH paC1.JeTa npouecca BnpbICK3 6eH3HH3.
103
B TeXHI1lJ.eCKOH Jll1TepaType Her e.lI.I1HOrO Jl.IHe H 1151 OTHOCI1Te.TJbHO
TOro, KaKOH K03<pqJI1IJ.l1eHT HYLKHO HCn0J1b30BaTb .lI.J1H paClJ.eTa npo-
IJ.eCca BnpbICKa: Cpe.lI.HI1H acp H.111 MrHOBeHHbIH a (HJ1I1, KaK ero He-
TOlJ.HO Ha3bIBaIOT,- HCTHHHbIH, TaK KaK acp - peaJ1bHO CYllJ.eCTBYIO-
llJ.HH napaMeTp, 11 n03TOMY ero C TaKHM LKe OCHOBaHl1eM MOLKHO
Ha3bIBaTb 11CTI1HHbIM). 11.0 HaCTOHllJ.'erO BpeMeHI1 nYTeM OKaTI1H Ton-
J111Ba B 60M6e HenOCpe.lI.CTBeHHo onpe.lI.e.'IHJ111 TO.TJbKO K03<p<pI1IJ.l1eHT
loV
a cp =. (120)
Vo(p'- Po}
MrHoBeHHbIH K03<p<PI1IJ.l1eHT CLKHMaeMOCT11 onpe.lI.e.1HeTcH ypaB-
HeH11eM
I dV
a = v' dp . (I20a)
B BbIpa.iKeHI-IHX (120) 11 (120a):
V - KOHelJHbIH 06'beM TonJll1Ba noc.TJe ero CLKaTI1H .lI.0 AaB.1Je-
HHH p;
V o - HalJ.a.'IbHbIH 06'beM Ton.1J11 Ba, cooTBeTcTBYIOllJ.11H .lI.aB.1Je-
H11IO po.
113 aHaJ1H3a ypaBHeH11H (I20a) CJ1e.lI.yeT, ITO onpe.lI.emITb 1\03q,-
<p11IJ.l1eHT a MOLKHO, eCJ111 113BeCTHa IIp0I13BO.lI.HaH dVjdp. 11.aHHoe 06-
CTOHTeJ1bCTBO HB.1HeTCH OCHOBHblM 3aTpyn.HeHl1eM .lI..TJH Henocpen.cT-
BeHHoro .3KCnep11MeHTaJ1bHOrO ornpeAe.'IeHI1H .3TOrO napaMeTpa.
11. B. ACTaxoB [11], 10. 5L <DOMHH [72] 11 .lI.pyrHe 11CCJ1e.lI.OBaTe.1JH .lI.e-
J1a,,'I11 nOnbITKH paCClJHTaTb K03<p<pH IJ.l1eHTbI a H acp no CKOpOCTI1
3BYKa, KOTOPYIO onpe.lI.e,,'IH.TJI1 3Kcne pl1MeHTaJlbHo no BpeMeHI1 pac-
npocTpaHeH11H I1MnY.lbca B HarHeTaTeJIbHOM TpyoonpoBolIe 3alIaH-
HOH .lI..1JI1HbI.
11.J1H paClJeTa a H. B. ACTaxo B npe.lI.JIOLKI1JI [11] <POP MYJ1Y
u= _ I +pk +.. / I I + Pk ) 2 + _ , (121)
2p V \ 2p a 2 p p p p
f.lI.e
2 ( R2 +,,2 I )
k- --+-
- Er R2_,,2 I f.tn ,
R - HapYLKHbIH .lI.l1aMeTp Tpy6onpOBOJJ.a;
r - BHYTpeHHI1H .lI.l1aMeTp TpyoonpOBO.lI.a;
/In - K03<p<pI1IJ.11eHT nyaccOHa.
B <popMYJ1e (121) He YlITeHa 3a B11CI1MOCTb CKOpOCTI1 a OT .lI.l1a-
MeTpa TpyoonpOBO.lI.a dT' KOTopaH, CIOr.TJaCHO OnbITaM TaJIbOOTa [141,
npOT11BOnO.l0LKHa npl1HHTOH B TeOpHI1. TeOpeT11lJ.eCKI1 no paClJ.eTY
np11 YMeHbllleH1111 BeJ111lJ.HHbI d T CKOpOCTb a .lI.o.1JLKHa HeCKOJIbKO B03-
paCTaTb (pl1c. 41, KplIBaH 1). B .lI.eiikTBI1Te.:1bHOCTI1 (CM. KP11BYIO 2
Ha pHC. 41) np11 YMeHbllleH1111 .lI.11aMeTpa d T CKOpOCTb a YMeHblllaeT-
CH. CJIe.lI.yeT OTMeTI1Tb, lJ.TO .3TO OTHOCI1TCH TO,,'IbKO K TpyoonpoBo-
.lI.aM, y KOTOpbIX d T < 6 MM. YKa3at.lHoe HeCOOTBeTCTBl1e TeOp1111 11
104
OnblTa Tel\l 60.1bWe, lleM MeflMlIe 3HalleHHe dr. OTClO.l!.a c.1Je.l!.yeT,
llTO B lpOPMY.llY (121) He06xo.l!.HMO BBeCTH nonpaBO'lHbIH K03lpqm-
QHeHT, YllHTbIBalOlllHH B.IH5IHHe Ha CKOpOCTb a BHYTpeHHero AHa-
MeTpa Tpy60npOBO.l!.a. Ih06bI onpe.l!.e.1JHTb K03Q:>qJHQHeHT, H€06xo-
.l!.HMO npoBecTH .l!.OnOJIHHTeJIbHbIe cneQHa.1JbHbIe HCCJIe.QOBaHH5I.
B .l!.aHHoH pa60Te .l!..15I npHBe.l!.eHH5I B COOTB€TCTBHe OnbITOB pa3JIHll-
HbIX HCCae.l!.OBaTe.leH BocnO.1Jb30Ba.'IHCb 3aBHCHl\lOCTblO
1
a=-.
a 2 p
Cor.TJaCHO pHC. 41 paCxmK.l!.eHHe pacIIeTHoH CKOpOCTH a C no.'IY-
lleHHoH 3KcnepHMeHTa.TJbHO npH d r = 2 MM COCTaB.'I5IeT 4 %. c.TJe.l!.o-
BaTe,,'IbHO, .l!.JIH npHBe.l!.eHHH
pe3YJIbTaTOB OnbITOB [l0] B co-
OTBeTCTBHe C lpOPMY JIOH (I 21 )
HX Heo6xo.l!.HMO YMeHbwHTb
Ha 16%.
OTMelleHHoe HeCOOTBeT-
CTBHe B xapaKTepe npoTeKa-
a MiceK
fJOO
1250
f200
{
4
.7 OT tfl'f
PHC. 41. 3aBHcHMoCTb CKOpO-
CTH pacnpocTpaHCHH5I BO.TJII
.D:aBnCHH5I OT llHaMcTpa TPY-
60npOBO.D: a :
1 - paC'leT no q,opM}'."e (J2]);
2 - onblTHhle JJ.aHHhIe
o - OnbITbl Ta.;Ib6oTa; X - onbl-
'IbI ACTaxoBa
Q' fO- 6 fJ p ,
Cf1'/If{
f60 o,ff
f40 {j09
f20 0,07
fOO 0,05
80 o,OJ
60
{jOf
40 I !
47 0,75 0.8 (]85 (]9 {j95PT xf/;1
Pile. 42. 3aBIICIIMOCTb K03<j>Ij:JHI.\IICHTOB
It H OT nJlOTHOCTH Ton.1HBa:
i-a llPH p I KT/CM'; 2 - a npH
p 500 KT!C.,,'; 3 - IIPr Bbl'Hic."eHH"lii no
q,opMy.1e (1221
HH5I paC4eTHOH H 3KCnepHMeHTaJIbHOH 3aBHCHMOCTH a = f( d T ) .l!.aeT
OCHOBaHHe CllHTaTb BeJ1HllHHbI K03$qH1QHeHTOB a. H acp, onpe.l!.eJleH-
HbIe no CKOpOCTH 3BYKa a, TaKLKe npH6J'IHLKeHHbIMH. B CBH3H C 3TllM
npH paClJeTe npOQeCca BnpbICKa CHCTeMbI, pa60TalOlllei'I Ha pa3J1WI-
HOM TOnJlHBe, 6oJ1ee QeJ'IeC006pa3Ho nOJIb30BaTbCH 3KcnepmvIeHTaJIb-
HbIMH 3aBHCHl\IOCTHMH a. OT PT, nOKa3aHHbJ;\HI Ha pHC. 42, KOTopbIe
nocTpoeHbI no .l!.aHHbIM HeCKOJIbKHX HCCJIe.l!.OBaTeJIeH.
3aBHcHMoCTH nOCTpoeHbI .l!..1J5I aTMoc$epHbIx YC.'IOBHH H .l!..lH P =
= 500 KF;CM 2 . Ha pHC. 42 HaHeceHa TaKiKe 3aBHCHMOCTb K03$qm-
QHeHTa PT' BeJIHllHHa KOToporo .l!.JIH KaLK.l!.OrO 3HalleHH5I PT onpe-
.l!.eJ1HeTC5I H3 COOTHOWeHH5I
cto.106-ctsoo.106 R
= pPT'
500
( 122)
105
Tor,lJ.a 3aBHCI1MOCTb a OT p ,lJ..:1H Ka:tK,lJ.oro 3HalJemm PT npI16JII1-
}J-;:eHHO onpe!I,e.:1I1TCH q>OPMY.'IOll
a p = aO- P?p. (123)
3aBI1CI1MOCTb OT ..1aB.1eHI1H nJIOTHOCTI1
tP o pMy,,1e, nplfBe.rreHHoI1 B pa60Te [10]:
PTP = Po (1 + ap).
Ton.1I1Ba YlJHTblBaeTCH no
( 124 )
YpaBHeHHH (121), (123) 11
(124) npI1l\1eHlE\tbI ,lJ.J1Sl paClJeTa
r npol.(ecca BnpbIcK8 6e3 HcnO.!Jb-
30BaHI1Sl lJ,B1\l. OpH paClJeTe
BnpbIcKa Ha lJ,B;\l MO:tKBO pe-
UlaTb 60.1ee C.l0:tKHbIe 3aBHCHMO-
cni a OT p.
Opol.(ecc BnpbIcKa 6eH311Ha
paCClJIfTbIBaeTcSl no I13J10:tKeHHO-
MY BbIme MeTOJl,Y. OTlIHlJUe 3a-
KJIIOlJaerCH B TOM, lIro A.TJH Ka:tK-
,lJ.oro OTpe3Ka BpeMeHII).t no
<}>opMY.le (123) OnpeAeJlHerCH
I(}(} 2(}(} J(}(} 4(}(} f(}(} P Kf/CN 2 HOBoe 3HalJeHUe Up, npHlIeM ,lJ.aB-
.TJeHUeM p 3aJl,aIOTCH npI16.111-
:tKeHHO C YlJeTOM xapaKTepa 113-
lVIeHeHHH BeJII1lJHHbI n:aB.leHHH p
1 - v 48 CCT' ? _ V = 15 CCT" 3 _ B HalJaJ1e npOMe:tKYTKa BpeMeHlf
v 102 u.;'; 4 ....: v- = 200 CCT; 5 -' v !1t, KOTOpaH lf3BeCTHa lf3 pac-
470 CCT; 6 - ". 975 CCT lJera npOl.(eCCa ,lJ.JIH npeJl,bIJI,yme-
ro OTpe3Ka BpeMeHlf. Oorpern-
HOCTb B Onpe,lJ.eJIeHlflf p, paBHaH 5-10 KTjCM 2 , He BHOClIT B paClJeT
3aMeTHOll HeTOlJHOCTH. OUIU6Ka 6y.n.eT el1l.e MeHbll1e, ec.'1U paClJeT
BeCTH no <}>opMY.'Ie
(1
Nlc{l/(
11;00
T ---r
;
I
If
600
1200
rooD
800
1;00
()
Puc. 43. 3aBllcHMoCTb CKOpOCTII 3BYKa
OT aBJlCHHH B JKH,'\KOCTHX pa3J1HQHOH
BH3KOCTH:
p = P + PI
cp 2'
I13MeHeHHe nJIOTHOCTI1 6eH3HHa Y'lHTbIBaeTcH ypaBHefIHeM (124).
Oplf paC'leTe npOl.(eCca BnpbIcKa Ha 60J1ee TH:tKe.'IbIX TOnJIlfBax oco-
6bIX 3aTpY,lJ.HeHlfll He B03HlfKaeT. Oplf lfcnO.TJb30BaHHlf B .lJ.I13eJIe
oo.TJee BH3KHX TOn.'IlfB He06xo,lJ.HMO Y'IHTbIBaTb 3aBHCI1MOCTb CKOpO-
CTH a pacnpOCTpaHemIH lfMny.-Ibca OT BH3KOCTI1, B.'IHHHHe KOTOpOH
B03paCTaeT npl1 YBe.1I1lJeHHH ,lJ.aB.TJeHHH. Ha pHC. 43 nOKa3aHbI 3a-
BHCHMOCTH CKOpOCTI1 3BYKa a OT .n.aB.'IeHI1H CMeceH TOnJ1I1Ba C MaC-
JIOM. 113 pI1c. 43 c.'Ie,lJ.yeT, LITO OrpaHH'lI1l3aIOmI1MI1 KpI1BbIMlf HBJIR-
IOTCH 3aBI1ClfMOCTlf a = f (p) ,lJ..HH ,lJ.I13e.TJbHoro Ton.'IlfBa 11 'lHCTOrO
MaC.TJa, HO TO.TJbKO B ,lJ.I13e.TJbHOM Ton.1I1Be CKOpOCTb a npI1 YBe.TJJ11Ie.
HI1H 3Ha'leHlfH p OT P = 25 Kr;CM 2 ,lJ.0 P = 700 KTjCM 2 Bce BpeMH
B03pacTaeT. lfHTeHCI1BHOCTb B03paCraHI1H CKOpOCTU a npH YBe.'IUlJe-
HUH P YMeHbll1aeTCH. D..'IH MaCJ1a 6e3 npIIMeceH CKOpOCTb a npH
106
YBe,,'1H'IeHHH P Ha'IHHaeT Cpa3Y pe3KO YMeHbWaTbCH H npH p =
= 500 KT/Cld z COCTaBJIHeT TOJ1bKO 460 MiceK.
LIoi'IH CMeCH C y = 15 ccm CKOpOCTb a npH YBe.'1H'Iemm .D.aB.'IeHHSI
HenpepbIBHo B03paCTaeT .lI.O p = 600 KFlcM z , noc.'1e 'Iero npaKTH'Ie-
CKH coxpaHHeTcH HeH3MeHHoH. DpI1 CMeCHX C y> 15 ccm Ha6.:110-
.n.aIOTCH HBHO BbIpaLKeHHbIe KpHTH'IeCKHe TO'IKH. LIo P < Pnp CKO-
pOCTb a npH YBeJIH'IeHHH P B03paCTaeT, a .lI..'1H 06.'1aCTH P > Pnp
CKOpOCTb a YMeHbwaeTCH. LI.1H CMeCH C y = 102 ccm P"p =
= 300 KT/CM 2 , a .lI..'1H CMeCH C y = 200 ccm pnp = 100 KT/CM!.
B CMeCH C y = 470 ccm, B MaC.'1e C y = 975 ccm CKOpOCTb a Ha'IH-
HaeT YMeHbwaTbcH C MOMeHTa Ha'IaJ1a nOBbIllIeHHH .lI.aB.'1eHHH. DpH
paC'IeTe rH.lI.paB.'1H'IeCKHX YCTPOHCTB, B KOTOpbIX npHMeHHlOTcSl .iKH.lI.-
KOCTH C Y > 15 ccm, He06xo.lJ,HMO Y'IHTbIBaTb KpHTH'IeCKOe .D.aB.'1e-
HHe pnp KaK TO'IKY pa3pbIBa <}>YHKUHH, B KOTOpOH H3MeHHeTCH xa.
paKTep npOTeKaHHH 3aBHCHMOCTH a = f (p) .
3. PAC'fET npOL!.ECCA BnPblCKA TOnnJ1BHOM CJ1CTEMbl
IiE3 HArHETATEnbHoro TPYIiOnpOBOAA
Hacoc-cfJoPCYHKH c MexaHH eCKHM npH80.ll.0M. MeTOJI: paCQCTCi
npou.ecca BnpbICKa TonnHBa nacoc-<}>OPCYHIWH C 'MexaHH'IeCKHM
npHBO.lJ,OM n.'1YH.iKepa paCC1\1aTpHBaeTCH npH Hcno.'1b30BaHl1l1 c.'1eJI:Y-
lO HX THnOB pacnbIJUJTeJIeH: KJ1anaHHo-con.'10BOrO, BbmYCKaeMoro
JIeHKap30M (CM. pHC. 20, a), 6eClI.ITI1<}>ToBoro 3aI\pb1T01O (CM.
pHC. 20, 6) H KJ1anaHHO-COnJ10BOrO paCnbJ.1IHTe.'1Sl, npe.lJ,.'10.iKeHHOrO
npo<}>. 11. B. ACTaxoBbIM (CM. pHC. 200).
O.lJ,HOH H3 cy ecTBeHHbIx oc06eHHocTeH npou.ecca BnpbIcKa Ton-
JIHBa Hacoc-<}>0PCYHKO I SIBJ1SleTCH B.'1HHHHe Ha np()u.ecc BnpbIcKa
.lJ,e<}>opMau.HH MeXaHH'IecKoro npHBO.lJ,a. IIc('.'1e.lJ,oBaHHSI [73, 74] no-
Ka3a.'1H, 'ITO 3TO B.TJHHHHe MO.iKeT 6bITb J1.a)l\e 60.'1ee cy ecTBeHHbIM,
tIeM Boi'IHHHHe C.iKHMaeMOCTH Ton.'JHBa. 1Ie<}>opMau.HH _Mex.aHH'IeCKOrO
npHBO.lJ,a npH onpe.lJ,eJ1eHHbIX YC.'10BIUIX cy ecTBeHHo BJIHHlOT H Ha
pa60TY CHCTeMbl C HarHeTaTe.TJbHbIM Tpy60npoBO.lJ,oM. B 3THX cJ1Y'Ia-
SIX npHMeHHMa MeTO.lJ,HKa Y'IeTa BJIHHHHH .lJ,e<}>opMau.HH npHBo.n.a, H3-
JIO.iKeHHaH HH.iKe. I1pH paC'IeTe npou.ecca BnpblcKa coxpaHSllOTcH
)J,ony eHHH, npHBelleHHbIe B r.'1. II. 1Iono.'1HHTeJIbHO npHHHMaeTcH:
I) B.'1HHHHe BO,,'1H .D.aBJleHHSl npeHe6pe.iKHMO Ma.'10, n03T01\IY ero
He Y'IHTbIBalOT. B KaLK.lJ,bIli MOMeHT npou.ecca .lI.aBJ1eHl1e B J11060H
TO'IKe Hepa3.lJ,e.'1eHHOrO 06'beMa (HanpHMep, 06'beMa, 3aKJ1IO'IeHHO-
ro Me.iK.lJ,y n.TJYH.iKepOM H Hr.:10H HJIH K,,'1anaHOM) O.lJ,HHaKoBO. 1Iony
IlleHHe onpaBllbIBaeTcH TeM, 'ITO paccTOHHHe Me)J\.lJ,Y TOpU.OM n.'1YH-
LKepa H pacnbwHBalO HMH oTBepcTHSlMH HeBe.'lHKO (0,03-0,05 Jl
.lJ,.TJH Hacoc-<}>oPCYHOK 6blCTPOXO.lJ,HbIX .lJ,H3e.'1eH), a CKOpOCTb BbIpaB-
HHBaHHH .lJ,aB.TJeHHH (CKOpOCTb 3BYKa) 1300 MiceK;
2) llHHaMHKa pa60TbI MeXaHH'IecKoro npHBolla n.TJYHfKepa He
()Ka3bIBaeT B.'1HHHHH Ha npou.ecc BnpbIcKa;
3) 3aBHCHMOCTb Me.iKllY .lJ,e<}>opMau.HeH npHBO.lJ,a H .lJ,aB.'1eHHeM
Ton.'1HBa Ha n.'JymKep .TJHHeHHa. LIe<}>opMauHH npI1BoJ1.a, BK.'l104aH
107
AeqJOpwJaUlIIO nJIymKepa HerO TO,,'1, KaTe.15I .1 = knpf np"II., rD.e k np -
K03<}:J<}:JHU11eHT D.e<}:JopMaU11H npHBOD.a. J.13I'\'leHeHHe BeJ1H4HHbI k np
npH 113MeHeH1111 nO.'lOJKeH115I KY.'la4Ka HeBe,,'l11KO, 11 n03TOMY 3Ha'Ie-
H11e k np , onpeD.eJIeHHOe ,lW5I HeKOToporo cpeD.Hero nO.TIO)KeHH5I KY-
.TIa4Ka, MO)KeT 6bITb 11CnO.lb30BaHO H D.JI5I D.pyrHx ero no.'lOJKeH11H.
n p11 paCIIeTe Hacoc-<}:J0PCYHK11 C K,,'lanaHHo-con.'lOBbIM paCnbI.TJ11-
TeJ1eM THna JIeHKap3 D.On0J1H11Te.TIbHO npHHHMalOT, 4TO KOHTpO.lb-
HbIH K.'lanaH OTKpblBaeTC5J H 3aKpbIBaeTC5I MrHOBeHHO, KOrD.a D.aB"
Jlemie B Kal\lepe n.1YH)Kepa paBHO D.aB.'1eHHlO OTKpbITH5I (3aKpbITIHI)
KJIanaHa. B KOHKpeTHOM CJIY4ae npouecc Bnp CKa pa3D.eJI5IeTC5I Ha
3TanbI A.'15I arperaTa B u.eJl0M. JI.J15J Hacoc-cpOPCYHKH TIma JIeHKap3
3TH 3TanbI 6YD.YT c.leD.YlOUJ.HMU:
I) OT Ha4aJ1a D.BUJKeHU5I n,,'lYHJKepa D.O OTKpbITU5I KOHTpo.lbHoro
KJIanaHa;
2) OT I\lOMeHTa OTKpbITH5I KOHTpo.TIbHOrO K.TIanaHa D.O Ha4a.TIa
reoMeTpu4eClwH nOD.a4U;
3) reOMeTpU'leCKa5I nOD.a4a;
4) OT Ha4aJIa OTKpWTH5I OTce4Horo oTBepCTH5I AO nOCaD.KH KOH-
Tpo.lbHoro K.'1anaHa;
5) pa3rpY3Ka KaMepbI K,,'IanaHa OT D.aBJIeHH5I.
npH 3TOM npHHHMaeTC5I, 4TO Ton.TIHBO Ha411HaeT BnpblcKHBaTbC5I
B I\WMeHT OTKpbITH5I KOtITpo.lIbHOrO K.TIanaHa. JI..TI5I D.BYX D.Pyrux
paCnbIJ111Te.TIeH pa3611BKa Ha 3TanbI 11Ha5I H MO)KeT 3aB11CeTb OT
peJK11Ma pa60TbI annapaTypbI 11 D.aB.leHH5I OTKpbITH5I 3anopHoro op-
raHa. flpH D.OCTaT04HO 60JIblllOM D.aB"leHl1H OTKpbIT1151 3anopHoro
opraHa pa36HBKa Ha nepHOD.bI D..TI5I D.BYX D.pyrux paCnbI,,'l11TeJleH
c.TIeD.Y lO lIJ.a5I:
I) OT Ha4a.'Ia D.B11JKeH115I n.'1YH)Kepa D.O Ha4a.la reOMeTp114eCKOH
nOD.a411;
2) OT HalJaJla reo leTpHlJeCKOH nOD.alJH D.O HalJa.'1a OTKpbITH5I 3a-
nopHoro opraHa;
3) OT Ha4a.'la OTKpbITH5I 3anopHoro opraHa D.O 1!.OCT11)KeHH5I Hr-
J10H (KJIanaHoM) ynopa;
4) OT D.OCTH)KeHH5I HrJIOH (KJIanaHoM) ynopa D.O Ha4aJIa OTce4-
KH BnpblCKa;
5) OT HalJa.'1a OTCe4K11 D.O Ha4aJ1a nOCa.llKH Hr.'IbI (KJIanaHa);
6) OT Ha4aJIa nOCaD.K11 HrJ1bI (KJ1anaHa) D.O nOJ1HOH ee (ero)
nOCaD.KH Ha ce.llJ1o.
BBHD.Y MaJ10H Be,,111411HbI 06'beMa, 3aK.1I1O'leHHOrO Me)KD.Y 3anop-
HblM opraHoM 11 paCnbIJII1BalOlIJ.HM oTBepCT11eM, 3TanOM nOD.TeKaHH5I
TOnJ1HBa 113 3Toro 06"beMa noc.TIe 3aKpbIT1151 3anopHoro opraHa npe-
He6peralOT. JI.JI5I paCnbI,,'1HTeJ1eH 3aKpbIToro T11na oco6eHHOCT11 npo-
TeKaH1151 npou.eCCOB Ha Ha'laJIbHWX 11 KOHe'lHWX Y4aCTKax BnpWCKa
TOnJ1HBa, KOrD.a 3anopHbIH opraH Y)Ke OTKpbIT, a BnpblCKa elIJ.e HeT
H.TIH 3anopHbIH opraH elIJ.e He 3aKpbIT, a BnpbICK Y1Ke npeKpaT11JIC5I,
paCCMOTpeHbI BbIIlle. He OT,,'l114aeTC5I OT paccMoTpeHHoro TaK)!\:e
MeTO.ll Y4eTa BbIJKHMaHH5I TOnJ1HBa 113 KaHaJIa paCnbIJ1HBalOlIJ.11X OT-
BepCTHH npH paCnbIJ1HTeJIe 3aKpbIToro T11na.
108
DpII KJIanaHHO-COnJ10BbIX paCnbIJ1IITe.'1HX npOl..{eCC BbI}!{HMaHHH
TOn.:1HBa B KOHI.{e BnpbICKa OTCYTCTByeT. B HaQ8.'1e npOl(eCCa B03-
MO}!{eH HHTepB8.TJ BpeMeHH, KOr.n:8 KJ18naH y}!{e OTKpbJ.'lCH, HO
BnpbICK Qepe3 paCnbl.'IHBalOll.{He OTBepCTHH ell.{e He Ha'laJICH, TaK
KaK Ton.'1HBOM 3anOJIlmeTCH 'laCTb 06'beMa, pacn0J10}!{eHHaH Me}!{.n:y
K.'1anaHOM H pacnbI.'1HBalOll.{HMH OTBepCTI1HMH, KOTopaH OKa3a.'1aCb
CB060.n:HOH OT TOnm1l3a H3-3a BH6paI..{HH, KHneHHH Ton.'IHBa, YMeHb-
meHHH 06'beMa, 3aHliMaeMoro TOnJ1HBOM B pe3y.'IbTaTe CHH}!{eHHH
ero AaBJIeHHH. PaC'leT npOl..{eCca B Te'leHHe paCCMaTpHBaeMoro HH-
Tepn8.TJ8 He npeJ1.CT8n.7HeT TPYJ1.8, eC.TJH H3BeCTH8 neJIH'lHH8 06'beM8,
cB06o.n:Horo OT TOnJIHB8. 06bIQHO 3THM HHTepB8JIOM MO}!{HO npeHe-
6pe'lb.
Oco6eHHOCTbIO IWanaHHO-COnJ10BOrO pacnbI.TJHTe:IH, Oll.HaKO, HB-
./meTCH TO, 'lTO B Te'leHHe 3Toro HHTepBa.'Ia ra3bI He MorYT npo-
pBaTbCH B paCnbIJIHTeJIb, TaK KaK lI.aBJIeHHe npenHTcTByeT OTKpbI-
THIO K.:lanaHa H n03TOMY lI.aBJIeHHe nepell. 38nopHbIM opraHOM
BcerA£i 60.TJbIlle 1I.8B.'1eHHH nOCJ1e Hero. DpOpbIB ra30B B paCnbl.!1H-
Te.:lb npHHI..{HnH8JIbHO HeB03MO}!{eH npH K.'18naHHO-COnJIOBOM pacnbI-
.TJHTeJIe T8K}!{e B KOHl..{e npOl..{eCC8 BnpbICKa.
DpH paCCMOTpeHI1fI npOl(eCca BnpbICK8 no BceM 3TanaM YCTa-
HOBJleHO, 'lTO lI.ecpopMal..{HH npHBOll.a CKa3bIBalOTCH Ha npOl..{eCce
BnpbICKa npH Bcex 31'anax, KpOMe nOCJ1eAHerO - nOll.TeKaHHH Ton-
JIHBa H3 K.'IanaHHOH KaMepbI paCnbIJIHTe.TJH nOCJ1e nOCall.KH KOH-
Tpo.lbHoro KJ1anaHa (KJlanaHHo-con.'IOBOH pacnbI.'1HTe.'1b J1eH-
Kap3) *. .L{ecpopMal..{lfH npHBOll.a B.1HHIOT Ha BeJ1H'lHHY ceKYHlI.HOH
nOll.a'lH Ton.:1HBa n.'1YH}!{epOM, 3aKOH H3MeHeHHH npOXOll.HOrO ce'le-
HHH B OKRClX rH.:lb3bI nJ1YH)Kepa H Be.:1H'lHHY 06'beMa Ton.1HBa B CH-
CTeMe. B.'1HHHHe lI.ecpopMal..{HH npHBOll.a Ha Be.:1H'lHHY ceKYHlI.HOH
no.n:aQH TOfIJIHBa fI.1IYH}!{epOM YAaeTCH YQeCTb BBe.n:eHHeM B ypaB-
HeHHH 6a.TJaHCa CYMMapHoro K03cpcpI1I..{HeHTa C}!{I1MaeMOCTH TOnJ1HBa
II npIIBOll.a BMeCTO K03cpcpI1l..{I1eHTa C}!{HMaeMOCTH TOnJ1HBa.
CYMMapHbIH K03cpcpHI..{HeHT C}!{HMaeMOCTII
_ + -..L knpf _
a cy ." - a aoe", - a I _ V - a +
u :n;c 0
" 1+- d-
4V' n
k np :n;2
-d 4
16V' n
(125)
r.ne c - nOCTOHHHbIlt 1I..'1H lI.aHHOH nJ1YH}!{epHOH napbI .'1HHeHHbIH
pa3Mep;
V' - lJaCTb o6'beI\1a C}!{aTHH, He 3aBHCHlllaH OT lI.HaMeTpa O.:lYH-
}!{epa.
1-13 aHaJ1H3a ypaBlIeHHH (125) BHlI.HO, lJTO C YBeJ1HlJeHHeM lI.Ha-
MeTpa nJIYH}!{epa K03tPcpHIJ,HeHT aaeg; B03paCTaeT 60.'1bIlle, lJeM n.'1O-
'" fIpH Y'ICTC xapaKTepa .a:BHLKeHHH K.lla1TaHa elj:JopMal.\HH npHBo.a:a MorYT
OKa3aTb B.'1I1HHHC lIa BC.'!II'HlHY .D:aB.1CHIIH B Ha'-laJle 3Tana nO.D:TCKaHIIH.
109
T :n:c d ,} 1
I.IJ.aAb n.1YH)Kepa. O.lbKO npH - - YBe.'IIJ1IeHHe UiJeffj C B03-
4V' n
pacTaHHeM HaMeTpa n YH)Kepa npoHcxo HT npaKTHlfecKH nponop-
llHOHa.lbHO n.l0I.IJ.a H n.'IYH)Kepa.
TaK KaK Ha npollecce BnpbIcKa CKa3bIBaeTCH He Be.'IHlfHHa UiJe(/'J.
a UiJeffj V>i, TO B03paCTaHHe HCKa)KeHHH npOlleCCa BnpbICKa B pe-
3y.'IbTaTe C)j{HMaeMOCTH npHBO..'l.a npOHCXO HT npOnOpllHOHaJ1bHO
lfeTBepTOH CTeneHH YBe.'IHlfeHHH JJ.HaI\IeTpa n.'IYH)Kepa. l.h06bI CO-
XpaHHTb HeH3MeHHblM 3anaC npOlfHOCTH KOHCTPYKllHH npH YBe.'1Hlfe-
HHH liaMeTpa n.1YH)Kepa, .IWCTaTOlfHO nOBbICHTb )KeCTKOCTb npHBO-
a npOnOpUHOHa.TJbHO YBe.:1HlfeHHIO n.'10I.IJ.a H naYH)Kepa (ec.rnr
npHHHTb, lfTO ..'I.aB.leHHH BnpbICKa He B03paCTYT). TaK KaK HCKa)Ke-
HHH npollecca BnpbICKa H3-3a C)KHMaeMOCTH npHBo a B03paCTalOT
B lfeTBepTOH CTeneHH YBe.'1HlfeHHH AHaMeTpa nJ1YH)Kepa, TO B HeKO-
TOpblX C.1YlfaHX onpe e.'1HIOW:HM cpaKTopOM npH OlleHKe He06xo..'l.H-
MOH CTeneHH nOBbIlIleHHH )KeCTKOCTH npHBo a npH YBe.'1H4eHHH Ha-
MeTpa n'!lYH)Kepa MO)KeT HBHTbCH YC.loBHe no.1Y l leHHH BnpblCKa c
I\IHHHMa.lbHbIMH HCKa)KeHHHMH. n.1H 3Toro HV)KHO 06ecnelfHTb Ma-
able 3Ha l leHHH C)'MMapHbIX J1HHeHHbIX ecpOM-allHH npHBo a. Ocy-
I.IJ.eCTBHTb rIOc.le Hee OBO.TJbHO TPY HO, TaK KaK C YBe.J1H4eHHeM
celfeHHH .rr.eTaaeH B03pacTalOT HHepllHoHHbIe YCH.1HH, a YMeHblIleHH
lfHGla 3BeHbeB npHBo.rr.HT I< He06xo HMOCTII pacno.'1araTb Ky.'Ia4KO-
BhIH BaJ1 B rOJIOBKe JJ.H3e H. OTMelJeHHble TPYJJ.HOCTH 5lB.1J5IIOTC5J. 0,1-
HOH H3 npH4HH nOHBaeHH5J. npenaO)KeHHH 06 HcnO b30BaHHH Ha
BbICOKOcpOpcHpoBaHHbIx nH3e.'I5J.X nHeBM0rI1JJ.paB.1HlfecKoro npHBo;J:a
n.1YH)Kepa Hacoc-cpoPCYHOK. 4T06bI rIO,1lfepKH)'Tb Ba)KHOCTb YlfeTa
AecpopMallHH npl-IBOna, OTMeTHM, lITO nm! npHBo a Hacoc-cpOPCYH-
1m Ha BVXTaKTHbIX H3e.1HX 51M.3 Be.1WIHHa ual'(fj nOCTHraeT 60.'1ee
60% aT d npH ;J:aB.:'IeHHH 1000 Kr;CJrt 2 . .
EC.1H npHH5J.Tb BO BHHMaHHe, lJTO B.1HHHHe AecpopMaUHH npHBO-
.rr.a He orpaHHlfHBaeTC5J. H3MeHeHHeM ceKYH HOH nOJJ.alJH Ton HBa
n.l)'H)KepOM, TO CTaHeT HOW Ba)KHOCTb Y4eTa necpopMallHH npHBOna
npH COCTaB.'IeHHH pac4eTHblx ypaBHeHHH.
B.!IHHHHe LLecpopMaUIIH npHBolI.a Ha xapmuep H3MeHeHHH npo-
xonHoro celIeHHH B OKHax rH.lb3bI rI.:1YIUKepa H Be.1H l IHHY 06"beMa
Ton.'IHBa B CHCTeMe YlfHTbIBaeTcH c.leJJ.YlOlIlHl\I 06pa30M.
XOJJ. rO.l0BKH n.:l)'H)Kepa
h = h ll -.1 = h ll -k llp f llPII; (126)
3neCb h n - XOJJ. n.1YH)Kepa aT HalJa.'1a era JJ.BH)KeHHH npIl a6CO.'IIOT-
HO )KeCTKOM npHBOJJ.e;
,:1- CYMMapHaH .1HHeHHaH necpopMaUHH npHBOJJ.a.
no HaHJJ.eHHOMY 3HalfeHHIO h HaXOJJ.HT 3Ha l IeHH51 f 0 H V>i, KOTO-
pbIe H HCnOJlb3YlOTCH B paClfeTax.
PaCCMOTpIIM HaH60.1ee C.'IO)KHbIH .rr..:1H paClfeTa c.'IYlJai1 Hacoc-
CPOPCYHKH C pacnbI.:1HTe.'JeM 3aKpbIToro TIIna. npH 3TOM 6y.rr.eM ClfH-
TaTb, lJTO B Hacoc-cpopCYHKe HarHeTaTeJ1bHbIH K anaH OTCYTCTByeT_
110
Ha Ha'1a.JlbHOM Yl.JaCTKe nepBOrO :nalla paC'-leT Be.n.e'fCH 6e3 Yl.JeTa
OKI1MaelllOCTH TOn.1HBa 11 JJ.e4JopMau.l1lI npHBOJJ.a no ypaBHeHfUO (12).
Ha nepBOl\I lJ BTOpOM 3Tanax paCtIeTa I1r.'Ia HaxOJJ.HTcH Ha CelIJ1e II
npou.ecc BnpblCKa onHCbIBaeTCH ypaBHeHf-IeM 6a.laHca.
h n fl n cMJjcel(
/'fM
D
0,6
0,5
o.
43
0,2
1
/0,.,/12
1(t0 100
5,0 50
h n HM
liDO 1200 P I(tJcl'f2 D
6)
50D
1000
i
I
PI( 'C/12
il)
PI1C. 44. BcnOMoraTc.1bHbIC rpalj:Jl1KH. Hcno.1b3YClIIblC .!J..TJ5I npoBC.D.CHI15I
pac4cT8 Hacoc-<jJoPCYHKH c MeX8HH4eCKHlII npHBO.D:01\I:
a - XO;! nJlYH>Kepa H CKOpOCTH BbITeCHeHIHI HM Ton..rIHB3 riP" Il = 1500 H
n = 301) o(;!.MUI-l: 6 - lle OpMaUH}l npUBo.aa H3COC-Q,10PCYHKll; B - nJ10lll.a.I1,b
3KBHBaJIeHTHoro npo:xo.1J.lloro celleHHSJ B OJ{HC)X BTy.,1I\H nJ1YH:>Kepa npll pa3.nHlJ-
HblX flD.I10ncCHH5IX peflKH; i! - 06"beM noJJOCT}.1 BblCOKoro .l1.3B.J1eflH.R H8COC-
cjJOPCYHKII; Q - IICTMHHbill K03q,q,Hw!eHT C>I<HMaeMOCTI!; / - Hacoc-q,opcYHKa
C 38KPl,lTblM pacflbu1HTe.neM; 2 - f{"laI18HHO-con.noB3R uacoc-$oPCY1HW nocJle
OTKpblTlHI KOHTpo.11bJ-lOrO KJJanaHa: 3 - K.T1anaHHO-con.rJOB3H H3e:Oc-ij)opCYHl\a
110 OTl<pblTHJI KOfnpO "'1bHoro K.TJauaHa
YpaBHel.me 6a.13HCa Ha nepBOM 3Tane:
r-
( , 2 ) dPH f / 2 .. f
aV"Tknvfn ---;u-=tnClI-J.lo 0 \/ p V PH-Pec.
( 127)1
YpaBHemle (127)
- 1tJ(p,,; t)dt.
MOn eT 6bITb npeliCTaB.1eHO KaK dp" =
111:
PernaH ero B KOHe'lHbIX pa3HOCTHX, MO>KHO 3anHcaTb
!'!.. p _ P - p = M [ 1\J(PH. t) + 1/!I (PII, t) ]
H - H HI 2.
PerneHHe ypaBHeHHH (127) BbIrJIH.lU1T TaK:
fnCm-!lorfol } / 2 J! PHI-Pec
. P
2(aV HI + knpf )
PilI +
M=
=PH+
/2
!lofo l / -J!PN-Pec-fnCn
, P
2 (aV II + knpf )
.').t.
(127a)
HHTepBa.'I BpeMeHH !'!t 06bI'lHO npHHHMalOT cooTBeTcTBYIOllI.HM
0,5 0 H.'IIi 1 0 . B .1eBOH 'laCTH ypaBHeHIiH Bce Be.'IIi'lHHbI H3BeCTHbI no
M pe3YJlbTaTal\1 paC'leTa Ha IIpe-
N+r .lI:bI.lI:YllI.eM Y'laCTKe. Y paBHe-
HHe (127a) pernaeTcH rpaqm-
M 'IeCKIi C HCnOJlb30BaHHel\1 co-
OTHorneHHH (126). 3a.ll:aeMCH
HeCKOJlbKHl\1H 3Ha'leHHHMH PH
(06bI'lHO He 60Jlee Tpex). )J.mI
Ka)j(.lI:Oro H3 HHX BbI'lHCmleM
!/it-1 h H onpe.ll:emIeM V H . !-l ,fo, u.
IT pH 3TOM HCnOJIb3YIOTCH 3a-
BHCHMOCTH nma nOKa3aHHbIX
Ha pHC. 44.
0603Ha'lH1\I .'1eBYIO 'laCTb
ypaBHeHHH (127a) R, npa-
BYIO - D. PHC. 45, a HJIJ1IOCTpHpyeT MeTO.ll: rpa<pH'leCKOrO perneHHH
ypaBHeHHH (127a).
YpaBHeHHe 6a.'IaHCa Ha BTOpOM 3Tane:
( f 2 ) dPII .
uVII+k np n -=f"C n ,
dt
.Di.R
P'
Ip
0)
OJ
PI1C. 45. 1\ rpalj:JH4ccKOMY pCIllCHH!O ypaB-
HCHI1H:
a - (l27a): 6 - (13,1) H (135)
(128)
B KOHe'lHbIX pa3HOCTHX
P fnCm
III , 2 )
2(aVN+knpfn
!'!..t=p,,- f"C n ') !'!..t.
2 (aV" + knpf;;)
(128a)
PellIeHHe ypaBHeHHH (128a) aHaJ10rI1'IHO onHCaHHOMY .lI:.'1H ypaB-
HeHHH (127a). )J.aBJ1eHHe Ha'la.'Ia OTKpbITHH Hr.'IbI 3aKpbIToro pac-
nbI.'IHTeJ1H, onpe.lJ,eJ1HeMOe ypaBHeHHeM (39), 3aBHCHT OT BeJ1H'lHHbI
.lJ,aB.'1eHfIH B LtH.'JHH.lI:pe. HMeH HH.lI:HKaTopHYIO .lI:HarpaMMY, MO>KHO
* 'f..lo, B npllHl.\liDC, 51B.'IHCTCH Ij:JYHKI.\IlCH f ° 11 p" [45].
112
nOCTpOHTb 3aBHCHMOCTb P f/Jo OT yrJ1a nOBOpOTa KO.1JeH1JaTOrO HJIH
KYJ1a1JKOBOrO BaJIa H no nepeCeIJeHHIO ::nOH 3aBHCHMOCTH C 3aBHCH-
MOCTbIO 17>< (q» HaHTH yioJI, npfl KOTOpOM Hr.1J8 Ha4.HeT OTKpblB8Tb-
CS!. .3TOT MOMeHT S!BJ1S!eTCS! HaIJa.'IOM TpeTbero :,nana.
.l1..JIS! K.'IanaHHO-COIIJIOBbIX paCIIbJ.!IflTe.neif .n:aB.'IeHfle H8IJaJI8 OT-
KpbITHH KJ1anaHa
P o =PcjJo+P,,'
(129)
B OCTa.lbHOM MeTO.n: onpe.n:e.leHHH MOMeHTa HaIJaJIa .n:BH}KeHHH
I(.TWnaHa He OTJ1H1JaeTCH OT onHcaHHoro .lL.'IH Hr.'Ibi paCHbI.'lHTeJIH 3a-
KpbITorO nIna.
JJ.mI HaCo<><fJopCYHKH THna JIeHKap3 npHHHMaeTCH, 1JTO KJ1anaH
OTKpbIBaeTCH MrHOBeHHO, nplIIJeM 06'beM C}KaTlIS! nplI 3TOM YBe.'IlI-
1JHBaeTCH OT V>< .lLO Vt< + V p ". C HaIJa.'IOM .lLBH}KeHHH'lIrJ1bI IJlIC,TIO
ypaBHeHlIH, onHCbIBaIOll.{lIX npOlJ,eCC BnpbICKa, YBeJ1lIIJlIBaeTCS!.
YpaBHeHlIe 6aJIaHCa TpeTbero ::nana:
(aVII+knP{ ) H = fnCf1- cfc V ; -V p -p,, -fuCu'
YpaBHeHlIe .lLBH}KeHlIH 11 rJI bI onlICbIBaeTCH Bblpa}KeHHeM
B KOHKpeTHOM CJ1Y'lae pljj = PH' no:nOMY
M' d 2 y + {)'y = (fu-f )(PII-Pf/JoH- f p .
dt 2
(130)
(41) .
(131)
CBH3b Me}J(.lLY 17>< 11 17; onHCbIBaeTCH ypaBHeHHeM (43). ITepe-
fUlIlIeM ero .lL.'IH Harnero CJ1YIJaS!:
, k 2
Pf/J-P" = I +k 2 (plI-PI!)' (132)
,I:{.'JS! K.!JanaHHo-con.'JOBbIX pacfibl. r HneJ1eH B npaBoH IJaCTlI ypaB-
HeHHH 6aJ1aHCa OTCYTcTByeT noc.'Ie.lLHlIH IJ.TIeH.
YpaBHeHlIe .lLBmKeHHS! K.'JanaHa 3anlICbIBaeTC5I npn 3TOM cJIe.lLY-
IOll.{HM o6pa30M:
d 2 y ,
M' dt 2 + f:/y= fU(PH-Pf/Jo)-fupcjJ. (133)
Onpe.lLe.TIlIM P 113 ypaBHeHlI5I (132) 11 nO.lLCTaBI1M ero B BbIpa-
}KeHlIe (130). TOr.lL8 ypaBHeHl1e 6a.18Hca B KOHeIJHbiX pa3HocTHX
3an11rneTCSJ TaK:
.. /2 ( ki
fn[CflI-vAc V -p I +ki Y PIII-P"I-fuC UI
l+ t=
2 (aV IiI +knpf )
/ 2 / /;2 -
flcfcl -pI l+k2 YPH-Ptj+f"C,,-fnC n
=1711+ M.
2 (aV Il + knpf )
8 3aI<a3 748
113
Bblpa3I-1M
C = 2(Y-Yl) C
U ul '
M
OKOH'laTeJIbHO 3anHWe:'>I ypaBHeHJIe 6a.'1aHCa B KOHe'-lHblX pa3-
HOCT5IX:
1 - Y ---:;---
2 k l
fmCm- dc P I+kf J!PHI-p/jj-fuCUl .
PHI+ q t=
2 (aV III +knpf )
Y 2 ;--;;;-..- [ 2(Y-Yl)
J1cfc -- V l+k2 J;P,,-plj+fu M
= p -L V
Ii I .)
2 (aV" I +knp! )
Cu1]-fnCn
!1t.
( 134 )
YpaBHeHHe 6a aHca Ha TpeTbeM 3Tane A 5I KJIanaHHO-COnJIOBO-
ro paCnbIJ1I-1TeJI5I no npe,ll,.'ImKeHlIlo H. B. ACTaxOBa BbIrJ15IA11T
npoI1l.e:
. /2 ./ kf
fm C m-J1ctc V p \/ I +ki V P"l-PU,I
P"I + ) j.t =
2 (aIV"I +kn1Jf )
/ 2 ,,;--;;;-_
cfc t p y 1-4- k2 Y P"-Plj-fnCn
= PH+ ' !1t.
2 (aV" + knpf )
113 ypaBHeH115I (4 1) MO)KHO onpe,lI,emITb
A'y+B'
PII = . k 2
fu- f u(I- I+k2 )
(135)
(136)
Bblpa)KeHI-I5I ,lI,JI5I A' 11 B' .n.aHbI B 0603Ha'IeHlIHX K l}J0pMy.'1e
(53). npH KJIanaHHo-con.'10BOM pacnbI.:1HTe.Jle
A'y+B'
PII = ( k2 '
fu I- J + k2 )
B' - t P - 2M'YI - 2M'C m - t ' ( I - )
- u <po (M)2 M U 1+ k 2 PIjI'
3a.n.aBa5ICb HeCKOJJbKHMH 3Ha'-leHH5IMH y, MO)KHO ,lI,.TJ5I Ka)K,lI,oro
I-I3 HHX onpe,lI,eJ1HTb Pll no ypaBHeHHlO (136). 1J.aJ1ee, HCn0J1b3Y5J
npHH5ITbIe 3Ha'IeHH5I y H cooTBeTcTBYlOll.U1e HM 3Ha'-leHH5I Pll, BhI4H-
114
CJ1HTb npaBbIe 'laCTH ypaBHeHHH (134) H (1 5), o603Ha l IaeMble
AaJIee N + F, H nocTpoHTb HX B <PYHKI.I.HH y. JIeBble 'laCTH ypaBHe-
HHH (134) 11 (135) H3BeCTHbI no pe3y.1bTaTaM peweHHH Ha npe.lLbI-
AYIlleM y acTKe. 0603HaLIHM HX LIepe3 M. nepece eHHe npHMoH
M (y) C KpI1BOH (N + F) (y) .n.aeT HCKOMoe 3HaLIeHHe y, no KOTOPOMY
C HcnO,;1b30BaHHeM ypaBHeHHH (136) BbILIHCJ151eTCH PH H AaJ1ee no
ypaBHeHHIO (132) p . PHC. 45, 6 HJ1mOCTpHpyeT j\feTO.n. rpa<pHLIecKoro
peWeHI1H ypaBHeHHH (134) H (135).
npoI.l.ecc BnpbIcKa Ha LIeTBepToM 3Tane OflffCbIBaeTCH ypaBHeHH-
eM 6aJ1aHCa, TaK KaI\ Hr.'Ia (I\.1anaH) Haxo.II.I1TCH Ha yno pe:
(aVH+knP/ ) dPH =fnCn-Itefe"/ 2 J/p -PI4' (137)
dt P
B KOHeLJHbIX pa3HocTHX HMeeM
../2 V r
tmcm-!.tete P- I+k VPIII-P",
PHI+ M=
2 (a1V HI +knpt )
fJ
( "2 .r
!.tete} P- JI V - fnCn
2 (aV H + knpt )
PerneHHe 3Toro ypaBHeHlIH aHa.10mLIHO omlcaHHOMY .lI.J151 ypaB-
HeHHH (127a).
YpaBHeHHe 6a,;1aHca Ha n5ITOM 3Tane:
(aV +kni ) d: t " = fnCn-Itefe 11 -V !i;-p 14 -Itofo X
X 11 : V PH-Pee ; (139)
=PH+
!1t.
(138)
B KOHeIlHbIX pa3HOCTHX:
- .. /2 .. /2 1 l
fmCm-!.tolfol pYPHl-Pee-J..lete P-V l+k YPHI-Ptll
PHI+ 2 X
2 (aV HI + knpf n)
Ilofo y Y PH-Pee + !.tefe Y- VI :: X
:< yp;;=p;.-tnCn
2(aVH+k:pf )
X M = PH+
M.
(139a)
8*
115
PerueHHe ypaBHeHHH aHaJ10rJIlIHO OnHCaHHOMY )J.J1H ypaBHeHHH
(127a). MOMeHT HalJaJ1a nOCa)J.KlI lIfJ1bI onpen.eJ1HeTCH ypaBHeHH-
eM (65).
MOMeHT HalJ8JIa
noca)J.KH K.'IanaHa onpe)J.eJ1HeTCH ypaBHeHueM
fuPi/Jo + b'y,,-fu ( 1- k 9 ) P
I + k;. ,
PII=
fu ( I- )
I +k"
YpaBHeHIre 6aJlaHCa Ha ruecToM :nane:
(aVII+kni ) d " = fn C n-l1c!e V J p -pl{ -
-!tolo" / 2 JI PH-Pee -fuCu;
. V p
( 140)
(141)
B KOHelJHbIX pa3HOCTHX:
/2 . /21/
fntCnt-!.tolfOJ l p V P m-Pec -/1cfc V p V I +ki x
> V PHI-pu,l-fuClll
2 (aiV HI + knpf )
f - r- y -
2_ 2 k 2 r_
flofo p-YPH-Pee+/1 cfe Vp l+k 2 ¥PH-Pl\+
[ 2(Y-YI) 1
+ fu M CUI -fnCn,
2 (aV H + knpf )
PHI+
M=
=PH+
M.
( 141a)
Dpl1 KJ1anaHHO-COnJ10BOM paCnbIJ1l-ITeJ1e ypaBHeHl1e 6aJ1aHCa Ha
meCTOM .3Tane B KOHelJHbIX pa3HOCTHX npe)J.CTaBJIHeTCH TaK:
../2 /2 /ii r
fntCm-flolfol V pV PHI-Pee-flcie V p l' i+kft PHI-PU,I
PHI+ 2 ) X
2 (aIV III +knpf n
flofo vi V PH-Pec + flcie V V I 2k2 :-
X M = P + >; vP;;=P;; -fnC ft.t. (142)
H 2(aVH+knpf )
YpaBHeHHH (141a) II (142) perualOTcH COBMeCTHO C ypaBHeHlI-
eM (136). BeJ1lIlJIIHa P onpe)J.e.'1HeTCH no ypaBHeHlIlO (132). Me-
116
TO.ll. peI1leHHSJ ypaBHeHHH, onHCbIBaIOll.I.HX npou;ecc BnpbICKa Ha
IlleCTOM ::nane, aHaJ10rWleH OnHCaHHOMY lI.JISJ TpeTberO =nana.
Pa311eJ1eHHe Ha 3TanbI lI..1SJ Hacoc-qJOpCYHKH THna JIeHKap3 OT-
JlH'-\.3 1"C.H, K3K 6blJlO nOK3:'>'3HO, 0'> p33JJ. Jl mm H3 ,nanb\ Jl,JlH JJ.B'jX
.lI.pymx paCnbIJ1HTeJ1eH, lJ.TO BHOCHT HeKOTOpbIe H3MeHeHHH B pac-
'leTHble ypaBHeHHH. BnpO'leM, liB nepBOM 3Tane paC'leTHb1e ypaB.
HeHMS! lI.JIH BCeX TpeX THnOB paCnbJ.'IHTe.'IeH B npHHU;Hne coana.ll.aIOT.
O.ll.HaKO lI.J1H Hacoc-qJOpCYHKH THOa JIeHKap3 npHHHMaeTCH
dP II = dp
dt dt
11 p,,=P +Pt/10'
TorlI.a ypaBHeHHe 6a,J,aHCa Ha nepBOM 3Tane 3an11IlleTCH TaK:
,-
(aV,,+knpf ) d:; = fflCfI-!-toio II V PH-Pec; (143)
B KOHelJ.lIbIX pa3HOCTSJX:
fnCm-J-tolfol V : y PH!- 8C
P"l+
2 (a I V HI + knpf )
J-toto V 2 Jf PH-Pec -fnC n
- p ....)... {J M.
- "I 9
2 (aV H + kflpf;')
YpaBHeHHe 6aJ1aHCa .lI.J1H HaCOC- OPCYHKH THna JIeH ap3 Ha
BTOpOM 3Tane
( V 2 ) dp f 1 2 Ji .
a +knin - d =fnCn-!-to 0 - Pcp+PCPO-P8 C -
t p .
-!-tcfe I : -V P -Pq; (144)
(143a)
j KOHelJ.JlbIX pa3HOCTSlX:
fnCm-J-tolfol v/f VP I +Pcpo-P Bc -!1 e f c If JI P I -PqI
lI'4JI + 2 ) 0
2(a)V I + knpf n
"11 (2'1i . 1 !2 V ---;---
J-toto y p r PCP+Pt/JO-Pec+J-tcfe V - PtjJ-pt;-f,/C n
xM=p + 9 p M.
2(aV+ k np f;,) .
(l44a)
1\7-
YpaBHeHHe 6aJI8HCa Ha TpeTbeM 3Tane:
(aV +kni ) d:: = fnCn-flefe V : v P -Pq ;
(145)
B KOHe'lHbIX pa3HOCTHX:
.. 1 2 1 / '
fnCm-ref e V p . Pt/1I- P l/1
P I + M=
2((11 VI +knpf )
fltfc V .!.. V p -Pl/ -fnCn
- p ' + P M.
- dJ " )
2 (<xV + knpf
(145a)
MOMeHT nocaAKH KJIanaH<'l B nepBoM npH6JIH>KeHI1H onpeAeJ1HeT-
CH no ypaBIIeHHIO
PII = Pq.)o + PI! HJ1H P = PI!"
npH TaKOM nOAxoAe MOMeHT nocaAKH KJIanaHa npaKTH'leCKH
COBnaAaeT C MOMeHTOM npeKpall.{eHHH HCTe eHHH TOnJ1Ima H3 o6'be-
Ma, pacno.TJOLKeHHoro nepen. paCnbJJ1ImaIOll.{HI\HI OTBepCTHHMH (H3
KJIanaHHOH K<lMepbI paCnblmlTeJ1H). YpaBHeHHH, onHcbIBaIOw.He
npolLecc BnpbICKa TOll.'I11Ba Ha 'IeTBepTOM 3Tane, cOBnanaIOT C ypaB-
HeHHHMH BTOpOr6 nana.
YpaBHeHHe 6a.TJ.aHCa Ha nHTOM 3Tane:
dpt/1 .. /2"1/ '
aV pKdi = flefe V p r Pt/1-P I I"
(146)
npH npHHHToM MeTOAe onpeAeJ,eHHH MOMeHTa I10can.KH K.'IanaHa
AaBJ1eHHe B K.'JanaHHoH KaMepe pacnbwHTe.'IH B MOMeHT pa306w. e -
HHH KaMepbJ n.TJYH>Kepa OT KaMepbI pacnbI.TJHTe.TJ.H paBllO AaB.TJ.eHHIO
B lLHJ1HHApe B 3TOT MOMeHT npolLecca. nOATeKallH Ton.,HBa B KOH-
lLe BnpbIcKa HJIH, 'ITO TO >Ke, HCTeqeHHe Ton.1HBa Ha nHTOM 3Tane
3aBllCllT OT Toro, npH K8K0!l1 l1.8B.'leRllll ce.7 K.7an8H. EC.'lH KJIarraH
ceJ1, HanpHMep, npH MaKCHMa.TJ.bHOM n.aB.'IeHHH B UH.'II1Hn.pe, TO no
Mepe CHH)j{eHHH AaBJIeHHH B lLH.1HHApe HeIWTopoe IW.'U1"'leCTBO Ton-
.'IHBa BbiTeKaeT H3 KJ1anaHHOH KaMepbl pacnbWHTe,1H B lLH.1HH.n:p B
pe3YJ1bTaTe paClllHpeHHH Ton.1HBa npH YMeHbIlleHHH AaB.'IeHHH.
.D:a)j{e B 3TOM c.'1Y'Iae KO.'1H'leCTBO nO.lI.TeKaIOw.ero 1'on.'1HBa HH'lTO)j{-
HO MaJ10. n031'Ol\iy .n:.'IH 06bI'lHbIX i.te.'IeH paC'leT npOlLecca Ha nHTOM
3Tane MO)j{HO He np0l13BOAHTb_ npOlLecc nOllTeKaHliH Ba}KeH., OAHa-
KO, n.JJH 3Ha.1113a AbIM.leHHH AH3e.'1H H 3aKOKCOBbIBaHHH 'con.10BbIX
OTBepCTHH. .
118
B KOHe1JHbIX pa3HOCTSIX ypaBHeHHe 6aJlaHCa Ha nSITOM ,nane:
!-Ieie y- 2 V P l-PljI
P ,- P .J M=p +
2 (!LV "I< + kn"f;.)
y- -
2 -,--
!-Ieie - VP,p-PI{
P M.
2(aV"I<+knpf )
(146a)
.HaCOC-ll)OpCYHKH C ra30BMM npHBO.ll.OM. DpHHUHnHaJlbHaSI cxe-
Ma Hacoc-$oPCYHKH C ra30BbIM npHBOJI.OM nOK333H3 H3 pl:lc. 46.
B CBSI3H C OTCYTcTBHeM MeXaHH'IeCKOrO npI1BOJI.a
B ;J.aHHOM cJ1Y1Jae nonpaBKY Ha )J{eCTKOCTb npBBo-
.n.a He Y'IHTbIBalOT. 3aKOH ,lJ.BH)J{eHlISI n,;:JYH)Kepa
Hacoc-$OPCYHKII C ra30BbIM npHBO,lJ.OI\1 H3:\leHHeT-
CSI no pe)!(ffMaM B COOTBeTCTBIUI C xapaKTepcM
npOTeKaHHH ,lJ.aBc1eHIlH ra30B B UlI.1H1H,lJ.pe ;J,BIIra-
Te.1H. 3aKOH ,lJ.BH)J{eHllH llJIYH)J{epa 1\10)J{HO TaK)J{e
H3:\leHSITb npHcnoco6J1eHHSIMH, perY.JIHpYlOl.l.iHMH
.n.aBJ1eHI1SI ra30B B npOCTpaHCTBe Ha.'l. ra30BbE\f
110pUlHeM, 'ITO SIBJISIeTCH CYli{eCTBeHHbIM npe nIY-
Ill.eCTBOM paCCMaTpHBae!\WH Ton.JIHBHOH CHCTeMbL
B Hacoc-$opCYHKe C ra30BbIM npHB0..'10M npo-
uecc nO;J,a1JU Ton./mBa onHCbIBaeTCH ypaBHeHIlHMH
6a laHca TomulBa, KOTopbIe COCTaB.TJHlOTCH B CO-
OTBeTCTBMll C H3MeHeHIIeM rpaHW.JHbIX YC.l0BMII H
pernalOTCH COBMeCTHO JI..1H BceH CHCTeMbI B ue.10M,
O.n.HaKO B CI1CTeMe C r330BbIl\1 npI1BO.lI.OM nYTb
nJ1YH)!(epa h n Heo6xo,lJ.HMO BbIpa3HTb ypaBHeHH-
PHC. 46. npHRllHnH3.%Ra51 CXCMa Hacoc-lj:JoPCYHKH C ra30-
BblM npHBo.!J.oM
eM, onpe,lJ.e.1SIlOIll.HM B3aII!\lOCBH3B MeM,lJ.Y ,lJ.aBJ1eHUeM ra30B B llH-
J1HH.lI.pe ,J,Bur3TemI M JI.aBJIeHlleM TonmlBa. Cor.1aCHO pllC. 46 .JI.BII-
)J{eHMe n.'!YH)J{epa onpelle;JIHeTCSI COOTHorneHHeM MeM.n.y CIIJIOH, ,lJ.aB-
J1eHHH ra30B fzPz, JI.eHcTBYlOIll.eH H3 ra30BbIH nopmeHb, H Cll.JIOH ,lJ.aB-
J1eHIISI TOnJ1HBa, .lI.eHCTBYlOIll.eH Ha Topeu nJIYH)J{epa. C.JIe.lJ.oBaTe.'IbHO,
JI.<1SI paC'IeTa npouecca BnpbIcKa CHCTeMbl C ra30BbIM npI1BOJI.O:\I He-
06XO,lJ.IIMO IlMeTb IIHJI.HKaTopHYlO .lJ.HarpaMMY. Cor.JIaCHO npIIHUImy
pa60TbI CIICTeMbI Ha ra30BbIH nOprn€Hb. a 3I.{a1JHT II Ha nc1YH)Kep, co
CTOpOHbI UH.JIUHllpa JI.BlIraTe.1H JI.eikTByeT CIIJIa fzpz, KOTOpa5I ypaB-
HOBellllIBaeTCH CIWOH JI.aB.JIeHIlH TonmlBa. Ha TOpeU nJIYH}J(epa fnP",
CIWOH }J(eCTKOCTIl npY)J{HHbI n.1YH}J(epa {i"h n , nWUH Ha'Ia.ThHoi'I 3a-
T5I)J{KII npY}J(HHbI n.JIYH)Kepa fzPa, a T'a"K}J(e CIlJ10H HHepuHII .1BBiKy-
. d
li{HXCH BMeCTe C nJIYH}J(epoM Macc M -+,..-CHJU')I T,peHBH ra30Boro
.- . .--.di" -...
noplllHH II nJIYH}J{"epa Haco"ca He YlfiITbIBalOTCSI.
11"9
.l1.BH2KeHHe ra30BOrO nOpIlIH5I H nJIYH2Kepa IvI02KHO OnHCaTb
ypaBHeHHeM
. M d2h" + 6 h ' f - f f
--;jj2 "" T zPa - ZPZ- "PH'
(147)
DpHH5IB 5I paccMaTpHBaeMoro c YIJa5I c e aHH e paHee o-
nYl11.eHH5I, nOJIYIJHM
d 2 h" _ 2(h,,-h lll )
dt2 (M)2
2C lll
M'
(148)
Do cTaBHB aHHoe 3HaIJeHHe npoH3Bo HOH B ypaBHeHHe (147)
H peIlIa5I ero OTHOCHTe.1JbHO h n , 6y eM HMeTb
h = En -{"PH ( 149 )
" An'
r e
B" = f J.. 2Mh lll + 2MCIll - f .
zPz (M)2 M zPZ'
A" = 2M +.6 .
(lH)2' H
B 60.'lbIllHHCTBe HaCoC-$OPCYHOK, B TOM 'lHC.'le H C ra30BbiM
npHBOn;OM, HarHeTaTe.'1bHbIM KJIanaH OTCYTCTByeT HJIM, eC.'1H OH eCTb,
TO He HMeeT pa3rpY2KaIOl11.ero n05ICKa. B CB5l3H C 3THM B HHHHe
K anaHa He. npHHHMaeTCH BO BHHMaHHe. COfJ18CHO C eJ1aHHbIM O-
nYl11.eHH5I1\1 npou.ecc B paCCMaTpI1BaeMOH CHCTeMe M02KHO pa3 e-
HTb Ha CJ1e YIOI.lI.He 3TanbI:
.1) OT H8IJaJ1a BH2KeHHH nJ1YH2Kepa o nO.'1HOrO nepeKpbITHH
BcaCbIBaIOIll.HX OKOH;
2) OT 3aKpbITHH BcaCbIBaIOIll.HX OKOH o HaIJa a BH2KeHHH Hf.TIbI
q>OPCYHKH;
3) OT HaIJa.'la ABH2KeHHH HrJIbI q>OPCYHKH o no xo a ee K ynopy;
4) OT nOAXOAa H.r bI K ynopy o HaIJa.'1a OTKpblTHH OTCeIJHbIX
OKOH;
5) OT HaIJa.'1a OTKpbITHH OTCeIJHbIX OKOH o HaIJaJ1a BH2KeHHH
HfJ1bI OT ynopa;
6) OT HaIJa.'1a BH2KeHHH Hf.'1bI OT ynopa o noca KH HfJ1bI Ha
ce .'1o.
YpaBHeHHe npou.ecca B nepBoM 3Tane:
a (VH+ V ) dPH = fnCn- lofo ... I 2 V PH-PSC '
dt V p
DpH6.'1H2KeHHO pernaH 3TO ypaBHeHHe C YIJeTOM, \ITO h n onpe.n.e-
HIeTCH ypaBHeHHeM (149), no.'1YIJHIvI
"II x' f( '1.. '+ ) 2
"PII-PSC = -2+J; 2" +D",
(150)
120
r.ll.e
x' =
!lolow t If
[ ' ) f ]
2 u (V IICP + V" + A"
D"=
u (VHcp+V )P"I
( ' ) f
u V"cp+ V" + A"
+
A" [a(V"cp+V )+ ]
'n B "
'nhJ
, I
a ( V + V ) , -
"cp ",- A"
!lolo cpM If
[ ' ) I ]
2 (aVllcp+V" + A"
11 P"I-Pet;
E" f 2Mnhm + 2M n C m
= "Pz+ M2 M
f"Pa;
A" - 2M n , ()
- /1,t2 T II'
Cpe.ll.HHe 3HaqeHHH V"II. cp H f 0 cp Onpe.ll.eJIHlOTCH TaK )Ke, KaK H B
paCCMaTpHBaeMbIX CHCTeMax.
Ha BTOpOM 3Tane npOHCXO.ll.HT C)KaTHe TOnJIHBa B 06beMe Ha-
coc-qJOpCYHKH. .lJ.aBjleHHe Ton.1HBa Ha 3TOM nane 6Y.lI.eT Onpe.ll.e-
.'.lHTbCH CPOPMYJ10lI
p,,=
a (V IICP + V )P"I
, I
a (VIICp+V,,) + A"
I B"
+ [ 2 ]
A" a (VII cp+ V ) + :
'nhm
' ) I
a (V"cp+ V" +7
(151)
Bblpa)KeHHH .lI.J1H K03cpcpHUHeHTOB E" H A" Ha Bcex 3Tanax co-
xpaHHlOTCH HeH3MeHHbIMH.
Ha TpeTbeM 3Tane Hr.rIa paCnblJ"1HTeJIH HaXO.ll.HTCH B .lI.BH)KeHHH,
n03TOMY OCHOBHoe ypaBHeHHe npouecca 6Y.ll.eT
1 - / -
, dplI 2 k 2
a (V" + VII)----;tt = fnCn-I-tcfc p V 1 +k2 -V p,,-pz-fuCu.
. (152)
121
f1pll6J1l1LK eHHO lIH TerpllpYH 3TO ypaBHeHlle II peWaH ero OTHO-
CHTeJlbHO V PH - P" no.'1 Y4l1M
VP P ' - r.: J
11- Z - -2 ,-
-+ r
JI
n .)
( r+D"-
tuY
, f
a (\/" cp+ VJ + A"
pz'
(152a)
fn.e
cfcM · I 2 r
X" V p -V
. 2[a(\/,,<.p+V )+ : ]
k p 2 ki +k 2
; k cp =- 2
2
I +kcp
kf - 3Ha4eHl1e K03<p<PIIUlleHTa k 2 B Ha4a.TIe npOMeLKYTKa BpeMe-
HlI !1t;
D" = (l (V IICP + V )P"I + tuB"
a(VllcP+V )+ .:: A" [a (VIICP+VJ + : ]
fnhnt -+ tUYl " J'-
-y.. f PH.l-Pzl'
. f2., f2
a(V,UP+\/ )+ A: a(VH.CP+V )+ A:
YpaBHeHlIe (152a) Heo6xo.LI:HMO pewan COBMeCTHO C ypaBHeHII-
eM JI,BlILKeHIIH lIr.'ILI. C.'1eJI,OBaTe.1bHO, ypaBHeHlIe JI,BHLKeHlIH II r.'I bI
MOLKHO npeJI,CTaBlITb B BIIJI,e
A'y+ B'
PII" , k 2 . (153)
f2-fu(I- I+k2 )
YpaBHeHlIH (152a), (153) MOLKHO pewaTb rpa<p1I4ecKlI, 3aJI,a-
BaHCb 3Ha4eHHeM y H onpeJI,eJ1HH k 2 H k ZP' H HaXOJI,lITb 3Ha4eHHe PH.
no nepece4eHlIIO 3aBlIClIl\10CTeH PH. = f (y), nOCTpoeHHbIx no ypaB-
HeHHHM (152a) H (153), IIJUh HaX,OlIJITb npll6JIHLKeHHoe 3Ha4eHHe y
no MeTOJI,Y, H3.10llieHHoMY B 2 HacToHIlLeit r.1aBbI B npHMeHeHHII
K HarHeTaTe.'IbHOMY K.'IanaHY.
Ha 4eTBepT0l\1 -3Tane Hr:1 ,CTOH1: HenOJI,BlIlliHO y ynopa. YpaB-
HeHne npouecca JI,.1H 3Toro 3Tana:
V - r----;;-
, dp .. 2 . /.. k;"
a (V II -+ VII) --.!!.... = fnCn-fJ-cfc ", _ I .: ---:;- 11 PII-PZ'
. . & p , I+k;.. .
122
(154)
nOC,;le np 6.'IH>KeHHOrO H HTerpHp OBaHHH ypaBHeHHH (154) H pe-
meHHH era OTHOCHTe.'IbHO JI PM - pz no.1YlJHl\1
. - - ----
" .. / ( " ) '}
V-PII-P Z - y + V 1- - +D"-pz. (lF5)
r)J.e
!1cf C III !it r72
X" = [ P 2 ] V I + : ·
2 U (V H cp + V ) + :
D"= a(VllcP+V )PHI + fn B "
f2 [ f2 J
a(VHCP+V )+ A: An U(VIICP+V )+ A:
fnhnI X " 1..r P p
- .. 111- zl'
fl
( '1 F' ) n
n IIICP+ II +7
Ha nHTOM 3Tane HrJ1a HenOJ],BII>KHa, HO HalJHHalOT OTKpbIB3TbCSI
OTCelJHbIe OKHa. YpaBHeHHe 6a.'IaHC3 TOll.'IlIB3 6YlleT IIMeTb BRit
r-
d(VH+V ) d d PII =tnCn-/lJ0 1 / JlpH-P8c-/lCtcx
tIp
( - ;---y-
2 / k M
X -11 VPII-PZ'
p 1+ k M
( 156)
nOCJIe nplI6muKeHHoro IIHTerpHpOBaHHH ypaBHeHHH( 156)
JIY'lHM
no-
, / " V ' D"
PII+ U J PII-PBC+X P,,-Pz= .
( 157)
r.z:r.e
X"
11 0 t o cpl1t I / 2
u' I P .
2[a(VllcP+V )+ : r
!1cfcM /I FIT
[ p 2 ] II I +: M 2 .'
, . f n
2 a (VII cp + V H ) + A"
12-3
D"= n(VIICP+V )P"'1 fn B "
2 + r 't" ]
a(VIICP+V )+ : A" a(VHCP +V )+ *
fnhnJ ' 1/ " V
.) -0 r PHI-Pec-X PHI-Pz'
' ) t
n(VHCP+V H + A"
4 To6bI onpe,'J,e.m1Tb npOXO,'J,HYlO n.'IOIlla,'J,b OTce4HbIX OKOH f 0, pac-
C4HTaeM npH6.'IH2KeHHO COOTBeTCTBYlOIllHH XO,'J, h n no MeTo,'J,Y, npH-
HSITOI\1Y ,'J,..'ISI pac4eTa Be.'IH4HHbI h", B 2 HacToSIIllei'i r. I IaBbI. PernaTb
ypaBHeHHe (157) npoIlle rpacpH4ecKH, 3a,'J,aBaSICb pa3J1H4HbII\1H 3Ha-
4eHHSIMH PH' nOKa .'IeBaH IaCTb He CTaHeT paBHOH npaBOH.
Ha rneCTOM 3TaneppH OTKpbITbIX OTce4HbIX OKHax Hr..'Ia cpop-
CYHKH Ha4HHaeT ,'J,BHraTbCSI Ha noca,'J,KY. YpaBHeHHe 6aJ1aHCa Ton-
J1HBa 3anHrneTCSI B BH,'J,e
( ' ) dPH I 2 -
a VII + VII --;j{=fn C n-f1ofo -; V PH-Pec-f1cfcx
12 F k p
xl pV I+k p VPII-Pz-fIl C Il , (158)
YpaBHeHHe (158) ,'J,O.'I2KHO pernaTbCSI COBMeCTHO C ypaBHeHHeM
,'J,BH2KeHHSI HrJIbI ( 153). I1HTerpHpySI 3TO ypaBHeHHe, n0J1Y4HM
PH+ o 'VPH-Pec+X"l.l PII- pz+ iuY 2 =D", (159)
' ) in
n(V HCp + V H + A"
r,'J,e
D"= n(V"'cP+V )PHI + in B " +
a(VHCP+V )+ : A "[n(VHc p+v ) +f]
iuY. ' V " v
.) -0 PIII-Pec-X PHI-PzI'
( ' ) f
a V,., cp + V AI + A"
K03<P<PHI.I.HeHT 0 coxpaHHeTcH HeH3MeHHbIM, a B BbIpa)KeHJUI
,'J,JISI K03<p<pHI.I.HeHTa X" Be.'1H4HHa k 3aMeHHeTCSI Ha k: p '
PernaSI COBMeCTHO ypaBHeHHSI (1 58) H (153), nOJIY4HM
A'y+B' -!--o' { A'y+ B'
, ( k2 ) ' , ( k2 ) - Pec +
iu-iu 1-i+k2 iu -iu 1- I+k2
+ 'V" y ' A'y+B' iuY =D".
'" pz+ i 2
, ( ) ( V' )
fu-iu .1- 1 +k 2 a V,.,cp+ ,., + A"
+
(160)
1 4
3TH ypaBHeHHH peWalOTCH rpaqJH'leCKH TeM LKe l\1eTO.n:OM, 'ITO H
Ha nHTO!\I 3Tane. flo ypaBHeHHlO (153) o npe.n:eJ1 He 1\1 BeJII1'lHHY y, a
3aTeM no ypaBHeHHlO (159) - .n:aB.1JeHHe PH-
4. PAClfET npOLl.ECCA BnPblCKA TOnnHBA
AKKYMynSiTOPHblMH TOnnHBHblMH CHCTEMAMH
flpHHl(Hn .n:eikTBHH aKKYI\1YJ1HTOpHbIX CHCTeM OCHOBaH Ha BnpbIC-
Ke Ton.1JHBa npH nOCTOHHHOM .n:aB.1JeHHH. floCTOHHCTBO .n:aB.JIeHHH
BnpbICKa nbITalOTCH coxpmIHTb pa3J1H'lHbIMH nynII\1H. B O.n:HHX CH-
CTel\IaX Ton.1JHBHbIH Hacoc no.n:.n:epLKHBaeT nOCTOHHHbIM 3a.n:aHHoe
)],aB.'IeHHe B Cnel(HaJ1bHOM aKKYMY.JIHTOpe, KOTOpbIH coe.n:HHHeTCH C
<jJOPCYHIWH Tpy60npOBOll0l\1 BbICOKoro AaB.TJeHHH II B onpe.n:e.'IeHHbIe
<jJa3bI BnpbICKHBaeT TOnJ1HBO B l(H,,'IHHAP .n:BHraTe.'IH. B .n:pymx CH-
CTel\IaX nOCTOHHHoe .n:aB,,'IeHHe B JHIHHH HarHeTaHHH no.n:.n:epLKHBalOT
n,,'IymKepoM TOnJ1HBHOrO Hacoca, nYTeM npIIMeHeHHH Cnel(Ha.JIbHOrO
npIIBo.n:a nJlYHLKepa (npYLKHHHoro, nHeBMaTH'leCKOrO, rH.n:paB.'IH'le-
CKoro H .n:p.). B npaKTHKe nO.'IHOCTblO OCYLLleCTBHTb 3TOT npHHW1TI
He y.n:aeTCH, o.n:HaKO .n:aBJ1eHHe BnpbICKa B aKKYMYJ1HTOpHbIX CHCTe-
Max rvla,,'IO 3aBHCHT OT 'IHcna 060pOTOB.
TOnJ1HBHbIe CHCTeMbI C rH.LI:paBJ1H eCKHM aKKYMYJ1S1TOpOM 60J1b-
lllOH eMKOCTH. flo npHHUHny .n:eHCTBHH B ::nOli CHCTeMe BnpbICK Ton-
JIHBa .n:omKeH npOHCXO)],HTb 3a C'leT ::meprHH aKKYMy.'IHTOpa, B KO-
TOpOM .n:aB,,'IeHHe TonJ'IIIBa no.n:.n:epLKHBaeTCH nOCTOHHHbIM. KOJ1H'le-
CTBO no.n:aBaeMoro Ton.1JHBa perYJIIlpyeTcH H3MeHeHHeM BpeMeHH
OTKpbITHH nepenYCKHbIX OKOH HJ1H II3MeHeHHeM BpeMeHII OTKpbITHH
IIr.;'IbI 4>OPCYHKH_ B nOC,,'Ie.LLHeM cJ'IY'lae Hr.'Ia )],OJ1)Ima HMeTb Mexa-
HH'leCKHH npIIBO.n:. B COOTBeTCTBHH C npHHl(HnOM .n:eHCTBHH CHCTeMbI
npOl(eCC BO BXOJ1,HOM ce'IeHHH Tpy60npoBOlla pa3.n:e.1JHlOT Ha c.'Ie.n:y-
lOLLlHe ::nanbI:
1) npOXO)],HaH nJ10LLla.n:b neperrYCKHbIX OKOH (IIJIII rr,,'IOUJ.allb nOlI
KOHYCOM IIr,,'IbI 4>OPCYHKH) B03paCTaeT (nepHO.n: OTKpbITHH);
2) npoxo.n:HaH TIJ10LLla.n:b nepenycKHoro OIma (H.'IH n.'IOUJ.a.n:b no.n:
KOHyCOM HrJ1bI) He H3MemleTcH;
3) npoxo.n:HaH nJ10LLla.n:b (HJ1H n.'IOLLla.n:b no)], KOHYCOM IIr.'1bI) ne-
penycKHoro OKHa YMeHbwaeTcH (nepHo.n: 3aKpbITIIH)_
B CBH3H C TeM, 'lTO Ha nepBoM 3Tarre .n:aBJIeHHe TonmlBa B aK-
KYMYJ1HTope po.. = const, B.'IHHHHe MeCTHoro 06"beMa Ha npol(ecc
BnpblcKa MOLKHO He Y'liiTblBaTb. Tor.n:a ypaBHeHIIe npol(ecca 6YAeT
IIMeTb BII.n:
fTC T = foC o '
(161 )
r.n:e fa - IT.TIOUJ.a.n:b OTKpbITHH OKHa;
Co = /10 V : V PII- PIIT - CKOpOCTb nepeTeKaHI1H TOn.'IIIBa 'Ie-
pe3 OKHO; 3.n:eCb PH - llaB.JIeHIIe TOn.JIIIBa nepen: OKHOM; PHT:""'- .n:aB-
neHIIe TOrr.JIIIBa BO BXO.n:HOM Ce'leHHH Tpy60npoBOlla 3a OKHOM.
125
.LlaB:IeHHe P>iT H CKOpOCTb C T OnpeLle.'IHIOTCH cHcTeMoH (4). BbI-
pa3HB 3Ha4eHHH LlaB.'IeHHH H CKOpOCTH cor.JIaCHO BbIpallieHHIO (4)
H nOJ1.CTaBHB 3TH 3Ha1JeHHH B ypaBHeHHe JIepa3pbIBHOCTH JJ:BH)KeHHH,
nO.'IY4HM
I FT
F(t)+ W(t)= ap -'!.. o 1/ - V PH-Po-F(t)+ \f/(t)
IT J' P
HJIli
F(t)= Vb V 4W(t)+ 2(PH-PO)+ b-[W(t) + b],
( 162)
?
b 2 f "
=a p-W.
I; 0
Ha BTOpOl\I 3Tane npOXOJI,HaH n.'Iow.aAb OKHa f 0 He H3MeHHeTCH.
n03TOMY eC,,'IH Be.1W/HHa aMnJIHTy.n:bI OTpa)KeHHOH BO.'IHbI 6y.n:eT
npaKTH4eCKH UOCTOHHHOH, TO J1.BHllieHHe TOUJIHBa 'Iepe3 HeKOTopoe
BpeMH CTaHeT YCTaHOBHBlllHMCH. YpaBHeHHH nepBoro 3Tana npH Ie-
HHMbI H A.'IH BToporo 3Tana.
Ha TpeTbeM 3Tane npOKo.n:HaH n.'1ow.a.n:b OKHa H:IH w.em1 noJJ.
KonYCOM Hr lbI I13MeHHeTCH B CTOPOHY YMeHbllleHHH, T. e. nOBTopH-
IOTCH rpaHH4HbIe YC.'10BHH nepBoro 3Tana. C.i1e.n:OBaTe.'IbHO, ypaB-
HeHHH nepBoro 3Tana npHMeHHMbI H J1..'1H TpeTbero 3Tana.
TaKHM 06pa30M, B paCCMaTpHBaeMoii CHCTeMe npo ecc nO.lJ,a'lH
BO BXOJI,HOM ce4eHHH TPy6onpOBo.n:a onpe.n:eJIHeTCH O.n:HHM ypaBHe-
HHeM, B KOTOpOM B 3aBHCHMOCTH OT 3Tana H3MeHHeTCH TO.lbKO Be-
JIH1JHHa K03<P<l)H I1eHTa b. .Ll lH onpe.n:e:1eHHH H3MeHeHl-IH npoxo.n:HOll
n:IOw.allH O1ma (H.'lH n.l0w.allH no.n: KOHYCOM HrJIbI) no yr.l)" nOBO-
pOTa Ba.11a llBHraTe.lH MOLKHO 3apaHee nOCTpOHTb .n:HarpaMMY. OPO-
ecc B BbIXO.n:HOM celIemIH Tpy60npoBOAa paCC4HTbIBaeTCH TaK llie,
KaK H B CHCTeMe Henocpe.n:CTBeHHoro .n:eHCTBHH.
TOnJIHBHaJi CHCTeMa C B03.l1.YlllHblM aKKYMYJIJlTOpOM. Ton lHBHbIe
CHCTeMbI C B03.n:YlllHbIM aImYMy.'1HTOpOM no.'IY ' /HJ1H npeHMyw.eCTBeH-
Hoe pacnpOCTpaHeHHe B cB06o.n:Ho-noplllHeBbIx reHepaTopax ra3a
(COrr). Pa3pe3 3TOH TOU.1HBHOH CIICTeMbI nOKa3aH Ha pHC. 24.
0PHHHB, 4TO OTce4Ka He 6y.n.eT B.'lHHTb Ha BnpbICK Tonmma, npo-
ecc y aKKYMy.1HTopa MOlliHO pa3.n.e.1HTb Ha C.'Ie.n.YIOw.He 3Tanb1:
1) OT HalIa.'Ia OTKpblTHH nepenycKHoH w.eJIH .n:o MOMeHTa, Kor.n:a
npoxo.n:HaH n low.a.lI,b fllj CTaHeT paBHoH cYMMapHoH npoxo.n:HOH
nJ1ow.a.n:H HarHeTaTe.HbHbIX Tpy60npoBo.n.oB }:fT' nOTOMY lITO B pac-
CMaTpHBaeMOH CHCTeMe Ton.1HBO no.n:aeTCH B KaMepy cropaHHH He-
CKO.HbKHMII <PopcYHKaMII;
2) OT MOMeHTa BbIpaBHHBaHHH YKa3aHlIbIx u.10w.a.n:eH .n:o MO-
MelITa noca.n:KH fJ.'IYlIlliepa 8 lIa ynop H OT noca.n:KH nJ1YlIlliepa 8 lIa
ynop .n:o OK01I4alIHH nOJ1.a4H TOnJIHBa B HarHeTaTeJIbHMe Tpy6onpo-
BO.n:bI.
B Ha4a.'IbHbIH I\WMeHT nepBoro 3Tana, Kor.n:a n.'IOw.allb nepe-
nycKHoH w.emI 31Ia411Te.lbHO MelIbllle cYMMapHoII npoxo.n:Ho11 n.'10-
126
f.ZI.e
w.a.n.H HafHeTaTe.lbHbIX Tpy6onpOBO.n.OB, npou.ecc y aImYMYJl5ITOpa
6y.n.eT onpe.n.eJIHTbCH c.leAYIOw.Hl\UI ypaBHeHMHMH.
YpaBHeHHe 6a aHCa TOn HBa B npOXO HOM Ce4eHHH nepenycK-
HOH w.e.1M:
t C . V dPOK t . C ' f C
!-tIll Uj Uj + a aK - = aK aK Tn" .
dt
EC.'1M npeHe6pe l Ib B.1HHHHei\I 06"beMa Me)J{AY w.e.lbIO II HarHeTa-
Te.TJbHbIMH Tpy60npOBO.n.aMH, Be.1I14I1Ha KOTOporO OlIeHb Ma.1a no
cpaBHeHHIO C 06W.HM 06"beMOl\I Kal\IepbI lJarHeTaHHH, TO ypaBHeHHe
6aJlaHCa Ton.1HBa BO BXOJJ.HbIX ce4eHHHX HarHeTaTe.TlbHbIX Tpy60-
npOBO.LI.OB MO)J{HO 3anIlcaTb B BII.n.e
J:.tTCI' = f K!-tKCK' (164)
YpaBHeI.IHe J1.BH)J{eHIIH n,,1YH)J{epa 8 (CM. pHC. 24), KOTopoe BBH-
.u.y nOCTOHHHO .n.eHcTBYIOllleH Ha n.TJYH)J{ep Hell3MeHHoH CHJIbI MO)J{eT
6bITb 3anHcaHO TaK:
MaIO d ;K = f aK(PaK 11- PalO)'
(163)
(165)
r.u.e Pm' n - HaqaJlbHOe nOCTOHHHoe J1.aB.'l HlIe Ton.'lHBa, B03HHKaIO-
lllee BC.leACTBlIe .n.aBJleHMH B03.n.yxa Ha BO"3.n.YlllHbIH nop-
llleHb.
CIUIOH ynpyrOCTlI npY)J{HHbI 6 npeHe6perael\l, TaK KaK e Be.llI-
4l1Ha OqeHb Ma.1a no cpaBHeHHlo C Be.'11I4I1HOH CHJlbI .n.3B.1emm B03-
AYX3, .u.eHCTBYIOll1.erO H3 B03.u.YlllHbIH nopllleHb.
YpaBHemIH (163)-(165) pelilaeM MeTOJJ.OM KOHe4HbIX pa3HO-
CTeH C YljeTOM npHHHTbIX paHee AonYll1.eHHH. 1l.'lH ocYW.ecTB.'1emUI
n04JIeHHOrO HHTerpHpoBaHHH npe.n.cT8BHM ypaBHeHlIe (165) B BHJJ.e
MaKdC aK = faKPaK II dt-faKPaK dt.
l1HTerpllpYH .3TO ypaBHeHHe H pelilaH ero OTHOCHTeJ1bHO Can, no-
CJIe HeKOTopbIX npe06pa30BaHHiJ n0J1Y4HM
C = D- falLPaK !1t (166)
aK 2M aK '
rll.e
D = C aK1 + faKPaK Ii J.t _ faKPaK !1t.
A1 aK 2A1 aK
YpaBHeHHe (163) npeACTaBIIM B BH,a,e
!lUjfw,CUj dt+ aVaKdpaK = faKCaK dt+ f"C n dt.
OOC,,'le n04"leHHoro HHTerpllpOBaHHH 1I pellleHIIH .3TOrO ypaBHe-
HHH OTHOCIITeJIbHO CVj 6y.u.eM HMeTb
C - faKC aK , B 2aV aK PaK ( 167 )
lll- I
lllJlI cp ftlljf'lj cp8t lllJUj cpl1t
rll.e
B = faK C aK'1t + 2aV aK PaKI-!l,,J II< ClPLlIIAt+ 2fn Ah tl"
127
OOlI,CTaBHB JJ.aHHOe 3HaqeHHe C1.1.f B ypaBHeHHe (164),
t ' C - f ( faKCaK , B 2UV oK PaK )
T T - !-till Uj T .
!1ul'I{ cp !1Ujf'I{ cl)l1t Pul,,! cpM
T8K K8K lI,IIaMeTpbI HarHeTaTeJIbHbIX Tpy6onpOBO.LtOB nOqTH Bcer-
lI,a paBHbI, TO BO Bcex BXOlI,HbIX CeqeHlf5IX 3THX Tpy60npOBOlI,OB CKO-
pOCTH Ton.'1HBa 6YlI,YT OlI,HHaKOBbI H paBHbl cor.'1aCHO CHCTeMe ypaB-
HeHHM (4).
no.'1yqHM
(168)
P T + 2W(t)-p o
C T =
up
C.'1eAOBaTe.'lbHO, pellIHTb ypaBHeHHe (168) MOlliHO, eC.'1H YCTa-
HOB.1eHa B3aHMOCBH3b Me)J{lI,y AaBJ1eHH5IMH PT H Pm'. B c.'1yqae npe-
He6pe)J{eHH5I BJIHHHHeM KJ1anaHOB TpOMHHKa YKa3aHHYlO B3aHMO-
CB5I3b MO)J{HO onpelI,eJIHTb H3 BbIpaLKeHHH
C ll ! = V/ : V PaK-PT '
OOlI,CTaBHB B 3TO ypaBHeHHe BMeCTO C'14 ero 3HaqeHHe COrJIaCHO
BbIpa)J{eHHIO (167) H BbIpa3HB B HeM Can no ypaBHeHHIO (166),
nOJIyqHM
V PaK-PT = N' -'ljJPaK'
(I 68a)
rlI,e
L- B
I _,
12
!1Ujfu! cpM / p
+ 2aV aK
... 2 /2
2M aK !11I{fUj cp 1 / - !1Ujf'I{ cpM V -
p P
ECJ1H B03BeCHI ypaBHeHHe (168a) B KBalI,paT H pellIHTb ero
HOCHTeJIbHO PT, TO 6YJJ.eM HMeTb
. 1 2 N ' ) N ,2 2 2
PT=( + 'IjJ PaK- -'ljJPaK-
N'=
faKD
/2
t'I{fUj c fJ }/ p
faKM
'IjJ=
OT-
( 169)
EC.TJH B ypaBHeHHH (168) 3aMeHHTb C7' ero 3HaqeHHeM, BbIpa-
)J{eHHbIM 4epe3 lI,aBJ1eHHe H oTpa)J{eHHYIO BOJIHY, 8 Be.'1H4HHY PT-
era 3HaqeHHeM cor.'18CHO BbIpaLKeHHIO (169) H pewHTb HOBoe ypaB-
HeHHe OTHOCHTeJIbHO Pan, TO nO.'1YQHM
_" /r,,2 A
PaK - 21. + l 41,,2 --:;:' (170)
rlI,e
A=f.t.f, 1/( 2 N'+ "1:.fT Po+ "1:.fT N,2_ nfT W(f);
UjljJl p ap ap ap
128
LfT(l +2"1\'N'), . V 2 .
v = T lll!fll!'Ij:, - ,
ap p
I.f T 'lj:2
A=-.
ap
Do ypaBHeHluo (170) MmKHO onpelI.e.'l51Tb Bem1l111H)' Pan AO MO-
MeHTa, KorAa npOXOlI.Ha51 n.'lOIl..la,[(b f"UJ CTaHeT paBHOH. H.l:J1 60JIbille
"I:.fT' 113MeHeHHe npOXOlI.HOH. nJl0Il..la,[(H f"UJ MO)KHO 3apaHee npe,[(CTa-
BHTb B BH,[(e rpacpWIeCIWH 3aBHCHMOCTH, nOCKOJIbKY H3BeCTHa CKO-
pOCTb ,[(BmKeHl;l51 n.'l)'H)J{epa 11 (CM. pHC. 24), KOTOpa51 B 3TOM OT-
pe3Ke BpeMeHH OAIWBpeMeHHo onpelle.H51eT I1 CKOpOCTb OTKpblTI151
nepenycKHoH Il..leJIH.
B CB513H C TeM, 1.JTO Ha BTOpOM 3Tane f"UJ fT' MmKHO npI1H51Tb
. p + 2W(t)-p
PT = pan. B COOTBeTCTBHH C 3TI1M C T = aK. 0. Dpo-
ap
uecc Ha 3TOM 3Tane 6YAeT onpelleJl51TbC51 ypaBHeHHeM ,[(BI1}KeHII5J
n.'lYH)Kepa 8 (CM. pI1C. 24) H ypaBHeHHeM Hepa3pbIBHOCTI1 llBI1)KeHl15l
Ton.TII1Ba:
LfTC T + aV OK dpOK = faKCaK + fllC ll ,
dt
(171)
DpI16m1)KeHHO I1HTerpHpY51 3TO ypaBHeHI1e H nO,[(CTaB.'l5151 B no-
J1Y1.JeHHOe BbIpa)KeHI1e BMeCTO C T 3Ha1.JeHI1e pon I1 W (t) no ypaBHe-
HI1IO (4), a BMeCTO Can era 3Ha1.JeHIIe cor.'laCHO 3aBI1CHMOCTI1 (166),
rrOJlY1.JI1M
"I:. f A t [ PtJK+ 2\\7(t) -po ] ..L 2 V = f / tD - f 2 PadtJ.t)2
TL.1 I a aKPaK aKL.1 aK.
ap 2M aK
B",
r,[(e D HMeeT TO }Ke 3Ha1.JeHIIe, LITO II B ypaBHeHl1H (166).
PeIlla51 nOJ1Y'IellHoe ypaBHeHHe OTHOCI1Te.1JbHO Pan, no.rlY1.JI1M
D'
(172)
Po" =
Lf T M f K(tJ.W
-+2a.V aK +
ap 2MaK
Ji-A e
fM
V' = fo"MD-L [2\V(t)-pv1- B ".
ap
BOJIHa ,[(aBJIeHI151, H.n:yma51 OT mmYMy.'l51TOpa I\ CPopCYHKe, 6YJI.eT
onpeJI.emITbC51 BbIpa)J{eHHeM
F(t)= Pa,,-Po+ W(t). (173)
Do ypaBHeHHIO (172) MO)J{HO BbI1.JHC.'1HTb ,[(aB.'1eHI1e pan JI.O MO-
MeHTa nOCaJI.KI1 aKKYMy.HI1pYIOmero nJIYH)Kepa Ha ynop.
Ha TpeTbeM 3Tarre BCJle,[(CTBI1e HenOllBIilKHOCTH aKI\)'MYclI1PYIO-
Il..lero II,TlYH)J{epa K CPopCYHKe nOHJI.eT BO.'1Ha JI.aBJIeHI151, onpe,[(eJI51e-
9 3aKa3 748 129
.l\laS:! TO.'IbKO paClIIHp€HlI€M TOn.-llIBa B aKKYMYJ15ITOpe 1I .n.BlDK€HneM
n.'lymKepa 11 (CM. pIlc. 24). Ha 3TOM 3Tan€ npou.ecc 6y.n.€T onpe-
.n.€.'l5ITbC5I ypaBH€HlI€!\l Hepa3pbIBHoCTli
-.;' - C ' V dPaK t C
tT ria flK-= n fl.
dt
(174)
f1oc.le np1I6.'lmK€I1HOrO lIHTerplipOBaHliH ypaBH€HlIH (174) 3a-
MeHlIM B nO.1YlJ€HHOl\I BbIpa)J{eHlUi CKOpOCTb C r ee 3HalJeHHeM, BbI-
pa}K€lIHbll\l 1.Jep€3 .n.aB J 1€HlI€ pm, H BO.1HY W (t). P€lllHB HOBO€ ypaB-
H€Hll€ OTHOCHTe.:lbHO Pan, nOJlY1.JHM
J),.t GrIM
aVaKPalel + fnMn- fr- [U7(t)-Po]- fr
Pale = 2ap J),.t (175)
aVale+ fr-
2ap
BOJ1Ha .n.aBJ1€HHH, H.n.YW.aH aT aKKYMYJ1HTopa K <POPCYHK€, 6Y..J:eT
onp e ..J:€.:lHTbCH ypaBH€HHeM (173). f1pOu.€CC y <P0PCYHKH paCClJHTbI-
BaeTCH no M€TO.n.y, npHHHTOMY .n..'IH CHCTeM H€nOCp€.lI.CTBeHHoro .n.eH-
CTBHH.
TOnJ1HBHbIe CHCTeI\fbl C nPY*HHHbIM npHBo.n.oM n.'!YH>Kepa. f1pIl!l-
u.Hnna.1JbHaH cxellIa PaCClVIaTpllBaelVlOH CHCTeMbl, lIcno.lb3Y€l\IOH Ha
.n.H3e.le Hanz-Endrassik, nOKa3aHa Ha pHC. 21. HarHeTaTe.'lbHbIH
xo.n. ll.'IYH)J{€pa B 3TOU CHCTeMe OCYW.€CTB.1H€TCH no.n. .n.eHcTBIIeM
3HeprnH )J{€CTKOH npY)J{HHbI; BcaCbIBaIDw.n€ II OTCe1.JHble OKHa OT-
CYTCTBYIDT. Ko.1I1IleCTBO no.n.8B8e1\WrO Ton.'IHB8 perYJ111pyeTcfl 1I3-
MeHeHHeM xo.n.a nJ1YH}K€pa, 1I8rH€TaT€.1JbHbIH K.lanaH p83rpY)J{aID-
w.ero nOflCKa He IIM€eT. YKa3aHHbI€ KOHCTPYKTIIBHbI€ OC06€HHOCTII
HaCOC8 cyw.eCTB€HHO ynpOw.aIDT M€TO.n. paC1.JeT8 €ro npOll.ecca. Xo.!!.
n.1YH)J{epa Hacoca onpe.n.€Jlfl€TCfl paC'I€THbIM nYT€M. Cor.laCHO
pIlC. 21 Ha n.1YH)J{€P .lteikTBY€T CIIJla npY>KIIHbl pbI1.Jar8
F =b/h,<t -h), 076)
r.n.e h.M - B€.'lIIlJIIH8 3a.n.aHHoro OKaTII5I npY)J{IIlIbl;
h - TeKyw.e€ 3!i8lJ€HH€ Be.'lIIlJlIHbI lIarlIeTaT€.TIbHOrO XO;:(a
n.1YH)J{epa.
KpoMe Taro, Ha II.1YHn\:€p .n.eHCTBYIDT CII.la.n.aB.1JeHIIfl TOn.'IIIBa
f nPH' CHJIa )J{eCTKOCHj 06paTHOH npY}KlIHbI n.1JYH}Kepa 6nh H Cli.'la
d 2 h
liHepl.J,lIH JJ.BlI)J{yW.IIXC Macc M-. CII.'IV T P €HIIfl nJ1YH}Kepa BO
dt 2 .
BTy.'lK€ He YlJIITbIBaeM.. Tor.n.a JJ.BII>K€HlIe n.1YH}Kepa MmKHO onl1-
caTb ypaBHeHlI€M
iH - ; + 6nh + t nP" = 6(h.,,-h).
f1pI1HHMaeM, KaK Ii paHee,
--.E.2h = 2 (hn-h m ) 2C m
dt 2 J),.t2 J),.t
(177)
130
d 2 h
OO.ZJ.CTaBIlB ::ITO 3Ha l leHHe - B ypaBHeHHe (177) H penlHB 3TO
dt 2
ypaBHeHHe OTHOCHTe.J1bHO h n , no.1YlJH!\l
h = - fnP" '178 )
n A A' \
rn:e
B = oh + 2Mh n .
.11 (Mf'
A=( +O'O ) .
\M2. Tn
Cor.'IaCHO OTMe'IeHHbIM Bblrne KOHCTPYKTHBHbIlI-I OC06eHHOCTHM
paCCMaTpHBaeMOH CHCTeMbI npou:ecc Y HaCOCa pa3.ZJ.e.:1HeTCH TO,HbKO
Ha .ZJ.Ba 3Tana:
1) OT HalJa....Ia n:BHfKeHHH n.J1YHLKepa 11.0 HalJa,,'Ia .ZJ.BHllieHHH Ha-
fHeTaTe.'IbHOrO K.lanaHa;
2) OT HalJa.'Ia .ZJ.BHllieHHH HarHeTaTe.lbHoro K.:lanaHa 11.0 KOHI.{a
nO.ZJ.'beMa n.'IymKepa.
Ha nepBO:\>! 3Tane B KaMepe HarHeTaHHH, eC.'IH neT 06'be:\>Ia, He
3anO.lHeHHoro TOII.'lHBOM, nOC.:le,'.LHee CLKHI\1aeTCH AO .lJ:3B.:leHHH, CO-
OTBeTCTBYlOI..U.ero HalJa.'IY nO.ZJ.'beMa HarHeTaTe.lbHoro K.:lanaHa; eC,HH
eCTb CB060JI,HbIH 06'beM, TO CHalJa.'Ia nJIYHlliep COBeprnaeT XO.'IOCToi'r
Xo.:r, 3 33TeM Ton.lHBO H3qHH3eT ClliHM3TbCH B K3Mepe HarHeT3HHH.
YpaBHeHHe npou:ecca MOfKHO 3anHC3Tb B BHLl.e
f n C n = aV" cp dp" ,
dt
( 179)
rAe
V V'fll + V"2
"cp=
2
OpH6.'IHLKeHHO lUITerpHpYH ypaBHelme (179) H pern3H ero OT-
HOCHTe.1JbHO PH' nO.TJyqaeM
D
p,,={;,
( 180)
f'.lJ.e
D tn B , V
= --j-a "cpP"I;
A
b fn, V
=--r. a IICP'
A
Onpe.lJ.eJIHB p.. no ypaBHeHHIO (180), HaXO.lJ.HM BeJIH'IHHY h n .
9*
131
Ha BTOpOM 3Tane KJlanaH nOAHHMaeTCH H TOn.1HBO H3 KaMepbI
HarHeTaHHH Ha4HHaeT nocTynaTb B HarHeTaTeRbH n Tpy6onpOBO .
YpaBHeHHe-3TOrO 3Tana:
fnCn=a.V llcp dPH +trCr o (181)
dt
nOC.'1e npH6J1mKeHHoro HHTerpHpoBaHHH ypaBHeHHH (181) 3a-
MeHHM B n0J1Y4eHHoM BbIpaLKeHI1U CKOpOCTb C r ee 3HaI.JeHHeM, BbI-
paLKeHHbIM cor.'1aCHO 3aBHCHMOCTH (4). PewHB Tenepb HOBoe ypaB-
HeHHe OTHOCHTe.'1bHO PH' nO.TIYI.JHM
D'
PH = EY'
( 182)
r e
D' = fn B + eN + frMpo , frMW(t)
A II CPPHI 2 --r
ap ap
B ' =-.h. + V .L f r M
a. H cp , 0
A 2ap
nOCJle onpe e.'IeHHH PH HaXO!I.HM no <popMYRe (4) BeJ1HI.JHHY
aMn.'1HTY!I.bI BOJ1HbI F (t), H!I.)'II.{en OT Hacoca K <PopcYHKe, a no
)'paBHeHHIo (178) - BemII.JHHY h. PaCI.JeT npo ecca y <pOpC)'HKH
coxpaHHeTcH TaKHM LKe, KaK II .n:.1H CHCTeMbI Henocpe.n:cTBeHHoro
.n:encTBIIH.
frCrlM
2
r 11 a B a III. PAC'IET npO ECCA BnPblCKA TOnl1HBA
C nPHMEHEHHEM BM
1. OC05EHHOCTH MATEMATHIfECKOA. MOAEnH
H AnrOPHTM HCXOAHOrO METOAA PACIfETA
Oco6eHHOCTH nOCTpoeHHSI MaTeMaTH eCKOH MO)J.eJ1H BnpbICKa
TOnJ1HBa )J..IIS1 lI.BM. O)l.HHM H3 nepcneKTHBHbIX HanpaBJleHm'i B H3Y-
'IeHHH H ,lI,a.:lbHeHI1leM COBepI1leHCTBOBaHHH TOnJIHBHbIX CHCTeM ,lI,H-
3e.TIeH 5IB.rI5IeTC5I paC'IeTHO-TeOpeTH'IeCKHH aHaJIH3. DpHMeHeHHe
UBM paCI1lHp5IeT B03 lmKHOCTH paC<JeTHO-TeopeTIflleCKoro aHaJ1H3a
npOL(eCca nO,lI,a'IH TOnJ1HBa B .lI,H3e,,'I5IX, n03BOJ15I5I nOJIY'IaTb 60.'lee
r,,'Iy60KHe npe.lI,CTaB.JIeHH5I 0 npH<Jlmax H B3aHMOCB5I3SIX C,,'IO)J(HbIX
rImpO,lI,HH8MH'leCKHX flB.'IeHHH, B03HHK8roW.HX npH BnpbfCKe TOrr,TrH-
Ba, a TaK)J(e pa3pa6aTbIBaTb 60.'lee 060CHOBaHHble npaKTH<JeCKHe
peKOMeH.lJ:aL(HH no YCOBepIlleHCTBOBaHHIO Ton.'lHBHbIX CHCTeM. C HC-
nO.;lb30BaHHeM UBM n05IB.JI5IeTCH B03MO)KHOCTb B KOpOTKHll CpOK
paCC<JHTaTb npOL(eCCbI BnpbICKa TonJ1HBa .lI,.JIH 60JIbI1l0rO <JHC,lIa KOH-
CTPYKTHBHbIX BapH8HTOB TOn,,'IHBHbIX CHCTeM II BbI6paTb J1YlJIllHe H3
HHX. .lJ..1I5I 60"lee nO.'lHOrO HCnO,,'Ib30BaHH5I B03MO)J(HOCTeH UBM He-
06XO.lI,HMO, 1IT06bI MaTeMaTH<JeCKa5I MO.lI,eJIb npOL(eCca BnpblCKa
TOn,,'IHBa 6bwa .lI,Ono.'lHeHa 3a ClJeT OTKa3a OT HeKOTopbIX .lI,onYI1le-
HHH, L(eJ1eC006pa3HbIX npH PYlJHOM C<JeTe, H BbI<JHCJIHTe,TIbHbIH aJ1ro-
pHTM 6bW pa3pa6oTaH C YlJeTOM oc06eHHOCTeH H npeHivIYI1leCTB
UBM.
DbICTpO.lI,eHCTBl1e UBM n03BO,,'l5IeT OTKa3aTbcH OT MHOrI1X .lI,ony-
I1leI-Il1H, npHH5ITbIX npH PY<JHOM C<JeTe .lI,J15I yMeHbIlleHHH TpY.lI,OeM-
KOCHI paClJeTa, OTKpbIBa5I B03MO)J(HOCTH )I..'HJ YlJeTa HaH60JIee CY-
w.eCTBeHHbIX YTOlJHeHHH.
OnbIT paClJeTOB npOIl,ecca BnpbICKa Ton.'lHBa C npHMeHeHHeM
UBM nOKa3aJ1 L(eJleco06pa3HOCTb Y<JeTa pfI.lI,a <paKTOPOB, KOTopbIe
06bI<JHO He Y 1 Il1TbIBaIOTCH npl1 PY<JHbIX paC1IeTax: OCTaTOlJHbIX CBO-
60.lI,HbIX 06"beMOB, rImpaB.1HlJeCKOrO conpOTHBJ1eH115I Tpy60npOBO.lI,a,
YTeqeK TOnJHma B Hacoce H paCnbIJ1HTe,TJe, C)J(l1MaeMOCTH Ton.rrHBa
KaK <PYHKL(HH llaBJ1eH115I H TeMnepaTypbI, .lI.pOCCeJ1HpOBaH115I KaHa-
J10B B n.IIYI-DKepe npH OTce 1 IKe, 3aBl1Cl1MOCTH npOXO.lI,Horo CelJeHHSI
paCnbIJIl1Te.'I5I OT npOTHBO.lI,aBJIeHH5I, ynpyroCTH npHBO.lI,a, .lI,pOcce.IIH-
pOBaHH5I KaIJa.l0B B.lI,OJ1b nepbeB KJ1anaHa, pa3pbIBOB CnJ10IllHOCTH
Ton.'IHBa B I\OHL(e BnpbICKa, CHJlbI TpeHH5I npH CTparHBaHHH l1rJIbI
<P0PCYHKH. HeKOTopbIe 113 nepe1.JHCJIeHHbIX YT01.JHeHHH paC1.JeTa He-
L(eJIeC006pa3HO npHMeH5ITb BO Bcex paC1.JeTax. CJIe.lI,OBaTeJ1bHO,
HY}KHbI YHHBepCaJ1bHble aJ1rOpHTMbI H nporpaMMbI, n03B0J15IIOI1lHe
133
BbI60pOlJHO HCnO.1b30BaTb Te H.'IH HHbIe YTOlJHemUI, He H3MeH5HI
nporpaMMbI. KpOMe TOro, a_lropHTl\I H nporpaMMa paC'IeTa npou:ec-
ca BnpbICKa Ton.1HBa .n:O.'I)KHbI 06eCnelJHTb B03l\IQiI"HOCTb .lerKO, T. e.
6e3 cymecTBeHHoro H3MeHeHI-I5I nporpaMMbI, .n:OIIO.1H5ITb aaropHTM
paClJeTa HOBbIMH <paKTopaMH, YTOlJJI51fOmHl\UI paClJeT, H.1H H3MeH5ITb
HCxo.n:HbIe ypaBHeHH5I C u:e.'IbfO paClJeT3 HOBbIX BapHaHTOB KOHCT-
PYKU:HH TOIIJIHBHOH annapaTypbI.
Cor.'IaCHO 06Il.LeH TeoplIH npou:ecca BnpbICKa H3MeHeHHe rpaHUlJ-
HbIX YC.'IOBHII B OCHOBHOM TO.lbKO YBe.'IH'IHBaeT H.'JH YMeHblilaeT lJU-
C.10 lJ.lIeHOB B OT.n:eabHbIX ypaBHeHH5IX, a Ha HeKOTopbIX 3T3nax II
lJHCJIO ypaBHeHHH, 06ill.HH }J(e BH.n: ypaBHeHHH He H3MeH5IeTC5I. 1a-
KHM 06pa30M, pa3.n:e.'!eHHe npou:ecca Ha ::JT3nbI no cymeCTBY 51B.'I5IeT-
C5I <popMa.lbHbIM YlJeTOM U3MeHelUI51 rpaHWIHbIX YC.10BUi1.
npH HCn0J1b30BamfH UBM YlJeT H3MeHeHHlI rpaHH'IHbIX YC.10BHij
ynpornaeTC5I. YpaBHeHH5I npou:ecca Y Hacoca H y <POPCYHI\H 3anH-
CbIBalOT .n:.H5I HaH60.'Iee 06lll.ero 3Tana H nporpaMrvmpYfOT B 06lll.eM
BH.n:e 6e3 .n:onoaHHTeabHbIX npe06pa30BaHHH. H HHTerpHpOBaHH5I
CHCTeM ypaBHeHHH rpaHH'IHbIX YC.'IOBHII HCn0J1b3YfOT .n:Be OT.n;e.'IbHbIe
no.n:nporpaMMbI lJHC.lIeHHoro HHTerpHpOBaHH5I. OpaBbIe lJaCTH ypaB-
HeHHH rpaHHLJHbIX YC.IIOBHH paCC'IHTbIBafOTC5I J1Hlllb llBYM5I onepaTO-
paMH. 3TO 06eCneLJHBaeT B03MO)KHOCTb, He H3MeH:5I5I OCHOBHbIX one-
paTopOB nporpaMMbI, YBeJ1HLJHBaTb IWH YMeHblIlaTb KO.:1WIeCTBO
YLJHTbIBaeMbIX <paKTOpOB H paCCLJHTbIBaTb pa3.1l1LJHbIe BapHaHTbI
KOHCTPYKU:HH nYTeM .n;06aBaeHH5I H.1H 3aMeHbI COOTBeTCTBYfOlllHX
lJaeHOB ypaBHeHHH rpaHHlJHbIX ycaoBHH, KOTopbIe BbIlJHCa5lfOTCH B
.n:BYX YKa3aHHbIX onepaTopax.
AnfopHTM HCXO.n:HOfO MeTo a pac eTa npou:ecca BnpMCKa Ton-
JlOBa. HCXO.n:HbIM MeTo.n:OM paC'IeTa YC.IIOBHMC5I Ha3bIBaTb MeTOJI.
paClJeTa TOnJ1HBHoi! CHCTeMbI, COCT05lmei! H3 Hacoca 30.IIOTHHKOBoro
THna, Tpy60npoBOlla H 3aKpbITOH <POPCYHKH, 6e3 YlJeTa YTOlJHeHHli,
nepelJHc.'IeHHbIX B npe.n:bI.n:ymeM naparpa<pe. A.'IrOpHTM HCXO.n:HOro
MeTOlla paClJeTa B npHMeHeHIfH K PYlJHOMY CLIeTY H3JlmKeH B r.l. II.
npH MalllHHHOM CLIeTe .n:.!HI pac'IeTa .n:BH)KeHH5I TOnJ1HBa B TPY-
60npoBo.n:e 6e3 YLIeTa rH.n:paB.'IHlJeCIWrO conpOTHIB.'IeHH5I Hcnoab3Y-
lOT Te }Ke pellleHHH BO.'IHOBOro ypaBHeHH5I [CM. <pOpMy.lbI (3), (4),
(5)]. npou:ecc .n:BH)KeHH51 TOnJIHBa paccLIHTbIBaeTC5I no 3THM yp3B-
HeHH5IM C YlJeTOM Ha'la.'IbHbIX YC.'IOBHH H rpaHH'IHbIX YC.'IOBHII BO
BXO.n:HOM H BbIXO.n:HOM ce'IeHH5IX Tpy60npoBo.n;a.
06bIlJHO B Ton.'IHBHOH CHCTeMe I( HalJa.'!y C.'Ie.n:YIOlll.erO BnpbIcKa,
T. e. npH t = 0, .n:BH)KeHHe TonaHB3 B HarHeTaTeabHOM Tpy60npo-
BOlle npeI<paIuaeTC5I H YCTaHaBJ1HBaeTCH OCTaTO'IHoe llaB.'IeHHe, 1<0.
Topoe 3a1l3fOT npH6aH)KeHHO, a 3aTeM YTO'lHHfOT B pe3Y.lbTaTe pac-
:<JeTOB npou:ecca BnpbICKa TonaHBa.
TpaBHeHH5I rpaHH'IHbIX YC,,10BHH BO BXO.n:HOM Ii B BbIXO.n:HOM ce-
lJeHH5IX Tpy60npOBOJI.a onpe.n:e.'IHfOTC5I pe}J(HMOM pa60TbI n KOHCT-
pYKuHeli TOnJIHBHOH ClICTeMbI. Omi crpynnnpoBaHbI B IIBe ClICTeMbI
ypaBIleHlIH: Y Hacoca H Y <POPCYHKH. .151 Y.B:06CTBa nporpaMMHpo-
BaHlIH ypaBHeHlIH HanlIcaHbI .n:.II5I Han60.1ee 06m.ero 3Tana. B Ka-
134
LleCTBe K03<p<PlUI.HeHTOB nepe.n. OT.n.eJlbHbIMH IJ:JIeHaMH ypaBHeHHH H
B lJ.eJ10M nepe.n. npaBbIMH IJ:aCTHMH OT.n.e.'IbHbIX ypaBHeHIIH BBe.n.eHbl
CTyneH'laTbIe <PYHKllIIH ai, cue i = 1, 2, 3, 4. 4>YHKIIIIIi ai, npHHlIlVraH
3Ha L leHlIe Hy.'IH IIJIIi e.n.IIHHlJ.bI B 3aBHCHMOCTH OT nOJlOJKeHHbIX H3
HHX .10rlIIJ:eCKIiX YC.'lOBHH, onpe.n.eJ1H1OT BII.n. H KO.'lH'leCTBO ypaBHe-
HHH .n..1H Ka)f\:Aoro 3Tana p3C'leT3. IlpH'le:\i B nporp3lVIMe nepe.n. BbI-
IJ:HC,,'leHlIeM BbIpa:>KCHIIH, HMe1Olllero COMHO}KHTe.lb ai, YKa3aHHbIII
CO:.\IHO:>KHTeJlb 3Ha.'IH3HpyeTcH, H ec.1H OH OK33bIBaeTCH paBIIbIM HY-
J11O, .n.aHHoe BbIpa:>KeHHe He BbIIJ:HC,,'lHeTCH. KpOMe TOro, .n.H<p<pepeH-
lJ.Ha.lbHbIe ypaBHeHHH BToporo nOpH.lJ.Ka (ypaBHeHHH .rI.BH}KeHHH
IIr.lbI <POPCYHKH II HarHeTaTe.'IbHOrO K.lanaIW) CBeLJ:eHbI I\: ypaBHe-
HH10 nepBoro nopH.n.Ka.
fpaHnIJ:HWe YCJIOBHH Y Hacoca onHCWBa1OTCH ypaBHeHHHMH
.' r- )
%" = (t "C" -ao of0V: -; Jl l p,,- P 8 c 1-
( 2 V, ' I \ I
-aK IlJllr - p,,- PII -a l,P" )
p / fua
dp ( .. (2 VI ' I
= aKllll./l;J V p PII-P" +
+ aIf"C,,-trCr ) I ;
6nCG\/
dCII = [t" (PII-p )-t"p"p- h,J ;
drp 6nM
dh K -C
dtp - K 6n .
CKOpOCTb TOnJIHBa BO BXOLJ:HOM CeIJ:eHHH Tpy60npOBo.n.a B COOT-
;, "BeTcTBnH C pemeHHe!li BOJIHOBOrO ypaBHeHHH
I . j
C r =- [p -Po+2W(t) .
ap
I
1
I
I
(183)
(184 )
O.n.HOBpeMeHHO paCCLIlITbIBaeTCH npHMaH BO,TIHa, 06pa3Y1OUI.aHCH
Y Hacoca:
F(t)= P -Po+ \\7(t).
( 185)
<PYHKlJ.HH ao H an, npHHHMaH 3HaIJ:eHlIe 1 1I,,'lH -1, YI<a3bIBa1OT
.HanpaB.TIemle, B KOTOpOM LJ:BIDKeTCH Ton.'1HBO lIepe3 OKHa rlI.'Ib3bI H
'IJ:epe3 1\.l,maH:
ao = 1 npli P" > Pon;
ao= -1 npH PII < P6";
a K = 1 npH PII > P ;
a" = -1 npH p,,< p .
135
<l>YHKUHH aj = f(h", F,,) npHHHMaeT HyaeBoe 3Ha<JeHHe, eCJIH
HarHeTaTeJIbHNH KJ1anaH HaXO HTCH Ha ce JIe H paBHo eHcTBym-
lltaH Bcex BHeUlHHX CHJ1, eHCTBYIO HX Ha I{.lanaH (CHJIa F,,), npH-
>KHMaeT ero K ce.n:J1Y (aI = 0 npH h" = 0 H F" 0; aI = 1 BO Bcex
OCTaJ1bHbIX CJ1Y<JaHx); 3 eCb F" = f" (PH - p ) - f "P",p - bh".
rpaHWIHbIe YC.'10BI1H y Q:>OPCYHKH Onl1CbIBamTCH CHCTe!\IOH ypaB-
HeHI1H
dp,p I ' , I 2 ..f J 1 .
d;p= f..CT-(fJ.f)tjJ V (J V PtjJ-Pu.- a3 tu C ll. 6naVq, '
dC ll. [( ' ) , " ,1 u 3
= tll.- fll. (p",-Pq,0)-rfll.pq,-6 YJ 6nM' '
dy =c
dq> u 6n .
B COOTBeTCTBHH C perneHHeM BO.1HOBoro ypaBHeHHH HMeeM
C;= a [Po-P;b+2F(t- )].
I
} (186)
I
J
(187)
O.lI.HOBpeMeHHO paCC<JHTbIBaeM 06paTHym BOJ1HY W (t + ), KO-
L
TopaH <Jepe3 HHTepBc.l.1 BpeMeHH - 6Y.J.eT HcnO.lb30BaTbCH npH pac-
a
<JeTe rpaHWIHbIX YC.l0BHH y Hacoca:
U7 (t+ )=Po-PrJ)+F(t-- ). (188)
<l>YHKUHH a3 = f (y, F u) npHHHMaeT HYJ1eBOe 3Ha<JeHHe, eCJ1H IIr-
oI'1a HaXO.lI.I1TCH Ha C .lI..'1e (H.1JH Ha ynope) II paBlIO eHcTBYIo aH
Bcex BHernHHX CHoIl, )].eHcTBYlO IIX Ha I1r.1Y, nplI.lKlIl\IaeT ee K ce.lI.J1Y
(HoI'1H ynopy): a3 = 0 npII y = 0 II Fu 0 IIJ1H npH Y = Ymax H
F u ? 0; a3 = 1 BO Bcex OCTaJ1bHbIX CJ1Y<JaHx; 3.lI.eCb
Fu => (fu-f )(pq)- PcjJo) + f p -6'y.
BemI<JHHY ( lf) g.; 3a.lI.alOT B BII.lI.e Ta6JIIIUbI KaK Q:>YHKUHlO nO.lI.'be-
Ma IIr.'lbI. Ta6.'1IIua MmKeT 6NTb nOJ1yqeHa 3RcneplIMeHTaJ1bHO IIJ111
paCQeToM. OpH paCqeTe npouecca BnpbIcKa 3HaQeIJIIe ( lf)g; onpe-
.lI.e.'1HlOT no YKa3aHHoH Ta6J1IIue C nOMO bm no nporpaMMbI KBa.n:-
paTIIlIHolI HHTepno.'15!UIII1.
OnbITHbIe xapaK'teplICTIIKI1 paCnbIJII1TeJIeH (fJ.f) g; = f (y) Ton-
JIIIBHNX CIICTeM aBTOM06HJIbHOrO II3eJIH H 3-236 11 TpaKTopHoro
.lI.II3e.'1H lI.-50 nOKa3aHbI Ha pHC. 47.
Be.TJ:H<JHHY aB.leHHH no KOHYCOM II rJ1 bI MO.lKHO BbIQHC.TJ:HTb II3
YCJIOBIIH paBeHcTBa pacxo.lI.oB Qepe3 paCnNJII1TeJIb B ueJ10M 11 <Jepe3
COnJ10BbIe oTBepcTHH:
( lf)
fJtjJ= (!tcfc)2 (P.p-p,J+P'jO
136
(189)
BOJ1HbI ,Il,aBJleHHH, onpe,Il,e.TIHeMbIe no <popMYJ1aM (185) H (188),
nOl\Ieru:aIOTCH B CneI.J.HaJlbHO OTBeJ1.eIIHYIO I.JaCTb naMHTH, MO,Il,e.'1Hpy-
IOlllYIO Tpy60npOBOJ1., oTKY,II,a OHH HCnO,,'1b3YIOTCH no HCTeIJeHI-IH Bpe-
L
MeHH 't = -.
a
HaMenIM OCHOBHYIO
BnpbICKa Ton.lIIBa:
.1) nepeBO,Il, IICXO.Il.HbIX .n.aHHbIX B .Il.BOH'WYIO CHCTeMY CqlIC.TIeHI-1H,
paCIJeT nOCTOHHHbIX K03<p<plII.J.lIeHTOB H <pOpMlIpOBaHHe 6J10KOB, MO-
,lI,e.'1lIpy1OllI.HX Tpy60npo BO .Il.;
2) paCIJeT HCKOMbIX <PYHKI.J.UH
CHCTeMbJ ypaBHeHHH rpaHHIJHbIX YC-
J10BUH Y Hacoca npH nOMOlll.H no.Il.-
nporpaMMbI IJIICJ1eHHoro HHTerpH-
pOBaHHH ,II, H OIJepe,Il,HOrO 3HaqeHlIH
aprYMeHTa;
3) paCIJeT npOI.J.eCca B Tpy60npo-
BO.Il.e .Il.J1S1 OIJepe,Il,HOro 3HaqeHlIH ap-
rYMeHTa;
4) paCIJeT IICKOMbIX <PYHKI.J.lIH
CIICTeMbI ypaBHeHIIH rpaHI-IqHbIX YC-
,,'10BIIH Y <POPCYHKII npll nOMOlll.lI
nOlwpOrpaMl\IbI IJIICJleHHOro HHTe-
rpHpOBaHHH .II. H Oqepe,lI,HOro 3HaIJe-
HIIH aprYMeIJTa;
5) ne'laTaIIHe TeKYlllllx pe3YJlb-
TaTOB paCqeTa II npOBepl<a Ha OKOH-
IJaHlIe paCIJeTa. EC.'1H paCIJeT He 3a-
KOHIIeH, YBe,,'1H'IlIBaIOT aprYMeHT Ha
BeJIlIqlmy wara IIHTerpllpOBaHIIH II
nepeXO.Il.HT K n. 2, ecmI Me paC4eT
3aKOH4eH, nepeXOJ1.HT K nYHI<TY 6;
6) pac4eT II ne 1 IaTaHHe naparvIeTpoB, xapaKTeplI3YIOllI.IIX BnpbIcK
B I.J.e.TIOM, II OCTaHOBKa MaWIIHbI.
.10r1I4eCKYIO cxeMY a.TIrOplITMa pac4eTa
(ft.l)", MM2
0,4
----4
.! I I
I _ I
: I
IT-
I I
0,3
I
I
0,2
0,1
o
0.1
0,2
0,3 Y f1M
PHC. 47. 3KcncpHMcHTa.lbHbIC xa-
paKTcpHCTHKH:
1 - MHoro.nbIp'laTOrO paCnbIJIllTellH
)],H3eJI>I 5lM3-236; 2 - lIlTHQJTOBOro
paCnbI "1MTe TJSI TpaKTopHoro 1J.U3e 'IH
A-50
2. Bbl60P METOAA "IHCnEHHOrO HHTErPHPOBAHHSI
YPABHEHHIIt rPAHH"IHbIX YCnOSHIIt
B COOTBeTCTBIIH C npllHHTblMII npHHI.J.HnaMH nOCTpoeHHH a.lro-
pHTJ\Ia 6bI.'1H HCC,;'1e.Il.OBaHbI MeTO.Il.bI qHC.'1eHHOrO HHTerpHpOBaHHH
ypaBHeHHH rpaHlI 1 1Hb1X YCJIOBHH, npe.Il.YCMaTpHBalOllI.HX IICnOJ1b30-
BaHHe npaBbIx 4aCTeH .Il.H<p<pepeHI.J.Ha.'1bHbIX ypaBHeHIIH 6e3 .Il.OnOJI-
HHTe.'1bHbIX npe06pa30BaHHH.
C I.J.f.'1bIO BbI60pa MeTO.Il.a 4HC.'1eHHOrO HHTerpllpOBaHIIH npOBe-
,Il,eHbI cpaBHIITe.'lbHbIe paCqeTbI II npOBepeHbI c e.Il.YIOru:He MCTO.Il.bI:
MeTO.II. PYHre-KYTTa; HHTepnOJ1HI.J.HOHHaH <popMy.'1a AllaMca C no-
pH.Il.KOJ\I TOIIHOCTII 1z5, r.Il.e Iz - mar HHTerpH.pOBaHHH; 3KCTpanO H-
I.J.HOHHaH <popMy.TIa AAaMca C nOpH,II,KOM TOqHOCTH 1z5; HHTepno.TIH-
137
I{{WHHa5l <pOpMy.TJa An;alVIca C nOp5ID,KOM TOlJHOCTIl h 3 ; MeTOD, 3i1cle-
pa; y.lYlIilleHHbIi1 MeTOJJ. 3i1.TJepa-KoIllH; YJ1YlJrneHHbIi1 MeTO.LI:
3i1.'Iepa-KoillH C I-ITepa Hei1; MeTO.LI: 3i1.'Iepa C .LI:p06JIeHHeM rnara.
I1CXO.LI:5I 1I3 Toro, lJTO MeTO.LI: lJIIC.'IeHHOrO IIHTerplIpoBaHlUI AO.'1-
)KeH o6eCnelJHBaTb 3a.J.aHHYIO TO'lHOCTb paC'leTa npH MHHHMa.'1bHoi.f
3aTpaTe MailllIHHoro BpeMeHu, conOCTaB.'IeHbI paClJeTbI npu YC.'10BIIII
paBHbIx 3aTpaT :HaillUHHoro Bpe1\leHlL War HHTerpHpoBaHHH npu
nOM Mor 6bITb HeOJJ.UHaKOBbIM. HanpUMep, cpaBHHBaJIII paClJeTbI.
nOJlyqeHHbIe MeTO.J:Ol\l 3ii:.lepa
C h = 0,02° H MeTO.LI:OM PYHre-
KYTTa C h = 0,08°. B KaIK.LI:OM
cJ1YlJae Ha paClJeT 3aTpalJHBa-
J10Cb 7-8 MUH. f1orpeillHocTH
onpe.lI,eJ1HJIH KaK OTiWOHeHHe
paClJeTHbIX xapaKTepHcTIIK
BnpbICKa OT 3TaJIOHHOrO perne-
HH5I. 3a nOCJIe.lI,Hee 6bW nplI-
H5IT pe3YJ1bTaT npH6JIIIIKeH-
HOro paClJeTa, nO.JIYlJeHHOrO
pa3Jl11lJHbIMH MeTO.lI,aMII (PYH-
re-KYTTa, 3i'wepa, A.lI,aMca) C
.lI,OCTaTOlJHO MeJIKHM rnaroM
HHTerpHpoBaHHH, npH IWTO-
pOM Bce TPH pe3y.'1bTaTa npaK-
TIIlJeCKH COBnaJIH.
Ka3a.'10Cb, lJTO Ha1I6onee
3<p<pel\THBHbIMH .lI,O.'1)KHbl 6bITb
MeTO.lI,bl PYHre-KYTTa 1I A.lI,aM-
ca, KOTopbIe IIMeIOT BbICOKIIi'I
nopH.lI,OK TOtJHOCTII OTHOCIITeJIbHO rnara HHTerpllpOBaHII5I II IIlHpOKO
npIIMeHHIOTC5I npII paClJeTaX Ha DBM. O.lI,HaKO COnOCTaB.'1eHlle pe-
3y.TJbTaTOB paClJeTa nOI<a3bIBaeT, lJTO Ha HeKOTopbIX YlJaCTKaX nplI wa-
re HHTerplIpOBaHI1H, COOTBeTCTBYIOw.eM CpaBHIlTe.'1bHO He60.'1bW_IIM
3aTpaTaM MallIIIHHoro BpeMeHII, 3TH MeTO.lI,bI .lI,aIOT 3HalJHTe.1bHYIO no-
rpeWHOCTb.
XapaKTepHCTIIKII BnpblCKa, paCClJIITaHHbIe pa3.'1I-Jl!Ilbli\IH MeTOAa-
MIl, nOKa3aHbl Ha pHC. 48 B conOCTaBJleHHII C 3Ta.'IOHHbIM pewe-
HIIeM.
PaClJeT npHBe.lI,eH .lI,JIH Ton.TJHBHoi1 annapaTypbJ 5!N\3-236 Ha
HOMHH3.'1bHOM peIKHMe (n = 1050 o6jMuH, q'l = 120 MM 3 ), HeKOTO-
pbIe KOHCTPYRTIIBHbIe 3J1eMeHTbI H3i\IeHeHbI .lI,.'I5I no.'1YQeHII5I HBHO
BbIpaIKeHHoro nO.lI,BnpbIcKa.
3HaQeIUI5! MaKcIIMa.1bHoH TeKyw.eH norpernHOCTl! b ren H norpew-
HOCTII no IIK.'10B0i1 nO.lI,aqe {j,. nplIBe.rr.eHbI B Ta6.TI. 2.
f1orpewHoCTb
fO
5
PIIC. 48. PaC'ICTHblC xapaKTcpHcTIIKIi
BnpbICKa:
1 - 3Ta.rIOHHOe perneHue. npaKTlitJeCl\Ii
COBna.lI.alOur.ee c pemeHueM no MeToJI.Y
3f!. epa c )],p06.1eHHeM mara npH h
0,02 epao; :J - IIHTepnOJI>IU,HOHRaH .pop-
My,1J3 A.n.aMca nHToro IJOIHI.D.K8 TO'-lHOCTH
OTHOCHTe.'1bHO UJara npH h = 0.04 2pai); 3 -
MeTO)], PYHre-KYTTa npH h 0,08 epao
rpO
6 re ,,= lL\qll-L\qlmax .1OO 'o.
L\q" max
,138
r.n:e
I q" - !1q I max - MO.n:YJIb MaKCHMa.rIbHOH pa3HOCTH op.LIJIHaTbI
ftUl 3
3Ta.'10HHOrO 3aKOHa no.n:aI.IH q" - H Op-
2paO
.n:HHaTU 3aKOHa no.n:a4H, paCC4HTaHHoro npH
3a.IIaHHbIX mare H MeTon:e 4HC.'1eHHOrO HHTe-
,IUt 3
rpHpOBaHI1H !1q -
2pao'
op.n:I1HaTa 3Ta.rIOHHoro 3aKo-
q1< max - l\IaKCHMa.'lbHaH
Ha nOlI.a4H
() = I qU,K-qU, I
Ii
.q"K
-lOO .O,
rlI.e
q1j,1< - LI.HKJ10BaH nOlI.a4a, nOJIY4eHHaH npH pac4eTe 3Ta.'IOHHOrO
pemeHHH, B . tJI13;
q1J - IUiK.'lOBaH no.n:a4a, nO.'1Y4eHHaH npH 3a.n:aHHbIX lllare 11
MeTo.n:e 4HCJleHHOro HHTerpHpoBaHIHI, B .1t.M 3 .
norpeWHOCTb 'IHcneHHoro HHTerpHpOBaHHH
T a6,1U4a 2
BpeMS! paC4eTa B MUtt
nopS!- 7-9 14-16
)],OK
MeTOA TOQHOC- I
Tn Me- It B /8 TPK B/ 8q B It \8 TPK 8q B
TOAa cpao % % B 2pao B % %
no IIIlTCpnO H nOHHOll lj:Jop-
MY,IJC A;raMca h 5 0,04 45 7,0 0,02 10,0 2,5
PYHre-KYTTa h 4 0,08 7 1,5 0,04 6,0 2,0
Y.1Y'-lIllCHHbIll 3i1.1cpa-I\OIllH h 3 0,04 35 4,6 0,02 5,0 1,0
3i1.'Iepa 11 2 0,02 3 1,5 0.01 1,0 0,2
311.'Icpa c ;rp06 cHHCM lllara . h 2 0,02 1 0,4 0,01 0,7 0,1
HeCOOTBeTCTBl1e TeOpeTI14eCKOH II <paKT1I4eCI\.OtI TO<IHOCTl! pac-
4eTa MeTon.aMI1 A.n:aMca 11 PYHre- KYTTa 06'b5ICHHeTCH TeM. 4TO 3TH
MeTOlI.bI MOrYT 06eCne<IHTb y.n:OB.'IeTBOpI1TeJlbHYID TO<IHOCTb npH
CpaBHI1Te.'lbHO KpynHbIx lllaraX I1HTerpl1pOBaHI1H, eCJ111 B paCCMaTpl1-
BaeMoi1 06JIaCTI1 npaBbie 4aCTH I1HTerpl1pyeMbIx ypaBHeHHH I1MeIDT
HenpepbIBHble npOH3BO.n:HbIe lI.0 HeKOTOpOrO nop5I.n:Ka_
Opl1 HCnOJIb30BaHHI1 MeTO.n:a Pynre-KYTTa, y.'IY4llleHllOrO MeTO-
.n:a 3i1J1epa - KOllll1, a TaK:rKe MeTo.n:a 3i1_'1epa I1CKOMOe pemeHHe
pa3.TJaraIDT B pH.n: TetI.'IOpa B OKpeCTHOCTH Ka}J(.n:oi1 T04IU! Xi:
( ) ( ) ! X-Xi ' ( _ ) ! (X-Xi)2 " ( ) I
Lf X = Y X l . .. - Y Xi -, Y Xi T . .. .
. . I! 2!
Ec.'111 orpaHlII.II1BaTbCH JJ,BYl\IH nepBbIMH 4.'1eHal\1I1 pH.n:a Tet!JIopa,
TO no.'IY4HM <P0PMY,'lY 3i1.'Iepa, Tpe6YIOIll.YIO nenpepblBHOCTH TO.rlbKO
139
nepBOI! npOlBBOlUIOii HCKOMOrO peWeHHH, B HaWeM CJIV'Iae - He-
npepbIBHOCTH npaBbIX '1aCTeH ypaBHeHHH BnpbICKa. 3Ha'leHI1e nep-
BbIX TpeX '1"leHOB pHLLa HCnOJIb30BaHO B YCOBepWeHCTBOBaHHOM Me-
TOLLe 3l'wepa - KOWH, KOTOpbIH Tpe6yeT HenpepbIBHOCTH nepBbIX
npOlI3BOLLHbIX npaBbIX lfaCTeH ypaBHeHHH rpaHHlfHbIX YC.'IOBHH. Ha-
KOHeII:, 3Ha'leHHe nepBbIX nHTH '1.'JeHOB pHLLa TeCwopa MO)KHO no.'1Y-
llHTb no CPopMY.'Ie PYHre-KYTTa, I\OTopaH COOTBeTCTBeHHO Tpe6yeT
HenpepbIBHOCTH npOH3BOLLHbIX HCKOMOCI cpynKII:HH LLO '1eTBepToro no-
pHLLKa. Opu HCnOc'Ib30BaHHH cpOpl\Iy.l ALLaMca, cpOpMy.'IbI, uMeIOw.ue
60,!IbWJIH nopHLLOK TO'lHOC-
TH, TaKn."e Tpe6YIOT nenpe-
pbIBHOCTI1 npOII3BOLLHbIX
60.'Iee BbICOKoro nopHLLKa.
OpII 3TOM npOII3BOLLHaH
HCKOMoro peweHIIH 3aMeHH-
eTCH I1HTepnOJIHII:I10HHbIM
no.1HHOMOM HbIOTOHa.
OPII paC'IeTe BnpbICIW
np0I13BOLLHbIe HCKOl\IbIe
CPYHKII:UH I1MeIOT pa3pbIBbI,
Hanpmuep, B MOMeHTbI or-
paHWIeHHH LLBH)KeHI1H Ha.
rHeTaTe:IbHoro K.'IanaHa,
Hr.'lbI CPOPCYHKII II T. LL., T. e.
B OCHOBHOM Ha rpaHIIII:aX
3TanOB paC'IeTa.
TaKHM 06pa30M, B Ha-
weM C,;lYlJae MeTOLL C 60.!Iee
BbiCOKOH TeOpeTI1'1eCKOH
TOlIHOCTbIO npH warax, cooTBeTcTBYIOllI.HX cpaBHHTeJ1bHO He60.!IbWI!M
3aTpaTaM l\IaWHHHOro Bpel\leHII, MeHee 3cpcpeKTHBeH. 4eM BbIwe no-
pHLLOK TO'lHOCTII MeTOLLa, TeM 60.'IbWee KOJ1WIeCTBO npoII3BoLLHbIX
BbICWHX nopHLLKoB Y'lacTByeT B paC'IeTe II TeM 60.'IbWe YCJIOBHH LL.'JH
B03HHKHOBeIlI-I5I ,LI,Ono.'IHIITe.'IbHbIX norpewHocTeH B MOMeHTbI pa3pbI-
Ba npoH3BoLLHbIX.
PaC'IeTHbIe KpHBbIe ..'I,aB.leHHH HaLL TI.'IYH)KepOM, no.TJY'IeHHbIe no
HHTepno.'I5III:HOHHbIM cpopMy.:'IaM ALLaMca C pa3J'IHlfHbIM nopHLLKOM
TO'IHOCTH npH OLLI1HaJWBOl\! ware mnerpHpOBaHH5I, nOKa3aHbI Ha
pHC. 49. ConocTaB.leHlIe C :,na,;'IOHHbIM peWeHI-IeM nOKa3bIBaeT, '1TO
YBeJ1H'IeHHe nopHLLKa TO'lHOCTII MeTOLLa B 3TOM cJ1Y'Iae npu npO'lHX
paBHblx YC.TJOBIIHX BbI3bIBaeT YBe.'IlIlfeHlle norpeWHOCTII.
)],.151 J1I060ro 113 YKa3aHHbIX cnoc060B MmKHO n01I.06paTb TaKoH
Me.'1KUH war, npII KOTOpOM Bm-I5lHIIe LLonO.'IHUTe.lbHbIX norpeWHo-
CTeH B MeCTax pa3pbIBOB CTaHeT npaKTU'IeCKII He3aMeTHO. TaK, npII
3aTpaTe MaUlI!HHOrO Bpel\IeHI1 OK0J10 1 'i MeTOLL PYHre-KYTTa (h =
= 0,01°) LLaBa.'I b"lJ = 0,8%, MeTOLL ALLaMca mIToro nopH1I.Ka T01.JHO-
CTII -'- b"lJ = 0,2% npII ware 0,005°. 3TO MO)KHO 06'bHCHIITb Tel\!,
lITO KOJ1II'IeCTBO IIHTepBa.:10B IIHTerpHpOBaHII5I, COBna1I.aIOllI.IIX C T01.J-
PH XiJCM 2
600
400
200
20 32 38 rpo
Puc. 49. PaC'-ICTHbIC KpHBblC .il.aB.1CHUH Ha.!J.
TIJIYH)KCPOM:
1 - 3Ta 'IOHlIOe perneHlle; 2 - JlHTepnO.!l51I].lloH-
HaSI qJopMy."a A:I.aMCa TpeTbero nOpfl.D.Ka TOq-
HveTH OTHOCHTe '1bHO 111ara npH h = O 02 2pao;
3 - Ta >Ke Q>op"y. a. HO n"Toro nop>J)],Ka T04-
HOCTII OTHOCHTe.TJbHO rnara np" h = 0.02 zpaa
140
Ka:\HI pa3pbIBa npOl-I3B01I.HbIX H .D.alOI.U.HX .D.OnOnHHTe.'lbHYlO norpem-
HOCTb npH YBe.1WIeHHH I<0.'lH4eCTBa marOE, OCTaeTCSI HeH3MeHHbIM H
HX B.1HSIHHe, Co!le;:I,OBaTe.lbHO, VMeHbmaeTC5L
AHa.'lH3 MeTO.D.OB 4Hc.'leHHOrO HHTe-rpHpOBaHHSI nOI<a3a.1, 4TO .D..1SI
paC4eT8 ypaBHeHHII, onHCbIBaIOI.l{HX BnpbICK, c.1eAyeT nO.'1b30BaTbCSI
MeTO.D.al\IH, npeLI"bSIB.'lSIlOI.U.HMH MHHHl\Ia.'JbHbIe Tpe60BaHHSI K Henpe-
pbIBHOCTH npOlI3BO.D.HbIX nCKOMbIX <PYHKIJ.Hll. l\'\eTO.J. 3Ibepa B 60.1b-
merI CTeneHH Y.D.OB.leTBopHeT 3TOMY Tpe60BaIUIlO, H, KaK 3TO BHlI.HO
H3 Ta6.1. 2, norpemHocTb no IJ.HI<.'lOBOH nO.D.a1.J.e npH paclIeTe MeTO-
JJ,O:\I 3i'I.1epa C marOM 0,01 0 .D.OCTaTO'lHO Mana.
OpB l\lHOrOI<paTHbiX paC'IeTaX TOnJ1HBHOH annapaTypbI 3aMe4e-
HO, 4TO TeI<YI.U.aSI norpemHOCTb OTHOCHTe.J1bHO 3Ta.10HHoro pemeHIIH
B03paCTaeT npH 4HCJ1eHHOM HHTerpHpOBaHHH CHCTeMbI .D.H<p<pepeH-
IJ.Ha.lbHbIX ypaBHeHHIl Y Hacoca B OTpe30K BpeMeHH, IwrLIa Harne.
TaTeJIbHbIH I{.'1anaH HaXO;:I,HTCSI B n0J10)J{eHHH, npH I<OTOpOM TOn.rIHBO
nepeTeKaeT lIepe3 I.U.e.TIb KJlan8Ha. 3TO MO)J{HO 06"bHCHHTb TeM. 4TO
B 3TOT nepHO.D. B paC'IeTe Y'lacTByeT HaH6oJ1bmee I<OnH4eCTBO '1JIe-
HOB ypaBHeHHH H Be.'lH4HHbI nepBbIX npOH3BO.D.HbIX HCKOMbIX <PYHK-
IJ.Hii CpaBHHTeJ1bHO Be.TIHKH. DbIJ1a onp060BaHa MO.D.H<pHKaIJ.HSI MeTO-
JJ,a 3H:Iepa: MeTOJJ, 31l.'lepa C Ap06JIelIHeM lllafa npii h" > h"o.
B Te'leHIIe 3TOrO OTpe3I<a BpeMeHII HHTerpHpOBaHHe JJ,H<p<pepeHIJ.H-
aJIbHbIX ypaBHeHHH rpaHH4HbIX YC:IOBHH y HaCOCa npOBOAHTCH C
60.1ee MeJ1KHM lllarOM (B 3-5 pa3 MeHbme HCXO;:I,HorO). KaK BH.D.HO
H3 Ta6.1. 2, MeTO;:I, 3H.'lepa C .D.po6JleHHeM mara .J.aeT xopomIIe
pe3YJ1bTaTbI npH paC'IeTaX C OTHOCHTe.'1bHO KpynHbIM maroM.
TaKHM 06pa30M, pe3y.'lbTaTbI cpaBHHTeJ1bHbIX paC4eTOB nOKa3bI-
BalOT, '1TO .D.J1H rI1.D.pO.D.HHaMH4eCKoro paC4eTa Ton.'1IIBHOII CHCTeMbI
HaH60.'1ee IJ.e.TIeC006pa3HO npHMeHSITb MeTO.D. 3H.1epa C .D.po6.'1eHHeM
lllara '1HC.'1eHHOrO HHTerpHpOBaHnSI cnCTeMbI ypaBHeHHII rpaHWIHbIX
yTJ'10Bnii Y HaCOC8 npH hI< > h"o.
C TO'lKH 3peHlIH 3aTpaTbI MalllI1HHoro BpeMeHH HaH60.'lee 3<p-
<peKTHBeH MeTO;:I, 4HC:IeHHOrO HHTerpHpoBaHHSI ypaBHeHHH rpaHH'I-
HbIX YC.'10BHH, npHMeHHeMbIH 06bI'IHO npn PY'IHOM C'IeTe H onHcaH-
IIbII"I B 2 r.'1. II. PaC'IeTbI npoIJ.ecca BnpbIcKa Ha UBM C HcnO.'1b-
30BaHHeM 3Toro MeTO.D.a npn YC.'lOBHH 3aMeHbI rpa<pH'IeCKHX
pellleHHH pellleHHSIMH C nOMOI.l{blO HTepaIJ.HH nOKa38.'1II, '1TO BpeMSI
paC'IeTa COKpaI.l{aeTCH Ha 3-4 MUH.
B pSI.D.e paC'IeTHbiX HCC.'1e.D.OBaHHrI C HcnO.'lb30BaHHeM UBM MO)J{-
HO HcrrO.lb30BaTb nporpaMMbI, pea.'1H3YlOI.U.He I\1eTOII '1HCJ'1eHHOrO
HHTerpIIpoB8HIIH, onHcaHHbIH B r.'1. II. 3TO n03BO.'lSIeT cOKpanITb
M8WHHHoe BpeMSI. O.rr.HaKo TaKHe nporp8MMbI HivIelOT cYI.l{eCTBeH-
HbIe He.D.OCTaTKlI. OpH COCTaB.'1eHHH T8KHX nporpaMM npHxO.D.HTCSI
pea....IH30BbIBaTb 60.'1ee C.'10)KHbIII H rpOM03.D.KHH a.'1rOpHTM. 3aTpYLI-
HeHO BBe.D.eHHe YTo'lHeHHH H .D.Ono.1HeHHi1. EC.'1H )Ke BBe.D.eHHe YTO'l-
HeHHII cYI.l{eCTBeHHo YBe.'1H'IHB8eT CTeneHb He.'1HHeHHOCTH ypaBHe-
HHH rpaHH4HbIX YC.'10BHII, TO npH HcnO.'1b30BaHIIH YKa3aHHoro I\1eTO-
.rr.a '1HCneHHoro HHTerpHpOBaHHSI MorYT B03HHKHYTb HenpeOLIo.'1HMbIe
TPY.D.HOCTH.
141
3. AnrOPHYMbl YYOLlHEHHfi METOAA PAC"IETA
311.eCb npIIBO.'UITCH a.lrOpHTMbI HeKOTOpbIX YTOlJHeHHH, He06xo-
lI.HMOCTb KOTOpbIX npH paC4eTaX C HcnO.lb30BaHHeM UBM 6bWa
BbIHB.'1eHa npH ConocTaB.leHHH pe3y.'1bTaTOB rHn:pOll.HHaMJ1lleClmX-
paCl1eTOB Ton.1HBHbIX CHCTeM 6bICTPOXOn:HbIX lI.I13e.leH C OnbITHbE\IH
lI.-3HHbIMH.
HeKOTOpbIe H3 YT04HeHIIii Heu.e.leCoo6pa3HO npHl\IeHHTb BO Bcex
paCl1eTaX no c.lell.ylOllI.HM npJ1lIHHaM. Bo-nepBbIX, n:.'1H BBell.eHHH OT-
lI.e.TJbHbIX YTOl1HeHHH (HanpHMep, Yl1eTa TpeHl15I CTparHBaHHH HrJ1bI,
3KcnepHMeHTa.lbHbIX E03<pqmUJIeHTOB HCTelIeHHH l1epe3 OKHa rI:I.'1b-
3bJ) Tpe6YlOTCH .lWCTOBepHbIe .:JKcnepHMeHTa.lbHbIe .lIaHHbIe no KOH-
EpenlOMY Hcc.'1en:yeMOl\IY BapHaHTY Ton.'1HBHOH annapaTypbI. Bo-
BTOpbIX, He npH Bcex C04eTaHHHX KOHCTPYETHBHbIX napallIeTpOB II
He Ha Bcex pe.iKH:VIax HMeeT C!\IbIC.l npHMeHHTb HeKOTopbIe YTOl1He-
HlIH (HanpHMep, YTelJJ{H B 3a30pbI npeIUI3HOHHLlX coell.lIHeHHH, YLJeT
rHlI.paBJ1l1l1eCKOrO conpOTHB.leHHH Tpy6onpOBOl1.a 60.lee TOLJHbIM Me-
T011.0M [71]), TaK KaK OHH Yll..'1HHHlOT BpeMH pac4eTa, YC.10IKIUIlOT
nOll.rOToBKY lICXOll.HbIX lI.aHHbIX, a B HeKoTopblX c,nY laHX He YTO'lHH-
lOT pe3y.'1bTaTbI paC'leTa. B-TpeTbllX, lI..TJH BceCTopOHHero TeOpeTII-
'leCKOrO aHa.1H3a rHlI.pOlUIHaI\IHEH TOnJIHBHOH annapaTypbl YlI.06HO
n0J1b30BaTbCH \IeTO.ll.OM HCE.'1IOLJeHHH .lI.eHCTBHH Tex n.'lll HHblX <paK-
TOpOB. 003TOMY HeIWTopble H3 npnBe.ll.eHHblX HH.iKe YTOl1HeHHH c."1e-
lI.yeT npWVIeHHTb BbI60pO'lHO, co06pa3YHCb C u.eJ"1HlVIH paCl1eTa If
06'beKTOM paClIeTHoro HCCle.J,OBaHIfH.
YileT OCTaTO'lHbIX CBo60.ll.HbIX 06'beMOB. YCTaHOB.'1eHO, LITO 60.1b-
llIHHCTBO aBTOTpaKTopHbIX .lI.H3e."1e1I Ha HeKOTopblX, a lIHOr.ll.a I:I Ha
Bcex pa6011IIx pe)KHMaX IIMelOT B HarHeTaTe.'1bHOII l\IarI:ICTpa.1I:I OC-
TaTOl1HbIe CBo60.ll.HbIe 06'beMbl, CYllI.eCTBeHHO B.1I:IHlOllI.lIe Ha npou.ecc
BnpbICEa.
Cor.1JaCHO OCHOBHb);\I nO.'10)j{eHHHM MeTO.ll.a paCl1eTa npou.ecca
BnpbICKa Ton."1HBa C Yl1eTOM OCTaTOLJHbIX CB06o.ll.HbIX 06'be\lOB Bec"1H-
lmHY V oc 3aLl,alOT nepe..'1. Ha'lacl0M paCLJeTa npH6.1HllieHHO, 3aTeM
YTOl1HHlOT B pe3y.lbTaTe paCLJeTOB npou.ecca BnpblCK3.
)],J1H paCl1eTa BemJlHlHbI v'w YlI.06HO HcnO.l.b30BaTb ypaBHeHHe
6a.laHca TOnJIHBa, BOIUell.IUero 3a UHK.1J B HarHeTaTe.'1bHVIO M8nl-
CTpa.i1b l1epe3 K.'1anaH (q.,) H BbIIUe.ll.IUerO H3 MarlIcTpaclH 'lepe3
pacnbI.'1I:ITe."1b (q-q). B Hal1a.'1e nepBoro paCl1eTa npou.ecca BnpbICKa
3a.ll.aIOT KaEoe-TO npH6.1HllieHHoe 3Ha'leIIHe VOC!' Ooc."1e OIWH'laHIIH
paCl1eTa nO.ll.C4HTbIBaIOT no <POp:VIYJle (190) 06'beM V oc2 , OCTalOllI.Hii-
CH B HarHeT3Te.lbHoii MarI:ICTpa.'1H .lI.O HaLJa,la BToporo BnpblcE8, 3a-
TeM, nOBTopHH paC'leT C Ha'laJ"1bHbIM yc.1JOBlIeM V oc = V oc2, onpeLl,e-
JIHIOT V OC3 H TaK .lI.a.lee, T. e.
V Oci + I = VVCi-(qKi-q'ji)' (190)
Bbl ' Il:Ic.'1eHHH nOBTopHIOT, nOKa He 6Yll.eT BbIHOclHeHO YC.l0Bue
Voci+I V oo i'
npH paC1JeTaX 3a11.aHHYlO Be.1H<Umy V oc pacnpe11.e.1SIlOT no Ha-
fHeTaTe'J1bHOlI l\IarHCTpa.'IH cor."IaCHO <fJopMy.le (70), a npH HaJ1H1JIIH
:'mcnepH:\>IeHTa.lbHbIX 11.aHHbIX no pacnpe11.e.leHHlO V oc - COrJ1aCHO
3THM 11.aHHbIM. CB06011.HbIH 06'beM V OC.T pacnpe11.emllOT no 11..TIHHe
Tpy60npOB011.0B, pa3Ae.1SIH era Ha m <JaCTel\. LL.1H M011.e.1I1poBaHH>I
paBHoMepHoro pacnpeAe.leHHH no .!.I..llme Tpy6onpoBO.!.l.a 1JI1C.l0 1Ja-
cTei'I m ;.I.O.l}KHO 6bITb 11.0CTaT01JHO 60.1bllHlM. Y11.06HO nO.lb30BaTbCH
cHoc060M Y11.BOeHHH IW.IH1JeCTBa T01JeK m C ue.lblO npoBepKII, BbI3bI-
BaeT .1II ;.I.Boi'IHOe YBe.lwIeHHe m H3:\<IeHeHHe pe3y.lbTaToB paC1JeTa
CBbIwe 11.0nYCTIHIOi'I HOrpeW!lOCTH. EC.lH YKa3aHHoro 113MeHeHIIH
napaMeTpoB BnpbICKa He Ha6.11OlI.aeTCH, TO 1JHC"lO m ,lLOCTaT01JHO
Be"lHKO.
npII n0ll. e e HarHeTaTe.lbHOrO K.lanaHa CB060ll.HHH 06 eM B
wTyu.epe Hacoca Ha1JlmaeT YMeHbwaTbCH. Cor.laCHO npHHHTbIM 11.0-
nYllI.eHHH!\I, nOKa He BOCCTaHOBIITCSI cn,;10WHOCTb Tonmma, P = 0
dp
H, C"le11.0BaTe.lbHO, - = O. .J..1H paC<IeTa II3:\>leHeHI1H cB060nHoro
dt
06 eMa B llITyu.epe Hacoca V oc HanHweM ypaBHeHHe 06 e:VIHoro
6a"laHca 11..lSI HaII60,;lee 06mero 3Tana:
dV oc . 1I ( V 2 / , ) I
- = - ft/,i{fU/ - V PH-PH + IKCK -,
d p 6n
KOTOpbIM AonO.lHHIOT CIICTeMY ypaBHeHHH (183). npH 3TOM BBonHT
He06xonHMbIe OrpaHH1JeHHSI, COCTOHWHe B TOM, 1JTO ypaBHeHHe (191)
nO,;1)I\HO Y1JaCTBOBaTb B paC1JeTe no MOMeHTa BOCCTaHOBJ1eHI1H
cn,;10IlIHOCTH Ton,;lHBa B wTyu.epe Hacoca, nOC.le 1Jero paC1JeT Be11.YT
dV oc H 0
no V p aBHeHHlO cmIOWHOCTH Ton.lIma n p II = 0 H V OC . H = .
- &
3ano.lHHB CB06011.HbIii 06 eM B IlITyu.epe Hacoca, TOnJ1HBO Ha-
lIllHaeT rrocTyrraTb B Tpy60rrpoBon H 3anO.1HHTb cB06011.HbIe 06 eMbI.
BpeMH Ha 3anO.lHeHHe 01Jepe11.HOrO 06 eMa orrpene.'lHlOT no <fJOPMY-
.le (84), a o6panIbIe BO.1HbI, 06pa3YlOllI.HeCH npH 3anO.1HeHIIII :nora
06 eIVJa,- no <fJop1\ry.'1e (83). TaKHM 06pa30M paCC1JHTbIBalOT 3a-
nO.1HeHHe Bcex CB060ll.HbIX 06 eMoB, pacrro.laralOllI.HXCSI B Tpy6o-
npOBo.!.l.e (CM. cxeMY Ha pIlC. 30).
nOC,;le BOCCTaHOB.leHI1H cn.lOiliHOCTII B Tpy60npoBone TOrrJ1IIBO
lIallHHaeT nocTyrraTb B nO.lOCTb <fJOPCYHKII, 3anO.1HHH CB06011.HbIH
06 eM V oc.g,' AHa.lorIl1JHO paC1JeTY rpaHH1JHbIX YC.'IOBIli'I Hacoca, no-
I\a He BOCCTaHOB.'1eHa cn.lOiliHOCTb TOnJIIlBa B 06 eMe <fJOPCYHKIl,
dPcP
6Y11.eM IIMeTb P,p = 0 II = O.
LL.lJSI paC1JeTa I13MeHeHIIH cBo60nHora 06 eMa B <fJopCYHKe CO-
CTaBIIM 11.H<fJ<fJepeHu.IlaJ1bHOe ypaBHeHIle 06 eMHoro 6aJ1aHCa
(191)
dV oc . cP _ _ I C '
- T T .
d 6n
143
3TH!\'I ypaBHeHHel\I C.1eAyeT ,,10nOJIHUTb CliCTel\1)' (186). nO.lmKIIB
Heo6xo.11.HMble OrpaHl-II.JeHlUI, COCTOHllllIe B TOM, 1.JTO .11.aHHOe ypaB-
HeHHe .11.O.1)1(HO YI.JaCTBOBaTb B paC1.JeTe .11.0 MOMeHTa BOCCTaHOB.1e-
HHH Cn.10IllHOCTH Ton.1HBa B q>OpCYHKe, nOC.1e 'Iero paC1.JeT 6Y.11.eT
BeCTliCb no ypaBHeHI-IIO cn.TJOillHOCTH Ton.TJlIBa npH V f)c.fjj = 0 1I
dV oc c/J
= O. LLo BOCCTaHOB.1eHIIH cn.l0IllHOCTH Ton.1I1Ba B 06'beMe
dt
q>0PCYHJ<I1 Be.1J1lIHHbI 06paTHbIX BO.1H .11.aBJleHlIH onpe.11.e.:1HIOT cor.1ac-
HO BbIpa:tli:eHIIIO (6) lICXO.11.H II3 rpaHH1.JHOrO YC.TJOBliH pfjj = O.
DpH HcnO.:lb30BaHHH MeTO.11.a I.JHc.1eHIlOro HHTerpHpoBaHliH ypaB-
HeHHH .'J,BH:rKeHH5I Ton.TJIIBa B Tpy6onpoBo:J.e C YI.JeTOM BH3KOCTH [711
V ocm
/'1MJ
40
20
o
200
x
x
500 n OO/MUH 200
a)
500 n OO/HUH
5)
PHC. 50. 3aB!!CHMOCTb V DC OT '1HC.TJa 060pOTOB Ky.1a'-l-
KOBoro BaJlHKa:
a - aKTHBHbll1: xo)]. nol1YHR<epa 2 6 ..-1UI; 6 - aKTlfBHblfr xo.a.
n..'lYHMepa 1,3 }ilJ,1. Cn 1:01llHOrr "lHHuefi nOK833Hbi pac1.leTHbIe
A3HHLJe, KpecTHK3.\1H - 3KcnepIfMeHTa '1bHble
OCTaTOI.JHble CB06oIJ,Hble 06'beMbI MmKHO Y1.JeCTb no npHBe.aeHHbIM
ypaBHeHlIHl\1, npHI.JeM paC1.JeT 3anO.1HeHIIH CBo6o,.'].HbIX 06'beMOB B
Tpy6onpOBo.ae B onpe.ae.TJeHHO I CTeneHH ynpocTHTCH, TaK KaK HeT
Heo6xo.l1.IIl\IOCTH BbII.JIIC.1HTb 06paTHYIO BO.1HY .l1.aBlIeHHH; BpeMH H3
VOLT
3anO.1HelUle OI.Jepe,,1HOrO cB06o.aHoro 06'bel\Ia m onp e .l1.eJIMTCS!
no q>opMYJle
Ki V
r c. dt=
\ t, I ,
" Tn
Illi
r.l1.e C i , t - CKOpOCTb TOn.'IIiBa B Tpy6onpOBO.l1.e B MOMeHT 3anO.TJHe-
HMS! OI.Jepe.11.Horo i-ro CB060.l1.HorO 06'beMa.
DpI1lYlepbI Be.TJMI.JHH V oc , 3aMepeHHbIx npH OCIJ:MJ1.1orpaq>HpOBa-
HHM nO.'J,'beMa CTa6M.1M3MpYIOlllero IwanaHa .l1.JIH pa3.1H1.JHbIX I.JHCeJ1
060pOTOB TonmlBHOll annapaTypbI JI,M3e.1H 5IM3-236 B conOCTaB.le-
HUM C pe3y.lbTaTaMH paCI.JeTa, nOKa3aHbI Ha pHC. 50. 3al\lepbI H pac-
1.JeTbI npoH3Bo.11.H.lHCb npM .l1.BYX nO.TJO)l(eHHHX pellKH: B nepBOM
cJIY1.Jae nO.TJO)l(eHMe peHKH COOTBeTCTBOBa.lO q"lf = 115 .11M 3 npH n =
= 1050 06/MUH (puc. 50, a); BO BTOpOM - q"lf = 20 .11.11 3 npH n =
= 250 06/./vtUfl (puc. 50, 6). C YI.JeTOl\I norpeillHocTell, HaK.TJaAbIBae-
MbIX YC,iIOBlIHl\IlI .3KCneplIMeHTa.. conOCTaB.1eHHe pe3y.lbTaToB OnbITa
144
H paC4eTHWX aHHWX cBHAeTe bcTByeT 06 YAoB eTBopHTe bHoM HX
COBna eHHH.
I1cc.'1e.LJ:OBaHU5I nOKa3bIBalOT, 4TO ec:m lJa HOMHHa.lbHOM pe)J(H-
Me Ton.'1HBHOH CHCTeMbI H3e.151 5IM3-236 (n = 1050 06jJ,WH, qv, =
= 115 JItN 3 ) OCTaTOqHbIe cBo6o.ll.HbIe 06"beMbI OTCYTCTBYlOT, TO Ha
Bcex OCTa.lbHbIX pe)J(HMax C MeHblllHM qHUIO!\1 060pOT08 HJIH MeHb-
lllHM aKTHBHbIM XO.ll.OM nJ1ymKepa B HarHeTaTe"lbHOH MarHCTpaJ1U
lIMelOTC5I 06"beMbI V oC, CYI11.eCTBeHHO BaII5I1OI11.Ue Ha nO.ll.a4Y Ton HBa.
YCN PiJXr/CH2
0.01, f60
0.03 f20
0,02 80
o,Of 1;.0
\
0 0 \
28 30 .12 (jiG 21;. 2ff 28 JO 32 (jIc
PIIC. 51. 3aBHcHMoCTII nO.!J."bCMa HrJlbJ Y II .i\aB.1CHHH Pi! B .!J.aT'-IIIKC
nepe.D: $OPCYHKoi1:
I - OnLITHble q q = 20 ...ff.M 3 ; 2 - paC1..J:eTHbIe c yqeTOM OCTaTOtlHblX CBO-
OOJJ.HbIX o61 eMoB. q l{ = 20..1, -,u.4t 3 : 3 - paCqeTHbIe 6e3 y':zeTa V DC,
q l{ = 59J J1tAl 3
B"lH5IHUe OCTaT04HLIX CB060.ll.I1bIX 06"beMOB BbIpa}J{aeTC5I B
YMeHbllleHUH HKJ10BOH nOLlaqU, YBeJ1HqeHHH yrJ1a 3ana3 bIBaHH5I
.lI.eikTBHTe.TJbHOrO Haqa:ra rrO.ll.aqH, qaCTO Ha6J1lO.lI.aIOI11,HXC5I 60JIee
pe3KHX KOJIe6aHH5IX .lI.aBJ1eHHH TOnJ1HBa B KOHeqHWX 06"beMaX Ha-
rHeTaTe.'IbHOH MarHCTpa.'IH. OpH 3Ha [J1Te.'IbHOH BeJm4HHe V DC, CO-
CTaBJ15I1OI11.eH 30 % II 60.TJee OT HKJ10BOH rrO aqH, OCTaT04HbIe CBO-
60.JJIbIe 06"beMbI cYI11.eCTBeHHo H3MeH5I1OT rlI.!J:po lIIIaMIIqeCKIIe npo-
eccw, npoTeKalOI11.I1e B HarHeTaTeJ1bHOH MarHCTpaJ1U TOrrJ1HBHOH
CIICTeMbI, II BeCb npou.ecc BnpbIcKa TOnJIIIBa B I1J1IIH.lI.p .lI.BHraTe,,15I.
DpeHe6pelKeHIIe <paKTopOM yqeTa OCTaTOqHbIX CBo6o.ll.HbIX 06"be-
MOB npII paCqeTe npo ecca BnpWCKa TOOJ1I1Ba BHOCHT He.ll.OnYCTII-
MYlO oorpelllHOCTb, .lI.OCTIIralOI11.YlO 200% no I1K"10BOH nO.ll.aqe.
lh06bI o eHIITb BJIII5IHIIe Be.'!HqIIHbI V DC, Ha pIlC. 51 npII Be.ll.eH bI pe-
3y.lbTaTbI paCqeTa npouecca BnpbIcKa TOnJ1HBa annapaTypoi'I .lI.H3eJI5I
5IM3-236 Ha pelKHMe n = 250 06jNUH II qv, = 20 .il1N 3 , BbIITOJ1HeH-
HbIe C Y4eToM II 6e3 yqeTa BeJIIIqIIHbI floc, a TaK)J(e pe3YJIbTaTbI
OnblTa. B paccMaTpIIBaeMoM c Y4ae pac4eT 6e3 yqeTa OCTaT04HbIX
CBo60.ll.HbIX 06"beMOB Tep5IeT CMLIC.'!.
10 3aKa3 748
145
rHJJ.paBJ1H eCKOe COnpOTHBJ1eHHe Tpy6onpOBOJJ.a. .LLmI paCLJeT3
npOu.ecca BnpbICKa C YLJeTOM rlIJJ.paB.1H'IeCKOrO COnpOTIIB.leHlIH TPY-
60rrpOBOJJ.a u.eJIeC006pa3HO nOllb30BaTbCH JJ.BYMH MeTOJJ.aMII [43, 71],
n03ToMY 1I.BHfKeHi-Ie TorroillIBa B Tpy6orrpoBoAe paCCLJIITbIBalOT no 011-
HOMY 1I3 1I.BYX a.'1.rOpIITI\IOB, pea.'1.1I30BaHHbIX B nporpaMMe. PeweIlHe
ypaBIieHIIH HeycTaHOBI1BWerOCH ABI1)KeHI15I Ton.1I1Ba B Tpy6onpOBO;:I:e
cor.'1.aCHO npI16.'1.II)KeHHoMY MeT01l.Y [43] nplIBe1l.eHo B rJ1. II. TaEI1M
06pa30M, IICXOAHbIH a.lrOpI1TM pac'IeTa, nplIIIHTbIH nplI YC.'1.0BI1H
npeHe6pe)KeHI1H rlIJJ.paB.'1I1LJeCKI1M conpoTIIBaeHI1eM Tpy60npOBO;:I:a,
npaKTIILJeCKII He I13MeHHeTCH. .LLonOJIHeHI1e 3aKc1lOLJaeTCH B TOM, LJTO
nepeJJ. 3Ha'IeHI1HMII npHMbIX II 06paTHbIX BO.TIH, nplI6bIBalOllLlIX K
-k!:...
KOHu.eBbIM 06'beMal\I, BBOLlIITCH K03q>qJlIu.I1eHT 3aTyxaHlIH ea. 3TO
03HaqaeT, qTO ypaBHeHIIH (184), (185), (187), (188), nplIBeJJ.eHHble
nplI 1I3.'1.0)KeHI1II IICXOLlHoro MeTOJJ.a paCLJeTa, npI1MyT C.1eJJ.YlOll.!lIH
BIIJJ.:
C T = [p -Po+ W(t)e- k l
a9 - -
L
, -k-
F(t)= PH-PO+ W(t)e a;
C;= alp fpo-P.p+2F(t- )e- k l
( L / L ) -k..!::...
W t+ ) = Po-P.p+ Flt- ea.
(184a)
( 185a)
(187 a )
(188a)
3JJ.eCb Be.'1.IIQIIHY k paCCQI1TbIBalOT no q>opMYJ1e 1I..'1.H Typ6y.i1eHT-
Horo nOTOKa C YQeTOM Cpe1l.HeH CKOpOCTII Tonc1IIBa B Tpy6onpoBoJJ.e
B TeLJeHlIe BnpbICKa C cp :
JeC cp
k--
- 4d T .
( 192)
CKOpOCTb C cp Ha3HaQalOT npII6.1IILKeHHo, 3aTeM B KOHu.e paCLJeTa
BbIQIICJ1HlOT II rreLJaTalOT LleHcTBIITeol'1.bHOe 3Ha'Ielme Ccp, KOTopoe
BHOCHT B IICXOJJ.Hble 1I.aHHble 1I.J15I CJ1e1l.YlOllLero paCQeTa. f1paKTII'le-
CKII 3TO He YBeJIII'lI1BaeT TpYJJ.oeMKOCTII paC'leTOB, TaK KaK JI.mr
YTOQHeHIIH BeJ1IILJIIHN OCTaTOLJHOrO JJ.aBJIeHIIH (1IJ11I OCTaTO'lHOrO CBO-
60JJ.Horo 06'beMa) paCLJeT nOBTopHlOT HeCKO.'lbKO pa3.
KpoMe nplI6J1I1iKeHllOro YLJeTa rIILlpaBJ1l!QeCKOrO corrpOTIIB.'1.e-
HIIH, aJ1rOplITM npeJJ.YCMaTplIBaeT B03MOiKHOCTb YLJeTa rIIJJ.paB.'1.IILJe-
CIwro COnpOTI1BJleHI1H no 60J1ee TOLJHOMY MeT01l.Y. CKOpOCTb JJ.BHfKe-
HIIH TOn.'1I1Ba B Tpy60npoBoJJ.e B 3TOM cJIYLJae onpe1l.e.1HeTCH no
q>opMYJ1e (89a).
.LLJ1H paCQeTa CEopocTeH B rpaHIILJHNX Ce'leHIIHX Tpy6onpOBOJa
x = 0 II X = L IIcno.TIb3yeTC5I BTopoe ypaBHeHlIe CIICTeMbI (6), 3anI1-
caHHoe B KOHeLJHbIX pa3HocTHX. f10.1b3YHCb YKa3aHHblMlI ypaBHeHII.5I-
146
,MH H pellIeHIIH!\UI ypaBHeHHH rpaHH'lHbIX Yc.llOBHH, MO)J(HO npOC4H-
TaTb 3Ha4eHHe CKOpOCTeH TOn.1HBa BO BC X Y3JlaX .n:HarpaMMbI.
nOC.!le.n:OBaTe.lbHOCTb BbI4HC.leHHH TaKOBa. )J.IH MOMeHTa BpeMe-
HH, KOr.ZJ:a .ZJ:aB.'1eHHe B lllTyu.epe Ha4HeT nO.ZJ:HHl\IaTbCH, CKOpOCTb B
Y3.1e 0,1 (CM. pHC. 36) BbI4HCJIHIDT no <t>opMYJIe
I ( . . )
CO,I=CI,l+- P"I-P"O.
ap
( 193)
npH 3T01\! CKOpOCTH paBHbI HY.110 B Y3.1ax 1,1; 2,2 H .n.a.lee no
xapaKTepHcTHKe t = , a TaK)J(e B 06JIaCTH npaBee YKa3aHHoH xa-
a
paKTepHcTHKH, TaK KaK 06bI'lHO B Ton.1HBHbIX CHCTeMax K Ha4a.1Y
c.1Je.n.YIDru.ero BnpblcKa .n.BlUKeHHe TOnJIHBa npeKparu.aeTcH.
no <t>opMy.:1e (89a) BbI'lHCJIHIDT CKOpOCTH C 1 ,2, C 2 ,3 H .n:a.1ee no
xapaKTepHCTHKe .n:o CKOpOCTH C n - I ,1:" BKJ1ID4HTeJIbHO, a 3aTeM CKO-
pOCTb
I
C n ,1, = Cn-I, 1:" --(Pt/>T- Pt/>T-I).
ap
HCnO.lb3YH n0J1Y4eHHYIO Be.1I1'.JI1HY CKOpOCTH Ha BXO.n.e B <t>OP-
eYHK)', paCC4HTbIBaIDT rpaHlI4HbIe yC.1JOBHH y <t>OPCYHKH, 4TO 3aBep-
maeT U.HK.l paC4eTa, TaK KaK BbI4HC.'1eHbI CKOpOCTH B Tpy60npOBO.lI.e
L
H napaMeTpbI rpaHH4HbIX YC.'10BHH Y HaCOea .n:.'1H BpeMeHH t +-.
a
KaK nOKa3aJIH BbI4HCJleHHH, mar ceTKH no BpeMeHH ( t) 6e3
yru.ep6a AJIH T04HOCTH MO)J(eT 6bITb B me pa3 60.!lee KpynHbIM, 'leM
llIar LJHC.leHlIoro HHTerplIpOBaHIIH ypaBHeHIIH rpaHH4HbIX YCJ10BIIH
h, T. e.
( 194 )
M = mch,
r.n.e 11lc = 2, 4, 6.
3TO n03BOJIHeT cyru.ecTBeHHo YMeHbllIHTb Bpel\UI paCLJeTa. AJ1ro-
pHTM paC'leTa B .n.aHHOM e.'lY4ae .'!:ono.'lHHeTCH CJ1e.n.YIoWHM. )J.'lH
paCLJeTa nepB x 4acTeH ypaBHeHHH rpaHH'lH X YCJ10BHH y Hacoca
Tpe6yeTcH Be.1H4HHa CKOpOCTH C T , KOTopaH npH me 2 6y.n:eT pac-
C'lHTbIBaTbCH He Ha Ka)J(.n:OM llIare 'lHC.1eHHoro HHTerpHpOBaHHH.
n03TOMY 4T06bI nO.'1y<mTb Be.l HIIl1H bI CKOpOCTH .n.J1H paC4eTa ypaB-
HeHIIH rpaJUIIIHbIX YC.!10BI1H, Ha Ka){{.n:OM mare HHTerpHpOBaHHH IIC-
no.lb3YlOT Ta6.'1Hu.y 4eTbIpex nOCJ1e.n.HHX 3Ha4eHHH CKOpOCTH, no.'lY-
4eHHbIX no 1fJ0pMY.le (193), H npH nOMOll1.H no.n:nporpaMMbI Ima.n.pa-
TH4HOH HHTepnO.'1Hu.HH n0J1Y4aIDT BeJ1H4HHY C T .n:JIH 04epe.n:Horo
mara HHTerpHpoBaHHH. AHa.l0rH4HYID Ta6. r mu.y cKopoCTeH, paCC'lH-
TbIBaeMbIX no 1fJ0pMy.ne (194), npHMeHHIDT .n:.'1H 3KcTpano.'lHpOBaHHH
CKOpOCTH C;, Heo6xo.n.I1IYlOll npH onpe.n.e.1elIHH npaBbIx 4aCTeH ypaB-
HeHHH rpaHHLJHbIX YCJIOBHH y 1fJ0PCYHKII.
ConoCTaB.!leHHe .n:aHlIbIX paClJeTOB npH me = I H paCqeTOB, npo-
Be.n.eHHbIX C YKpynHeHHbIM marOM, nOKa3bIBaeT, qTO .'!:J1H 60.'lbllIHH-
CTBa pe)KHMOB HCC.!le.n:OBaHHbIX TOnJ1HBHbIX annapaTYP YKpynHeIUle
10* 147
rnara /).t B 2-4 pa3a IIO cpaBHeHHIO C rnaroM h He BbI3bIBaeT 3aMeT-
HbIX IIorpernHOCTeii B BbPlH-C.TIeHI-IHX.
068 aJ1rOpHTMa yqeTa rH paB H4ecKoro conpoTHB eHHH Tpy6o-
npoBo a npe nOJIaraIOT onpe eJIHTb Belm4HHY A no O H01\fY H3 BYX
BbIpa:>KeHHH: fIO cpopMy.'1e 5.'Ia3Hyca JIH r.'1a KHX Tpy6
A= I
if 100 Re
no cpopMY,,'Ie I1 eJ1bqHKa JIH rnepoxoBaTbIx Tpy6
I
A= d 2
( I, 14 + 2 Ig : )
( 195)
(196)
PUC. 52. 3aBHcHMoCTII 4>aKTopa rn.D:paBJlH'ICCKO-
ro conpOTHBJleHII5I k u 1II0.D:YJlCll OTHOCHTeJlbHbIX
OTKJlOHeHHi1 1 I'll B % OT CKOpOCTH TOnJlUBa B Tpy-
60npOBO.D:C:
I - no q,opMYJIe DJIa3Hyca; 2 - no q,opMy.,e lI)],eJIb-
'IHKa; 3 -1"'P.pmaxl: 4-,"'qljl
UpH HCIIOJIb30B8HHH cpOpMy.'lbI 5.II83HYC8 npe BapIITeJIbHO peKO-
MeH yeTcH BbIHBHTb, He HB./meTCH .'IH nOTOK .'1aMHHapHbIM, Tor 8
I! 1jcel< BMeCTO 38BHCHMOCTH
(195) HYfKHO npHMeHHTb
BbIpa)KeHHe J1H J18MH-
HapHoro IIOTOK8.
UpHMeHeHHe cpOPMY-
J1bI J1H rnepoxoBaTbIx
Tpy6 CBH3aHO C pacqe-
TOM 60.'Iee BbiCOKHX CKO-
pOCTeH BHfKeHH51 Ton-
J1HBa B Tpy60npOBo e.
I1T06bI npHMepHO OIIpe-
eJ1HTb 06.'IaCTH HcnO.IIb-
30BaHHH cpOPMYJI .'IH
BbIqHCJ1eHHH A, 6bIJIH
npoBe eHbI cpaBHHTeJ1b-
HbIe paCqeTbI C p83.TIHq-
HbIMH cpe HHMH 3a
BnpbIcK CI\:OpOCTHMH
80 C /'fjceK
BHfKeHHH TOIIJ1HBa JIH
TOnJIHBHOH annapaTypbI,
HMeIOIlLeH Tpy60npoBO
HaMeTpoM 2 MM. Upn
3TOM BO BceM H8IIa30He
H3MeHeHHH CKOpOCTH KH-
HeM8THQeCI\YIO BH3KOCTb
/U.I3eJIbHoro TOrrJIHB8 rrpHHHM8.IIH paBHOH v = 0,1 c.M 2 /ceK ( JIH
cpe Hero 8BJIeHH51 300 KF/C.M 2 ) H rnepoxoB8TOCTb /). = 0,016 .MM.
Pe3YJ1bT8TbI paCQeT8 H306pafKeHbI H8 pHC. 52. H8 rp8cpHKe BBep-
xy npHBe eH8 38BHCHMOCTb .p8KTOp8 rH p8B.'IHQeCKOrO conpOTHB-
JIeHHH k OT cpe HeH CKOpOCTH TOnJ1HB8 B Tpy60npoBo e, paCCQH-
T8HH851 no .pOPMYJI8M 5JI83HYC8 (195) H I1 eJ1bQHK8 (196), BHrI3Y
400
100
300
200
o
20
40
60
148
OT.'IO)l{eHbI MOlI.VJIH OTHOCHTe.'1bHbIX OTKJ10HeHHH IVIaKCHMa.'1bHbIX
,l1.aBJIeHHH TOnJ1HBa B <}:J0pCYHKe I P{/j max I (CnJ1011IHaH JIHHHH) H l.{HK-
JIOBbIX nO,l1.aq I q1J I B np0l.{eHTaX (IlITpHXOBaH J1HHHfI):
= (PtjJmaxI-PtjJmax2).2 .100-
P</JnJax ,
PtjJmaxl + P</Jmax2
ql; = (Qljl-qlj2)' 2 . 100.
Q( I + QU.2
I1H,l1.eKCOM 1 OTMeqeHbI napaMeTpbI, nOJIyqeHHble B pe3YJ1bTaTe
pacqna npol.{ecca BnpbIcKa no <}:JopMYJ1e DJ1a3Hyca, HH,lI,eKCOM 2-
no <}:JopMy.'1e }I.lI.e.'1bqHKa. AHa.'1H3 pe3YJ1bTaTOB cpaBHHTe.'IbHbIX pac-
'leTOB nOKa3a:I, qTO JJ.J1f1 JJ.H3e:IbHOrO Ton.'IHBa npH JJ.HaMeTpe Tpy60-
npOBO,l1.a 2 AUJ B ,l1.Hana30He Cpe,l1.HHx cKopoCTeH ,l1.0 60 MiceK pac-
XmK,lI,eHHe B pe3YoilbTaTax paCqeTa He npeBbIIIlaeT 1 % no l.{HKJIOBOH
nOll,aqe. l!.J1f1 60.lbIIlHX .lI.HaMeTpoB Tpy60npOBO.ll.a H .lI.JIH TOnJIHBa C
60.'lbIlIOIi BH3KOCTblO C.le.ll.yeT npHl\IeHHTb cpOPMY.'lY B.'1a3Hyca Ha
BceM pa60qeM lI.Hana30He CKopOCTeH (npH Typ6Y:IeHTHOM nOTOKe).
OJJ.HaKO npH paC'leTaX npOl.{ecca BnpNcKa .lI.H3eJ1bHOrO TOnJ1HBa
co Cpe.ll.HHMH CKOpOCTHMH (60.'lbll1e 60 MiceK) HJ1H npH paClleTax
.lI..'lfl MeHee BH3KHX Ton.1HB (6eH3HH) coileAyeT conOCTaB.TIHTb BeJIH-
IlHHbI cpaKTopa rH.lI.paB:IHlleCKOro conpOTHB.'1eHHH, KOTopbIe paCCqH-
TbIBalOT no cpopMy.laM (195) H (196). EC.1H BeJ1HqHHa k, BbIIlHCJ1eH-
Hafl no cpopMy.le I1,l1,e.'IbIlHKa, 3al\IeTHO npeBbIlllaeT 3HaqeHHe k,
HaH.lI.eHHOe C nOMOll1.blO <}:JOpMy.TIbI 5.la3Hyca, c.le.ll.yeT nOJIb30BaTbCH
3aBHCHMOCTblO, npeJJ..1OLKeHHoH I1JJ.eoilbqHKOM.
l!..lfl onpeJJ.e.leHHH 06.lacTH npHMeHeHHH npH6.'1HiKeHHOro MeTOJJ.a
6bI.1H CJJ.eJIaHbI cpaBHHTe.lbHbIe paCqeTbJ JJ..'1H HOMHHaJIbHOrO pe)l{H-
Ma Ton.1HBHoH annapaTypbI JJ.H3e.1H 5IM3-236 npH HOi\UlHaJ1bHOM
pe)l{I!l\Ie (n = 1050 o61MuH, h a ... m = 2,55 MJU). PaClleTbI CJJ.eJ1aHbI
JJ..lH pa3:IHIlHOH lI.:IHHbJ Tpy60npOBOlI.OB H .lI.:IH lI.BYX 3HalleHHH cpelI.-
Hero cpaKTopa rHlI.paBoilHqeCKGrO conpOTI1B.leHHH. K03cpcpHl.{HeHT CO-
npOTIIB.T\eHHH onpe.ll.e.'1H.1H no cpopMy.'1e I1.l1.eoi'IbqHKa (196). B nepBoM
I
CJlyqae k cp = 80 - npH = 0,02 JUM H d T = 2 MM, BO BTOpOM
ceK
k c1' = 230 npH = 0,025 MM H d T = 1,6 AJJ1L
ceK
OTK:IOHeHHH pe3Y:IbTaTOB paCqeTa npol.{ecca BnpNcKa npH6JIH-
)l{eHHbIM MeTO,ll,Ol\i OT pe3Y:IbTaTOB, nOoilyqeHHbIX 60:Iee TO'IHbIM Me-
TO.ll.OM Y'IeTa rH.lI.paBJIHqeCKOrO conpOTHB.1eHHH, npHBelI.eHN B
Ta6.1. 3. B Hell npHHHTbI c.lelI.YlOw.He 0603HaqeHHH:
6 TC '" - l\WKCHIVra"lbHoe TeKYll1.ee OTKJlOHeHHe op.ll.HHaTbI xapaK-
TepHcTHKH Bnpb!CKa;
61' max - OTK.T\OHeHHe IVIaKCHMa.lbHoH Be.lHqHHN p{/j max;
6'1 - OTiVIOHeHHe II.HKoilOBOH nO.ll.a'IH.
RaK BHJJ.HO H3 Ta6.TI. 3, OTK.'lOHeHHfI pe3Y.;lbTaToB paCqeTa no
npH6J1H)I{eHHbIM MeTO.ll.aM B03paCTalOT npH YBe.1JfILIeHHH .lI.oi'lHHbl TPy-
60npOBO.ll.a H cpaKTopa rH.lI.paB.TIHqeCKOrO conpoTHB.leHHH, npHqeM
149
Ta6j1Ul{a 3 OTKJ10HeHlHI MaKCUMaJ1bHbIX .n:aB-
OTKJlOHeHHe pe3YJlbTaToB pac'IeToB J1eHUH B paCnbIJIUTeJ1e ptjj max He-
OT 3TaJlOHHOrO MeTOll.a BeJ1UKU, HCKa)J{eHHH)J{e xapaK-
TepuCTuKU BnpbICKa U Be.llUlJUHbI
UHKJIOBOH no.n:alJH 60JIee 3HalJH-
Te.llbHbI.
Ha pilC. 53, G, 6 H306pa)J{eHbI
xapaKTepHcTuKH BnpblcKa, pac-
ClJHTaHHbIe no npIl6.'Iu)J{eHHoMY
U no 60.llee TOlJHOMY MeTo.n:aM
Y4eTa rH.n:paBJIUlJeCKOrO con po-
TUB,;1eHIlH. XapaKTepHo, 4TO npH
B03pacTaHHll 3Ha4eHHH L H k cp
MaKCHMaJ1bHWe .n:aBJ1eHHH
BnpbIcK3 II, CJIe.n:OBaTeJ1bHO, M3K-
CUM3.'1bHbIe Op.n:HHaTbI xap3KTe-
pHCTHK BnpbIcKa HecymecTBeHHo
OT.'IHlJaIOTCH. 3TO MO)J{HO 06"bHC-
HHTb TeM, lJTO npH BbI4HCJ1eHHH npH6J1H)J{eHHbIM MeTo.n:OM aI{TOP
rH.n:paB.'II-r4ecKoro conpOTHB.TJeHHH npHMeHHeTCH nOCTOHHHbIM .n:.Tm
Bcero paC4eT3.
OTK,;10HeHHe B %
a 1\ I 5 p max I 5 11
meK
npH k = 80 IjceK
620 2,0 I 0,3 I 0,4
1650 5,3 1,0 1,0
2890 11,4 1,3 2,6
npH k = 230 I/ceK
620 6,2 I 1,3 I 0,5
2890 24,7 0,7 7,0
8
{i
{i{i 48
11)
28
J2
J6
0)
40
\110
PHC. 53. XapaKTcpllcTHKII BnpbICKa:
<1 - L 2890 JltJlt, k 230 ; 6 - L 620 JlI..., k 80 ;
ceK eel(,
1 - paCC'-lH'IaHHbre no npH6JIH>KeHHoMY I\leTOl1Y; 2 - no 60 lee 104-
HOMY MeTO Y
Pe3y.'IbTaTbI H COnOCTaBJIeHHe paC4eTOB no YKa3aHHbIM MeTo.n:aM
YlJeTa rH.lI:paBJ1H4eCKOro conpOTHBJ1eHHH Ha pa604HX pe)J{HMax Ton-
.'1HBI-IbIX CHCTeM .lI:H3e.'Iei'I ceMei'IcTB3 51M.3 H TpaKTopHbIX .n:H3e.'1ell
lI.-50 H Jl-60 nOKa3bIBaIOT, 4TO npHMeHeHHe npH6.TJH)J{eHHoro MeTO.ll:3
[43] .n:JIH 60.'IblllHHCTBa aBToTpaKTopHbIX .lI:1I3e.1eH np3KTH4eCKil He
BHOCHT ;rOnOJ1HHTe.'1bHbIX norpelllHOCTeH no cpaBHeHHIO C 60.'Iee
"T04HbIM MeTO.ll:OM [71] YlJeTa rH.n:paB.'1H4ecKoro conpoTHB.1eHHH. O.ll:-
HaKO npu paClJeT3X 60.'1ee .n:.'IHHHbIX Tpy6onpOBO.ll:OB, a TaK}Ke npH
YBeJ1HlJeHHH aKTop3 rH.lI:paB.1HlJeCKOrO conpoTHB.'1eHHH B pe3y.'1bTa-
Te nOBbIllIeHHH CKOpOCTH ..QBH)J{eHHH HJ1H BH3KOCTH Ton.1HBa CJ1e.ll:yeT
150
-
n0.1b30BaTbCH 60.'Iee T01.JHbIM MeTO.llOM Y1.JeTa rHApaB.1H1.JeCKOrO co-
n pOTlIB.leHHH.
YTe'lKU B HaCOCe H paCnbIJIUTeJ1e. D..1H Y4eTa YTe1.JeK npH pac-
lJ:eTe npouecca BnpbICKa C HCnO.'Ib30BaHHeM UBlVl ue.'IeC006pa3eH
MeTO.ll, H3JIO.>KeHHbIli B pa60Te [17] H .llOno.1HeHHb11i 3aBHCHMOCTblO
BH3KOCTH OT .llaBJIeHHH H Y4eToM YBeJIH1.JeHHH 3a30pa B pe3YJIbTaTe
o6umx .lleq>opMauHH HaCOCHoro 3.1eMeHTa.
3aBHcuMoCTb BH3KOCTH TOnc'IllBa OT .llaBJleHHH l\IO)KHO BbIpa3uTb
TaK:
!-l;p = LTCP,
r.lle L;p - K03<p<pHUHeHT .llHHaMH1.JeCKOH BH3KOCTH npH TeKyllteM
.llaBJ1eHHH Ton.'IHBa;
c - nO<:ToHHHbIli K03<p<pHUHeHT, 3aBHcHI.IJ.Hll OT <pH3H1.JeCI<HX
cBoikTB TOnJ1HBa (.ll.TIf! .llH3e.'IbHoro Ton.'IHBa c = 1,0025);
p - .llaBJIeHHe TOnJ1HBa B Ha.lln.'IYH/KepHOl\I npoCTpaHcTBe H.'IH
B 06"beMe <POPCYHKH.
OpH paC1.JeTe YTe1.JeK C.'Ie.llyeT y'IHTbIBaTb Cpe.llH101O BH3IWCTb Ha-
xO.lUl.llterOCH B I.IJ.e.'IH Ton.'IHBa:
_ tr \ ' P _ fl r (c P - I)
flrp- - C dp-
P L. pin c
( 197)
K 03<pqHIuHeHT
3 ( I ) 2
B=I+ 2 T
( 198)
YlJ:HTbIBaeT H3MeHeHHe <pOpMbI ynaoTHHlOI.IJ.erO 3a30pa B pe3y.rrbTa-
Te 3KcueHTpHUHTeTa n.rrymKepa I H.1H Hr.lbl (32; 3.lleCb i-'- .ll.'IHHa
yn.l0THHIOI.IJ.ell lJaCTH nJ1YH/Kepa in HJIH Hr.ilbI iu-
flpH OTCYTCTBHH cyxoro TpeHHH (3 = 1,1 -7- 1,15 [17].
AHam13 peKoMeH.llaUHll no paC1.JeTY 3a30pa b." Me/K.llY n.rrYH/Ke-
pO:'.i H ru.lb30ii nOKa3a.TJ, 1.JTO
b ll = b r + b o + b p + b 3 + b,,;
c Y1.JeTOM Toro, 'ITO
b n = l'r + b o + b p + fJ 3 H fJ K = Bp,
nO.;lY1.JUM
b,,=fJn+Bp; (199)
3.lleCb b r - TeXHOJIOrHlJeCKHll 3a30p;
b o - YBe.1H1.JeHHe 3a30pa B pe3y.lbTaTe OBa.'IbHOCTU nJIYH/Ke-
pa H rH.TJb3bl;
6 p - YBe.1H1.JeHHe 3a30pa H3-3a npO.llo.'IbHbIX pHCOK;
b J - YBe.'IH1.JeHHe 3a30pa Bc.TJe.llCTBHe ynpyroH .lle<popMaUHH
rH.lb3bI nOH 3aTH/KKe illTVlieoa Hacoca:
b.. - YBem14eHHe 3a30pa B pe3YJ1 TaTe .lle<lJopMauHH n.lymKe-
pa H rHJIb3bI, BbI3BaHHoli .llaB.'IeHHeM TonJ1HBa;
151
b n - IICXO..'I,HbIII 3a30p npH OTCYTCTBHH H36bIT04HOrO ..'I.aB.le-
HIHI TOn"lHBa;
B - K03<p<PHI.I.HeHT, XapaKTepH3YlOllI.HH KOHCTPYKI.I.11l0 11 ta-
TepHa.l n.1YH:iKepHOM napbl.
C Y4eTOM YT04HeHHM no <popMYJ1aM (l 7)- (199) pacxo.n. 1.Jepe3
3a30pbI B 30.10THHKOBOii 4aCTH n.'IymKepa Z I I\IO)J{HO npe.n.'CTaB11Tb
TalC
Z n(p"-Pec)(6n+Bp,,)3 IP,,lnc ,
I = (Jon T
61n [ (hn -h l) + I } tT(cP"-I)
r Bn _
..L n(PH-Pec)(6 n + BplI)3 lP/i In c
I (JOT
61n [ (hm -h n ) cos \' + I ] I-LT (c P " -1)
rOT
(200)
r.ne (J8n, (JOT - cTyneH4aTbIe iPymuum:
(Jen = 0 npH h n < h l;
(Jen = 1 npH h n > h I ;
(JOT = 0 npH h n > h n3 ;
(JOT = 1 npH h n < h n3 ;
h 1' h n3 - nO.n."beMbI n.1YH)J{epa, COOTBeTCTBYlOllllle reOMeTpH-
eCKHM Ha1.Ja,;lY H KOHI.I.Y nO,.'J,a'1H;
'V - yrOJI HaKJIOHa OTCe1.JHOII KpOMKH.
B iPopMy.'Ie (200) nepBbIM 4.1eH onHCbIBaeT pacxo.n 1.Jepe3 BnYCK-
Hoe OKHO, BTOpOII - 1.Jepe3 OTce4Hoe OKHO rH,;lb3bI nJIymKepa. Pac-
xo.n. 1.Jepe3 nopllIHeBYIO 1.JaCTb n.TJYH)J{epa
nd n (6 n + BplI)3 IP lnc
Z. = , (201)
- 12ln tT(cPII-I)
r.n.e Ln - .n.'-UIHa yn.10THHIOllI.eII nOBepXHOCTH n"lYH)J{epa.
Pacxo.n. 1.Jepe3 3a30pbI Me)J{.n.y Hr.10H H KopnYCOM paCnbI,JIHTe.'IH
ndu6 2P lnc
Z3 = (202)
12lu IT(CP4>-1)
npH pac'IeTe C Y1.JeTOI\I yre4eK a"lropHTM paCqeTa 113MeHHTCH
cJle.n.YlOllI.HM 06pa30M. Be.TJH4HHbI ZI, Z2 H Z3, BbIqHCJIeHHbIe no iPop-
My.1aM (200), (201) H (202), .n.onO.1HHT nepl3bIe ypaBHeHIHI CHCTeM
( 183) H (186).
ConOCTaBJIeHHe pe3YJIbTaTOB paCqeTa npoI.I.ecca BnpbIcKa c Y4e-
TOM H 6e3 yqeTa YTe4eK B Hacoce Ha HOMHHa.JIbHOM pe)KHMe Ton-
"lHBHOII annapaTypbI .n.H3eJ15! 5IM3-236 nOKa3aHO Ha pHC. 54. npH
paCqeTaX npHHHI\Ja.TJOCb b n = 0,35. 10- 3 CM, B = 0,32. 10- 6 CM 3 /Kc.
YqeT YTe1.JeK B .n.aHHOM CJIY4ae npHBeJ1 K yMeHbllIeHHIO I.I.HKJ1()BOH
152
no.u.a'-lH Ha 1,5 JlUt 3 H YMeHbllleHHlO
Jl-IaKCHMa.lbHoro .n.aBJIeHI1H B Ip0P-
cYHKe Ha 16 KF/CM 2 . OCTaTO'-lHOe
.n.aB.leHHe VMeHbIlIHJIOCb OT 10 .!I.O
6 Kr;CM 2 . .
60.'1ee 3aMeTHO B.'1HHlOT YTe'-lKH
npH rH.n.po.!l.HHaMH'-leCKHX paC'-leTaX
Ton.1HBHOH annapaTypbI C YBeJ1H-
'-leHHbIMH 3a30pal\IlJ H.'IH pa60Te Ha
MeHee BR3KOM Ton.1HBe.
Y eT C}I{HMaeMOCTH TOnJ1HBa
KaK YHK HH .n.aBJIeHHD npH cpe.n.-
HeH 3a BnpbICK TeMnepaType TOnJ1H-
Ba. Ilpe.!l..'1araeMbIH a.lropHTM pac-
'-leTa n03B0J1HeT onpe.n.eJ1HTb K031p-
IpH HeHTbI GKHMaeMOCTH B KaMepe
HarHeTaHHH fl", H B lllTyu.epe Haco-
ca fl B lpopcYHKe aifJ B 3aBHCHMO-
CTH OT .n.aB.TJeHllH Ton.'1HBa Ha Ka)K-
.n.OM lllare HHTerpHpoBaHHH. D.:IH
paCqeTa llCnOJlb30Ba.aI1Cb 3KCnepl1-
MeHTa.'1bHbIe .n.aHHbIe no Be.'1WIHHaM
K03 Hu.HeHTa cfKHMrleMocTH B 3a-
BHCHMOCTH OT .u.aB.leHHH H OT cpe.n.-
HeM 3a U.HK.'1 TeMnepaTypbI Ton.1HBa
[72]. Cor.nacHo pa60Te [72] cpe.n.HHM
yen
0,02
0,01
p
Kr/cn 2
400
300
200
100
PHC. 54. 3aBHcHMoCTII nOA"bCMa
Hr.lbI Y II ,'!.aBJ!CHHH prfi B paCITbI-
.lHTC.1C:
J - €5e3 Y1.IeTa YTelleK B Hacoce
(q I{ 113.9 .11.1{3); 2 - C Y'leTOM YTe-
'Ie" B Hacoce (q q 112.4 MM 3 )
K03 Hu.HeHT C)KHMaeMOCTH
a=
, ,
,a l a 2
a +_ p +_ p 2
o 2 3
(203)
, ,
,a I a 2
l+a P +_ p 2-+-_ p 3
o 2 '3
rAe a ; a;; a - :mcnepHMeHTa.lbHbIe K03 Hu.HeHTbI, HB.TJHlOlll.He-
CH YHKu.HeH TeMIIepaTypbI Ton.1HBa.
AHamJ3 ':noll OPMY lbI nOKa3bIBaeT, '-lTO C YBe.1WIeHHeM .n.aB-
.TJeHHH OT Hy.1H .n.O 900 KF/LW 2 3HaMeHaTe.'Ib H3MeHHeTCR no Be.TJH-
'-lIme B He3Ha'IHTe.lbHbIX npe.n.e.TJax (OT 1,00 .n.o 1,05). Ilo3ToMY .n.mI
paC'-leTOB TOllJIIIBHOH annapaTypbI ;:J,H3e.'1eM HMeeT CMbIC.l 3HaMeHa-
Te.'1b nplIHHTb nOCTOHHHbIM II paBflbIM 1,02. 3TO ynpOlll.aeT OPMYJ1Y
IJ He BHOCHT 3aMenIOM norpelliHOCTH B paC'-leT. ConOCTaB.TJeHHe pac-
'leTOB npou.ecca BnpbICKa Ton.1HBHbIX annapaTYP 5I3TA II H3TA c
I"ICnO.lb30BaHHe:\i opMy.'lbI (203) II ynpOlll.eHHOM opMy.lbI. Y KOTO-
pOM 3HaMeHaTe.'1b paBeH 1,02, nOKa3bIBaeT, l.JTO pacxofK.n.eHHH B pe-
3YJIbTaTaX npaKTlIqeCKH OTCYTCTBYlOT. B pa60Te [72] 1{o3 Hu.HeHTbI
OPMYJ1bI (203) YKa3aHbI B MefK.n.YHapo.n.HoH CHCTeMe e.n.HHHu., no-
CJIe nepeBO.!l.a B TeXHlIqecKYlO clicTeMY e.n.HHHu. H BBe.n.eHIIH nOCTOHH-
153
Horo 3IIaMeH8Te.1H Be.1HqHH8 CpenHerO K03!f>qmuHeHT£1 OIWlIl£1eMO-
CTH 6y D.eT
a=ao+a,p+ a2p 2,
(204)
l"D.e I\0 3 <p!f> HI-llIe HTbI ao, a" a2 - !f>YHKUIHI Cpe.LI:HelI 3a BnpbICR TeM-
nepaTypbI TOnJ1I1Ba B COOTBeTCTBYIOllI.eM OO"beMe;
00 = b +b (T -273)+ b ' (T -273)2;
Q, = b; + b'; (T -273);
02 = b ;
3JI.eCb T - TeMnep£1Typa Ton.'1lIB£1 B OK.
D.JIH D.II3eJlbHOro TOO.1HBa IW3!f>!f> IIIure HTbI 3THX !f>0PMYJI paBHbI:
, -6" 6
b o =61,1.10 ; b o =0,258.10-;
b; = 0,921.10- 6 ; b; = -29,6.10-9;
" 9' I'
b I =-0,151.1O-; b 2 =16.4.10--.
Pe3YJlbT£1TW paCqeTOB npouecc£1 BnpwcKa TOnJIHBa annapaTypoH
Jl.H3e. r UI 5IM3-236 H£1 H01\IlfH£1.'1bHOM pe)/\MMe H306p8)KeHbI H8
pHC. 55. f1pl1 113MeHeHlU1 CpeD.He-
fO 3a BnpblCK K03!f>!f>BUl1eHTa
OKHMaeMOCTI1 (acp) OT 70. 10- 6
AO 50.10- 6 CM 2 /KF 3aMeTHO H3-
MeH5!IOTCH xapaKTep 3£1KOHa no-
JI.£1qH H UHKJIOBaH nOl{£1qa (c
106,6 no 116,6 J11J11 3 ). DpB pacqe-
Te C nepeMeHHbIM 3HalleHHeM KO-
3<p4Hll1. If eHT£1 OKIfl\faeMOCTH ql; =
= 110,5 MM 3 .
PaClleTaMH yCTaHOBJIeHO, qTO
eCJIH .a:alKe Be.nwfHHy acp no.ll:o-
opaTb TaK, 4T06bI 11.I1KJ10BbIe no-
D.aqH, no.TJY4eHHbIe B pe3YJIbT£1Te
paC'leTOB C nepeMeHHbIM K03<p-
roO
Y !f>Bl1.HeHTOM C)J{HM£1eMOCTH H C
acp, COBna.i1aJ1H, TeM He MeHee
XapaI\Tep H3MeHeHHH napaMeT-
pOB BnpblCKa 00 Bpel\leHH 6YD.eT
3aMeTHO OTJ1lJIIaTbCH. Bce 3TO
YK£13bIBaeT Ha l1.eJIeC006p£13HOCTb HCIIOJIb30BaHlBJ npH paCqeTaX npo-
uecca BnpbICK<:1 TOTIJII1Ba Ha U,BM K03<P<PHUl1eHTa C)J\HMaeMOCTll KaK
<PYH K U H I1 ,!I,aBJleHI1H II CpeJI.HeJl 3a BnpbICI( Ter.wepaTypbI TOnJIHBa.
.u.POCCeJ1JfpOB8Hlfe K8H8JIOB B.lI.OJIb nepbeB KJI8n8H8 II .lI.pocce-
J1IIpOB8H1fe K8H8J10B B nJIYH>Kepe nplf OTCe'lKe. Y4HTbIBaH BaIKHOCTb
154
Aq "'Hf paiJ
--.
i
I
I
{I
f2
8
o
30
38
{l2
.14
PRC. 55. XapaKTepHcTHKa nOAa'-lR:
J - npJ1 a = 50-10- 1 -; C",t::'/h-r; 2 npu
a f(p); 3 - I1pH a = 70'/0-' C_Il' hI
)J.::I5I paC'IeTa npOll.eCca BnpblC1\a TOllJUlBa npaBH:lbHOro BbI60pa 3<p-
q>eKTI1BHbIX npOXO,[(HbIX Ce'leHU1f BnYCIWblX H OTCe'lHbIX OIWH rfl.i1b-
3bI, nOC.1eLtHHe 6bIJ1H onpe.rre.'leHbI 3KCnepHMeHTa.'lbHO. OpO.'lHBKa
{)TCe'lHbIX OKOH rI1.'lb3bI, npOBe.rreHHaH B MAlI.H Ha cneu.I1a.lbHOII
VCTaHOBKe, nOKa3a.18, 'lTO npH OTCe'lKe 60.'lbllloe B.'IHHHHe OKa3bI-
BaeT .rrpOCCeJUlpOBaHHe KaHaJIOB B nJIYHiKepe. npOm-IBl a npOH3BO-
,!1.H.laCb Ha BCeM pa60'leM LtHana30He npOXOLtHblX Ce'IemIII npI1 H3-
MeHeHHH nepenalI.a lI.aB.'IeHHII OT 30 lI.0 150 Krlol?. AHaJIII3 3Kcne-
pHJ\.IeHTa.'lbHOII 38BHCHMOCTH 3KBHBa.lJeHTHOro npoxOlI.HOro Ce'feHHH
IZaHa.'IOB B n.'IymKepe H OKH8 rH.'Ib3bI OT Bem-I'IHHbI OTKPbITIH! OIma
rHJlb3bl no 06pa3YIOllI.eii mlYHiKepa f1.h" (pHC. 56) nOKa3aJI, '1TO
lI.pOcce.'IHpOBaHHe B KaHa.'IaX n,;lymKepa OK83bIBaeT 3aMeTHoe, a
npH !J.h n > 0,2 CM onpelle.rl5IlOU(ee BJIHHHlfe fIa Be.'llf'lHHY ( If) OT'
{p.I)om CM2
I
I --+- -1-
_--t' I ,
I
I
PHC. 56. 91j:Jlj:JCKTHBHbie 0,070
3KBHBaJiCHTHble npoxo -
HbIC CC1.JCHHH OTCC'-IHbIX
<JKOH C Y1.JCTOM .D:pOCCC.1H- 0,012
pOBaHHH Kalla.10B B 1I.'1YH-
JKCpC HaCOCOB npll ncpc- 0,008'
na.D:ax .D:aB.'1CI!H5I npO.TJI1BKI1
p B KF/CM2:
o - 30; D = 90; x - 150; 0,004
Cn..'1011IHaSI 'HHHH - Hacoc
5!3TA-100.11I I; IllTpHXO-
BaR _ 'TH-5
O'feBHlI.HO, 'lTO Y'leT 3cpcpeKTHBHbIX npOXOlI.Hb!X Ce'leHlIII OKOH
THJIb3bI, onpe.n.e.leHHbJX 31\CnepHMeHTa.'lbHO, ,[(aeT B03MO)KHOCTb
:YTO'lHHTb p8C1.JeT. lI.JUJ paC'IeTa npOIJ.eCCa BnpbICKa IJ.e.'leC006pa3HO
110J1b30BaTbCH pe3YJ1bTaTaMH npO.'IHBKH B BH.rre Ta6.'lHIJ. 3Ha'leHHH
.( If)OT = f( h,,) (pHC. 56) H (1lf)6" = f(!1h,,) (pHc.57).
OpH HcnO.TIb30BaHHH Ta6.1HIJ. 3I{CnepHMeHTa.lbHbIX 3cpcpeKTI1BHbIX
:npOXOLJ.HbIX Ce'leHlIII 'lepe3 OKHa rH.'lb3bI a.TJ.ropHTM paClJeTa npeLty-
'CI\1aTpHBaeT BbI60PKY Be.1H'lHH (/If)oT H (/If)6'' nplI nOMOIll.H nolI.-
nporpaMMbI KBalI.paTII'lHOH HHTepno.'IHIJ.HI1.
EC.1H 3KcnepHMeHTa.1bH e ,!1.aHH e no npOJIHBKe OKOH rH.'lb3
.OTCYTCTBYlOT, He06xolI.HMO YlJeCTb .rrpocce.'IlIpOBaHlIe B KaHa.'Ie nJlYH-
)Kepa npll OTCe'lKe. EC.'lH npHpaBHHTb pacxolI. Ton.1l1Ba 1.Jepe3 3CP-
'cpeKTHBHoe npOXOLJ.HOe Ce'leHlIe B KaHa.'laX n.:1YHLKepa (f.lf) K" I\ pac-
xo.n:y B 3cpcpeKTHBHoM npoxo:J:HOl\1 Ce'leHf!I1 'lepe3 OKHa ru.1b3bI
j.lOTfOT' TO 3KBIIBa.'leHTHOe npOXOLtHOe CelJeHlIe KaHa.'lOB B n.'lYH}Kepe
.J-I OTce4Horo OKHa rH.'lb3bI l\1mKHO nO,;lY411Tb B BHlI.e
(Pf)CT = POTtOT .. / I 9 '
V I+k;;
(205)
155
T,&e
k = V.OTt OT
n .
(/If)Kn
HeCKO.lbKO I\1ellbIlIt' B.'Ul5IeT lIa npOlI.eCC BnpbICIW TOnJ1HBa .n:pOC-
Ce.J1HpOBaHHe KaHa,;10B B.n:O,;lb nepbt'B K.lanaHa. O.n:HaKO Y4eT YKa-
3aHflOrO .n:pOCCe.'IHpOBaHII5I n03BO.'I5IeT, KpOMe TOrO, 60:Iee T04HO
Y4eCTb Clf.'IbI, .n:eHCTBYIOmHe HB KaBnBn co CTOpOHbI Ha.n:n.1YH)J(ep-
HOTO npOCTpaHCTBB. DpH nepeTeKallHH TOil.'IHBa 'lepe3 K.'IBnaH
BCae,n:CTBHe .n:pOCCe HpOBaHH5I .n:BYX nOC e.n:OBaTeabHO paCnOa02KeH-
HbIX Ce'leHHII (y nepbeB H B lIJ.e H no.n: pa3rpY30'lHbIM n05ICKOM) H3
fJ.11 )un
CH2
I obi I
, & \
, .Q I
I ---------r
I 'A I i
/1 1
I I
D,OlD
0, 010
0,002
0,08
0.12
0,16 tJh n [M
PilC. 57. 31j:Jlj:JcKTIIBHbIe npoxO.D:HbIC Ce4CHH5I BblllYCKHblX OKO!!
npII ncpcna;rax .J,aB.1CHil51 npo.1ilBKH tlP B KrjCJH 2 :
0-20; L - 80; X - 14U; cn.101lIlla" :mHH" - Hacoc 513TA-IOO.I!I!;
lllTpHXOBafi - rTI-I-3
D.1IOllJ.a.n:b (f" - f ) .n:ei!cTByeT ,n:aB.lellHe P:, OT J1lflIHOe OT ;!.aB.1JeHIUI
pu H OT .n:aB eHH5I p .
DpH nepeTeKaHHH TOil.'UlBa IIepe3 HarHeTaTe.'IbHbIH K.lIanaH BbI-
pa./KeHHe .n:.:J5I paC'leT8 3KBHB8.1eHTHOrO npOXO,n:HOrO Ce'leHH5I MO)KHO
3anHCaTb
(l-1f ")3K6 = l-1uJ III 1 jr I 9 '
It I + k
(206)
r.n.e
k K = -1!:.l1l.fUj .
fK-f
Onpe.n.e.71HTb ,&8B,;leHIIe (p: - p ), .lI.eIICTBYIOllJ.ee Ha n.1JOmaJJ.b
Un - f ), MO)KHO H3 YC.l0BH5I p8BeHCTBa KBa.n:paTOB paCXOJJ.OB 'lepe3
K.'IanaH B ue.l0M, a TaK}Ke 'lepe3 IIJ.e.'Ib IlO.n: pa3rpY)J(aIOIlU1M no-
5ICKOM:
> 2 ' 2 N ,
(1-1/,,);K6- (PH- PH) = (!-lUjfl,,)2 -(PH-PII)'
p P
156
npHHHMaH BO BHHMaHlle 4JOPMYJ1Y (206), nOJIYIlHM
" , I ( ' )
PII-PII = --:;- PII-P" .
I +k
(207)
B nepBoe ypaBHeHHe CHCTeMbI (183) BMeCTO BeJ1HIlHHbI /loro
nO.il-CTaBHM ( lf) OT, BbIIlHCJ1eHHOe no 4JopMY,,'le (205). B nepBOM H
BTOpOM ypaBHeHHHX CHCTeMbI (183) BMeCTO /lUffUf nO.il-CTaBHM
(/If,,,),,,,,,,, onpen:eJIeHHOe no 4JopMYJIe (206).
C YIleTOM 4JOPMYJIbI (207) ypaBHeHHe .n:BHllieHHH KJIanaHa npH-
:\1eT BH.n:
dC K [t ' ( ' ) fK-f; ( ' ) t Bh ] (J!
T= K P'.l-PII + 2 PH-PH - KP,,- K 13M"
If l+kK n
Ha pHC. 58 nOKa3aHbI pe- IJq I1l1o/ZPUi!
3Y bTaTN paC'IeTa npouecca
BnpbICKa TOnJIHBa Ha HOMHHaJIb-
HOM pelliHMe TOnJ1HBHOH annapa-
TYPbI .n:H3eJ1H 5IM3-236. HaH-
60.1bllIee B.1HHHHe Ha pe3Y.'lbTa-
TbI paCIleTa OKa3bIBaeT YIleT
.n:pocq JIHpOBaHHH Ha pe)KHMaX
Ma.lbIX nepe.n:aIl H 60JIbllIHX 060-
pOTOB. TaK, npH pacIleTe npouec-
ca BnpNcKa TOnJIHBHOH annapa-
TYPbI .n:H3eJ1H 5IM3-236 Ha pelliH-
Me q1.f = 34,4 JUlt 3 H n = PIIC. 38.
= 1050 06/.MUH npeHe6pellieHH€
.n:pocce:mpOBaHlleM B nJlymKepe
npHBO.il-HT K CHHllieHHlO UHKJIO-
BOrI nO..'l,alIH .n:o 24,4 JW.M 3 .
3aBJfCJfMOCTb cYMMapHoro npoxoJJ,Horo CelleHJfSJ pacnbfJIJfTeJUI OT
npOTJfBoJJ,aBJ1eHJfSl, npH pacIleTe npouecca BnpbICK3 TOnJ1IIB3 B cpe-
.n:y C npOTHBOI.I.aB.1eHHeM B3lliHO YIlecTb, 'ITO 34J4JCKTHBHoe Ce'IeHHe
con,,10BbIX oTBepCTHH B pe3YJIbTaTe CHmKeHHH K3BHT3UHH 33MCTHO
B03pacTaeT no cp3BHeHHlO C Be.1HlJHHOH, nO.'lYIIeHHoH npOJ1HBKOII
npH aTlVlOc4JepHoM npoTHBo.n:3B.'leHHH. D..1H YIleT3 3aBHCHMOCTH .n:eH-
CTBHTe.TJbHOrO K034J4JHUHeHT3 HCTelIeHHH /lc 'Iepe3 con.TJOBbIe oTBep-
CTHH OT npOTHBO..'l,aB.'IeHHH MOlliHO HcnO.lb30BaTb 3MnHpHIlecKYlO
4JOPMYJIY, npeLI-J10llieHHYIO B. n. D.MHTpeHKo,
8
<4
o
29
.JJ
.17
Ii'
P aC4CTllbiC xapaKTcpHCTIIKI1
BnpblCKa:
1 - c yqeTOM ,n,poCCeJ1lipOBaHHH 100,,'HB3 B
Ka Ha,,'1aX n "'1YHiKepa npH oTCeqKe; 2 - ue3
Y4eTa
Pc = l; + "
Be.TJHIlHHa l;' onpeLI-e.'lHeTCH npOJIHBKOH lJCpe3 con.TJOBbIe OTBep-
t!THH p3CnbIJ1HTe.TJH npH aTMoc4JepHOM npOTHBO..'l,aB,,'IeHHH.
157
3Ha4eHfle BbI4HCJ1HeTCH B 3aBflCHMOCTH OT 4f1CJ1a KaBflTa HH K:
= 0,15 npH K <, 1,6; = 4,6 npH K>- 1,6;
(K + 6)1.7
3JI,eCb K = Pcf>-Pli .
PI!
YBe:III4eHfle lc npfiBOJI,flT K B03paCTaHflIO CYMMapHOrO npOXOII.-
Horo ce'IeHHH pacnbI.lf1TeJIH, KOTopoe B JI,aHHOM CJ1Y l Iae BbI4f1C.TIHIOT
no $Opl\Iy.'1e
( tf)(/J = /lcf cf1Hfll
V (/lcfd 2 + (/l,lHf
YnpyrocTb npHBOAa. B HeKOTopbIX KOHCTPYKll.flHX TOnJ1I1BHbIX
HaCOCOB B pe3YJIbTaTe ynpyrocTfi npfiBOJI,a AeHCTBflTeJIbH H xapaK-
Tep JI,BlDKeHHH n.TYIUKepa MOMeT 3aMeTHO OT.TIWIaTbCH OT 3aJI,aHHO-
ro, 4TO OKa3 BaeT onpeJI,eJ1eHHOe BJII1HHl1e Ha npOll.eCC Bnp CKa
TOnJlf1Ba. B 60.'TbllHIHCTBe c.'1Y4aeB 'IaCTOTa co6CTBeHHbIX KO.'1e6aHHlr
npl1Bo,a.a Ton.1IIBHoro HaCoca 3Ha4f1Te.HbHO npeBbIlliaeT 4aCTOTY
BnpbICKOB Ton.1HBa 11, C.leJI,OBaTe.TIbHO, BJII:IHHfleM CfI.l HHepll.flII npfl-
BOJI,a Ha fl3MeHeHlIe nOJI,'beMa H CKOpOCTlI nJ1YHMepa MmKHO npeHe-
6pellb.
)],e$opMall.HH npfiBOJI,a npOflCXOJI,flT, B OCHOBHOM, BCJIeJI,CTBl1e
CKpY4f1BaHIIH Ba.'1a HaCOca. OOJI,'beM 11 CKOpOCTb n.1YHMepa C Y4e-
TOM ynpyroCTfi rrpIIBOJI,a MOMHO .'1erKO paCC4HTaTb, eCJIH BbI'II:IC.TIHTb
Ha Ka;'K,a.OM llIare 4IIC.lemlOro flHTerpl1pOBaHHH JI,eHCTBHTeJ1bHbIH
yrO.l nOBopOTa Ky.la4IW:
M KP
<Pa= <P-c-'
rJI,e <P - TeKyTll.HH yro,JI nOBopOTa Ba.la npfl paBHOMepHOM Bpa-
llI.eHlIH KYJIa4Ka;
M"p - MOMeHT CKpY'II:IBaHIIH Ba.'1a;
C - npHBe.rr.eHHaH MeCTKOCTb rrpHBOJI,a; Bem-I4HHa ee MmKeT
6bITb onpeJI,e.'1eHa, HanpfiMep, no MeTOJI,HKe [74].
loMeHT CKpY4IIBaHIIH BaJIa paBeH npoH3Be.rr.eHHIO HOpMaJ1bHOH
K nOBepxHocTfi KY.'1a4Ka CfI.'1bI F'/tOPM Ha ee n"le40 l, npH4eM
l = (Rr +- h n + Ro) sin 1jJ; F 1I0p.1l = P"fn ;
cos ,
3JI,eCb 1jJ - yrO"l MeMJ],y cfI.TIOli F '/top." H OCblO n.1YHMepa;
Rr, Ro - paJI,HYCbI TO.'1KaTeJ1H H Ha l Ia.'1bHOH OKPYMHOCTH KY-
.1a'IKa.
Pa3pbIB CnJ10lUHOCTH TOnJ1HBa B KOHll.e BnpbICKa. HecMoTpH Ha
HeKOTopbIe pa3.'1I1'II:IH B MaTeMaTH4eCKOM onHcaHHH, $H3f14eCKOe
npeJI,CTaB.leHfle pa3pbIBOB cn.1011IHOCTH CBOJI,HTCH K C.len.YIOllI.eMY:
1) B MeCTe pa3pbIBa cn.lOlliHOCTH TOnJII:IBa n.aBJIeIme KaK B MHJI,-
Koil, TaK H B napo06pa3HOH $a3ax paBHO HYJIIO (HJ1H J],aBJIeHI11O Ha-
158
CbIlI.I.eHHbIX napOB). 3TO rpaHH1.JHOe YC.'IOBHe HCnO.'Ib3yeTC5I LI:.'I5I BbI-
1.JHC.'IeHH5I OTpa)J{eHHbIX OT MeCTa pa3pbIBa BO.;"1H LI:aB.JIeHH5I, CKOpOCTH
}lBH)J{eHH5I rpaHl.JIJ,bI pa3Ae.la H Be.'IH1.JHHbI cBo6oAHOrO o6'beN/a;
2) npH paC1.JeTe 06'beMa o6pa3YlOlI.I.HXC5I nycToT BJIH5IHHe BbILI:e-
.'IeHHOrO npH 06pa30BaHHH pa3pbIBoB CITJIOlUHOCTH B03Ayxa H napoB
Ton.1HBa He YLIHTbIBaeTC5I;
3) npHHlil\1aeTC5I, 1.JTO B Te4eHHe Bpel\IeHH 7Be.1H1.JeHH5I CBo6oLI:-
Horo 06'beMa B IWHe1.JHbIX 06'beMaX HarHeTaTe.1bHOH MarHcTpa.T]H B
Tpy6onpOBOLI: BTeKaeT Ton.1HBO, a He LI:Byxcpa3Ha5I cpeLI:a, ec.1H CBO-
60LI:HbIH 06'beM He npeBbICH.1
BeJ1H1.JHHbI KOHe4Horo 06'beMa.
llTo6bI MaTeMaTH1.JeCKH
Y1.JeCTb pa3pbIBbI cn.T]OlUHOCTH
TOnJIHBa B KOHIJ,e BnpbICKa no
MeTOLI:HKe, nOCTpoeHHOH Ha
nepe L IHC.1eHHbIX .D.OnylI.l. eH1l 5IX,
MO)!{HO BocnO.'Ib30BaTbC5I
ypaBHeHH5IMli (191) II (192), JOO
oTpa)J{alOlI.I.llMH YMeHblUeHlle
OCTaT04HbIX CBo6o.D.HbIX 06'be- 200
MOB B Ha1.Ja.1bHhIH nepHO.D.
npOIJ,eCca BnpbICKa. TaK KaK
He 3aH5IThIe Ton.'IliBOM 06'be-
MbI B IlITYIJ,epe Hacoca Vn H
B CPopCYHKe V ng; MorYT YMeHh-
illaThCH Ii YBeJIII1.JllBaTbC5I, TO
ypaBHeHH5I llX H3MeHeH1l5I BO
Bpel\IeHll 5IBJIHIOTCH 06lI.1.HM
CJ1Y1.JaeM ypaBHeHHH H3MeHeH1l5I BeJIll1.JllH V oC.>< II V DC.g;.
B 06ll.1.eM CJIY1.Jae npll pa3phIBax cn.T]OlUHOCTli B KOHIJ,e BnpbICKa
CBo60LI:HbIH 06'beM V Ii MO)KeT 113MeH5IThC5I no.D. B.'I1l5IHHeM paCXOLI:3
Ton.'1IIBa Qepe3 IwanaH, paCXOLI:a Ton.JIHBa 1.Jepe3 BXOLI:HOe ce4eHHe
Tpy60npOBOLI:a, a TaK)J{e HaCOCHoro LI:eHCTBH5I HarHeTaTeJlhHOrO KJ1a-
naHa. 06'beM V ng; IIW)J{eT H3MeH5IThCH nOLI: B.T]HHHHeM paCXO.D.a Ton-
J1HBa 1.Jepe3 BXOLI:HOe CeQeHHe Tpy60npOBo.a:a H HaCOCHoro .a:eHCTBHH
Hr.'IhI CPOPCYHKII. TaKHM 06pa30M, y"a3aHHhle LI:Ba ypaBHeHHH MO)l{-
HO 3anHcaTb Co'Ie.a:YlOll.I.HM 06pa30M:
YCH
0,02
(J 2 {
Pip
K rjCH 2
400
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28 32 36 4() o
PIIC. 59. 3aBHcHMoCTH nO.D:"bCMa IIr.TJbI y
H .!J.aB.1CHH5I prfi B paClIbWHTe.1C:
1 - c YlleTOl\1 TpeHHH nOKOH npH cTparH-
BaHI-IH ur.'Ibl; 2 - oe3 )itleTa
dV 1i [ (2 v , ] I
= - !-tuJ", V p PIi- pli+f"CI(-fTC T ;
(208)
dV nlP l ,. ] 1
-= - fTcT-tuCu -.
d 6n
(208a)
YpaBHeHHeM (208) CJIe.n.yeT .n.onOJ1HHTh CHCTeMY ypaBHeHHH rpa-
H1JHhIX YCJ10BIIH Y Hacoca (183), ypaBHeHHeM (208a) - CHCTeMY
)$paBHeHIIH rpaHH1JHbIX YCJIOBHH Y CPOPCYHKH (186). 3TH ypaBHeHH5I
159
KaK 60.'Iee 06WJIe OTpa)KaIOT TaIGKe II II3MeHeHIUI OCT3T04HblX CBO-
60AHbIX 06"beMOB B H34a.'Ie BnpbICIW.
YTo HeHHe OeJ1H'IHHbl )l,aOJ1eHHSI 0 Ha'laJ1e nO)l,'beMa HI" J1bl c1Jop-
CYHKH. ECJII1 ,'LeHCTBHTeJ1bHOe }xaBJIeHHe B HalJa.le nO.J,"beMa Hr.'lbI
[11] p O npeBbIlilaeT CTaTHlJeCKH pery.1HpyeMoe Ptjj'J, He06xo)J,HMO
YTOtlHHTb Be.'IHlJHHY ,'LaB.TJeHHH B HalJa.TJe nO)l,"beMa Hr.lb!. A.TJrOpI1TM
p3ClJeTa npOCT: )1,0 Ha4a.TJa nO.a:"beMa Hr.'IbI BMeCTO 3H3lJeHI1H ptjj'J B
TpeTbeM ypaBHeHl111 CI1CTeMbI (4) MmKHO I1CnO.1b30BaTb p o'
PaClJeTLI npo ecca BnpbIcKa HOMI1HaJIbHOrO pe:iKHMa TonJ1HBHoH
annapaTypbI )J,H3eJI51 5lM3-236 C YlJeTOM H 6e3 Y'H Ta BeJIHlJHHbl p o
nOK33aHbI H3 pHC. 59. .3KcnepHMeHT8.1bHbIX JJ:8HHbIX no Be.1HlJIJHe
p o He 6bl.J10 nO.'IY4eHO, n03TOMY Be.1I1'-IHHa p$ = 200 K.r{C.M 2 6bIJIa
3aJJ:aH8 np0I13Bo.1bHO. ConOCTaB.1eHlIe nOK83blBaeT, lJTO YlJeT Be.IH-
lJl1HbI P:o B onpe,'LeJIeHHOH CTeneHI1 CKa3bIBaeTCH Ha napaMeTpax
BnpbICKa Ton.1HBa. OJ1,HaKO JJ:J15I onpe.a:eJIeHlJH 3TO I Be.'1H'lHHbI B K8:iK-
)l,OM KOHKpeTHOM CJ1Y'Iae Tpe6yeTcH .a:OBO.lbHO CJ10)!{Hoe 3KcnepH-
MeHTaJIbHOe HCCJ1e.n:osaHHe.
4. OCHOBHblE YPABHEHHSI H AnrOPHTM YTO'fHEHHOrO METOAA
PAC'fEU npOLl.ECCA BnPblCKA TOnnHBA
YTOlJHeHI15I MeTo,aa paC'leTa, H3.'ImKeHHbIe B npe)J,bI.D:yu.(e!\1 napa-
rpacpe, n03BOJIHIOT )J,onomiHTb I1CXOllHbIH lVIeTO.n: paC'leTa. PellleHHe
ypaBHeHHII HeYCTaHOBI1BlllerOCH .n:BH)KeHI1H TomiHBa C Y'leTOllI rH.J.-
paBJ1HlJeCKOrO conpOTHB.'IeHI1H B npe,a araelVIOM aJ1rOpl1TMe MO:iKeT
6bITb pea.'1H30BaHO .n:SYMH nYTHMH.
Cor JIaCHO npI16.1I1LKeHHOMY MeTO.n:y Y4eTa rH,apaB.ll1lJeClWrO CO-
npOTHBJIeHHH BeJIl1lJHHbI .n:aBJ1eHHH 11 CKopOCTeH B Tpy60npOBo.n:e
onpe.n:eJIHIOT C nOMOIllbIO BOJ1H )J,aBJ1eHIIH, nepe.n: KOTOpbIMH BBO,'LHT
-I'.!:..
K03<p<pI1 IIeHT TpeHH5I ea. Be.1H4HHY npmVIOH BO.1HbI ,aaBJIeHIIH,
06pa3YIOIllei1cH Y HaCOca, II 06paTHoi1, 06pa3YIOllI.elICH Y <P0PCYHKII,
onpe.n:eJIHIOT no ypasHeHIIHM (185a) II (188a), CKOpOCTH BO BXO.J.-
HOM II BbIXO)J,HOM CelJeHH5IX Tpy60npOBO)J,a -- no ypaBHeHI1HM
(184a) II (187a). f1pH pea.'IH3a HH 60J1ee TOlJHOrO MeTO.n:a Y'leTa
m.n:paB.'1IIlJeCKoro conpoTHB.1eHl1H [71] n:opocTH )J,BmKeHHH TOnJIHBa
B Tpy60npoBo.n:e paCClJHTbIBaIOT no ypaBHeHHIO (89a), a BO BXO)J,HOM
11 BbIXO,a:HOM CelJeHI1HX Tpy60npoBorra -- no ypaB+IeH115IM (193) 11
(194). K03<p<pHuHeHT rHApaB.1HlJeCKOrO conpOTIIB.'1eHHH MO)KeT
6bITb BbI'II1C.TJeH no <tJopMYJ1e (195) H.TJH (196), H.TJH no cpaKTopy
rH.n:paB.'IHlJeCKOrO conpOTHBJIeHHH k, nO YlJeHHoMY 3KcnepHMeH-
Ta.TJbHO.
npo ecc .n:BmKeHH5I TOn.'IHBa B Tpy60npOBOlI.e paCClJHTbIBaIOT C
YlJeTOM HalJa.'IbHbIX YC.l0BHH. B 60.1bWHHCTBe Ton.1HBHbIX CIICTeM
nepe.n: Ha'Ia,10M c.'Ie.n:YIOli{erO BnpblcKa .n:BIUKeIIHe Ton.'IHBa npeKpa-
llI.aeTCH, II CKOpOCTb npHHHMaJOT paBHoH Hy.1IO. OCTaTOlJHbIII CBO-
60,aHbIII 06"beM H"lH OCTaTOlJHOe lI.aB.1eHHe 3a.a.aIOT npH6.1H)KeHHO H
150
3aTeM YTO<JmUOT B pe3YJ1bTaTe HeCKOJIbKI1X paClJeTOB npou.eCC3
BnpbICKa TOn.'1I1Ba. KaIKLl.Oe nOC,;leLl.YlOlllee 3HalJeHlIe V oc, 3aLl.aBae-
!llOe nplI paC<JeTe O<JepeLl.HOrO BnpbICKa, HaXOLl.HT no 4>OPMY J1e (190),
OCHOBaHHoii Ha ypaBHeHlIlI 6aJIaHCa Ton.'1lIBa, BOllleLl.lllero B TelJe-
Hne u.lIK.'la B HarHeTaTe.lbHYIO MarncTpa.!Jb II BbIllleLl.lllerO H3 MarH-
CTpa.1J.n lJepe3 pacnbI.'lIITe.'lb.
AHa.'lOrWlHo onpeAe.'lHIOT OCTaTOlJHOe Ll.aB.leHHe. KarKLl.Oe nOC.le-
.J:YlOlllee 3Ha<JeHHe OCTaTOlJHOrO Ll.aB.leHHH po HI. 3aLl.aBaeMoe npIl
paC'IeTe OlJepeLl.HOrO BnpbICKa, onpeLl.e.1HIOT no 4>opMy.1J.e
P " = P . . -+- (qKi-qu.i)
0<,1 0' I V
ca.
ECJ1II B HarHeTaTe.'lbHOM Tpy6onpOBOLl.e HMelOTCH OCTaTO'lHble
CBo6oLl.HbIe 06"beMbI, He06xoLl.HMO paCClJHTblBaTb 3anO.'lHeHHe paBHO-
MepHO pacnpeLl.eJIeHHWX no Ll.JIHHe Tpy60npOBOLl.a m CBo60Ll.HWX
06"beMOB. BpeMH Ha 3anO,;lHemIe O'iepeLl.HOrO CBo6oLl.HOro 06"beMa
4>POHTOM Ll.BHIKYlllerOCH Ton.1J.HBa BbIlJHC.'lHIOT no 4>opMYJIe (84),
o6paTHbIe BO.1HbI, o6pa3YIDilluecH npu 3anO.'lHeHIiH ::Horo o6"be!.\1a,-
no 4>opMYJ1e (83).
fHLl.pOLl.lIIIaMH'IeCKHH paC4eT npoH3Bo,[J:HT npH COBMeCTHOM pe-
weHHU ypaBHeHuH HeycTaHoBuBweroCH. lI,BHIKeHHH Ton.1J.HBa B TPy-
6onpoBoAe H ypaBHeHHH rpaHH4HbIX YCJIOBflii. .
CHCTeMa ypaBIIeHHH rpaHH<JHbIX YC.l0BUii y Hacoca (183) B co-
OTBeTCTBUH C H3.'lO)l eHHbIMH YT04HeHHHMH 3anHllleTCH TaJ :
[ r-
: = fnCn-IJo(/lf)o / + V I PH-PBC /-
;-<JK/lUJU( , ,/ ,I 9 · I 2 VI PH- P I-
I T k V P
-IJlfKCK-ZI- Z2 ] I ;
6na. H V H
dp [ / r /2 1/ 1 ' I
- d = IJKlLuJ,,! 1. -------z 1 / -I{ PH-PH +
Ip t I + k" ' P -
+ IJIf"C,,-f TCT ] G , ;
_ 6na. H V H
)
(209)
, [ { - {-
dVm, I / 2 _ / '
- d = - /luJU( -----;;- 1 / - JI PH-PH +
Ip I + k P
] G.)
+ IJlf,l..',,-fTC T -=-;
6n
dC" [ ' ( ' )
dq;"= I" PH-PH +
f,,-f (PH-P )-f"P"p-fJhK ] 6n G M l ;
I +k
dh" = C" ..!!L. .
dip 6n
11 3aKa3 748
161
CTyneH1.IaTbIe CPYHKl.(HH 0"2 H 02' npHHHMalOT 3Ha1.JeHH5I HYJISI HJlH
e.ll.lIHlIl.{bI B 3amIClI!\IOCTH OT Ha:IO)l{eHHbIX Ha HHX YC<'IOBHH:
02 = 0 H 0; = 1 npH V I; > 0 H p = 0;
02 = 1 1I 0"; = 0 npH p > 0 H V I; = O.
EC.'HI cnaOlllHOCTb Ton.1HBa He BOCCTaHOB:leHa, 02 = 0 1I 0; = I,
rrpaBYIO 1.JaCTb BToporo ypaBHeHlISI CliCTeMbI YMHO)l{alOT Ha HYJlb H
paCC1.JlITbIBalOT H3MeHeHH5I BeJ1l11.JHHbI V II' ECJ1H nOCJ1e BOCCTaHOBne-
HH5I CnJ10111HOCTH 02 = 1 H 0"; = 0, Ha HYJ1b YMHO)l{alOT npaBYIO 1.JaCTb
TpeTbero ypaBHeHH5I CHCTeMbI H no BTOPOMY ypaBHeHHIO CHCTeMbI
paCC1.JHTbIBaIOT H3MeHeHHe .lI.aB.'IeHH5I Ton.1HBa B lllTYl.(epe Hacoca.
K03cpcpHl.(lIeHTbI C)I{HMaeMOCTli Ton.'IHBa au, a: H aifj BbI1.JHCJ151IOT
KaK CPYHKl.(HH OT .lI.aB.leHlISI II Cpe.ll.HeH 3a l.(HK.'I Tel\mepaTypbI Ton-
JlHBa no cpopMy.'le (204), B KOTOpylO BMOCTO .lI.aBJleHH5I p nO.ll.CTaBJI5I-
lOT .!I,aB.'leHHe B COOTBeTCTBYlOlI.{HX nO.10CTHX: pu, P HJllI pifj.
3cpcpeKTHBHoe npOXO.ll.HOe Ce1.JeHlIe OKOH rlIJ'Ib3bI
(/1f)0 = (/1f)6n + (l-Lf)OT'
npll Ha.'IH1.JIHI 3KcnepllMeHTa.'IbHOrO MaTepHa:la 3cpcpeI{TlIBHbIe
npOXO.ll.HbIe Ce1.JeHH5I BnYCKHbIX H OTCe'lHbIX OKOH rll.'lb3bI onpe.ll.e.l51-
lOT no Ta6JIIIII,aM (!-tf) en = f ( hn) H ( lf) OT = f ( hn) npll nOMOll.{H
nO.ll.npOrpaMMbI KBa.ll.paTH1.JHOH HHTepnO.151l.(HH. EC<1H OnbITHbIe .lI.aH-
HbIe OTCYTCTBYIOT, TO npllHHMalOT (lInen = !-tenten, a (lIf)OT BbI1.JHC-
JIHIOT C Y1.JeTOM .n.pOCCe.'llipOBaHl1SI B KaHa.1aX n.1YH)I{epa no CPOPMY-
Jle (205). P aCXO.ll.bI 1.Jepe3 3a30pbI B 30.10THHKOBOH H noplllHeBoH
'laCT5IX n.1YHfKepHoH napb! ZI H Z2 onpelle.151IOT no BbIpaMeHH5IM
(200) 1I (201).
npll perneHHH CHCTeMbI (209) He06xo.lI.HMO Y1.JHTbIBaTb c.ne.lI.Y!:O-
lI.{He 3aBHCHMOCTH K03cpcpHI.{HeHTOB ypaBHeHHH rpaHH1.JHbIX YCJIOBUH
Y Hacoca:
C n =6n dh n ;
dq>
V" = V"o+tn(hnmax-hn);
(/1f)o = 0 npH 'PeNn -< 'P -< 'P,,,n;
(/1t)6n = f( hn) npH 'P < 'P""n;
(J.tt)OT = f( hn) npH 'P > 'P""n;
tll!=O npH O<,h K <hK.o;
tll! = f(h,,) npH h K > h"o;
3.l1.eCb 'Pmn H tpi'xn - yrJIbI reOMeTpH1.JeCKoro Ha1.JaJla H KOHna nO)J.a1.JH.
ECJIH TOnJIHBHa51 CHCTeMa HMeeT 30JIOTHHKOBblH KJIanaH, aJIro-
162
pl1TM paC4eTa HeCKOJ1bKO 113MeHI1TCH. npl1 nepeTeKaHl1l1 4epe3 30-
OTHI1KOBNH K anaH 113 Ha n YHMepHOrO npOCTpaHCTBa B illTYUep
HaCOCa TOnJ1l1BO npOXO I1T 4epe3 Ce4eHlle no,n: nOCa,n:04HbIM nOHC-
KOM KJlanaHa (0603Ha4HM I--l.. f : ), a 3aTeM 4epe3 60KOBble OTBep-
CTI1H B ce,n: e K.;lanaHa, KOTopbIe nOCTeneHHO OTKpblBaIOTCH B pe-
3y.1JbTaTe no,n:'bel\Ia pa3rpY;'KaIOllLero nOHCKa 30JlOTHl1KOBOrO KJ1a-
naHa (0603Ha411l\I 3TO npoxo,n:Hoe ce4eHHe I--l"f:). B KOHI.{e BnpblCKa
K.lanaH Ha4HHaeT onYCKaTbCH Ha 3anopHbIH KOHYC ce,n:J1a. nOCJIe
TOro KaK UH.1HH,n:pH4eCKHll pa3rpYMalOllLHH nOHCOK KJlanaHa nOJIHO-
CTblO nepeKpoeT 60KOBbIe OTBepCTHH .B ce,n:JIe (npH h" = h1<o) , Ha-
rHeTaTe.'lbHaH MarI1CTpa.'1b OTK"lI04HTCH OT Ha,n:OJ1YHMepHoro npOCT-
paHCTBa H Ha4HeTCH XO,n: pa3rpY3KH K"laoaHa, Opo,n:OJIMalOllLHHCH
,n:o noca,D,KI1 ero Ha 3aoopHbIH KOHYC ce,n:JIa.
TaK KaK Opl1HUHO paOOTN 30 OTHI1KOBOrO K aoaHa B OCHOBHOM
aHaoilOnl4eH npHHUHOY paOOTbI rpl16KOBOro K.1JaOaHa. TO a.lrOpl1TM
paC4eTa 113 IeHHeTCH He3Ha4HTe.'lbHO. TaK. CHCTeMa ypaBHeHI1H
(209) M3MeHHeTCH B pe3y.1JbTaTe Taro. 4TO BMeCTO BemlqHHb! k" B
CMCTeMe (209) BbI4I1CJ1HIOT
k _ ilK t:
1(.3- In '
I-lKI f K
r)1e
f;=F1(h K );
f:' = F 2 (h K ),
KpOMe Taro, BMeCTO OO'beIVIa V>i onpe,n:e,,'1HIOT V>ia:
VHa=V H npM hK=O;
Vlla=VH+V K npM hK>O;
3,n:eCb V" - 06'beM Ton"lMBa, HaXO,D,HllLerOCH MeM,n:y KJ1anaHOM 11
ce,D,.'lOM npM h" = O.
Kor,n:a paCC4MTbIBaeMaH TOnJIHBHaH CHCTeMa HMeeT K.1JanaH-KOp-
peKTOp, CHCTeMa ypaBHeHHH (209) H3MeHHeTCH B pe3YJ!bTaTe TOro,
4TO 3<p<peKTHBHoe npoxo)1Hoe Ce4eHl1e Qepe3 llI.eJIb K.'lanaHa 1--l1.Ii
3aMeHHeTCH 3<p<peKTI1BHbIM npoxo,n:HbIM CeQeHHeM ( lf)"Jl.,,:
npM h K = 0 (I--lf)KU = 0;
npM 0 < hI( < h KO (I--lf)KA. K = (l--lf)KOP;
npM h K > h KO (l--lf)KU = (I--lf)KOP + l--luJ U{'
r,n:e I--lf..op - 3<p<peKTHBHoe npoxo,n:Hoe ce4eHMe KoppeKTHpYlOllLero
OTBepCTHH.
11* 163
rpaHHqHWe YCJ10BHH Y OPCYHKH (186) C yqeTOM YTOqHeHHH
onHCbIBalOTCH CHCTeMOH ypaBHeHHH
dp [ ' I "2
d: = fTCT-( f)i/J V P 1 1 p",-p'(-
-03(fu-fu,)C u - Z3 ] 6 a. V ;
wJ..p ifJ
dV mp r ' ] 04 .
- = - fr C r- 0 3(fu-f",)C u _ 6 '
d n
dC [( ' ) ( ' ) " ] 03
d U = fu- fu (Pet'-P<I>.) + fu-fw pifJ-fJ y+ fWP,( 6nM' ;
dy = C u ....!!L.
d 6n
(210)
CTyneHlJaTbIe <PYHKUHH 04 H 0; npHHHMalOT 3HalJeHHH Hy.m! tIJI"
e.l!.HHHUbI B 3aBHCHMOCTH OT Ha,;10MeHHbIX Ha HHX YC.10BHH:
04 = 0 H o = 1 npH V net > >- 0 Jf Pef; = 0;
04= 1 H 0 =0 npH Pet> >0 H Vn.p=O.
OOKa CIIJ10111HOCTb TOn.'IllBa B 06"beMe OPCYHKH He BOCCTaHOB-
J1eHa, 04 = 0 H 0 = 1, paClJeT Be.l!.YT no BTOPOMY ypaBHeHHIO CHCTe-
MbI (210), a dpl/J = 0 H pg, = O. Ooc.1e BOCCTaHOBJIeHHH cn.rIOlliHOCTH
d
TOnJIHBa 04 = 1 H 0; = 0, B paCqeTe HCII0J1b3YIOT ypaBHeHHe, a
dVn<l> = 0 H Vng; = O.
d
Pacxo.l!. Z3 qepe3 3a30pbI B pacnbI.1HTe.1e onHCbIBaeTCH ypaBHe-
HHeM (202).
3<p eKTHBHoe npOxo.l!.HOe CelJeHHe pacIIbwHTe.1H ( f) g" 3a.l!.a-
BaeMoe B BH.l!.e Ta6.1HubI B <PYHKUHH nO.l!."beMa Hr.1W (xapaKTepHcTH-
KH pacnbWHTeJ1H), BbIlJHC.1HIOT npH nO!\IOIlUI nOLI:IIpOrpaMMbI KBa.l!.-
paTl1'IHOH HHTepIIOJ1HUHH.
XapaKTepncTHKa paCnbIJIHTeJIH MOMeT 6bITb onpe.l!.e.leHa 3KCIIe-
pHMeHTa.1bHo HJ1H 3a.l!.aHa, HJIH npe.l!.BapHTe.lbHo paCCqHTaHa aHaJIH-
THlJeCKH.
CHcTeMY (210) MOMHO HCnOJIb30BaTb ,Zl}IH paClJeTa npouecca y
OPCYHKH C 6eclllTH TOBbIM pacIIbI.1HTe,TIeM, ec.1H npHHHTb fm = O.
Ho npH 3TOM Be,;lHlJHHY P .l!..'IH ll1TH TOBoro 11 6eCll1TH<pToBoro pac-
nbIJ1HTe.'1ei-i c.'1e.J.yeT paCClJHTbIBaTh no pa3.1HqHbIM opMy.laM: .l!.JIH
PIIC. 60. YKpynHcHHaH 6.10K-cxcMa nporpaMMbI paC'IeTa npol.\ccca BnpblcKa TOnJlIlBa
B ;UI3C.TJ5IX
164
1. cl>op lIIponaHllc .10fll'-lCCKHX nYTeH nporpaMMbI
t
2 f1CPCBOlJ, HCXOlJ,HbIX llaHHblX B .!J.BOH'-IHY!O CHCTCMY
. C'-IIIC.1CHIIH, nC'-IaTb ncpBblx 150 H'-IeCK
.J.
PaC'-ICT nOCT05lHHb!X K031j:J1j:J1II.\HCHTOB ypaBHcHHi1, co-
3. CTaB.1CHHC Ta6nIJI.\ II BOCCTaHOB.1CHHC ncpcMcHHbIX
KOMall.!J.
I
4. cl>opMf!pOBaHHe 6.'IOKOB, 1O.!J.e.1Hpy!OmHx Tpy6onpo-
130;r
t
5. 06pamcHHc K CTaHlIapTHOH nO.D:npOrpaMMe '-IHCJlCHHO-
ro HHTCrplJpOBaHli51
BbI'-IHCJlCHHC npaBblx 'lac-
6. TCII ypaBHeHHH rpaHII'-IHbiX
ycaoBHH y Hacoca -7
.j,
4HC.1CHHoe IJHTCrplJpOBa-
11 . HHC .D: m p<P c pCHl.lHa.1bHbIX
ypaBHCHIlf! y Hacoca no
3i1.1CPY
......-
PacnpC.D:CaHTCnb nYTcH I
1 7 .
!
Pac4cT 3anO.'IHeHIIH Ton- ,
.1HBOM CB060.D:Hb!X 06"bC-
MOB B Tpy6onpOBO.D:e
1
BbI4IJC.1CIIIJC BO.1H .l!,aBJIC-
8 Hf!51 11 npOllBIJ)\{CHf!e IIX B
. 6J10KaX 3ana3D.b!BaHH>!.
PaC'-ICT BJlHHHHH Ij:JII.TJbTpa
19.
npOBcpKa YC.!JOBHH: D.O-
Ill.TJ8 JIll npHMa51 BO.TJlIa
,!\aBnCHH5I .D:O <POPCYHKH
Bbl'-lHc.!JeHf!e npaBbIX '1RC-
10.Tci1 ypaBHcHIIH rpaHH'IHblX
YCJlOBIIH Y <POPCYHKH
f1poBcpKa YC,10BHH: na4a- r HeT
12.JlO .TJf! H3l\1CH5ITbCH ;raBnc- -----
HHe B IllTyuepe
1.
IHeT
13. f1poBepKa YC.l0BIJH:
q>i = q>j + hmc
!
PaC4CT CKOpOCTCH B.10.%
14 xapaKTCpHCTIJK IJ B KOHI.\C-
I . BbIX CC'-IeHH5IX. f1pO.D:BIJ-
)\{CHliC CCTKH
I
J],a .J, J
QHc,lcHHoe IIHTcrpllpoBa-
I ...... 15. HHe ,lJ:H<plj:JcpCHI.\HaJlbHbIX
ypaBHcHHH Y <POPCYHKH
-7 no 31!JlcPY
......-,
.:.
napaMCTpOB ,......_
/ 16. Pac4cT HCKOTOpbIX JJ.onOJlHIITCJlbHbIX
BnpbIcKa. ne'-laTaHHe PC3YJIbTaTOB
1-
I7 . f1poBcpKa Ha OKO!l'-laHHe paC'lCTa
J],a
f1c'laTaHllc napa:\lcTpoB, xapaKTcpH3Y!OU.\liX Bnpb!CK
18. B l.\eaOM. Ol.\eHKa npaBH.lbHOCTH Bbl60pa OCTaT04Horo
.D:aB.TJCHIIH (pa3pC>KCHH5I), CCJIH BKJIIO'-ICH KJlIO'-I 40
J eTOn
I HCT
165
6eClliTHcpTOBoro paCnbIJIHTeJISI no cpopMYJIe (189), .lI;JIH lliTHcpTOBO-
ro - no cpopMy.'Ie
. (flf)
PtjJ = PtjJ---;;-(PtjJ-p,,),
(flf)
(211)
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npoBo.n.e, CHCTeMbI ypaBHeHHll rpaHH1.JHbIX YCJ10BHll y Hacoca H Y
CPOPCYHKH MorYT 6bITb TaKMe peaJJH30BaHbI B nporpaMMe B pa3.'IH1.J-
HbIX BapHaHTax. YHHBepCaJ1bHbIll a.1JrOpHTM n03BO.1JHeT B 3aBHCHMO-
CTH OT ueJ1ell H YCJ10BHH paC1.JeTHOrO HCCJ1e.n.OBaHHH npHMeHHTb HJ1H
He npHMeHHTb Te HJ1H HHbIe YT01.JHeHHH paC1.JeTa II.'lH BbI1.JHC.'1HTb He-
KOTopble H3MeHeHHbIe KOHCTPYKUHH Ton.'1HBHoi'I annapaTypbL TaK,
K03CPllJHUHeHTbI !-len, !-lor, a MorYT 6bITb 3a.n.3HbI Cpe.lUIHMH 3Ha1.Je-
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OTpIIuaTe.'1bHbIX .n.aB.1Jemlll H T. ..'l.. Donee no.n.p06HbIll nepe1.JeHb Ba-
pIIaHToB paC1.JeTa npIIBe.n.eH .n.3.'1ee.
TaKIIM 06pa30M, OCHOBHaH J10rII1.JeCK3H cxeMa paC1.JeTa OCTaeTCH
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llie, HO .n.onO.'1HIITeJIbHO nepe.n. nepBbIM nYHKTOl\1 BBe..'l.eH onepaTOp
<pOpMHpOBaHIIH .'10rII1.JeCKIIX nYTell nporpaMMbL
00.n.P06HO nOC.1e.n.OBaTeJ1bHOCTb paC1.JeTa M,0MHO npoc.1Je.n.HTb no
YI<PynHeHHoll 6.'lOK-CXeMe nporpaMMbI (pnc. 60).
S. KPATKOE onHCAHHE nporPAMMbl PAC'IETA
npoqEccA snPblCKA TonnHSA
Pa3BepHYToe orUIcaHne nporpaMMbI 3aHHJIO 6bI l'vIHOrO MeCTa, .n.a
H B 3TOM, Ha Halli B3rJ1H.n., HeT He06xo..'l.IIMOCTII. 003TOMY OCHOBHoe
BHIIMaHHe 3.n.eCb y.n.eJ1eHO TeM oc06eHHocTHM nporpaMMbI, KOTopbIe
OTJ1H1.JaIOT ee OT pKe CYl.L{eCTBYIOI.L{HX.
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Ka3aHa Ha pIIC. 60. OnepaTop 1 <popl'vlHpyeT J1OrII1.JeCKHe nYTII npo-
rpaMMbL OOHCHIIM, 1.JTO no.n. 3THM nOHIIMaeTCH. OpOrpaMl'vla noCTpo-
eHa TaI<, 'ITO n03BO.'1HeT npouecc BnpbICKa Ton:UIBa paCC1.JIITbIBaTb
pa3.1II1.JHbIMH MeTo.n:aMII B 3aBIICIIMOCTII OT ueJ1ei'I H YC.'10BHH IICC.TJe-
.n.OBaHHH. OporpaMMa MOMeT Y1.JHTbIBaTb II.'1H He Y1.JHTbIBaTb II3Me-
HeHHH B KOHCTPYKUllll TOnJ1HBHOll annaparypbl, a TaK)Ke HeKOTopble
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.n.ycMaTpIIBaeTcH B03MOMHOCTb BbIBo.n.a pe3YJ1bTaTOB B BII.n.e Ta6JIIIU
HJ1II rpacpHKOB. BbI60p BapHaHTa paC1.JeTa 06eCne1.JHBaeTCH 3a.n:aHII-
eM COOTBeTCTBYIOl.L{erO Ko.n.a ,nOrII1.JeCKHX nYTei'I. Ko.n. npe.n.CTaB.1HeT
C060ll 'IHCJIO, COCTOHl.L{ee 1I3 15 II.HllJp H onpe.n.eJ1HlOl.L{ee .'10rII1.JeCKYIO
cxeMY nporpaMMbL Pa60Ta nporpaMM Ha1.JIIHaeTCH C TOro, 1.JTO aHa-
JIH3HpyeTcH KO.n. II 1lJ0pI\mpYIOTcH 3a.n.aHHbIe KO.n.OM .'10rII1.JeCIme ny-
TH nporpaMMbL Ko.n. MOMHO COCTaBHTb, no.1Jb3YHCb c.'Ie.n.YIOIII.IIl'vlH
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166
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11.2
11.3
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IV.I
IV.2
IV.3
V.I
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npo.r\0.1>KCHHe Ta6.TJlil.\bl
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Koro nYTH TOIlol1HBHOii annapaTYPbJ Koro nYTH TonnHBHOH annapaTYP
XII. 1 TpcHllc npn cTpafliBa. XIIl.2 Cpc..1:II5I5I CKOpOCTb 13
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XIIl.I CpC.!J.!HHJ CKOpOCTb 13 100 1'a6.1111.\a pC3y.'1bTaToB
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= 13211211211110. Ko 03HaqaeT, 'ITO paCqeT rH paB.'1HqeCKOrO
conpOTHBJleHHH npOH3BO HTCH no npH6J1H eHHOMY MeTo y (CM. 1.1 L
HCn0J1b3yeTcH <paKTop rH paB HqeCKOrO conpoTHB eHHH, 3a aHHHH
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nO 6HpaH cooTBeTcTBYIOII.J:HII KO .'10rHqeCKHX nYTen, MOJKHO
peaJ1H30BaTb MHorHe MeTO bI paCqeTa npoI.{ecca BnpbIcKa TOn,,'IIIBa.
BKJ1IO'IaH HCXO HbIH MeTOA. Pacxo AeHIIe B MeTo ax 'IHC"leHHoro
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KOTopbIe Heo6xo.lI.I1Mbl .n.Jlfl paCqeTa no BbI6paHHoMY BapHaHTY.
168
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( X ) ( X
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a
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L.6n
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a.64
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3a.lI.aHHOM MeTO.lI.e paCqeTa, nOJ1HOCTblQ HCK.1.lQ'Ia.1MCb. C 3TOH :JKe
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paBHbIe HHTepBaJIbI aprYMeHTa. LlJI5! BbJ60plm 3Ha1J.eHIIli M3 3THX
169
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pbI Bnpb1CK8. OCHOBH8f1 <PYHK-
ll.H5I noro oncpaTopa - ynpaB.'I5ITb BbIAa'lCH HH<popMaUHH 'lCpe3 3a-
JJ.aHHbIH HHTcpBaJ1. PC3YJIbTaTbI MorYT nC'laTaTbCfI Ha Y3KyIO nc-
qaTh, a TaKTh:e, eC.!lH BK.!llOqeH KJlIOq 100, Ha lllHPOKYIO neqaTb C no-
MOI.IJ.hlO a.'1<paBHTHO-ll.H<ppoBoro ne'laTalOI.IJ.cro YCTpoi'IcTBa (Au,nY),
npHqCM COOTBCTCTBYIOI.IJ.H I .'IOnlqCCKn I nYTb (XIV. 1 HJ1H XIV.2)
onpeJ!.c.'I5IeT Bli.n. BbIBOJJ.a.
B03Mo}(\Ho nC'laTaHHC pC3y.ilbTaToB Ha Au,ny B BHJJ.C Ta6m:IIJ;
HJ1H rpa<pHKoB.
OKOHqaHHe pac'IcTa npOBCp5ICT onepaTop 17. npH OKOHqaHHH
HHTepBaJIa paCqCTa B pa60TY BCTynacT oncpaTop 18, nCqaTalOlUHH
napaMcTpbI "t, (q" - q1j) H q1j, xapaKTepH3YIOlUHe BnpblcK B ll.eJIOM,
noc.'1e qero MalllHHa OCTaHaB.'IHBaeTC5I. no BC.'1HqHHe (q" - q1j)
MOMHO Oll.eHHTb np8BH.1bHOCTb BbI60pa 3HaqeHHH Po HJIH V oc H, H3-
MeHHB YKa3aHlIbIC BCJ1H'lHHbI, C nYJIbTa nOBTopHTb paC'lCT. npH
BK lIOqCHHOM KJllO'le 40 (CM. pHC. 60) H3MCHCHHe po HJ1H V oc B CJIY-
'lac HenpaBI1.'lbHoro HX BbI60pa npOI1CXOTIliT aBTOMaTHIJCCKH 6C3 oc-
TaHOBKH U,BM, noc.'IC 'lero B pa60TY BCTynacT oncpaTop 3. Ha'lI-!-
HalOIHHH nOBTopHbIH paC'lCT.
170
8,0
6,0
o
o
31
37
39
33
Iff
35
PHC 61. XapaKTcpncTHKH BnpbIcKa Ton-
.1JlIBHOi1 annapaTypbl .D:U3CJ!H ]1-60 np"
n = 900 06/htUf!., q" = 77,5 .\Ut 3 :
1 3KcnepHMeHTa :]bH8H; 2 - paCqeTHaff
cpO
BK.11D1IeHl1e K.l104a 4 B npoLI.ecce pac4eTa Bbl3blBaeT nepexo.n: K
onepaTopy 18 C noc.le,n:poIlleH OCTaHOBKOH rvrawIIHbI. ECJ1H B MO-
MeHT pa60TbI onepaTopa 18 BKJIlDlIeH KJIlDlI 1, TO nellaTaIOTC5I, KpO-
Me Toro, Ta6.111LI.bI II K03cpcpl1LI.HeHTbI, paCC1.JI1TaHHbIe onepaTopoM 3.
ConocTaB.'1eHHe paclIeToB IjCN
npoLI.ecca BnpbICKa TOnJ1HBa
YTollHeHHbIM MeTo.n:OM. pea.'1H30-
BaHHbIM B BH,n:e nporpaMMbI A.15I
UBM l'vlHHcK-22, C 3KcnepHMeH-
Ta:JbHbIl\UI .n:aHHbIMH, .B3SlTbIMH H3
pa3.'IH1.JHbIX HCTOllHHKOB, nOKa3a-
JIO, liTO pe3YJIbTaTbI paC1.JeTa 10t
YT01.JHeHlIbIM MeTo.n:OM YAOB.le-
TBOpHTeJ1bHO COrJ1aCYlOTC5I C
OnbITOM. TaK, H306pallieHHbIe Ha Pi} r/CM2
pIlC. 61 pe3YJ1bTaTbI cTpo6oCKO-
nHpOBaHH5J MOlliHO conOCTaBHTb
C pac4eTHoH xapaKTepHcTHKOH
BnpbIcKa. Ha pHC. 62 nOKa3aHbi
pe3y.TJbTaTbI OCLI.HJIJIOrpaq:>HpOBa-
200
HHSl B COnOCTaBJIeHI1H C paC1.JeT-
HbIMH .n:aHHbIMH.
CpaBHeHHe pe3Y.'IbTaTOB pac-
f.J.eTOB no.n:a1.JH Ton.HIIBa pa3J1WI-
HbIl'IIH TOnJIHBHbIMH CHCTeMaMH
6bICTPOXO.n:HbIX .n:H3eJIeH no 0011-
caHHoll nporpaMMe C onbITHbIMI1
.n:aHHbIMI1 nOKa3aJIO, 1.JTO 60JIb-
WHHCTBO pa601lIlx pelliIlMoB MO-
llieT 6bITb paCC4I1TaHO C y.n:oB.'1e-
TBopIlTe.'1bHOH T04HOCTblO, cono-
cTaBIIMoH C T04HOCTblO 3KcnepIl-
MeHTa. HaH60JIblliee BJIH5IHl1e Ha
YT01.JHeHHe paC IeToB 4aCTH1.JHbIX,
a B HeKoTopbIX c.'IY4aSlx H HOMH-
Ha.'1bHbIX pelliHMOB OKa3bIBaeT
VlieT OCTaT01.JHbIX CBo60.n:HbIX
06"beMOB. Ha Bcex pelliHMax LI.e-
JIeC006pa3HO Y411TbIBaTb rH.n:paBJIH4eCKOe conpOTHBJIeHHe Tpy6o-
npOBo.n:a, OKIIMaeMOCTb TOnJIHBa KaK CPYHKLI.HlO .n:aBJIeHII5I H TeMne-
paTypbI 11 .n:pocce.'1I1pOBaHHe B KaHaJ1e n.'1YHlliepa npH OTce4Ke. DpIl
paC4eTe TOllJIHBono.n:a4I1 CHCTeMaMH C I13HOWeHHbIMH npeLI.H3I10HHbI-
MH coe.n:HHeHH5IMII I1J1H paC4eTe BnpbICKa 6eH3I1Ha CJ1e.n:yeT Y4I1TbI-
BaTb YTe1.JKH TonJ1MBa 1.Jepe3 3a30pbI. OCTaJ1bHbIe YT01.JHeHMSl, npM-
Bel1.eHHbIe BbIwe, BO MHorIlX CJIY4aSlX MeHee 3Ha4HTeJIbHO B.'IH5IlOT Ha
pe3Y JIbTaTb1 paC1.JeTa, XOT5I I1MeIDTC5I C04eTaHHf! KOHCTPYKTHBHbIX
napaMeTpOB TOIIJ1I1BHbIX CIICTeM, npH KOTOpbIX 3TII YT01.JHeHH5J Balli-
lIO Y4eCTb,
qOJ
0,02
100
25
JO
40
(pO
PHC. 62. 3aBHcHMoCTH nOJ.\"bCMa Hr-
Jlbl Y H .D:aI3.TJCHHH Pi! B .D:aT'-IHKe y
OPCYHKH TOn.TJHBHOH annapaTYPbl
J.\1I3C.151 5IM3-236 npll n =
= 450 06/MUH., q1J = 122 MM 3 :
1 - :=mcnepHMcHTa.r1bHaH; 2 - paCqeT-
Ha>1
r naB a IV. 3KcnEPHMEHTAnbHOE H PAC'fETHO-
TEOPETHLfECKOE HCCflEAOBAHHE TonflHBHblX CHCTEM
ABHrATEflEJi"I C BocnnAMEHEHHEM OT C>KATHSI
1. METOA 04EHKH nAPAMETPOB npOLlECCA snPblCKA
TOnnJIISA no PE3ynbTATAM TEOPETH'IECKOrO PAC'IEU
OC06€HHOCTblO TeOpeTl-flleCKHX MeTO.lI.OB paClJeTa, H3JIOLKeHHbIX B
r.1. II HIlI, 5IB.'UleTCH TO, IJTO B CBH3H C KOHe'IHOH CKOpOCTblO pacnpo-
CTp3HeHHH .lI.aB 1eHl1H ypaBHeHl1H .lI.Bl1LKemlH nOTOKa TOnJIl1Ba COCTaB-
J15IIOTC5I pa3.n:eJ1bHO !I..1H BXO.lI.HOro H BbIXO.lI.IfOrO CeIJeHHH HarHeTa-
Te,,'IbHoro Tpy6onpOBo.n:a. PaCCMaTpl1BaeMbIH MeTO.lI. ynpOll.laeT
paCIJeT, HO 3aTpYJI,HHeT ou,eHKY KaIJeCTBa pa60TbI CHCTeMbI B u,eJIOM.
B TO LKe BpeM5I TaKHe BonpOCbI, KaK 06pa30BaHHe pa3pbIBOB nOTOKa
Ton.'IHBa H He 3anOJIHeHHbIx TOnJIHBOM 06'beMOB, ou,eIlKa 06w.eH
KOHCTPYKTHBHOi'l KOMI10HOBKH TOD.11HBHOH CHCTeMbI H BbI60p IWHCT-
PYKTHBHbIX pa3MepoB ee 3.'IeMeHTOB, Tpe6YIOT XOT5I 6bI npH6JIlDKeH-
Horo onpeJI,eJ1eHH5I B3aHMOCB5I3H MeLK.lI.Y xapaKTepHCTHKOH BnpblcKa
H OCHOBHbIMH 3.TJeMeHTaMH H napaMeTpaMH Ton.'IHBHOrO Hacoca,
<}"JOPCYHKH H HarHeTaTeJ1bHoro Tpy6onpOBO.lI.a. 'Ka3aHHYIO B3aHMO-
CBH3b, .n:aLKe npH6J1HLKeHHYIO, MOLKHO no.1YIJHTb TO.1JbKO nYTeM co-
CTaBJ1eHHH H aHa.1H3a ypaBHeHHH npouecca TonJ1HBOnO.lI.aIJH, o611.1ero
JI,.'IH CHCTeMbI. CocTaBHTb TaKoe ypaBHeHHe Hcc.leJI,yeMoro npou,ecca
MOLKHO, eC.1H Ha 3Tane, BO BpeM5I KOToporo .lI.eikTBYIOT OCHOBHbIe
HCKaLKalOll.lHe cpaKTopbI, HeCKO.lbKO npeo6pa30BaTb ypaBHeHHH rpa-
HHIIHbJX YCJIOBHH Y HaCOC3 11 y <}"JOPCYHKlI, a 33TeM HX 0606ll.!.HTb,
HCn0J1b3Y5I .lI..1J5I 3TorO OCHOBHbIe nOJlOLKeHlI5I TeopHH npou,ecca BnpbI-
CK3 TOnJ1HBa. ..a.1J5I perneHH5I nocTaB.1JeHHOH 3a.n:aIJH C.I0LKHM ypaB-
HeHHH (13) II (14), BbIpa3HM B HHX CKOpOCTb C T IJepe3 BOJIHbl .lI.aB-
JIeHH5I, noc.'Ie IIero no.1YIJHM
dPII . dp ( 2 f
a.V,,-+aVn-O=°fnCn-J..I.Jo - JI P,,-P8C-
dt dt P
- F(t)- \\7(t).
ap ap
(212)
OpO.lI.H<}"J<}"JepeHu,IIpyeM ypaBHeHHe (15) no t H 33TeM pernHM ero
dp" .
OTHOClITe,1IbHO ill.
dp" = d 2 C" + C f dp
dt I,,' dt 2 I" K T dt .
]72
OOlI.CTaBliB 3TO 3Ha'ieHIie dPH B ypaBHeHIIe (212) Ii pewIiB HO-
dt
Boe ypaBHeHIie OTHOCIiTe.'1bHO !!:Y (t), nOJIY'IUM
ap
f T /2 / ( M d 2 C K 6 \
-F(t)=f C -fl f l i -J P . - p -aV -. -+-C J -
ap n n 0 0, p n BC n\ fK df2 fK K
-a ( V ...L V' ) dp - \F ( t ) . ( 213 )
II. II dt dp
BbIpa311M B ypaBHemiH (40) CKOpOCTb C; 'Iepe3 BO.'lHbI lI.aB.ile-
HIiH I1 3a1IIiWel\1 3TO ypaBHeHue B BHlI.e
f T ( L ) V dp t/1 . t f T ( L )
-F t-- =a q'- dt T nCn+Qp--W t+- . (214)
ap G ap a
T1J,e
/2 r,
Qc=flcfcCc=flctc V pi PtfJ-Pu,'
OpOlI.H<p<pepeHUIipOBaB IIO t ypaBHeHIie (41). IIO.'1Y'IHM
M' d 2 C u ...LfYC = (f - f ' ) dptj> ...!- f' dp
u dt 2 ' " " l{ dt " U dt .
LI.onycTHM. 'ITO
(214a)
dpq. dp
dt dt'
PeWI1B C 3THM .n:onYll1.eHHeM ypaBHeHHe (214a) OTHOCI1Te.'1bHO
Cu, 6y.n:eM I1MeTb
C = dpt/1 _ M d 2 C q
U 6' dt 6' dt 2
KaK H3BecTHo, IIPI1 paC'IeTe IIpouecca Ton.'1I1BOno.n:a'lH 6e3 Y'leTa
BH3KOCTII IIpI1HHMaIOT
(215)
F (t) = F ( t - ).
EC.'1I1 Tenepb npeo6pa3yeM ypaBHeHIIe (214) c Y'IeTOM YKa3aH-
HbIX .n:on5'IlleHIIH II BbIpa}KeHHH (213) H (215) Ii pewHM ero OTHOCIi-
Te,,'1bHO f n C n, TO lIo.lY'IIIM
(f C ) l - f /2 1/ V ( M d2CK...L ()C K )
n n (1- ) = tolo V P J' PH-PSC+a. II --'-;' ' T +
+a.(VI<+V ) dp ]( L ) + ( a.V</.>+ ) dpt/1 +M . d 2 C u _
dt 1- - 6' dt 6' dt 2
a,
- : [W (t+ )-W (t- )]+Qp. (216)
173
B ypaBHeHllH (216) HHAeKC (t- ) 03HallaeT, liTO BeJIH1JHHbI
'IJIeHOB, 3aKJIIO'IeHHbIX B KBa1I.paTHble CK06KH, npHHllMalOTC5I no liX
I L )
3Ha'IeHHIO 1I.JIH MOMeHTa BpeMeHH t- . lb aHa.1H3a ypaBHeHllH
(216) CJ1e.n:veT, liTO eCJIH 6bI He 6bl.'I0 IICKaLKalOlIJ,erO BJ1HHHIIH Bca-
CbIBalOllJ,HX -H OTce'IHbIX OKOH BTY.1KH n.1YHLKepa ('I.l1eH 2), HarHeTa-
TeJIbHOrO I{.'lanaHa (lI.1JeH 3), 06'beMOB V ll , V , VgJ ('IJIeHbI 4, 5, 6)
II OTpaLKeHHbIX BO.1H (lIJ1eH 7), TO xapaKTepHCTHKa BnpbICKa
('I.l1eH 8) COOTBeTCTBOBaJIa 6w 3aBHCHMOCTH 06'beMHOH CKOpOCTH
n01I.a1JH Ton.1JHBa nJIYH)KepOM Hacoca OT yr.la nOBopoTa Ky.1JallKOBOro
BaJ1HKa (lI.leH 1), onpe.n.eJ1Hel\WH npoqm.leM Ton.1HBHoro Ky.lallKa.
YCTaHOB.'leHO, liTO OCHOBHbIMH HCKa)!(alOIll.HMH <paKTopaMH 5IB-
J1HIOTCH 06'beMbI CHCTeMbI H CLKHMaeMOCTb TOnJIHBa, KOTopble Me)]{-
.n.y C06011 B3aHMOCBH3aHbI. 3TH <paKTOpbI .n.eHCTBYIOT Ha BceM npo-
T5ILKeHHH npOI.(ecca BnpbICKa. OCTa.J1bHbIe <paKTOpbI, KpOMe OTpa-
)!(eHHbIX BO.1H, AeHCTBYIOT Ha He60.'lblllHX y acTKax Ha1JaJ1a H KOHI.(a
HCC.1e1I.yeMoro npOI.(ecca. BJ1H5IHHe OTpa)KeHHbIX BO.1H Ha npoI.(eCC
BnpbICKa 3aBHCHT OT xapaKTepa HX H3MeHeHH5I. ECJ1H OTpa)KeHHbIe
BO.'lHbI W He II3MeH5IIOT CBoero 3HaKa H a6CO.1JIOTHVIO Be.'lHlIHHV aM-
L . .
nJ1HTy.n:bI, TO, Ha1JHHaH C MOMeHTa t = -, OHH nepeCTalOT HCKa)!(aTb
a
npOI.(eCC BnpbICKa. B 3TOM CJ1Y1Jae OTpaLKeHHbIe BO.1HbI BJIHHIOT Ha
npOll.eCC BnpbICKa TOJIbKO B Te'IeHlIe ero HallaJIbHoro nepHO.n.a b..t =
2L
-. OpH pe3KOM H 1JaCTOM H3MeHeHHH 3HaKa OTpaLKeHHbIX BO.'1H
a
HX B.J1HHHHe YCHJIHBaeTCH, 1JTO HHTeHCH<pHll.HpyeT B CHCTeMe Ko.'le6a-
Te.'lbHbIe npOI.(eCCbI, KOTopbIe MorYT 06pa30BaTb 1I.OnOJIHHTe.'lbHble
BnpbICKH. Kor.n.a pa3HOCTb OTpaLKeHHbIX BO.'lH nO.'lO)!(HTe.lbHa, TO
lIJIeH 7 BbIpaLKeHHH (216) 6y.n:eT onpe.n:eJ1HTb HeKoTopylO 06'beMHYIO
CKOpOCTb TOn.1HBa, .n.onOJ1HHTe.lbHO nocTynalOllJ,ero B CHCTeMY H3
KaKorO-TO .n.pyroro HCTOl(HHKa. TaKHl\1 .n.onOJIHHTeJIbHbIM HCTOl(HH-
KOM MO./KeT 6bITb Ton.1HBO, C)KaTOe B 06'beMaX CHCTeMbI. B nepHO.rr.
OTcellKH, KOnIa .rr.aB.i1eHUe B CHCTeMe YMeHblilaeTcH, TOnJ1HBO, C)Ka-
Toe B YKa3aHHbIX 06'beIVIaX, Hal(HHaeT paClllHpHTbCH, C03.n:aBaH ero
.n.onOJIHHTeJlbHYIO no.rr.a1JY B ll.H.1HH.n.p .rr.BHraTeJIH. OTCIO.II.a c.'le.rr.yeT,
liTO B nepHO.n: B03paCTaHHH .n:aBJIeHHH pa3HOCTb YKa3aHHWX BO.J1H
1I.O.'l)KHa 6bITb OTpHI.(aTe.lbHOH, a B nepHO.n: YMeHbllleHHH .n:aB.1JeHlIH
nOJIO)KHTe.l1bHOH.
B.'lHHHHe OKOH BTY.1KH n.1YH)Kepa CKa3WBaeTCH B TOM, 'ITO Ton-
JIHBO HallHHaeT no.n.aBaTbCH B HarHeTaTeJIbHWH Tpy60npOBOlI. paHb-
llle MOMeHTa nO.1Horo nepeKpbITHH BcaCbIBalOllJ,HX OKOH, a npeKpa-
Ill.aeTCH no.n.alla TOnJ1HBa lIepe3 HeKOTopoe BpeMH nOCJ1e HallaJIa
OTKpbITHH OTcellHbIX OKOH. TaKJIM 06pa30M, 06llJ,eJI3BeCTHaH 4Jop-
MYJIa .n:.'lH onpe.n:eJIeHHH K034J4JJIUHeHTa no.n:allH Ton.'lHBHOH CHCTeMbI
'11 - qu,
1< - fnhaKT
174
HB.'lHeTCH YC.'lOBHOH, TaK KaK npn BbIBO..'!.e 3TOfi cpOpMy.'lbI 6bJ.TI0 C.lJ.e-
.'IaHO .lJ.OnYlUeHne 0 HeB03M0)1<HOCTH nepeTeKaHHH TOn.'lHBa B HarHe-
TaTeJ1bHbII1 Tpy60npOBO.lJ. npE OTKpblTbIX BCaCbIBalOlUHX HJII1 OTCeq-
HbIX OKHaX BTy.1JKH nJ1YHJKepa. OOC.'leJJ.OBaTe.'lbHOCTb paCqeTa
npOI.{eCCa BnpbICKa, II3JIO:iKeHIHaH B pa60Te [5], npaKTlI'leCKH He 113-
MeHH.'laCb. JJ..1H H.'I.1IOCTpalUIIfI C'vleTo.n.OB OI.{eHKII napaMeTpOB npOI.{ec-
ca BnpbICKa II KaqeCTBa pa60TbI Ton.'lHBHOH CIICTeMbI (0603Ha t IHM
::ny Ton.1IIBHYIO CIICTeMY TH)I Hal\m HcnO.1b30BaHbI pe3YJIbTaTbI pac-
4eTa npOI.{ecca BnpbICKa Ton..1.HBa O..'!.Horo H3 6blCTPOXO.n.HbIX OTetJe-
CTBeHHbIX ..'!.H3e.1eii (Ta6.'1. 4, )5).
KaK H3BeCTHO, n.10lUa.n.b no..'!. KpIIBOH H31\IeHeHIIH 06'beC'vIHoH CKO-
pOCTH BO Bpel\1eHII onpe.n.e:'IH1eT pacxo.lI. )KH..'!.KOCTIL 003T0I\1)' npHBe-
.n.eHHbJe B Ta6J1. 4, 5 .n.aHHbJe n03BO.15HOT nOCTpmITb 06lUHH JJ,.'IH C1I-
Ta6Jlu/1a 4
PaC'ICT npoll.\ecca BnpblcKa Y Hacoca
LlaHo: d n = 14 M.tl. fn= 1,54, il!= 1000 C6!.tWH, L=756.tUI, d T =2,5 .tUI;
pacnlbl.lIlTc.lb 8 X 0,35
Cn, P II , P'N' F(tj. ilK' C K , Vii" C.tt S t \\7 (t).
",0 KT /a,,- '0'
CAt CCK Kr:c_ 2 Kr:c.- 2 ell cuJceK C.- t8 Kr;Clo'-
23 - 3,0 - - - - - -
24 124,5 6,£8 - - - 2.29 0,085 -
25 131,0 9,9 - - - 2,85 0,070 -
26 137,5 15,5 - - - 2,22 0,050 -
27 144,3 36,2 - - - 2,18 0,030 -
28 233,5 £0,0 81,0 11,0 0,0016 32,0 2,14 0.016 -
29 158,5 159,5 144,2 74,8 0,0260 261,0 2,10 0,063 -
30 165,5 253,0 230,2 160,2 0,0787 371,0 2,05 - -
31 172,5 341,0 322,0 271,0 0,1539 531,0 2,01 - -
32 179,3 406,2 406,2 336,2 0,21£0 252,0 1,96 - -
33 186,7 470,4 470,4 400,4 0,2738 404,0 1,92 - -
34 194,2 548,0 548,0 478,0 0,3174 119,0 1,87 - -
35 202,0 620,0 620,0 550.,0 0,3499 271,0 1,82 - -
36 210,0 673,0 673,0 603.,0 0,3665 99,5 1,76 - -
37 217,5 741,0 - 616.,0 0,3712 28,4 1,71 - -55,0
38 225,5 798,0 798,0 715.,7 0,3638 - 1,66 - -12,3
39 233,5 776,0 776,0 795,,0 0,3355 - 1.61 - 89,0
40 242,0 764,0 764,0 745 0,2965 - 1;55 - 51,0
41 250,0 798,0 798,0 719,,4 0,2487 - 1,50 - -8,6
42 236,5 740,0 740,0 625.0 0,1911 - 1,44 - -35,0
42,5 224,0 682,0 682 563.5 0,1600 - 1,38 0,920 -48,5
43,5 218,0 487,0 471,7 307.0 0,1153 -776,0 1,35 0,032 -!N,O
44,5 206,5 259,0 256,4 72.4 0,0652 -445,0 1,29 0,044 -114,0
45,5 195,0 103,0 92,0 -109.0 -0,012 - 1.23 - -131.0
46,5 - - 108,0 -132.0 - - - - -170,0
47,5 - - 199,0 -.79.0 - - - - -208.0
48,5 - -- 323,0 55,,0 - -- - - -1£'8,0
49,5 - - 376,5 180,,5 - - - - -176,0
50,5 - - 383,0 167,,0 - - - - -145,0
175
Ta6Au/{a 5
PaCqeT npo ecca BnpblCKa y IjIOPCYHKH
JJ;aHo: d n = 14 ,\UI, n = 1000 06/ MUH, L = 756 _\UI, dr = 2,5 ,ILl!,
paclIblo1lITeJlb 8XO,35
F (1- ). w( t+ .£.). y, c y , P F , k' I! cfccc ,
",0 "1/1' -
, a KT CM l-i-k' CM3!C K
Kr CM 2 KF/c.M 2 CM CM/£'eK KT CM'
31,7 - - - - 70,0 1,0 - -
32,0 11,0 0,2 - - 80,8 1,0 - -
33,3 89,5 -55,0 - - 214,5 1,0 - -
34,0 160,2 -12,3 0,009 53,4 242,5 100,0 0,043 -
35,0 271,0 89,0 0,030 200.0 252,0 138,5 0,55 103,3
35,5 305,0 -. 0,050 721,0 258,6 199,0 0,77 124,0
36,0 336,2 51,0 0,050 0,0 355,0 273,0 0,77 145,5
37,0 400,0 -8,6 0,050 0,0 479,0 369,0 0,77 169,0
38,0 478,0 -35,0 0,050 0,0 583,0 449,0 0,77 186,5
39,0 550,0 -74,0 0.050 0,0 694,0 535,0 0,77 203,5
40,0 603,0 -104,5 0,050 0,0 777,5 587,0 0,77 213,0
41,0 616,0 -120,0 0,050 0,0 806,0 620,0 0,77 219,0
42,0 715,7 147,5 0,050 0.0 933,0 718,0 0,77 236,0
43,0 795,0 -205,0 0,050 0,0 J071 ,0 826,0 0,77 253,5
44,0 745,0 -209,0 0,050 0,0 1024,0 790,0 0,77 242,0
45,0 719,4 -188,0 0,050 0,0 977,5 752,0 0,77 242,0
46,0 625,0 -146,0 0,050 0.0 841,0 648,0 0,77 224,0
47,0 473,0 71,0 0.050 0,0 614,0 472,0 0,77 191,0
48,0 200,0 11,0 0,050 0,0 259,0 199,5 0.77 124,0
48,2 - - 0,050 0,0 201,0 154,8 0,77 109,5
49,2 -70,0 -70,0 0,020 -180 70,0 24,5 0.35 43,6
49,5 -107,5 -61,0 0,008 -304 23,5 1,9 0,08 12,1
49,7 -120,0 -50,0 0,000 0,0 0,0 0,0 0,00 0,0
CTeMbI 6a.'1aHC TomUIBa [5]. ll.HarpaMMa 6a.'1aHCa Ton.'IHBa (pHC. 63)
n03BO.'UleT yCTaHoBHTb, B KaKHe MOMeHTbI BpeMeHII II Kal': I1CKa>KaIOT
npOI.(eCC BnpbICKa OT.rr.e.'IbHbIe <j:JaKTOpbI. Ha pHC. 63 EO.'IIIqeCTBO
Ton.TIHBa, BbITeCHe.HHoro n.'IYH>Kepo:\I Hacoca, 3allITpMXOBaHo np5I-
MbIMM, napa.TI"TJeJ'IbHbIMM OCM a6cI.(lIcc, a KO.1WIeCTBO Ton.'1IIBa, BnpbIc-
HYToe <j:JOPCYHKOH,- np5IMbIMII, napa.'I.'Ie.'1bHbIMIi OCII Op.rr.IIHaT.
Ha pUC. 64 nOKa38Ha 3aBUCHMOCTb BO.1H .rr.aB"leHIl5I F (t) II
L
W(t + - ) OT yr.la nOBopoTa Ba.la Hacoca, nOCTpOeHHa5I no pac-
a
qeTHbIM .laHHbIM Ta6.1I. 4, 5. 1-13 puc. 64 C.il, e.rr.yeT qTO a l\m.1IIlTy.rr.bl
oTpaLKeHHblx BOJIH H3MeHSIIOTCSI B llllIpOKIIX npe.rr.eJ1ax (OT + 180
.J,O - 420 Kr;CM 2 ), CJ1eJJ:OBaTe.lIbHO, oTpaLKeHHble BO.IIHbI B .rr.aHHOM
cJ1yqae OKa3bIBalOT Ha xapaKTepIlcTlIKY BnpbIcKa 3aMeTHoe B.1Il5IHlle.
3aBlIcIIMoCTII, 11300pmKeHHbIe Ha pIlC. 64, .rr.alOT B03MO)KHOCTb
onpe.rr.eJUITb xapaKTep npoTeKaHIUI npou.ecca BnpbIcKa no ,LJ:Jume
HarneTaTe.1JbHOro TpyoonpOBO.LJ.8 .LJ.JISI pa3JIHQHbIX Mo!\teHTOB Bpel\IeHH,
a TaK>Ke B pa3JUIQHbIX ceQeHll5IX TpyoonpOBOJI.a. CooTBeTcTBYIOIlI.lIe
3aBliClIMOCTil l\WrYT OblTb nOCTpoeHbI no .J,lIarpal\lMe-CeTKe HJIlI ny-
TeM HenocpeJl,CTBeHHoro onp JI,eJI€HHSI aMnJ1IITYJl, BOJIH Jl,aBJIeHIISI.
176
.£{HarpaMMa BOJ1H )1aB.TIeHHH (pnc. 65) CTpOllTCH B KoopAIIHaTax
t L (BpeMH, )1.rIIIHa Tpy60npoBo.n:a). 80.1Ha F(t), B03Hi1I\alOll.{aH y
t
Hacoca, 3a Bpe:\IH -lI.OCTHraeT pacnbI.1HBalOll.{Hx.oTBepCTHH, a BO.1-
a
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(I
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200
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50
0 20
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-f50
-200
-250
-300
-350
-400
-450
-500
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PHC. 63. TOn.TJIIBllbIi1 6a.1aHC CHC-
TCMbI npll BnpbIcKc
ca. Pa3pe3a5I ,lJ,HarpaM:\IY (pnc. 65) no
ropH30HTa.1H, MO)J\HO nOJ1YlJI1Tb xapaK-
Tep npOTeKaHI1H npo ecca B CHCTeMe
.lI.rI5I BbI6paHHoro MOMeHTa BpeMeHH. a
pa3pe3a5I ee no BepTHKa.rIH,- npoTeKa-
HHe npo ecca BO BpeMeHH B BbI6paH-
HOl\I CelJeHHH. 3Ha 1 IeHH5I aMn.1HTY.lI
BO.TJ:H ,lJ,aB.TJ:eHHH HaHeceHbl Ha ceTKe
,lJ,.rI5I BOJ1H F (t) B npaBoi'! lJaCTH, a .lIJ1H
BO.TJ:H W (t) - B .rIeBoi'! lJaCTH .lIHarpaM-
F(t)Kr/c1'!2
I
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400
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-zoo
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PIIC. 64. 3aBHcHMoCTb aMn.1HTY.D:b! BOJIH
L
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u
BopoTa BaJIa Hacoca:
, - F(t): 2 - Ir-(t + -;-)
MbI. YKa3aHHbIe XapaKTepHCTHKH npo ecca MO}KHO nOTpOHTb, TaK-
)J e HCn0J1b3)'5I 3aBHCHMOCTH, H306pa>KeHHble Ha pHC. 64. HanpH-
Mep, B CelJeHHH Tpy6onpOBO.lIa, KOTopoe Bbl6paHo Ha paCCT05lHHH
Lt OT Hacoca B MOMeHT t, .lIaBJ1eHHe H CKOpOCTb 6Y,lJ,YT onpe,lJ,e.n:HTb-
('51 <popMy.TJ:aMI1
PTLI=Po+F(t- I )-\\7(t+ tdLI ); (217)
C rLI = a [F(t- 1 )+W(t+ Ld L, )]. (217a)
12 3aK<13 748
177
Bblpa3HB Bpe:\1H B rpallycax yrJla nOBOpOTa Ba.1a HaCOCa, :\lmKHO
HalITH, liTO OT HaCOCa K Ce'ieHlIlO L 1 B l\IOMeHT t nOJJ.OH,rr,eT BO.1Ha,
6L
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- a
BO.1Ha, 06pa30BaBIUa5IC5I TaM B l\WMeHT
3TH BO.1HbI HaxOAHT no .lI.HarpaMMaM Ha pHC. 64
HJ1H 65. Ha pHC. 66 nOKa3aHa 3a-
BHCHMOCTb .lI.aBJ1eHH5I Tonmma OT
yr la nOBopoTa BaJIa Hacoca .lI.JUJ.
pa3.1H'iHbIX CeI.JeHHH HarHeTa-
Te.lbHoro Tpy60npOBO.Il.a. 113
8Ha.'1H3a npliBe.lI.eHHbIX 3aBHCH-
MOCTelI c.1e.lI.yeT, liTO npou:eCCbI B
pa3. T m'iHbIX ce'IeHH5IX HarHeTa-
re.lbHoro Tpy60npoBOlla CllBI1ra-
IOTC5I no <pa3e H HeCKOJ1bKO BH.lI.O-
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( 6(L-L))
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PHC. 65. JI.HarpaMMa-ccTKa BO.'1H .!J.aB.TJC-
HH5I
/JKf/cM 2
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800
600
400
200
PHC. 66. 3aBHcHMoCTb .D:aBJlCHHH
Ton.1l1Ba OT yr.1a rroBopoTa BaJla Ha-
coca B pa3.1H41lbIX CC4CHH5IX HarHe-
TaTCJ1bHoro Tpy60npOBO.D:a:
1 - 30 c." OT Hacoca; 2 - 47 CJr OT
Hacoca; 3 - 80 C...1-l OT Hacoca
H3MeH5IIOTC5I. B CeI.JeHliH LI = 47 CJ'rt OT Hacoca B03HHKaeT pa3pbIB
CnJ10111HOCTH .Il.BIUKeHlI5I JKH.lI.KOCTH, npO.lI.0.'IJKaIOIlI.HHC5I CBbIllle 3°
yrJIa nOBopOTa BaJIa Hacoca.
flpouecc paCC'iHTbIBaJIC5I no e.Il.HHOH MeTO.Il.IIKe, a l\laTe:\IaTWIe-
CKHe .rr.eHCTBH5I C nO lY'iaIOIlI.HMHC5I npH pa3pbIBe CnJIOlllHOCTH OTPH-
u:aTe.lbHbIMH .Il.aB.TIeHIf5IMH npOIf3BO.LJ}fJ1IfCb TaK )Ke, KaK C peaJIbHO
CYIll.eCTBYIOIlI.HMH napaMeTpaMH. B BbIXO.Il.HOM CeI.JeIHIH HarHeTaTe.lb-
Horo Tpy60npoBolla pa3pblB CnJ10111HOCTH npaKTH'ieCKH COBnalla.'1 C
MO:\leHTOM nocallKH HrJlbI Ha Ce.lI.oIlO. OllHaKo Ha paCCT05IH:m L[ =
= 30 CM OT Hacoca BO BpeM5I npou.ecca BnpbICKa pa3pbIBOB CJ1.TIOlll-
HOCTH nOTOKa TonollHBa He Ha6J1IO.lI.a 10Cb. TaKI1e pa3pbIBbI MorYT
178
nOHBHTbC5I II B 3TOl\1 CeqeHHH, HO Ha npOl.l.eCC BnpbICKa OHH BJIH5ITb
y:tKe He 6y.n.YT.
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60npOBO;:J.a B pa3.:lHlJHbIe l\IO.'IfeHTbI npol.l.ecca BnpbICKa nOKa3aHO Ha
-puc. 67. Cor.lacHo 3aBHCIL\lOCTHl\l Ha pHC. 67 B Tpy60npoBo;:J.e pa3-
pblB cn lOIllHOCTH MO:tKeT HacTynHTb TOJIbKO npH !p = 50,5° Ha .n.o-
BO,;'lbHO 60JlblllOM YlJaCTKe (aT 70 .n.o 80 Cjw). TaKoH pa3pblB CnJIOIll-
HOCTH .n.O.1J:tKeH 3aMeTHO B,,'IHHTb Ha <POpMHpoBaHHe OCTaTOlJHOrO
.n.aB.TIeHHH, a CJIen:OBaTe.TIb-
HO, H Ha nocJIe.n.YIOI.UHH
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lJeT KOJIe6aHHM .n.aB.'IeHHH
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MY Be.'IlJIUlHa po onpe.n:eJIH-
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Ha pHC. 68 H306pa:tKeH
..'I:HarpaMMbI, nOKa3bIBalO-
He H3MeHeHHe CKOpOCTH TOnJ1HBa C T no .n:mme HarHeTaTeJIbHOrO
Tpy60npoBo.n: a . Ope.n: e J1b) H3MeHeHH5I CKOpOCTH OlJeHb BeJIHKH, oco-
oeHHO B I{OHll.e npol.l.ecca BnpblcKa .!1.JIH 46,5 H 50,5° yrJIa nOBopoTa
Ba.'la Hacoca. Pe3KHe nepexo.n.bI 01' CHH:tKeHHH CKOpOCTH C T K B03-
paCTaHHIO, OT nOJIO:tKHTeJIbHbIX cKopocTeM K oTpHll.aTeJ1bHbIM 3a-
TPY..'I:HHIOT onpe.n:eJleHHe cpe.n:HeH CKOpOCTH C T no .n:JIHHe Tpy60npo-
BOlI,a. 003TOMY rHlI,paBJIHlJeCKOe conpOTHBJIeHHe Tpy60npoBo.n:a,
BbllJHCJ1eHHOe no cpe.n:HeH CKOpOCTH Ton.TIHBa, 51BJIHeTCH BeCbMa npH-
6.'IH:tKeHHbIM.
AHamI3 TeOpeTlILJeCKOrO paClJeTa npou.ecca BnpbICKa n03BO.:1H.'1
YCTaHoBHTb TaKHe oc06eHHocTH era npoTeKaHHH, KOTopbIe .3KCnepH-
MeHTa.'1bHbIM nYTeM B HaCT05lI.Uee BpeMH onpe.n:eJIHTb HeB03MOIKHO.
OCHoBHbIe paClJeTHble napaMeTpbI' npou.ecca BnpbICKa (MaKCHMaJIb-
12* 179
P T XrjC/1 2
1000
900
800
200
100
o
so
70 L CM
60
PI1C. 67. (13McHcHlle ,AaB.TJCIlIIH Ton.1l1Ba B
pa3 I1'-1Hble MOMCHTbI BpCMCHI1 no .D:.TJHHC
HarHCTaTCJlbHOrO Tpy60npoBoAa
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.n.aHHbIMH. .II.J1H nOJlHOH OIJ,eHKU Ka4eCTBa pa60Tbl Ton"lHBHofI OICTe-
MbI He06xo.n.IfMO npoaHam131IpOBaTb npOIJ,eCC BnpbICKa Ha HeCKO.lb-
KUX peTh:HJliJaX. npIf rICn0J1b30-
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He npe.n.CTaBJ1HIOT OC06bIX 3a-
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113 aHaJlH3a ypaBHeHHH
(216) c.'1en:yeT, ITO B CHCT,e-
Max Henocpen:CTBeHHoro .n.eiI-
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OTKJIOHHIOWHM pacnpe.n.eJle-
Hue TOnJ1HBa BO BpeMeHH OT
3aKOHa, onpen:e.'1Hel\noro npo-
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HB.'1HeTCH CJKaTHe TOIIJlHBa B
06'beMaX V n, V If V!p, Co-
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npou.ecca BnpblcKa 6y.n.eT YMeHbllIaTb 06"beMHYIO CKOpOCTIb no.n.a'HI
Tonmma, TaK KaK l.[aCTb ero OCTaeTCH B 06"beMaX V n, V If V g; B
C1KaTOM COCTOHHHH. Bo BTOpOH nOJlOBHHe npoTeKaHH5I BnpblCKa
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BO, C)KaTOe B YKa3aHHblx 06'beMaX, Hal.[HeT paCllUIp5ITbC5I, YBe.1H4.U-
Ba5I TeM CaJ\IbIM KO.'1H4eCTBO Ton.1HBa, no.n.BO.rI:HMOrO K pacllbImmaro-
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C, Mice/(
50
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PIIC. 68. 113MeHcHHe CKOpOCTH TOn.rmBa C T
no .D:JlHHe HarHeTaTCJlbHOrO Tpy6onpOBO.LI.a
B pa3J1H'-IHbIC MOMeHTbl BpeMeHH
180
2. SnHSlHHE HA XAPAKTEP
TOnnHBOnoAA "IH KO:HE"IHblX
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naHa II Hr"lbI <j)OPCYHKH). ECJ1H BeJ1H1JHHbI a6"beJlWB V 11. H V' 3Ha.
H
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6a"lblllHHCTBa TllDaB Tan.mIBHbIX CHCTeJII Henacpe.n:CTBeHHara .n:eiI-
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neplIa;l.a Bo,3paCTaHlIH .n:aB.'1eHIIf! C.>KH:Vlae!\IaCTb TanoJ1HBa (5YAeT
YMeHblllaTb KaK a;VID"lHTY.J.Y HaqaJ1bHara IIMnYJ1bCa, TaK II KO.JIHqe-
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paBHa HY.'IlO.
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OKaTae B 06"beMe V:' aCTaHeTCH B "lHHHH HarHeTaHliH H 4aCTb
ero eI.IJ;e Ma.>KeT 6bITb na.n:aHa B UI1.'IIlH.II-P .lI.BUraTeJJH. Ca3.n:aJJaCb
MHeHIIe, 1JTO 1JeM 6a.'1bllle BeJ1U1JUHa a6"beMOB cHCTe 1bI, TeM MeHbllle
ee npou3Bo.n:HTe.'1bHaCTb. O.n:HaKO anblT 3Taro He no.n:TBep.>K.n:ae'T.
Ha pUC. 69, a, 6 naKa3aHa 3aBliCHMaCTb UUK.laBaR na,.n:a1Jn
TOnJJUBa qv, aT BeJ1H1JHHbI a6"be?1a V:' nocTpaeHHaH no, ,Il,aHHbIM
10. r. BaTJ1HHa [51]. Cor.'IaCHO pUC. 69 Be.'IH1JUHa qv, pe3Ka YMeHb-
rnaeTCH np11 YBe.'1H1JemlH o,6"beMa V TOJJbKa.n:a onpe.n:e.l1eHHo,ro
era 3Ha1JeHmI (B paccMaTpuBaeMaM c"lY1Jae.n:a V 4 -7- 5 ,CM 3 ),
181
nOCJle IIero BJIHHHHe ::Horo 4>aKTopa Ha q'i 3Ha lJHTe.lbHO Yl\ieHbllla-
eTCH II CTaHOBHTCH TeM I\IeHbllle, IIeM I\IeHbllle lJHC 10 060pOTOB Ba.la
TonJ1HBHoro Hacoca. DpH BbICOKHX 060pOTax (n = 1200 o6jJ\tuli)
BJIHHHHe 06'beMa V Ha qv, TIpeKpaIIl.aeTcH TIOC le Toro, KaK 06'beM
V ;:::: 38 CM 3 , npH n 800 o6jMUH B.:1IIHHHe 06'be!\1a V Ha qv,
npaKTHIIecKH npeKpaIIl.aeTcH npH V ;:::: 5 CM 3 . DO-BH,lI.HMOMY, 3TO
HBJIHeTCH cne,n:CTBHeM 3aBIICIIMOCTII OT Be,IJIIIIIIHbI V ,n:BYX napa-
MeTpoB: KO,'1IIlJeCTBa TOn,'IIIBB. OCTBlOIIl.erOCH B mIHHlI HBrHeTBHHfI
dp
BC)KaTOM COCTOfIHlUf, H BeJ1HIIHHbI np0I13BOllHOH
dt
q,./'Iff/lfUK/J
75
95
85
E5
55
95
o 8 IE 24 12 40 48 v; CH f 0 8
0)
16 24 J2 40 48 vtpCH.J
0)
PIIC. 69. 3aBllcIIllloCTb BeJIII'lIlHbl q1J npH h a ".. = 18 MAt:
a - OT 06."eMa V ; 6 - OT 06."eMa V tfJ; 1 - 11 - 300 06/MUli; 2 - n 600 06/MUIi;
3 - n = 800 06{MUH; 4 - 11 1200 o6/ft!U1I
DOKa KO,IJI1IIeCTBO TOn.!lI1Ba, OCTalOIIl.erOCH B 06'beMe V: B
C)KaTOM COCTOHHI1I1, MeHbllle qv" BeJ1I1IIHHa 3TOrO napaMeTpa 6y,n:eT
CYIIl.eCTBeHHO 3aBHCeTb OT Be,IJHIIHHbI V , TaK KaK 3HalJHTeJlbHaH
IIaCTb nepHO,n:a BnpbICKa TOn,'1HBa OpOTeKaeT BO BpeMH XO.LI.a OJ1YH-
)Kepa, BC.le,n:CTBIIe IIerO OKHl\1aeI\IOCTb TOTI.'1HBa B 06'beMe V t
CHH)KaH CKOpOCTb nOllalJH TOTImma, 6Y.LI.eT Te:M CaMbIM 3al\1eTHO
YMeHblllaTb BenHlJHHY qv,. .rr.eHCTBIITe lbHO, npH V = 5 CJu 3 , npI1HHB
a = 0,00008 CM 2 jKT, P; max = 300 KTjCM 2 , nOJ1YIIHM
I1V = aV p: =0,00008.5.300 = 0,12 C.M 3 ,
T. e. KOJ1HlJeCTBO TOn<1HBa, C)KaTOrO B 06'beMe V ' Y)Ke 3HBIIHTeJlb-
HO npeBbIlilaeT BemIlJHHy q'l' B TaKHX YC.l0BI1HX 60JlblllaH lIaCTb
TOOJ1I1Ba BnpbIcKIlBaeTcH B pe3YJ1bTaTe paclllHpeHlIH ero 113 06'beMa
V . B 3T0l\1 c.;lYlJae Be,IJI1III1Ha qv, 6y.n:eT 3aBI1CeTb OT TOro, HaCKO.lb-
KO p max npeBbIIllaeT pifJO II .LI.BB.'IeHlIe nOca.LI.KI1 Hf.lbI. fIpH 60JIblliOM
P max ' HanpHMep, TIpn n = 1200 06jJ\/UH (CM. pnc. 69), Be,IJnIII1Ha
182
qv" KaK nOKa3bIBaeT OnblT, B03paCTaeT. 3aTeM B AHana30He OT
V = 25 CM 3 .n.o V = 38 C.M 3 BemPlHHa q"4 YMeHbwaeTCH .n.o
3HaqeHHH V = 5 -7- 6 C,ff 3 H .n.a.'Iee 3Ta BeJIHqHHa npaKTWIeCKH co-
xpaHHeTcH HeH3 IeHHoH. He3aBHcIDIOCTb q"4 OT Be.'lIlqnHbI V YKa-
3bIBaeT Ha TO, 'ITO PH max He3Ha'll1Te.'lbHO npeBbIWaeT PrjJO. 113
pHC. 69, a CJ1eJI.yeT, 'ITO npn n :::s; 800 06(MUH. JI.aB.'IeHI[e P : max TaK
;\1a.10 npeBbIwaeT Be lH'IHHy PrjJo, 'ITO Y)J{e npIl V > 5 CM 3 BeJ1HllU-
Ha q"4 CT3HOBHTCH He 33BHCHMOi"[ aT 06"beMa V .
B.'IHHHne BemIllIlHbI 06"beMOB (V., + V ) H3 alVm lI1TYD:Y BO.'IHbI
F (t), a, CJ1e.n.OBaTe.J1bHO, II Ha F (t _!::.... ), a TaKLli:e Ha JI.aB.TJp.Hlle
a
prjj MO)J{HO OIleHIlTb no .n.llarpaMMaM Ha
pliC. 70. Cor J1aCHO pHC. 70 YBe.'IHlleHHe
CYMMbI YKa3aHHbIx 06"beMOB B 4 pa3a (OT
2 .n.o 8 c,u 3 ) YMeHbllI3eT 3MnmlTY.n.y BOJI-
L
HbI F(t --) Ha 19%, a .n.aBJIeHile prjJ Ha
a
21,5%. Cor.TJaCHO npllBe.n.eHHblM .n.aHHbIM
.n.aB leHHe Ton.'IHBa H3MeHHeTCH XOTH H
3aMeTHO, HO Bce )Ke B 3Hall1lTeJ1bHO MeHb-
weH CTeneHH, lleM BeJ1HllHHa 06"beMa
( V., + V: ).
B TOM CJ1YlIae, KOr.n.a Be llllIHHa 06"be-
Ma V rjJ 6y.n.eT CYIII.eCTBeHHO npeBbIWaTb
Be.'IHlIHHY 06"beMOB (V., + V ), 60J1bWaSI
lIaCTb OKaTOrO TOnJIHBa cOCpe.n.OTOlIIiTCH
B 06"beMe V rjj, paCn0J10)J{eHHOM OKOJIO
paCnblJ'IliBalOIII.IlX OTBepCTHH. B paCCMaT-
pliBaeMbIX YCJ10BIlHX nOC.TIe HalIa:1a OTcelIKIl paCllIHpeHlle Tonmma
B 06"beMe VrjJ 6y.n.eT YCKOPHTb noca.n.KY Ha ce.n.JIO HarHeTaTeJIbHOrO
Ji:,;'IanaHa H 3an.ep)J{HBaTb pa3rpY3KY ,cHcTeMbI, coxpaHHH Be lHlIIiHY
n.aB 'IeHHH prjJ Ha BbICOKOM ypoBHe, lITO BbI30BeT YBe.'IlilIeHHe nepnO.lI.a
OTKpbITHH HrJIbI <P0PCYHKH. EC.'IH B CUCTeMe C 06bILIHOH 3aKpbIToi"I
<P0PCYHI\OH: npH 1l3MeHeHIlH 06"beMa V rjJ BeJIlllIliHY q1f coxpaHHTb He-
H3:\IeHHOH, TO, KaK c.TJe.n.yeT 113 pliC. 71, 06"beMHaH CKOpOCTb nOJI.alIli
YMeHbwaeTcH, npo.n.o.'I)J{HTe.'IbHOCTb BnpbIcKa B03pacTaeT, a caM npo-
uecc CMeIII.aeTCH no <p33e B CTOPOHY YBe:'I1IlIeHHH BpeMeHH 33na3.lI.bI-
BaHHH.
113 .n.narpaMM Ha pHC. 71 BHn.HO, lITO YBemIlIeHHe 06"beMa V rjJ
6o,;'Iee 3al\1eTHO I1CKa)J{aeT xa paKTepHcnIKY BnpbIcKa, lIel\I H3MeHeHHe
06"beMa V . . DbI.TIO npoBepeHo B.'UIHHIIe Ha xapaKTepIlcTHKy BnpbIC-
1\3 o6"be:\1a V rjJ npll pa3.'IlIlIHbIX HalIa.'lbHbIX YCJIOBH5J.X: npll Po =
= 52 KrtCM 2 H Po = 0, T. e. Korn.a B CHCTeMe 06"beM V oe =
= 0,0065 CM 3 . Pe3YJ1bTaTbI npOBepKIl nOKa3aHbI Ha pHC. 71, H3
KOToporo CJ1e.n.yeT, lITO npll HaJIIllIHII OCTaTOlIHoro 06"beMa HeCKOJ'Ib-
KO YM HblllaeTCH npOIl3Bo.lI.I1TeJ1bHOCTb Ton lHBHoii CIiCTeMbI II
500
2
4
PHC. 70. 3aBHCII1I10CTb .D:aB.TJC-
L
HHfI Pifi H BO.'1Hb! F(t--) OT
a
BeJlH'-IHHbl 06"bCMa V u:
J - JJ.aB. eHHe P t/J: 2 - BO_18a
p(t --;-)
183
C,lI,BHraeTCH B CTOPOHY 3ana3,J,bIBaHlIH Ha4aJ1a BnpbICKa. ct>Op?lIa )Ke
XapaKTepHCTHKII BnpbICKa 11 MOl\IeHT OKOH4aHHH nOJJ,a4H TOn.JllIBa
.0CTaIOTCH npaKTH4eCKH HeH3:\IeHHbIMH.
)],.'151 ou.eHKH 3aBIfCH"'lOCTH B.1HHHHH 06'beMa V g; 11 KOHCTPYKUIUI
cpOPCYHKH Ha 3aKOH nO,LI,a4H TOnnHBa paCOIOTpHl\I npou.ecc BnpbICKa
TOnJ1I1BHOH CHCTeMbi C lllT1IcpTOBOH cpOPCYHKOI1. 113-3a Ha.1H4IIH
lllT1IcpTa Be.1H4HHa npOXOJJ,HOH n.'10Ill,aJJ,H paCnbIJUlTeJ1H HeLKO.'1bKO
3aBbIllleHa no cpaBHeHHIO C 3aKpbITOH cpOPCYHKOH, KpOllIe TOro,
BeJ1If4HHa npOXOJJ,HOM nJ10Ill,aJJ,H pacnbI-
JIHTeJIH 3aBHCHT OT nOJJ,'beMa Hr.'lbI.
3TH KOHCTPYKTHBHbIe oc06eHHOCTH
cpOPCYHKH C03JJ,a1OT BO BpeMH npou.ec-
ca BnpbICKa 4aCTbIe nepHO,lI,bI ,.1,lIc6a-
J1aHCa Me)KJJ,Y nOABO,LI,HMbIM H BnpbIC-
KHBaeMbIM TOnJIHBOM, BCJIeJJ,CTBHe 4ero
KpHBaH H3MeHeHHH .lI.aBJ1eHHH H xapaK-
TepHCTHKa BnpbICKa HMelOT HBHO BbI-
pa:tKeHHbIH Ko.1Je6aTe.'lbHbIH xapaKTep,
a noc.'le OKOHLJaIUlH npou.ecca BnpbICKa
B CHCTeMe B 60.'IblllHHCTBe c.'IY4aeB 06-
pa3yeTcH pa3pell{eHHe, T. e. HeKOTO-
pbIM cB060JJ,HbIH 06'beM, He 3anO.'lHeH-
HbIH TOn,;'IHBOM.
Ton.'IHBO, HaXO.ll.HIlI,eeCH B 06'beMe
V g; B C.iK8TOM COCTOHHffH, rrpu B03HHK-
HOBeHHII JJ.Hc6a.laHca Ha4IIHaeT pac-
llIIIpHTbCH II TeM caMbIM HeCKonbKO
YMeHblllaTb Bem-I4HHY 3Toro JJ.IIc6a-
,'laHca. OTCIO,lI,a CJ1e.ll.yeT, 4TO npH YBe-
,;lII4eHIIII 06'beMa V g; MO:tKHO 3Ha4II-
Te.'lbHO Yl\IeHblllIITb Ko.1Je6aHHH JJ.aB.le-
HIIH TOnJ1HBa II IIr.'lbI cpOPCYHKII H TeM
caMbIM 06ecne4HTb 60JIbillee BpeMH ce4eHIIH BbIXOJJ.Horo OTBepCTIIH
H 60JIbillee cpeJJ,Hee .lI.aBJIeHHe BnpbICKa. 3TO 06CTOHTeJIbCTBO MO)KeT
3aMeTHO YMeHblllIITb npO.ll.O'-'DKHTe.'IbHOCTb nO.ll.a 1H TOnJIHBa H YJIY4-
llIHTb Ha YKa3aHHbIX pe:tKHMaX xapaKTepHCTHK)' BnpbICKa. Ha pHC. 72
H306pa:JKeHbl pac4eTHbIe .lI.HarpaMMbI, nOKa3bIBalOIlI,He B.'lHHHHe 06'b-
eMa V if; Ha xapaKTepHcTHKY BnpbIcKa Ton,;1HBHoH CHCTeMbI C Haco-
COM YTH-5 npH pa60Te ee CO llITHcpTOBOM cpOPCYHKOM, H J1IOCTPHPY-
IOIll,He HeKOTopoe Y.1Y4llIeHHe napaMeTpOB npou.ecca BnpbICKa npH
YBeJ1H4eHHH 06'beMa V rf>. O.II.HaKO 3Ha4HTeJIbHOe B03paCTaHHe 06'be-
Ma V fP 3aMeTHO YMeHbllIaeT MaKCHMa.:IbHYIO Be.1JH4HHY .II.aB.'lemI5I
TOnJIHBa Ha Bcex pe:tKH1IJax pa60TbI TOnJIHBHOH CllCTeMbI H CYIl.I,eCT-
BeHHO YXY.II.llIaeT napaMeTpbI npou.ecca BnpbICKa.
Ha pHC. 69, 6 6bI.'Ia ll306pa:tKeHa 3aBHCHMOCTb q1J. OT BeJ1H4HHbI
06'be:VIa V g; npli pa3,TIH4HbIX 060poTax BaJ1a TOnJUlBHoro Hacoca.
XapaKTep npoTeKaHII5I KpIIBbIX, KaK II npH H3MeHeHHH 06'beMa V '
cYIlI,ecTBeHHo 3aBIICHT OT 4I1C.1Ja 060pOTOB. B pacOrIaTpHBaeMoM CJIY-
184
8
4
8
I;
o
26
PHC. 71. B.TJH5IHHC Ha xapaKTcpH-
CTHKY Bnpb!CKa Be,1H'-IHHb! 06"bC-
Ma V q, H Ha4aJlbHbIX YC.TJOBIli1:
1 - cepHAHaR TonJIHBHaR CHCTeMa
511\\3-236; 2 - TonJIHBHaR CHCTeMa c
V q,= 7 CM'; Po = 52 KT/c,1I'; 3
Ton. HBHaR CJlCTeMa C V I/J 7 c...';
V ocm = 0,0065 c...'
'1ae OnTII?vIaJJbHbIl\I, nO-BH,rUiMOMY, HBJHIeTCH HOl\IHHa.1JbHbIH pe)l{I1:\I
(fl = 800 06/M.UH), rrpIl KOTOpOM C YBeJJW!eHHeM V!fj .10 11 CAt3
Be.1HqHHa q1j B03pacTaeT, a 3aTe I HaqHHaeT Yl\:IeHbIlIaTbcH, npHqe:M
c YBe.1HqeHHel\l 06"beMa V!fj 6o.1bIlIe 36 C.M 3 rrpaKTUqeCKH CTaHOBHTCI1
He 3aBHcHMo.i1 OT :=nOTO napaMeTpa.
XapaKTepHO, 'ITO rrpH n =
= 1200 06/M.UH rrpH YBe.1JHqeHHH V g;
3HaqeHIle q1j Bce BpeMH YMeHbiliaeT-
CH, a rrpH n = 300 06/M.UH xapaKTep
rrpoTeKamuI 3aBHCHMOCTH q1j =
= f (V g;) rrOlI.06eH xapaKTepy rrpo-
TeKaHHH 3aBIlCHMOCTH q1J = f (V ).
.lJ.IlarpaMMbI, Il306pa)KeHHbIe Ha
pIlC. 69, a, 6, YKa3bIBalOT Ha C.1JO)l{-
HYlO 3aBIlCIlMOCTb rrapaMeTpoB rrpo-
u.ecca BrrpbIcKa OT 06"beMOB V H
V H Ha Heo6xo)J.IlMOCTb I13yqHTb
HX lI.OrrOJ1HHTeJJbHO 3KcIIepHMeH-
Ta.1bHO H TeOpeTHqeCKH. OpH cYIlI.e-
cTBYlOIlI.eM COCTOHHHH HCCJJelI.OBa-
HHH 3Toro Borrpoca MO)KHO .iJlUlib
c.u.eJJaTb BbJBO.u., qTO qeM 60JJbIlIe
06"beMbI cHcTeMbI, Tel\I MeHee yn-
paBJJHeM npou.ecc BnpbJCKa. TeM
MeHbilie .u.aBJ1eHHe BnpblcKa, qTO MO-
)KeT C03.n:8Tb He6.1aronpHHTHbIe yc-
JJOBHH npoTeKaHHH npou.ecca Torr-
JJHBOnOlI.a'IH, oco6eHHo Ha peJKI1MaX
Ma.1bJX n0lI.aq Ii 060pOTOB. 11mI aB-
TOTpaKTopHbIX .zr.H3e.lelI no oco6eHHO onacHo, TaK K8K OHii pa60Ta-
lOT B IlIHpOKOM .iUfana30He H3MeHeHHH IJHCJ1a 060pOTOB H HarpY30K.
'1 M,.,Yzpai!
15
10
5
29 JI
97'
JJ
PUC. 72. B.1HHHHC BC.'1I1'-1HHbI 06c-
CMa V rJj IllTIlIj:JTOBOi1 Ij:J0PCYHKH
Ha xapaKTcpllcTHKY BnpblcKa npll
Q'I = const = 73 .1I_JI 3 :
1 - V 1/1- 0,5 CM'; 2 - V'P= 4,5 c.,,,
3. ponb nnYH)f(EPHOA nAPbl TOnnHBHOrO HACOCA
H npOCl)HnSi TonnHBHoro KynA'IKA
B npOLtECCE BnPblCKA TonnUBA
Cor.1aCHO ypaBHeHHlO (216) OCHOBHbDI q.;leHOl\I TonmlBHoro
6a.'IaHCa 11:.151 BCeH CHCTeMbI, xap8J<TepJI3YlOIIJ:HM nOCTYJ1J"JeHHe
TOnmIBa B Ka:\lepy HarHeTaH1111 HaCOCa, HB.1HeTCH np0I13Be.zr.eHHe
{nCn, T. e. CKOpOCTb H3J\IeHeHHH 06"beMa, OnHCbIBael\lOrO rr,1JYH)I{epOM
npH era .n:BIf)KeHiflI. BCJJe1(CTBHe 3TOro n.;lYH)KepHaH rrapa H npo.
cpII.1Jb TonJ1I1BHOrO KY.;laqKa, onpe.zr.e.'UllOIIJ:I1H xa paKTep II3MeHeHHSI
CKOpOCHI Cn, OK83bIBalOT Ha cpOPMIfpOB8HlIe Xapal<TeplfCTHKH
BnpbICKa 60.1bIlIoe B.1HI1HHe. Iho6bI YCIJ.'IHTb 3TO BJJHI1HHe, Heo6xo-
lI.Ill\W YMeHbIlIHTb 06"belllbI CHCTeMbi. EC.1JH 06"beJ\IbJ V n If V BeJ1lIKH,
TO, KBK c.1Je.zr.yeT If3 pHC. 73, BCJJe.zr.CTBHe BJJHHHHH C)!{HM8eMOCTH
185
TOnJ1HBa YBeJ1HIleHHe nJlOllI.aJI,II nOnepeI.JHOrO CeI.JeHHH n.'IYH/I epa Ha
33% He BbI3bIBaeT 3aMeTHoro H3MeHeHHH B xapaKTepHCTHKe
BnpbICKa, a CJ1e,lJ.OBaTe.IJbHO, H npOlI3BO,lJ.IlTe.TJbHOCTH CHCTe!\1bI. B
CBH3H C 3THM ycnelilHo <}JOpCHpOBaTb Ton.m1BHYIO CHCTeMY no npo-
1I3BOJ].HTe.lbHOCTII IO)KHO TO.'IbKO nYTeM KO'\ID.'IeKCa Mep, HanpaB-
.TJeHHbIX Ha CHHMeHHe
B.'IHHHHH CMHMaeMOCTH
TonmIBa:
1) VMeHblllHTb 06'be-
MbI V.,: H V ;
2) YMeHblllHTb npo-
H3BOJ].HYIO d p ;
dt
3) YBeJ1HI.JHTb J].Ha-
MeTp nJ1YHMepa d n ;
4) YBeRHI.JHTb CKO-
poeTb J].BHMeHHH nJ1YH-
9'0 Mepa Cn;
5) HeCKORbKO YBeRH-
I.JHTb npOxo.ll.HYIO nJ1O-
ll1.aJ].b pacnblmmalOllI. HX
oTBepcTHI1 fc.
Heo6xo.LUIMOCTb YMeHbllleHHH 06'beMOB V.., H V npH q>OpCH-
pOBaHHH CHCTelllbI no npOII3BO,'UITe.'IbHOCTH nO.ll.TBepMllaeT pIlC. 74,
H3 KOToporo c.'IeJ].yeT, 'lTO npII Ma.'IOII Be.'IH HHe 06'be!\Ia (V "II. + V )
BRHHHHe J].IIaMeTpa n.1JYH/I(epa Ha npOlI3BoDJITe.1JbHOCTb CIICTeMbI,
B03pacTaeT.
YMeHblllHTb Be.'IHI.JIIHY !\IO/ImO nYTel\I HeKoToporo )'Be..'IHI.Je-
HHH cYMMapHoH npOxO.ll.HOH n.'IOllI.a.ll.H pacnbWHBalOll1.IIx oTBepCTHH
fc. OJ].HaKo H3MeHeHHe nOCJleJ:HeIILI.o.'IMHO 6bITb cor.'1aCOBaHO C
pa60I.JHM npoueceoM J].H3e.'IH.
YBemII.JeHHe n.l0ll1.aJ].H fc MOMeT OKa3aTb 'lepe3 oTpaMeHHbIe
dp dp
BORHbI HeKoTopoe Bml5IHHe II Ha -. Ho Ha - 60.lee 3q><}JeK-
dt dt
.
THBHO !\1O}KHO B03J].elICTBOBaTb nYTel\I II31\IeHeHIIH OTHOlllemm -r
'T
HJ1H H3:\IeHemIH CKOpOCTH C n . T. e. npOq>HRH TOnmIBHOrO KY.1JaI.JKa.
u dp
3TH nYTH B03J].eHCTBIIH Ha Be.1IIIJ:IIHY - OLJ:HOBpeMeHHO OKa3bIBa-
dt
lOT 60.'IblllOe B.'IHHHIIe Ha 06ll1.HH XapaKTep npOTeKaHHH BnpbICK3
TOnJ1HBa, n03TOMY B03MOMHOCTH HCnOJIb30BaHIIH HX OrpaHIII.JeHbI.
DpII TaKOM KOM6HHHpOBaHHOM U3MeHelIIIH KOHCTPYI<THBHbIX
napaMeTpOB TOnRHBHOII CHCTel\1bI !\IQ)KHO, KaK nOKa3aHO Ha pHC. 75,
fIpH YBemII.JeHlIII LJ:HaMeTpa d n OT 12 LJ:O 16 J tM. a BemII.JIIHbI fe OT
8 X 0,3 J].O 8 X 0,4 MM YMeHblUIITb npOLJ:OR.?KHTeJ1bHOCTb BnpbIcKa
186
lIt{ ,.,,.,YepaiJ
40
30
20
fO
o
5
fO
f5
20
30
PHC. 73. B.1HHIIHC LIHaMcTpa n.1ymKcpa lIaco-
ca lIa xapaKTcpHcTIIKY Bnpb!CKa Ton.1HBa
01' 18.5 .0,0 L3° yr.la nOBOp01'a Ba.la HaCOCa npll npOH3BO.lune.lbHO-
<:1'H qlj = 0,28 Z/l{UK/l, HJUl npn Hen3MeHHoil npOLLOJDKI-!TeJIbIlOCTH
YBeJIHlUlTb npoH3Bo:l.l-!Te ,bHOC1'b CUCTei\lbI. OLIHaKo B03MOfKIlOCTH
.popcnpOBaHlIH Ton.'1IIBHOH CHCTeMbI
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pa3rpY)KaIOl.l.I.lilI nOSICOK HaXO.l.l.liTCSI B KaHaJIe rHe3Lla, Hendcpe.rr.-
CTBeHHoe nepeTeKaHlie TOnJIliBa H3 06"beMa V1/. B 06"beM V OTCYT-
cTByeT. B 3TO:\I nepHoJJ.e LlaCTb TOnJ1HBa, BbITeCHSIeMaSI n.'IYHLKepOl\1
H3 KaMepbI HarHeTaHHSI, OCTaeTCSI B 06"beMe V1/. B CLKaTOM COCTOSI-
HliH, a OCTa.;lbHoe Tonmmo HJI.eT Ha 3anOJIHeHHe 06"beMa, oCB060LK-
191
.lJ.aeMOro npH .lJ.BmKeHlIH K,JIanaHOM. TaKOH )J(e 06'beM TOnJlHBa
KJ1anaH BbITeCmIeT H3 IllTyu.epa HaCOCa, nplI'IeM O.lJ.Ha 'IaCTb 3TOrO
TOnmlBa nOCTynaeT B HafHeTaTe.lbHbIH. Tpy60npOBO).!., a .lJ.pyraH
OCTaeTCH B 06'be!\le V B OKaTmI COCTOHHIIII. TaKIIM 06pa30M,
B.rHUIHHe KlIanaHa Ha npouecc BnpbICKa B 3TOT nepHO.lJ. ero .lJ.BH)J(e-
HHH 3aK.llO'IaeTCH B TOM, 'ITO CKOpOCTb nocTynJleHHH TonmlBa B
Tpy60npOBO.J. onpeAelUIeTCH CKOpOCTblO .iIBH)J(eHHH KJ1anaHa. Bo
BTOpOM nepIlo.lJ.e .lJ.BH)J(eHIIH. KOr.lJ.a pa3rpY)J(alOI.l.lHH nOSJ.COK Haxo-
.lJ.HTCH BHe KaHaJla rHe3.lJ.a OT !\IOl\leHTa ero BbIXO.lJ.a .D.O Ha'Ia.la OT-
Ce'IKH, B.1I1HHHe HarHeTaTe.llbHOrO KJIanaHa Ha npou.ecc BnpbICKa
Ton.1HBa B U.HJlHH.lJ.pbI .lJ.BHraTeJ1H C Bocn.'IaMeHeHHeM OT C)J(aTHH 6y-
.lJ.eT He3Ha'IHTeJ1bHbIM.
f10CJle OTCe'IKH Tonmmo Ha'IHeT nepeTeKaTb H3 06'bexIa V B
06'beM V H. B 3TOT nepHO.lJ. npollecc BnpbICKa CYI.l.leCTBeHHO 3aBHCIIT
OT CKOpOCTII 06paTHoro .D.BH)J(eHHH K.'IanaHa, T. e. OT npOIJ,o.'IJKH-
TeJ1bHOCTH ero .lJ.BIUKeHHH ,lI.O I\IOMeHTa BXO,ll.a pa3rpY)J(alOI.l.lero
nOHCKa B KaHa.'I rHe3,l1.a. 4eM npo,ll.o.'I)J(HTeJIbHee 3TO .lJ.BH)J(eHHe, TeM
60.'IbIIle H3 JIHHHH HarHeTaHIIH BblTe'IeT TOnJ1HBa 'Iepe3 OTCe'IHbIe
OKHa, 'ITO l\IO)J(eT CYI.l.leCTBeHHO CKa3aTbCH Ha Be.'IH'IHHe OCTaTO'IHOrO
.lJ.aB.leHlIH, C03JI.aBaH 6.1aronpHHTHbIe YC.'IOBHH .lJ.J1H 06pa30BaHHH
OCTaTO'IHbIX 06'beMOB. f1pH 6bICTpOM BXO.lJ.e pa3rpY)KalOI.l.lerO nOSJ.CKa
KJ1anaHa B KaHaJl rHe3JI.a pa3rpY3Ka J1HHHH HarHeTaHHH 4cpe3 OT-
Ce'IHbIe OKHa 6Y.lJ.eT He3Ha'IIlTec1bHOH. B 3TOM CJ1Y'Iae pa3rpY)J(alO-
I.l.lHH nOHCOK ,lI.OJ1)J(eH IIMeTb 60J1bIIlHe pa3l\1epbI. TaK KaK IIHa4e
I\IOrYT B03HIIKHYTb .iI.onOJ1HIHeJ1bHbIe BnpbICKH. TaKHM 06pa301\1, BO
BTOpOM nepIIO,ll.e .lJ.BH)J(eHIIH HarHeTaTe.'IbHbIH K.llanaH MO)J(eT cYI.l.le-
CTBeHHO Bc1HHTb KaK Ha xapaKTep OKOH'IaHHH TeKYI.l.lerO BnpblCKa, TaK
II Ha Ha'Ia.'IbHbIe YC.'IOBHH nOCJ1e.D.YIOI.l.lero BnpbICKa. TpeTHH nepHO.J.
.D.BH)J(eHHSJ. Ha3bIBalOT pa3rpY)J(alOI.l.lIIM XO,ll.OM KJlanaHa. EC.'IH B nOM
nepH011.e eI.l.le npO.lJ.OJI)J(aeTCH BnpbICK TOnJlHBa, TO CKOpOCTb nOCa,ll.KH
KJ1anaHa Ha ce,ll.Jlo TaK)J(e 6Y.lJ.eT B.'IltHTb Ha xapaKTep OKOH'IaHHH
nponecca BnpbICKa. 4el\1 6bICTpee KJ1anaH CH.lJ.eT Ha Ce.lJ.Jl0, TeM
6bICTpee 3aKOH'IHTCSJ. nO.D.a'Ia TOnJ1IlBa. .3TOT nepno,ll. .iI.BII)J(eHHH K.la-
naHa OKOH'IaTeJ1bHO q,opMIIpyeT Ha'IaJlbHbIe ycnoBlIH nOC.le,ll.YIOI.l.lero
BnpbICKa.
C.'Ie.lJ.OBaTeJlbHO, HarHeTaTeJ1bHbIH K.lanaH B OCHOBHOM BJ1HSJ.eT
Ha nponecc oCB060)J(.lJ.eHIIH (pa3rpY3KY) TOnJ1IIBHOH CHCTel\-lbI OT
C)J(aToro B HeH Tonmma. .3TO BmUIHHe 3aBIICIIT OT napaMeTpOB
HarHeTaTe.lbHoro K.lanaHa, 'IlICJ1a 060POTOB, KOHCTPYKTlIBHbIX napa.
MeTpOB n.1YH)J(epHofI napbI II npoq,IIJIH TOnJIlIBHoro I{YJ1a4Ka, KOTO-
pbIe q,OpMlIPYIOT xapaKTep npOTeKaHlIH OTCE'4KII, a Cne.lJ.OBaTeJ1bHO.
'IaCTlI'IHO 1I pa3rpY3KH nlIHlIII HafHeTaHIIH. .n106bIe MepbI no YJ1Y'I-
IIleHHIO xa paKTepHCTIIKII BnpbICKa npn nOMOI.l.lII HarHeTaTe.'IbHoro
KlIanaHa, B OCHOBHOM, onpe.D.eJ1HIOTCH ero B.1nHHIIeM Ha pa3rpY3KY
J1nHnH HarHeTaHnH. HanplIMep, npn YBe.1WIeHlUl 3a30pa Me)J(.D.Y
pa3rpY)J(alOI.l.lIII\I nOHCKOM II CTeHKOH KaHaJla 4aCTb TonmIBa 6Y.D.eT
nepeTeKaTb 'Iepe3 3TOT 3a30p. f103TOMY YCKopeHIIe K.'IanaHa npn
192
BbIXO.lI.e pB3rpYLKaIOlll.erO nOHCKB lI3 KBHBJIB rHe3Aa 6Y.lI.eT He3HaIlH-
Te.1bHbIM, BCJIe.lI.CTBlie 'lerO IWanaH nOJ],HIIMaeTCH Ha He60.1JbIllYlO
BbICOTY, IlTO YMeHbIllIIT pa3rpY3KY J1IIHHII HarReTaHIiH II YBe.1lfllIIT
npOII3BOJ],IITeJIbHOCTb CIiCTeMbI, HO npli 3TOM B03paCTaeT OnaCHOCTb
B03HIIKHOBeHIIH J],OnO,,1HIITe.1JbHbIX BnpbICKOB. 113MeHHTCH TaKLKe
3BBIICIIl'vIOCTb pB3rpY3KH OT 4HCJIB 060POTOB, lITO, B CBOlO OlIepeAb,
lI3J\IeHHT 3BBlICHMOCTb q1.f = f(n). OOJ],06HOe LKe B,,1II5IHHe 6yJ],yT
OKa3bIBaTb YMeHbIlleHHe MaKCHMa.'IbHOro nOJ],'beMa KJ1anaHa, YBeJIII-
1..JeHIIe LKeCTKOCTII H CIiJIbl Ha1..JaJIbHOli 3aTHLKKII npY}KIIHbI K.1JanaHa,
YBe,,'III1..JeHHe II.1JII YMeHbIlleHIIe pa3rpY301..JHOrO xOJ],a KJ1anaHa II J],p.
OnbIT nOKa3bIBaeT [13], 1..JTO J],JIH KaLKJ],oro C01..JeTaHIiH ,meMeHTOB
TonaIIBHOH CHCTeMbl HMeeTC5I CBoe OnTIiMaJIbHOe C01..JeTaHlie napa-
MeTpOB HarHeTaTeJ1bHOrO KJIanaHa.
B COBpeMeHHbIX TOnJ1IIBHbIX CIiCTeMax 60J1bIllOe BHHMaHue y.n.e-
.'I5IeTCH HepaBHOMepHOCTIi no.n.a4H TOnJ1IIBa OT.n.eJ1bHbIMIi cel<UIIHMII
CHCTeMbi. B 3Ha1..JHTeJIbHOli CTeneHII HepaBHOMepHOCTb onpe.n.emleTCH
60.1bIllHMlI KOJIe6aHlIHMlI BeJ1II1..JIIHbI BHYTpeHHero .n.IIaMeTpa HarRe-
TaTe,,1bHoro Tpy60npOBo.n.a 11 3Ha1..JIITeJ1bHbIM pa3HOOOpa3I1eM rH.n.paB-
JIlI1..JeCKIiX xapaKTepHCTHK pBCnbIJIHTe.'IeH. )J,OCTH}KeHlIe npH pery.'IH-
pOBaHHH CHCTeMbI 3B.lI.aHHOH pBBHOMepHOCTH nO.lI.a1..JH TOnJIHBa OT-
J],e.1bHbIMlI ceKUIISlMIi TpeoyeT 3aTpBTbI 3HB1..JIITeJIbHOrO Tpy.n.a II
BpC:\leHII. YCTaHOB.rIeHO, tITO Kor.n.a Po> 0, TO .lI.OBOJIbHO OOJIbIllOe
II3MeHeHIIe BeJ1II1..JIIHbI 3Toro napBMeTpa (npHMepHO Ha 20 --
30 KrjCM 2 ) He OKa3bIBaeT 60JIbIllOrO B.'1IIHHIIH Ha npOII3BOJ],IITe.'1b-
HOCTb CHCTeMbi. OpH YKB3BHHbIX II3MeHeHH5IX BeJIII1..JIIHa q"lf 1I3MeHH-
JIBCb HB 1,5--2,5%. BbIIlle ObI,,10 nOKB3BHO, 4TO nplI nOMOUlH
HarHeTaTe.1JbHOrO KJ1BnaHa MO}KHO CYUleCTBeHHO YBeJ1II1..JHTb 3HB1..Je-
HlIe po II TeM caMbIM 3al\leTHO YMeHbIllIITb BJ1IIHHlIe HB BeJIlJllHHY q"lf
Ko e6aHHH BeJIIItIIIHbI d r H rII.n.paBJ1II'leCKIiX xapaKTepIIcTHK pacnbI-
JIIITeJIeli. HaII60J1ee npocTo H B TO }Ke BpeMSI 1l0CTaT01..JHO 3cpcpeKTIIB-
HO 3TO 06CTOHTeJIbCTBO HCnOJIb3yeTcH nYTeM YBeJII11..JeHHH Ha4aabHOH
3aTH}KKH npYLKHHbl KJIanaHa, BCJ1e.n.CTBIIe Ilero B03paCTaeT J],BB.'1eHHe
p" H YMeHbIllaeTCH npO.lI.OJ1LKHTeJ1bHOCTb BToporo nepIIO.lI.a. n03TOI\IY
OCHOBHaH pa3rpY3Ka CIiCTeMbI npOH3BOJ],HTCH pa3rpY30IlHbIM XO.lI.OM
K.'1anaHa. 3TO npOBepeHO onbITOM, B CBSl3H C tIeM B COBpeMeHHblX
aBTOTpaKTopHbIX .n.H3eJISlX .lI.aB.'1eHHe p" .lI.OCTHraeT 12-16 Krlorl. 2 .
YMeHbIlleHHe IIJ1II B03pacTaHHe BeJIHtIHHbl Lcfc paCnbIJIHTeJIH oy-
,l(eT cnocoocTBoBaTb HeKoTopoMY YBeJ1H4eHIIIO HJIH YMeHbIlleHHlO
BpeMeHH nOCa,l(KH HrJIbI Ha ce.n.JIO, B CB5I3H C 'leM 3TOT cpaKTop
TaKLKe BHOCHT cooTBeTcTBYIOll\ee H3MeHeHHe B pa3rpY3KY .'1IIHHII Ha-
rHeTaHIiH. BmlHHI-Ie KOJIeOBHI-IH BeJIII'lIIHbI cf c B ,l(OnycTHMbIX npe-
,l(e.'Iax Ha npoH3BO,l(IITe.'1bHOCTb ceKUHH no YKa3aHHbIM BbIIlle npH-
lIHHaM 6y.n.eT TeM MeHbUle, tIeM BbIIlle HatIa,,1bHaH 3aTH}KKa npY}KHHbl
HarHeTaTeJIbHOrO KJIanaHa.
BJIIIHHfle Ha<ra.l1bHbIX YCJIOBIIH Ha npouecc BnpbIclw cYll\ecTBeH-
HO II3MeHHeTCH II B03pacTaeT, KorJ],a nepeJ], BnpbIcKoM Ton.'1IIBO
HaXOJ],IITCH B COCTOHHIIH pa3pe}KeHIIH, T. e. B JIHHHH HarHeTaHH5I
IIl\lelOTCH OO'beMbI, 3anO"lHeHHbIe na paMH TOnJ1IIBa II BbI.n.eJIHBllIIIMCSI
13 3aI<a3 748
193
lI3 HerO B03;a:YXOM. B 310M c.'IYlJae H3MeHeHHe Ha"IaJIbHbIX YC.HOBHlj
cyrqecTBeHHO CKa3bIBaeTCH Ha xapaKTepe npOTeKaHHH npouecca
BnpbICKa Hero napaMeTpax. YCTaHoB.leHO [16], lJTO CHCTell1a C
HaCOCOM YTH-5 npn ee pa60Te C IllTH<}>TOBOH <}>OPCYHKOH BMeCTO
OCTaTOlJHOro ;a:aBJIeHHH HMeeT oCTaTolJHwM o6 eM. ITpH YCTpaHeHHH
3Toro o6 eMa nVTeM 3aMeHW cepHHHoro KJIanaHa KJ1anaHaMH KOH-
CTPYKl1.HH MAD.H (pl1C. 82) npOH3Bo;a:HTeJIbHOCTb CHCTeMbI B03pOC"la
60JIee qeM Ha 40%. Oc06eHHocTblO onHCbIBaeMoro KJ1anaHa HB-
JIHeTCH Ha.TIH"we ;a:BYX npY)KHH: OCHOBHOM 1 C 3aTH)KKOH 12-
15 KrtC.M. 2 H BcnoMoraTe:IbHoM 2 C 3anDKKoM MeHee I KrtCN. 2 . ITpy-
11'7 HH¥Z/lO#
(2
B
2
4
0
4 40 J2 rpo
PHC. 82. CTa6!JJlfl3f1py-
IOlI.\HH KJIanaH KOHCT-
pyKI.\HH MA]111
PIIC. 83. XapaKTcpIlcTIIKa BnpblcKa
CIICTCMbl YTH-5 npH pa60Te ee:
1 - c cepniiHblM KJIanaHOM; 2 - co
cTa6nJIH3HPYJ01ll.HM KJIanaHOM
)KHHa 1 ;a:eHcTByeT Ha KJIanaH ;a:o ynopa 3, 3aTelVI KJ1anaH Haxo;a:HTC5I
no;a: B03;a:eHcTBHeM 10JlbKO CJIa60H npY)KHHbI 2. IToCJIe BnpbICKa
;a:aBJ1eHHe JIHHl1H BcaCWBaHHH npeo;a:OJIeBaeT CHJIY 3aTH)KKH CJ1a60H
npY)KHHbI H nepelVIerqaeT K.'IanaH 110 BbICOTbI, cooTBeTcTBYIOII.I.eif
paBHOBeCHIO CHJI, ;a:eikTBYIOII.I.HX Ha KJIanaH. Bo BpeMS! 3Toro
nepeMern:emm KJIanaH JIH60 nOJIHOCTblO BbI6HpaeT cBo6011Hble
06 eMbI B JIHHHH HarJ:IeTaHHH, JIH60 YMeHbIllaeT HX Ha 3HaQHTe.1JbHYIO
BeJIHQHHY, B pe3YJIb1aTe Qero npoH3Bo;a:HTeJ1bHOCTb CHCTel\1bJ 3aMeT-
HO B03paCTaeT. Ha pHC. 83 npHBe;a:eHbI xapaKTepHcTHKH BnpbIcKa
TOnJIHBa CHCTeMbI YTH-5 C cepHHHbIM KJIanaHOM H C KJIanaHOM KOH-
CTPYKl1.HH MAIU1.
BJIHSIHHe HarHeTaTeJIbHOrO Tpy6onpOBOJI.a Ha xapaKTepHcTHKY
BnpblcKa. OCHoBHaR «PYHKl1.11R HarHeTaTeJIbHoro Tpy6onpoBo;a:a-
no;a:Bo;a:HTb TOnJIHBO J( «PopcYHKe nYTeM nepeJI.alJH C«pOpMHpoBaHHoro
y Hacoca HMnYJ1bCa F (t), nepeMeII.l.alOrqerocH no Tpy60npOBOJI.Y K
cpopcYHKe co CKOpOCTblO 3BYKa. CKOpOCTb JI.Bll)KeHHH )KH;a:KOCTH
'194 BI''\ £r.x
H3MeH5IeTCH He TO.'1bKO BO Bpei\IeHH, HO II no ;J,.J"IHHe HarHeTaTeJ"IbHOrO
Tpy60IIpOBO;J,a (01. pHC. 68) .
06paTHMC5I elll.e pa3 K pHC. 67 H 68. 113 paccMOTpeHH5I H306pa-
lKeHHbIX Ha HHX 3aBHCHMOCTeH CJIe;J,yeT, qTO B Tpy6oIIpoBo,lI,e
IIpOHCXO,lI,5IT CJ10lKHbIe H, nO-BH,lI,HMOMY, BalKHbIe IIpOI.J.eCCbI .I!.."I5I <pop-
MHpOBaHH5I xapaKTepHcTHKH BIIpbIcKa TOII.IHBa. .lIaBJ1eHHe H CKO-
pOCTb Ton.IHBa IIO .ll,.'IHHe Tpy6onpOBO.lI.a pe3Ko H3MeH5IIOTC5I.
O.lI.HaKo rrpH 3TOM ;J,O HaqaJIa OTCeqKH OHn He YMeHbllIaIOTC5I .lI.O
HY.IH. K.OJIe6aHI1H ..'I.aBJIeHHH H CKOpOCTH pe3KO B03paCTaIOT noc.Ie
HaqaJ1a OTCeqKH. B 3TOT nepno.lI. oco6eHHO 3aMeTHO H3MeH5IeTC5I
CKOpOCTb TOII.TII-IBa C T - B HeKOTopbIe MOMeHTbI, HanpHMep IIpl1 46,5
11 50,5° yr.J13 IIOBopOTa KYJ1aqKOBOrO BaJI3 Hacoca, Ha O,lI,HO:\1 KOl!I.J.e
Tpy6onpOBO.lI.a TOIIJIHBO ,lI,BI1>KeTCH K Hacocy, a Ha ,lI,pyroM - K <pop-
CYHKe. n pH cp = 50,5° Ha KOHI.J.aX Tpy6oIIpOBo,lI,a TOIIJII1BO TeqeT B
O.lI.HOM HanpaBJIeHI1H, a Ha He6oJIbllIOM yqaCTKe BHYTPH Tpy6onpoBo-
,lI,a - B ,lI,pyroM,' qTO YKa3bIBaeT Ha B03MO>KHOCTb o6pa30BaHI1H
OCTaTOqHbIX 06'beMOB He TOJIbKO B KOHeqHbIX 06'beMax y Hacoca H y
<POPCYHKH, HO 11 BHYTPH Tpy6oIIpOBO,lI,a, npnqeM OCTaTOQHbIe 06'beMbI
MorYT 06pa30BaTbC5I B HeCKOJIbKnX MeCTax. B par:cMaTplmaeMoM
c.JIYQae pa3pbIB nOTOKa npOHcxO,lI,HT npl1 cp = 50,5° Ha yqaCTKe OT 70
.lI.O 80 CM, T. e. OK0J10 <POPCYHKH.
06pa30BaHI1e CBo6o,lI,HOrO 06'beMa B03MO>KHO, eCJII1 ,lI,aBJ1eHHe PT
MeHbme ,lI,aB.JIeHI1H napoo6pa30BaHHH. npH PT 60JIbmeM .rraBJIeHI1H
IIapoo6pa30BaHI1H, HeCMOTpR Ha HaJIHQl1e B Tpy6onpOBO,lI,e npOTI1BO-
IIOJI0>KHbIX CKopOCTeH, pa3pbIB CnJIOmHOCTH nOTOKa He HaCTynaeT.
O,lI,HaKO c..Ie,a:yeT rrOMHI1Tb, qTO npOTHBOnOJIOlKHbIe CKOpOCTI1
YCHJ1I1BaIOT onaCHOCTb nOHBJIeHH5I pa3pbIBOB,
Bm1HHIfe KOHCTPYKTHBHbIX napaMeTpOB HarHeTaTeJ1bHOTO TPy-
60IIpOBo.rra Ha xapaKTep BnpbICKa MOlKHO ou.eHHTb H3 ypaBHeHHH
(216). HaIIHmeM .9TO ypaBHeHl1e ,a:JI5I IIepl10,lI,a aKTHBHoro xo,a:a,
KOr,lI,a OKHa BTYJIKH nJIYHlKepa 3aKpbITbI, HrJIa <POPCYHKH npHlKaTa
K ynopy, pa3rpY>KaIOllI.l1H nORCOK HarneTaTeJIbHOrO KJIaIIaH3 Haxo-
,lI,HTC5I BHe KaHaJ1a rHe3,lI,a, T. e. BJ1HHHHe KJ1anaHa He yqHTbIBaeTCR.
.lIJIR .9THX YCJIOBHH ypaBHeHHe nO,lI,aqH TOnJ1HBa 6Y,lI,eT Hl\leTb cne-
,lI,YIOllI.HH BH,lI,:
:3!1:o Q = [, C(I)-a ( V(I) + V' ) dP ] ,-a viI) dpcfJ +
,. 't j c n n 11 11 dt (t- ) Y' dt
+ [W{I)(t+ )-w (t- )]. (218)
BJIHHHHe HarHeTaTeJIbHOrO Tpy6oopOBO,lI,a Ha pacxo,lI, Qc yqHTbI-
BaeTCR QJIeHOM (4), BeJ1HqIIHa KOToporo 3aBIICHT OT pa3HocTII
aMOJIIITY,lI, OTpa>KeHHOH BOJIHbI, o6pa30BaBllIeHC5I B ,lI,aHHbIH MOMeHT
y <POPCYHKII, II IIO,lI,Ome,lI,llIeH CIO,lI,a OT Hacoca OTpa>KeHHOH BOJ1HbI,
2L
B03HIIKllIeH y <P0PCYHKH paHee Ha BpeMH -. 3HaK pa3HOCTH
a
aMnJIHTY,lI, IIOKa3bIBaeT xapaKTep BJ1HRHHR .9TOrO <paKTopa Ha
13* 195
BeJ1WIlmy Qc. KorLI.a pa3HOCTb aMnJIHTYLI. OTpHI aTeJIbHa, TO qaCTb
TOnJ1HBa fnCn, nOLI.aBaeMaH nJ1YH>KepOM, OCTaCTCH B 06'beMe Tpy6o-
npOBOD.a B C2KaTOM COCTOHHHH, eC.Tm 2Ke n0J102KHTe.TIbHa - C>KaTOe
B 06'beMe TOnJ1HBO paCllIHp5IeTCH, lITO B paCCMaTpHBaeMbIH MOMeHT
BpeMeHJI CJ1Y2KHT LI.OnOJIHIITe.1JbHbIM IICTOQHJfKOM mnaHHH paCnbI.1JH-
F(t- , W(t+ )
KfjcM 2
-200
-400
C r
MjceK
80
800
600
400
o
2
PRC. 84. 3aBHcllIIIoCTb BO.'1H .D:aB-
JlCHH5I II CKOpOCTH TonJlHIJa
OT d r :
I - f(t _l:..); 2 - C T ;
a
j"C; CHYceK
L
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a
fP
26
24
22
cr ttB
Ke/
68
64
K;:2 fHJ
ffOO
1000
2,5 J 3,50'r /'1/1
PHC. 85. 3aBHcHMoCTb napaMcT-
pOB npOl.\ccca BnpblCKa OT BCJlH-
1.HlHbl d r
JIIO
160
80
0 42
J8
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PHC. 86. BJlIiHHHe BC.1H4H-
UbI d r Ha OO"beMHym CKO-
pOCTb B TpyoonpOIJo.D:c:
1 - d T = 2,5 .M.M; 2 -d T =
= 3 .MM; 3 - d T = 3.5 AIM
BaJOll..{IIX OTBepCTIIH. 3TOT BbIBOLI. nOLI.TBep2KJI:aeTCH plIC. 84, Ha
L L
KOTOpOM nOKa3aHa 3aBHCHMOCTb W(t +-), C T H F(t --) OT
a a
dr. Ha pHC. 85 1I306pa}KeHbI nOJI:06HbIe .IKe 3aBIIClIMOCTlI JI:JUI G t ,
<p H ptJj max. 113 paCCMOTpeHHH 3aBHCIIMOCTCH Ha plIC. 84 H 85
196
CJIe.n:yeT, lITO .n:JUI HCCJIe.n:yeMoi'I CH-
CTeMbl ).{HaMe'Tp Tpy6onpOBO).{a
d r = 3 MM 5IBJI5IleTC5I onTHMa.i1bHbIM.
YBe.TJIfIIeHUe HJIH YMeHbllIeHue .n:ua-
MeTpa d r BbI3bllBaeT YMeHbllIeHue
npOI-I3Bo).{uTeJ1bHOCTU CHCTeMbI If
.lI.aBJIeHIfH pif> ma". Cor.TJaCHO ypaB-
HeHUIO (218) H puc. 84 YBeJ1UIIeHUe
.n:HaMeTpa d r Hta OCHOBHOM 3Tane
n.eMnq,uPyeT K(»J1e6aHHe OTpa)f{eH-
HblX BOJIH. O).{HtJIKO, KaK CJIe.ll.yeT H3
pHC. 86, a TaKMe puc. 84, B KOHlI.e
npolI.ecca BopbIC'Ka !<OJIe6aHU5I BO.TJH
).{aBJIeHU5I CTaHOB5ITC5I HaCTOJIbKO
3HaIIUTeJ1bHbIMU. QTO B03HHKaeT ).{o-
fIOmlHTeJIbHbIH BnpblcK TOOJIHBa.
TaKHM o6pa30M, eCJIH Ha6JIIO).{a-
>TC5I ).{OOOJIHI1ITe.TJbHble BOpbICKH
oj 0)
PHC. 87. OCI.\HIJlJlOrpaMMb! .D:aBJleHHH
Bmpb!CKa:
a - npH d r 1,,5 .MM; 6 - npH d.. =
2 AtAt
PHC. 89. BJJllfHHlle Ha xapaK-
TepHCTHKY IBnpblCKa .D:JlHHbl
HarHCTaTeJlbHOrO Tpy6onpoBo-
,!\a .lI.HaMeTpOM d.. = 2 .M.M:
J - l = 550 At.,,!; 2 l = 1290 JI.'<
;;'
F(t- )
xf/C1f2 \ 3(2
1800
1600
MOO
f200
fOOO
600
400
PliO
o
t5 2,0 2.5 1,0 .1,5 d, I1N
PIIC. 88. 3aBHcHMoCTb xapaKTepa
npoTcKaHHH npol.\ccca BnpblcKa OT
BeJlH'J:HHbI d..:
A - 06JIaCTb B03MO.>KHbIX .n.onOJIHHTeJIb-
HblX BnpbICKOB; E - 06J1aCTb OTCYT-
CTBHH pa3phlBOB cnJIOIliHOCTH nOTOKa H
lI.OnOJlHllTeJlbHblX BUPb!CKOB; B - 06-
.:1.aCTb Bo3MO)KHbIX pa3pblBOB CI1.,'10IllHO-
CTH nOTOKa TOnJIHBa; J - p(t - ).
L'
s' )],JISI dn 14 MM; 2 - P(t- -;;).
6 2 )],JI" d n - 13 JUf
tJr; I1I1Y poiJ
JO
fO
!pO
20
o
10
25
15
20
(pHC. 87). TO [IX MO)f{HO 3HaQHTeJ1bHO YMeHbWHTb,
J1HKBH).{HpoBaTb 0YTeM YMeHbllIeHH5I BeJ1H'IHHbI dr.
a UHor.u.a If
DpH BbI60pe
197
JJ.onycTuMoli BeJ1UIlUHbI d T lI.eJIeC006pa3HO UCnO"lb30BaTb ..'I,UarpaM-
MY (puc. 88). B TOM CJ1Yllae, KOrJJ.a 06'beMbI CUCTeMbI 3HaIlUTe"lbHbI,
YBe"lUlleHUe JJ.J1HHbI HameTaTeJIbHOrO Tpy6onpOBOJJ.a 6YJJ.eT CMeJ..I.{aTb
TO.lbKO £pa3bI npoll.eCCa BnpbICKa. CaMa )Ke XapaKTepHCTHKa
BnpbICKa (pHC. 89) cYJ..I.{ecTBeHHo He 113MeHUTC5I. Ha puc. 89 xapaK-
TepUCTUKH BnpbIcKa no £pa3alVI COBMeJ..I.{eHbI. Dpu Ma.TJbIX o6'bel\1ax
CUCTeMbI YBeJ1UlleHHe JJ."lUHbI Tpy6onpoBoJJ.a I\W)KeT CYJ..I.{eCTBeHHO
113!\IeHUTb pa3rpY3Ky J1UHUH HarHeTaHHH, a C.TJeJJ.OBaTe.TJbHO, H Ha-
lla.1bHbIe YC.TJOBHH nocJ1eJJ.YIOJ..I.{ero BnpbICKa.
5. BnHSlHHE LlHcnA O&OPOTOB BAnA
TonnHBHoro HACOCA HA XAPAKTEPHCTHKY BnPblCKA
B3aUMOCBB3b YCToiilJHBOCTH pa60TbI Jl.H3eJ1B C 3aBHCHMOCTbIO
q1f = f (n). B TOnJIUBHbIX CUCTeMax C MeXaHUlleCKUM npUBOJJ.OM H
HameTaTeJIbHbIM Tpy6onpOBOJJ.OM CKOpOCTb JJ.BU)KeHUH nJ1YH)Kepa U
npO..'l,OJ1)KUTeJ1bHOCTb npOll.ecca BnpbICKa U3MeHHIOTCH nponopmIO-
HaabHO H3MeHeHuIO IlUCJ1a 060pOTOB. TaKUM 06pa30M, npH YMeHb-
llIeHUu 060pOTOB npOTeKaHue nponeCCOB B CHCTeMe JJ.OJI:>KHO 3aMeJJ.-
J1HTbCH, npH YBe.'lHlleHHU - YCKOpHTbCH, npUlleM eCJ1U 6bI He 6bIJ10
UCKa:>KaIOJ..I.{UX £paKTOpOB, TO 3aMe.n;,,'leHHe U YCKopeHHe npOll.eCCOB
JJ.O.TJ:>KHO npOHCXOJJ.HTb nOIlTH npOnOpll.HOHa.TJbHO H3MeHeHUIO IlUC-
J1a 060pOTOB. OJJ.HaKO H3-3a HaJIHIlHH HCKa:>KalOJ..I.{UX £paKTOpOB .n;eii-
CTBHTeJ1bHaH npOJJ.OJ1)KHTeJ1bHOCTb nOJJ.aIlH. TOll.TIHBa, B03paCTaHue
JJ.aB.leHHH U JJ.pyrHe napaMeTpbI HaXOJJ.HTCH B 60JIee CJIO)KHOli
B3allMOCBH3H C IlHCJ10M 060pOTOB. OCHOBHbIMH napaMeTpaMU, onpe-
JJ.e.1HIOJ..I.{UMU YKa3aHHYlO B3aUMOCBH3b, HBJ1HIOTCH CKOpOCTb JJ.BU)Ke-
HUH nJ1YH)Kepa U yrJIOBaH CKOpOCTb BaJIa TOnJIHBHoro Hacoca.
B 3 :noll rJIaBbI 6bIJ10 nOKa3aHO, IlTO CKOpOCTb C n MO)KHO
U3!\IeHHTb npu nOMOJ..I.{H npO£pHJ1H TOnJIHBHOrO KYJIallKa H npH HeH3-
MeHHbIX o60poTax. O.n;HaKo npH .nOM yrJ10BaH CKOpOCTb BpaJ..I.{eHlIH
KyJIallKa He H3MeHHeTCH, IlTO HBJIHeTCH OCHOBHbIM £paKTOpOM, onpe-
JJ.e"lHIOJ..I.{UM, KaKHM 6YJJ.eT BJIUHHHe YKa3aHHbIX napaMeTpOB Ha xa-
paKTepHCTHKY BnpbICKa TOnJ1HBa. DpH YBeJIHlleHHH n C n nOBbIllIaeT-
CH BCJIeJJ.CTBHe B03paCTaHUH yrJ10BOli CKOpOCTU. D03TOMY aKTHBHbIli
XO,il, nJ1YH)Kepa npH HeH3MeHHOll npOJJ.O"l)KUTeJ1bHOCTH, BbIpa)KeHHOii
B rpa.n;ycax yrJ1a nOBopOTa BaJ1a Hacoca, 6YJJ.eT coxpaHHTbCH no-
CTOHHHbIM JJ.J1H Bcex 060POTOB, KaK 6bI CU,,'lbHO HH U3MemmaCL
BemIIlHHa Cn. CJ1eJJ.OBaTeJ1bHO, B paCCMaTpHBaeMOM CJ1Yllae HeT
B03!\W)KHOCTH YBeJIHIlHTb q1f npH qJn = canst HJIU YMeHbllIHTb qJn
npH q1f = const. 3TOT HeJJ.OCTaTOK COBpeMeHHbIX TOnJIHBHbIX CUCTeM
He n03BO.TJHeT BO BpeMH pa60TbI H3MeHHTb xapaKTep npOTeKaHHH
3aBHCHMOCTH q1f = f (n), KOTOpbIli BJIHHeT Ha YCTOllllUBOCTb pa60TbI
JJ.U3eJ;IH B 3aJJ.aHHOM pe)KHMe.
LlJIH YCToiillHBOli pa60TbI .n:U3eJ1H Heo6xoJJ.HMO, IlT06bI 3aBHCH-
MOCTb q1f = f(n) npOTeKaJ1a, KaK nOKa3aHO KpHBoli 2 Ha pHC. 90.
B 3TOM cJIYllae npu npOH3BOJIbHOM YBeJIUlleHUU IlUCJ1a 060pOTOB
3Ha1leHUe qi.j. 6y.n:eT YMeHbllIaTbcH, a npH YMeHbllIeHuH IlUC"la 060-
198
pOTOB - B03paCTaTb, npemlTCTBYH TeIVI caMbIM KaK pa3HOCY, TaK H
no.1HOH OCTaHOBKe .lI.BHraTemI. O.ll.HaKO .lI.JIH 60J1bUlHHCTBa TOnJIHB-
HbiX CHCTeIVI TpaHcnopTHbIX .lI.H3eJIeH 3aBHCHIVIOCTb q1J. = f(n) npo-
TeKaeT, KaK nOKa3aHO KpHBOH 1 Ha pHC. 90, 'lTO He 06eCne'lIIBaeT
YCTOH'lHBYIO pa60TY .lI.H3emI. TaKOH xapaKTep npOTeKaHHH 3aBHCH-
MOCTH q1J. = f(n) oc06eHHO onaceH .lI.JIH TpaHcnopTHbIX JIH3e.rIeH,
KOTopbIe pa60TalOT B llIHpOKOIVI )].Hana30He H3MeHeHHH 'lrrCJIa 06opo-
TOB H HarpY3KH.
I{JIH H3MeHeHlIH xapaKTepa npOTeKaHHH 3aBHCHMOCTH q1J. = f(n)
npUMeHHIOT perYJIHTOp 'IHCJIa 060pOTOB. B 3aBHCHMOCTn OT 'InCJIa
060pOTOB BaJIa )].BHraTeJ1H pery.'UlTOP npn YBeJIHlIeHHH 'lHCJIa 060-
pOTOB rrepeMemaeT peHKY Ton-
JIHBHOro Hacoca B CTOPOHY
YMeHbllleHHH no)].a'lH Ton.'IHBa, a
fq
Z/l(UI<n
n 05/HUH
PilC. 90. B03MO}l{Hble xapaKTepbI
npoTcKaHilH 3aBilCHl\IOCTH
q.. = f(n)
f 6/lIuK/J
Yf
o
2
I; ".
lj UK/lbl
m-1 m
PIIC. 91. nepeXO.D:Hb!H nepHO.D: Ton-'
.1HBHOH CHCTCMbl: q'll - 3Ha'-lCHile
AO H3MeHCHIIH nOJlO1KCHHH peRKH;
q'l2 - 3Ha'-lCHIIC, cooTBeTcTBYIOlI.{ee
HOBOMY nOJlOLKCHHIO peRKH
npH CHH*eHHH 'lHCJIa 060pOTOB - B CTOPOHY YBeJIH'leHHH no)].a'lH
TOnJIHBa. O)].HaKO Ka'leCTBO pa60TbI perYJIHTOpa cYll.{eCTBeHHo 3aBH-
CHT H OT nepexO)].Horo npo ecca B TOnJ1HBHOH CHcTeIVIe, TaK KaK Tpe-
6ye:\1aH BeJ1H'lHHa q1J. 06eCne'lHBaeTCH He MrHOBeHHO nOCJIe nepeCTa-
HOEKH perYJIHTopOJ\-1 peilKH TOnJIHBHOrO HaCOCa. B nepeXO)].HOM
rrepHo)].e H3MeHeHHe no)].a'lrr q1J. HOCHT KOJIe6aTe.'IbHbIH xapaKTep
(pIlC. 91). DP0)].OJI*HTeJ1bHOCTb nepexo)].Horo nepHo)].a 3aBHCHT OT
KOHCTPYKTHBHbIX CooTHollleHHH Me*)].y ::weMeHTaMH TOnJIHBHOH CH-
CTe:\1bI, cpH3H'leCKHX KOHCTaHT TOn.TIHBa H .lLPyrnx cpaKTopoB.
B TeopHH perYJ1HpOBaHIlH nepexo)].HblH npouecc TOnJIHBHOH CH-
CTeMbI He Y'lHTbIBaeTCH, n03TOMY cpaKTOp YCTOH'lHBOCTH
Fa = S.M-K(kI'rJeSan +ql{S'ljn),
dM
r.lLe S.., = ----E- - H3MeHeHlle l\lOMeHTa conpOTHBJ1eHHH no yrJIOBOH
dro
CKOpOCTH Bpall.{eHHH Ba.'Ia )].BHraTe.'IH;
'I1e - 3cpcpeKTHBHbIH K. n. .lI.. )].BHraTeJIH;
San = - H3MeHeHHe q1J. no yr"10BoH CKOpOCTH Ba.'Ia Ton-
dro
.'IHBHOrO Hacoca;
199
d}l
B'I1n ----.!!...... - H3:\leHeHIIe 3<}:><}:>eKTHBHOrO K. n. )1,. )1,BHraTeJ1H no
dw
yrJIOBOH CKOpOCTH ero BaJ1a paCC'IHTbIBaeTCH npH
..'I.OnymeHHH (XOT5I 060CHOBaHHH 3TOMY OTCYT-
CTBYlOT), 'ITO Tpe6yeIllaH. BeJ1H'IHHa q"lj. .n:OCTH-
raeTCH MrHOBeHHO nOCJIe nepeCTaHOBKH pery.1H-
TOpOM peHKH TOII.TIHBHOro Hacoca,
MO)KHO OTMeTlITb, lITO no.n:alIa q"lj. TeM 6bICTpee npHHHl\IaeT
HY)KHOe 3Ha'leHHe, 'IeM MeHbllle 06'beMbI V n, V , V g;, )1,JIHHa Tpy60-
npOBO.J,a L H 3a30pbI B COeJ1.HHeHIIHX peHKH TOnJ1HBHOrO Hacoca C
n.llYH)KepOM H perYJ1HTOpOM. DOJIbIIIOe 3HalIeHHe .II.J1H 06ecnelIeHIIH
YCTOHlIHBOH pa60TbI TOnJ1HBHOH CHCTeMbI, perYJIHTOpa H .II.BHraTeJIH
B u.e.'IOM HMeeT yro.ll HaKJ10Ha OTcelIHOH KpOMKH nJ1YH)Kepa. 4eM
60J1bllle yrOJI , TeM 6oJ1ee pe3KO npH nepeMemem'iH peHKM Ton.1HB-
Horo Hacoca 6Y.II.eT H3MeHHTbCH BeJIHlIHHa q"lj.' CJ1e.II.OBaTeJ1bHO, npH
60.'IbIIIHX 3HalIeHHHX .II.a)Ke He3HalIHTe.llbHbIe C.llY'laHHbIe KOJIe6a-
HHH B CHCTeMe perYJIHpOBaHHH MorYT 3aMeTHO H3MeHHTb nOJ1.alIY
q"lj., '-ITO npHBo.n:HT K HenpepbIBHOMY B03.II.eHCTBHlO pery.'IHTOpa Ha
peHKY Ton.'IHBHOrO Hacoca, T. e. npenHTcTByeT YCTOHlIHBOH pa60Te
.II.H3emI. HenpHeMJIeM H OIleHb Ma.'IbIH yrOJI 13, TaK KaK B 3TOM C.1Y-
Ilae .n:a)Ke npH He3HalIHTeJ1bHOM H3MeHeHHH q"lj. perymnop JIO.'I)KeH
nepeMemaTb peHKY Ha 60JIblllYlO BeJ1HlIHHY. TaKHM 06pa30M, npH
BbI60pe BeJIHlIHHbI yrJ1a [3, a TaK)Ke .n:pyrHx napaIlleTpOB TomlHBHOH
CHCTeMbI CJIe.II.yeT YlIHTbIBaTb He TOJ1bKO He06xoJIHMOCTb 06ecnelIe-
HHH IleTKoro BbIKJ1lOlIeHHH nO.II.alIH H Tpe6yeJ\lOH npOH3BO.II.I1TeJ1bHO-
CTH Ha Bcex pa60lIHX pe)KHMaX, HO H He06xo.II.HMOCTb C03.II.aHHH
YC.'IOBHH .lI:.TJH YCTOHIlHBOH pa60TbI CHCTeMbI perYJ1HpOBaHHH.
KaK H3BeCTHO, Ha pe)KHMaX BHeIIIHeH xapaKTepHCTHKH pei'lKa
TOnJIHBHOrO Hacoca npH)KaTa K ynopy H perYJ1HTOp He pa6OTaeT.
BC.lle.II.CTBHe 3Toro YCTOHIlHBOCTb pa60TbI )J:H3eJIH no BHeIIIHeH xa-
paKTepHCTHKe 06yc.'IaBJIHBaeTCH TOJIbKO 3aBHCHMOCTblO qv, = f(n),
nOJ1YlIaeMOH C TOnJ1HBHOH CHCTeMOH 6e3 perYJ1HTopa. LLJIH 06ecnelIe-
HHH HeOOXO.II.HMOH 3aBHCHMOCTH qv, = f(n) Ha pefKHMax BHeIIIHeH
xapaKTepHCTHKH B 60J1bIIIHHCTBe CJ1YIlaeB npHMeHHlOT cneu.HaJ1bHbIe
MexaHHlIeCKHe KoppeKTopbI, KOTopbIe npH CHH)KeHHH lIHC.J1a 060po-
TOB nepeMemalOT peHKY B CTOPOHY YBeJIHlIeHHH nO.II.alIH. LLe.llalOTCH
TaK)Ke nonbITKH nYTeM HeKOToporo H3MeHeHHH 3JIeMeHTOB TOnJIIIB-
HOH CHCTeMbI ocymecTBHTb eCTeCTBeHHoe rH.II.paBJIHIleCKOe KoppeK-
TlrpOBaHHe CKOpOCTHOH xapaKTepHCTHKH nO.II.a'lH. O.II.HaKO, HeCMOTpH
Ha TO, lITO B HeKOTopbIX CHCTeMax .II.JIH KoppeKTHpOBaHMH xapaKTe-
pHCTMKH nO.II.aIlH .II.OBOJ1bHO IIIHpOKO HCnOJIb3yeTcH HameTaTeJ1bHbIH
K.'IanaH C pa3rpY)KalOmHM nOHCKOM, TeopHH norD Bonpoca nOKa
eme pa3pa60TaHa He.n:OCTaTO'lHO. Ha pHC. 92 nOKa3aH xapaKTep
npoTeKaHHH 3aBHCHMOCTM q'tf = f(n) B OOJIaCTH lIHCJIa 060POTOB,
6J1H3KHX K lIHCJIY 060POTOB, npM KOTOpOM .II.OCTHraeTCH MaKCHMa.lb-
HbIH KPYTHmHH MOMeHT KaK npM paooTe CMCTeMbI C MeXaHM'IeCKHM
KoppeKTopoM, TaK H 6e3 Hero. TaKHM 06pa30M, TO'lHOCTb paclIeTa
npou.ecca perYJIMpOBaHHH 6bICTpOXO.II.HOrO .II.H3eJ1H 3HalIHTeJ1bHO
200
nOBbICHTC5I, eCJUI Y'leCTb OC06eHHOCTll pa60TbJ TOnJ1llBHOH CllCTeMbI.
TaKOH Y'leT KOHCTPYKTllBHbIX II rll.n.paBJ111'leCKliX napaMeTpOB TOn-
.;l11BHOH CliCTeMbI npll paC'leTe npouecca perYJ111pOBaHliH Tpe6yeT
pa3pa60TKlI l\IeTO.n.OB CO'leTaHliH TeOpHH pery.'UIpOBaHHH C TeOpHeH
npOu.ecca BnpbICKa. PeWeHHe ::nOH 3a.n.allll MOlli.eT 3HallllTe.lbHO
nOMO'lb .n.aJlbHeHweMY COBepweHCTBOBaHlI1O pa60'lero npou.ecca
,J.H3e.1H.
BJ1HDHHe KOHCTPYKTHBHbIX H rH)J,paBJIHIIeCKHX napaMeTpOB Ton-
JIHBHOH CHCTeMbI Ha 3aBHCHMOCTb q1f = f (n), Clli.HMaeMOCTb TOnJIHBa
OKa3bIBaeT 60J1bWOe BJ1HHHHe He TOJ1bKO Ha npou.ecc BnpbICKa, HO H
Ha xapaKTep npOTeKaHllH 3aBHCH- e/l/liK/l
MOCTM Q" [(n). HeKOTopoe rrpe . '
cTaB.;leHlle 0 B.1llHHllll Clli.llMaeMO- a07
CTll TOnJIHBa Ha 3aBHCHMOCTb q1f = 06 (
= f(n) MOlli.HO nOJlY'lHTb H3 aHaJIH- 2
3a ypaBHeHHH (21 u 6), KOTopoe 6e3 405 500 900 (300 n OOjMliH
BHeCeHH5I 60.'1blliOH norpewHOCTH B
peweHHe nOCTaBJIeHHOH BbIllie 3a-
.n.a1J:H MOlli.HO ynpocTHTb, eCJ1H .n.ony-
CTIITb, 'ITO .rr.BHlli.eHllH HarHeTaTe.'1b-
Horo KJIanaHa II llr JIbI q>OPCYHKlI
5IBJIHIOTCH paBHoMepHO YCKopeHHw-
d 2 C d 2 C
:\iH. npll 3TOM .rr.onYIIJ.eHllll np0113Bo.n.HbIe H ---'!.. 6y.n.YT paBHbI
dt 2 dt 2
Hy.11O.
. BJ1l1HHHe Clli.HMaeMOCTl1 TOnJ1HBa B OCHOBHOM 3aBHCHT OT Be.ll1-
1J:l1Hbl OO'beMOB V"Ii' V' , VF-, n p OH3Bo.n.HOH dp H ee 3HaKa, KOTOpbIH
n dt
BO BpeMH npouecca BnpbICKa H3MeHHeTcH, 113MeHHH TeM caMbIM II
xapaKTep BJ1l1HHl1H Ha 3aKOH nOlla1J:l1 Clli.l1MaeMOCTl1 TOnJ1l1Ba. no
3TOMY np113HaKY npou.ecc BnpbICKa MOlli.HO pa3.n.eJIl1Tb Ha Tpl1
nepl1o.n.a, nepBbIM nep110.n.OM HBJ1HeTCH BnpblCK TOnJ1l1Ba 3a BpeMH
<lKTHBHOro xo.rr.a nJIYHlli.epa. B 3TOM nepHo.n.e OKHa BTYJIKH nJIYHlli.epa
jaKpbITbI, HrJIa q>OPCYHKl1 npl1lli.aTa K ynopy, pa3rpYLKalOIIJ.l1H nOHCOK
HarHeTaTeJIbHOrO KJIanaHa Haxo.rr.l1TCH BHe KaHaJia rHe3.rr.a. C.rr.eJIaB
.n.onYIIJ.eHl1e, 'lTO MaKCl1MaJIbHWe .n.aBJ1eHl1H TOnJ1l1Ba B Cl1CTeMe
P max II PrP max onpe.n.eJIHIOTCH BOollHOH no.n., a1J:l1 B03Hl1KalOIIJ.eH y
Hacoca B MOMeHT Ha1J:aJ1a OTCe1J:Kl1, nOCJ1e np110J1l1LKeHHOro nO'lJIeH-
Horo l1HTerpl1pOBaHl1H OOll.l.ee ypaBHeHl1e no.n.a'IH TOnJ1l1Ba .n.J1H 3TOro
nepl1o.n.a MOLKHO 3anl1CaTb B Bl1.n.e
q = fnhaK - [a(Vn cp+V )(p max -P n)l (t- ) -aVq, (Pq,max - Pq,n)-
"'om
-fuY+ \ [ w ( t+ ) -W ( t- )] dqJ,
6nap .J a a
PRC. 92. 3aBRcHMoCTb q.. = fen)
npH pa60TC CIICTCMbI:
J - C MeXaHHqeCKHM KoppeKTopoM;
2 - 6e3 MeXaHHQeCKOro KoppeKTopa
(219)
"'n
r.n.e q' - KOJIl11J:eCTBO Ton.ll1Ba, nOllaHHoro 3a nepl1o.n.
t{
aKTl1BHOrO xo.n.a n.1yHLKepa;
201
V 1< cp - 06"beM KaMepbI HarHeTaHllH, CpeAHliH 3a BpeMH
BnpbICKa;
p max II prjj max - MaKCliMaJIbHbIe JI.aBJIeHllH TOnJ1IiBa B 06"beMaX
V II V rjj;
p1<n, pg;n - .D:aBJIeHlle Ton.'IliBa B 06'beMaX
MeHT nOJIHOrO nepeKpWTllH
OKOH BTYJ1Kll nJ1YHLKepa;
fuY - KOJ1Il1leCTBO TOnJIllBa, 3anOJIHllBllIero 06"beM,
oCB06mK.D:aeMbIH llrJ10H <POPCYHKll npH ee
nO.D:'beMe;
(jJn - yrOJ1 nOBopOTa BaJ1a Ton.'lllBHOrO Hacoca, COOT-
BeTCTBYIOI.U;HH MOMeHTY n0.'IHOrO nepeKpbITlIH
BcaCblBalOI.U;llX OKOH;
(jJom - yrOJI, COOTBeTCTBYIOI.U;HH MOMeHTY HaqaJIa OT-
KpbITliH OTCeqHbIX OKOH.
B 3TOT nepllO.D: nJIYHLKep nO.D:aeT B J111HlllO HarHeTaHHH Bce
TeOpeTllqeCKli He06xoJI.llMOe JI.JIH 06eCneqeHllH 3aJI.aHHOH np01l3BO.D:ll-
TeJ1bHOCTli KOJIllqeCTBO TOnJIliBa. paBHoe f nhonT' O.D:HaKO 3Haqll-
TeJIbHaH qaCTb 3Toro K0J111qeCTBa OCTaeTCH B JIllHllll HarHeTaHHH B
CLKaTOM COCTOHHllll, a qaCTb ero paCXO.D:yeTcH Ha 3anOJIHeHHe
06"beMa fuY. DpH6JIHLKeHHbIH paCqeT nOKa3bIBaeT, qTO HanpliMep, B
TOnJ111BHOH CliCTeMe 5I3T A B MOMeHT Ha qaJIa OTKpbITliH OTCeqHbIX
OKOH OK0J10 60% fnhanT TOnJ111Ba HaXO.D:HTCH B CLKaTOM COCTOHHllll B
JIllHllll HarHeTaHHH. DpHHHB K03<p<pHlu1eHT nO.D:aqH CliCTeMbI 1]n "'"
= 0,8 -7- 0,9, HaH.D:eM, qTO 3a BpeMH npOXOLK.D:eHHH nJ1ymKepoM hunT
B UHJIHH.D:P .D:BHraTe.'lH BnpbICKHBaeTCH TOJIbKO OK0J10 50% q'J'
TaKliM 06pa30M. KaK BeJIllqllHa 1]1<. TaK II xapaKTep npOTeKaHHH
q1.j. = f( n) CYI.U;eCTBeHHO 3aBHCHT OT TOro, KaK npll YBeJ1HqeHHII HJIH
YMeHbllIeHHH 060pOTOB H3MeHHeTCH COOTHomeHHe MeLK.D:Y I OJIHqe-
CTBOM TOnJIHBa, BnpbICHYToro nOCJIe HaqaJ1a OTCeqKH B UII.'IllH.D:P
.D:BHraTeJIH, H KOJ1IiqeCTBOM BbITeKllIerO 3a 3TO LKe BpeMH B OTCeq-
HYIO J1HHlllO.
BTOpOH nepHO.D: HaqHHaeTCH C MOMeHTa OTKpbITHH OTCeqHbIX
OKOH II npO.D:OJILKaeTCH .D:O MOMeHTa pa306I.U;eHHH 06"beMOB V 1< II V .
B CBH3H C OTKpbITHeM OTCeqHbIX OKOH npIIMeM, [ITO B 3TOM nepllOJI.e
.D:aBJ1eHHe TOnJIHBa YMeHbIllaeTCH, BCJ1e.D:CTBHe qero npOH3BO.D:HaH
dp "
- IIMeeT OTpHlJ:aTe.'lbHbIH 3HaK. qTO YKa3bIBaeT Ha paCIIIHpeHIIe
dt
TOnJ1HBa B 06"beMaX V 1<. V H V rjj. 4aCTb paCIllllpHIOI.U;erOCH TOnJ1HBb
6Y.D:eT BnpbICHYTa B lUIJIHHJI.P .D:BHr3Te.'leM. 3 OCTaJ1bHOe TOnJ111BO
qepe3 npO.D:OJ1bHbIe II nOnepeqHbIe KaH3JIW nJ1YHLKepa 6Y.D:eT nOJI.BO-
.D:HTbCH K OTCeqHbIM OKHaM II BbITeKaTb B .'lHHHIO OTCeqKH. DpH 3TOM
BeJ1HqHHa K03<P<PHlJ:lleHTa nOJI.aqH CHCTeMbI 1]1< 6Y.D:eT TeM MeHbllIe.
qeM 60JIbIlle qomc. T. e. KOJIllqeCTBo TOnJ1HBa. BbITeKIllerO B JIllHHIO
OTCeqKH, II Ha060pOT. qeM MeHbIlle qomc. TeM 60J1bIlle Be_1HqllHa
1]1<' DJ1YHLKep BO BpeMH BTOpOrO 3Tan3 npO.D:OJILKaeT BbITeCHHTb
TOnJIliBO. XOTH H3 3TOrO KOJIllqeCTBa B H3rHeT3Te.TJbHbIH TPy60npo-
V II V rjj B MO-
BCaCblBalOI.U;lIX
202
BO,J, 6y.n.eT nO.n.aHO Ma.10 TOn.'IHBa. OAHaKO B 06ru.eM ypaBHeHHH
BTOpOrO nepHO.n.a yqeCTb ,ny no.n.aqy lLeJIeco06pa3HO. C yqeTOM
C.n.e:laHHbIX 3aMeqaHHM o6ru.ee ypaBHeHHe BTOpOrO nepHO.n.a MO)!{HO
3annCaTb B BH)1.e
q" = fnh + fa (V H + V )(P max-P K)l +aV if> (Pt/Jmax-P K) +
"'K
+ /:a p J [w (t+ )]dlp-
_ [ V : . ; S to V P -P d J , L (220)
"'om (t--;;)
ueCb h - nYTb, npOM1l.eHHbIM nJ1YH)!{epOJ\I BO BTOpOM nepH01l.e
)1.0 pa306ru.eHH51 06'beMOB V1/. H V ;
P K' P K - )1.aBJIeHH51 B 06'beMaX (V1/.+ V ) H V g; B MOMeH1
pa306ru.eHH51 HarHeTaTeJIbHbIM K.'IanaHOM 06'beMa V1/.
C 06'beMOM V ;
!pom, !p" - yrJIbI nOBopoTa BaJla Hacoca B cooTBeTcTBYIOru.He
MOMeHTbI HaqaJ1a OTCeqKH H pa306meHH51 06'beMa V H
C 06'beMOM V ;
f.tom - K03tP<jmlLHeHT pacxo.n.a OTCeqHOM J1HHHH;
Pom - .n.aBJ1eHHe B JIHHHH OTCeqKH, BeJ1HqHHa KOToporo npH-
H51Ta HeH3MeHHOM.
TpeTHll nepHO.n. HaqHHaeTC51 C MOMeHTa pa306ru:eHH51 06'beMa V H
C 06'beMOM V HarHeTaTeJIbHblM KJlanaHOM 11. npo.n.OJI)!{aeTC51 .11.0
no.1HOM noca.n.KH HrJIbI tPOPCYHKH Ha ce.n..1Jo. B 3TOT nepHO.n. Haxo.n.SIT-
C51 B 1l.BH)!{eHHH He TOJ1bKO HarHeTaTe.'IbHbIH KJ1anaH, HO H Hr JIa
.pOPCYHKH. HameTaTeJ1bHbIll KJlanaH, eCJIH OH HMeeT pa3rpy)!{alO-
ru.I1M n051COK, npH CBoeM .n.BH)!{eHHH YBe.TJ.HqHBaeT 06'beM V ' T. e.
OCBo6o)!{.n.aeT 06'beM, onHCblBaeMbIM npH llBH)!{eHI-IH KJIanaHa pa3-
rpy)!{alOI1..lHM nOSICKOM, npHqeM 3TOT 06'beM )1.0JIfKeH 3anOJIH51TbCSI
Ton.1HBOM. I1rJIa )!{e tPOPCYHKH, Hao6opOT, npH CBoeM 1l.BH)!{eHHH
Yl\IeHbllIaeT 06'beM V!p' T. e. BbITeCH51eT H3 Hero TOnJ1HBO, KOJ1HqeCTBO
KOTOpOro paBHO 06'beMY, onHCblBaeMOMY HrJIOM I1PH ee .n.BH)!{eHHH.
B 3TOT nepHO)1. 06'beMbi V1/. H V pa306ru.eHbI, n03TOMY paCllIHpSIIO-
ru.eecSi TOnJIHBO .TJ.HHHH HarHeTaHHSI H BbITeCH51eI\lOe Hr.TJ.OM tPOPCYHKH
6y.n.YT H3pacxo.n.OBaHbI Ha BnpbICKI1 B lLHJ1HH)1.P )1.BHraTeJI51 H Ha 3a-
nOJIHeHHe 06'beMa, OCB060)!{1l.aeMOrO K.TJ.anaHOM. 06ru.ee ypaBHeHHe
no.n.aqH TonJ1HBa B 3TOT nepHO.n.:
q' = aV (P K -P n\t_ ) + aV if>(P K-Pif>n)+ fuY+
'+in
+ 6::P .f [W (t+ )-W (t- )]dlp-fKh , (221)
"'K
203
r.n.e P: n - .n.aBJIeHHe TOnJIHBa B 06'beMe V B MOMeHT B03HHKHOBe-
L
HHH BOJ1HbI F(t --) Y HacOCa;
a
p<jju - .n;aBJIeHHe TOnJIHBa B 06'beMe V cP B MOMeHT nOCa.n.KH HrJIbI
Ha ce.rl.J1o;
cpn - yro.TJ nOBopOTa BaJIa HaCOCa, COOTBeTCTBYlOI.l.{HH MOMeHTY
nOCaAKH HrJ1bI Ha ce.n.JIO;
h: - pa3rpY30'lHbIH XO.n. HameTaTe.lbHOrO K.lanaHa.
CJ1Q)KHB ypaBHeHHH (219), (220) H (221), nOJ1Y'lHM 06I.l.{ee
ypaBHeHHe .!l:JIH nOJ1HOH IJ.HK.l0BOH no.n.a'lH
(I) (2) (3)
ql! = q' + q" + q'" = in (ha"T-f-h )+ VII(p ; + V (p-: P K) +
( 5)
+ VtjJ(P-;=-PtPuH -- --f r i H [ W ( t+ : ) -W ( t- )] -
6nap a a
'Pn
(7)
(61
,'-'P"
. !-lor I 2 .. V '
--f"hK-fj;;V/ P J fo P,,-Pordcp.
'Por
-----
(222)
B ypaBHeHHH (222) 'lJleHbI (2), (3), (4) H'laCTH'lHO (5) xapaK-
TepH3YlOT BJ1HHHHe Ha BeJ1H'lHHY qt> MeCTHblX 06'beMOB H CLKH!\lae-
l\IOCTlI TonmlBa, npH'leM 'lJIeH (2) HBJIHeTCH oTpHIJ.aTeJIbHbIM, TaK
KaK AaBJIeHHe P n B MOMeHT nepeKpbITHH nJIYHLKepOM BcaCblBalO-
I.l.{HX OKOH 'laI.l.{e Bcero 3Ha'lHTeJIbHO MeHbllIe .n.aBJIeHHH P K B
MOlVleHT pa306I.l.{eHHH 06'beMa V1/. C 06'beMOM V . C.TJeAOBaTeJIbHO,
lI.leH (2) YMeHbllIaeT Be.1H'lHHy qt>. BJ1HHHHe 'l.TJeHOB (3) 11 (4)
3aBHCHT KaK OT BeJ1H'lHHbI pa3HoCTH .n;aBJIeHHH, TaK H OT Seml'lIlHbI
06'beMOB V1/., V H V<jj. Pa3HOCTb AaBJIeHHH (P n -P: u ) H
(P<jjn - pg;u) Ao.1LKHa 6bITb He3Ha'lHTeJIbHOH, npH'leM B 3aBHCHMO-
CTH OT KOHCTPYKTHBHUX napaMeTpOB H 'lHCJIa 060pOTOB 3TH pa3HO-
CTH MOrYT 6bITb KaK OTpHIJ.aTeJIbHbIMH, TaK H nOJIOLKHTeJ1bHbIMII.
BBH.n.y He3Ha1.:JHTeJ1bHOCTH pa3HOCTH YKa3aHHbIx AaBJIeHHH, OCO-
6eHHO Ha HOMHHaJIbHOM peLKHMe, BJ1HHHHe 'lJ1eHOB (3) H (4) Ha
SeJ1H'lHHY qt> B OCHOBHOM 6y.n.eT onpeAeJIHTbCH 06'beMaMH V H V cP,
KOTopbIe OT 'lHCJ1a 060pOTOB He 3aBHCHT. Ha Apymx pe)J{HMax Be-
J1HqHHa YKa3aHHblx pa3HoCTeH J:I.aBJIeHHH MQ)KeT H3MeHlITbcH, o.n.HaKo
3TO H3MeHeHHe TaKLKe 6y.n.eT He3HaQHTeJ1bHbIM, n03ToMY OHO He
MO)J{eT 3aMeTHO YMeHbllIaTb HJIH YBeJIH1.:JHBaTb qt>. TaKHM 06pa30M,
xapaKTep H3MeHeHHH qt> = f(n) B OCHOBHOM AOJI)J{eH onpe.n.eJIHTbCH
3aBHCHMOCTblO OT 'lHCJ1a 060POTOB, JIH60 060HX 'lJIeHOB (5) H (7).
JIH60 o.n.Horo H3 HHX. 113 aHaJIH3a BblpaLKeHHH AJIH 'lJIeHOB (5) H (7)
CJIe.n.yeT, 'ITO npH rrpOQllX paBHblx YCJIOBllHX 3TH qJIeHbI .n.OJILKHbI
B03pac.:raTb nponopUHOHaJIbHO YMeHbllIeHHlO 'lHCJIa 060pOTOB. B
204
,LI,eJ"ICTBI1Te.lbHOCHI }Ke lI3-3a BJllI5!HlI5! C}KlIMaeMOCTlI 11 ,LI,pOCCe.llHpO-
B8HIIH TOnJllIB8, 8 TaK)Ke ,LI,pyrIIx <paKTOpOB YKa3aHHOH BbIllie npo-
nOpl\IIOHa.TJbHOCTII HeT. 4.1eH (5) B OCHOBHOM qepe3 n.'IOlIlanb f T
yqIITblBaeT BJ1HHHHe ,LI,HaMeTpa HarHeTaTeJlbHOrO Tpy60npoBona,
KOTOpbIH OT qHCJ1a 060pOTOB He 3aBHCHT. BJ1HHHHe ,LI,J1HHbI Tpy60npo-
BO,LI,a CKa3bIBaeTCfI Ha BeJIll'lHHe OTpameHHbIX BOJ1H, aMn.'IHTY,LI,a
KOTOpbIX npn np01JHX paBHbiX YCJ10BHfIX 3aBliCIIT OT L, TaK KaK 3TOT
n8paMeTp onpe,LI,eJ15IeT nYTb OT HaCOC8 ,LI,O <POPCYHKH. OAHaKO nplI
H3I1IeHeHlIlI 06"beMOB CHCTeMbJ, LJHCJ1a 060pOTOB If ,LI,pyrHx napaMeT-
pOB OTpa}KeHHbIe BOJ1HbI, a CJ1e,LI,OB8Te.TJbHO, II 'weH (5) TaKJKe 6ynYT
H3:\IeH5ITbCfI, npIILJeM MorYT II3MeHflTbCfI KaK BeJIHqHH8 aIlm.71HTynb!
BO.1HbI, TaK H ee 3HaK.
:VIs aHaJIH3a BbIpa}KeHHfI ,LI,J1fI qJIeHa (5) c.le,LI,yeT, LJTO pa3HOCTb
Me}K,LI,y aMnJ1HTynaMH OTpameHHbIX BOJIH I1lOmeT 6bITb 60JIbIlIOH,
eC.1H 3TH aMnJIHTY,LI,bI npOTHBOn0J10mHbI no 3HaKY HJ1H cyrnecTBeHHO
pa3.1HqHbI no a6COJIIOTHOH BeJIHLJHHe. O,LI,HaKO yKa3aHHbIe YCJ10BHfI B
OCHOBHOM B03HIIKaIOT npH pe3KHX HapYllIeHHfIX xapaKTepa TeqeHH5I
Ton.1IIBa. B 60JIbllIIIHCTBe me CJIyqaeB pa3HOCTb aMnJ1HTY,LI, OTpa-
}KeHHbIX BOJIH no a6C0J1IOTHOH BeJ1HqHHe He3HaqHTeJ1bHa, n03TOMY
'weH (5) He MomeT OKa3blBaTb peruaIOIUero B.1JHHHHfI Ha xapaKTep
npOTeKaHHfI 3aBHCIIMOCTH q1J = f(n).
H3 paCCMOTpeHIIfI qJ1eHOB ypaBHeHIIfI (222) CJIe,LI,yeT, LJTO KaK
Be.1H1JHHa q"ij, TaK II 3aBHCHMOCTb q"ij = f(n) B OCHOBHOM onpe,LI,e-
.11fIIOTCH cooTHorueHIIeM Me}K,LI,y q.leHaMII (1) II (7). 3HafI, qTO npIf
OTCeqKe n.TJYHmep B HameTaTeJIbHbIH Tpy6onpOBO,LI, nO,LI,aeT MaJIO
Ton.1HBa, KOJIHqeCTBO ero MomHO He yqHTblBaTb H YKa3aHHoe BbIllie
COOTHOliIeHHe Mem,IIY KO.1IHqeCTBOM TonJ1HBa, nO,LI,8HHOrO nJ1ymKepOI\1,
If KOJIHqeCTBOM BbITeKllIero B .'IHHIIIO OTCeqKIf I\10}KHO BbIpa3IITb
K03<PtP H l\HeHTOM
w = fnhaKT .
qOTC
(223)
ECJ1H Ha OCHOBe npOBe,LI,eHHorO aH8JIH3a ypaBHeHHfI (222) c,LI,e-
JIaTb JI.OnyrneHHe, qTO
q,{= fnhaKT-qoTc,
TO C yqeTOM npe,LI,blJI.ymen 3aBIfCHMOCTH nO.1IYQUM C.1Je,LI,yIOmyIO
<POPMYJIY:
ql! = fnhaKT( 1 -+ ).
(224)
TaKIIM 06pa30M, npII6J1IImeHHO K03tP<plII.U1eHT
6Y,LI,eT onpeJI.eJ1fITbCH BbIpameHIfeIlI
( I )
- 1--
'I11i- (W)2'
nOL(aLJH CHCTeMbI
(2248)
TOrL(a
qll = f n haKT 'I1I1'
(225)
205
113 aHa.m13a ypaBHeHHR (225) cae.n:yeT, 1.JTO 1.JeM 60J1blIle fnhanr
H fI', TeM 3Ha1.JHTec1bHee 6y.n:eT q1.f lWIl, .n:pyrHMH CJ10Ba1-lH, I.JeM
MeHbille BO Bpell1H Henocpe.n:cTBeHHoH CBR3il 06'beMa V u C 06"bellWM
V nepeTeI.JeT ToniUIBa B .'1HHHIO OTCeI.JKH, TeM 60J1blIle 6YJJ.eT
BnpblcHYTO TonJ1ilBa B UHJIHH.n:p J(BHraTe.'1H. EC.'11f 6bI BMeCTO OTCelJKH
nOJJ.a1.Ja TonJ1HBa JJ.03HpOBaJ1aCb .n:pyrHlII cnOC060M, TO B UHJ1HH.n:p
JJ.BHraTe.'J51 6bIJIO 6bl nO.n:aHO TOn.'IHBO, paBHoe no 06'beMY f nlzanT,
T. e. ero c:m:UMaeMOCTb He OKa3aJIa 6bI
Ha npOH3BOJ.l.HTe.'lbHOCTb CHCTeMbI 3aMeT-
Horo B.'lHHHHH.
K.aK H3BeCTHO' CKopOCTHaH xapaKTe-
pHCTHKa no.n:a'lH q1J. = f(n) npOTeKaeT
npH HeH3MeHHOM 3Ha1.JeHHH h anT . O.n:HaKO
xapaKTep H3MeHeHHH fI', a CJIe.n:OBaTe.lb-
HO, H q1.f = f(n) 3aBHCHT OT BeJIH1.JHHbI
lz anT , 'lTO C .lI.OCTaTO'lHOH y6e.lI.HTeJIbHO-
CTblO HJIJIIOCTpHpyeTcH pHC. 93. B CBOIO
01.Jepe.lI.b, BeJIH'lHHa h anT B3aHMOCBH3aH8 C
K034>4mUHeHToM fI', KOTOpbIH OK83bIBaeT
BJIH5IHHe H8 hanT BO BpeM5I perYJIHpOBa-
HII5I CIICTeMbI. PerYJIHpOBaHH€ CHCTeMbI
'lallI.e Bcero npOH3BOtl,HTCH npH 060po-
Tax, COOTBeTCTBYIOIll.HX HOMHHaJIbHOMY
pe:m:HMY, KOTopbIe B 6bICTPOXO.n:HbIX J.l.JI-
3eJIHX HBJIHIOTCH tl,OCTaT01.JHO 60.1bmHMH.
BCJIe.n:CTBHe 3Toro BeJIH1.JHHa qOTC 6y.n:eT
CYIll.eCTBeHHO 3aBHceTb OT ApOCCeJmpOBa-
HHH TOnJIIIBa B OTCeI.JHbIX KaHa,,'1aX H OT-
BepCTlI5IX, npH1.Jel\'! .lI.poCCeJIlIpOBaHHe Tel\'! 60JIblIle. 1.JeM BbIlIle o6opo-
TbI. Ho 1.JeM 60JIblIle .lI.poCCeJ1HpOB8HHe, TeM nplI MeHblIleM aKTHB-
HOM XO.lI.e .n:OCTlIraeTCH Tpe6yeMaH npoH3Bo.n:I1TeJ1bHOcTb. TaKoH me
34>4>eKT o6eCne1.JHBalOT YC.'lOBHH, onpe.lI.eJIHIOIll.He BO BpeMH OTCe1.JKI1
npo.n:OJI1KHTeJ1bHOCTb coo6meHHH 06'beMa V"H. C 06'beMOM V , B -CB5I-
3H C TeM, 1.JTO YKa3aHHbIe 4>aKTopbI 3aBll'CHT OT 1.JHCJIa OOOpOTOB, OHM
TaK1Ke onpe.lI.eJIHIOT xapaKTep npOTeKaHH5I 3aBlICHMOC'TH UlIKJIOBOH
nO.lI.8"IIH TOnJIHBa OT 'IHCJIa 060pOTOB.
B 4 HaCTOHllI.eH r.'1aBbI 6bIJIO nOK838HO, K8K MO:m:HO B.'1II5ITb
Ha xapaKTep npoTeKaHHH 3aBHCHMOCTH q1.f = f(n) nYT€M H3 leH€HIIH
napaMeTpoB HarHeTaTe,,'1bHOrO KJ1anaHa, Kor.lI.a nOCJ1e.lI.HHII If MeeT
pa3rpy:m:alOIll.IfH nOHCOK. DpH OTCYTCTBHH Y KJ1anaHa pa3rpy:m:alO-
llI.ero nOHCKa ero B03.n:eHCTBHe Ha 3aBIfCHMOCTb q1.f = f (n) cyIll.e-
CTBeHHO YMeHblIlaeTCH. B 3THX YCJIOBHHX .lI.JIH KoppeKTIIpOBaHIIH
xapaKTepIICTlIKII no.n:aI.J1I q1.f = f(n) He06xo.n:IIMO IICn0J1b30BaTb .n:py-
rHe B03MO:m:HOCTH: B lJaCTHOCTH, YBeJIHI.JHBaTb JIJIH YMeHblIlaTb .n:Ha-
MeTp OTCe'IHoro KaHaJIa, KOTOpbIH 06bI1.JHO CBepJIHTC5I B ueHTpe
nJIYH:m:epa, II.1H H3MeH5ITb npOXOAHYIO nJIOIll.a.n:b npope3H nOBepXHO-
CTlI nJIYH:m:epa, BbmOJIHHIOIll.eH Te :m:e .pYHKUHH, 'ITO H OTCe1.JHOH
f/q zjl.(Ul<ft
0,25
0,20
0.1
300 500
700
n OijHUH
PHC. 93. XapaKTepHCTHKH
qll = f(n} npM pa3J1H'-!HbIX
nOJlOLKCHHHX pei1KH Ton-
JlHBHOro Hacaca
206
I{aHaJ1. DpIP-IHHbI, Onpe,lI,eJIHIOm:He BJUIflHHe :noro napaMeTpa Ha
3aBHCHIIWCTb q1J. = f( n) ,- CJ1e,lI,CTBHe ero B03,lI,CllCTBHH Ha OTCeqKV.
a c.'Ie,lI,OBaTe.lbHO, H Ha BeJIHqHHY aKTHBHoro XOjI.a nJIYH1Kepa BO Bpe-
::\I5J perYJ1HpOBaHHH CHCTeMbI Ha npOH3BO,lI,HTe.'IbHOCTb. DOCJ1e,lI,Hee-
npOH3BO,lI,HT npH BWCOKOM qHCJIe 060pOTOB H 60JIbillOll npOH3BO,lI,H-
Te.TIbHOCTH, KOr,lI,a JJ.pocce.TIHpOBaHHe B OTCeqHOM KaHa.'Ie H:m npope3H
OKa3bIBaeT Ha BeJ1Hqlmy q1J. MaKCllMa.lbHoe BJIH51Hlle.
ECJIll BeJIllqllHW npOXO,lI,HOll nJIom:a,lI,H OTCe'-lHOH npope3M llJIll
,lI,HaMeTpa OTCeqHOrO KaHa.'1a MaJIbI, TO nOCJ1e HaqaJ1a OTCe'-lKH BCJIe,lI,-
CTBue 60JIbIllOro ,lI,poCCeJ1l-IpOBaHHH B HarHeT JTeJIbHbIH Tpy6onpOBO,lI,
6Y,lI,eT nO,lI,aHO em:e 3HaqHTeJIbHOe KOJIH'-IeCTI30 TOnJIHBa. B 3THX
YC.TIOBHHX Tpe6yeMYIO npOH3BO.lI.HTeJIbHOCTb ClICTeMbI MO>KHO o6e-
Cne'IRTb npH cpaBHHTeJIbHO He6oJIbIllOM aKTHBfIoM xO.lI.e nJIymKepa.
Ho, KaK H3BeCTHO, npH MaJIOH npOXO.lI.HOH nJ10m:a,lI,H OTCeQHOrO Ka-
HaJIa ,lI,pOCCeJIHpOBaHHe TOnJ1HBa B 3TOM KaHaJIe cymecTBeHHO
3aBHCHT OT qHCJIa 060pOTOB. B CBH3H C 3THM lIPH CHII>KeHHH qHCJIa
060pOTOB KO.1HqeCTBO TonJU-IBa, nO,lI,aBaeMOrO B HarHeTaTeJIbHblH
Tpy6onpOBO,lI, nOCJ1e OTCeqKH, YMeHbillaeTCH, JaK KaK B03paCTaeT
KOJIHqeCTBO TOnJIHBa, nepeTeKaIOm:ero B OTCeqHYIO JIHHHIO. B03M02K-
HO, 'ITO 3Ta npHqHHa HBJ1HeTCH OCHOBHOH, BbI3bIBaIOIll.eH YMeHbIlleHIle
BeJIHqHHbI q... npH CHHLKeHHH qUCJla 060pOTOB.
ITpH 60JIbillOH npOXO,lI,HOll nJIow.a,lIH OTCeqIIOro KaHaJIa ,lI,pOCce-
J1HpOBaHHe Ton.HHBa B HeM He3HaqHTe.'1bHO H n03TOMY MaJIO 3aBHCHT
OT qHC.'Ia 060pOTOB. B .3THX YC.l0BHHX BCJ1e,lI,CTBHe BbICOKoro ,lI,aBJIe-
HUH TOIIJIHBa B CHCTeMe H MaJIOrO JJ.pOCCeJIHpOBaHHH B OTCe'IHOM
KaHaJIe ,lI,.lSI 06eCIIe'IeHHH 3a,lI,aHHOH npOH3BO,lI,HTeJIbHOCTH nOTpe-
6yeTcH 3HaQHTe.lbHO 60J1billHH aKTHBHbIll XO,lI, nJ1YH1Kepa, 'IeM IIPH
MaJ10I\I ,lI,l-IaMeTpe OTCe'IHoro KaHa.la nJ1YH2Kepa. ITpH YMeHblIleHHH
'lHC.'1a 060pOTOB ,lI,pOCCeJIHpOBaHHe B OTCeqHOM KaHaJIe IIpaKTH'leCKH
COXpaH51eTC51 HeH3MeHHbIM, n03TOMY KOJIH'IeCTBO TOIIJ1HBa, IIepeTe-
KalOIll.ero B OTCe'IHYIO JIHHHIO, B 60J1billeH CTeneHH 6Y,lI,eT 3aBHceTb
aT nepeIIa,lI,a .D,aBJ1eHHll, KOTOpbIH YMeHbIllaeTC51. ITpH YMeHbilleHHH
'IHCJIa 060pOTOB B OTCe'IHYIO JIIiHHIO nepeTeqeT MeHbIlle TOnJIHBa, B
pe3YJIbTaTe qero BeJIH'-IHHa q" B03paCTeT. CJIe.n.OBaTeJIbHO. aKTHBHwR
XO.lI. nJIYHLKepa, He06xo.rUIMbIH npH pa60Te CHCTeMbl Ha HOMHHaJ1b-
HaM peLKHMe, HBJ1HeTC5I 3aBHCHMblM OT YCJlOBHH, orrpeJI,eJIHIOm:HX
npOTeKaHHe IIpou.ecca TOrrJIHBOIIO,lI,aqH npH QHc.rre 060pOTOB MeHbllIeM
qHCJIa 060POTOB, COOTBeTCTBYIOw.ero HOMHHaJIbHOMY pe)KHMY.
Ha pHC. 94 IIOKa3aHbI 3aBIiCHMOCTH q1j = f(n), CHHTbIe IIPH pa-
60Te CHCTeMbI C IIJIYH2KepaMH, B KOTOpbIX K8Ha.1IbI HMeJIH pa3JIH'IHbIE'
.D:HaMeTpbI. I-IcXO,lI,H8H TO'IKa, cooTBeTcTBYIOm:a5I HOMHHaJ1bHOMY pe-
1KHMY, BO Bcex CJIY'I8HX perYJIHpoBa.1aCb Ha O,lI,HY Ii TY 2Ke BeJ1lIqHHY
q1J.. I-I3 pHC. 94, a BH,lI,HO, 'ITO H3MeHeHHeM ,lIHaMeTpa OTCeQHOro
KaHaJIa npaKTHQeCKII M02KHO C03,lI,aTb J1I060H HaKJ10H IIpOTeKaHHH
3aBHCHMOCTH q'tf = f(n), T. e. xapaKTepHcTHKY llO,lIaQH M01KHO KOp-
peKTHpoBaTb 6e3 npHMeHeHH5I ,lI,OIIOJ1HHTeJ1bHNX MeX8HHQeCKHX
YCTPOHCTB, IIO.3TOMY 38,lI,aHHaH npoH3BO,lI,HTeJ1bHocTb 6Y,lI,eT 06ecne-
'IeH8 npH MeHbilleM aKTHBHOM XO,lI,e llJIYHLKepa J10 cpaBHeHHIO C npe-
207
JI,bI.n:Yll1.HM CJJYlJ:8eM. OpH 3TOM ApocCemrpOB8HI1e 6y.a:eT YMeHbW8Tb-
CH rrpH CHH>KeHHH tlIIC.1a 060pOTOB.
BJIlHlHHe HCJ1a 060POTOB BaJIa TOnJIHBHOrO Hacoca Ha OCHOBHbIe
napaMeTpbI npou.ecca BnpbIcKa. npH H3MeHeHHH lJHCJIa OOOpOTOB
npouecc Ton.1I1BOnO;LalJH BO BpeI\leHH 3aMe.a:.'I5IeTCR H.1l1 YCKopReTCfl.
B COOTBeTCTBHH C 3THM .IT.OJI>KHbI
H3MeHflTbCH H £IapaMeTpbI £Ipo-
l.\eCca BnpbICKa. f1pH CHIDKeHHif
llIICJJa OOOpOTOB OCHOBHbIe nOKa-
3aTeJJH: )J.aBJJeHI1e, npo.a:OJI>KU-
TeJIbHOCTb nO,lI,alIR B rpa,lI,ycax
nOBopOTa BaJIa U )J.pyme napa-
MeTpbI .lI.0Jl}KHbl YMeHbIllaTbC5I B
COOTBeTCTBHH co CHH)K€HHeM CKO-
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Ha pRC. 94, 6 R300pa}KeHa
38BHCHMOCTb )J.aBJ1eHI15I TOnJIHBa
B IllTYl.\epe Hacoca H I):>0PCYHKH
OT 'I-HCJIa OOOpOTOB. 113 8H8JIH3a
nOM 3aBHCHMOCTH CJIe)J.yeT, lJTO
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HeHHIO lJUCJI8 060POTOB, a .a:aB-
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Ha pHC. 94, 6 nOKa3aHa TaK-
}Ke .l(HarpaMMa 3aBHCHMOCTH
(jJn = f(n). 113 nOlI ,lI,HarpaMMbI
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HOCTb BnpbICKa npn YBemllJeHHH
lIHCJ1a OOOpOTOB B03paCTaeT 00-
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.TJeHHH B.1JHRHHH ,C>KHMaeMOCTH
TOnJ1HB8 Ha KOHel.( np0l.\eCC8 BnpbICKa. 003TOMY {5] 1):>0pCI1pOBaHHe
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OCYIlleCTBJISITb nYTeM npOBe.l(eHH5J KOMnJIeKCa Mep. Hanp8BJIeHHbIX He
TOJIbKO Ha YBeJIll't.J.eHlle npOH3BO,lI,llTeJIbHOCTH CllCTeMbl, HO II lla co-
xpaHeHHe HeH3MeHHOM np0JI.0J1}KHTe.'lbHOCTH BnpbICK8 TOnJIHB8. Pa-
Hee OTMelJa.10Cb, lITO npH YBeJJHlJellHH lJHCJIa OOOpOTOB B03paCTalOT
KOJJeOaHHSI ,lI,aB.TJeHHSl H CKOpOCTH, B pe3YJJbTaTe lJero MorYT B03HHK-
HYTb BTOpJ1lIHbIe nO,lI,"beMbl HfJIbl H .a:onOJJHHTeJJbHbIe BnpbICKH, cyme-
CTBeHHO yxy.a:IllalOIlI.He 3KOHOMHlJ.HOCTb JI.H3emL B HaCT051ll1.ee BpeM51
MO)KHO YCTaHOBHTb onaCHOCTb nOSIBJIeHH5I )J.onOJIHlITe.JIbHbIX BUpbIC-
P;'P'/J
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PMC. 94. BJ1MHlme 'UlCJIa 06opoTon Ha
rrapaMeTpbl npol\ecca nnpblCKa:
a - BJIH>JHHe Ha 3aBHCHMOCTb ql{ = fin)
.n;pocce...'JHpOB8HH}l TonJIHB8 B KaHaJIe nJIYH-
>Kepa: J, 2, 3 - 3aBHCHMOCTH q lj= fIn) npl1
pa3JIH4HblX )],HaMeTpnx I<aHaJIa B nJIYHlliepe;
8 - BJ1HRllHC 'lHCJla 060pOTOB ffa napaMcT-
pbl npo ecca BITpb'CKa )],JISI JJ.HaMeTpa Ka-
HaJIa nJIYH>Kepa, cooTBeTcTBYIOIl\ero )],H-
arpaMMe J Ha pHe. 94, a; J - d,,= 3 lIUt;
2 - d,,=2 JIIJII; 3 - dK \,5 1I111l; 4
AaBJIeHHe Y Hneoca; 5 - )],aB. eHHe Y q,op-
CYHKH; 6 - npOJlOJ11KHTe :YbHocTb BnpbrCKa
fl'n
208
KOB npH <pOpCHpOB3HHH CHCTeMbI no npOH3BOD,HTeJIbHOCTH H IIHC.TJY
060pOTOB [6], 3 T3K)Ke H3MenITb nYTH HX D,eMn<pHpOB3HHH HJIH no.rr-
IIoro )'CTp3HeHHH.
H3 pUC. 95 nOK33aH3 J1,I1arp3MMa, Ha KOTOpOH onpeJ1,eJ1eHbI LI.O-
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CTpoeHa J1,.TJH CHCTeMbI TH no <popMy.rraM pa60TbI [6]. CornacHo
pEC. 95 B CHCTeMe TH npH YBemllle- (
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BnpbICKOB. MepbI 60pb6bI C ,D,onOJI- 800
HHTeJ1bHbIMH BnpbICK31\IH 6bI.'IH
paCCMOTpeHbl HaMIl paHee. HanO I-
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l\IeHeHHe KOHCTPYKTHBHbIX napa-
MeTpOB HarHeTaTe.1bHoro K.TlanaHa
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Te.1bHbIe BnpbICKH, HO H3MeH5IIOT H
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uecca Ton.1HBonOAa'IH. TI03TOMV
BCerJ1,a Heo6xoJ1,HMO npoBepHTb pa-
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cneQHaJ1bHOH YCTaHOBKe, TaK H I1a
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CTBHfI pa3pblBOB CI1.rlOlUHOCTH nOTOKa If
Ollu..'1HHTe.nbHblX BnpLICKOB: B - 06-
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HB.1HeTCH 3aBepUlaIOlUHl\1 Y3.101\1 Ton.1HBHOH CHCTeMbI, KOTOpbIH
3aKaHlHmaeT <pOpl\IHpOBaHHe 3aKOHa TOll.'IHBOnOJ1,allH, HenOCpeD,-
CTBeHHO conpHKaCaeTC5I C K3I1IepOH cropaHIm H BnpbICKI1B3eT B Hee
TODJ1HBO.
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.1HH Bcex 3J1eMeHTOB TonnllBlIOH CHCTeMbI B opraHH3aQHH npOQeCCa
Ton.rrHBOnOD,alfH H BbID,aeT ero OKOHlfaTe.1bHbIe oapaMeTpbl. D03TOMY
OT Q:J0PCYHKH 60J1bUle '-1el\I OT J1,Pyroro Y3J1a TOOJ1HBHOH CHCTel\Ib1
Tpe6yeTcH lJeTKaH, BbICOKOKalJeCTBeHlIaH pa60Ta.
BJ1HHHlle Q:JOPCYHKH Ha xapaKTepHCTHKY BopbICKa B OCHOBHOM
onpeJ1,eJIHeTcH:
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,D,aHHOH r.1aBbI;
2) Hr.1oH <POPCYHKH, BbInOJ1HHIOlUeH Q:JYHKUHIO 3anopHoro opraH a
H OKa3bIBaIOlUeH BJ1H5IHHe Ha xapaKTepHCTHKY BnpbICKa He TOJlbKO
Te:\I, 'ITO onpeD,eJ1HeT Halla.fIO H KOHeu nOAalJI1 Tonc1HBa, HO 1I CBOHMJf
14 3aKa3 748 209
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3) cYMMapHoH IIpOXO.ll,HOH IIJ10I.IJ.a.ll,blO paCIIbIJ1HBalOI.IJ.HX OTBep-
CHIH, OT BeJ1HqHHbI KOTOpOH cYI.IJ.eCTBeHHo 3aBHC5IT npOH3BO..'!.HTe.'lb-
HOCTb CHCTeMbl, ee CKJIOHHOCTb K .lI,OnOJIHHTeJIbHbIM BnpbIcKaM H B
HeKoTopoH CTeneHH xapaKTep npOTeKaHII5I 3aBI1CHMOCTH q'f = f(n).
BJlURHUe Ha xapaKTepucTuKY 8npblCKa U2Jlbl £/JOPCYHKU. Cor.rJac-
HO paCqeTHOH cxeMe CHCTeMbI Ha pHC. 23 H aHaJ1H3Y ypaBHeHlIH
(219) - (222) Ha npol.{ecc nO.ll,aqH TOIIJIHBa MOfYT BJ1HHTb: d u -
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.lI,BH)KYI.IJ.HXCH C HeH qaCTeH; C u - CKOpOCTb .lI,BH)KeHHH HrJ1bI; Pifjo-
Haqa.'lbHa5I 3aTH)KKa IIPY)KHHbI HrJ1bI; fll - BeJ1HqHHa npoxo.ll,HOII
II.'lOI.IJ.a.ll,H (I.IJ.eJ1H) Me)K.lI,Y KOHYCOM HfJIbI H ee Ce.ll,J10M.
DpH nO.ll,"beMe HfJIa oCBo6o)K.lI,aeT 3aHHMaeMbIH elO 06"beM,
II03TOMY <IaCTb TOIIJIHBa, nO.ll,BO.ll,HMOro K CPopcYHKe, paCxO.ll,yeTC5I Ha
3an0J1HeHHe YKa3aHHoro 06"beMa. DpH onycKaHHH Hr.'la 6y..'!.eT
BbITaJ1KHBaTb 3TO TOnJ1HBO B 06"beM V ifj. .1J.aHHoe HBJ1eHHe HanOMH-
HaeT npOl.{eCCbI HailOJIHeHHH H HafHeTaHHH Hacoca, IIOqeMY OHO H
Ha3bIBaeTCH HaCOCHbIM .lI,eHCTBHeM HrJIbI, BJIHHliIfe KOToporo 3aBHCHT
OT CKOpOCTH ee nO.ll,"beMa H onycKaHH5I.
1.:13 .lI,HafpaMMbI 6a.rJaHca Ton.rJHBa (CM. pnc. 63) BHJI.HO, qTO B
MOMeHT nOJI.XO.ll,a HfJ1bI K ynopy fnCn = 80 cMslceK; fTC; =
= 175 cM 3 /ceK, a fJ.cfcC c = 125 cM 3 /eeK. y13 3TOfO c.'le.ll,yeT, qTO B
3TOT MOMeHT pacxo..'!. TOnJ1HBa npeBbIIllaeT npHXO.ll" n03TOMY .lI,aB.le-
HHe pifj 6Y.ll,eT YMeHbIllaTbC5I. 3TH l.{HCPPbI C .lI,OCTaTOqHOH IIO.TIHOTOH
HJ1J1IOCTPHPYIOT 3HaqeHHe HaCOCHOfO .lI,eHCTBH5I HrJ1bI KaK cpaKTopa,
HCKa)KalOI.IJ.efO xapaKTep IIpOTeKaHHH npou.ecca BnpbICKa.
B COBpeMeHHbIX TOnJ1HBHbIX CHCTeMax 6bICTPOXO.ll,HbIX .lI,H3e;leH,
B KOTOpbIX ..'!.HaMeTpbI nJIYH)KepOB COCTaBJ151IOT 8-14 MM, qaI.IJ.e
BcefO npHMeHHIOTCH HfJ1bI CPOPCYHKH C d u = 6 MM, qTO He HB.'lHeTCH
pau.HOHaJ1bHbIM. EOJIee u.eJ1eC006pa3Ho B TOIIJIHBHblX CHCTeMax C
d n = 8 -7- to MM, CBoHcTBeHHbIx .lI,JIH aBToTpaKTopHbIX ..'!.H3e.1eH,
HCn0J1b30BaTb Hf.'lbI C d u = 5 MM. B 3TOM CJ1yqae npou.ecc MeHbille
HCKa)KaeTCH HaCOCHbIM .lI,eHCTBHeM HfJIbI, a Ha caMY Hr.1Y .lI,eHCTBYIOT
MeHbillHe CH.rJbI .lI,aBJIeHHH TOIIJ1HBa.
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06"beMa V g;. ECJIH 3Ta Be.JIHqHHa cOH3MepHMa C 06"beMOM, KOTOpbIH
oCBo6o)K.lI,aeT HJIH 3aII0J1H5IeT npH CBoeM .lI,BH)KeHHH Hf JIa, TO IIPH
nO.ll,"beMe HfJ1bl, KaK 6bIJIO nOKa3aHO, C03.l1,aeTCH ,!I,Hc6aJ1aHC Me)K.lI,y
nocTynJ1eHHeM H paCXOAOM TOnJ1HBa, qTO MO)KeT 3aMeTHO YMeHb-
IllHTb .lI,aB.!JeHHe pg;.
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HOH CTeIIeHI1 6Y.ll,eT IIOKpbIBaTbCH B pe3YJ1bTaTe paCIllHpHIOI.IJ.erocH
TOnJIHBa, qTO YMeHbillaeT BJ1HHHHe Ha IIpOl.{ecc BnpblCKa HaCOCHOfO
,!I,eHCTBHH HrJIbI.
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KaK OT ero BeJ1HqHHbI 3aBHcHT KO.rJHqeCTBO TOnJIHBa, nocTynHBillero
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210
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nb1JIHTeJIei'I, OC06eHHO aBTOTpaKTOpHb1X JJ.H3eJIei'I, TOnJIHBHb1e CHCTe-
l\IbI KOTOpbIX IIMelOT nJ1ymKepbI He60.'IbillOrO JUlaMeTpa, COH3MepH-
l\lble C .D.HaMeTpOM HrJ1b1, paBHbIM B 60.TIbIlInHCTBe CJ1YlIaeB 6 MoW.
YCTaHOBJ1eHO [5], liTO Be.ln-
lJHHa f... 2flcfc HBmleTCH
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BnpbICKa .D.pOCCe.1IIpOBaHHe
TOnJIHBa B 3TO:\1 CelleHHH,
BC.lelJ,CTBHe lJero npH 3HalJH- 500
TeJ1bHOM YMeHbIlIeHHH Be.J1H- Po
lJHHbI P nOHBJIHlOTCH .D.Ono.Jl- Kf/c/'l
HHTe.'IbHbIe BnpbICKII. 120
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MeTpbI npol.l,ecca BnpbIcKa CH-
CTeMbI TH nOKa3atIO Ha
pHC. 96. 1'13 pHC. 96 CJ1e.lI.yeT,
liTO Po II Ipn npH Yl\1eHbillemIH
lIHC.'Ia 060pOTOB HeCKO.1JbKO
H3MeHHlOT Be.'IHlJHHY, liTO Ha
xapaKTep npOTeKaHHH IIX
.lI.HarpaMM nOlJTH He BJ1HHeT.
J],aBJleHHe pifJ npH n = 1000
06jMUH I13MeHHeTCH 60.'Iee
pe3KO, lJeM npH n = 600
06jMUH. OplI Ymax < 0,6 MM
B,,'IHHHHe 3Toro napaMeTpa
CTaHOBIITCH 60JIee cYll.I,eCTBeH-
HbIM. J],JIH IICnbITbIBae:\wH CII-
CTeMbI npH Ymax = 0,6 MM
npOXO.D.HaH nJ10ll.l,a.D.b f... 2flcfc. Ha pnc. 97 nOKa3aHO BmIHIme
Ymax Ha xapaKTeplIcTHKY BnpbIcKa. COrJIaCHO plIC. 97 .D.OnOJIHHTe.lb-
HbIe BnpbIcKII nOHB.'IHlOTCH Y)Ke nplI Ymax = 0.28 MM. Ho B CHCTCMe
TH d n = 13 MM, a d u = 6 MM. OpH MeHbIlIHX 3HalJeHlIHX d n .LI.Ono.1J-
HIITe.JlbHbIe BnpbICKII 6YlJ,YT B03HHKaTb npn MeHbIlIHX nO.lI."he:\Jax Ymax.
003TOMY TOnJIHBHbIe CHCTeMbI C .D.HaMeTpOM d n = 8 -;- 10 JI1M npn
Ymax = 0,28 MM pa60TalOT 6e3 .D.OnOJIHHTe.1JbHbIX BnpbICKOB TOn,,'IHBa
B l.I,IIJIHH.D.pbI .D.H3eJIH.
Opn paClIeTe npOllecca BnpbICKa lIall.l,e Bcero nplIHHMalOT, '-ITO
HrJ1a <POPCYHKII Ha IIUlaeT nO.LI.HHMaTbCH npH AaBJ1eHHII p,(J = PifJO.
O.lI.HaKO 3KCnepIIMeHTaJ1bHO YCTaHOBJleHO, liTO IIrJ1a cpOPCYHKII (B
3aBIICHMOCTII OT pe)j(JIMa) Ha'-l1IHaeT nO.lI.HlIMaTbCH npH PrfJ > PifJO
Ha 50-100 Kr;CM 2 . 06"hHCHHeTCH 3TO CHJIaMII IIHepUHH CTpanma-
HHH, TpeHHH II .lI.PyrHMH CIIJ1aMH, paC'-IeT KOTOpbIX B HaCTOHll.I,ee
14* 211
Pf/J K t7 CH2
HOO
80
'\.
"'- I
-
-
x, --- :--
'........ x .1
x
\ I
" I
,. ""--
I>-.. 0 2
,
'" - I
0
x........ 2
x I
I
900
700
40
o
!q,"
21
17
o fl2 {N 46 0,8 1,0 1,2 j!muxl'fl'f
Pl1c. 96 3aBI1CI1MOCTb napalllcTpOB npOl.\ee-
ca BnpblCKa OT BCJIIIQHHb! nO.D:"bCllla I1r JlbI
npH:
1 - n = 1000 OO/l,"'fi; 2 - n 600 06/MUfi
BpeMH 3aTpY HHTeneH. Ha XapaKTep npOTeKaHHH npouecca nO a4H
TOnJ1HB£1 paCCM£1TpimaeMbIH q>£1KTOp He OKa3bIB£1eT 3aMeTHoro B.'IH5I-
HIiH, 3£1 HCKm04eHHeM HeKOToporo YBenlfI.JeHIiH 3£1na3 bIBaHHH
H£14aJ'l£1 BnpbICKa. H£1 pHC. 98 nOK£13aH£1 3£1BHCHl\lOCTb napaMeTpoB
npouecca BnpbIcK£1 OT Be.TIH4HHbI q1J npH p£16oTe CHCTel\IbI TH Ha
n = 1000 06/MUH H n = 300 06/MUH. 113 3THX H£1rp£1MM cneJ.yeT,
4TO nr.'Ia nO.l{HHl\1aeTCH npH Pfljn > prjjO, npH4eM .l{.'JH n =
= 1000 06/MUH .:ITO npeBblllleHHe OCTIlraeT 100 KT/Ot 2 , a J1H
n = 300 06/MUH - 25 KT/cM 2 . npH n = 1000 06/MUH aBneHHe
BnpbIcKa p npeBbIlllaeT .l{aB.TIeHIle Ha4an£1 nO "beMa Hr.lbI TO.'IbKO
ml q'f > 0,14 2/U,UKJ7. .3TO 03Ha4aeT, 4TO B CHCTeMe TH npH
/Jfl MM¥epaiJ
30
fO
.
fO
'.
...........
40
o
10
20
30
PHC. 97. BJlli5lHIIC nO.D:"beMa HfJlbI Ha xapaKTcpHcTHKY BnpblcKa CHCTCMbI TH:
1 - Ymax 0,28.....'; 2 - Y max = 0,1 AIM; 3 - Ymax 1,5 AUf; 4 - Ymax 1,0 ."AI;
5 - Y max 0,51 M."
q'f < 0,14 2/U,UKJ1 Hr na q>OPCYHKH o ynopa He OXO HT. n pH
n = 300 06/MUH Ha BceM H£1na30He H3MeHeHHH q1J .l{£1BJ1eHHe
P < Prim, npH4eM B 06.TIaCTH Ma.TIbIX 3H£14eHIIH q1J BeJ1H4HHa p =
= 15 -7- 40 KT/CM 2 , T. e. aBJ1eHH51 BnpbICKa TaK ManbI, 4TO Ha 3TH X
pefJ{Hl\1aX TPY.l{HO O)KH.l{aTb y.l{OBneTBOpHTeJ1bHoro cMeceo6pa30Ba-
HHH. )J.aBJ1eHHe Prfi npH n = 300 06/MUH COBna.l{aeT no BeJ1II4HHe c
Pfljn, nO.l{TBep)K.l{a5I TeM caMbIM, 4TO IIUIa He .l{OCTHraeT ynopa.
IlpH n = 1000 06jMUH .l{aBneHHe Prjj, Ha4I1HaH c q1j > 0,075 2/U,UKJ1,
CTaHOBHTCH cyru:ecTBeHHo 60.'1bwe .l{aBJ1eHHH prfm. BeJ1H4HHa fjJn .lH
n = 1000 06/MUH npH YBe.'IH'IeHlIH q1J B03paCTaeT 60J1ee pe3Ko, 4eM
no o6HaH )Ke 3aBHCHMOCTb npI1 n = 300 06/MUH, 4TO nO.l{TBep)K aeT
q>aKT 60.'IbWerO B.1I1HHIIH C)KHMael\WCTH Ton.TIHBa npI1 n =
= 1000 06/MUH, 'leM npH n = 30006/.MUH.
HHOr.l{a xapaKTep npoTeKaHHH npouecca BnpbIcKa oueHHBaIOT
no OCUHJWOrpaMMe .l{aBJIeHHH prfi. COrJ1aCHO pliC. 98 TaKaH npH6JIH-
)KeHHaH oueHKa npHeMJIeMa TOJIbKO .l{JIH pe)KI1MOB, 6J1H3KHX K
HOMHHaJIbHoMY, KOr.l{a HrJ'la q>OPCYHKH 3Ha4IlTeJ1bHOe BpeMH npH)Ka-
Ta K ynopy, T. e. KOr.l{a .l{aB.'leHIIe P > prfio, HO npII 3TOM Heo6xo-
.l{HMO YQI1TbIBaTb, 4TO .l{aBJ1eHIIe Ha4a.la nO.l{"beMa 11 rJI bI Ha
212
50-100 KFjOt 2 npeBbIlllaeT .iJ.aBJ1eHlIe Pg,o. Ha pllC. 99 nOKa3aHa
3aBlIClI lOCTb .iJ.aBJleHlHI Ptjm OT llllC.la 060pOTOB npll lICXOn:HOM .:WB-
JIeHlIII Halla.'lbHoti 3annKKlI
npYiI\.I1HbI II rJl bI PrPo
= 200 KF/0.1 2 . Cor,;'laCHO
pllC. 99 pa3HoCTb ;.I,aBJ1eHlIH
PrPn II PtjJo 3aBlIClIT TO.'lbKO
OT q'l II 1.JlIc.'la 060POTOB,
TaK KaK Bce T01.JKlI C pa3-
JlH1.JHbIMH BeJ1HllllHaMH .'1e-
/KaT Ha O.iJ.HOC! np5JMOH.
CJlen:OBaTeJ1bHO, pa3HOCTb
(PrPn - PtjJo) 3aBlIClIT, B OC-
HOBHOM, OT AHHaMHKH ClI-
CTeMbI, CKOpOCTlI HapaCTa-
dp.p
HlI5J .iJ.aBJ1eHlI5I -, MaCCbI
dt
HrJlbI, :tKeCTKOCTlI npY:lI\.I1-
Hbl, lIHepI.I.lIl1 TpOraHH5J Hr-
JIbI, a TaK)Ke conpOTHBJ1e-
HHH ee .iJ.BH)KeHHlO. XapaK-
Tep 3aBHCHMOCTH Me)KJl.Y
Jl.aBJleHHeM prPn H 1.JHCJIOM
060pOTOB np5JMOJ1HHeHHbIH,
HO TaJ,a51 3aBHCHMOCTb nplJ-
MeHHMa TOJ1bKO npM pa6o-
Te ClICTeMbI B aTMoc<}Jep-
HbiX YCJI0BlI5JX:
PcP" = (pcf:>0-7)-+-0,12n.
(226 )
B CB5J3H C TeM, 1.JTO Hr-
JIbI C Jl.HaMe1'poM d u =
= 6 MM npmvleH5JlOTC5I lllll-
pOKO, <POPMYJIOH (226)
MO)KHO npH6JIH)KeHHO OI.I.e-
HHTb BeJIH1.JHHY PrPn Jl.JI5J
MHorHX TOnJIHBHbIX ClICTeM.
.lJ.JI5I 60JIbllJeH 06111HOCTH
<}JOPMYJIbI (226) OTJIO)KHM
no OCII a6CI.I.HCC BTOpOH na-
pal\leTp BMeCTO n - npo-
1I3BeJl.eHlIe fnCn, rJl.e C n -
CKOpOCTb nJ1YH)Kepa B MO-
MeHT nOJl.'beM8 HrJIbI (CM. pnc. 99). B ::ITOM
(17;
f8
f"
fO
6
"00
JOO
x
200
fOO
405 qq c/4I1KR
PHC. 98. 3aBHcHMoCTb napaMCTpOB npol.\cc-
ca BnpbJCKa OT BC.1H'IHHbl q1.f:
/ - P", npn 11 1000 061."1111; 2 - P", liP"
11 1000 06/"","; 3 - P,p" npH 11
1000 06/..WII; 4 - P gin npH 11 300 o6/..ul1l.
5 - P npH 11 300 06/."ulI; 6 - "'n npn
11 = 1000 06/ 1tllH; 7 - <P tl npu Il = 300 OVIJtllH
P n
Kf/cH2
300
zoo
100
°
.
tJ
200
,
600
,
Igg
8 q o fl, DO/HI1 H,
26 2 ./",0, cH.yceK
"00
,
IJ1:6
04J
PHC. 99. 3aBllcHMoCTb Ha4aJla nO.D:"bCMa
HrJlbl CHCTCMb! TH OT '-IHC.TJa 060pOTOB H
npOH3BC.!J.CHH5I f n en !{.TJH pa3J1H4Hb!X Ha-
rpY30K
CJlYllae
PcPn = {p,po-7)+0, 347 fn C n'
(227)
213
113J\IeHeHHe Ha1J.aJIbHOH 3aTHX<:KH nPYX<:HHbI HrJIbI q>OpCYHKH YBe-
JIMqMBaIOT lI,aB.'IeHMe P O 11 ptjj, qTO MOx<:eT HeCKOJ1bKO M3MeHHTb
paCnpelI,eJlemIe TOIIJ1MBa BO BpeMeHH. Ho npI1 3TOM YJlY'IllIaeTCH
Me.'IKOCTb paCnbIJlHBaHHH B pe3YJ1bTaTe nOBbIllIeHHH CKOpOCTH HCTe-
1J.eHHH TOnJlI1Ba H IIOCalI,KH Mr.'IbI Ha CelI,Jlo I:IPH 60.'lee BbICOKOM 3Ha-
qeHlIH Ptjj. O.lI.HaKO .lI.aBJ1eHHe PrjjO MO)KeT B03paCTaTb TOJlbKO .lI,0 He-
KOTOpOro npe.lI.eJla, TaK KaK 1J.eM BUllIe PrjjO, TeM 6bICTpee BbIXOIUIT lI3
CTpOH YIIJ10THHIOmHe KOHYCbI HrJIbI H ee Ce.lI,J1a. BCJleJI.CTBHe 60Jlee
6bICTpOH IIOCa.lI,KH HrJIbI Ha Ce.lI.J10 pa3rpY3Ka .'lHHHH HarHeTaHHH
fl,Kflc,.l. YMeHbllIaeTCH, 'ITO IIpHBO.lI,HT K YBe.1H'le-
600 HlfIO po.
Ha pHC. 100 IIOKa3aHa 3aBHCI\ 10CTb
.lI,aBJ1eHlfH prjj H Po OT .lI.aBJleHlfH PrjjO, IIO-
JIY1J.eHHaH A. 11. TIOJI030Bb1M. HHOr.lI,a
lI,OIIOJlHHTeJIbHbIe BIIpbICKH nbITalOTCH
YMeHbllIHTb nYTeM YBeJlH'IeHHH .lI,aBJleHHH
Prfjo, COrJ1aCHO pHC. 100 3Ta Mepa He
MO)KeT .lI.aTb 60JlbllIOro 3<p<peKTa, TaK KaK
npH YBeJlH1J.eHHH Prfjo B03paCTaIOT .lI,aB.'Ie-
HHH ptjj 11 Po, 'lTO YCHJ1'IlBaeT KOJIe6aTeJlb-
HbIe HB.leHHH, a C.'Ie.lI.OBaTeJlbHO, H .lI,ono.'!-
HHTe.1bHbIe BnpbICKII. TaKH:\l 06pa3mI, B
HeKOTopbIX C.'IY'laHX YBe.'IH'leHI1e .lI,aB.ne-
HHH nocaAKH Hf.1b1 He 6Y.lI,eT OKa3bIBaTb
Ha .lI,OnO.'IHHTeJ1bHbIe BIIpbICKII lI.em<pH-
pYlOIl..lerO BJlHHHHH.
B.iIWlH.Ue H.a np0l{ecc 6npblclW cYMMapH.OU npoxoihLOU n/LOU{aou
pacnblJ1U6a.'OU{ux OT6epCTuu. B CHCTeMax HenOCpelI.CTBeHHoro .lI.eH-
CTBHH .n:aBJleHHe H CKOpOCTb BnpbICKa TOnmma B 3Ha1J.HTeJIbHOH CTe-
neHH 3aBHCHT OT OTHOllIeHHH f n . 4eJ\! 60.1bllIe 3TO OTHOllIeHHe,
f e
Te1\l BbIllIe .n:8BJIeHHe H CKOpOCTb BnpbICKa. TIoC.le.n:HHe, B CBOlO O'le-
pe.lI.b, BJ1I1HIOT Ha MeJlKOCTb paCObIJIlmaHlI5I TOnJllIBa H .lI.pyrHe
napaMeTpbl opol.!,ecca cMece06p330BaHHH. YKa3aHHoe OTHOllIeHHe
OK33bIB3eT 60JlbiliOe BJIHHHHe Ha pacnpe.n:eJIeHHe TOOJ1I1Ba B 06'beMe
KaMepbI cropaHHH, Ha npOH3BOlI.lne,TJbHOCTb TOnJUlBHOH CHCTeMbI,
OCT3TO'lHOe .n:aBJleHlle H .n:PYrHe napaMeTpbI npouecca BopbICKa.
BJlHHHHe nJ10Il..lalUI fc H3 oapaMeTpbI npouecca BnpbICK3 51BJ15leT-
CH CJ1e.n:CTBHeM HCKa)J(alOmHX <p3KTOPOB, B oepBYIO 01J.epe.n:b, CX<:H.
MaeMOCTI1 TOnJIHBa. TIpH OTCYTCTBIHI HCKa)K3IOIl..lHx <paKTOpOB
CKOpOCTb BnpbICK3 TOnJ1HBa oope.lI,e. T IH.laCb 6bI COOTHOIlleHHeM
C enp = f" C n . B 3T01\l cJlY'lae YBe.'IH'leHile H.'IH YMeHbllIeHHe I1.10ma-
fe
.n:H fc BbI3bIBano 6bI COOTBeTCTBYlOUJ,ee YMeHbIlleHHe H.'l11 YBe.1H'leHHe
CKOpOCTfI C enp , npJI'leM .n:aB.'IeHJIe P H3MeHH.TIOCb 6bI npmw npo-
nopUHOHaJIbHO H3MeHeHHlO n 2 , a H3 npOlI3Bo.n:HTeJlbHOCTb CIICTel\lbI
nJ10Il..lalI.b fc He B.IHHJla 6bl.
214
/;/;0
520
J60
';: t:ftft
200 2lfO 280 J20p,p,KflcH'
PliC. 100. 3aBHcliMoCTb .D:aBJlC-
Hlill prf; J! Po OT BC,lIH'-IHHbJ
,ZJ;aBJICHliH PrfiO :
1 - Po; 2 - PljJ
B JI.eHCTBI-ITeJIbHOCTH LKe HCKaLKalOlU.He cpaKTOpbI TaK H3MeHHIOT
npouecc BnpbICKa, I.JTO HanHCaHHOe BbIIlle COOTHOlIleHUe JI.aLKe npH-
6JIHLKeHHO He xapaKTepH3yeT ero. HanpUMep, eCJ1I-I B peaJ1bHbIX YCJIO-
BH5!X npH YBeJ1lll.JeHHH W101U.aJI.H fc CKOpOCTb BDpblCKa TOnJIHBa
6Y.J. eT YMeHblIlaTbCH B 60J1blIleH CTeneHH, l.JeM H3MeHeHlIe fe, TO npH
HeII3l\1eHHOlI npO.n.0.1LKIITeJIbHOCTH BnpbICKa npOH3BOJI.HTeJ1bHOCTb
CIICTeMbI YMeHblIlaeTC5I. EC.TJH LKe CHHLKeHHe CKOpOCTH BnpbICKa 6y-
JI.eT OTCTaBaTb OT B03paCTaHHH nJ101U.aJI.H fc npH HeH3MeHHOH npo-
JI.0:J)!\I1Te.TJbHOCTH nO.n.aI.JH TOnJ1HBa, TO npOH3BOJI.HTeJ1bHOCTb CHCTeMbI
YBe.1III.JHBaeTCH. D03TOMY npOH3BOJI.HTe.TJbHOCTb CHCTeMbl B Hal.JaJIe
YBe.;1J-Il.JeHHH fe 6y.n;eT B03paCTaTb, CTf(c(tl
a nOC.le HeKOToporo 3Hal.JeHH5! f,. 50 -
YMeHbllIaTbCH.
B COBpeMeHHbIX TOnJIHBHbIX
cHCTeMax MOMeHT nepexo.n;a OT
OJI.HOrO BHJI.a 3aBHCHMoCTH K .n.py-
rm.lY onpeJI.eJ1HeTCH OTHOllIeHHe:\1
lE.. H CKOpOCTblO JJ,BlILKeHII5!
fc
nJ1YHLKepa. TaKHM OOpa30I\1, B
KaLKJI.OH TOnJIHBHOH CHCTeMe MO-
MeHTY nepexo.n;a OT o.n.Horo BflJI.a
3aBHCHMOCTH K JI.pyrOMY 6YJI.eT
COOTBeTCTBOBaTb CBOH npOXOJI.-
Ha5! nJIOlU.a.n.b paCnbIJIHBalOlU.Ex J _ TH;
oTBepCTHII. PaOOl.JaH nJlOlU.a.n;b
nOc.1eJI.HHX MOLKeT COBnaAaTb H
3H8 l IHTeJ1bHO OTJ1f1I.J8TbC5I OT npoxo.n;HOH nJJ01U.8.n;H, COOTBeTCTBYlOlU. eH
1\1OMeHTY YKa3aHHoro nepexo.n.a. DO.3TOMY Ka)J{JI.aH TOnJIHBHaH CECTe-
Ma HMeeT CBOH B03MO)J{HOCTII HCnOJIb30BaHHH .3TOrO <paKTopa JI..1H
H3l\IeHeHlUI xapaKTep'HCTHKH BnpbICKa II ee napaMeTpOB, I.JTO' Ha-
npIIl\lep, nOJI.TBepLKJI.aeT pHC. 101.
Ha pIlC. 101 JI.HarpaMMbl nOKa3bIBalOT 3aBHCHMOCTb CpeJI.HeH
CKOpOCTH H npo.n;OJ1)J{HTeJ1bHOCTH BnpbIcKa TOnJ1l-IBa, a TaKLKe npoH3-
BOJI.I1Te.TJbHOCTl-I CHCTeMbI TH -loT nJIOlU.a.!J.I-I f c. CHCTeMa TH -I OT-
JIH4aeTCH OT CHCTeMbI TH npo<pUJ1eM TOnJIHBHorO KYJIal.JKa U HeKO-
TOpbL\1 H3MeHeHHeM cnoc06a OTCeI.JKH. 113 pHC. 101 c.TJeJI.yeT, I.JTO B
CHCTeMe TH-l YBeJ1lII.JHBaTb fc > 0,92 MM 2 HeueJ1eco06pa3Ho, TaK
KaK npH 3TOM C 6np .cP Hal.JIIHaeT yMeHbllIaTbcH 50. lee pe3KO, npo-
JI.O.l.iKHTeJ1bHOCTb BnpbICKa npaKTHI.JeCKH coxpaHHeTCH HeH3MeHHOH,
B03paCTaHHe npOH3BOJI.HTeJIbHOCTH CHCTel'v1bI npeKpalU.aeTCH H Hal'v1e-
l.JaeTC5I TeHJI.eHUII5I K ee CHIILKeHHIO. B CHCTeMe TH npH fe > 0,92 MM
Tel\mbI YMeHbllIeHlIH npOJI.OJI)J{HTeJIbHOCTH BnpbICKa He H3MeH5IIOTC5I,
a C 6np .cP COXpaH5IeTC5I HeH3I'v1eHHOH. CJ1eJI.OBaTeJ1bHO, npH He06xo-
.n;IIl\IOCTH B CIICTeMe TH MO)J{HO IICn0J1b30BaTb paCnbIJIHTe.1JH, y
KOTOpbIX fo > 0,92 MM 2 . Dpn BbI60pe npOXOJI.HOH nJ101U.aJI.H f CJIe-
JI.yeT nOMHHTb, 'ITO npH 60JIblIlOH BeJ1lII.JIIHe .3TOH nJIOlU.aJI.H Tpy.n;Hee
06ecnetIHTb YJI.OBJIeTBOpHTeJIbHYIO pa60TY JI.BHraTeJ15I Ha pe.iKHMaX
215
40
1jJ;
28
'!6cg [ 21;
220
180
J
o
475 480 485 490 495 fc MM 2
Pl!c. 101. 3aBl!Cl!MOCTb napaMeTpoB
npol.\ccca BnpbJCKa OT BCJlH'lHHbl ll.'JO-
lI.\a.D:n f c .D:ml cnCTCM:
2 - TH-l; 3 - pacxoJ/, 1"onJ1llBa
lJ,JISI CHCTeMbI TH-l
M8J1bIX nOJ1,8'l 11 060POTOD, T8K }{8K CKOpOCT11 HCTe'leH11H MOrYT
6bITb O'leHb MaJlbI, n03TOMY MeJlI<OCTb paCnbIJIHBaHHH TonJIHB8 6y eT
HeJ1,OCT8 TO 'lHOH, a pa60Ta J1,BHrare.!lR B CBR3H C 3Tlfl\f HeYJ1,OB.leTBO-
pHTeJ"IbHofl.
Ha pHC. 102 1l306pa)KeHa 3aBHCUMOCTb npO.J.o.DKHTeJ"IbHOCTI1 II
J1,8B.leHHH BnpbIcKa OT npoxo.J.HOH n.l0lI.l3JI,H lcfc npB pa3mPlHbix
.rr.Ha IeTp3x H3rHeT3Te.lbHoro Tpy6onpOBOlI.a. XapaKTep npOTeKaHI1H
paCCl\IaTplIBael\IbIX KpHBbIX XOTH. H He
CH.lbHO, HO Bce )Ke 3aBHCHT OT BeJ1l1-
I.JHHbI dr, npn'le:\I 60.1ee 33MeTHO 3TO
CKa3blBaeTCH Ha 3aBHCHMOCTH p =
= f (Ilcfc). Eo.J1bllIee y;\IeHbllIeHIle aB-
.1eHlffI npH d T = 1,5 oM}'! HB.IH.eTCH
c e.rr.CTBHeM HHTeHCHBHOH pa3rpY3KH
ClICTel\IbI B CBH31I C Y:\leHbWeHHe\1
06"beM3 H3rHeT3Te.lbHoro Tpy6onpo-
BOJI,a.
800
600
400
1jJ;
f6
f2
f]2
PHC. 102. 3aBHCHlIIOCTb
lJ,aBJlCllliSl PcP 1I npo-
.;J.O.'DKIITCJlbHOCTH Ipn
OT !let e npH pa3JJU4HbiX
3Ha'lCHHHX d T :
1 - t ZI 'Ut; 2 - 2 ) .UI;
3 - 3 AIM; 4 - 4 ."."
yJolJol
(t.f
{l,2
{I, 1
.fF
PHC. 103. BJlHHHHe n.'1oru.a,!\H
te Ha BC.'IH'-IIIIlY Ymax H xapaK-
TCp .D:BHLKCHHH Hr.TJbl:
- f c 7,7.10-' c.,,";
2 - f c = 15,4' 10-" CIoI'
J13MeHeHlle BeJUI'lHHbI lde CYllI.eCTBeHHO BlIlUIeT Ha XapaKTep
.llBH;,!{eHJ15I Hr JIbI iPopcymm, 'lTO C J1.0CTaTO'lHOH y6eJ1,HTeJ1bHOCTblO
HJIJIIOCTpHpyeT pHC. 103. Yl\leHbWeHHe nO}J."beMa HrJIbl. a B CBH3H C
3THM II npoxo}J.HoiI nJIOlI.l3}J.II fl4' KOTOpaf! 1Omer CTaTb H CTaHO-
BHTCH npH 60JIbllIlIX H3MeHeHlIf!X fc MeHbllIe 3TOH nJIOllI.a H, OK33bI-
BaeT 60JIbllIOe BJIHHHHe Ha napaMeTpbI npou.ecca BnpbIcKa, B TOM
I.JHCJ1e H Ha npOH3BOlI.HTeJ1bHOCTb CHCTeMbi. C H3MeHeHHeM nJ"IOllI.a H
fc H3MeHHeTCf! T3Kme xap3KTep OCTaTOIlHbIX KOJIe63HlU"f, IlTO .rr.elIaeT
Heo6xo,rI,lIMbIM npOBepHTb CHCTeMbI Ha HaJIH'llle JI,OnOJ1HHTeJIbHbIX
BnpblCKOB npH yrvreHbIlleHIfIl 3Toro naparvreTp3. Ha pHC. 104 II306pa-
lKeHbl .l1.HarpaMMbI, onpe}J.eJIRIOlI.lHe J1,OnycTHMbIe npeJ1,eJ1bI H3:\1eHeHllf!
llJIoru.alI.H fc 1J.JI51 Jl.BYx CHCleM THlla KKA3. CpaBHHTeJIbHO Y3KHe
npe.rr.eJ1bI ll3rvreHeHHf! nJIow.3.rr.H fe, OrpaHHI.fHB3fOlI.lHe pa3J1HIlHbIe
06J1aCTH npOTeK3HHSI npou.ecca BnpblCKa, CBl1 eTeJIbCTBYIOT 0 60.:"Ib-
llIervr BJIHHHHH 3Toro naparvreTp3 Ha OCTaTOI.JHbIe K0J1e6aHHH .l1.3B.1Je-
216
HUSI II CKOpOCTlI. HapRLlY C 31'H1\1 YKa33HHbie npe.n.e.1bl 3aBl1CHT 01'
COOTSeTCTBHSI ;\leLK.iJY KOHCTPYKTHBHbIMH 3.'Iel\leHT3l\Ul TOn.1I1BHOH
CHCTel\IbI, B CBSI3H C llel\I nOJl06HbIe JlIIarpaMl\IbI, onpe)].eJIHIOI1.U 1e
)].OnYCTllMble npe.n.eJlbl H3Mem mm nJlOl.l.J.a.n.ll fc, He06xoD.llMO pacclm-
TbIB3Tb AJlH K3LKAOH HCC.J1e..'l.ye!'.IOH TOnJlHBHOH CHCTeMbi.
H3 peLKUM3X M3.1bIX IIOjl,31.J. II 060pOTOB npll )':\ICHbll1eHlHI B.llI
YBeJ1lI1.J.eHlIH IIJlOl.l.J.3.n.I1 fe X3p3KTep U3J\1eHeHHSI napaMeTpOB npo-
uecca BnpWCKa OTJlHllaeTCH 01'
H36JlIO..'I.3eMOrO H3 HOMHH3.1bHO:\I
peLKliMe. f1plI YBeJ1)1l1eHHH fc B
2 pa3a )].3BJleHHe p; YMeHbll1aeT-
t,F(t- )
J(;;t...,2
fOOO
800
600
1;00
200
o
0,008 j1 c!c CM 2
PlIC. 104. LI.lIarpaMMa, nOK33b1B31Olll.aSl AO-
nycTHMblC npc.!J.c.1bl H3MCHCHIISI n.TJOll.\a.D:1J
!cfc .LI.. SI ;J.BYX CHCTeM THna K:K:A3. 06.TJac-
TI1 A, E. B xapaKTcpll3YIOT Te >Ke YC.10BHSI,
4TO H Ha pHC. 95
YMM
fJ,2
o
y?t t 1 \ LL I I
c,Kt KI I n
pxf/c11 2
220
2
J
f40
60
1
7,7 9.7 ff,7 fJ,7!c'fO C/'I z
PHC. 105. 3aBliCHMOClb napa-
MCTpOB npol.\ccca BnpbIcKa OT
n.'l01l.\3;I.H f c Ha pCLKuMe Ma-
.'IbIX nO.D:a'-l
npl1 II = 300 061_IIUH:
1 - PiP; 2 - Pcp; J - PH
CSI nOllTll B 4 p333 (puc. 105), B TO BpeMH K3K jl,aB.neHHe prft H3i\Ie-
H5Ie1'CH B npe.n.e'!13X 10 KrtCM 2 II TO.;IbKO Ha 10-15 KrtCM 2 npeBbl-
waeT )].aBJleHHe pg,o. BOJlee 3aMeTHO H3MeHHeTCH ;J.aBJleHIIe pn,
YMeHbwaHCb npH YBe.nHlleHHH fc C 285 )].0 240 KFlcM 2 . 0POII3BO)].H-
'IeJlbHOCTb CllC'IeMbl, HeCMOTp51 Ha YBeJlW.leHlle fe, YMeHbll1aeTC51 C
OT = 2,5 KeItt JlO G T = 1 KeItt, B TO BpeMH KaK npOJlo.nLKHTeJ1bHOCTb
BnpWCKa npaKTH1.J.eCKH coxpaHHeTCH He1I3MeHHOH. 3aBHClIMOCTl1 H3
pHC. 105 nO.il.TBeplli)].aIOT He06xo.1I.llMOCTb qeTKOH 1I BbICOKOK3 l JeCTBeH-
HOH pa60TbI cl>OPCYHI<H, TaK KaK He3HallIITe"lbHoe OTKJlOHeHHe 01'
HOpMbI ee nap31\1eTpOB cnoc06Ho cymecTBeHHo HCKa3I1Tb nap3l\leTpbI
np o ueCC3 BnpblcK3 TOIIJ1HBa, oc06eHHo H3 peLKI1MaX l\la.nbIX no.n.aq H
060pOTOB.
BmulHHe Ha napaMeTpbI npoLlecca BnpbIcKa npOTHBOAaBJIeHHH
CpelI.bI, B KOTOpylO nOJl,aeTCH TOnJ1HBO. B cOBpeMeHHblx ..'I.BHraTeJlHX
C BOcn.13MeHeHHeM OT CLKaTHH B 60.rJbIIlHHCTBe c.rIY1l3eB npHMeHfIeT-
217
CH Ha.n:.n:YB, n03ToMy TOnJIHBO I-Ia'lHHaeT H npeKpamaeT BIlpbICKII-
BaTbCH npH BblCOKliX JJ,aBoI'leHHHX ra30B B lI.HJUlHJJ,pe JJ,1l3eJ1H. DpoBo-
JJ,HTCH pa60TbI no npOBepKe B03MO)J{HOCTH I1Cn0J1b30BaHHH HaJJ,LLYBa
nopHJJ,Ka P... = 5 -7- 6 KrlcM. 2 . B CB5I3H C 3THM B03HHKaeT Tpe60BaHlle
o Heo6xoJJ,llMOCTH npoBepKll BJIllHHllH
Ha napaMeTpbI npol.\ecca BnpbICKa
npOTllBOJJ,aBJIeHllH cpe.n:H, B KOTOpyro
nOLLaeTCH TOnJ111BO.
DpllHHTO C'IliTaTb, 'ITO npOTllBO-
JJ,aB.'leHlIe cpeJJ,bI He OKa3bIBaeT 3aMeT-
HOro B.'1IIHHIIH Ha napaMeTpbI npOl.\ec-
ca BnpblCKa. OnblTbI HH)J{. H. C. 30Jlo-
TapeBa nOJJ,TBep)J{JJ,aroT 3TO. BMeCTe C
Te"'I cor JIaCHO cpaBHllTe.lIbHbIM paC'le-
TaM npOH3Bo.n:HTe.nbHOCTb CHCTeMbI npH
BnpNCKe TOnJ111Ba B aTMoc epy npll-
MepHO Ha 5 % npeBbIllIaeT npoH3BoJJ,lI-
Te.'1bHOCTb TOll )J{e CIICTeMbI nplI BnpbICKe TOnJ1IIBa B cpeJJ,Y c npOTII-
Bo.n:aBJ1eHlIeM 50 KrtCM. 2 . 3KcneplIMeHTaJ1bHO YCTaHOBJIeHO (pIIC. 106),
"-ITO npM nOBbIIlleHlBI nponIBoJJ,aBJ1eHlIH cpe.n.bl OT aTMoc epHoro JJ,O
GrJ(Z/'i
i IItf=B
o 20. 1;0 60 P" Xr/CH z
Puc. 106. 3aBucIIMoCTb TIpO-
H3BO.D:IITCJlbHOCTU TOTIJlHBHOi1
CIICTCMbl OT npoTHBo.n:aB.TJC-
HlUi Cpe.ll:bl, B KOTOpylO Brrpblc-
KIIBaCTC5I TOTIJIUBO
q;O
J5,D
.J/;,6
.J ,Z
.JJ;8
2
JJ,
o fO fOO P"
Puc. "107. 3aBHcuMOCTb MO-
.MCHTOB Ha'-laol1a nO.D:"bCMa
UrJ1bl H Ha'-la.la BTIpbICKa
TOnJlIIBa OT BCoI1U'lUHb! .n:aB-
JlCIIHH ra30B B l.\U.1HH,1\PC
Jl.H3eJlR:
1 - MOMeHT HaLlaJIa BnpbIcKa
TOnJIHBa; 2 - MOMeHT Ha4a-
JIB no.n'beM8 nr.nLI <f,10PCYHKH
0' Mjcox
fIIOO
f200
fOOO
800
fOO
Il fOO 200 300 400 500 PT xrjCl1,2
Puc. 108. 3aBllcuMoCTb BCJlII'-IHHb! CKO-
pOCTII a OT .n:aB.1CHH5I npH Ha.111411H
B Tpy60npOBO.D:C CMCCU Ton.TJHBa
C ra30M
:90 Kr/CM. 2 npOII3BOJJ,IITeJIbHOCTb CllCTeMbI YMeHbWaeTCH Ha 6,7%. I13
JIpe.n:bI.n:ymero CJlelI.yeT, 'ITO npH BbICOKOM npOTIIBo.n.aBJ1eHIIH B03-
MO)J{eH 3Tan, Ha KOTOpOM IIrJ1a nOJJ,HIIMaeTCH 6e3 BnpblCKa TOnJ1IIBa.
BCJleJJ,CTBlIe qero C03JJ,aroTcH YCJlOBIIH JJ,JIH npOHIIKHOBeHllH ra30B B
06"beM JIHHHH H8rHeT8HHH. COrJIaCHO pHC. 107.n:.nH CHCTeMbI TH npH
P... = 150 KrIC.M 2 npOlI.OJI)J{HTeJIbHOCTb nOlI."beMa HfJIbI 6e3 BnpbICK3
218
Ton.1HBa paBHa 0,8 0 yrJ1a nOBopOTa BaJIa Hacoca. B TeIIeHlI€ ::noro
nepIIO..'l.a rOp5lIIHe ra3bI MorYT npoHHKHYTb B paCnbIJIHTeJIb H nepe-
rpeTb HrJIy, C03..'1.aB TeM caMbIM 6.'IarOnpH5ITHbIe YCJ10BH5I ..'I.JI5I 3aBH-
C8HII5I Hr.'1bI H HapYll1eHII5I pa60TbI €€ ynJIOTH5IlOII1.HX KOHYCOB.
npOHHKHOB€HH€ ra30B B J1HHHlO HarHeTaHH5I MO.>KeT cYII1.ecTBeHHo
1I3l\IeHHTb CKOpOCTb pacnpocTpaHeHHfI 3BYKa B TOnJ1lIBe, KOTopoe-
BC"1e..'l.CTBUe HaJIHII1I5I ra30B 1I3 O..'l.HOpO..'l.HOII JKlI..'I.KOCllI npeBpalll.aeTcfI
B ..'I.Byxcpa3HYlO Cpe..'l.Y. KaK nOKa3amI OnblTbI [14], B ..'I.Byxcpa3Hoii cpe-
)].e CKOpOCTb pacnpoCTpaHeHHfI 3BYKa cYlll.eCTBeHHo YMeHbll1aeTC5I C
O)].HOBpe leHHbIM B03pacT8HHeM ee 38BHCHMOCTH OT )].8BJI€HI!fl TOrr-
.'1lIBa pr B Tpy6onpoBo)].e. npll Ma"10ii BeJ1HIIHHe )].aBJIeHHfl Pr CKO-
pOCTb pacnpOCTpaH€HHH 3BYK8 B )].Byxcpa3Hoii Cpe..'l.€ (pHC. 108)
npaKTHIIecKH CTaHOBHTC5I paBHoH CKOpOCHI pacnpoCTpaHeHHH 3BYKa
B B03..'1.yxe. TaKaH 3aBHCHMOCTb CKOpOCTH 3BYKa OT .lI;aBJIeHHH Pr
l\!O)KeT cYII1.eCTB€HHO B.'IIUlTb Ha XapaKT€p npoTeKaHHH npou€cca
rrO;J,aIIH TOnJ1HBa.
7. OC06EHHOCTH PA60TbI TonnHSHOIit CHCTEMbi
HEnOCPEACTSEHHoro AERcTBHfl
HA PA3nH HbIX TonnHSAX
B r.1. II OTMeIIaJIOCb, IITO rrpncnoc06.TJeHHe TOnJ1HBHOH CHCTeMbI
K pa60Te Ha pa3"1HIIHbIX TOnJ1HBaX B OCHOBHOM onpe)].eJ1HeTCfl pa3-
.'lHqrr€M HX <PH31i'I€CKHX KOHCT8HT. H8 pHC. 109 nOKa3aH8 3aBHCH-'
MOCTb aKTHBHoro xo)].a rrJ1ymKepa OT Be-
COBoii rrpOH3BO)].IlTe.'IbHOCTH CIICTeMbI AJIfi
pa3JlIl1.J.HbIX TOnJIlIB. 113 plle. 109 cJIeJJ.Y-
eT, '-ITO rrpH pa60Te CHCTeMbI Ha )].H3e.TIb-
HOllI TOrrlII-IBe H KepocHHe paCXO.>K)].eHlIe
B aKTHBHbIX xo)].ax n.TIYH.>Kepa He3Ha1.J.H-
TeJ1bHO. npH nepexo)].e Ha 6eH3HH aKTHB-
HbIH XOJJ. n.'lYH)Kepa JJ.OJ1)KeH 6bITb cy-
lll.eCTBeHHO YBeJIHIIeH, TaK KaK y)].eJIbHbIH
B€C 6€H3HHa 3HaIIHTe"1bHO MeHbille YJJ.c.'Ib-
Horo Beca )].1I3eJ1bHOrO TOnJ1HBa, a ero
C.>KHMaeMOCTb 3Ha l IllTeJ1bHO 6 O.'1bille. no
OCI1..lIJIJ10rpaMMaM )].aBJI€HlIfI, CH5ITbIM n€-
pe)]. cpOPCYHKOii B HarHeTaTe.TJbHOM TPy-
60npOBOJJ:e, 6bIJ10 YCTaHOBJ1eHO, 1.J.TO Ha
HOl\1HHaJIbHOM pe)!nIMe II 6JIH3KHX K HeMY
peJKHMaX xapaKTep OCUIIJ1J1orpa 1!\1 JJ:aB-
J1eHlIH nplIMepHO lIJJ:eHTII1.J.eH. H3MeHfIeT-
C5I TOJ1bKO BeJIH1.J.I1Ha MaKCHMa.J1bHoro .n.aBJ1eHIIfI TOnJ1HBa. .1l.J1H 6eH-
3HHa JJ:aBJI€HH€ pmax npHM€pHO Ha 170-200 KTjCJrt 2 M€Hbll1€, 'leM
.n.JIH JJ:1l3eJ1bHOrO TOITJIHBa. npH IIIeHbll111X nOJJ:aIIax Tonmma, HanpII-
Mep 50% OT HOMIIHaJ1bHOrO pe)KHMa, pacXO)K.n.eHlle B OCUHJI.TJOrpallI-
Max .n.aBJ1eHIIH B03paCTaeT, oco6eHHO npll pa60Te CHCTeMbI Ha 6eH-
219
n UKT
HH
;;4
42
t6
0,8
to
<;8
E, 9 C, K?j'l
42
PHC. 109. 3aBHcIIMoCTb aK-
THBHoro XO.D:a nnYHLKcpa
OT 4aCOBoro pacxoAa Ton-
.TJ!1Ba AJIH pa3.TJH4HbIX
TOnJlHB:
1 - J].1-13eJlbHOrO; 2 - Kepo-
cHHa; 3 - 6eH3HHa B-70
3HHe. CJ1e;J.OBaTeJlbHO, LJT06bI npHcnoco6HTb TOnJ1HBHYlO CHCTeMY
).I,J1H pa60TbI Ha pa3.1H'IHbIX TOn:mBaX, oc06oe BHHMaHHe Heo6xo).l,H-
MO y).l,e.1HTb oTpa6oTKe nponecca BnpbICKa Ha pe)f{flMaX Ma,JIbIX no-
).I,aLJ H 060pOTOB.
Ha pHC. 110 H306paLKeHbI COBMemeHHbIe 3<iBI1CHMOCTH napaMeT-
pOB nponecca BnpbICKa OT LJHC.la 060pOTOB npH pa60Te CHCTe:\IbI Ha
pa3J1HLJHbIX TonJ1HBaX Ii G r =
4 K2/tJ., LJTG npHMepHo COOTBeT-
cTByeT 50% HarpY3Kl1 OT HOMH-
HaJlbHoro peLKHMa. OpH pa60Te
CHCTeMbI C n = 1000 06jMUH
(pHC. 110) B CJIYLJae nepexon3 C
JJI3eJIbHara TalI.1lma lIa 6eH3IIH.
p; Kr/CM 2
I
f 2 -
3
f
:::- .3
3 2 .--,:
- -
=- ..-
f
300
200
100
(("
e/l(lIKn
q07
L!065
q06
'1 055
;
(2
10
8
6
.f00 600 700
800 n OO/l1l1H
PIIC. 110. 3aBHcHMoCTb napaMCTpOI3
,npol.\ccca BnpbIcKa OT 411C.1a 060po.
'TOB npH pa60Tc CHCTCMbI Ha pa3.1H4-
HbIX TOn.ll1BaX (G r = 4 Kel'L)
npH n = 1000 061.MUH:
1 - .a,H3eJlbHoe TOnJIHBO; 2 - KepOCHH;
3 - 6eH3HH 5-70
f.
NJ
KrjCI12
200
o
--
((II
8/1.I11Kn
0,030
{j020
0,010
o
300
500
700 n Olf//'!UH
PIIC. III. 3aBHCJUIOCTb napaMcTpoB
npol.\ccca Bnpblc a OT '-IHCJla 060po-
TOB npll pa60Tc CHCTCMbI Ha pa3-
JlH4HbIX Tl.Jn.'IIBax (G r = 2 Keitt)
npH n = ROOO o61.MUH:
1 - ,l1,H3eJIbHoe Ton..'HBO; 2 - KepocHH;
3 - GeH3HH 5-70
).I,aB.1eHHC BnpbICKa y;\<leHblIlaeTCH Ha 100 KrjC,M2. C Y:\leHblIleHlIel\l
LJHC.la 060pOTOB paCxaLK).I,eHIie B BeJ1'HqIIHe l\1aKtHM3J1bHara ).I,aBJIeHIIH
BnpbICKa CHHLKaeTCH ).1,0 40 KrjcM 2 . PacxOLK).I,eture LKe B np0).l,OJILKH-
TeJIbHaCTII nO).l,aqn Ton.rUIBa Ha Bcex o6op01'ax npaKTfI1IeCKH He
n3MeHHeTCH.
Ilpn perYJIHpaBaHHH CHCTeMbI Ha na).l,aqy G r = 2 Kc/'I. H n =
= 1000 06jMUI-l Hacoc npeKpamaeT nO).l,aBaTb oeH3HH npn n =
= 750 06jMUH (pnc. 111). OpH pa60Te HaCOC<l Ha ).I,H3eJlbHOM Ton-
JIHBe 11 KepocHHe na).l,aqa npO).l,aJ1LKaeTCH ).1,0. n = 300 06/JI1UH.
O).l,HaKa npH n = 300 06/MUI-l q1l ).I,J1H KepacHHa B 2 pa3a MeHblIle no.
cpaBHeHl1lO C q1l ).I,JIH AH3eJ1bHOra TanJ1HBa.
Ha pHC. 112 naKa3aHa BJIHHHHe capTa TanJIHBa Ha n3Hac nJIYH-
LKepHOll napbl [81]. 113 pHC. 112 CJ1e).l,yeT, LJTa qepe3 300 IJ.. pa60Tb!
Ha 6eH3IiHe BeJ1HqHHa q1l YMeHblIlIIJ1aCb C 0,14 ).1,0. 0,07 ej4uKA, T. e.
220
Ha 50%, B TO BpeM5I KaK npH pa60Te Ha AH3eJ1bHOM TOnmIBe B
TelieIUle Toro Me BpeMeHH non.alia q1J YMeHblUHJIaCb TOJIbKO Ha 6%,
3KCnepl1MeHTa.'lbHO YCTaHoB.1JeHO, liT y; 2jqUKIi
.1.;151 06ecnelleHiHI yn.OBJ1eTBOpUTeJ1bHOH " ffEB
pa60TbI TOnJ1HBHOH CHCTel\lbl Ha pa3.'lHli- f
HbIX TOnJIHBaX He06xo.lJ.HMO: 409
a) npH nepexon.e Ha 6eH311H non.o- 2
6paTb OnTHMaJ1bHbIH yrO.;l onepe}KeHH5I 407
no.n.aliU TOnJ1l1Ba; 0 100 200 JOO "
6) npe.lJ.ycMoTpeTb B n.'lymKepHoH PHC. 112. B.'1I1HHHC COpTa
nape .n.peHaMHoe YCTPOHCTBO; Ton.'lHBa Ha H3110C 1I.1YR-
B) HMeTb .n. B yxno3uUHOHHbII1 ynop }KCpHOi1 napbl no .D:aHHbIM
:\!aKCUMa.T!bHOH nORaliU; UHI1LU1:
J - l{H3e :'JhHoro. 2 oeH3H-
r) 3H34HTe.TJbHO nOBbICHTb ;J,aB.leHHe Ha
TOn.1JHBa B J1IIHHH BCaCbIBaHl1H, liTO 60JIee
ue.1JeC006pa3HO 06eCnellHBaeTC5I npHMeHeHHeM .lJ.BYX nOJI,Ka 4HBalO-
IUHX HaCOCOB, O.n.HH If3 KOTOpbIX RO.'lMeH nOMeIUaTbC5I B HanOpHOM
TOnJ1HBHOM 6allKe, T. e. 6bITb 3aTOn.'leHHbIM.
8. TOnnHBHblE CHCTEMbl C HACOCAMH PACnPE,QEnHTEnbHOrO THnA
B CB5I3H C TeM, liTO B OCHOBY paClIeTa npouecca nOJI,aliH TOn.1HB3
CHCTeMOH C paCnpeJI,e. T !l1Te.'lbHbIM HaCOCOM n0J10MeHa npHHUHnHa.TJb-
Ha51 CXeMa pOTOpHOrO HaCOca, 3TOT HaCOC 6bIJ1 npHH5IT HaMIl B Kalie-
CTBe QCHOBHoro 06"beKTa H npH onHCaHl1l1 3KcnepHMeHTa.;lbHbIX
HCCJ1e.n.OBaHHH.
Ha pHC. 40 6bWH H306pa}KeHbI pac4eTHbIe JI,HarpaMMbI nYTH
naYHMepoB, BpeI\HI-CeliemI5I HarHeTaTeJ1bHbIX If BcaCbIBalOIUHX OKOH,
a TaKMe H3MeHeHI1H CB060.lJ.HbIX 06"beMOB B KaMepe HarHeTaHl151 U
.1aBJ1eHl1H p. 113 pHC. 40 CJ1eJI,yeT, liTO JI,aB.TJeHHe P1i HaliliHaeT B03-
paCTaTb nOCJ1e BbI60pa n.TJyHMepaMH CBo60JI,HOro 06"beMa V OC1i .
D.aBJIeHHe P1i JI,OCTHraeT MaKCHMaJIbHOH BeJ1I!liHHbI HeCKOJ1bKO paHb-
we npHXOJI,a nJ1YH}KepOB B B. M. T., 33TeM 6bICTpO YMeHbwaeTC5I II B
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222
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HO C BJIHHHHeM HHepIUIH nOTO-
Ka LKHRKOCTH H oco6eHHOCTf{-
l\1M )J.HHaMHKH pa60TbI npHBO-
.lI.8 H8COC-Q)opCYHKH. ECTb OC-
HOBam1H .n:YMaTb, 1J:TO B YCJIO- 40
BHHX BnpbIcKa TOnJIHBa B cpe-
.lI.Y C npOTHBO.lI.aBJIeHHeM pac-
TSiHYTble Y1J:aCTKH na.lI.eHHR
;r,aBJIeHHH B KOHue npouecca
OTCYTCTBYIOT. 06 3TOM :110-
LKeT CBH.lI.eTeJIbCTBOBaTb pHC.
118. BH.lI. 38BHcHMocTeH q"lJ =
= f (n), nOJIY1J:eHHbIX H a .lI.BH-
faTeJIe n cTpo6ocKone, C6J1H-
LKaeTCH, KOr.lI.a npn onpe.n:eJ1eHIIH I.I.HKJ10BOH nO.lI.a1J:H Ha cTpo6oCKone
He Y1J:IITblBaeTCSi no.n:a1J:a TOnJIHBa H8 Y1J:aCTKaX 3aMe.lI.JIeHHOro Cna.lI.8
.n:aBJIeHIIH B KOHue npouecca. nOJIyqeHHe Ha p51.n:e peLKHMOB pa60TbI
- p -
KflcH 2 KrjcH 2
1000
1
500
o
JO
20
10
0)
o
B.H.m. . JO
--'
-.0::::::::;
r---...... --'
u Co
---...::.;
'-
A
}f
}2
500
}J
f250 n OO/MIiH
750
1000
PIIC. 118. OnbITHbIe xapaKTcpllcTllKH TOnJlH-
BOnO aqll no 060poTaM
.6 - Ha CTpOOOCKorre; . - Ha CTp060CKone
oe3 yqeTB no,naqH Ha yqaCTKe 3aMe.ltJIeHHorO
cna.n.a .naB.neHuii B KO}{[ e npoltecca; 0 - H8
.ABHraTe_Te; 1 - ha = 2,&4 .\lM; 2 - ha
1,88 .'LIf; 3 - h a = 1.24 "LIt
9
10
2 3
1100
200
20
B.l1.m.fjJ'
10
0)
PllC. 119, XapaKTepllcTllKll .D:aBJlCHllH BnpblcKa, nOJlY'lcHHb!C Ha
CTpo6ocKone (cnJ!oIllHl>IC J1llHllll) II Ha .D:BllraTeJ1e (IIlTpHXOBbIC)
npll n:
a - 1500 06/_IfIIl/; 6 - 500 06/MUU; I, 2. 9 - Ha4a_TO aKTHBHot'! n01\a'",;
3, 4, 10 _ KOHe aKT!lBHOil n01\a4H; 5. 6 - ha = 1,88 .If_\l; 7, 8, 13,
14 - h a 0,7 MM; ll, 12 - ha 2,64 MM
15*
2'27
ABflra eMR flKMOBOH nOna H paBHOM H n8)Ke HeCKO bKO 60 bllleH
Be.1J1lHnlbI, H3MepefllIOH npn BnpbJCIW B cpe.n.y 6e3 np01J.IBOl1.aB e-
HHfl, CBfI3aHO C YBeJmQeHl1eM K03<pqHH.l.HeHTa paCXOJ1,a P8CIlbWHBalO-
I<r/CN2 UUIX OTBepCTHH npH BnpbICIW B
p I' Cp e l1.Y C npOTHBo.n.aB eHHeM.
PIlC. 119 HJWlOCTpHpyeT CTeneHb
COBnaneHlIH xapaKTepHCTl1K .naB-
.'1eHHH BnpLIcKa, nO.'1YQeHHL1X oc-
l\u,,1..'10rpa<pHpoBaHfleM na .n.BIlra-
Te e H Ha cTpo6ocKorre. Pe3y.1b-
T8TbI Il3MepeHIlfl nOK83bIB8fOT,
QTO yc.J10mUI pa60Tbl H8COC-<pOp-
cyHKH Ha C1'p060CKon Jl,ona-rot{-
HO 6JIH3KO cooTBeTcTBYfOT YC.10-
BIIHM pa60TbI ee na ABI1ra1'e.1.e.
DpH HCCJ1eJ1,OB8HHHX lllHpOKO
IICnOJIb30Ba.m1Cb pac4eTHbIe Me-
TonbI. 1J.ocToBepHocTb paC1.JeTOB
rrpoBepeH8cpaBHeHHeM HX pe-
3y.'lbTaTOB C OIIbITHbIMH AaHHb1-
MH H8 60JIblliOM '1Hc e peJKH-
I\1OB. Ha pIfe. 120 npUBe,lI.eH rrpu-
Mep TaKoro epaBHeHHfI, 113 KOTO-
poro CJ1e.n.yeT, QTO paCqeTbI, BbI-
rrOJ1HeHHbIe C YlJeTOM .n.elpopMa-
HH, Yl1.0B eTBOpHTeJ1bHO COBna-
AalOT C pe3Y J1bTaTaI\UI OITbITOB.
Puc- J20. CpaBIJCHHe paC'IcTHbIX H ORbJT- Ha pue. 121 n05ICHHlOTeH H3)"-
RblK 3i\BHCl!MOC-reI\ npl1 h p = 6,\ )f!A!, 1.JaeMbIe napa1\leTpbl npoIJ.ecca
/1 = 1500 o6j.uUH (I BapHanT cHcTeM{'!): BnpblCKa. B Aono.'1HeHHe K Hm,\
I, 5 pe3Y 'lbTaTLI cTpo60CKOJTUPOB8HH}r;
2 H 4 - pe3YJ1bT37bl pacqeToB C Y4eToM paeC1\1aTpIlBalOTCH TaK)J{e epe.ll.-
"e,pOpM3ljHB npBBo"a; 3 - "aBJJe1me nepell Hf!f! 06'beMnaH CKO p OCTb nO.n.8rH!
COO.10BblMll O"fBepCTJlSJMH npH a6co.nionfO
>KCCTKOM npHBo)],e TOITJ111Ba 'l pe3 O BepC'nj5'l paCTIb1-
J1l1Tem! Qrfi.cP Ii Cpe.nHHe .n.aB.'Je-
p .cp.n' 3TlI Be.rm<IrtHbl onpe,lI.e.'lHlOTCf! CJ1e.n.ylO-
Q _ 6nqli .
t/J.cp--,
IfnY
Qt/J.cpY
PIjJ.cP. t =
2g f
tOOD
1200
800
!foa
o
a(tl
C,.,Jjtel(
1.;.0
20
206
202
HlHI BnpbJCKa P cp.t H
Il1.IlMH BbIpa)j{eHHHMIl:
PI/J.cP-tJ =
(228)
? ?
18n-q;j
g,' \\; f
(229)
'i'
n
S p - PI,dq;
o
q;n
Ka.!\'15¥H0 H3 pIlC. 121, !I}IH Hacoc-<poPCYI1KH B CB5I3H co 3I1aqn-
Te.1bHbiMu.J1eq>0plVIaUHHMlI npJIBOn8 uenecoo6pa3Ho BBeCTII nOHHTUH
228
o reO:UeTpWIeCKO:\I II JJ.eHCTBHTe.lbHO:\[ nepHO.D,aX aKTHBHOH nOJJ.aLJH II
COOTBeTCTBeHHO 0 Ha4a.le II KOHIJ,e reOMeTpH4eCKOro II .n.eHCTBI1Te.lb-
Horo neplIO,lJ,OB aKTHBHOH no.n.a4H. DpH 3TOM reOMeTpH4eCKHH nepII-
O.D, aKTHBHOH nO.D,a4H OTHOCHTCSJ K CJIYLJaIO a6COJIIOTHO )KeCTKOro
npHBon.a HaCOC- OPCYHKH. B .D,aJJbHeHllIeM reOMeTpH4eCKIIH neplI01I.
aKTlIBHOH nOAa4lI Ha3bIBaeTCfI B HeKOTopbIX CJIY4afIX nepHO.D,OM
3KTHBHOH nO.J,aLJI1. HaLJa.1D
H KOHeIJ, .D,eHCTBIITe.lbHoro
nepnO.J,a aKTIIBHoi-i n01I.3LJII
3ana3lI.blBaIOT no cpaBHe-
HHIO C COOTBeTCTBYIOil.{Ifl\[fI
MOMeHTaMII reOJ\leTpHLJe-
CKoro nepno.n.a aKTHBHoi't
n01I.a'lH B CBfI3H C .n.e!j:Jop-
M3IJ,HeH npHBO,lJ,3, npWleM
3ana3lI.bIBaHHe KOHIJ,a no-
.n.a4I1 3HaLJHTe.lbHee 13 CBfI3H
C 60JlbllIHMH YCIWIUI.MlI,
.n.eHCTBYIOWIIMH Ha npHBOlI.
B KOHue 3KTHBHoro XO.D,a
nJ1YH)Kepa.
BAUfl1-lUe pe3/CU.Ma pa-
60Tbl a2pe2aTa. Ha puc.
122, 123 H 124 nOKa3aHbI
3aBHCHJ\lOCTH, IW.1IOCTp-H-
PyIOil.{He BJIHHHHe 'IHC.'Ia
060pOTOB Ha xapaKTepH-
CTHKy H napaMeTpbI BnpbIC-
Ka TOnJIHBa. BH1I.HO, 4TO
H3l\IepemIOe B rpa.lI.YCax
onepemeHile BnpbIcKa no
OTHOllIeHIIIO K Ha4aJ1Y aKTHBHoH nO.lI.a4H HeCKO.lbKO B03paCTaeT C
YBeJIll'lemleM 'illCJla 060pOTOB B CBfI3H C 3<p<peKToM 1I.pOCcemlpoBa-
, HHH TOnm1Ba B OTBepCTlUIX n.'1YHmepa 11 ero BTYJIKII. 3arra3.n.blBaHIIe
I .
AeIlCTBHTe.lbHoro KOHua nO.D,aLIH no OTHOlllemHO K KOHIJ,Y nepHOlI.a
: 3KTHBHoii n01I.aLJU B03paCTaeT C YBeJIHLJeHlleM LIllC.la 060pOTOB BC.le.D,-
CTBHe YBe.1H4eHHH 3ana3.D,bIBaHliH KOHIJ,3 .D,eHCTBHTeJ1bHOrO nepHO.D,a
aKTlIBHOH rr01I.aLJH no OTHOlllemHO K KOHIJ,y reOMeTpHLJeCKOrO nepIf01I.a
aKTHBHOH nO.D,aLJH H YBe.1HLIeHlIH nepHO;:I,a cnaJJ,a 1I.aB.'1eHHH nOOle Ha-
qaJIa OTCeLJKH.
DpH Bcex 3HaLJeHllfiX aKTHBHoro XOlI.a npOJJ,OJI2KHTeJ1bHOCTb
BrrpbICKa, Bblpa)KeHHaH B rpaAycax yrJIa nOBopoTa KYJIaLIKa, 3aMeT-
HO B03pacTaeT npM YBeJIll'leHHIf lfHCJla 060pOTOB B CBH3H C HBJIe-
HHeM JJ,poCCeJUlpOBaHH5I H cmHMaeMOCTblO TOnJIHBa, a TaK2Ke B
pe3YJ1bTaTe YBe.'1HLJeHHH npo.n.OJI)KHTeJIbHOCTH .n.eHcTBHTe.nbHoro ne-
pHOJI.a aKTHBHoH nOLIaLIH, BbIpameHHoH B rpaJI.ycax. DOJI.cLJeT npo-
.'LO.TlmHTe.'1bHOCTH BrrpbIcKa, BbIpameHHoH B e.n.HHHuax BpeMeHH, no-
Ka3bIBaeT, qTO noc.1eAHHH 3aMeTHO YMeHblllaeTcfi C YBeJIHLJeHHeM
229
"'II' clI'IceK
r.
ppKf/c#l
60
JP..
f200
56
"JP..
fOOO
40
800
30
600
10
270
Z68 Zlf6
Zf4 Z6Z
PIIC. 121. napaMeTpbl BllpblcKa:
I 3 - COOTl eTCTBeHHO HaqaJIO reOMeTpR'-:leCKOrO
H .n.cnCTBHTe...'1bHOrO nepHOJl.OB aKTltBHOll nOlJ,a\lH;
2, 4 - COOTBeTCTBeHHO KOHen reOMen)MqeCKoro
Ii. AeiJcTBHTeJIbHOrO nepnOp.OB aKTHBHm1 n01{a lIi;
l - npO.D.OJ1w;,nTeJlbHOCTb reOMel'pll'-:leCKOro
nepHo.n.a 8KTHBHOfI no.n.aQH; ffJ a - npo.u.O '1}l(H-
Te.'1bHOCTh .a.eilCTBHTCJIbHorO nepHo.n.a 8KTHDHoil
no.u.aQH; ,6(f'08 - onepe>KeHHe Haqalla BnpbICKa;
.:\Q) 38 - 3ana3,lI,bIBaHne KOH a BrrpblCK3
CKOpOCTH BpaIIleHHH H3-3a cOKpaIIleHIUI npO.n.OJ1LKHTeJIbHOCTlf nepHO-
1I.a aKTHBHoii nOl1.aqH (YBeJIlfqeHH51 CKOpOCTlf nJIYHLKepa).
M8KCJIM8.IJbHOe II cpe.n.HJIe )1.8BJIeHHH BrrpbICKa cymeCTBeHHO
nOBbIllJaWTCH C yneJ1HQeHHeM tmCJIa 060POTOB, OC06eHHO npH nOJIO-
LKeHl:IHx peHKH, o6ecneQl:IBaIOIIlIiX 60JIbWYIO nOl1.aQY TOnJ1IiBa. ;:ho
YBeJUf'leHIIe, O)1.HaKO, MeHee pe3Koe, qeM MOrJIO 6bI 6bITb npn He-
CLKJIMaeMOM TOI1.TII1Be Ii a6COJIIOTHO LKeCTKOM npHBOl1.e.
P;'-Pl1
xllcl1 2
500
fJ -A
KflcH2
500
7 8
I /3
I 4
'\ 5
Ii I\v 6
\
fOOO
fOOD
30
20 10
UJ
}f}
2f} If}
0)
B.lt.m.(j!°
Puc. 122. BJl1iHHue '-IllC.TJa 060pOTOB Ha xapaInepHcTllKY .D:aBJlCHHH
BnpblcKa (ocuHJJJ1orpalj:JupoBaHHe, IV BapuaHT cUCTeMb!):
a --- h a= 2,64 M...1-t; (j - h 0. = 0.5 )'otAl; I. 7 H3QaJ10 aKTHBHoH IJo,a,a1.£l1;
2, 8 - KOHeI1 3KTHEHOH lIo)],a4H; 3 - Il = 1500 06/,""11; 4 - 1/
= 1200 06/MIIII: 5 - 11 700 061."UII; 6 - 11 = 500 06:.1111"
l1CCJ1e.n.OBaHHble npe)1.eJIbI QIiCeJI 060pOTOB Ii nO.l!.aQIi nOKpbIB8IOT
nOQTH BCe nOJ1e peLKHMOB QeTbIpeXT8KTHOrO l1.H3eJ1H 6e3 Hal1.l1.YBa
C pa60QHM 06'beMOM )1.0 1,1 Jl Ii QHCJ10M 060POTOB )1.0 3000 B MIiHYTY
(3a HCKlII()qeHHeM peLKRMa MRHHMaJIbHb!X 060pOTOB xo.nOC'foro
xon: a ).
Oplf 3TOM npel1.eJIbI Ii3MeHeHIfH MaICCI1M8JIbHOro H Cpe)1.HlIX ,a,aB-
JIeHIiH BnpbICK8 BeCbM8 BeJIHKIi 230-1560 "r/C.M. 2 )1.JIH J\WKCHMaJIb-
HarD 11.8BJIellliH Ii 80-690 "T/cM 2 ,lJ,JIH (p - P'l)cP.t.
}J.JIH Bacoc-<tJopcyl!KH OKa3bIBaeT pewaIolll.ee BJ1IlHHIle Ha X8-
p8KTep H3MeHeHHH UHKJIOBOii n0l1.aQH npH H3MeHeHIiH 4HCJIa
060POTOB .n.BHraTeJIH CJIe.n.YIOIIlee:
1) cyMMapH8R C}KHM8eMOCTb TOnJIHB8 H npHBOl1.a, BlIHHHHe
KOTOpbIX CBO.n.HTCR K YMeHblIIeHHIO IJ:HKJ10BOH nO,lJ,aQH C YBeJIlfQeHHeM
060pOTOB B CBH31I C nOBbIweHlfeM l1.8BJIeHlIH B CIiCTeMe. On:HaKo n:e-
cpopMHpyeMocTb np fiBOli. a B.'IHHeT He TOJ1bKO Ha cYMMapHYIO
230
CllilIMaeMOCTb TOnJIHBa H npHBO.lI.a, HO H Ha npO.lI.OJ1lliHTeJIbHOCTb
.lI.ellcTBHTe.IJbHoro nepHO.l{a aKTHBHOll nO.l{alJH;
2) .lI.pOCCeJIHpOBaHMe TOnJ1HBa B OKHax rMJIb3bI nJIYHlliepa, BJ1MH-
HMe KOTOpOro .l{JIH paccMaTpMBaeMoll CHCTeMbI CBO.lI.HTCH K YBe.'1Hqe-
HMIO HKJIOBOH nO.lI.aqM C nOBbIllleHMeM 060pOTOB;
3) npO.l{OJIlliMTeJIbHOCTb .lI.ellCTBHTeJ1bHOrO nepHO.l{a aKTHBHOH
nO.!l,aqH, BJIHHHMe KOTOpOH TaKllie CBO.l{HTCH K YBemllJeHHIO llHKJ10BOll
nO.!l,aqH C B03paCTaHHeM qHCJIa 060pOTOB.
. (p -P.Jcp
Y7n KflC/' f 2
30 650
(P -pJml1x
xl/eH 2
1500
f
\
fOOO
500
o
500
750
fOOO f250 fl 00; HUH
(7)
1 I!l
20 450
/0 250
!!
')0
(p;" -Pqkp
KrjCH 2
800
600
400
o
500 750
fOOO
0)
1250n O/f/HLIH
PIIC. 123. 3aBHcHMoCTH, nOJlY'-ICHHbIe OCI.\HJlJlorpaqmpoBaHHeM .D:JIH IV BapHaHra
CHCTeMbI:
a - np0J1.0.,'DKHTeJIbHOCTH H M3KCHM3,iIbHbIX .n.aBJIeHHH BnpblCK3 OT 1.Juc.:rra 060pOTOB KYJIa1.JKa;
6 - CpeJI.HHX .u.3BJIeHHH BnpblCKa OT 1.J:HCJIa OOOpOTOB ]{YJIa'lKa; [ - npon.OJDKliTeJIbHOCTb
nOAa-'lu; II - MaKCHMaJIbHoe J],3BJleHHe BnpbICK3; III - CpeJ1.Hee no BpeMeHH .naBJIeHHe;
IV - cpe)J.Hee .n.aBJIeHHC BnpblcKa. nOJlyqeHHOe nJI3HlIMeTpnpoBaHHeM xapaKTepHcTHKH .n.aB-
JleHuii BnpbICI<a; 1 - h a 2.64 JIM'; 2 - h a 1.88 .lf1.1t: 3 - h a 1.24 ,".If I; 4 - ha 0,92 .lfl,";
5 - h a = 0,7 .lf1.1t; 6 - ha 0,5 .If""
Ha pHC. 124 BH.l{HO, qTO npH 60.lJblllHX nO.lI.aqaX npeo6"Ja.lI.aeT
BJ1MHHHe ClliHMaeMOCTM, npM MaJIbIX - COBMeCTHOe B.TII15IHHe lXpOCCe-
mrpOBaHHH H npO.lI.OJ1lliMTeJIbHOCTH neHCTBHTeJIbHOrO nepHO.lI.a
aKTHBHOll nO.lI.aqH (CM. TaKllie pMC. 118).
PHC. 125 H 126 HJ1JIIOCTPMPYIOT BJIHHHHe aKTHBHoro XO.l{a nJ1YH-
lliepa Ha xapaKTepHCTHKH H napaMeTpbI BnpbICKa. BH.lI.HO, qTO
KalJeCTBeHHO H3MeHeHHe cpa3 BnpbICKa TOnJIHBa COBna.lI.aeT C xa-
paKTepOM H3MeHeHHH reOMeTpHlJeCKHX cpas, T. e. no Mepe YMeHbllle-
HHH aKTHBHoro xO.lI.a HaqaJIO BnpbICKa 3ana3.lI.bIBaeT, a KOHell
HaCTynaeT paHbllle. OnepellieHHe HalJaJIa nO.lI.alJH OTHOCIITeJIbHO
231
"'1 l1e I/UKII
f
60 2
40
20
0
.JOO
7
'.'\
8
ffOO n OOjl1lJH 400
800 n 05/I1IJH
5)
PIIC. 124. OnbITHbIC xapaKTepllcTHKII nO.D:a'lH TOnJlIIBa
no o60poTaM:
a - III BapHaHT CHCTeMbI; 6 - VII BapHaHT CHCTeMI>"
1 hp 3,75 "tM; 2 - hp = 6,75 MM; 3 - hp = 10,7 "tM;
4 -- hp 14,4 MM; 5 - h p = 3,15 .MM; 6 - hp = 6,74 M.";
7 - hp 11,\ ."."; 8 - hI' 15,75 MM
P -Pu.
KflcN 2
1'100
600
{ 2 f7 /"\9
34-
;\
/
/ ,(
. x
I
\
I .
If' \
/! Ii II
,,-,
P -Pu.
Xf/cM 2
fOOO
500
f 8
2 7
J 6
4-5
9
x ,....fO
Hf
"f "
/1/' f2
,,1'1 f}/i I
f200
fOOD
800
400
200
o
JO
20 fO
0)
8.l1.m. rji"
JO
20 fO
0)
B./'I.m.l,P°
PHC. 125. B.lI1HHIIC aKTHBHoro XO.D:a n.1YHLKepa Ha xapaKTcpHcTIIKY
.D:aBc1Cl!Hi1 BnpbIcKa (ocI.\!JJI.TJOrpaq,HpoBaHlle, IV BapHaHT CHCTCMbl):
a - 11 = !5oo 06/."UH; 6 - 11 = 600 06/.MUH; 1, 2, 3, 4 - Ha'laJIO aHTHBHof!
no)],a4H; 5, 6, 7, 8 - KOHe aKTIlBHoii nop,a4H; 9 - h a 2,64 MM;
10 - ha = 1.88 MM; 11 - ha 0.92 MM; 12 - ha O,5 ."M
232
reOMeTpH4eCKoro YBeJ1H4HBaeTCH npH YMeHbWeHHH aKTHBHOrO xo a
B CBH3H C pacryweH npO OJ1:tKHTe.'IbHOCTbIO rrepHOAa pOCCeJ1HpOBa-
HHH TOn HBa B OKHaX rHJ1b3W n YH:tKepa O Ha4a a aKTHBHOH rro-
a'm. 3ana3l1.bIBaHHe KOHlJ.a BnpbICKa no OTHoweHHIO K KOHIJ.Y nepH-
o a aKTHBHOH nO,'J.a4H 3aMeTHO B03paCTaeT rrpH YBeJ1H4eHHH rrOAa4H
Tom-rHBa. 3TO CBH3aHO C YBeJ1H4eHHeM 3ana3 bIBaHHH KOHIJ.a efl'"
CTBHTe bHoro rrepHo a aKTHBHOH rrO,lJ.a'lH no cpaBHeHHIO C KOHl.{O:\l
reoMeTpH4eCKoro nepHo a aKTHBHOH rro a4H II 6o.'1ee .'IIlTeJ1bHbIM
(P/,-Pq)ml1J1 {i . (p;'-Pq)cp
Krjaf 1 Kr/CHt
20 800
f500
fOOO
x
20 30
40 50 'Iq He/l/llKIl
oj
f '"
fO
JE
.Jff
Pnc. 126. 3aBHcHMoCTH, nOJlY'-ICHHbIC OCI.\IIJ1J10rpaIj:JHpoBaHHcM .D:.TJH IV BapHallTii
CHCTCMbI:
a - npOJJ.OJI1KHTe.llbHOCTH H MaKCHMaJIbHbrx .naBJIeHHH: BnpbICK3 OT LlHKJIOBOii: no.n.aIlH;
6 - cpeJI.HllX .u.3BJIeHHii BnpbICKa OT 4,HK.TIOBOfi rro.n.a'In; I - npOJI.OJI>KllTeJIbHOCTb nO)l,a-
4H; II - MaKCHMaJIbHOe )],aBJleHHe BnpbICKa; III - cpe)],Hee no BpeMeHH )],aBJIeHHe;
IV - cpeAHee .lI.3BJIeHHe Bnpb1CK3. nonyqeHHOe IIJI3HHMeTpnpOB3HHeM xapaKTepHcTHKH
.D.aBJIeHHti BnpbIeKa; 1 - n = 1500 06/MUH; 2 - n = 1200 06/MUH; 3 - n 700 06/MUII;
4 - n = 500 06/MUH
600
400
2fJO
!l 0
(p -Pq)CPn
Kr/CHt
600
20 30
110 50 0t Hell/llKIl
5)
nepHO,lJ.OM crra,lJ.a aBJIeHHH (rroc e OTCeQKH) B CBH3H C 6o.TJee Bbrco-
KHM lI.aB.'leHHeM B CHCTeMe B Ha4aJ1e OTce4KH.
Ha Bcex pe:tKIlMaX eHCTBHTeJlbHaH rrpO,lJ.O :tKIlTe bHOCT
BnpbICKa :\1Horo 60J1bWe rrpO OJ1:tKIITeJ1bHOCTH nepHO,lJ.a aKTIlBHOH
nO a4I1 H3-3a YBe I14eHIIH npO OJ1:tKHTeJ1bHOCTH efICTBHTeJ1bHOrO
nepHO,lJ.a aKTHBHOH nO,lJ.8QH H B.7JHfmHfI cpaKTopOB C:tKHMaeMOCTH II
.n:pOCCeJ1HpOBamlH B Ha4aJ1e H KOHIJ.e no.n:a4H. C YMeHbweHHeM aK-
THBHoro xo.n:a nJ1YH:tKepa ,lJ.eHCTBHTeJIbHaH npO,lJ.o.'I:tKIITe.!IbHOCTb
BnpbICKa YMeHbwaeTCH, HO B MeHbweH CTeneHII, 4eM npo.n:o :tKII-
Te bHOCTb nepIlo.n:a aKTIIBHOH rro.n:a4H.
Do ,lJ.8HHbIM [551 npH n = 2000 06/.MUfl B 30He M8 bIX 8KTIIBHbrx
XO.n:OB Ha6J1IO,lJ.aeTCH ,lJ.a:tKe TeH,lJ.eHIJ.HH K YBeJ1H4eHHIO .n:eHCTBHTeJlb-
23.3
HOH npO.n.OJI}J{MTe.lbHOCTM BnpbICKa npM YMeHbWemlI1 aKTMBHOrO
xo.n.a nJ1YH}J{epa Hacoc-4>oPCYHKM AP-21 B CBH3M C 6bICTpO B03-
paCTaIOIlI.MM npM 3TOM onepe}J{eHHeM HaIIaJIa BnpbICKa.
MaKCMI\Ia"lbHOe .n.aB.'leHHe BnpbICKa B03paCTaeT C YBe.'HIIIeHIIeM
nO.n.aIIH, npHIIeM 60.TJee 3al\IeTHO Ha BbICOKHX IIHCJ1aX 060pOTOB.
CKOpOCTb YBeJIHIIeHHH P max MeHbWe B 30He 60J1bWHX nO.n.aII.
OCHOBHOH npHIIHHOH B03paCTaHHH P; max C YBeJIHIIeHHeM nO.n.aIIH
SIB.1HeTCH y.n.JIHHeHHe npO.n.O,,'1}J{HTeJ1bHOCTH .n.eHCTBHTe,,'1bHOrO ne-
pHO.n.a aKTHBHOH nO.n.aIIH. YMeHbWeHHe }J{e CIWpOCTH B03paCTaHlIH
paCCMaTpHBael\lOrO napaMeTpa B 30He 60JIbWHX no.n.a1.J CBH3aHO C
BJIHHHHeM <paKTOpa C}J{HMaeMOCTII.
YBeJ1lIIIeHHe P max npH YMeHbWeHHH xo.n.a peHKH BeCbMa
3Ha1.JHTeJ1bHO. TaK, npli n = 1500 06/MUH BeJ1lIIIHHa P max B03-
pacTaeT OT 710 .n.o 1550 Kr;CM 2 npH YBeJ1lIIIemlH no.n.aIIH OT 20 .n.o
60 MC/I1UKJ7. Cpe.n.Hee .n.aBJIeHlIe BnpbIcKa TaK}J{e 3aMeTHO B03pac-
TaeT C YBeJIH1.JeHHeM no.n.aIIlI TOnJ1HBa. HanpHMep, (p - P1J)cp.n
B Tex }J{e npe.n.eJIax 1I3MeHeHlIH q1J nOBblwaeTCH OT 360 .n.o 850 KF/CM 2
f1plIMeHHTe.lbHo K 6bICTpOXO.n.HbIM TpaHcnopTHbIM .n.H3eJ1HM C KaMe-
pOH THna feCCe,,'1bMaHa cnoc06HoCTb paccMaTpHBaeMoH CHCTeMbI
06ecneIIHBaTb 3HaIIHTe,,'1bHOe YBe.1HIIeHHe .n.aBJIeHHH BnpbIcKa npH
YBeJIWIeHIIH IIHCJ1a 060pOTOB H no.n.aIIH CJIe.n.yeT ou.emIBaTb nOJ1O-
}J{HTeJIbHO, TaK KaK npH 3TOM .n.OCTHraeTCH He06xo.n.lIl'.lOe pacnpe.n.e-
J1eHHe TOnJIHBa B 06"beMe KaMepbI cropaHHH, YCKopeHHe npOu.eCCOB
nporpeBa, HcnapeHHH H ropeHHH TOnJ1HBa. OnbITbI nOKa3aJIH, IITO
npHMeHeHHe Hacoc-4>oPCYHKH THna AP-21A3 oGecne1.JHBaeT npH
IIHCJ1e 060pOTOB KOJ1eHIIaTOro BaJia IIeTupexTaKTHoro .n.H3eJIH 3000 B
S
MHHYTY C pa3Mepal\IH -= 105/115 BbIHrpbIw B y.n.eJ1bHOM pac-
D
xo.n.e TOnJIHBa AO 14 2/(U.A.C. ) no cpaBHeHMIO C npeneJ1bHO
<POpcHpoBaHHoH TOnJIHBHOH annapaTYPoH pa3.n.eJIeHHOrO TIIna. f1pH
paBHblx .n.aBJIeHIIHX BnpbIcKa .n.JIH Hacoc-4>oPCYHKII cYIlI.eCTBeHHo
MeHbWMMII OKa3bIBaIOTCH KOHTaKTHbIe .n.aBJ1eHHH B nape pOJIlIK
TOJ1KaTeJ1H - KYJ1aIIOK.
YCT3HOBJIeHO, 1JTO B u.eJ10M OTKJIOHeHHH .n.eHcTBHTeJIbHOrO 3aKOH3
no.n.aIIM OT reoMeTpMIIecKoro, npe.n.cTaBJIHIOIlI.ero C060i'I 33BMCMMOCTb
o6"bel\1HOH CKOpOCTM BblTeCHeHMH TOnJIHBa nJ1YH}J{epoM B 4>yHKU.MM
BpeMeHM (yrJ13 nOBopoTa), YBeJ1MIIHBaIOTcH C nOBbIIlleHHel\1 IIHC.'1a
060pOTOB. .D:JIH I-IV BapHaHToB npH 60JIbIllHX IIHC,,'13X 060pOTOB
3TH OTKJ10HeHHH P3CTYT H npH YMeHbweHHH no.n.aIIM B CBH3H C
YBeJIHIIeHHeM nepMo.n.3 .n.pOCCeJ1HpOB3HHH TOnJIHB3 B OKHax rHJIb3U
nJIYH}J{epa nepe.n. H3II3J10M aKTlIBHOH no.n.3IIli.
f1pH M3JIbIX IIHCJIaX 060pOTOB 06"beM BnpUCHYTOro TOnJIHBa
.n.OCT3TOIIHO 6J1H30K K 06"beMY, omIcaHHOMY nJ1YH}J{epOM 33 nepHOI(
aKTHBHOH no.n.aIIH. .D:.TJH 60J1bIllHX aKTHBHbIX XO.n.OB 06"beM BnpbICHY-
Toro Ton.TJHB3 MeHbIlle BbITeCHeHHoro nJIYH}J{epOM, npH1.JeM p33HHu.a
B03paCT3eT C YBeJIHIIeHHeM 1.JHCJIa 060pOTOB. f1pH M3JIbIX aKTHBHbIX
XO.n.3X nJ1YH}J{ep3 (60JIbIllHX xo.n.ax peHKH h p ) 3aKoHoMepHocTb 06-
234
p3TH3H, HO BHOBb pa3HHu.a HeCKOJIbKO 60J1bllIe npH 60J1ee BbICOKHX
llHCJ1aX 060pOTOB.
TIpII BCeX llIICJ1aX 060pOTOB 3aBIICIIMOCTb q1J. - h p no LIT 11 .'IlmeH-
Ha, LITO HBJIHeTCH <paKTOpOl\1 6.1arOnplJoflTHbIM C TOllKI1 3peHIIfI
npOeKTI1pOBaHIIfI H 3KcnJ1yaTau.HH CHCTeMbI perYJ1IIpOBaHIIH ,n:H3eJIH.
BAURHue npoxo8Hoeo ce-
tteHUR oT8epcTuii pacnbl.i1UTe-
AR, 3,n:eCb B03MO)KHbI JI,Ba Me-
TO,!J.a aHa.rIlI3a [55].
1. BJ1HflHHe npoxo,n:Horo
CelleHIIH aHaJ1H3I1pyeTcfI ,n:J1f1
CJ1YllaH, Kor,n:a no,n:alla TOnJ1H-
Ba npII HOl\{J1Ha.rlbHOM llHC.TJe
060pOTOB OJI,HHaKOBa ,n:JIfi
Bcex 3HalleHHH npoxo,n:Horo
Ce'leHHfI. TaKoH no,n:xo,Q npeJI.-
CTaB,,'!fleT HHTepec C TO'lKH
3peHHfI npoeKTHpOBll.{HKa Ton-
JIHBHOH annapaTYpw. B 3TOM
C.1Y'lae aKTHBHbIH XO.rr. nJ1YH-
)Kepa MeHbllIe npH 60.TJbllI0l\1
npoxo,n:HOM Ce'leHHH B pacnw-
mneJ1e. Ha pHC, 127 I10Ka3a-
HbI 3aBHCHMOCTH, HJ1JIIOCTpH-
pYIOIl.(He B.'IlIHHHe npoxo,n:Horo
Ce'leHHH paCnbIJ1HBaIOIll.Hx OT-
BepcTHH npH 3TOM YCJIOBHII.
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CKa no OTHOllIeHHIO K lHaIla.TJY
nepHo,n:a aKTHBHoH no,n:aIlH,
eCTeCTBeHHO, He 3aBHCHT OT
npoxo,n:Horo ceIleHHH B pacnw-
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ro YBeJ1HIleHHH nepHOJI.3 ,n:pOC-
CeJIHpOBaHHH II CKOpOCTH
nJIYH)Kepa B HaIla.TJe no,n:aIlH B
CBH3H C H3MeHeHHeM He06xo-
,QH!\IOrO aKTHBHoro xo.rr.a nJIYH)Kepa npeHe6pe)KHMO MaJ10). no 3THM
npl1'fHHaM H3MeHeHHe JI,eHCTBHTeJ1bHOrO HaIlaJ1a BnpwCKa CJIe,n:yeT 3a
H3l\IeHeHHeM HaIlaJ1a nepHOJI.a aKTHBHOH no,n:a'll1, T. e. 3ana3.llbIBaeT
no Mepe YBeJ1HIleHHH npoxo,n:Horo ceIleHHfI B paCnbIJIHTeJIe. 3ana3,n:bI-
BaHHe KOHu.a BnpbICKa no OTHOllleHHIO K KOHU.Y nepHo,n:a aKTHBHOH
nO,J.aIlH YMeHblllaeTCH C YBeJ1H'leHHeM fc B CBfl3H C YMeHbllIeHHeM 3a-
na3,J.bIBaHHfI KOHu.a ,n:eHCTB'HTeJIbHOrO nepHo,n:a aKTHBHOH no,n:a'lH no
OTHOllIeHHIO K KOHl.{y nepHo,n:a aKTHBHOH no.rr.a'lH, a TaK)Ke BCJIe,lJ.-
CTBHe YMeHbllIeHHfI nepHo,n:a nOHH)KeHHfI ,n:aBJ1eHHfI noc.lIe HaIlaJ1a
OTceIlKH H3-3a MeHbllIeH BeJ1H'lHHbI ,n:aBJ1eHl1H B HaIla.IIe OTceIlKH. B
pe3Y.IIbTaTe npo,n:OJI)KHTeJ1bHOCTb BnpbICKa Ton,,'!HBa 3al\1eTHO YMeHb-
235
P,,,,,x
K!jC/ft
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Pnc. 127. 3aBHcHlIIOCTb napaMeTpoB
BnpblcKa OT npOXO.D:HOro CC4CHIIH pac-
nblJlnBa!OlI.\lIX OTBcpcTni1, Bb!paLKeHHoro
B np0I.\CHTaX (cTpo60cKonnpoBaHHc,
II BapHaHT, fe = var, q = 0,75 q ",
q " = 70 A/Z/ljUKJl):
J - Halla",o OTCqeTa: I J - 30H3 reOMCTpH-
trecKoro nepHo.n.a aKTHllHoiI no.nalIH: III -
30H3 onepe>KeHHH Haq31I3 BnpbICK3 q; 06;
IV 301i3 33na3)J..b1B3HHH KOHl\a BnpblcK3
/),<P 30 ; 1/ - npOJl.OJI.iKHTeJIbHOCTL snpbIcKa.
3alllTpHXOHaHa OOJIaCTb npoxo.lI,HbIX CeqeHHir
cepHfiHhIX pacnbllIHTe.;'1eJi. 3a 100% npHHHTo
HOMHH3JIbHOe CeqeHHe cepHIi:Hblx paCl1bIJIH-
Teneri
waeTCH C YBe.1HIIeHlieM fc. CKOpOCTb Y;\IeHbWeHHH npO)],O.l)KUTeJIbHO-
CTII BnpbICKa C B03paCTaHHeM fc HeCKOJlbKO BbIWe npH 60.1bWe:II lJIIC-
JIe 060pOTOB.
IvlaKcHMa.TJbHoe )],aBJ1eHHe BnpbICKa YMeHbWaeTCH C YBe.1I1lJeHUeM
fe nOlJTH no mmelIHOMY 3aKOHY, nplIlJeM HeCKOJ1bKO 60JIee pe3KO
npH 60abweM lJlICJle 060pOTOB. flpH n = 1600 o6jMufl p max
YMeHblllaeTcH OT 2200 )],0 1200 KF/Ot 2 npH YBeJ1HlJeHHH Fe B 1,75 pa-
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u I B u
H3MeHeHlIH )],aBJIeHllH BnpbICKa npOnOpUHOHa.TJbHO -. ,J,eH-
(f!cf c)2
CTBHTe.1bHOCTH ,J,aB.:leHlIH BnpbICKa C YMeHbllleHHeM npOXO)],HOrO
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dp
MOCTH (YMeHbWeHlle Fc BbI3bIBaeT YBe.1HlJeHlle cpaKTOpa acy.M V -
dt
BCJle,lI.CTBIIe YBeJ1I1lJeHHH dp ).
dt
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r THBHbIM Cpe)],CTBOM KOppeKUHH CKOpOCTHbIX XapaKTepHCTHK TOn.1H-
; BOnOAalJH, npHlJeM C YMeHbllleHHeM Fe KoppeKUIIH paCTeT B CBH3I1 C
nOBbIllleHHe;\1 AaBJleHHH B CHCTeMe H TeMna HX pOCTa C lJIIC.10M
060pOTOB. O)],HaKO I13MeHeHIIe Be.TJIIlJIIHbI fc B03MO)KHO )],0 H3BeCTHbIX
npe)],e.lOB, TaK KaK OHa OKa3bIBaeT cYIllecTBeHHoe BJIHHHHe Ha Bce
npOlJHe napaMeTpbI BnpbICKa TOnJIHBa (npo)],OJ1)KHTe.JlbHOCTb
BnpbIcKa. )],aB.1eHliH BnpbICKa). KOTopbIe TaK)Ke 3aMeTHO BJ1I1HlOT H3
pa60TY )],H3e.TJH.
KaK II B CHCTeMax C TOnJ1HBOnpoBo)],oM, cpe)],HHH 06"beMHaH
CKOpOCTb BnpbICKa TOnJ1HBa B03pacTaeT C YBeJ1I1lJeHIIeM fc B CBH3Ii
C cOKpaIlleHHeM npo,lI.OJ1)KIITe.TJbHOCTH BnpbICKa [CM. ypaBHeHI1(>
(228)]. B TO )Ke BpeMH cpe)],Hee )],aBJ1eHIIe BnpbICKa 3aMeTHO
YMeHblllaeTCH npH YBeJ1HlJeHHH npOXO)],Horo CelJeHHH OTBepCTHII B
pacnbI.TJHTeJ1e. cBH)],eTeJ1bCTBYH 06 YXY)],llleHHH paCnbIJ1HBaHHH.
2. BJ1I-IHHHe npoxo)],Horo CelJeHHH aHaJ1H3HpyeTcH npH nOCTOHH-
HOM nO.TJO)J{eHHH perYJ1HpYlOIlleH peHKH. TaKoH nOAXO)], HHTepeceH
)],.TJH aHaJ1I13a )],aHHbIX 3KCnJ1yaTaUHH )],H3eJ1H. Ha pHC. 128 )],aHbI
3aBIICHMOCTII, I1J1J1IOCTPHpYIOIllHe BJ1HHHHe Fe )],JIH 3Toro c.1)'lJaH.
Onepe)J{eHHe BnpbICKa O)],I1HaKOBO )],J1H Bcex 3HalJeHliH fe. flo OTl\1e-
lJeHHbIM BbIllle npHlJHHaM 3ana3)],bIBaHHe KOHua BnpbICKa no OTHO-
llleHHlO K KOHUY nepHo)],a aKTI1BHOH no)],alJH YMeHblllaeTCH, a npo-
AOJl)KIITeJ1bHOCTb BnpbICKa cOKpaIllaeTCH npH YBeJ1W.JeHHH npoxo,J,-
Horo CelJeHHH. TaK, npH n = 1800 06jMUfl H h p = 0 npo)],OJ1)KHTeab-
HOCTb BnpbIcKa B rpa)],ycax yrJ1a nOBopoTa Ky.TJalJKa YMeHblllaeTCH
C 22,7 )],0 18,7 npH YBeJIHlJeHlIH fe Ha 40%. MaKcHMYM AaBJ1eHlIH
BnpbIcKa YMeHblllaeTcH C YBe.1I1lJeHHeM npoxo)],Horo CelJeHHH B
paCnbIJ1HTeJ1e )],J1H 060HX HCCJIe)],OBaHHbIX pe)KIIMOB pa60TbI Hacoc-
cpOPCYHKH, npHlJeM 60.TJee HHTeHCHBHO npH 60J1bllleM lJHCJ1e 060pOTOB
H 60JIbllleH nO,lI.alJe TonJ1HBa. 3aBHcHMoCTb p max OT npOxo,lI.HOro
CelJeHHH J1HHeHHa. MaKCHMaJ1bHaH CKOpOCTb BnpbIcKa B03paCTaeT
236
C YBeJ1II4eHIIeM fe, TaK KaK npHMOH 3<p<peKT YBeJIl14eHIIH npoxo;J.-
Horo ceIIemm npeBa.'IlipyeT Hall. BJIHHHIIeM YMeHblileHIIH AaB.leHIIH
BnpbICKa.
f1pII h p = 7 .M.M II n = 1200 06j.MUH cpeAHee AaB.'IeHlIe BnpbIcKa
)"Be.llIIIHBaeTC5! npH YMeHblllemm npoxoAHoro CeIIeHII5! B pacnbI"ll1-
Te"le, npHIIeM CKOpOCTb YBeJIllIIeHIIH p .cP.t MeHblile npl1 Ma.'IbIX
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cpeAHee no BpeMeHII AaBJ1eHHe BnpbIcKa YMeHblilaeTcH npli YMeHb-
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(229) BlIII.HO, IITO 3TO 1\1Q)KeT I1l\1eTb l\1eCTO BCJ1eII.CTBlIe npe06na-
AalOIII.ero BJIHHHlIH Yl\IeHblileHIIH q1f II YBeJ1IIIIeHH5! qJn HaII. B.'InHHl1e 1
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MO)KHO YBe.'IHIIIIBaTb II.O onpeII.eJIeHHbIX npeII.eJ10B npOXoII.HOe ce4e-
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nYCTlIl\10MY CHH)KeHHlO n.aBJ1eHHH BnpbICKa. B ueJ10M HCn0J1b30BaHlle
paCnbIJ1HTeJ15! C 60J1blllHM IIpOXOII.HbIM ceIIeHHeM MO)KeT YX)"II.lllIITb
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B IIaCTHOCTII, IIHOrII.a OKa3bIBaeTC5! Heo6xon.HMbIM YBe.1IIIIeHHe MHHI1-
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peHKH 3al\1eTHO B03pacTaeT C YBeJIlI'-IeHIIeM npoxoII.HOrO CeIJeHIIH
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lllIIX IIIIC.'laX 060pOTOB. Cpe11HHH CKOpOCTb BnpbIcKa B03paCTaeT
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'-IeHHel\1 KaJIl16pa B03pacTaeT HeCKO.flbKO onepellieHHe BnpbIcKa no
OTHOllleH11IO K Ha4aJ1Y nep110II.a aKT11BHoH nOII.a'IH B CB5!3H C YBe.flH-
XIeH11eI\I nep110II.a II.pOCCe.'I11pOBaH11H TOnJIHBa nepeII. Ha4aJ10M
aKTHBHoH nOII.a'-III. BnpbIcK np11 60.'IblileM KaJI116pe Ha'-I11HaeTCH,
-eCTeCTBeHHO, n03AHee. f10CJle HaIIa.'Ia aKT11BHoH non.aII11 06'beMHbIe
.CKOpOCTH 11 II.aBJ1eH11H BnpbIcKa npII 60JIblllel\1 KaJ1116pe B03pacTaIOT
6bIcTpee, '-ITO CB5I3aIlO C 60.1blll11I\1II CKOpOCT5II\HI n.>lYH)Kepa B 3TOT
nepIIOII.. B ueJ10ll1 OKa3bIBaeTC5I B03MOlliHbIM H3MeH5ITb B HeKoTopbIX
Ilpen,eJ1ax 11HTerpa.1bHbIH 3aKOH n011a411 TOIl.'IHBa 11, C.>leAOBaTe.'IbHO,
KO.ll1'-IeCTBO TOIlJ1HBa, nOII.aBaeMoro 3a Ilep11oJI: 3an:eplliKI1 BOCnJIa-
237
MeHeHHH. MaKCHMaJlbHOe JJ.aBJ1eHHe BnpbICKa B03paCTaeT, a npOJJ.o.l-
)KHTeJIbHOCTb BnpbICKa pleHbliiaeTCH C YBeJIHqeHHeM KaJIH6pa .:1:0
onpeJJ.e,,'IeHHoro 3HaqeHI-IH. ,L{a,,'1bHeHlllee YBe.'1HqeHHe KaJ1H6pa BJ1eqeT
3a C060H CHH)KeHUe Be,,'1UQHHbI P max ' B OCHOBHOM, B CBH3H C
YMeHbllleHHeM CKOpOCTH nJIYH)Kepa B KOHl e nepHo.n.a aKTHBHOH no-
.n.aQH. f1pO.n.OJI)KHTeJIbHOCTb BnpblCKa npH 3TOM OCTaeTCH HeH3MeHHOH.
P max P max P cpt P cPt
K(/CH 2 KrjCH 2
Kt7cH 2 Kr/CH 2 700 420
2000 1100
650
1800 - 900
1600 700
84
66
4 60
110 1110 % 100 I/O ao %
PHC. 128. 3aBllcIIMoCTb napaMcTpoB BnpblcKa OT npOXO.D:Horo Ce'-lCHHH OTBCpCTllii
B pacnbI.1HTC.TJC, Bb!pa>KeHHOrO B np0l.\eHTaX (cTp060cKonHpoBaHHc,
II BapHaHT, f c = var, h p = 0):
a - q,a3bl no)],a"H H MaI<CHMa.'bHble )],aB.leHHH BnpblCI<a npH II = 1800 OO/MUII.; 0-
l\HKJIOBaH no)],a4a H cpe)],H!!e )],aB.,eH!!H BnpbIcKa; I, II, III, IV, V - 0603Ha4eHHSI CM.
Ha P!!c. ]27
HeCMOTpH Ha MeHblllYIO CKOpOCTb n.'1YH)Kepa B KOHLl,e BnpbICKa
H, CJIe.n.OBaTeJIbHO, MeHblllYIO CKOpOCTb YBe.'1H eHHH npOXO.n.HOrO
CeQeHHH OTCeQHOrO OKHa, CKOpOCTb na.n.eHHH .n.aBJ1eHHH nOCJ1e HaQa-
JIa OTCeQKH B03paCTaeT C YBeJIHQeHHeM KaJIH6pa I. 3TO eJl,Ba ,,'1H
MO)KHO 06"bHCHHTb MeHbllleH CKOpOCTblO nepeMeru.eHHH TOnJIHBa
nJ1YH)KepoM. BH.n.HlvIO, OKa3bIBaeT B.TJH51HHe 6oJ1ee paHHHH nocaJl,Ka
Ha ce.n.J1o KJ1anaHa Hacoc-q>oPCYHKH [55]. B pe3Y.'1bTaTe npH 6o.'1bllleM
KaJIH6pe MeHblllee KOJ1HQeCTBO Ton.'IHBa no.n.aeTCH B KaMepy cropa-
HHH C MaJ1bIMH CKOpOCTHMH B KOHlI.e npOllecca BnpbICKa.
I C YBCJ!HqCHHCM KaJlH6pa HaqaJ!O OTCe'-lKH HaCTynacT npH BCC I\ICHbIllCi1 CKO-
pOCTH nJlYHLKcpa Ha HHcna.D:a!Ollleii BCTBH KpHBOit CKOpOCTH.
238
YBe.1H'leHHe Ka.rm6pa BJ1e'leT 3a C060H npH HeH3I\IeHHO 1 nOJIO-
)J{eHliH perYJ1HPYlOllI.eH peHKH YBe.TJH'leHlle IJ,HKJ10BOH TIO,lJ.a'lH
TOnJ1llBa. O,lJ.HOBpeMeHHO TIPH 60JIbIIIel\l KaJIll6pe n HOi\nIHaJ1bHOl\1
xO,l],e peHKH YMeHbIIIeHHe BeJ1ll'lHHbI q1J C YBeJ1H1JeHHeM 'IllC.ila 060po-
TOB OKa3bIBaeTCH MeHbIlIHI\I. 06a 3TH HB.neHHH l\lOrYT 6bITb 06"bHC-
HeHbI YBeJIll'leHlleM nepno,l],a ,lJ.pOCCeJIHpOBaHlIH TOnJillBa B OKHaX
rIWb3bI nJ1yH)J{epa nepe,lJ. Ha'la.10M aKTlTBHOH nO,lJ.a'ln.
f1pll 3KCnJ1yaTaI.J.lln HaCOC-<p0PCYHOK 113!\leHeHHe Kac1H6pa He-
pe,lJ.KO HCnOJIb3yeTcH KaK Cpe,lJ.CTBO n3MeHeHHH onepe)J{eHHH Ha'laJ1a
BnpbICKa OTHOCHTeJIbHO B. M. T. He-
06XO,lJ.HMO, O,lJ.HaKO, I-DleTb B BH,lJ.Y 11
,lJ.PyrHe 3<p<peKTbI, BbI3bIBaeMbIe H3Me-
HeHHeM KaJ1H6pa. CJ1e,l],yeT TaK)J{e Y'lH- 24
TbIBaTb, 'lTO eCJ1H KaJ1H6p Hacoc-<pop-
CYHKH BbI6paH TaI<, 'ITO npH HOMH- 20
HaJIbH0I1 TIOpI.J.HH nO,l],aBaeMOro TOnJ1H- 2.2 L;9 2.6 2,8 .J,OCn cp l1fcCK
Ba aKTHBHaH nO,l],a'la npOHcxO,lJ.HT I.J.e-
.1HKOM npH B03paCTalOllI.eH CKOpOCTH
nJ1YH)J{epa, TO YMeHbIlIeHHe nO,lJ.a'lH
TOnJIHBa B pe3yJIbTaTe 60J1ee TI03AHe-
ro Ha'la.'la nepHO,lJ.a aKTHBHOH nOAa'lH
6Y,l],eT conpOBO)J{,l],aTbCH nOCTeTIeHHbIM
YBe.'UI'leHlle 1 Cpe,lJ.HeH CKOpOCTH nJIYH-
)J{epa B nepllO,l], aKTHBHOH nO,lJ.a'lll, a
3TO MO)J{eT OKa3aTbC5I 6JIarOnpllHTHbJ:\1
<paKTOpOM ,lJ..1H pa60TbI ,l],H3eJIH Ha Ma-
JIbIX 'lllC.lax 060POTOB, MaJibIX Harpy3Kax, a TaK)J{e npll XOJIOCTOM
xOJI,e.
AHaJIll3 B.TJll5lHH5I Ha npOI.J.eCC BnpbICKa npo<pHJIH KYJ1a'lKa n03BO-
mw BbI51BllTb 3aBHCHI\IOCTb Me)J{,lJ.Y np0,l],OJI)J{HTe.TJbHOCTblO BnpbICKa
B rpa,lJ.ycax nOBopOT8 KYJIa'lKa H Cpe,lJ.HeH CKOpOCTblO nJIYH)Kepa 3a
nepllO,lJ. aKTHBHOH nOAa'lH (pllC. 129). YMeHbIIIeHlle npo,lJ.OJI)J{llTeJIb-
HOCTH BnpbIcKa 3aMe,l],JIHeTCH C YBeJIH'IeHl-IeM cpe,lJ.HeH CKOpOCTH
nJIYH)J{epa. YMeHbllleHHe Be.'IH1JHHbI qJn C B03paCTaHllel\l cpenHelI
CKOpOCTlI nJ1YH)J{epa CBH3aHO. B OCHOBHOM, C YMeHbllleHHe!\l npo-
JI,OJl)J{HTe.TJbHOCTll nepHOJI,a aKTHBHoH no,lJ.a 'lH. 3aMe,lJ.J1eHHe )Ke
YMeHbIlIeHll51 np0,lJ.OJI)J{llTeJlbHocTH BnpbIcKa npH 60JlbIlIHX 3Ha'le-
HHflX CKOpOCTll nJ1YH)J{ep8 CBfl3aHO C BJIHflHHeM HB.'leHlllI ,lJ.pocce-
J1llpOBaHI-UI H C)J{HMaeMOCTH. DbIJlO YCTaHOBJ1eHO TaK)J{e, 'lTO B
60JIbIlIHHCTBe CJIY'IaeB YBeJ1ll'leHHe Cpe,lJ.HeH CKOpOCTll nc1YH)J{epa
BeJI,eT K YBeJIH'leHHIO Cpe,lJ.HerO H MaKCHMaJIbHOrO ,lJ.8BJIeHHH BnpbIc-
Ka H YMeHbIIIeHlllO KOJIll'leCTBa TOnJ1llBa, nO,l],aHHOrO 3a I.J.llKJI. 3Ta
3aKoHoMepHocTb, O,lJ.HaKO, He YHllBepCaJ1bHa, TaK K8K cpe,lJ.HflH
CKOpOCTb nJIYH)J{epa 3a nepllO,lJ. aKTHBHOH nO,lJ.a'lll He OTpa)J{aeT
nOJIHOCTblO BJ1ll5lHllH npO<pllJ1H KY.'la'lKa Ha npOI.J.eCC BnpbICKa.
BJ/.wuiUe o67JeM.a TonJ/.uea B nOJ/.OCTU BblCOK020 oaBJ/.eHtlR. HG
enpblcK. f1pll ll3MeHeHllH 06"beMa H3MeHHeTcH CTeTIeHb BJ1HHHllH
Ha npou.ec c BnpblcKa <paKTopa oKHMaeMocTH TOllJ1lIBa. KOMllJ1eKC,
PHC. 129. 3aBHcHMoCTb npo-
.D:OJUKHTeJIbHOCTH BnpblcKa OT
CPC.'J,HCit CKOpOCTH n.TJYHLKcpa
B ncpHO.l.\ aKTHBHoH nO.l.\a'-lii,
nOJIY'-IeHHaH npH n =
= 1800 06jMUH H h p = 0
( cTp06oCKollHpoBaHHe,
II BapHaHT CHCTCMbl,
C n = var)
239
Bblp3)K31OlI.{HH B.mUIHHe 1I.ecpOpMau.HH npHB01I.3 B yp3BHeHlIH Cn,10lil-
HOCTH, He 33BHCHT npHMO OT 06'beMa TOnJIHBa B nO.'JOCTH BbICOKoro
1I.3Bc'1eHIfH, eC.'JH, KOHe1.JHO, nOCJ1e1I.HHH H3MeHHeTCH npH HeH3MeHHOM
.1I.HaMeTpe nJ1YH)Kepa. 01I.HaKO paCCMaTpl1B3eMbIII 06'beM B.'JHHeT Ha
CKOpOCTb nOBbIUIeHHH 1I.aBJIeHIIH, 3 1.Jepe3 Hee II Ha KOMn.rleKC
k,..,pf,.., dPII , BbIP3)K31OIl(HH B.'lHHHHe 1I.ecpopMau.HH n.'l)'H)Kepa.
dt
p
I<rjCI1 '
2100
q, f800
CH:1
ceK
75 1500
60 1200
45 900
30 600
15 .JOD
27 .JO .19
PHC. 130. Pac4cTHbIC 3aBHCHMOCTH 06"bcMHoI! CKOpOCTH
H .!J.aB.TJCHHi1 BnpblcKa OT yr.TJa nOBopoTa Ky a4Ka npll
pa3.1H4HbIX 3Ha4CIIH5IX 06"bCMa KaMCpb! nJlYBLKcpa B KOB-
I.\C aKTIIBIlOH nO.D:a'-lH (II BapllaHT, V" = var):
I - II fl 392 "U,3; /I II II 4GI _"M 3 (Hacoc-q,opcYHKa
AP-21); /II - VII 6{j8 ..",,"; IV - V II = 1288 "'M 3 ; 1- Ha-
Qaol10 reOMeTpW-IeCKoro nepHo.na aKTHBHoii no.n.aQll; 2 - KOHeu
reoMeTpHllecKoro nepno.1.a 31\THBHOfl nO.1.aQH
PIlC. 130 H 131 H.'J.JllOCTPHPYlOT BmlHHlle 06'beMa B Hacoc-cpop-
cYHKe Ha xapaKTepHcTHKn H napaMeTpbI BnpbIcKa [55]. CKOpOCTb
)'MeHbUIeHlIH 06"bei\13 npH nOA'beMe nJIYH)Kepa, a TaK)Ke OCT3JIbHbIe
nap3MeTpbI, BK.'l101.J3H nO.TJO)KeHHe peHKH H 06'beM B KaMepe K,lana-
Ha, COXpaHHJIHCb He1l3MeHHbIMli 1I.JIH BCCX p3C1.JeToB. 3TlI 3aBHCH-
i\IOCTH npe1I.CTaB.'JHlOT HHTepec TaK)Ke 1I.J1H aHaJ1H3a fl:vmy.'lbca
1I.aBJ1eHHH, C031I.aB3ei\IOro B Hacoce Ton.m1BHOH ann3 paTypbI pa31I.e-
J1CHHOrO THna. YBe.TJHLJeHHe 06'beM3 B.'le'IeT 3a C060H He60JIbUIOe
3ana31I.bIBaHHe H31.JaJ13 BnpbIcK3. B TO )J(e BpeMH 33n331I.LIBaHHe
Ha1.J3J13 .n.eHCTBHTeJIbHOrO nepno.n.a aKTHBHOH n01I.aLJH no OTHOlileHllIO
K Ha1.JaJ1Y reOMeTpHLJeCKOrO nepIf01I.3 no.n.31.JH YMeHblil3eTC5L CKO-
pOCTb YBe.mILJeHIIH QtjJ II P B CPYHKU.HH yrJIa nOBopOTa KY laLJK3
:240
noc.le Ha'IaJ1a BnpbICKa CYII.{eCTBeHHO MeHblile npH 60.1bllIeM 06"beMe.
M.aKCHMa.TJbHbIe 3Ha'IeHHH COOTBeTCTBYIOII.{HX Be.1H'.JHH TaK)!{e npH
3TO:\I HH}Ke. KaK CJleLI.CTBHe, 3ana3,tJ,bIBaHHe KOHua LI.ellcTBHTe.'IbHoro
nepHOAa aKTHBHoli nOLI.a'IH no OTHOllIeHHIO K KOHUY reOMeTpH'IeCKOrO
nepHO,tJ,a YMeHblilaeTCH C YBeJ1H'IeHfieM 06"beMa B CliCTeMe. CKOpOCTb
naLI.eHHH LI.aBJ1eHHH nOC.le Ha'IaJ1a OTcelIKH TaK}Ke MeHbllle npH
60.1bllIeM 06"beMe KaMepbI nJ1YH}Kepa. f103TOMY KOHeu BnpbICKa
npHMepHO COBnan:aeT npH Bcex HCC.'IellOBaHHbIX 3HalIeHHHX 06"beMa,
XOTH KOHeu LI.eHCTBliTeJlbHOrO nepHOLI.a aKTHBHOH nO,tJ,alIH HaCTynaeT
npn 60J1bllIeM 06"beMe B }{aMepe n'
C m
nJ1YH}Kepa paHbIlle. pellHee llaB- 2
J1eHHe BnpbICKa YMeHbIllaeTC5I C 1Jf;
YBe.'IH'IeHI1eM V.
B HCCJle,tJ,OBaHHOM ,tJ,Hana30He
H3MeHeHHH 06"beMa MaKCIIMaJ1b-
Hoe n:aBJleHHe BnpbICKa YMeHb-
IllaeTCH OT 2350 ,UO 980 KTjCM 2 ,
a cpe,UHee no BpeMeHH ,UaBJleHHe
BnpbICKa YMeHbiliaeTcH OT 850
,tJ,0 380 KTjCM 2 . 3aMeTHOe YMeHb-
IlleHHe ,UaBJleHHH BnpbIcKa C B03-
pacTaHHeM BeJlHlIHHbI V HBJ1HeT-
CH O,tJ,H"HM H3 06"bfICHeHHH Toro
tlJaKTa, lITO B TOnJ1HBHOH anna-
paType pa3,UeJleHHOrO THna,
Hl\IeIOII.{err HepeLI.KO ,tJ,OBOJlbHO
60,lbmoCI 06"beM TOn.TJIIBa Y Ha-
coca (KaMepa n.1YH}Kepa +
+ llITyuep), HeB03MO}KHO LI.O-
CTIIrHYTb BbICOKHX llaBJ1eHlIi-i
BnpbICKa YBeJlH'IeHlieM CKOpOCTI1 H LI.I1aMeTpa nJ1YH)Kepa. f1oC.1eLI.Hee
oco6eHHO TPY,tJ,HO OCYII.{eCTBHTb, TaK KaK C YBeJIHlJ.eHHeM LI.Il8MeTp8
nJ1YH)Kep8 B03p8CT8eT H 06"beM B ero KaMepe. KpoMe Toro, B 060HX
C.TJYlJ.8HX BJlHHHHe C)!{HM8eMOCTH YBeJ1HlJ.HB8eTCH BCJ1eLI.CTBHe TeHLI.eH-
dp
UIUI K poCTy dt
KOJ1HlJecTBo TOnJIHBa, nOLI.8B8eMOro 3a UHKJ1, n8n:aeT C YBeJlH-
lJ.eHIIeM 06"beM8 BCJIeLI.CTBHe 8KKYMYJ1HpOB8HHH B CHCTeMe K KOHUY
aKTI1BHOH n01l8lJ.H 60J1bIlleH LI.OJ1H nepeMeII.{eHHOrO nJlYH}KepOM Ton-
J1HBa (TOJlbKO lJ.8CTb 3Toro TOnJ1HBa nOLI.aeTCH B LI.8J1bHerrilleM B
K8!\Iepy cropaHHfI, 60JIbIlI8H )Ke lJ.aCTb nepeTeK8eT B nOJlOCTb HH3-
Koro LI.8BJIeHHH), 8 TaK)Ke H3-3a MeHbIllero 3ana3LI.bIB8HHH KOHua
LI.eikTBHTeJ1bHOrO nepHOLI.8 8KTlIBHOH nOJJ.alJ.H no OTHOIlIeHHIO K KOHUY
reO:MeTpHlJ.eCKOrO nepHOLI.8. f18LI.eHHe UHKJ10BOH nOJJ.alJ.H B YK838HHbIX
BbIllie npeJJ.eJl8X YBeJ1HlJ.eHHH 06"beMa 3H8lJ.HTeJ1bHO: OT 70 JJ.O 58 Mi!.
f1P0JJ,OJl}KHTeJ1bHOCTb BnpbICK8 T8K)Ke HeCKOJ1bKO YMeHb1ll8eTCH npH
YBe.'IHlJ.eHHH V, lJ.TO CBH38HO, B OCHOBHOM, C YMeHbllleHHeM 3an83LI.bI-
BaHHH KOHua JJ.errCTBHTeJlbHOrO nepHOLI.8 aKTHBHOH nOLI.alJ.H no OT-
16 3aI<a3748
1800
11,00
500
$I;
2f
19
JOO
ffOO
VHM.J
700
PIIC. 131. PaC'-ICTHbIe 3aBHCIIMOCTH na-
paMcTpoB BnpbIcKa OT BCJlII'-IIIHbI nOJlHO-
ro 06"bCMa Ton.1HBa B CHCTCMC BblCOKoro
LI.aBJlCHH5I, onpe.D:c.1eHlloro .D:JlH MOMeH-
Ta KOHl.\a aKTHBHoro XO.l\a oJlymKcpa
(II BapHaHT, V" = var). 3a 100% npH-
HilT 06"bClIl B Hacoc-lj:JoPCYHKC AP-21
241
HOIlleHHIO K KOHU.Y reOMeTpH'J.eCKOH nO,lJ,aqH. 3TO, O,lJ,HaKO, CnpaBe,lJ,-
JIHBO TOJ1bKO npH HeH3MeHHOM nOJIO)KeHHH perYJIHpYIOll1.eH peHKIL
DpH YC,,10BHH nOCTOHHCTBa U.IlKJIOBOH nO,lJ,aqIl np0,lJ,OJI)KHTeJlbHOCTb
BnpbICKa B03paCTaeT C YBem-IqeHlleM 06'beMa B CHCTeMe.
DbIJIO HaH,lJ,eHO paCqeTaMH H nO,lJ,TBep)K,lJ,eHO onbITaI\1H. 'ITO rIPH
60J1hIlleM 3HaqeHIIJi 06'beMa B CIlCTeMe MeHhIlleH OKa3hIBaeTCH IIH-
TeHCHBHOCTh YBeJIHqeHHH ,lJ,aBJ1eHH5I BnphICKa npH YBeJIHqeHl1H 'lIlCJla
060POTOB, OCo6eHHO B 30He BhICOKJIX 'lnceJI 060pOTOB. CpaBHeHl-Je
xapaKTepJICTJIK TOnJIIIBOnO,lJ,aqn no qHCJIY 060pOTOB BhUIBHJ10. 'no
A' npH MeHhIlleM 06'beMe B CHCTeMe
Kr/CI1 UHKJIOBaH no.zUlqa C YBeJIHqeHIleM
1200 'lHCJIa 060pOTOB YMeHbIllaeTCH B
MeHhlUeH CTeneHH (cpaBHeHIIe
npOBo.u.nJIOCh npH n0J10meHIUI
peUKJf, 06eCne'lJfB8101lIeM 60.'1b-
rnylO rro.u.aqy TOnJIJfBa). TaKO"
pe3YJIhTaT 6hIJI, B qaCTHOCTJI, 3a-
<PllKCHpOBaH I1pll cpaBHeHHlI 3K-
crrepUMeHTaJIbJ-IhIX 3aBJICHMOCTeH
q"lJ- = f(n) .u.JISl IV H V BaplJaH-
TOB. 3TO cBll.u.eTeJIhCTByeT 0 TOM,
qTO npHMOH 3<p<peKT BJ1IU!HIISI
MeHblllero 06'beMa B Cl1CTeMe Ha
BeJ111'J:HHY LU1KJ10BOH rro.u.aqH
60.Jlhrne. qeM BJIHHHHe YBeJIlI-
qeHHbIX 3HaqeHHH dp
dt
R'lUJlHue aeq;op.M.al1;ufi. .M.exa-
HUt-lec/weo npuBoi)a 1-Wcoc-q;op-
C!}HKU. Upn 60J1hIllOM K03<pqm-
u.neHTe .n.e<popMau.HH YBeJIH'lHBaeTCH 3HaQeHUe cYMMapHoro K03<P<PH-
u.neHTa C)KHMaeMocTH, a TaK)Ke 3ana3.u.hlB3lOT HaqaJIO n oco6eHHo
KOHeu. .u.eHcTBHTeJIhHOrO nepHo.u.a aKTHBHoH no.u.aqlI no cpaBHeHlllO C
cooTBeTcTBYIOll1.HMH reOMeTpHqeCKHMII 3HaqeHIIHMli. PHC. 132 1-1<1.'1.10-
CTpHpyeT BJIHHHHe ynpyrocTH npHBo.u.a na xapaKTepHcTHKY .u.aB.'1e-
HHH BnphIcKa. fpa<pHKH HMelOT o6ll1.ee HaqaJIO. B ,lJ,eHcTBHTeJIhHOCTH
H8q3JIO BnphIcKa IIpn 60JIbIlleM 3HaqeHHH k np He3Ha'lnTe,,'1bHO 33na3-
,lJ,bIBaeT, KaK BHAHO, nOCJ1e HaqaJIa BnpblcKa ,lJ,aBJ1eHlI51 YBe"lHqH-
BalOTCH Me,lJ,JIeHHee H ,lJ,OCTHraIOT MeHhlll'l-IX 3HaqeHHll npn 60J1bllleM
K03<p<pHl.LHeHTe Ae<popMau.HH. DOJIee Toro, MOMeHT ,lJ,OCTHLKeHHH MaK-
cHMYMa .u.aBJIeHnH HaCTynaeT npH 3TOM n03.u.Hee 1-1 npo.n.omKHTeJlh-
HOCTb BnpblcKa OKa3hlBaeTCH 60JIbllleH B CJIyqae 6o.rree LKeCTl<.Oro
npHBo,lLa.
B H3BecTHoll Mepe H3MeHeHHe xapaKTeplIcTHKli BnpwcKa TOOJIn-
B8 npn YBeJIlIqeHHII Ae<PopMHpyeMocTH MeXaHlIQeCKOrO np1.IBOLl.8
5lBJIHeTCH 6JIarOnpHSlTHhIM C TOqKlI 3peHIuI MHrKoH, 3KOHOMlIQHOii II
6e3AhIMHOH pa60ThI ABHraTeJ1H. B caMOM .u.eJ1e, npH 60J1hllleM
3HaqeHlIH k np CKOpOCTh BrrphlcKa YBeJIHQHBaeTCSl Me,lJ,JIeHHee H.
800
-" 400
o 4 8 fIlo
PHC. 132. PaCqeTHble xapaKTepHcTH-
KII .D:aB eHIIH Bnp cKa .D: H pa3.TJHQ-
HblX 3Ha'-leHIiH K03cpcpliI.\lieHTa .D:e-
cpopMaI.\HIi npllBO.D:a npH hI' =
= 6,1 MM; n = 1500 o6jMUIi (I H
III BapHaHT , K... p = var):
J - K np 0; 2 - K np = 10,7 X
x 10- 4 AUt/KT; 3 - K np = 19,2 X
X 10- 4 ,"_"/KT
242
CJIeJI.OBaTeol'IbHO, l\IeHbllIee KOJ1HIleCTBO TOnJ1HBa nO.D.aeTC5I B lI,HJII1H.D.P
3a nepI10A 3aJI.ep)l{KI1 BOCnJ1aMeHeHH5I. B KOHlI,e BnpbICKa (B nepHOll
OTCelJKI1 nO.D.alJH), KOrJI.a ow.yw.aeTC5I He.D.OCTaTOK KI1CoI'IOpO.D.a B
KaMepe CrOpaHlI51, AaBJ1eHI1e J CKOpOCTb BnpbICKa naJI.aIOT pe3KO
BC.1e.D.CTBI1e paCnp5lMJIeHI151 npI1BO.D.a II YBe:IHlJeHI151 CKOpOCTH
llBI1)1{eHH5I nJIymKepa B nOT nepI10.D.. B pe3y.TJbTaTe MeHbllIee KO.1I1-
lJeCTBO TOnJ1HBa nO.lI.aeTC5I B KOHlI,e npOll,eCca C YMeHbllIaIOw.I1MHC5I
.lI.aB.TJeHI1HMH BnpbICKa.
BbI5IB,j1eHHbIH xapaKTep B.1I151HI151
npOll,eCC BnpbICKa n03B0J1HJ1 aBTOpy
Ae OpMall,HH npHBO.lI.a Ha
B 1958 r. peKOMeHLJ:OBaTb
600
800
1200 n OO/HUH
, ,
P<p mux. /(f/cM 2 Pcpmax ,/(r/ CM 2
2000 1800
1600
1200 60
'It( 1400
!fJ:i Me;quK/I
66
1000
0.0 0 0*
0,0020
0, 0035 Knp H,.,jl(r
400
PHC. 133. PaC'-ICTHble 3aBHCHMOCTH napa-
MCTpOB Bnpb!CKa OT K03<j>qJHl.\HeHTa .D:e<j>op-
Mal.\lIH npHBO.D:a npH n = 1800 06jJltuH;
h p = 0 (II BapHaHT, Knp = var)
PHC. 134. OnblTllble 3aBHCHMOCTH
l.\HKJlOBOi1 nO a'-lH TOn.TJIIBa II MaKCH-
MaJlbHblX .D:aBJlCHHH BnpbIcKa OT 4HC-
Jla 060POTOB KYJlaQKa (cTp06oCKO-
nHpoBaHHe, II H III BapHaHTbI
cHcTeMbI) :
1 - l( np = 7,OS.I(j-' I>IM/KT;
2 - K np 19,2.10-' .>lM/KT
KOHCTPYKlI,I1IO MexaHlIlJeCKOrO npHBO.lI.a .lI.J151 nO.1YlJeHI151 CTynemlaTO-
ro 3aKOHa nO.lI.alJH. fl03.lI.Hee aHaJIOfHlJHOe npe.lI.JIOLKeHHe 6bIJIO
HCCJ1e.D.OBaHO B lJ,HI1T A [70].
113 pHC. 133 BH.lI.HO, 'ITO MaKCHMaJ1bHbIe H Cpe.D.HHe .D.aBJIeHH5I
BnpbICKa YMeHbllIaIOTC5I C YBeJIHlJeHHeM k np , npHlJeM .lI.aB.1eHHe
p max na.lI.aeT 60JIee pe3Ko. flpO.lI.OJILKHTeJ1bHOCTb BnpbIcKa H
KO.TJH'IeCTBO nO.lI.aBaeMOro 3a lI,IIK.1 TOnJIIIBa, HanpoTHB, B03pacTaIOT
C YBeJIH eHHeM K03 HlI,HeHTa k np BCJ1e.lI.CTBHe YBeJ1IIlJeHH5I np0.lI.o. TJ -
LKHTeJ1bHOCTH .lI.eHCTBHTeJ1bHOrO nepHO.D.a aKTIIBHoH nO.lI.alJII no
cpaBHeHIIIO C reoMeTpHIlecKHM. B paccMoTpeHHbIx 3AeCb HCC.1e.lI.O-
BaHH5IX .lI.Hana30H H3MeHeHHH 3HalJeJIIIH k np .D.OCTaTOlJHO BeJIIIK. Ha
npaKTIIKe 3HalJHTeJ1bHOe YMeHbllIeHIIe Be.11I'-IIIHbI k np B03MOLKHO
TOJIbKO nYTeM pa.lI.IIKa.TJbHOrO II3MeHeHII5I KOHCTPYKlI,IIII npIIBO.lI. a ,
16* 243
HanpHlVIep, paCnOJlO)KeHIIeM Ky.'IalJ.KOBoro BaJ1a B rOJlOBKe UH:UIH.lJ.pa.
B npOTl1BHOM CJ1YlJ.ae CTpeMJ1eHHe YBeJ1HlJ.HTb )KeCTKOCTb .lJ.eTaneH
HeII36e)KHO BbI30BeT YBe.'IHlJ.eHHe MaCCbI .lJ.BH)KYlll.HXC5I WeMeHTOB,
lJ.TO Kpai'me He)Ke.1aTeJ1bHO. YBe.'IHlJ.eHHe K03<p<PIIUHeHTa k"p orpa-
HHlJ.eHO Be.1HlJ.HHOH 3anaCa npOlJ.HOCTH Jl,eTaJ1eH,
113 pHC. 134 BH.lJ.HO, lJ.TO npH 60J1bIllHX .lI.e<p0pMaUH5IX npHBO,'Ia
MaKCHMaJ1bHOe .lI.aB.'IeHHe B03pacTaeT C YBeJ1HlJ.eHHeM lJ.HCJ1 060po-
TOB ;\Ienee HHTeHCHBHO. 113MeH5IeTc5I TaK)Ke xapaKTep 3aBHCHMOCTH
lUIK.10BOH nO.ll.a4II OT lJ.IICJ1a 060pOTOB.
TIpii 60.TIee )KeCTKOM npIIBo.lXe UIIK.TIOBa51 nO.ll.a4a 3aMeTHO Y:\IeHb-
I113eTC5I C YBeJlH4eHIIeM lJ.IIC.'Ia 060POTOB, npii 60.'Iee .lI.e<P0pMIIpyeMoM
npIIBO.lXe OHa MaJ10 II3MeH5IeTC5I C II3MeHeHHeM 'IHCJla 060pOTOB.
TIoc.1e.lXHee CB5I33HO lJ.aCTIIlJ.HO C B.'III5IHHeM YBen1I4IIBaJOlll.erOC5I
3ana3.lJ,bIBaHII5I KOHua .lJ,eHCTBIITeJ1bHOrO nepHO.lJ,a aKTHBHoi'I nO.lJ,a'm.
.l.LpyroH npH4IIHoi'1 OTMe4eHHoro xapaKTepa II3MeHeHII5I IJ,IIKJIOBOH
nO.lJ,alJ.II. 51BJ151eTC5I HaJ1II4IIe, B c.'IYlJ.ae CII.'IbHO .lJ,e<popMIIpyeMoro
npIIBO.lJ,a, ynoM5IHYToro BbIIlle YlJ.aCTKa 3aMe.lJ,.'IeHHOrO cnaA3 CKOpO-
CTeH nnpbICKa B KOHue npOlJ,ecca (CM. pIIC. 117), y.lJ,.TIIIH5IlOllI.eroc5I C
YBeJIIIlJ.eHHeM lJ.IICJ1a 060pOTOB.
OnblTbI nOKa3aJlII TaK)Ke, lJ.TO npii CH.'IbHO .lJ,e<popMIIpyeMoM
npIIBO.lJ,e pe3Koe YBe.'IIIlJ.eHIIe YCKopeHH5I nO.lJ,BH)KHbIX .lleTa.1eH
Hacoc-<poPCYHKH B nepHO.lJ, OTCelJ.KH no cpaBHeHHIO co 3H3lJ.eHII5IMlI,
nO.1YlJ.eHHbIMH npH a6coJllOTHO )KeCTKOM npIIBO.lJ,e, npIIBO.lJ,IIT K n05lB-
J1eHHIO y.lJ,apHbIX HarpY30K B npHBO.lJ,e, CHII)KeHHIO Ha.lJ,e)KHOCTH ero
pa60TbI II n0J10MKe .lJ,eTaJleH. Ha pHC. 116 BII.lleH pe3Y.'IbTaT YLI3PHOH
BCTpelJ.H KOpOMbICJl3 C TOJ1KaTeJleM Hacoc-<poPCYHKH nOC.'Ie OKOH4a-
HII5I npolJ,ecca (IV BapII3HT cHcTeMbI). B CB5I3H C OTMeI.JeHHbIl\I
npe,'J:cTaBJ151eT HHTepec naTeHT <pHpMbI GMC, npe.lJ,ycM3TPHBaJOlll.IIH
Opr3HHlJ.eCKOe BKJlIOlJ.eHHe B KOHCTPYKUHIO H3COC-<POPCYHKH nHeBllla-
THlJ.eCKOrO .lJ,eMn<pepa, nOBbIIll31Olilero Ha.lJ.e)KHOCTb pa60TbI H3COC-
<POPCYHKH. Ha CTeneHb YBeJlHlJ.eHH5I YCKopeHHi'I .lJ,eTa.'IeH B nepno.J
OTCeI.JKH 3HalJ.HTe.TIbHO BJ1H5IeT CKOpOCTb na.lJ,eHH5I J1.aBJ1eHH5I, 3aBHC5I-
llI.a5I, B CBOIO OI.Jepe.lJ,b, OT <pOpMbI OTCelJ.HOro OTBepCTl15I. TIO.lJ.60pOM
nOC.'Ie}.lHero MO)KHO, CJ1e.lJ,OBaTeJ1bHO, BJlI15ITb, nOIlUlMO npOlJ.ero, H3
Ha.lJ,e)KHOCTb pa60TbI npI1BO.lJ,a Hacoc-<p0PCYHKH.
BJlUflHUe aUaMeTpa nJlYHJlCepa. PaCI.JeTbI H on bIT bI BbI5IBIWI1
cnp3Be.lJ,.TIHBOCTb BbIBOJ1.0B, C.lJ,e.TIaHHbIX npI1 3Ha.TII13e BJIH5IHI151
.lln3MeTpa nJlYH)Kepa Ha BeJ1I1'IHHY CYMMapHoro K03<p<pHUI1eHTa
C)KHMaeMOCTH, a CJ1eJ1.0BaTeJ1bHO, H Ha npouecc BnpbICKa. OK333JIOCb,
'ITO YBeJ1HlJ.eHHe .llI1aMeTpa nJ1YH)Kepa OT 6,35 J1.0 8,5 MM He npHBO-
.llI1T K yneJ1I1lJ.eHI11O .llaBJleHHH BnpbICKa npH coxpaHeHlIH HeH3111eHHOH
UHK.'IOBOH nO.lJ,alJ.H TOnJ1I1Ba. AHam13 6bIJI BbIllOJlHeH .lJ,.1I5I n =
= 1500 06/MUH, q1f = 65 M2/l.{UKJl. TIpI1 paClJ.eTe YlJ.I1TblBaJ10Cb YBe-
JII1I.JeHHe 06"beMa C)K3TI151 npH 60J1bIlleM IU1aMeTpe nJ1YH)Kep3.
O.lJ,H3KO OTBepCTH5I BO BTYJ1Ke n.'IYH)Kepa 6bIJ1I1 npI1H5ITbI O.lJ,HHaKO-
BbIMH npI1 060I1X J1.naMeTpax n.'IYH)Kepa, lJ.TO, KOHelJ.HO, OKa3aJ10
BJlH5IHHe Ha pe3YJ1bTaTbI paClJ.eTOB. Bce npo'me napaMeTpbI CIICTeMbI
6bIJ1H npHH5ITbI no III BapnaHTY.
244
TO.lbKO nplI Y;\leHbIlIeHIIlI K03<pqmllneHTa k np npOnOpllBOlWJ1bHO
YBeJ1BlleHBIO 3HalleHlIH fn ;\JaKClIMa.TJbHOe .n:aB.'1eHBe BnpbICKa npB
d n = 8,5 MM OKa3a..'10Cb Ha 16% BbIIlle, 1.JeM npB d n = 6,35 MM.
Ha pBC. 135 nOKa3aHa 3aBBCHl\lOCTb 06"be;\lHOH CKOpOCTlI II
.n:aBJleHlIH BnpbIcKa B <PYHKllIIB Yf.'Ia nOBopoTa Ky.lallKa, nOJ1YlleHHaH
o f/J cNYceK
p' Kr/c,..,2
f20
600
2*00
gO
1800
60
1200
.10
18 2+ :10 :16 "2,/,°
PHC. 135. PaC'-ICTHbIC 3aBHCIJMOCTH 06"bCMHOit CKOpOCTH
H .D:aB'lcHHi1 BnpblcKa OT yr.1a nOBopOTa Ky.TJa'-lKa np!!
pa301IJ411blX 3Ha'ICIIHHX nOnCpC'-IHOrO CC4CHHH I1J1YHLKepa
(n = 1800 o6/fnUH, h p = 0, II BapllaHT CHCTCMbl,
fn = var):
1 - HaGaJIQ reoMeTpH'tJecKoro nepHo.u,a aKTHBHo:fi no.naQH; 2..
3, 4. 5 - COOTBeTCTBeHHO KOHel{ reOMeTpH1leCKOro nepHO,lI,a
aKTHBHoH no)],a'IH l\JI" KpHBbIX I, [[, [[I, IV; I - f n
0,507 _1",,' (160%); If - f n 0,412 .1<..,' (130%); [[I -
f n 0,317 ."..,' (Hacoc-q,opcYHKa AP-21, 100%); IV - f n=
= 0,222 M..,' (70%)
B J.PyroH CepHlI paC4eTOB npB 3HalllITeJlbHO 60.'1ee )j{eCTKOM npnBO-
.n:e [55]. Halla.'10 nepHOlI,a aKTHBHOH nOlI,alllI, 06"beM, onlIcaHHbIlI
n.'1YH)j{epOM nplI ero aKTlIBHO:\1 XO,iJ,e, 06"beMbI B CBCTeMe B Ha4aJIe II
KOHlle aKTIIBHoro XOlI,a, a TaKfKe xapaKTep 1I3MeHeHIIH 3KBlIBaJ1eHT-
Horo npoxo/woro Ce1.JeHlIH oTBepCTlIH B nJ1YH)j{epe B ero BTYJIKe_
COXpaH5J.1IlICb OlI,HBMB II Te:\>IH )j{e npn Bcex BCc.'1e.n:OBaHHbIX 3Halle-
HBHX f n. KOHe4Ho, aKTBBHbIH XO.n: n.'lYH)j{epa II CKOpOCTb B3MeHeHHH
06"be!\Ia B CBCTeMe npB nOlI."beMe nJ1YHfKepa 6bJ.1IB npH 3TOM pa3-
.'lBllHbIMH. DpollHe napaMeTpbI TaKlIe )j{e, KaK BO II BaplIaHTe. 113
plIC. 135 BIIlI.HO, llTO C YBe.'1lIlleHlIeM fn onepe)j{eHlIe BnpbIcKa B03pa-
245.
CTaeT, JJ.aBJleHIle BnpbICKa nOCJIe ero Haqa.TJa YBeJIHqIlBaeTCH B
<PYHKUHH yrJ1a nOBopOTa KYJ1aqKa 6bICTpee u AOCTHraeT 60:.bllIHX
MaKCHMaJ1bHbIX 3HaqemIii. 3ana3JJ.bIBaHHe KOHI.(a JJ.eikTBHTe.!IbHOrO
nepHOJJ.a aKTHBHOH nOJJ.aqu no OTHOIlleHHIO K COOTBeTCTBYIOIII.eMY
reOI\leTpHqeCKOMY 3HaqeHHIO 3aMeTHO 60J1bllIe npH 60.TJbllIHX 3Haqe-
HHflX ceqemifl nJIymKepa. GJJ.HaKO 6JIarOLl.apH MeHbllIeH BeJIllqHHe
aKTlIBHoro xOJJ.a MaKClIMpI JJ.aB-
J1eHlIH BnpbICKa HacTynaeT npu
3TOM paHbllIe.
Ha puc. 136 H306pa2KeHbI na-
pal\leTpbI npol.\ecca BnpbIcKa B
<PYHKl.\IUI CeqeHHfI nJIYHLKepa.
MaKCHMaJIbHOe H cpeJJ.Hee JJ.aB-
JIeHHfI BnpbIcKa B03pacTalOT C
YBeJIHqeHHeM f n, npHqeM p max
nOBbIliiaeTCfI HHTeHCHBHee. I1po-
JJ.OJ1LKlITe.TJbHOCTb BnpbIcKa
YMeHbliiaeTcH C YBeJ1HqeHHeM fn
BnJIOTb JJ.O onpeJJ.eJ1eHHOrO 3Ha-
qemifl; nplI JJ.aJ1bHeHllIeM B03pa-
CTaHHH fn Ha6JIlO,lI.aeTCH TeHJJ.eH-
UHH K YBeJ1HqeHHIO npoJJ.OJ1LK'I!-
TeJ1bHOCTlI BnpbIcKa. I1oCJ1eJJ.Hee
CBfl3aHO C 6bICTpbIM YBe.TJHQeHII-
eM 3ana3JJ.bIBaHIIH ,lI.eHCTBIneJIb-
Horo HaqaJIa OTCeqKH no cpaB-
HeHHIO C Haqa.1JOM OTCeqKH npH
a6COJIlOTHO LKeCTKOM npUBOJJ.e.
U,HKJIOB3H nOJJ.aqa YMeHbliiaeTCH
npH YBeJIlIqeHHH fn BnJIOTb JJ.O
HeKOToporo KpHTHQeCKOrO 3Ha-
'IeHHH, nOBbIllIa5ICb npn JJ.a.lb-
HeHllIeM YBeJ1!1qeHlIH CeqeHHH
nJ1YHLKepa. I1pH M3J1bIX 3HaQe-
HHHX fl1' c.leJJ.OBaTe.!IbIIO, npc06-
.'IaJJ.aeT BJIHHHHe Ha xa paKTep
H3MeHeHlIH q"tj B <PYHKUHH fn <paKTopa CLKHMaeMOCTH. I1pH 60.'1bllIHX
3Ha1JeHHflX fn HaQHHaeT npe06.1aJJ.aTb B.TJHHHHe <paKTOpOB JJ.pocce.mI-
pOBaHHH H 3ana3JJ.bIBaHHH KOHua ,lI.eHCTBHTeJ1bHOrO nepHOJJ.a 3KTHB-
HOH nOJJ.aQH.
113 CKa3aHHoro c.'IeJJ.yeT, 'ITO TOJ1bKO npu LlOCTaTO'IHO )J{eCTKOM
npHBOJJ.e JJ.HaMeTp nJIYHLKepa MOLKeT paCCMaTpHBaTbCH B KaqeCTBe
3<p<peKTHBHoro cpeJJ.CTBa BJ1HflHIIH Ha npouecc BnpbICKa.
B J IU5/.flUe Tuna paCnbtAUTeJlR. PaCCMaTpUBalOTCH HaCOC-<pOPCYH-
KH C TpeMH THnaMU pacnbJ.'IHTe.neH:
1) KJ1anaHHO-COnJ10BbIM 3aBOLla JIeHKap3 (BaplIaHTbI I-IV);
2) 6eCllITI1<pToBbIM 3aKpbITbiM (BapHaHTbI VI H VII);
246
,
P"cpi
XrjCM Z
800
600
f8
f4
fO
60
'+0
fOO
. p
Xr/CMz
2800
2'100
2000
1600
1/,
Mefu,uK/I
70
60
f,,%
PllC. 136. PaC'-ICTHbIC 3aBHCHMOCTll na-
paMcTpoB BnpbIcKa OT nOnCpe'-lHOrO ce-
'-ICHllH nJlYHLKepa, Bb!pa:iKCHHOrO B npo.
l.\eHTaX (n = 1800 06/MUH., h p = 0,
II BapllaHT CHCTCMbI, f n = var):
/ - 30Ha reOMeTpW-ICCKoro nepHoJ:ta aKTHll-
HOll nOJJ..aqH; J I - 30Ha onepe>KCHIIH HaqaJIa
Bnpb1CK3; I J I 30H3 38na3,[J,blBaHH5I KOHl.l,a
BnpblcKa: IV - npo;I.o..'nKHTe :]LHocTL BnpLIC-
K3
3) KJIaIIaHHO-COIIJIOBbIM, IIpe.D.JIO)KeHHbIM 11. B. ACTaxoBbIlVI (Ba-
pHaHT V, puc. 200).
npeuMymecTBa IIOCJ1eJJ:Hero paCIIbIJIUTeJIH IIepeJJ: 06bIlJHbIM
3aKpbITbIM paCIIbIJ1HTeJ1eM 06eCIIelJlfBaIOTCH 6J1arO.D.apH MeHbIlIeH
Macce IIO.D.BH)KHbIX .D.eTaJ1eH <POPCYHKH; MeHbIlIeH BeJIHlJHHe IIO.D."beMa
KJlaiiaHa H 3HeprHH Y.D. a - Qn,Q", C1f3jCl'K
pa ero 0 ce.D.J10 npH no-
caA!<e; OTCYTCTBHIO Ha-
COCHoro .D.eHCTBHH HrJlbI
H oco6eHHo HBJIeHUIO 80
BbI)KHMaHHH B KOHue
npouecca; OTCYTCTBHIO
npeUH3H01lHOH napbI Hf-
J1a - HaIIpaBJIHIOmaH.
n peIIMymecTBa ne- 40
pe.n. paCIIbIJIHTeJ1eM 3a-
BO.D.a J1eHKap3 06ecne-
lJHBaIOTCH B pe3YJIbTaTe 20
MeHbIlIefO 06"beMa Ton-
J1HBa Me)K.D.Y 3al10pHbIM
opraHOM H paCIIbIJ1HBaIO- 0
mmI OTBepCTHeM; 60J1b-
IlIero .D.aB.leHHH OTKpbI - On. 0", cH 3 /celi
THH 3anopHoro opraHa; 50
Ha.TJHIlHH HanpaB.1HIOmeH
Y KJIanaHa. 30
Ha pHC. 137 IIOKa3a-
Hbl OnbITHbIe 3aBHCJII\IO-
CHI 06"beMHOH CKOpOCHI 10
BIIpHCKa TOnJIHBa B
<PYHKUJIH yrJIa nOBopOTa 0
Ky.lalJKa, nOJIyqeHHbIe
.D..1H VII BapHaHTa.
BIIpbICK TOIIJ1lIBa Ha
Bcex HCCJIe.D.0BaHHbIx pe-
)KHMaX HalJlUJaeTCH 110lJ-
TH O,'J,HOBpeMeHHO H Ha-
CTYIIaeT IIpHl\1epHO CIIYC-
TH 1° IIoBopoTa KYJIalJKa
nOCJle HalJaJIa aKTHBHoH
IIO,'J,alJJI. TaKJIM 06pa301\1,
IIPH 3aKpbITOM paCIIbIJIHTeJ1e 3a nepHO.D. .D.pOCCeJIHpOBaHHH B HalJaJIe
no.:ralJH TOnJIHBO He IIOCTYIIaeT B UHJIHH.D.p. XapaKTep H3MeHeHHH Qif>
B <PYHKI..UIH yrJIa IIOBopOTa KYJIalJKa OTJIHIlaeTCH OT HMeIOmero MeCTO
B HaCOC-<popCYHKax AP-21 H AP-21A3. BeJ1HlJHHa Qif> B03paCTaeT
B HalJa.le BnpbICKa 6bICTpO, .D.OCTHraH 3HalJeHHH, npHMepHO COOTBeT-
CTBYIOmero .D.aBJ1eHHIO OTKpbITHH HfJIbI (Y1JaCTOK .D.pOcce.1HpOBaHHH
nOTOKa IIOjJ. KOHYCOM IIfJIbI B HalJaJIe BIIpbICKa). 3aTeM clmpoCTb
247
J
NO
236
\pO
Qn
3
224
rI'
2'10
2J2
228
236
0)
PIIC. 137. 3aBllcIIMoCTII 06'bCMHOH CKOpOCTil
anpblcKa OT yrJla nOBopoTa KYJla'-lK3 (VII aa-
pHaHT CHCTeMbl):
a - n 1400 OU/MUII; U - n = 500 o6/."ulI; I -
hp = 3,25 MM; 2 - hp !5,5 M."; 3 - Ha4aJIO reO-
MeTpwlecKoro nepHo..na 3KTHBHOiI nOJI.aQH: 4 - KOHelJ,
reOMeTpW:leCKOrO nepHoJJ.a aKTHBHoi'[ no.nal.lH ,u..ilH
hp = 15,5 MAt; 5 - KOHe reoMeTpH4eCI<oro nepHo)],a
aKTHBHoi,[ nO,[latjH JX.JIp h p = 3,25 ,MAt
B03paCTaHHH QifJ 3aMe,n:J1HeTCH. DpH 60JIbllH1X 060pOTaX nOHBJIHeTCH
YLJaCTOK, Ha KOTOpOM 3HaLJeHHe QifJ He YBc.'1J111HBaeTCH, a CJIe,n:OBa-
TeJ1bHO, He B03paCTaeT ,n:aB.'1eHHe BnpbICKa. 3TO HBJ1HeTCH CJ1en:CTBH-
eM HaCOCHoro ,n:eHCTBHH Hr J1bI npn ee non:'he:\le. OnHcaHHaH 'IaCTb
npOll.ecca BnpbICKa COOTBeTcTByeT ,n:BH}KYlIJ.eHC5I HrJIe. Ha pe}KHMax.
npH KOTOpbIX HrJ1a npH no,n:'beMe ,n:OCTHraeT ynopa, n:aJ1bHeHll1ee
TeLJeHHe npoll.ecca BnpWCKa nOLJTH aHaJIOrH HO npoueccy B 6a30BOH
Hacoc-cpopCYHKe. DpI1 MaJibIX LJHCJlax 060pOTOB n nOllaLJaX nr.la,
BH,n:HMO, He ,n:OXO,n:HT n:o ynopa, HO n 3,n:eCb npOll.eCC BnpbICKa npH
OTKpblTOH nrJ1e nO.D.06eH npOll.eccy B 6a30BOH Hacoc-cpopCYHKe 1.
Dpn BbICOKnx LJHCJlax 060pOTOB B KOHlI.e BnpbICKa BHOBb Ha6.110-
n:aeTCH YLJaCTOK nOLJTH nOCTOHHHbIX 3HaLJeHHH QifJ, LJTO 06'bHCHHeTC5I
HaCOCHbIl\1 ,n:eHCTBHeM Hr.'lbI npn ee nOCaD:Ke. CTyneHbKa Ha 3aBHCH-
MOCTH QifJ = f (fj!J<) B KOHlI.e npOllecca CO(()TBeTcTByeT MeHbll1eMY
3HaqeHHlO QifJ' a CJ1en:OBaTeJ1bHO, H n:aB.'1eHHH BnpbICKa, LJeM COOT-
BeTCTBYlOlIUfe 3HaLJeHI1H 3THX napaMeTpOB B HaLJaJ1e BnpbICKa B
CBH3H C H3BeCTHWM 3cpcpeKTOM ,n:HcpcpepeHlI.HIaJIbHOH nJIOlIJ.a,n:KH. ,LLa-
J1ee BeJ1l1LJHHa QifJ nan:aeT npH 3aKpbIBaIOlIJ.eHCH Hr J1e (YLJaCTOK.
n:pOCCeJ1HpOBaHHH nOTOKa non: KOHYCOM Hr.1JbI B KOHlI.e BnpbICKa).
DepHO,n: na,lJ,eHI1H CKOpOCTH BnpbICKa B KOHlI.e non:a11H paCTHHYT,
oc06eHHO npH BbICOKHX LJHCJ1aX 060pOTOB.
Ha pHC. 124,6 nOKa3aHbI 3aBHCHMOCTII lI.HKJ10BOH nO,iI.a'IH ,lJ,.lH
III H VII BapHaHToB. CpaBHeHHe nOKa3bIBaeT, LJTO HMeeTCH TeH,lJ,eH-
lI.HH K 60.1bllleMY na,lJ,eHHlO UHK.'10BOH nO,lJ,aqH C YBeJJHLJeHHeM LJHCJ1a
060pOTOB rIPH l\Ia.'1bIX BbI,lJ,BH}KeHHHX peHKH B cJ1YLJae HcnO.'1b30Ba-
HHH 3aKpbITOrO paCnbIJ1HTeJ15!. DpH 60JIbll1HX I3W,lJ,BH}KeHH5IX peHKH
B03pacTaHHe lI.HK.1JOBOH no,n:aqH C YBeJ1HLJeIfmeM LJHCJIa 060pOTOB
npOHCXO,lJ,HT B MeHbll1eH CTeneHH npH 3aKpbIToM paCnbIJ1HTene.
,LLJ15I no.1JYLJeHH5I TOH }Ke nO,lJ,aLJH TonmIBa npH 3aKpbITOM pacnbI-
mITeJ1e Tpe6yeTC5I 60J1b1llHH aKTHBHbIH XO,lJ, nJ1YH}Kepa. Bce 3TO
l\IO}KeT 6bITb 06'b5ICHeHO l\IeHblllHM BJ1H5IHHeM ,n:poCCeJIHpOBaHH5I
TOnJ1HBa B HaLJaJ1e BnpbIcKa npH Hacoc-cpopcYHKe C 3aKpbITWM pac-
rIbIJIHTe.1JeM, CBH3aHHbIM C 60JIbllleH BeJ1WIHHOH ,lJ,3BJ1eHH5I OTKpblTHH
33nopHoro opr3Ha H MeHee np0,lJ,OlI}KHTeJ1bHbIM nepHO,lJ,OM ,.'I,pocce-
.JIHpOB3HHH B HaLJ3JIe BnpbIcKa (nOCJ1e,lJ,Hee - B pe3YJIbT3Te HCnOJ1b-
30B3HHoro I3 H3COC-cpopcYHKe C 33KpbITbIM p3CnbIJ1HTeJ1eM xap3K-
Tepa H3MeHCHHH reOMeTpHLJeCKHX cp33 npH H3MeHeHHH xon:a
pery.1JHpYlOll1.eH peHKH; CM. pHC. 115).
YCT3HOBJIeHO, 'ITO npH O,lJ,HH3KOBOD UHKJ10BOH nO,.'I,3LJe B Hacoc-
cpopcYHKe C 33KPbITbIM paCnbIJIHTeJ1eM np0,/JLo.'1}KHTe.1JbHOCTb BnpbIC-
K3 MeHbllle, 3 nepHO,lJ, reOMeTpHLJCCKOH non:aQH 60J1bllle, qeM B H3COC-
cpopCYHKe C KJI3n3HHO-COnJ10BbIM p3CnbIJ1HTeJ1eM. DpH 3aKpbITOM
p3CnbIJ1HTeJ1e npe,lJ,CTaBJ15IeTCH B03MO}KHbIM HeCKOJ1bKO YBeJ1HLJHTb
BeJ1HLJHHy cpe,lJ,HHX CKopOCTeH H ,n:aBJIeHHH BnpbiCK3, oc06eHHO npH
1 HCC.1CJJ,OB8HHbIC PC)KHMbl HC OXBaTblBalOT HHTepBaJla HeYCToii'-lHBoi1 pa60Tbl
1j:J0PCYHKH.
248
60JIbllIHX BbIJ(BH1KeHHHX peHKH. 3<p<peKT, aJ(HaKa, 3Ha1.J.lueJleH JII111Ib
Ha peLKI1MaX, 6JIH3KI1X K peLKI1MY MHHHMaJ1bHbIX 1.J.HCeJI a6apOTOB
XaJIaCTara xa.lla. TIpH 3TaM BC.:le1l.CTBHe 6aJIbllIerO YAeJIbHarO Beca
Y1.J.aCTKaB nOJ(.heMal1 onYCKaHI1H IIrJIbl npH Ma.1JbIX IJ,I1KJIOBbIX 1101l.a-
1.J.ax, Ha KOTOpbIX CYll\eCTBeHHbIIII HBJIHeTCH J(paCCeJIIlpYIOLQI1H
3<p<peKT Ce1.J.eHI1H no.ll KaHycaM I1r.rIbI, HeCMaTpH Ha BbIcaKoe 1I.aBJIe.
HHe Ha1.J.aJ1a na.ll'heMa Hr.1JbI, BemI1.J.I1HbI cpe.II.Hera .llaBJIeHlIH nepe:l
CaII.'lOBbIl\I1I OTBepCTHHMH Ha paCCMaTpHBaeMbIX peLKHMax MarYT
OKa3aTbCH Jj,OCTaTaLJHO HII3KIIMI1. CJ1e1l.yeT HMeTb TaKLKe B BI1.II.Y, 1.J.Ta
npll cpaBHemlli BnpbICKa TOnJII1Ba a6allMII HInal\I1I Hacac-<popCYHaK
npl1 Ha.'IH1.J.1111 npaTI1Ba1l.aBJIeHI1H cpeJJ.bI, a TaKLKe npH OJJ.HHaKaBOM
xapaKTepe perYJIl1pOBaHHH naJ(a1.J.H pa3J1H1.J.HH nOJIY1.J.HJ1HCb 6bI MeHee
3Ha1.J.I1TeJlbHbIMH. 3TO, B 1.J.aCTHOCTH, CBH3aHO C TeM, 1.J.TO npOTI1BOJ],aB-
.1JeHl1e Cpe.II.bI npenHTcTByeT aTKpbITHIO KJlanaHa 11 cnoco6cTByeT
OTKpblTl1IO HrJ1bI. B KOHlJ,e BnpbICKa, HanpOTHB, I1pOTHBOJJ.aBJIeHHe
npemITCTByeT 3aKpbITI1IO I1rJ1bI 11 cI1aca6cTByeT 3aKpbITI1IO KJlanaHa.
B ueJ10M. npH KJlanaHHa-CaII.'IOBaM paCnblJ1I1TeJ'1e npOTI1BOJJ.aBJIeHI1e
6.rIaranp11HTHO BJ1I1HeT Ha npolJ,eCC BnpbICKa,
TIpl1 KOHCTpYl1pOBaHHH HacaC-<popCYHKI1 C 3aKpbITbIM pacnbIJ111-
TeJ1eM aKa3aJl0Cb C,,'1aLKHbIM nO,,'1Y1.J.HTb Y.II.OB.:leTBopIlTe;rIbHYIO rl1.ll-
paBJII11.J.eCKYIO xapaKTepHCTI1KY <POPCYHKH B aCHOBHOM B CBH311 C
OrpaHH1.J.eHHeM ra6apl1THbIX pa3:\lepOB npYLKI1HbL
D.J1H IV. V H VI Bapl1aHTOB 6bI.JJQ BbIllOJ1HeHO cpaBI-Une.IJbHOe
paC1.J.eTHOe HCCJIeJ(OBaHlIe npolJ,ecca BnpbIcKa Tan.1HBa. I1cC,,'1eJJ.oB3-
Hl1e nOJ],TBepJ(l.wo, B 1.J.3CTHaCTII, 1.J.TO JJ.JIH V BapHaHTa He6a.'1bIllIIMIl
aK33bIBaIOTCH nOJJ.'heM KJIanaHa H CKOpOCTb era B MaMeHT IlacaJJ.Kn
Ha ceJ(.:la, 1.J.Ta J(aJ1LKHO cIlaca6cTBoBaTb nOBbIIlleHHIO Ha.n.eLKHOCTH
pa60TbI 11 J(OJlrOBe lHaCTH paCTIbIJ1HTeJI5I.
TIa pe3YJ1bTaTaM paC1.J.eTaB V H VI BapHaHTbI a6eCIle1.J.IIBaIOT
3aMeTHO 6aJ1ee BbIcaKHe J(aBJ1eHHH BnpbIcKa (MaKcIIMa,,'1bHbIe II
cpe.n.HlIe) Ha peLKI1Me lI1HHI1MaJ1bHbIX 1.J.IKeJ1 a6apaTaB xa.TJaCTara
xo.n.a. TaK, .n.J1H VI BapIIaHTa cpe.n.HIIe 1I.aBJ1eHII5I BnpbIcKa B1I.Boe
6aJlbllIe, 1.J.eM .n.JIH IV. o n bIT bI Ha .n.BHraTeJIe 06HapYLKlIJ1H 3aMeTHoe
YJIY1.J.llIeHHe 3KOHOMII1.J.HOCTII H CHHLKeHl1e caLKeo6pa30BaHH5I Ha
peLKIIMax MaJ1bIX no.n.a1.J. H 1.J.IIce.TJ a6apaTaB IlPH npHMeHeHHH V Ba.
pHaHTa BMeCTa IV.
YJIY1.J.IlleHHe .3KaHaMH1.J.HOCTH Ha 3THX peLKHMax nOJ1YlJeHa H npn
HCIlaJ1b3aBaHHH <popcHpaBaHHaro BapHaHTa TOnJ1HBHOH annapaTypbI
pa3J(eJIeHHOrO THna C 33KpbITbIM paCnbIJ1HTe.TJeM.
TIa pe3YJ1bTaTaM paC1.J.eTOB H anbITaB Ha pa601.J.HX pe)KHMaX 3TH
:lBa BapHaHTa CHCTeMbI TanJ1HBanaJ(a1.J.J{ He a6eCne1.J.HBaIOT 3aMeTHa-
ro YBeJIH1.J.eHHH Cpe.n.HHX .n.aB.1JeHHH BnpbICKa no cpaBHemHO C
IV BapHaHTaM, aco6eHHo npH BbICOKIIX 1.J.HCJIaX 060pOTOB. OCTaeTcH
npe.n.nOJ1araTb, 1.J.Ta YJ1Y1.J.IlleHHe YCJIaBIIH pa3BHTII5I <paKeJIa H pac-
nbI"TJHBaHHH TanJ1IIBa CBH3aHO C KaHcTpYK1u-reii paCnbIJIHTeJIeH. TIpH
HCnaJIb3aBaHHH V BapHaHTa, K CaLKaJIeHHIO, YXYAIllaIOTcH naKa3a-
Te.1JII .n.H3eJ151 Ha pe)KIIMaX 6aJIbIllHX na.n.a1.J. II lJHCeJ1 06apaTaB na
cpaBHeHHIO C nOKa3aTeJIHMH, a6eCnelJIIBaeMbIMH npn IV BapIIaHTe.
249
B CBH3H B OCHOBHOM C 60JIbllJHM 06"beMOM TOOJ1HBa, 3aK 1:IOlleHHOrO
Me)K.n.y O.TJYH)KepOM H paCObIJ1HBalOIl..lHMH OTBepCTlIflMH.
Hacoc-ljJoPCYHKH c ra30BblM npHBO.u.OM. HeCMOTpH Ha 60J1bllJH€
npeHMYIl..leCTBa HaCOCOB-cpOPCYHOK C ra30BbIM npHBO.n.OM, pa60T no
3THM CHCTeMaM opHBe.n.eHO Ma.J1:0. Oope.n.e.'1HeTCH 3TO KaK C,,'IO)KHO-
CTblO 3KcnepHMeHTa, TaK II TPy.n.HOCTHMH, CBH3aHHbIMH C 06ecoe-
'leHHeM Ha.n.e)KHOH pa60TbI ra30Boro npHBo.n.a, KOTopbIe He opeo..'{o-
JIeHbi .n.o CHX nop. Ha pHC. 138 H306pa)KeHbI .n.HarpaMMbI nYTII II
CKOpOCTH n.'1YH)Kepa, KOTopbIe nOKa3bIBa1OT, liTO noc.'Ie Ha'la.'1a
C n H/cex'h n I1M
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PRC. 138. DYTb Ii CKOpOCTb JI:BlILKCHHII
llJIYHLKcpa Hacoc-cpoPCYHKH C ra30BbiM
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PHC. 139. OClllIJIJIOrpaMMbI .D:aB-
.1CHII5I Hacoc-lj:JoPCYHKlI C ra30-
BbIM npliBOJI:OM, CHHTble npll HC-
113MCHHOM nOJIOJKCHIIH peHKH II
pa3.111'1Hb1X '-IHCJlaX 060pOTOB
Ba. a .D:BHraTCJlH:
1 - 1600 06/.,,,,"; 2 - 1200 06.'."Ufl;
3 - 800 o6f."'UH
OTCe'lKH CKOpOCTb nJIYH)Kepa pe3KO B03paCTaeT II .n.OCTHraeT
C n 12 .M/ceK. .lI.J1H Yl\leHbllJeHHH CKOpOCTH, a CJ1e.n.OBaTeJ1bHO, H
YCKopeHHH ,lLBH}KeHHH nJ1YH)Kepa H CMHrlleHHH ero y.n.apa 0 TOPIJ.O-
BYIO cTeHKY BTYJ1:KH, KOTOpylO nJ1YH)Kep B HeKoTopbIX c.'1Y'laHx
nOJIHOCTblO pa3pYllJaJI, 6bIJ1H npHMeHeHbI )KH.n.KOCTHbIe 6ycpepa. Ha
pHC. 139 npI1Be.n.eHbI .n.HarpaMMbI .n.aB.J'IeHHH TOnJIHBa, CHHTbIe npn
HeH3MeHHOM nOJIO)KeHHH peHKM Hacoca, HO npM pa3HbIX 'IHCJ1aX
060pOTOB BaJ1a .n.BHraTeJIH. Ha pHC. 140 OOKa3aHbI ,lLHarpaMMbI
AaBJIeHHH, CHHTbIe OpH HeH3MeHHbIX 'IHCJIaX 060pOTOB Ba.J'Ia .LI.BHra-
TeJ1H, HO .n.JIH pa3HbIx nOJIO)KeHHH peHKH TOOJIHBHOrO Hacoca. 113
pHC. 139 c.J1:e.n.yeT, 'ITO Hacoc-cpopCYHKa C ra30BbIM OpHBOAOM o6ecne-
'IHBaeT BeCbMa BbICOKHe napaMeTpbI npOllecca BnpbICKa. Cpe.LI.Hee
AaBJIeHHe BopbICKa (CM. pHC. 140) COCTaBJ1HeT 600 Kr;CM 2 .LI.JIH
G r = 32 KZ/'i H 500 KTjcM 2 .n.J1H G r = 23 KZ/'i. f1pO.n.OJ1)KHTe.JlbHocTb
BnpbIcKa OpH G r = 23 KZ/'i paBHHJIaCb .......36° yrJ1a nOBopOTa BaJIa
.ABHraTeJl5I, B TO BpeM51 KaK CHCTeMa TH C TaKOH n.'IYH:tKepHOH
napoH o6eCOe'lHBa.'Ia YKa3aHHYlO OpOH3Bo.n.HTeJ1bHOCTb 3a 45-46°.
250
XapaKTepHbIM SIBJU:leTCSI pe3KOe OKOH'IaHHe npoQecca BnpbICKa, a
TaK)Ke 60J1blIlaSI YCTOH'IHBOCTb pa60TbI CHCTeMbl. KaK CJIe,'J,yeT H3
pHC. 139 H 140, xapaKTep H3MeIHeHHSI JIaBJ1eHHSI npaKTH'IeCKH He
3aBHCHT OT pe)KHMa pa60TbI JIBHraTe.TJSI.
Ha pHC. 141 H306pa)KeHa 381BHCHMOCTb napaMeTpoB npouecca
BnpbIcKa Hacoc-<poPCYHKH C ra30BbIM npHBOJI,OM OT 'IHC.la 060pOTOB.
JLHarpaMMbI y6e)KAaIOT, 'ITO Ha YKa3aHHbIe napaMeTpbI He3Ha'lH-
Te.lbHO B.TJHSIeT Be.TJH'IHHa n, 'ITO,. nO-BHAHMOMY, SIBJISIeTCSI OCHOBHOH
np H'IHHOH, 06ecne'lHBalOlIlej.,! BbICOK)'1O
3KIOHOMH'IHOCTb AI13e.J1SI Ha Beex CRO-
pOICTHbIX pe)KHMaX ero pa60TbI.
Ha pHC. 142 nOKa3aHbI cY;\1!I'JapHbIe
KpHBbIe pacnpeAeJ1eHIISI TOn.1HBa BO
Bp1eMeHH JI,ml CHCTeM C ra30BbIM 11
p", KrjCM2
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600
400
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PHC. 140. OCIJ:H.TJJlOrpaMMbI .D:aB-
.'1CHlUI Hacoc-ljJoPCYHKH C ra30-
BbI l npHBO.D:OM, CHHTble npll
n = 2000 o6j.MUH BaJia 1{BHraTc.1H
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npol.\ccca BnpblcKa Hacoc-ljJoPCYHKH C
ra30BbIM np!lBO.D:oM OT '-IHCJla 060pOTOB
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)1.01\1 npOTeKaeT 60J1ee 6J1arOnpHSI'THO AJISI pa60'lero npouecca JIn3e.TJSI
no cpaBHeHHIO C nOA06HOH AHaqpaMMoH CHCTeMbI C MeXaHHlJeCKHM
npUBOtI,Ol\L TonJ1HBHaH CHCTeMa C ra30BbIM npHBOtI,OM 60.1ee npH-
.cnOC06JIeHa JI,J1SI AH3eJ1SI C HatI,tI,y"BOM, 'IeM CHCTeMa C MeXaHIIlJeCKHM
npIiBOtI,o:\I H Tpy6onpoBonOM. KiaK CJIeAyeT H3 aHaJIH3a pHC. 143
16], napaMeTpbI npoQecca BnpbIclKa CHCTeMbI C ra30BbIl\I npIIBo,'J,o:\1
npn YBeJ1H'IeHHH HaAAYBa y.TJY'llIlaIOTcSI. HanpHMep, COrJ1aCHO
pHC, 143 npH YBe.TJII'IeHHII HaAJlyBa OT 1,5 JlO 3,1 KrtCM 2 npoII3Bo.J n -
Te.lbHOCTb CHCTeMbl B03paC'raeT Ha 6 K2/1f., npOAOJI)KHTe.JlbHocTb
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ra30BbIM npHBOJlOM napaMeTpbI I1pOQecca BnpbICKa B OCHOBHOM
onpeJleJIHIOTCSI JlaBJ1eHHeM ra3a B QHJ1HHJlpe ABliraTeJISI, n03TOMY
3TH napaMeTpbI JlO.Jl)KHbI B I\leHiblIleH cTeneHH, 'IeM B CHCTeMe C
MeXaHH'IeCKHM npHBOJlOM, 3aBHceTb OT 'IHCJIa 060POTOB, npOXOJlHOH
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rrpl1BOAOM CBH3aHO C 60J1bllIl1Ml1 TpYAHOCTHMl1, rr03TOMY Ha,n:efKHO
pa60TalOll.{l1X 6bICTPOXO,n:HbIX Hacoc-cpOPCYHOK C ra30BbIM npHB01J:OM
rrOKa ell.{e HeT. KpOl\le TOrO, rrpl1 l1CrrOJ'1b30BaHHl1 Hacoc-cpOPCYHOK C
ra30BbIM rrpHBOJ],OM B03HHKalOT HeKOTOpbIe TPy,n:HOCTH npH KOH-
CTpYHpOBaHHH r0J10BKH 11l1J1HHApa, TaK KaK AJ1H 06eCneLJeHIIH
Tpe6yeMbIx AaBJ'1eHI!H BrrpJbICKa He06xoAHMbI 60JIblliHe OTHOllIeHI1H
fzlf". 3TH He!I,OCTaTKH HeCKO.TJbKO OrpaHHLJHBalOT 06J'1aCTb rrpHMe-
HeHHH HaCOc-cpOPCYHOK C n:130BbIM npHBO,n:OM.
10. TOnnHBHblE CMCTEMbl AKKYMynSiTOPHOrO THnA
TOnJ1HBHaH CHCTeMa C rH)J.paBJlH eCKHM aKKYMYJ1HTOpOM H HarHe-
TaTeJ1bHbIMH Tpy6onpOBO)J.,aMH. IlpHHL\l1nHa.'lbHaH cxeMa TaKO ! CHC-
TeMbI rrOKa3aHa Ha pHC. 26. Ha pHC. 144 11306pafKeHbI !I,HarpaMMbl
q1f = f (n), l1MelOll.{He Bl1,n: rnrrep60J1, LJTO rrOKa3bIBaeT He3aBHCII-
MOCTb ,n:aB.TJeHHH TOrrJ1HBa H rrpo,n:OJ'1fKl1TeJIbHOCTH BnpbICKa OT LJl1c.'la
060pOTOB. B paCCMaTpHBateMoM CJ1YLJae AH3eJ1b AO.'lfKeH pa60TaTb
YCTOHLJHBO, OAHaKO 3HaLJHTeJ1bHOe B03paCTaHHe q1f rrpH YMeHbllIemm
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.'IeMOH.
252
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J{OTOpbIH npH YMeHbWeHHH <JHCJIa 060POTOB YMeHbllJaJI 6bI BeJlH<JHHY
-Q1j, <JTO MO)KHO C.n:eJ1aTb nYTeM YMeHbWeHH5I .n:aBJ1eHH5I TOIJ.1IHBa B
aKKYMYJl5ITOpe HJIH YMeHbWeHH5I npOLlOJ1LKHTeJlbHOCTH BnpbICKa.
TIO.1Ha5I He3aBHCliMOCTb .n:aBJIeHH5I II npOLlOJI)KIITeJ1bHOCTH BnpbICKa
'()T <JHCna 060pOTOB B03MO)KHa rrpII OTCYTCTBlili HarHeTaTe.HbHOrO
Tpy6orrpOBOLla. fIpli HaJIlI<JHlI HarHeTaTe.'IbHOrO Tpy6orrpoBoLla, KO-
"TOpbIH Heo6xOLlHlYI, ec.'m aKKYMYJ15ITOp pacrrO.'IO)KeH BHe rO.'IOBKII
H{Jt.{(]/iO nOQ(]t.{li mon/lli8u
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Pile. 145. OCllH.TJ.lorpaMMa l.\aB.1t'IUH! aKKYMY.TJ5ITOpHoi1 CI1CTCMbI
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np5IMoyro.llbHHKa, <JTO LlO.II)KHO 6bJ.TIO 6bI COOTBeTCTBOBaTb npliHUHrry
.n.eikTBH5I CHCTeMbI. 3TO orrpeLleJl5IeTCSI TeM, <JTO BCJ1eLlCTBlle KOHe<J-
Hoil CKOpOCTH pacrrpoCTpaHe-
Hll5I HMrry.'IbCa LlaB.leHHSI B
1\;fQ1\leHT OTKpbITH5I nepenycK-
E.oro OTBepCTlISI, KOTopoe
npolIcxoLlllT ,n:OBOJIbHO pe3Ko,
y cpOPCYHKH B03HHKaeT ,.'.l,HC-
(5a.'laHC !VIe)K,n:y nocTynJIeHHe!VI
II pacxoLloM Ton.1HBa, B pe-
3y.lbTaTe <Jero BeJ1H<JHHbI Ptjj H
(jJn CTaHOB5ITC5I 3aBliClIMblMH
OT 1JHCJ1a 060pOTOB. OLlHaKO,
J{aK CJ1e,n:yeT lI3 pIle. 146, 3a-
BHClIMOCTb 3THX napal\1eTpOB
(}T <JHCJIa 060pOTOB He3Ha1JlITeJ1bHa. 3KcnepllMeHTaJ1bHO YCTaHoBJle-
HO, <JTO nYTeM YMeHbWeHH5I ,n:J1HHbI H YBeJIH<JeHlI5I ,n:HaMeTpa Tpy6o-
npoBo,n:a YKa3aHHbIH ,n:Hc6aJIaHC MO)KHO cyrn;ecTBeHHo YMeHbwHTb.
I1cCJIe,n:oBaHliSI nOKa3aJIH, <JTO npoIJ,o.'I)KlITeJ1bHOCTb BnpblcKa 11
npOH3Bo,n:lITe.'IbHOCTb aKKYMy.1S1TOpHOH CHCTeMbI MorYT 6bITb oTpe-
rYJ1IIpoBaHbI Ha J1106ylO BeJIH1JHHY He3aBHCHMO OT <JlIClIa 060POTOB,
'I.JTO pacllUlpSleT, no cpaBHeHlIlO C clicTeMoH Herrocpe.n:cTBeHHoro
.Llei1cTBlISI, B03MO)KHOCTli nplicnoco6J1eHlISI npouecca BnpbIcKa 1<
YCJ10BlISlM 3KCnJ1yaTaUIH1 ,n:lI3eJ1S1. B paccMaTpHBaeMoH CHCTeMe
Heo6xoLlHMO CneUH3J1bHOe perYJ1HpYIOrn;ee YCTPOHCTBO LlJI5I H3MeHe-
HHSI rnnep60J1H1JeCKOH 3aBHCHl\WCTH q OT 1JHCJIa 060pOTOB. KOH-
CTPYKUHSI CHCTeMbI CJ10)KH3 H MeTaJIJ10eI\lK3. OLlHaKo CHCTe1\I3
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h
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800
Pue. 146. 3aBHcHMoCTb qJn = fen) aKKY-
MYJlHTOpHOi1 CHCTeMb! ,'\JI5I pa,,:
I - 300 "rJCM'; 2 - 525 "r/co'd'; 3 -
720 "rjol'
253
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1JHCe.'l 060pOTOB.
TOnJlHBHaJl CHCTeMa C B03.IJ.YIlIHblM aKKYMYJlJlTOpOM. 3KCnepHMeH-
Ta.JlbHOe HCC,,'Ie,n,OBaHHe TOnJIHBHOn CHCTeMbI nO.IJ.06HOrO THna 6bIJIO
npOBej],eHO B TO BpeMH, KOrj],a Ha JIT3 eLU:e TOJ'IbKO Ha,,'Ia)J{HBa,,'IOCb
npOH3BOj],CTBO j],BHraTe,,'IeH TIma
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pOB ra3a (crrrf) {9]. I1cc,,'Ie.J.ye-
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npe)I,Ha3Ha1.JeHa j],J1H OJ],Horo H3
nepBbIx 06pa3IJ.OB crrrr.
p
Kr/CH 2
400
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400
200
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120
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9'0
8
PIIC. 147. 113111eHcHHe no YC.10BHOMY yr-
JlY nOBopoTa Ba.TJa .D:BHraTCJlH napaMcT-
pOB TOn.TJIIBHOH CHCTCMbl cnrr:
1 - OnblTHaH KpRBaS! ;:IiIH 3aKpbl1oir cpop-
CYHKll; 2 - paCqeTHaH KpHB3f1 .lI...-lf1 3aKpbI-
TOti q,OPCYHKH; 3 - paCqeTHa" KpHBa" )],,1"
OTKpbITOi1: 4>OPCYHKH; 4 - OnblTHaSf KpHB3H
AJI" OTI<PbITof, q,OPCYHKH; .5 - pac4eTHa"
KpHBaH )],JI" OTKpbITOfr q,OPCYHKH; 6 - pac-
'JeTHaSl KpHsafi ;J..:rUI OTKpbITOir cbOPCYHl{H;
7 - onblTHaH Kpusan :x..,1H OTKpbIToff q)Qp-
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PHC. 148. 3aBHcHMoCTb napalllCTpOI3
npol.\ccca BnpblcKa CHCTCMbl cnrr OT
'-IHCoW pa60'-lHX I.\HKJlOB B IIIHHYTY npH ce
pa60Te C 3aKpbITbIMII lj:JopCYHKaMH:
1 - 25% OT HOMHH3JIbHoro; 2 - npl[ HO-
MHHa.%HOM (1000Jr)
Ha pHC. 147 H306pa)J{eHbI paC1JeTHble H 3KcnepHMeHTa.'lbHbIe
j],HarpaMMbI, nOKa3blBalOLU:He 3aBHCHMOCTb j],aBJIeHHH TOnJ1HBa H
CKOpOCTH j],BH)J{eHH51 aKKYMYJ1HpYIOLU:.ero nJ1YH)J{epa OT YCJIOBHOro
yrJ1a nOBopOTa Ba.na TOnJ1HBHOrO Hacoca. YCJ10BHbIM 3TOT yrOJI
Ha3bIBaeTCH nOTOMY, 1JTO, KaK H3BeCTHO, y crrrr BaJIa HeT, n03TOMY
1JHCJIO UHKJIOB pa60TbI crrrr B MHHYTY npHpaBHHBaJIH 1.JHC,,'!Y
OOOpOTOB. CorJlaCHO pHC. 147 j],aBJIeHHe BnpbICKa TOnJ1HBa H j],aB.'Ie-
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254
BeJIHqHHbI (500 KTjcM. 2 ), KOTopaH onpe.n:eJ1HeTCH CHJ10H .n:eiicTBHH
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xapaKTep, HO co 3HaqHTeJ1bHO 66.'1blllHM OTHOCHTeJ1bHbIM KOJIe6aHH-
eM BeJ1H1JHHbI aMnJ1HTY.n:, HMeeT CKOpOCTb .n:BH)KeHHH aKKYMy.'1HPYIO-
llJ.ero n"lYH)Kepa. MaKCHMaJ1bHaH CKOpOCTb .n:BIl)KeHHH YKa3aHHoro
nJ1ymKepa .n:OCTHraeTCH B Ha1JaJ1bHbIH nepHO,lJ. .n:BH)KeHHH H paBHa
1,3 MiceK. I1paBJl.a, xapaKTep KOJIe6aHHH HeCKOJIbKO H3MeHSIeTCH B
3aBIlCHMOCTH 01' Taro, C KaKHMH
<t>opCYHKaMH pa60TaeT CHCTeMa,
3aKpbITbIMH HJIH OTKpbITbIMH.
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Ka paBHo 575 KTjCM. 2 , 1JTO He-
CKOJ1bKO BbIllie Jl.aBJI,eHHH TOnJIH-
Ba B aKKYMY JIHPYIOlI.{eH II0J10CTlI.
HeKoTopoe npeBbIllleHHe BeJIH1JH-
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JIHeTCH CJle.n:CTBHeM B.'1HHHHH
YJl.apHOH BO.'IHbI. PaCqeTHaH JI,H-
arpaMMa .n:aBJ1eHHH BnpWCKa
YJl.OB.'1eTBOpHTeJIbHO COBna1I.aeT C
3KcnepHMeHTaJ1bHOH JI,HarpaM-
MOH, KOTopaSI 6WJ13 onpe.n:eJIeH3
npH pa60Te CIICTeMbI C OTKpbI-
TOH <t>OPCYHKOH.
Ha pHC. 148 H306pa)KeHbI 3a-
BHCHMOCTH OCHOBHbIX napaMeT-
pOB paCCMaTpHBaeMOH CHCTeMbI
OT 1JHC.TIa pa601JHX l(HK.'IOB B MII-
HYTY, CHHTbIe nplI pa60Te CHCTe-
MbI C 3aKpbI1'OH <t>OPCYHKOH.
DpHBe.n:eHHbIe .n:HarpaMMbI aHa-
JIOrHqHbI .n:HarpaMMaM CHCTeMbI
Henocpe.n:CTBeHHoro .n:eii:cTBHH. HanpHMep, qlf Ha HOMHHaJ1bHOM
pe)KHMe npH YBeJ1H1JeHHH 1JHCJ1a l(HKJIOB HeCKOJIbKO YMeHblllaeTCH,
3 Ha pe)KHMe 0,25 01' HOMHUaJIbHOrO B03pacTaeT. O.n:HaKo YKa-
3aHHble H3MeHeHHH q"IJ no cpaBHeHHIO C CHCTeMOH Henocpe.n:cTBeH-
Horo Jl.eHCTBHSI 3Ha1JHTe.'IbHO MeHbllle. DpOJl.O.'I)KHTe.'IbHOCTb BnpblcKa
qJn Ha pelKHMe 0,25 01' HOMHHaJIbHOrO B03pacTaeT MeHee pe3Ko,
1Jel\1 npH HOMHHaJ1bHOM pe)KHMe. OTHOCHTeJIbHOe H3MeHeHHe Be.TIH-
1JHHbI 3Toro napaMeTpa npHMepHo TaKoe )Ke, KaK H B CIICTeMe Heno-
cp e 1I.CTBeHHoro .n:eHcTBHH. CJ1e.n:yeT OTMeTHTb 01JeHb MaJIYIO BeJ1H1JHHY
.n:aBJ1eHHH BnpbIcKa Ha pe)KHMe 0,25 01' HOMIIHaJ1bHOrO, KOTopaSI
3Ha1JHTe"lbHO YCTynaeT BeJ1H1JHHe 3Toro )Ke napaMeTpa H8 TaKOM )Ke
pe)KIIMe pa60TbI CHCTeMbI Henocpe.n:cTBeHHoro .n:eHcTBHH. CJIeJl.OBa-
TeJlbHO, HCnbITblBaeMaSI CIICTeM<J He 6y.n:eT 06eCneQHBaTb y.n:OBJIeT-
BOplITeJIbHbIe napaMeTpbI npoueCC8 BnpbICKa Ha pe)KHMaX MaJIbIX
no.n:aq H 1JHCeJI 060pOTOB. Ha pHC. 149 H306pa)J{eHbI nOJI,06HbIe )Ke
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255
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2,5
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PUC. 149. 3aBllcHMoCTb napaMcTpoB
npol..\ccca Bnpb!CKa CIICTCMb! cnrr OT
4HCJa I.\UK.TJOB B MIIHYTY npH ce pa60Tc
C OTKPblTb!MU 1j:J0pCYHKaMII:
1 - P aK; 2 - P
pIlC. 149 HeCKO.'1bKO OTJIl11.JaIOTC5I OT llI-IarpaMM Ha pUC. 148,oco-
6eHHO ,':1,.'151 3aBHCHMoCTeH q'l = f(1+) H qJn = f(1.I)'
P",
Kf/cM2
500
400
300
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256
ff. 0 HEKOTOPOJ'f B3AHMOCBSl3H XAPAKTEPHCTHKH
BnPblCKA TonnHBA C PA&O'lHM np0Ll.ECCOM
ABHrA.TEnst C BocnnAMEHEHHEM OT C>KATHSI
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COOTBeTCTBU5I xapaKTepuCTIIKH BnpbIcKa oc06eHHOCT5Il\1 KOHCTPYKlUIl1
11 YCJIOBH5IM 3Kcn.JIyaTa1um LI.H3e.TI5I. B 60.TJblllHHCTBe pa60T no HCCJIe-
LI.OBaHHIO BJ1H5IHH5I na
pa601.JHM npo ecc ;J,H3e-
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TOB TOnJIHBHOH CHCTeMbI
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npou.ecca BnpblcKa OC-
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nOA06paTb Tpe6yeMYIO xapaKTepHCTHKY BnpbIcKa, a 3aTeM c03Aa-
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,LLJ15I HCCJIe,n:OBaHU5I BJ1UflHH5I Ha pa601.JHH npouecc -'\H3em1 BUAa
xapaKTepHCTHK BnpbICKa nOCJ1e,n:HHe C03AaBaJilICb npH nOMOIllH
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PHC. 150. OCI.\If.1.1orpaMMa 3KcncpHMcH-
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pa3HbI no q,opMe, n03ToMY nOTpe6oBaJIOCb onpe.lI.eJIHTb 60JIee 06-
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.lI.eJ1ax 250-575 KT/CM 2 . IlO-BH.lI.IIMOMY, BCJ1eJ],CTBIIe OKOHQaHII5!
OOLJ:aQII Toomma B KaMepy cropaHHH .lI.0 HaQaJ1a BOCnJ1aMeHeHII5!,
HeCMOTp5! Ha 60.'1bIllHe pa3JIIIQII5! B xapaKTepIIcTIIKax BopbIcKa, 3a-
MeTHoro H31\IeHeHHH HHJ],IfKaTopHbIX J],HarpaMM pa60TbI J],BHraTe.'!5J
06HapY:tKeHO He 6bIJIO. O.lI.HaKO BO Bcex OObITaX Ha6JIIOJ],aJ10Cb 3aBbI-
IlleHHoe 3ana3J(bIBaHHe BOCnJ1aMeHeHIISI TOnJIHBa. TaK, 3ana3J],bIBa-
HIle BOCnJIaMeHeHII5! KOJIe6aJ10Cb B npeJ],eJ'!ax npII n = 1600 06/MU1i
OT Ti = 0,0028] J],O Ti = 0,0042 ceK, a J],J15J n = 2000 06/MU1i OT
'ti = 0,00208 J],O 'ti = 0,00308 ceK.
TaKue Be.1HQIIHbI Ti CJ1eJ],yeT 06"b5!CH5!Tb CJIeJ],CTBIIeM 3aBbIIlleH-
HbIX 3HaQeHHH K03q,q,Ul(IIeHTa H36bITKa B03.lI.yxa, TaK KaK J],BHraTeJIb
pa60TaJI opIIMepHo Ha 50% OT Nc"II.' B paccMaTpIIBaeMoM J],BHraTe.'1e
npII HaJ],LJ:YBe OKOJIO p.,. = 1,3 KT/cM 2 H n = 1800 06/MU1i npH pac-
17 3aKa3 748 257
'/6
JOD
'/2
8
4
,0
'10
30
.If
PHC. 15L XapaKTcpllCTHKa BnpbIcK:!
3KcnCplllllC!lTaJJbHbIX TOnJlIIBHbIX
CHCTCl\I:
I - J\" 13; ? - No l' 3 - X. 11;
4 - Nfl-Ii)'
XO.ll.e OKOJIO 22 KF 3ana3.l1.bIBaHHe BOCnJ1aMeHeHHH COCTaB.fJHJIO
'ti = 0,0022 eeK, 'lTO BnOJIHe conOCTaBHMO C HHlliHHMH npe.ll.e.fJaMH
YKa3aHHbIx BbIll1e 3Ha'leHHH 'ti.
KaK H3BecTHo, HaH60J1ee pe3Ko xapaKTepHcTHKa BnpbIcKa B.aImeT
Ha pa60l.JHll npo ecc .lI.H3eJISI npH MaJIblX K03iPiPH HeHTax H36b1TKa
B03Ayxa, n03TOMY onHcaHHble HHllie
OnblTbI CJIe.ll.yeT C'lHTaTb B'eCbMa
npH6JIHrKeHHOH nonwTKoH HeCKOJIb-
KO OCBeTIITb paccMaTpHBaeMbIH BO-
npoc. AHaJIH3 pe3YJIbTaTOB OnblTOB
nOKa3aJI, 'lTO COOTHOll1eHHe MelliAY
KOJIH'leCTBaMH TOnJIHBa, nO.ll.aHHOrO
C YMeHbll1alOIUHMHcSI CKOpOCTSIMH
QYMeubw II B03pacTalOIUHMH CKOpOC-
TSIMH Qeoi3p, cYIUecTBeHHo BJIHHeT Ha
rp9
I
40
.15
.10
J 50
80 100 lif) r;Yl'fell'bUl ft
r; 1103p 0
PIIC, 152. 3aBHcHMoCTb aana3.D:bl-
BaHIIH BOCnJlaMCHeHHH 'Pi, Bblpa-
LKeHH;aH B rpa.D:ycax yrJla nOBO-
pOTa BaJJa JJ.BHraTCJJH, OT OTHO-
qY"'eltbUl
IllCHHH % npH n:
qeoap
1 - 1600 o6/Alult; 2 - 2000 06/M.Wi
/Jp
- Kr/(Cf1 2 .;:paO}
.19'
f5
f2
8
t 0l;
i B1A:-n
lifE
-)( -x-
l
55
f
45
;:;r Y .f
f80
2
f50
4 j" 5 fop elepr70
PilC. 153. 3aBilcHMoCTb napa-
MCTpOB pa60'lcro npou;ccca
.lIH3C.TJ5J: OT cpc.lIHeH cKopocnl
rrO.lIa'-lH TOnJJHBa 3a 1000
BnpblcKoB rrpH n:
1 - 1600 o6fM.Wi; 2
2000 o6/M.ult
3ana3AbLBaHHe BOCnJIaMeHeHHSI (pHC. 152). COrJ1aCHO pHC. 152 npH
B03pacTaHHH qVM.eltbUl npHMepHo B 2 pa3a neplIO.ll. 3ana3AblBaH1I5I
qeoap
BOCnJIaM'eHeHlISI YBeJIH'lHBaeTCH B 1,46 pa3a npH n = 2000 06/MUH, a
npH n = 1600 06/MUH- B 1,8 pa3a. 113 3Toro CJIe.ll.yeT, 'lTO nY'feM
YMeHbIlIeHlIH YKa3aHHoro BblIIle OTHOll1eH1I5I MOLKHO COKparn;aTb ne-
pHOA 3ana3AblBaHH5I BOCnJIaMeHeHHSI, 'lTO, B CBOlO O'lepeAb, AOJIlliHO
3aMeTHO YMeHbll1aTb llieCTKOCTb pa60TbI .lI.H3eJISI. BeJIH'lHHa cpeA-
HeM CKOpOCTlI nOAa'lH C enp e/epa8 TaKllie BJIH5IeT Ha napaMeTpbI
pa6o'lero npoqecca. KaK cJIe.AyeT H3 pHC. 153, npH YBeJIH'leHHH
cpeAHeM CKOpOCTH BnpblcKa OT 4 AO 7 e/epa8 3a 1600 BnpblcKoB
Y.lI.eJ1bHbiM pacxo.ll. TOnJIHBa npH n = 1000 06/MUH H npH n =
258
= 2000 06jMUH YMeHbliiaeTcfI, npHqeM 3aBHCHMOCTH ge OT n npoTe-
KaIOT nO.L{06HO, TOJIbKO no a6COJIIOTHOH BeJ1HqHHe ge npH n =
= 1600 06jMUH BbIllie no cpaBHeHHIO C ge npH n = 2000 06/MUH.
OIQHOCTb .L{BHraTeJIfi npH n= 1600 06jMUH B cJIyqae YBeJIHqeHHfI
Cenp.cp B03pacTaeT, B TO BpeMfi KaK npH n = 2000 06/MUH npaKTH-
qeCKH coxpaHfIeTcfI HeH3MeHHoH. YMeHbllIeHHe ge npH nOBbIllIeHHH
Cenp.cp cOnpOBO:lli.L{aeTcfI pe3KHM B03paCTaHHeM !1 p , KOTopoe YBe-
<p
JIHqHBaeTCfI .L{a:llie B HeCKOJIbKO 60JIbllIeH
CTeneHH no cpaBHeHHIO C Cenp.cp. f10J1Y-
qeHHbIe pe3Y.TIbTaTbI .L{aIOT OCHOBaHHe C.L{e-
J1aTb BbIBO.L{ 0 TOM, qTO nOCTOfIHHafi BbI-
COKa5I CKOpOCTb BnpbICKa TOnJIHBa Hepa-
U:HOHaJIbHa. CKOpOCTb BnpbICKa JIOJ1:lliHa
6bITb nepeMeHHOH, npHMepHO TaKOH, KaK
npH cTyneHqaTOM BnpbICKe, T. e. 3a ne-
pHOJI 3ana3JIbIBaHHfI BOCnJ1aMeHeHHfI
JIOJ1:lliHO 6bITb nOJIaHO TOJIbKO TO KOJ1Hqe-
CTBO TOnJIHBa, KOTopoe Heo6xo.L{HMO JIJlfI
YCTOHqHBOrO BOCnJ1aMeHeHHfI, qTO no.L{-
TBep:lli.L{aeT u:eJ1eC006pa3HOCTb npHMeHe-
HHH cTyneHqaTOH xapaKTepHCTHKH
BnpbICKa.
Ha pHC. 154 nOKa3aHbI 3aBHCHMOCTH
na paMeTpoB pa6oqero npou:ecca JIH3eJIfi
OT MaKCHMaJ1bHOrO JIaBJIeHHfI TOnJIHBa
prjj max' CJIe.L{yeT HanOMHHTb, qTO KaK npH
H3MeHeHHH Cenp.cp, TaK H MaKCHMaJIbHO-
ro .L{aBJIeHHfI Prjj max !}JopMa xapaKTepHcTHKH BnpbIcKa, MeJIKOCTb
paCnb!J1HBaHHfI, pacnpeJIeJIeHHe TOnJIHBa no 061>eMY KaMepbI cropa-
HHfI, npOJIOmKHTeJIbHOCTb BnpbIcKa H ,II,pyrHe napaMeTpbI TaK:llie
cYIQeCTBeHHo H3MeHfIJIHCb. I13MeHeHHe KaKoro H3 YKa3aHHbIx napa-
NIeTpOB 5IBJ1fIeTC5I pellIaIOIUHM, YCTaHoBHTb HeB03MO:lliHO. .lJ.aHHbIe
OnbITbl npH6,mDKeHHo onpeJIe.'15IIOT TOJ1bKO HeKoTopbIe .L{OnycTHMbIe
npeJIeJIbI H3MeHeHHfI TOro HJIH JIpyroro napaMeTpa npou:ecca Bnpblc-
Ka, OTKJ1a.L{bIBaeMOro no OCH a6CU:HCC.
COrJIaCHO pHC. 154 YlKe npH P max = 450 KFfcM 2 3KOHOMlIq-
HOCTb .L{1I3eJIfi npaKTHqeCKII He H3MeHfIeTC5J. f10J1yqeHHbIe pe3YJ1bTa-
TbI nO,II,TBep:lli.L{aIOTCfI npaKTIIKOH 3KCnJ1yaTaU:HII 6bICTPOXOJIHbIX
aBTOTpaKTopHbIX JIH3eJ1eH, B KOTOpbIX .L{aBJ1eHlIe BnpbICKa pe.L{KO
npeBbIlliaeT 450 KFjcM 2 . Ho B TO:llie BpeMfi B 3KcnJlyaTauliH
IIMeIOTC5I TOnJIHBHbIe CIiCTeMbI, HanpliMep Hacoc-!}JOPCYHKH, B
KOTOpbIX JIaBJ1eHHe BnpbICKa 3HaqHTeJIbHO BbIllie. f10-BIiAIiMOMY.
npe.!I,eJIbHa5I OnTliMaJIbHa5I BeJIlIqHHa P max 3aBHCHT TaKlKe OT
YC.l0BHH npOTeKaHI-1fI npou:eCCOB cMeceo6pa30BaHHfI H crOpaHH5I.
XapaKTep BJ1HfIHHfI ,II,aBJ1eHII5I, B CBOIO Oqepe,II,b, 3aBliCHT OT qlICJ1a
060pOTOB. COrJIaCHO paCCMaTpHBaeMOMY CJ1yqaIO qeM BbIllie qlIC.'IO
17* 269
trOC 2
400
300 x x
"
55 f
45
fezj(/1.C.'I)
f80
{70
200 300 400p; KrjCl1 2
PHC. 154. 3aBHcHMoCTb napa-
MCTpOB pa604cro npol.\ecca
.!J.H3Cn51 OT .D:aB CHHH Torr HBa
prfi max rrpH n:
1 - 1600 06/MUII;
2 - 2000 06/MUIi
060POTOB, TeM MeHbllIe Ha napaMeTpbI pa6oqero npouecca ,lJ,BHra-
TeJI BJIH eT H3MeHeHl-H' p rnax' 3a HCK.'IJOqeHHe1\I Te::\lllepaTypbI
OTXOn:mUHX ra30B f r .
Ha pHC. 155 H306pa2KeHa 3aBHCl1MOCTb napaMeTpOB pa6olJero
npOliecca ,lJ,H3eJHI OT npO,lJ,OJUKHTeJIbHOCTH BnpbICKa TOnJIHBa. B.1IHH-
HHe qJn Ha napaMeTpbI pa6oQero npouecca J.LBlIraTe.151 B ::ITOM
oIYQae TaK2Ke 3aMeTHO 3aBl1Cl1T OT
'lI1CJ1a 060pOTOB. OnbITbI nOKa3aJIH,
ITO YBeJII1QeHlIe npO,lJ,OJ12KI1TeJIbHO-
CTH BnpbIcKa 3aMeTHO YXY,lJ,llIaeT
Xr/(Cf12.cpaJ)
:
if Gm!E 12 .
50 I i
45 I
ffe z/(J7 c.'/)
; :
23 27 31 35 39 4J 9;
Puc. 155. 3aBHcHMoCTb napaJIICTpOIJ pa-
6o'lcro npol.\ccca L(U3Co151 OT npo.D:OJ1LKlI-
TC,1bHOCTH nO.D:a'-lll Toumwa IjJn upn n:
I - 1600 06j,"UH; 2 - 20llO {)6j wlI
f
2
PHC. 156. PcrYJ1HTop xapaKTcpllcTIIKn
BupblCKa
napaMeTpbI pa6olJero npouecca ,lJ,BHraTeJl51, nplllJeM C YMeHbllleHHei\I
QHCJla 060pOTOB BJIH HHe YKa3aHHorO cpaKTOpa B03paCTaeT. K Qncay
Hcc.TIe,lJ,OBaHIIH, H3YQaJOllJ.I1X BJ1H5IHl1e Ha pa60lJHH npOll.eCC ,lJ,H3e,151
xapaKTepHCTHI{ nO,lJ,alJl1 TOnJ1HBa, OTHOC5ITC5I H pa60TbI no 113YQeHlIIO
CT)'neHlJaToro H ,lJ,BOHHoro BnpbICKa. B pa60Te [7] cTyneHlJaTa51 xa-
paI<Tepl1CTHKa BnpbIcKa o6eCnelJHBaJIaCb npn nOMOllJ.H perY.1IHTopa
xapaKTepHcTHKH BnpbIcKa (PXB), pa6oTalOIlLero Ha npnHlI.Hne ne-
penycKa Ton.TIHBa B 3a,lJ,aHHble MOMeHTbI npOTeKaHI15I npouecca
BnpbIcKa.
PXB (pHC. 156) COCTOIlT H3 Kopnyca 4, HMeIDllJ.ero npHTepTbI1I
nJ1YH2Kep 3 C KOCbIM BbIpe30M H oceBbIM KaHaJ10M E, B I<OHue KO-
Toporo npeLlycMoTpeHo nOnepelJHOe cBepJleHHe, BbIXOLL5IlUee B Bblpe3.
Kopnyc IIl\1eeT nepenycKHoe OKHO A, npOXOIl.Ha51 nnOllJ.a,lJ,b KOTOpOro
l\!O)KeT 113l\1eH5ITbC5I npH nOMOllJ.H IIrO.lb I I3TOrO K.TIanaHa. nnYH)Kep
HarpY2KeH 2KeCTKOH npY2KHHOH 2, HalJa.'lbHa51 3aT5I2KKa KOTOpOi'1
pery.'lHpyeTC5I ynopoM 1. nOLL nJIYH2KepOM 3 npOCBepjleH ropH30H-
260
Ta.'!bHbIH KaHaJ1 r C BepTHKa.'!bHbIM OTBepCTI-IeM, COe,.'I,HH5JIOllJ.HM
KaHa.'! lI., C npOCTpaHCTBOM no,n, nJ1ymKepOM. rJpH60p ",!Q1KeT
BK.1IOlJaTbCH B J1I060M MeCTe TOnJIHBHOH CIICTeMbI. PXB B03,n,eHCTB'y-
eT Ha XapaKTepHCTHKY BnpbICKa CJ1e,n,YIOllJ.HM 06pa30I\I: AaBJ1eHHe
TOll.'II1Ba lJepe3 KaHaJIbI lI. II r .LleHcTByeT Ha nJ1YH.lKep 3. Kor,J,a
CIIJla ;I.aBJleHH5J Ton.1HBa npeBbIcHT CHJ1Y HalJaJ1bHOH 3aT5JLKKH npy-
lKHHbI 2, n.1YH}J{ep 3 HalJHeT nepeMem;aTbcH, B pe3y.'lbTaTe lJero
p tp Kr/cM2 pcp Kr/CM2 ptp Kr/CM2
....
400
800 800
200
500 600
0 10 fjJo
400 400 400 8
I
200 200 200
0 10 20 3D fjJo 0 20 r,00 0 10 (f0
a) 6) B}
PHC. 157. npHMCpbI OCl.\IIJIJlOrpaMM .n:aB.leHHH npH pa60Tc CHCTCMbI C PXB npH
n= 1000 06/MUfl H G T :
a - 22 Krt..; 6 - 16,4 Kr;..; B - 9,3 Kr;..; 2 - 4,7 KT/..
lJepe3 HeKOTOpOe BpeMH BbIpe3 E COBMeCTHTCH C OKHOM A, BCJIe,n,-
CTBHe 1Iero lJaCTb TOOJ1HBa H3 KaHaJ1a lI. lJepe3 KaHa.'lbI r H E, a
TaK)Ke OKHO A H llITylI.ep 5 6Y.LleT nepeTeKaTb B TOnJ1HBHbIH 6alJOK
H H3MeHHTb CKOpOCTb no.n.alJH TonJ1HBa B LI.HJIHH.n.p ,n,H3eJIH. BCJIe,n,-
CTBHe nepenycKa TOnJ1HBa OCHOBHOH TOnJIHBHbIH Hacoc ,Il,OmKeH
HMeTb 60JIbllIYlO npoH3Bo,n,HTeJIbHocTb. C.'le.LlyeT OTMeTHTb, lJTO
HalJaJ1bHaH 3aTHLKKa OPYLKHHbI 2 I\lOLKeT H3MeHHTbCH II BO BpeMH
pa60TbI TOnJ1HBHOH CHCTeMbI.
rJpHMepHbIe OCLI.HJIJIOrpaMMbI ,n,aB.'IeHHH npH pa60Te CHCTeMbI C
PXB nOKa3aHbI Ha pHC. 157, a-c. Ha pHC. 157, a H306paLKeHa
OCLI.HJ1.'IorpaMMa ,n,aBJ1eHHH BnpbIcKa p npH nOCTaHOBKe PXB y
Hacoca. OCLI.HJ1JIOrpaMMa .n.aB.'IeHH5J HMeeT BbIpaLKeHHYIO cTyneHlJa-
TYIO <POp MY, O,n,HaKO npH H3MeHeHHH HarpY3KH HJ1H lJHCJIa 060pOTOB
<popMa ,n,HarpaMMbI TaKLKe pe3KO H3MeH5J.'IaCb. 9TOT HeIwcTaToK HC-
lJe3aeT OOCJ1e nepeCTaHOBKH PXB K <PopCYHKe. KaK CJle,n,yeT H3
OCLI.HJ1JIorpaMM Ha pHC. 157,6, B, c, H3MeHeHHe nOJIOLKeHHH PXB
261
3Ha t Hne.'lbHO YMeHbIllaeT BJIHHHHe npOH3BOJ.I.HTeJIbHOCTH CHCTeMbI Ha
XapaKTep npOTeKaHHH J.I.aBJ1eHHH p . YMeHbIllaeTCJI H 3aBHCHMOCTb
<pOpMbI OCQHJ1JIOrpaMM J.I.aBJIeHHH OT qHCJIa 060pOTOB. OnbITbI Ha
J.I.BHraTeJ1e C TOnJ1HBHOH CHCTeMOH, HMelOI1..LeH PXB, 6bI.'lH npOBeJ.I.eHbI
c npHMeHeHHeM HaJ.I.J.I.YBa H 6e3 HerO. TIpH pa60Te J.I.H3eJI5I 6e3 HaJ.I.-
,n:YBa HCn0J1b30BaHHe PXB YMeHbIllH.TJO CKOpOCTb HapaCTaHHH ,n:aB-
J1eHHH cropaHHH dp nOqTH B 2 pa3a (pHC. 158, a). O,n:HaKo YJ.I.e.1b-
dip
II;
!Jp xrlf:/'6lpoiJ)
!J\I'
16
/Jp xr/(C/12. lpa iJ)
/J\I'
18
fO
8.
-
i
c- o !
- -..0
fJ e 8/(/1.C-")
12
210
f90
6 I;
6 C T Kl/,! 10 12 II; G T Kif/,!
a) 0)
dp
PHC. 158. BJlf!f!HHC PXB Ha - npH paooTe p'H-
dip
3eJlH:
a - 6e3 HaMyna; 6 - C Ha)],)],YBOM; I - 6e3 PXB;
2 - c PXB
o fO 20 30 Po xrjCI1 2
PIIC. 159. 3aBHcHMoCTb
g. = f(po}
HbIH pacxo,n: TOnJIHBa npH 3TOM B03pacTaeT npHMepHO Ha 2,5-3%
no cpaBHeHHIO C ge, KOTOpbIH HMeeT ,n:BHraTeJ1b npH pa60Te C CHCTe-
MOH 6e3 PXB.
ITpH HCnOJIb30BaHHH Ha,n:,n:YBa BJ1HHHHe
TeJ1bHO OCJ1a6eBaeT. KaK CJIe,n:yeT H3 pHC.
npHMeHeHHe PXB YMeHbIllaeT dp TOJ1bKO
dip
YJ.I.eJ1bHbIH pacxoJ.I. TOnJ1HBa npH pa60Te ,n:H3eJ1H C cHcTeMaMH,
HMelOI1..LHMH PXB H 6e3 HHX, npaKTHqeCKH cOXpaHHJ1CH HeH3MeHHbIM,
HanOMHHM, qTO HaJIHqHe ,n:aBJ1eHH5I Po 3aMeTHO YJ1yqIllaeT napa-
MeTpbI pa60qero npoQecca ,n:H3e.'l5I oco6eHHo Ha pe2KHMaX MaJIbIX
no,n:aq H qHCeJI 060pOTOB. OJI:HaKO, KaK CJ1e,n:yeT H3 pHC. 159, B
Ka2KJ.I.OM COqeTaHHH ,n:H3eJI5I C TOTIJIHBHOH cHcTeMoH HMeeTCH CBOH
OnTHMaJIbHaH BeJ1HqHHa OCTaTOqHOrO ,n:aBJIeHH5I. B CBH3H C 3TIlM
,n:J1H cTa6HJIIl3aQIlIl BeJ1IlqIlHbI Po ueJIeC006pa3Ho IlCn0J1b30BaTb
HaJ.I.J.I.YB J1IlHHIl HarHeTaHIl5I TOnJ1HBHOH CHCTeMbI, T. e. J.I.OnOJIHHTeJIb-
HYIO nOJ.I.nHTKY 3TOH JIHHHH TOnJ1HBOM ,n:o 3aJ.I.aHHOrO J.I.aBJIeHH5I.
flpIlCOOc06J1eHlle ,n:JI5I TaKOH no,n:nHTKH onHcaHO B pa60Te [13]. Ha
pHC. 160 Il306pa2KeHa npHMepHaH OCUHJI.lJOrpaMMa ,n:aBJ1eHIl5I Ton-
JIIlBa J.I.J1H CHCTeMbI, HMelOI1..LeH no,n:nHTKY J1HHHH HarHeTaHHH, a Ha
pIle. 161 - HarpY30QHbIe xapaKTepHcTHKH J.I.H3eJ1H ):(-20 npH pa60Te
3Toro J.I.H3eJ1H C YKa3aHHoH TOnJIIlBHOH cHcTeMoH npH Po=35 KFjCM 2 .
262
PXB Ha dp 3HaqIl-
dip
158, 6, npH HaJ.I.J.I.YBe
Ha 25-30%, npHqeM
KaK CJIe.D.yeT 113 aHaJ11I3a pHC. 161, qeM MeHbllIe qHCJIa 060pOTOB
.D.H3emI, TeM 3KOHOMHqHee pa60TaeT .D.H3eJ1b, qTO HBJIHeTCH Henocpe.D.-
CTBeHHbIM CJIe.D.CTBHeM npHMeHeHHH Ha.D..D.YBa JIHHHH HarHeTaHHH
TOnJ1HBHOH CHCTeMbI. 06-
llI.eH3BeCTHO, qTO MaKCH-
Ma,,1bHbIH H3HOC .D.H3eJIH
HMeeT MeCTO npH ero pa-
60Te Ha MaJIbIX nO.D.aqax
H qHCJI3X 060pOTOB. n pH
npHMeHeHHH H3.D..D.YB3
Ton.1HBHOH CHCTeMbI B
CBH31I C 3aMeTHbIM YJIyq-
llIeHHeM pa6oqero npo-
u:ecca H3 YKa33HHbIX pe-
}KH!vlaX H3HOC .D.eTaJIeH
.D.H3eJIH lJ:OJI.>KeH YMeHb-
IlIHTbCH, qTO HeCKOJ1bKO
YBe.1HqHT ero pecypc.
npH pa3pa6oTKe Me-
TO.D.HKH paCqeT3 npou:ec-
ca BnpblcKa HaMH He yqHTbIBaJIHCb YTeqKH TOnJ1HBa qepe3 3a30p
nJIymKepHoH napbI. 3TO .D.OnYllI.eHHe 6bIJ10 3KcnepHMeHTaJIbHO npo-
BepeHo .D.PYrHMH HCCJIe.D.OBaTeJIHMH. Ha pHC. 162 nOKa3aHbI
pe3Y.1bTaTbI OnbITOB, BO BpeMH
KOTOpbIX nJIOTHOCTb nJ1YH.>Kep-
HOH napbI H3MeHHJ1aCb B IlIHpO-
KHX npe.D.eJ1ax.
FI?7.C.1I)
J O
300
260
220
f80
140
2 6 10 Ne/T.c.
PHC. 161. BJIHHHHe nO.D:rrHTKH Ton.1H-
BOM ,1HHHH HafHeTaHHH TOllJlHBHOU
CHCTCMbl Ha aaBIlCHMOCTb
ge = f(N e } npH:
I - 1600 o6jMulI; 2 - 1400 o6/."ulI;
3 - 1200 o6jMllH
'"
'"
T'
Om",m,", 'fiU
90° B.H.m.
.".
PHC. 160. OCI.\HJlJlOrpaMMa .D:aB.leHHH TOllJlHBa
npH pa60Te CHCTCMb! C Ha.D:.D:YBoM JlHHHH HarHCTa-
HHH
G T
Kej¥
(9
pz
Kf/cN 2
100
90
80
t; If pz
700 t r
500
p, /ole
ej(ii.c.I.f)
{gO yr,
lie
Il.c.
1{0
90
no
150
f600 {700 f800 {gOO n OOjNI1H
PIIC. 162. B.'IHHHHe Ha napaMeTpbI pa-
6o'-lcro npo ecca H3eJlH llJIOTHOCTH
llJIymKcpHoll rrapb!
COrJ1aCHO .D.Harp3MMaM H3 pHC. 162 Ha napaMeTpbI pa6oQero
fIpou:ecca .D.H3eJ1H He OKa3bIBaeT 3aMeTHoro BJIHHHHH .n:3.>Ke .D.eCHTH-
263
KpaTHoe II3MeHeHHe nJ10THOCTH nJ1ymKepHoll napb!. OnblTbI nOKa-
3am! [70], '-ITO H3MeHeHHe B llIHpOKHX npe,lLeJiax 3a30pa MeLK,lLY
HrJIOll II KopnycoM paCnbIJ1HTeJJ5I TaK:tKe He BJIH5IeT Ha napaMeTpbI
pa6o'-lero npou.ecca ,lLH3eJI5I. )J.a:tKe npH 3a30pe to MKM ,lLH3eJIb pa60-
TaeT HopMa.fJbHO. 13o.fJee Toro, .3TH LKe OnbITbI nOKa3bIBaIOT, LITO
YBe.'IHL!eHHe YKa3aHHoro 3a30pa ,lL0 HeKOToporo npe,lLeJia CYIlleCTBeH-
HO YMeHbillaeT KOPP03HPYIO Hi'i .3<p<peKT npH nOna,lLaHI-IH B Ton.1lIBO
MOpCKOll BO,lLbI, KOTOpa5I nO'-lTH BCer,lLa npHCYTCTByeT B TOnJIlIBHbIX
6aKax CY,lLOBbIX ,lLH3eJIell, a TaKLKe npH HCn0J1b30BaHHH TOII.'I11B C
60.fJbIll11M CO,lLepLKaHHeM cepbI.
K HaHMeHee YCTOll'-lHBbIM napaMeTpaM TOnJIHBHOll CIICTel\lbI B
nepBYIO O'-lepe,lLb CJIe,lLyeT OTHeCT11 Ha'-laJIbHYIO 3aT5I:tKKY npY)KIIHbI
HrJIbI <POPCYHKH, BCJIe,lLCTBHe '-Iero
BeJIWIHHa ,lLaBJIeHH5I Ha'-laJ1a nO;J,'be-
Ma HrJ1bI B .3KCIIJIyaTaII,HH 3Ha'-lH-
TeJ1bHO OTKJ10H5IeTC5I OT 3a,lLaBae-
MOll npH pery.1HpOBaHHH.
Ha pHC. 163 H306pa:tKeHbI :1;11a-
rpaMMbI, nOKa3bIBaIO He 3aB11CH-
MOCTb ge H gi OT Prfjo. Cor.1acHo
npHBe,lLeHHbIM ,lLHarpaMMaM KaK B
..'I.H3eJI5IX TI1I1a B-2, TaK H B ,lL113eaHX
THna M-50 npH YBeJ1H'-IeHHH PrJ;o,lLO
HeKoToporo npe,lLeJia Y,lLe.'lbHbIH
paCXOA TOnJ111Ba YMeHbillaeTcH. LLJIH
..'I.H3eJIell B-2 gi YMeHbiliaeTcH ,lLO
PrJ;O = 320 KT/CM 2 . DO-BH,lLHMoMY, B
npe:1;eJIax 300 KT/CM 2 HaXO,lLHTCH H
onTHMa.'lbHa5I BeJIH'-IHHa Ptjjo ,lLJJ5I ,lLH3eJIell THna M-50. Pa6o'me Be-
JIHLIHHbI Prfjo .TIeLKaT B npe,lLeJ1ax 150-200 KT/CM 2 . B .3TOM HHTepBa.fJe
,lLaBJIeHHll YMeHbIlleH11e Prfjo Ha 20 KT/CM 2 YBeJ1H'-IHBaeT Y,lLe.fJbHbIH
pacxo,lL TOnJIHBa Ha 3,5-4 e/A. c. If., '-ITO COCTaBJI5IeT 2-2,5% OT ge.
D03ToMY :tKeJIaTeJ1bHO, '-ITo6bI BeJIH'IHHa Prfjo B YCJIOBHHX .3Kcn.1yaTa-
U.HH YMeHbillaJIaCb He 60JIee '-IeM Ha 2,5 KFjcM 2 . Ebmo 6bI II,e.1eco-
o6pa3Hee HMeTb Prfjo 60JIbille 300 KT/CM 2 . O,lLHaKO npH 60.'lbillUX 3Ha-
'-IeHH5IX Prfjo cy ecTBeHHo YMeHbillaeTC5I Ha,lLe:tKHOCTb yn.fJOTHHIOIllHX
KOHYCOB I1r.fJbI H ce)J.J1a Kopnyca paCnbIJ1l!Te.fJ5I. CJIe,lLyeT OTMeTHTb
TaK)Ke, '-ITO YCTaHOBJIeHHbIe B npaKTHKe npH perYJIHpOBaHHH CIICTe-
MbI )J.OBOJIbHO Y3KHe npe)J.eJIbI )J:onycTHMbIX OTKJIOHeHHll Be.1JI1'!l1H
Prfjo (O::!: 2,5 KT/CM 2 ) BnOJ1He 06ocHoBaHbI H HX LKeJ1aTe.fJbHO TO'lHO
C06.fJIO,lLaTb.
Be.'II1'-1HHa nO,lL'beMa Hr.fJbI <popcYHIm nO,lL6HpaeTC5I,lL.1H Ka)K,lLoro
Tuna ,lLBHraTeJ1eH B 3aBHCHMOCTfi OT YC.'IOBIIH npOTeKaHHH npOu.eCCOB
cMeceo6pa30BaHHH H CrOpaHI1H, a TaK)J{e onaCHOCTH B03H11KHOBeHH5!
Harapo06pa30BaHHH. B aBTOTpaKTOpHbIX ,lLH3e.fJHX 3TOT napaMeTp H3-
MeHHeTC5! B npe,lLeJiax 0,28-0,32 MM. B03paCTaH ,lL.fJH 6bICTPOXO.:IHbIX
,lLH3eJ1eH Cpe,lLHeH MO HOCTI1 (N e = 800 -7- 1500 A. c.) ..'1.0 0,45-
0,5 MM. HapH,lLY C 3THM cor.fJaCHO pIlC. 164, nO-BH,lLHMOMY, KaLK,lLbIH
9,., t'
ej(n.c.
180
2
1
140
200 240 280
J20 p . Kr/C/12
PHC. 163. BJIH5IHIIC Ha'-laJIbHOH
3aTHLKK!f HfJlbI 1j:J0PCYHKH Prfio Ha
3KOHOMII'-IHOCTb .D:1I3C.TJ5I:
1 - gi f(p tft ). 1{H3e.1b THna B-2
no A. II. nOJI030BY; 2 - g"
f (p tJ;o)' )],H3e.% THna M .50
264
.n:BHraTe.1b HMeeT CBOIO OnTHMa.1bHYIO BemI411HY Ymax. .D.m! .n:H3eJIH
TlIna M-50 onTHMa.1bHbIM HBJ1HeTCH Ymax = 0,45 -7- 0,46 MM. Ral(
YMeHbllleHHe, TaK H YBe.'IH4eHHe noro 3Ha4eHH5I Ymax Bbl3bIBaeT B03-
paCTaHHe ge. C1e.n:yeT OTMeTHTb, 4TO npH Ymax > 0,6 MM 3aBHCH-
MOCTb ge OT 4HC.1a 060pOTOB 3Ha4HTe.'lbHO YMeHbliiaeTcH.
DpH H3roTOB.'IeHHH paCnbI.1J1TeJleH oc060e BHJ1MaHHe HY./KHO y.n:e-
.;15ITb T04HOCTJ1 cBep.1eHH5I pacnbIoi1llBalOIlI.Hx oTBepCTHiL COrJIaCHp
pJ1c. 165 OTK.10HeHHe B CTOPOHY YMeHbllleHJ1H H B CTOPOHY YBe.1H4e-
HH5I Be.1HIIHHbI ,l1,HaMeTpa pacnbWHBalOIlI.erO OTBepCTl15I He6JIarOnpH-
5ITHO CKa3bIBaeTCH Ha y.n:eJIbHOM pacxo.n:e TOnJIHBa. PaCnbI.'IHBaIOIlI.He
oTBepCTH5I ,a,a>Ke o.n:Horo paCnbI.TIHTeJ15I B 60.1blllHHcTBe c.1Y4aeB HMe-
lOT HeCKO.1bKO pa3.1JH4Hble JI.HaMeTpbI. B CB5I3H C 3THM TOnJ1HBO pac-
npe.Qe.1HeTC5I no OT.n:e.1JbHbIM OTBepCTH5IM HepaBlIOMepHO, LITO TaK)Ke
t r °C
600
500
Y'eqpzc. )
f70
f60
t]3J 435 0.37 0.39 cfc HH
trl:
500
400
ge Ej(II.C. q)
f70
fbO
0,3
-<r
.......,.,..
45
41
0.9 Y MM
PHC_ 164. 3aI311CHMOCTb t T H ge
CT Ymax npll Or = 22 Ki'-/'l;
n = 2000 06/MUH
PHC. 165. BJlH5umc OTK.TJOHC-
IIH5I BC.TJH'-IHHbl de na t T H ge
l\IO.lKeT H3l\IeH5ITb cMece06pa30BaHHe, a c.TJe.n:oBaTe.lbHo, H 3KOHOMHLf-
HOCTb pa60TbI ,LI,BHraTe;rj5I. XOT5I 60J1blllOrO B.'IHHHHH :=noro cpaKTopa
Ha 3KOHOMH4HOCTb AJ13eJ15I 3aMe4eHO He 6bJJ10, o.n:HaKO 3TOT JI.ecpeKT
JlIO>KeT BbI3BaTb 60JlbllIYIO HepaBHoMepHocTb K034JcpHIJ:HeHTa H36bITK3
B03.n:yxa no o6beMY I<aMepbI cropaHHH II TeM caMbIM YBe.TJH4HTb B OT-
JI.e.1JbHbIX MeCTax onaCHOCTb neperpeBa nOplllH5I. TaKIIe /Ke noc.1Je1I.CT-
BH5I MOR,eT BbI3BaTb YBO,l1, cBepJla npH H3rOTOB.1JeHHH paCnbI.'lHBaIO-
UUIX OTBepCTHH. CJ1eAyeT TaK>Ke OTMeTJ1Tb, lITO npJ1 HaJ1J14HH B KaMe-
pe crOpaHH5I .n:H3eJI5I BHxpeBbIX JI.BH>KeHJ1H B031I.yxa HepaBHOMepHOCTb
pacnpe.n:e.1eHJ15I TOnJ1HBa no OTBepCTH5IM paCnbIJIHTe.'I5I H HeKOTopbIe
OTKJIOHeHHH B HanpaBJ1eHHH ocei'J OTBepCTHH BJIH5IIOT Ha pa60LIHi'J npo-
uecc .QH3e.1J5I 3Ha4I1Te:IbHO MeHbllle. B nepBYIO 04epeJI.b 3TO OTHOCHTC5I
K .n:H3eJ1HM C npOTHBOn0J10>KHO .n:BH>KYIll.J1MI1C5I nOplllH5IMJ1, a TaK)Ke K
1I.BJ1raTe.15IM, B KOTOpbIX npJ1MeH5IeTC5I nJ1eH04HOe J1.;1H 4aCTH4HO n.'Ie-
HOLfHoe Clllece06pa30BaHHe, TaK KaK B KaMepax crOpaHH5I 3THX 11BH-
raTeJIeH HMeIOTC5I CHJIbHble B031I.YlllHbIe nOTOKJ1. 01I.HaKO nOJ1HOCTbIO
HCI(.TJI04HTb B.1J15IHHe OTMe4eHHbIX 11ecpeKTOB Ha pa604HH npouecc 1I.H-
3e.TJ5I MORmo TOJ1bKO nYTeM HX yCTpaHeHH5I, 1I.JI5I 4ero Heo6xo1I.H1HO
1I.aJlbHeHlllee COBepllleHCTBOB3HHe TeXHO.TJOrHH H3rOTOBJ1eHH5I TOnJIHB-
HOH annapaTypbI.
r naB a V. PE>101Mbl P A50Tbi 3AKPblTbiX CDOPCYHOK AH3EI1ER
Pa3BHTHe 06Ill.eii TeopHH npoIJ,ecca BnpbIcKa TOnJ1lIBa JJ.OCTI-IrJIO
TaKoro cOBepIlleHcTBa, lJTO CTaJIO B03MOrKHbIM rrpOBOJJ.HTb paClJeTHO-
TeOpeTHlJeCKlle llCCJIeJJ.OBaHllH TOrrJ1HBorrOJJ.aJOIll.llX CllCTeM pa3JIlllJHO-
ro Tllna. OJJ.HaKO JJ.JIH aHaJIll3a HeKOTopbIX CJ1YlJaeB pa60TbI TOrrJIllB-
HbIX CllCTeM JJ.ll3e.TleH He BcerJJ.a YJJ.06HO H IJ,eJ1eC006pa3HO npHMeHHTb
06Ill.He MeTOJJ.bI paClJeTa. K. TaKHM CJIYlJaHM MO}KHO OTHeCTH aHa.TIH3
perKHMOB pa60TbI 3aKpbITbIX <P0PCYHOK.
113BecTHo, lJTO rrpll BrrpbICKe TOnJIHBa B03HHKaJOT YCTOHlJHBbIe II
HeYCTOHlJHBbJe perKHMbI pa60TbI 3aKpbITbIX <POPCYHOK, llMeJOIll.HX pac-
nbIJIHTeol1b C rHJJ.paBJIlllJeCKH ynpaBJIHeMbIM 3anopHbIM opraHOM. He-
YCTOHlJHBaH pa60Ta <P0PCYHKH, KOTOpyJO Ha3bIBaJOT TaK}Ke JJ.P06H-
llI.eH, xapaKTepH3yeTcH KOJIe6aTeJIbHbIMH JJ.BH}KeHHHMH 3arropHoro
opraHa pacrrbI.rmTeJIH H COnpOBO}KJJ.aeTCH xapaKTepHbIM 3BYKOM. He-
YCTOHlJHBaH pa60Ta 3aKpbITbIX <POPCYHOK I-Ja6JIJOJJ.aeTC5I. npH BnpbICKe
TOnJ1HBa Ha nYCKOBbIX pe}KllMaX pa60TbI JJ.H3eJ151., a TaKrKe npll KOH-
TpOJ1e <POPCYHOK B 3aBoJJ.cKHX YCJ10BH5I.X. ClJHTaeTC5I., lJTO HaJ1HlJHe
KOJIe6aHllH 3anopHoro opraHa npll perYJ1HpOBamfH <P0PCYHKH Ha PYlJ-
HOM CTeHJJ.e YKa3bIBaeT Ha TeXHlllJeCKH llcnpaBHoe COCT05IHHe pacnbI-
JIllTeJIH. HeKOTophIe llCCJ1eJJ.OBaTeJ1H npeJJ.J1araJOT no lJaCTOTe K0J1e6a-
HllH npOBOJJ.HTb 6e3pa36opHYJO JJ.HarHOCTHK)' TeXHHlJeCKOrO COCTOHHHH
<POPCYHOK Ha JJ.BHraTeJ1e HJIH CrreIJ,HaJ1hHOM CTeHJJ.e. KpoMe TOro,
npeJJ.nOJ1araJOT lJTO npH HaJIWJ.HH KOJIe6aHHH 3anopHoro opraHa pac-
llhIJIHBaHlle TOnJ1HBa CTaHOBHTCH 60JIee MeJIKHM H YJIYlJmaeTCH lJeT-
KOCTb OTCelJKll KOHIJ,a BnphICKa.
OJJ.HaKO B 3KCnJIyaTaUHH JJ.JIHTeJ1bHaH HeYCTOHlJHBaH pa60Ta CH-
CTeMbI BnpbICKa MO}KeT nOBhICHTb H3HOC TPYIll.HXCH II onopHhIX no-
BepXHOCTeH JJ.BHrKYIll.HXCH JJ.eTaJ1eH paCnhIJIHTemI H BbI3BaTb pa3pe-
rYJ1HpOBKY <POPCYHKH. MOrKeT rrpOH30HTH TaKrKe n0J10MKa npYrKHHbI
.cpOPCYHKll.
XapaKTep, aMnJ1llTYJJ.a II lJaCTOTa K0J1e6aHHH 3anopHoro opraH a
3aBHCHT OT KOHCTPYKTHBH X oco6eHHOCTeH paCn JIHTeJIH H npY}KH-
HbI, perYJIHpOBOlJHhIX napaMeTpOB H Macc JJ.BHrKYIll.HXCH JJ.eTaJIei'r
<POPCYHKH, JJ.J1HHbI HarHeTaTe.HbHOH MarHCTpaJIH, YCJIOBHH OTparKe-
HHH BOJ1H JJ.aBJ1eHHH Y ee BXOJJ.Horo KOHIJ,a H CKOpOCTH nOJJ.alJH Ton-
.'IHBa HaCOCOM. DOJJ.60pOM 3THX 3JIeMeHTOB MOrKHO B.'IHHTb Ha HH-
TeHCHBHOCTb K0J1e6aHHH H YCTpaHHTb HeYCTOHlJHBbIe pe)KHMbI pa60-
266
TbI <POPCYHOK B .lI,lIana30He pa6olJI-Ix lJlKeJ1 060pOTOB II HarpY30K
.lI,113e.1H.
3KcnepUMeHTa.'lbHOe I1CCJ1e.lI,OBaHl1e H TeOpeTHlJeCKI-IH aH3JIH3 pe
)IUI!\IOB pa60TbI <P0PCYHKI1 B CBH311 CO C.TIO:>KHOCTbIO B03HHKaIOllJ,IlX
HB.TIeHHH Be.lI,YTCH B npe.lI,n0J10:>KeHlIll, lJTO Ton.TIIlBO nO.lI,aeTCH K <pop-:
CYHKe npli nOCTOHHHOM .rr.aBJIeHHH. Hcc.rre.rr.yeMaH CHCTeMa COCTOHT
(pHC. 166) H3 aKKYMY.JIHTOpa 1 .lI,a B.JIeHllH ,
.lI,pOCCe.JIHPYIOllJ. erO KpaHa 2, HameTaTe.JIbHO- - . '/ , F' . 1 .
ro TPy6onpoBo.rr.a 3, npY)J{HHbI 5, BepxHen 4 I!!
H HH:>KHeii 6 Tape.JIOK npY)I{HHbI, wTaHru 7,
Ptp;1&,
b-
7 _
8
9
L
PIIC. 166. PaCQCTHa51 CXCMa C 1j:J0PCYHK0i1,
Ton.1HBonpOBo.D:OM !J aKKYMYJI!ITOpOM
.D:aBJlCHHH
J1H,"
p ....
J1cfc -
Kopnyca <POPCYHKH 8, Kopnyca paCnbIJIHTeJIH 9, 3anopHoro opra-
Ha 10.
HCCJIen;OBaTb pa60TY <POPCYHKH M01KHO no HK ru.zipaBJIHlJeCKHM
xapaKTepHcTHKaM [38, 39], a TaK)J{e C YlJeTOM .lI,HHaMHlJeCKHX HBJIe-
HliH, B03HHKaIOllJ.HK npH KO.JIe6aHliHK 3anopHoro opraHa [29, 38, 44,
87, 88].
1. AHAnH3 PEH<HMOB PA60Tbi Q)OPCYHOK
no HX rHAPOAJ1HAMJ1'fECKJ1M XAPAKTEPJ1CTJ1KAM
H C Y'fETOM AJ1HAMHKH ABJ1>KEHHSI Hrnbl PACnblnHTEnSi
AHaJ1H3 pa60Tbl cl>OPCYHOK no rH)I,pO)I,HHaMlI'IeCKHM xapaKTepHC-
THKaM. XapaKTepl1CTHKH <POPCYHOK H MeTO.lI, aHaJ1I-I3a B03MO:>KHbIX
pe.llmMOB HX pa60Tbl C nOMOllJ.bIO TaKHX xapmnepl1CTI-IK 6bIJ111 npe.lI,-
JIO:>KeHbI r. r. Ka.JII-IWeM {38, 39]. .QaJ1bHeHllIee YTOlJHeHl1e xapaKTe-
pHCTI1K <POPCYHOK C.lI,eJ1aJIH r. r. Ka.'1I1Ill H H. <1>. 3.lI,:>K1I6HH.
Ha pHC. 167 H3 KHHrI-I 3TIlX aBTopoB [40] .rr.aHbI B03MO:>KHbIe
Tl1nbI xapaKTepl1CTI1K 3aKpbITOH <POPCYHKI1 C MHoro.lI,bIplJaTbIM pac-
nbl.1I-ITeJ1eM. KaK YCTaHoB.'1eHO, KOJIe6amIH 11 rJ1 bI MorYT B03HHKaTb
J1HllIb B 06JIaCTH paCXO.lI,OB TOnJ1HBa, r.lI,e KpHBaH PCT = f(QifJ) HMeeT
OTpHn.aTeJIbHbIH YKJIOH. B 3aBHCI1MOCTI1 OT BI1.lI,a XapaKTepl1CTI1KII
<POPCYHKI-I H3MeHHeTCH .lI,nana30H paCXOJ],OB, npn KOTOpOM B03HI1KaeT
HeYCTOHlJIlBa51 pa60Ta, II xapaKTep KO.'le6aHIUI Ilr.TIbI. TaK, .lI,.151 xa-
267
paKTepHCTHK I, II, III HeYCToHIIHBa5I pa60Ta cpOPCYHKH OTMelJaeTCH
B .lI.Hana30He ceKYH.lI.HbIX nO.lI.alJ TOW1HBa HaCOCOM HJ1H H3 aKEYMY-
J.I5ITOpa .lI.aBJIeHH5I Qrn < Qa < Qnp. DOCa.lI.Ka HrJIbI Ha ce.lI.JIO 11 no-
.iIYlJeHHe npepbIBHcToro BnpbICKa B03MO)KHbI, ec.rm .lI.aBJ1eHHe Pmin B
Kopnyce pacnbI.1HTe.,I5I MeHbllle .lI.aBJIeHH5I 3aT5I)KEH npY)KHHbI, T. e.
npH XapaI(TepHCTl!Ke THna I. ECJm cpOPCYHKH HMelOT xapaI<TepH-
CTHKH THna I V H V, TO OHH BO BCeM .lI.Hana30He paCXO.lI.OB TOmmBa
pa60TalOT YCTOH'lHBO. YCTOH'lllBa5I pa60Ta 6Y.lI.eT II npll XapaKTepll-
CTHKaX I, II, III, IwrJ]:a nOJ]:a'la Qa < Qrn H Qa > Qnp.
PCT
I
PCT
J[
PCT
m
Pip.
Pm,n
P'Po
Pmin
p'P.
fro
I
I
fl"p
f)",
0,
f)m
QKP fl'l'
PCT
IY
PCT
v
Pmo,,
Pm,n
. Ptpo
p",.
Om=fKp
f/'I'
PI1C. 167. Tl1ilbI xapaKTc-
pl1CTI1K 3aKpbIToH 1j:J0PCYH-
KH C MHOrO.D:bJp'-laTb!M
paCnbIJUJTC.TJCM
I)tp
1l:.I5I 6bICTpOH oll.eHKlI BH.lI.a xapaKTepHCTlII(lJ cpOPCYHKI1 npl1 113-
MeHeHHH ee KOHCTPYKTHBHbIX H perYJIHpOBO'lHbIX napaMeTpOB npe.lI.-
J10)KeHbI 6e3pa3MepHbIe KpHTepHH H rpacpHKH [40].
eTO.lI. xapaKTepHcTHK .lI.JI5I aHaJIH3a pa60TbI cpOPCYHOK npocT H
n03BO.15IeT npH6JIlI)KeHHO Oll.eHlITb pe/KHMbI ee pa60TbI. C nOl\IOllI.bIO
xapaKTeplICTIlK MOLKHO npoaHa,;lH3HpoBaTb BJlH5IHHe HeKoTopbIX
KOHCTPYKTHBHbIX oc06eHHocTeit cpOPCYHI(lJ Ha pe)KlIMHbIe napaMeT-
pbI B HeYCTOHlJHBOH 06JlaCTH pa60TbI H XapaKTep KO.TJe6mm{1 3a-
nOpHOrO OpraHa.
He.lI.OCTaTOK MeTO.lI.a XapaKTepHCTHK COCTOHT B TOM. 'lTO OH He
YlJHTbIBaeT .lI.HHaMlJIleCKHX 5IBJleHHi\, B03HHKaJOlll.HX npH Ko.le6a-
Te.lbHbIX .lI.BH)KeHIUlX HfJ"Ibl pacnbIJ1HTe.TJ5I, H He onpe.lI.eJI5IeT lJaCTO-
TbI KOJle6aHHH 3anopHoro opraHa.
AHaJ11f3 pa60TbI (jJOPCYHOK C y eToM .lI.IfHaMIfKIf JI.BIf1KeHIfJI If rJI bI
paCnbIJ1IfTeJ1JI. 1lJ15I YTOlJHeUH5I BJ1H5IHI15I KOHCTPYKTHBHbIX oc06eHHOC-
Tell cpOPCYHKH Ha BeJIHlJHHY pe)J(lJMHbIX napaMeTpOB H lJaCTOTY KO-
.le6mlHH 3anopHoro opraH a pellialOTC5I COBMeCTHO ypaBHeHH5I .lI.H-
HaMHlJeCKOrO paBHOBeCH5I HrJIbI H 6aJIaHCa pacxo.u.a TOnJ1HBa lJepe3
268
<j)OPCYHKY. 0pH6J1HllieHHOe peWeHHe 3THX ypaBHeHHll 6b1.10 ).(aHO
ewe O. J1IOTlJ,eM. .D.lliOH OOJ1b .D.eH-rapTor [29] c,n:e.'IaJ1 6o.1ee CTpO-
rIIll BbIBO,n: ypaBHeHHSI ,n:BHllieHHSI Hr.1bI. .D..1f! aHa.'1H3a 3TOfO ypaB-
HeHHf! HCrr0J1b30BaHbI KpiITepHH YCTOllIIHBOCTH Payca- rYPBHlJ,a.
B Ha3BaHHbIX pa60Tax npHHHMa.10cb, IITO ,n:aB.1eHHe PCT AelIcTByeT
na BCIO I1JlOI1l.a,lLb rronepeIIHoro ceIIeHHH IIr.'1bI II pacxo,lL TOll.'1HBa IIe-
pe3 pacnbWHTeJ1b npS:lMO npOnOpl{UOHa.1eH rrO,lL"beMY Hf.1bI.
T. <P. KY3HelJ,OB [44] YTOIIHH.1 BJ1Hf!HHe pacrrpe,n:e.1eHHf! ,lLaB.'1eHlUI
1'Orr.'1HBa Ha nonepeIIHoe ceIIeHHe Uf J1bI B ypaBHeHHH ,lLIIHaMHIIeCKoro
paBHOBeCHf!. O.lI.HaKO .lI.OrrYI1l.eHHe 0 npf!MOll rrpOnOplJ,HOHa.'1bHOCTf!
pacxo,n:a TOrrJ1HBa II nO.lI."beMa Hr.1b1 He,lLOCTaTOIIHO cTporo H He rro-
3BO.1f!eT BeCTH Ko.1UIIeCTBeHHbIlI aHa.1H3, Tal, KaK K03<p<PHlJ,HeHT
npOnOplJ,HOH8J1bHOCTH HeH3BeCTeH. 50.lee CTpOfoe H HHTepeCHoe pe-
meHue CHCTeMbI ypaBHeHHH .lI.HHaMHIIeCKoro paBHOBeCHf! Hr.'1bI pac-
nbI.1IITemI H 6aJ1aHCa pacxo.lI.a TonmlBa IIepe3 <POPCYIIKY C YIIeTOI\I
ypaBHeHHf! paCxo.lI.a ,lLaJI r. r. Ka.1l1w [38]. BbIBO.lI. OCHOBaH Ha 113-
BeCTHOM npl1eMe Ha.'ImKeHI1f! Ma.'1bIX B03MYW.eHHlr Ha nO.:10LKeHl1e
-cTaTH'leCKOfO paBHoBecHSI HfJ1bI. B pe3y.'1bTaTe 6bIJ10 no.'1Y'leHo .lI.11<p-
<pepeHlJ,Ha.'1bHOe ypaBHeHHe .lI.BmKeHHf! I1r.'1bl <POPCYHKH
d 3 y(t) -+- A d 2 y(t) -i- A dy(t) _.1.. A l ( I ) = 0,
dt 3 . 2 dt 2 ' I dt . OY
(230)
T.lI.e y (I) = .1.y - OTK.':IOHeHHe Hr.1bI OT nO.'10LKeHI1f! paBHOBeCHf!,
painepH3yeMoro Be.1HIIIIHaI\1H YCT, Qrfj, PCT;
/ oN , )
A9= ( t}- . oP CT . ) .
.. M' (XV", oN '
. iJQ",
0,\' oN
Al = __.!.._J oK l _ oY CT . oK[ ...L . ap;;
M' L OYCT oN iJQ",' aV",
iJQ",
aN
oP CT
xa-
aN
oQrp
(231 )
aN
oQ.p
oK )]
. oQ; ;
/
_l ( _
aV", ,()PCT
(W
I ( ' oK 1 OYCT
Ao= - ..
M'aV", oY cT - aN
oQ",
3.lI.eCb Kl (PCT' Qrfj, YCT) = 0 - ypaBHeHl1e
Hf.!1bI;
N (PCT' Qifj, YCT) = 0 - yp8BHeHHe pacxo,lLa Ton.'1HBa IIepe3
.lI.pOCCeJ1HpYIOI1l.He Ce IeHI1f! paCnbIJ1H-
Te.11f!.
oK 1 )
aP CT
aN
oP CT
oN
uQ", ,
CTaTH'leCKOrO paBHOBeCHf!
269
. JJ.JISI. JUIHeapll3alJ,lUI 3a)J,a1.111 npllHllMa.1l0Cb, 'ITO OTKJIOHeHllSi p,
I1Q(/j, l1y OT BeJIll'IllH PCT, Q(/j, YCT HaCTOJ1bKO Ma.'lbI, 'ITO B npe)1,e:laX.
llX ll3MeHeHllSi 'IaCTHbIe npOll3BO)1,HbIe no COO"fBeTCTBYIOll1.llM nepe-
MeHHbIM MorYT C1.IllTaTbCSI nOCT05IHHbIMll, T. e. BeJ1ll1.IllHbI K03<pqm-
lJ,lleHTOB A 2 , AI, Ao onpe)1,e.llSIIOTC5I no 3Ha'IeHl15IM PCT' Q(/j, YCT, B351-
TbIM ll3 XapaKTepllCTllK <popcYHlm.
JJ..151 )1,a.1bHeHrnerO aHaJ1ll3a B pa60Te 138] HCnOJIb3YIOTCSI KpHTe-
pHIf Payca-fYPBllUa, no KOTOpbIM B YCTOH'IllBOH 06JIaCTll Bce K03<p-
<plllJ,lleHTbI (A 2 , At. Ao) )1,OJ1lliHbI 6bITb n0J10llillTe.'IbHbIMll 11 )1,0.1lliHO
C06JIIO)1,aTbc5I HepaBeHcTBo
A2AI-Ao > O. (232)
JJ.aJIbHeHrnee npe06pa30BaHlle BeJIll1.IllH A 2 , At. Ao npoH3BO)1,llTCH
dP CT dYcr
C nOMOll1.blO yr_10BbIX K03<p<plllJ,lleHTOB - H -.
dQq, dQq,
I1cno.'Ib30BaHlle yrJIOBbIX K03<p<plllJ,lleHTOB )1,,JI5I onpe)1,eJ1eHll51 rpa-
HlllJ,bI nepeXO)1,a ll3 YCTOH1.IllBOH 06.llaCTll pa60TbI <POPCYHKll B Heyc-
TOH'IllBYIO ll.1Jll npll perneHllll ypaBHeHll51 (230) He )1,aeT TO'IHbIX pe-
3YJIbTaTOB II 51B_l51eTCH )1,OBO.:lbHO TpY)1,OeMKllM. lJ.BM n03BO.'I5IIOT Be-
cm aHaJIll3 ypaBHeHllH (230) II (232) B 60.lee 06ll1.eM Bll)1,e 6e3
BBe)1,eHll51 yrJIOBbIX K03<p<plllJ,lleHToB. OJ:!.HaKO conOCTaB.leHlle pac-
'IeTHbIX )1,aHHbIX, nOJlY1.IeHHbIX no ypaBHeHlllO (232) C Y'IeTOM pa-
BeHCTB (231), II 3KcnepllMeHTaJ'IbHbIX nOKa3bIB8eT, 1.ITO npll onpe)1,e-
JICHHOM C01.IeTaHllll KOHCTPYKTllBHbIX 3J1eMeHTOB CllCTeMbi 'IaCTOTa
KOJIe6aHllH II BeJ1ll'IllHa pellillMHbIX na paMeTpoB <POPCYHKll cYIllecT-
BeHHO OT,,'Ill'IalOTC5I. 06"b5lCH5IeTC5I 3TO TeM, 'ITO B paccMaTpIIBaeMoM
MeTO)1,e paC'IeTa He Y'IllTbIBalOTC5I BOJ1HOBbIe }lBJIeHllSi B HarHeTa-
TeJ1bHOM TOnJ1llBOnpOBO)1,e II npYllillHe.
2. onPEAEnEHHE '1ACTOTbl KonE6AHHA Hrnl:>l PACnblnHTEIISI
C Y'IETOM BonHOBblX SlBnEHHA B HArHETATEnbHOA MArHCTPAnH
H npY>KHHE CDOPCYHKH
Y'IeT )1,llHaMH'IeCKllX 51BJ1eHllH, npOllCXO)1,51ll1.flX B HarHeTaTeJ1bHO I
MamCTpa.'lll II npYllillHe <p0pcYHlm npll KO_'Ie6aHll5lX ee 3anopHoro
opraHa, 6bIJI C)1,eJ1aH B llCCJ1e)1,OBaHll5lX [87, 88]. TaM 1Ke )1,aHO cpan-
HeHllE' paC1.IeTHbIX II 3KcnepllMeHTa.llbHbIX 3Ha1.JeHllH qaCTOTbI KOJ1e-
6aHllH llrJ1bI pacnbIJ1llTe"l51. IlOCKOJ1bKY no.'lyqeHHOe B pa60Te [87]
xapaKTepllCTll1.JeCKOe ypaBHeHlle C01I.epllillT 3KcuepllMeHTa.:'IbHO onpe-
)1,eJ1HeMbIe BeJ1ll'IllHbI, OHO HeY)1,06HO )1,J1H llcnO,JIb30BaHll51 B paC1.IeT-
HbIX llCCJIe)1,OBaHllSIX H 3)1,eCb He npHBO)1,llTCSI. KpoMe TOro, OHO npH-
rO)1,HO .JIllrnb )1"TI5I <POPCYHOK C MHOrO)1,blp1..IaTbIMH pacnbUUITeJI5IMII H
HrJIOH B Ka'IeCTBe 3anopHoro opraHa. HmKe 1I.e"laeTC5I nOnbITI(a IIO-
JIY'IHTb ypaBHeHHe B 60J1ee 06ll1.eM BH)1,e.
BbIBO)1, xapaKTepHCTH ecKoro ypaBHeHHSI )1.J1J1 paCqeTa K0J1e6aHHH
3anopHoro opraHa <}IOPCYHKH. C yqerOM )1.H.HaMH.\leCKH.X SlBJ1eHH." B Ha-
fHeTaTeJ1bHOH MarH.CTpaJ1H. II. npY1KH.He. BbIBO)1, xapaKTepllCTH'IeCKOrO
ypaBHeHHSI C1I.eJ1aH HaMll COBMeCTHO C llHlli. f. JJ.. MaCJ1SIHbIM. BbI-
270
BOlI. OCHOBaH Ha MeTOlI.e, npelI.J10)!(eHHOM f. f. KaJIHilleM [38]. Q>H3H-
qeCKaH MOlI.eJ1b pacnpocTpaHeHHH H OTpa {eHHH BOJ1H lI.aBneHHH B
HarHeTaTe.;'IbHOH MarHcTpanH H BO:IH lI.e<popMa HH B npY)!(HHe npH-
HHMaeTCH TaKOH )!(e, KaK B pa60Te [87]. BonHa lI.aBJ1eHllH, HlI.Yll.{aH
OT <P0PCYHKH, OTpa)KaeTCH OT BXOlI.HOrO KOH a HarHeTaTeol1bHOH Ma-
rHCTpaJIH, qTO yqHTbIBaeTcH K03<P<PH HeHToM -1 a 1. faIlIe-
HHeM BO.'lH lI.aBJ1eHHH npH HX lI.BH)!(eHHH no HarHeTaTe.1bHOH MarH-
CTpa.'lH npeHe6peraeM. Bo.'IHa .l(e<popMa HH, pacnpoCTpaHHlOll.{aHCH
OT nO.l(BH)!(HOrO K Heno.l(BH)!(HOMY KOH Y npY)!(HHbI, qaCTHqHO oTpa-
)!(aeTCH OT onopbI, qTO yqHTbIBaeTcH I{Q3<p<pH HeHToM an 1. OpH-
HHMaeTCH, 'ITO raIlIeHHH BO.'lH .l(e<p0pMa HH npH HX .l(BH)!(eHHH B
npY)!(HHe He npOHCXO.l(HT.
I1CXO.l(I-IbIM HBnHeTCH ypaBHeHHe CTaTHqeCKOrO paBHOBeCHH 3a-
nopHoro opraHa, KOTopoe 3anHCbIBaeTCH B HeCKOJ1bKO HHOM BH.l(e,
qeM B pa60Te [38]:
K (PCT' Q"" YCT' P n) = 0,
r.l(e PCT, Q"" YCT - .l(aBneHHe B Kopnyce paCnbI.'IHTeJ1H, CeKYH.l(HbIM
paCXO,lI, TonnHBa qepe3 <P0PCYHKY H nOnO)!(eHHe
3anopHoro opraHa npH CTaTHqeCKOM paBHOBeCHH
nOCne.l(Hero, onpe.l(eJ1HlOll.{He CHJ1Y .l(aBoI1eHHH Ton-
nHBa Ha 3anopHbIH opraH;
Pn - CHna, npOTHBO.l(eHCTBYlOll.{aH nepeMell.{eHHlO 3a-
nopHoro opraHa. OHa C03.l(aeTCH B 3aBHCHMOCTH
OT KOHCTPYK HH <POPCYHKH npY)!(HHOII H.'lH .l(aB-
.'leHHeM rH.l(p03anOpHOH )!(H.l(KOCTH.
CMell.{eHHe 3anopHoro opraHa OT nOol10)!(eHHH CTaTHqeCKOrO paB-
HOBeCHH Ha /).Y npHBO,lI,HT K nOHBJ1eHHlO H36bITOqHOH CII.'IbI, npHpa-
ll.{eHHlO <PYHK HH K, KOTopaH ypaBHoBeIlIHBaeTCH CHnaMH HHep HH
H TpeHHH:
/). + /). Q + /). ..L /)'P _
iJP CT P iJQ", '" iJY CT y, iJF n n
_M, d2( y) -tt d( y) = 0
dt 2 dt '
(233)
r,lI,e !1p - H3MeHeHHe .l(aBneHHH B 06'beMe V", paCnbIJ1HTenH;
/).Q", - H3MeHeHHe 06'beMHOrO pacxo.l(a TonnHBa qepe3 .l(pocce-
nHpYlOll.{He CeqeHHH pacnbWHTenH;
/)'P n - H3MeHeHHe YCHmfH, npOTHBO.l(eMCTBYlOll.{erO nepeMell.{e-
I-IHlO 3anopHoro opraHa.
YpaBHeHHe pacxO.l(a TOnJ1HBa qepe3 .l(pOCCenHpYlOll.{He CeqeHHH
pacnbWHTeJ1H npH CMell.{eHHH /).Y [38]:
aN A + iJN A Q + aN A _ 0
-u.p -£.1 '" -u.y- .
iJP CT iJQr/J iJY CT
(234)
YpaBHeHHe (234) CnpaBe.l(nHBO, eCJ1H npHHHTb, qTO npH nepeMe-
ll.{eHHH 3anopHoro opraHa coxpaHHeTcH Hepa3pbIBHoCTb nOTOKa.
271
5aJ1aHC paCXOAa TOn HBa 4epe3 OPCYHKY C Y4eTOM BO H aB-
.JIeHHH B HarHeTaTe.'IbHOH MarHCTpa.'IH npH CMeIlteHHH y:
(Q , ' Q ) . Q ! ' Q ) " d{l'.y) + V d{l'.p)
aT...l a -{ <jJT.J 4' = tu0---;;t a Ij.J '
(235)
r e Qa H Qif> - o6"bel\!Hoe KOJ'IH4eCTBO Tonmma, BTeKaIOIlterO B
OPCYHKY H BbITeKaIOIlterO 4epe3 pocce.'IHpYIOIl1.He
ce4eHHH paCnbIJ1HTeJ1H npH CTaTH4eCKOM paBHoBe-
CHH 3anopHoro oprana (Qa = Qg;);
t'l.Qa - H3MeHelIHe 06"beMnOrO KO.'IH4eCTBa TO n.'Ilma , BTe-
KaIOIltero B OPCYHKY, H3-3a BO.'IH aB.'IeHI1H B Ha-
rHeTaTe bHOH MarHCTpa H;
fuo - nonepe4Hoe ce4eHHe 3anopHoro opraHa, BbI3bIB aIO-
Il1.ee npH ero nepeMeIlteHHH H3MeHelme 06"beMa V g;.
llJ1H onpe e.'IeHHH Be H4HH ft.p H ft.Qtjj Bocno.'Ib3yeMcH perueHH-
eM BOJ1HOBOrO ypaBHeHHH J15I BbIXO Horo ce4eHHH HarHeTaTeJ1bH01I
MarHCTpa.'IH. 06Il1.ee aBJleHHe B 06"beMe V tjj pacnbI.'IHTe H C yqeTOM
BO.'In aBJ1eHH5I:
Prj) = pcr + ft.p = pcr+ W(t)-F(t). (236)
AMWUlTy.u:a BO.l:HLI F(t) 3aBHCHT OT YC.'IOBlIH OTpmKeIlIIH BO.'IHLI
Wet) y BXOAHoro Kon.Qa HarHeTaTe."IbH01I MarHCTpaJ1H:
F(t)= -oW(t-T), (237)
2L
r e T = - - BpeMH BH)KeHHH BO.1HbI aB.'IeHlIH no narHeTaTe.'Ib-
a
HOH MarHCTpaaH B 06a KOH.Qa.
1I3MenelIHe ..'l.aBneHHH B 06"beMe V if> C Y4eTOM BbIpa)KeHH1I (236)
H (237):
!..\p = W(t)+oW(t-T).
(238)
VI3MeHeHHe o6"beMHoro KO.'IH4eCTBa Ton.rIHBa, BTeKaIOIlterO B op-
CYHKY,
, iT
!1Qa = fr1.C r = -- [W(t)-oW(t- T)]. (239)
ap
BeJ1HlJHHa j,Pn 3aBHCHT OT KOHCTPYK.QHH OPCYHKH H CKOpOCTH
nepeMeIltenH5I ee 3anopHoro opraHa. 50 bIlIoe pa3noo6pa3He KOH-
CTPYK.QHH OPCYHOK He n03BO.'IHeT paCCMOTpeTb Bce B03MOfKHbIe
OPMYJ1bI J1H nO C4eTa Be.1H4HHbI ft.Pn, n03TOMY OrpaHHlJHMCH HC-
C.'Ie OBaHHeM OPCYHOK C MexaHH4eCKHMH npyJKHHaMH H HaH60J1ee
npOCTbIX KOHCTpYK.QHH rHAp03anopHbIX OPCYHOK. OpH nOM .'IH
Bcex THnOB coxpaHHIOTCH 06IltHOCTb HBJ1eHHH, B03HHKaIOIl1.HX B npy-
)KHHaX, H OCHOBHbIe n0J10fKeHHH BbIBOAa.
llJ1H OPCYHOK C MexaHHLleCKOH npY)J{HHOH npH Ma.'IbIX CKOpO-
CTHX nepeMeIlteHHH 3anopHoro opraHa (6e3 Y4eTa BO.'IHOBbIX HBne-
HHH B npyJKHHe)
ft.P n = -6' ft.y.
(240)
272
OpH BbICOKHX CKOpOCTSIX nepeMeIl.1.eHHSI 3anopHoro opraH a Ha-
6JIIO!l:aeTCSI HMny.'IbCHOe B03,lLeilcTBHe B03MYllIaIOIl.1.eH CI-J.'IbI Ha no-
,lLBH1KHbIH KOHell. nppKHHbI. B pe3y.'IbTaTe B npY)J(HHe B03Hl1KaIOT H
pacnpOCTpaHSIIOTCSI BO.'JHbI Ae<roPIVJall.HH. Be.'IHlJHHa I1Pn B 3TOM c.'IY-
lJae M01KeT onpe,lLe.'J5!TbCSI 113BeCTHOH 3aBHCHMOCTbIO H3 conpOTHB-}
J1eHHSI IVIaTepHaJ10B:
I1P nx = t'"EAEF)",
(240a)
r,lLe I1Pnx - .lLl1HaMIIlJeCKOe YCHJ1He B J1I060M CeqeHHH np, Y)!{llHbI
OTCTOSIIl.1.eM Ha paCCTOSIHHH x OT ee nO,lLBH)J(Horo KOH-
ll.a;
I1Ex - OTHOCIITe.i1bHaSI ,lLe<ropMall.HSI B paCCMaTpHBaeMOM ce-
qeHIIH;
(EF)" - )KeCTKOCTb CelJeHl1SI 3KBHBa.'IeHTHOro CTep)J(HSI, KOTO-
pbIM 3aMeHSIeTCSI npY)J(HHa npH aHa.'JH3e.
)l\ecTKocTb (EF)" 3KBHBa.'1eHTHOro CTep)J(HSI, )J(eCTKOCTb npy-
)!mHbI, yro.'l 8 nO,lL'beMa BHTKOB II ,lLJ1IIHa npOB0J10KH Ln npY)J(IIHbI
CBSI3aHbI II3BeCTHbIMH COOTHOIlleHIISIMII:
( EF ) = . ( F ) = :nd 2 . Ln .
" :nD3' P.1 4 [Pn'
{j' = .
:nD 3 i p ,
c= :rrd J G
32 '
s
t g 8=-.
TeD '
i
Ln = ipnD;
I
,
(241 )
J
Ef;
J.
t-
CKOpOCTb pacrtpocTpaHeHIISI ynpyroH
BO.'lOKII npY)J(HHbI
C - KPYTH.'IbHaSI )J(eCTKOCTb npOB0J10KH npY)J(HHbI;
S - Illar BHTKOB;
D H d - Cpe,lLHHH ,lLHaMeTp npY)J(HHbI lJ ,lLlJaMeTp npOBOJIOKH;
G - MO,lLYJIb ynpyroCTlJ BTOpOro pO,lLa;
l- ,lLJ1HHa 3KBHBaJleHTHOro CTep)J(HSl (npY)J(IIHbI);
.I;. ip - lJHC.'IO pa60lJHX BHTKOB.
, J13 BbIpa)J(eHHSI (241) CJ1e,lLyeT, lITO
(EFt, = {j'L n tg 8; l
l = ips = Ln tg 8, J
J
r,lLe
(242)
,lLe<ropMall.HH B,lLOJIb
npo-
an = ..!!... 11 I G = 1! f>'L . (243)
V 2 D V Pn M n
CKOpOCTb pacnpOCTpaHeHHSI ynpyroH ,lLe<ropMall.HII B,lLO.'lb OClI
3KBHBa.'leHTHoro CTep)J(HSI (npY)!{HHbI)
.. ( (EF).1 sd (G.. f 6'[2 (243a)
0. 1 = V (pF)" = V2 :rrD2 1 p;;- = V M n '
18 3aKa3 748 273
OTHorneHHe CKopOCTeH.pacnpOCTpaHeHHH ynpyroH e$opMa HH
B OJ1b OCH H npOBOJIOKH npY.iKHHbI
= =tge. (244)
an Ln
BpeMH npOXO.iK.D.eHHH BO.lIHbI .D.e$opMa HH no npY.iKHHe B 06a
KOH a
T _ = 2Ln
n- .
a" an
DpH pacnpocTpaHeHHH BOJIH ynpyrHX .D.e$opMa HH no 3KBHBa-
JIeHTHoMY CTepMHlo (npYMHHe) nepeMe eHHe nO.D.BH.iKHoro (x = 0)
KOH a 3KBHBa.1JeHTHOro CTepMHH, paBHoe nepeMe eHHIO !1y 3anop-
Horo opraHa, H npHpa eHHe € OTHOCHTeJIbHolI .n;e<popMa HH onpe-
eJIHIOTCH perneHHeM BOJ1HOBoro ypaBHeHHH
iJ2u(t, x) 2 iJ2u(t, x)
-a
iJt 2 "iJx 2 '
nOCJIe perneHl1H KOToporo H cooTBeTcTBYIO HX npe06pa30BaHHH no-
JIyqHM
u(t, x) = {(a)-x)-anf(a"t +x-21); (245)
e(t, x) = -[f' (a)-x) +anf'(a) +x-21)]; (245a)
v(t, x)=aa[f'(a)-x)-a n f'(a)+x-21)J, (2456)
r.n;e u(t, x); e(t, x); vet, x) - nepeMe eHHe, OTHOCHTeJIbHaH .n;e-
$opMa HH H CKOpOCTb nepeMellie-
HHH CeqeHHH Ha paccToHHHH x OT
no.n;BHMHoro KOH a CTep.iKHH.
(245) BH.D.HO, qTO .n;JIH no.n;BHMHoro KOH-
113 aHaJIH3a ypaBHeHHH
a (x = 0) nepeMe eHHe
y = f(aj)-a n f(a:i-21).
Depexo.D.H K aprYMeHTY BpeMeHH H 0603HaqHB
nepeMe eHHH y (t), nO.lIyqHM
y = y(t)-any(t- Tn).
npHMYIO BOJ1HY
(246)
BeJIHqHHa .n;onOJIHHTeJ1bHOH OTHOCHTeJIbHOU .D.e$opMa HH onpe-
.n;eJIHeTCH H3 BbIpa.iKeHHH (245a) H (2456) "PH x = 0:
I
!18 = -( 8I --\-. 8II) = --(VI + VII)'
a"
HO
_ dy(t) .
VI- '
dy(t-Tn)
VII = an'
dt
Tor a
8= _ [ dy(t) +a dy(t-T n ) ] .
a" dt n dt
(247)
274
OOJJ.CTaBHB 3Ha'leHHe !lB, HaHJJ.eHHoe no cpopMYJIe (247), H
(EF)", onpeJJ.e.TJeHHOe no BbIpaMeHHIO (242), B 3aBHCHMOCTb (240a)
C Y'IeTOM paBeHcTBa (244), no.'IY'IHM npli x = 0
!lP = _ 6'Tn [ dy(t) +u dy(t-T n ) ] .
n 2 dt n dt
lI..TJH COBMeCTHOrO perneHIIH yp aBHeHIIH (233) , (234) II (235)
nOJJ.CTaBIiM B HIIX 3Ha'leHIIH b..p, b..Qa, b..y II I1P n , BbI'IIIC.'IeHHbIe COOT-
BeTCTBeHHO no q>opMYJIaM (238), (239), (246) H (248). 113 BbIpa-
MeHIIH (234) HaXOJJ.IIM I1Qg; II nOJJ.CTaB.'IHeM B ypaBHeHII5I (233) H
(235). OocJ1e npe06pa30BaHHu COBMeCTHoe perneHHe JJ.BYX nOJ1Y'IeH-
HbIX JJ.IIq>q>epeHIwaJ1bHbIX ypaBHeHIIu aHaJIOrHI.JHO pa60Te [87] no-
3B0J1HeT HaUTIi xapaKTepliCTH'IeCKOe ypaBHeHHe JJ.JIH paccMaTpliBae-
MOll CIiCTeMbI TO£I.11H Bon oJJ.a'l II:
. )
( M'Z2+'I'}Z+ , 6'T n . I+Une-ZTn z+ oK . oYcr - X
iJPn 2 l-ane- zTn oQtjJ aN oYcr
oQtjJ .
aN aN
oP cr + Ir 1- ue- ZT ) + (t oYcr )
-. uoz- X
ap I +ue- ZT aN
oQtjJ oQtjJ
/ aN )
X ( - . 8p;; -0
oP cr oQtjJ -.
oQtjJ
YpaBHeHHe (249) 51B.151eTC5I HaII60.TJee 06Il1.IIM .lI.J1H aHaJ1II3a KO-
JIe6aHHU 3anopHoro opraHa q>OPCYHOK pa3JIIIQHWX THnOB: KJ1arraH-
HO-COrrJIOBOU, lllTlIq>TOBOU II C MHoroJJ.bIpQaTbIMH paCnbIJIIITeJIHMII.
OHO Y'IIiTbIBaeT OCHOBI-IbIe KOHCTPYKTIIBHbIe napaMeTpbI q>OPCYHKII,
HarHeTaTeJ1bHOU MarIICTpaJ1II II npYMIIHbI.
3Ha'leHII5I 'IaCTHbIX npOII3BOJJ.HbIX q>YHKlIJIH K H N onpeJJ.e.TJ5IIOT-
CH H3 q>OPMYJI CTaTIIQeCKOrO paBHOBeCHH 3anopHoro opraH a cpop-
CYHKII II pacxoJJ.a Ton.TJHBa Qepe3 JJ.pOCCeJ1HpYIOIlI.IIe Ce'leHII5I pacnbI-
.1IITeJ1H.
lf aCTHble C/lylJ.au xapaKTepUCTUlJ.eCKOcO ypaB1-WHufl. 1) lI.J151 KO-
pOTKIIX II MeCTKIIX npYMIIH (Tn -- 0; Un = 1) MOMHO npeHe6peQb
HaJ1II'IHeM B HIIX BOJ1H JJ.ecpopMaIJ:HH, TorJJ.a, npIIHHMa51 BeJ1II'IIiHY
b..P n , BbI'IIICJIeHHYIO no BbIpaMeHIIIO (240), a b..y = y(t), 6YJJ.eM
HMeTb
x ( aV..
(248)
(249)
aN
ay;;
aN
oQtjJ
oK )
-X
oY cr
( 'MIZ2+{tZ+ ()' + .
oPn oQtjJ
18*
275
oQ",
oN . oN
au;; )( oK oK ap;; ) = O.
oN oP CT - oQ", ' oN
oQ", / . oQtfy
BbIpaLKeHlfe (249a) MOLKHO nO.1)'lJlITb If3 06I.ll.eH <f>OPM)'.1bI
ECJIli nOJIOLKlfTb an = I, TO
-x (av.,z-
oN
--ap;;
oN
f l_ fJ e- zT )
+ . +
ap I + fJe- zT
I
+(,"",-
(249a)
(249) .
I +fJne- zTn
1- fJne- zT n
zT n zT n
e 2 + e- 2""
zT n zT n
e---:r- _ e 2
zT n
th-
2
zT zT n
Dplf Tn -+ 0, th - no.n.CTaBliB 3Ha l IeHlfe th B BbIpaLKe-
2 2
HHe (249) If c.n.eJIaB COKpaI.ll.eHHSI, no.'1)'lJHM <f>OpM)'J1)' (249a).
2) Dpli OTC)'TCTBI1If HarHeTaTe.'1bHOrO Tpy60npOBo.n.a (T = 0;
(J = I) H3 <f>OPM)'J1bI (249) HaH.n.eM
oN
( 1 M , 2 + ." , oK b'TlI I + fJne-zT n + oK oY CT oK ) X
z uz,-.-. Z -.---
oPn 2 I _fJlle-ZTn oQ", --.!!!!... oY cT
, aQ", .
aN oN oN
X ( a.V Z - "7fP;;; ) , ( t z _ ay;; )( oK _ OPCT ) = 0
tfy oN T uO aN oP CT aQ. oN .
- - "'-
oQ", oQ", oQ", /
(2496)
3) £e3 yqeTa KOJIe6aHHH B npYLKHHe H HarHeTaTeJIbHOH MafH-
CTpaJIH (Tn = 0; an = 1; T = 0; (J = 1) H3 BbIpaLKeHHSI (249) no-
JIYlJHM
aN oN
( M'Z2+ti'Z+ 6f+ . ay;; ) , ( a.V z- oP CT ) +
oP n oQ", oN oY CT 4' oN
oQ", / oQqJ
aN oN
+ ( fuo z - au;; ) . ( _ . a;;;;: ) =0, (249B)
oN ap CT iJQ", oN
oQ", / \ oQ", /
276
cJJopCijHKa C 2u8paBJlU'leC1WU npijJ1CUHoU. 1) LL.TU! CPOPCYHKIf, Y
KOTOpOH 06"beM (Va) rH,lI,p03anOpHOH )KII,lI,KOCTH COCpe,lI,OTO'leH OKO-
.;'10 Hr.ibI, BOJ1HOBbIX 5IB.'IeHHH B HeM He B03HIIKaeT. npeHe6pera5I
YTe'lKal\IH rImp03anopHOH )KH,lI,KOCTIf, no H3BeCTHOMY COOTHOllieHIIlO
HaXO,lI,Ifl\1
f
!1.Pn= --.1y= --Oa.1y,
aaVs
.
r,lI,e UJ = - - )KeCTKOCTb rIIAp03anopHOII npY)KIIHbI.
(laVa
nO.'IY'leHHOe BbIpa)KeHIIe ,lI,.151 f','.P n TO)K,lI,eCTBeHHO 3aBIICIIMOCTII
(240), CJIe,lI,OBaTe.TJbHO, ,lI,J15I TaKIIX CPOPCYHOK cnpaBellc1I1BO xapaK-
TepIICTWIrCKoe ypaBHeHIIe (249a).
2) LLJI5I CPOPCYHOK, Y KOTOpbIX rHllp03anOpHa5I iKIIllKOCTb Haxo-
llIITC5I B KaHa.1e ll.1IIHOH La II Ce'leHIIeM fa, Beml'H-IHY /1P n MO)KHO
HaHTII, paCCl\laTpIIBa5I :ony )KIfllKOCTb KaK ynpYrHH CTep)KeHb >KeCT-
KOCTblO (EF) a = .h..-. HCXOllHoe ypaBHeHIIe llJI5I :onoro CJIY'Ja5I:
(la
!1.P n = !1.Ea(EF)a . = .1Ea . ..
fa aa
(250)
HcnO.1b30B3B lla.'Iee ll.15I OTbICKaHII5I clEa pellleHHe, aHa.10rII'lHOe
BbIpa)KeHIIlO (247), nOACTaBIfM nOJIY'leHHOe 3Ha'leHIIe B CPOPMYJ1Y
(250), Torlla
/1P = _ baTa [ dy(t) +0 dy(t-T a ) ]
n 2 dt a dt '
(251)
T _ 2La
rlle a - - BpeM5I llBII)KeHII5I BO.1HbI ,lI,aB.'IeHII5I no KaHaJ1Y C
aa
rHAp03anopHOH )KUllKOCTblO B 06a KOHII.a;
aa - CKOpOCTb pacnpocTpaHeHH5I BO.1HbI .n.aB.1eHIf5I B
rH.lJ:p03anOpHOlI )KIfllKOCTIf;
Oa - IW3cpcpUII.IfeHT, Y'lHTbIBalOlll.lfi1 YC.'IOBIf51 OTpaiKe-
HII5I BOJ1HbI .lJ:aBJleHU5I Y BXO,lI,Horo KOHII.a KaHa.TJa
C rUAp03anopHOH iKII.lJ:KOCTblO.
YpaBHeHH5I (251) U (248) TO)K.lJ:eCTBeHHbI, 'CoTIe.lJ:OBaTe.'IbHO, .lJ:JIH
paccMaTpIIBaeMoH rUllp03anopHoii CPOPCYHKIf npIIMeHIfMo BbIpa)Ke-
HIfe (249), npu 3TOM {) = 6a H Tn = T 3'
PerneHHe XapaKTepHCTH eCKOrO ypaBHeHHH npHMeHHTeJ1bHO K TOn-
J1IfBHOH CHCTeMe .lI.H3eJ1eH 51M3. PellieHIfe ypaBHeHl15I (249) B 06w.el\l
BIf.'l.e ,.'J.OCTaTO'lHO Tpy.n.oel\lKO [88], n03TOMY OrpaHH'lIIMC5I aHam130M
'laCTHoro c.'IY'la5I, KorJ],a KO 1e6aHl15lMU B npY)KIfHe npeHe6peralOT
[68]. 1.1.,,151 3TOrO npllBe,.'J.eM 3aBIfCIfMOCTb (249a) K BIf;!y
cD (z) + mp(z)e -Tz = 0,
(252)
277
rJI.e
<D(z) = AZ3 +- BZ2 + Cz + D;
'IjJ(z) = A Z 3+Ez2+Gz+H;
A = aV cjJM';
aN
B = aV,pf}-M' ap CT + M' !..:.. ;
oN ap
aQ,p
c=av,p ( aK {)' + . : T - ) -f} : T _
ap n aQ,p aN oY CT aN
aQ,p aQ,p
-fu ( aK . : T - ) +f} ;
oQ,p..!!..!!.....- oP CT ap
oQ,p .
oN oN
D = _ . oY CT _ ap CT ( oK {)' _ \ +
oP CT oPn oY cT ) . 1 1
oQ,p oQ cjJ
+ ( {)' + . O T _ oK ) !!:..;
oPn oQ,p oN OYcT ap
oQ,p
E=B-2M' '
ap ,
G=C-2f} .
ap ,
H=D-2 ( {)' + oK , O: T _ ) !!:...
oPn oQ,p oY CT ap
iJQcjJ J
:y paCnbIJ1I1TeJ1f! <POPCYHKll JI.ll3eJ1ei1 51M3 f uO = f u.
TIOCKO.7IbKY HllLKe 6YJI.eT JI.aHO cpaBHeHlle pe3YJ1bTaTOB pa<
no t!}J0pMy.'1e (252) C perneHllf!Mll, cooTBeTcTBYIOll1.llMll K0J1e6aJ
B 6ecKoHe4Ho JI. llHHOi1 HarHeTaTe bHoH MarlicTpa ll liJ1ll OTC
278
(253)
(254)
(255)
Bl-IlO KOlIe6aHHM B nOCJ1e.lI.HeM:, nOJ1YIIHM He06xO.lI.HMbIe .lI.JIH ::noro
<p O pl\IYJ1bI.
113 ypaBHeHHH (252) npH 0' = 0 HJIH T -+ 00
-(J
<D(z) = O.
(256)
BbIpa)KeHHe (256) onHCbIBaeT KOJle6aHH5I 3anopHoro opraHa
npH HarHeTaTeJIbHOM: MarHCTpaJIH 6eCKOHelJHOM .lI.J1HHbI.
CJ1YlJaM: OTCYTCTBHH K0J1e6aHHM: B HarHeTaTeJIbHOM: MarHCTpaJ1H
H npY)KHHe, paccMaTpHBaeMbIM: B pa60Te [38], onHCbIBaeTCH <POp MY-
J10M (249B). OH MO)KeT aHaJ1H3HpOBaTbC5I H no ypaBHeHHlO (252),
eCJ1H npHHHTb 0' = ] H T = O.
MeTO.lI. pelIIeHHH ypaBHeHHH (252) paccMaTpHBaeTC5I .lI.JIH 3aKpbI-
TOM: <POPCYHKH C MHOrO.lI.blplJaTbIM paCnbIJ1HTe.'leM, KOTopaH cxeMa-
TI1IIeCKI1 nOKa3aHa Ha pHC. 166, a ee paCnbIJII1TeJIb Ha pI1c. 31. lI.J1H
noM: <P0PCYHKI1 ypaBHeHHe CTaTI1lJeCKOrO paBHOBeCI1H HrJIbI HMeeT
BI1.lI.
PCT(fu-f )+ p;Tf +Pn = 0,
(257)
r.lI.e
Pn = -Pq,ofa-fJ'YcT;
(258)
3.lI.eCb
f,; - nJIOll.J,a.lI.Ka I1rJ1bI, Ha KOTOpylO .lI.eMcTByeT .lI.aB-
J1eHHe P;T. 00 Mepe nO.lI.'beMa I1rJIbI BeJ1I1lJI1Ha
nd 2
f YMeHblIIaeTcH OT f = + npI1 Y = 0 no
, nd K
f u = 4. HeKOTopbIe HCCJIe.lI.OBaTe.'lI1 npI1HI1-
MalOT f = O. B .lI.aJ1bHeIIlIIHX paCIIeTax 3TOM:
rJIaBbI f ' = 05 ...::.. ( d 2 + d2 ) 0
u ' 4 X PK '
f = ...::.. ( d 2 _d 2 )
.it 4 u x
- nJ10ll.J,a.lI.Ka I1rJ1bI, Ha KOTOPYIO .lI.eMcTByeT .lI.aB-
JIeHI1e p!fJo.
YpaBHeHI1H pacxo.n:a TOnJII1Ba lJepe3 .n:pOCCeJ1HpYlOll.J,I1e
H con..'10BbIe OTBepCTI1H paCnbIJII-ITeJ1H:
ceIIeHHH
ry
, Q p I _ O .
P - p ---
CT Ij 2 '(fJAc)2 - ,
ry
Q p
N(PCT' Qq" YCT) = PCT-Pq--.X(YCT) = 0,
2
(259)
(260)
r.lI.e
I I
X (YcT) = (!1cf C>2 + (!1Hf H)2
(261 )
279
BeJ1H4HHa, 06paTHaH KBaApaTY 3KBHBaJ1eHTHOrO npOxOA-
Horo ce4eHHH pacnbIlIHTe.1H;
f.., - nJIOlll.aAb MHHHMa.1bHoro npOXOAHoro ce4eHHH Me)j{AY 3a-
nopHbIMH KOHycaMH. llJ1H Y;?:: d PK ( ctg.2...-ctg 2!.. ) n.10-
222
llI.a,n:b f.., IJ.OAc4HTbIBaeTcH no 4>opMYoi1e (45).
MCK.1lO4aH H3 BbIpa)j{eHHH (257) Be.;1H4HHY P;T' HaH,n:eHHYlO no
4>opMYJ1e (259), no.rrY4HM
.J '
K(PCT' QcfJ' YCT' Pn)=PcT(fu-t )+ Q;p . ( t ; )2 +P"f:+Pn=O. (262)
Pema51 COBMeCTHO ypaBHeHH5I (260) H (262) C Y4eTOM BbIpa)j{e-
HHH (258), onpeAeJ1HM 3aBHCHMOCTH Q(/j = f (YCT) H PCT = {(YCT):
rT I
I Pc/Jofa-P"fu+b'YCT
Qc/J=V pl/ f ,
" (!tcfd 2 + (t u- f u)z (Y CT )
(263)
_ Pc/Jofa-P,JU+b'YcT ( )+
PCT - , 'X YCT P",
fu ( ' )
(!tcfcF + fu-fu Z(Y CT )
(264)
YaCTHbIe npOH3BOAHbIe onpeAeJ151lOTC5I .lI.H4>4>epeHlI,HpOBaHlieM
ypaBHeHHiI (262) H (260):
oK _ _.'. oK f . I
oP CT - tu tu, oQc/J == (!tcfcF pQrp.
oK =0. = 1.
aYcT ' oPn '
..!!..!!....- _ l' oN _ _ Q ( ) .
o -, O Q - P rp'X YCT ,
PCT rp
'J
oN = _ pQ;p . OX(Y CT )
oY CT 2 oY CT
(265)
r,n:e
OX(YCT) = _ . o!tllfH
OYCT (!tHfll)3 oY CT
(266)
OOACTaBHB HaHAeHHbIe 3Ha4eHHH 4aCTHbIX npOH3BOAHbIX B 3a-
BHCHMOCTH (255), nOJIY4HM
280
A = aV£j1M'; i
B - V . .'< -'- Ai' + M ' fT .
- a £j'U I - ,
pQq,Z(Y CT ) ap
°X(Y CT )
C - V 11.' I V f pQ 0Y cr + it +
-a t/JU ,a t/J-'-'---:--
( tcfd 2 X (Y cT ) pQq,Z(Y CT )
f [t .', f I ] , ... f T
+ u u-tu-t-- ( f ) 2 .=--- ( ) T l!"-;
!-tc C X YCT ap
OX (Y cr )
D = 6' Qt/J . °YCT ( f -r ) +
pQq,X(Y cT ) 2 Z(Y CT ) It u (267)
[ , .J °Z(Y CT ) ]
+ f r fu pQ;p oY cr '()' .
_ (!-tcfcf . . X(YCT) -;- ,
E=B-2M' '
ap ,
G=C-2tt .
ap ,
[ OX (Y cr ) J
H=D-2 -+. PQ£ . °Y cr +()' .
(!-tete> 2 X (Y cr ) _ ap
BeaW.JHHbI K03<P<PI1ll.l1eHTOB A, B, C, D, E, G, H
HBJIHIOTCSI Te-
°X(Y cr )
oY cr
(266)
rrepb <PYHKl.{Hei'I TO.:'IbKO rroaO)J{eHI1H Hr:IbI. 3Ha'leHHH X (YCT) ;
I1 Qif; HaXO,lI,SITCSI COOTBeTCTBeHHO ITO <popMYJ1aM (261),
H (263).
)],aJIbHei'Irnee perneHfIe COCTOHT B OITpe,lI,e.leHHH KopHeH ypaBHe-
HHSI (252) ITPH H3BeCTHblX 3Ha'leHHHX BXO,lI,Hll1.HX B Hero K03<p<pHll.H-
eHTOB. npH 3TOM B 06JlaCTH HeYCTOHqHBOH pa60TbI <POPCYHKH KOp-
HH .l1.0.1)J{HbI 6bITb MHHMbIe C UO,lIO)l{HTe,lbHOH JLei'IcTBHTeJIbHOH 'la-
CTbIO. Ka)J{.l1.aH ITapa KOMITJ1eKCHbIX KopHeH Z" = A" :!:: iffi" COOT BeT-
cTByeT KOoi'Ie6aHHlO HrJ1bl C qaCTOTOH K-H rapMOHHKH. l1rJ1a 6YAeT
IWJ1e6aTbCH C qaCTOTOH TOIl rapMoHHKH, ,lI,.'IH KOTOpOH 'A" HMeeT HaH-
60oi'Ibrnee 3HaqeHHe, eCJ1H n0J10BHHa aMIT.'IlITY,lI,bI Ko.'Ie6aHHH He upe-
BbIrnaeT paCCTOHHHH OT nO,,'IOllieHHH ll.eHTpa I{Q.TJe6aHHH ,lI,O ce,lI,J1a.
Kor,lI,a aMUJ1HTY,lI,a KO,'Ie6aHHH 60Jlbrne 3Toro paCCTOHHHH, I1rJ1a KO-
oJ'Ie6oi'IeTCH C qaCTOTOH coJ'Ie,lI,YIOll1.eH rapI\WHHKH. Ha rpaHHl.{e YCTOH-
tIHBOCTH "." = 0 HrJ1a COBeprnaeT rapMOHWIeCKHe KOoi'Ie6aHHH. ll,,'IH
YCTOHqHBOH 06J1aCTH pa60TbI <POPCYHKH 'A" < O.
281
YpaBHeHHe (252) HMeeT 6eCKOHelJHOe MHo:m:eCTBO KopHeH. 11.0'151
ux OT CKaHH5I OCTaTOqHO y o6eH H HarJ151AeH MeTO TpaeKTopHH
KopHeH [19]. B 3TOM MeTOAe HCnOJIb3YlOTCH Ba ypaBHeHHH, nepBoe
H3 KOTOpbIX n03B0J1HeT nOCTpoHTb TpaeKTopHlO KopHeH B Koop HHa-
Tax I.n - iw n , BTopoe - nOCTpOHTb B Tex :m:e Koop HHaTax JIHHHH
paBHbIX 3HaqeHHH cr. TO'IKH nepeCeqeHI1H TpaeKTopHH KopHeH C JIH-
HHHMH cr = const alOT HCKOMbIe perneHHH. rpa<l>H'IeCKOe perneHHe
3a aqH Mo:m:eT 6bITb 3aMeHeHO aHaJIHTWleCKHM B CJIYlJae npHMeHe-
HH5I l..I.BM. PaClJeT CYIllecTBeHHO ynpolllaeTCH npH onpe eJ1eHHH pe-
1KHMHbIX napaMeTpOB H lJaCTOT K0J1e6aHHH HrJIbI J1H rpaHHI.I.bI ne-
pexo a OT YCTOHqHBOH pa60TbI <l>OPCYHKH K HeYCTOH'IHBOH.
11.mI rpaHHI.I.bI YCTOHlJHBOCTH An = 0 ypaBHeHHH TpaeKTopHH KOp-
HeH H KpHBbIX cr = const npeo6pa3YlOTCH K BH y
{A2w 6 -I- (BE -A(C + G}l w 4 -I- (CG- BfJ -ED)w 2 -I- DfJ} tg wT-
-{(B-E)Aw 5 -1- [CE-BG-A(D-fJ)] w 3 +(DG-CfJ)w] = 0; (268)
A2(cr 2 -1)w 6 + [cr 2 E2_B2_2A(cr 2 G-C)] w 4 -1-
-I- (2BD-2cr 2 EfJ -I- cr 2 G2 _C2)W 2 -I- cr 2 fJ2_ [;2 = o. (269)
BbIpa:m:eImeM (269), KOTopoe nO.ll:CTaHOBKOH npHBO.ll:HTCH K ypaB-
HeHHlO TpeTbero nOp5l1I.Ka HJ1H pernaeTCH Ha l..I.BM no CTaHlI.apTHOH
nporpaMMe, onpe eJ1HeTCH 3aBHCHMOCTb w = f (y). LLaJ1ee HaXO 51T-
-CH Te 3Ha IeHHH Wnp H Ynp, npH KOTOpbIX J1eBaH 'IaCTb ypaBHeHHH
(268) o6paIllaeTcH B HYJIb. f10CK0J1bKY 3TH 3Ha'IeHli5I O HOBpeMeHHO
Y OBJ1eTBOp5l1OT 060HM ypaBHeHHHM, OHH HBJIHlOTCH HCKOMbIMH pe-
meHHHMH. 11.J1H 3Ha'IeHHH cr = ::!:: 1 Bblpa:m:eHHe (269) npHBO HTC5I K
1\.Ba paTHoMY ypaBHeHHlO, 'ITO ynpoIllaeT perneHHe 3a alJH.
PaClJeTbI H3J1o:m:eHHbIM MeTO OM 6bIJ1H BbInOJIHeHbI J1H <l>OPCYH-
KH .lI:H3eJ1eH 51M3 C I.I.eJ1blO OI.l.eHKH BJ1HHHH5I JIHHbI HarHeTaTeJIbHOH
MarHCTpaJIH H YCJIOBHH OTpa:m:eHH5I BOJ1Hbl 1I.aBo'leHHH y ee BX01I.HOrO
1\.OHI.I.a Ha nOoi'lo:m:eIme rpaHHI.I.bI YCTOHqHBOCTH H lJaCTOTY KO.1Je6aHHII
Hr J1bI.
I1cXO.ll:IIbIe napaMeTpbI, npHHHTbIe npH paCqeTe:
_ Kr / ceK 2
M' = 353. 10- 1 ' ; it = 0,04 Kr. ceKfcM;
CM
a = 80. 1O- 6 04 2 /Kr; Vg; = 1,58 CM 2 ; 6' = 200 Kr/CM;
fr = 0,0314 CM 2 ; P = 0,84. 10- 6 Kr. ceK2fcM 4 ;
a = 0,12. 10 6 cMfceK; d u = 0,6 CM;
d pn = 0,12 CM; <I = 60°; T = 59°; L = 5 7- 150 CM; d x = 0,26 Chi;
p.cfc = 0,00278 CM 2 ; lu = 1; pv, = 0; p o = 125 KF/CM 2 ; -1 a
l.
Pac1leTHbIe 3aBHCHMOCTH qaCTOTbI KOJIe6aHHH 'V np OT .lI:JIHHbI Ha-
THeTaTeJ1bHOH MarHCTpaJ1H .II.J'lH + 1 a 0 nOKa3aHbI Ha
pHC. 168, a, a JIH -1 a 0 - Ha pHC. 168, 6. 3HaqeHHH pe-
* BCJlII'-IHHa pg; 0 6blJla BbI6paHa IICXO.ll.H 113 TCXHHtJeCKIIX B03MOLKHOCTCH CTCH-
.,lla nocTo5JHHOII nO.D:a'-lH. .
282
LKHMHbIX napaMeTpOB (Y"p H Q"p) <POPCYHKH .lJ.JIH rpaHHIJ;bI YCTOH-
IJHBOCTH H306pa)KeHbl COOTBeTCTBeHHO Ha pHC. 169 H 170.
Ha pHC. 168, a HaHeCeHbJ LJaCTOTbI KOJIe6aHHH Hr.'lbI C pa3J1H'lHbI-
MH rapMoHHKaMH, cooTBeTcTBYIOllLHe YCJ10BHIO I,,, = O. 3TH lJaCTOTbL
H cooTBeTcTBYIOlll.He HM 3U8LJeHI-IH pe}KHMHbIX nap8MeTpoB <POPCYU-
KH H8 pHC. 168, a, 6 H 169 H 170 nOK83aHbI CnJ10111HbIMH .'lHHlISIMH.
o
v rq
\.,
Il rli
2000
_J')lnf
_V rs
(000
2000
VI
t--
V n ,
fOOO
a)
¥27r""UJT 5/27T
- /'11
7T;' 7.:fj;i"g;i?T
o
20
40
60
80
100
120
1M
LCM
PI1C. 168. 113MeHeHI1e '-IaCTOTbl KO.1c6aHlill Hr.1bl 1I npYLlmHbl <lJ0PCYHKH,
a TilK)KC cTo.16a )KI1.!J.KOCTH B HafHCTaTCJlbHoi1 MarHCTpaJlII B 3aBIlCIIMO-
CTI1 OT .!J..1IIHbl nOCJJC.D:HCH npH:
a) +J?U? 0; 6) -! ..U O
C YBe.'lH'leHHeM .lJ..'lHHbl L lJaCTOT3 Ko.'le68HHH nOCTeneHHO CUH-
)KaeTCH, 3 3H3LIeHlIe Y"p (Q"p) B03p8CT8eT, CHCTeM3 CT3HOBBTCH .lJ.H-
H3MHLJeCKH MeHee YCTOHLJHBOH. KOr.lJ.8 no Mepe YBeJ1lILJeHHH L npo-
n
H3Be.lJ.eHlle wT CTaHOBHTCH KpaTHbIM -, CK3 L IKoo6pa3HO B03p3cTaeT
2
LJaCTOT8 C nepeX011.OM Ko.'1e6mmH Ha c.'le11.YIOlll.YIO 6o.'lee BbICOKYIO
rapMOHll1<Y. DpH 3TOM BeJIH l lHH3 Y"p (Q"p) YMeHblilaeTcSI, T. e. 11.H-
H3MllLJeCKaSI YCTOHLJHBOCTb CHCTeMbI lJaCTHLIHO BOCCTaHaBJ1HB3eTCH.
. n
T3KHe nepex011.bI Ua6JII011.3IOTCH npH a > 0, eCJ1H roT = (2K - I) -;
2
;t
npB a<O, eCJIB wT= (2K+ 1)- (rAeK=0,1,2,3,...-nOpSI11.-
2
KOBbIH HOMep r3pl\WUHKH KOJIe6aHHH), LITO COOTBeTcTByeT .lJ.JIliHe
283
I'
--
-- --
'k p CM
4018
o,011f
0,010
0,006
O UJT I
0,002
0 ?(J 4(J 60 S(] {(](] 120
(}"p
1/ eNfteK
30
I
L CM
PHC. 169. 113MCHCHHC pCLKHMHbIX napaMeTpoB Ij:JOPCYHKH Ha rpaHHl.\e YCToii.-
'/HBOCT!! B 33B!!CHl\rOCTI! OT ,J:.1!JllbI lIarHCTaTCJ1bHOH MarHcTpa.111:
/, 2. 3. 4 - nOp>l)J.I<OBblJ"i HOMep rapMOHHKH" - 0 = 1.0; -"-"-" (J .
0,90; (J = 0,75
Qxp
elf!
eeK
0,014
--
...
JO
-<::"
(I'
20
Y"pCM
0,0f8
I
0,010
I l
0,006 . I
/ i //,
f27r<;;GJT Jjz1( ./ flnT UJ T,;; 7j27r
4002
0 20 40 60 80 100 ftO 140 LCM
Pile. 170. 113MCHCHHC pCLKHMHbIX napal\teTpoB 1jJ0PCYliKH Ha rpaHlIl.\e YCTOil-
'-IHBOCTH B 3aSHCHMOCTH OT .D:JlHHbI HarHcTaTc.1bllOi1 ManlcTpa.TJ!1:
/, 2, 3, 4 - nop")],I<OBbIi! HOMep rapMoHHKH; (J = -1,0;
= 0,90; - '-'- a = -0,75
284
HarHeTaTe.'1bHOli MarnCTpa.7JH 24, 110, 200 CM H T. D.. (pHC. 168, a) H
66,156 CM H T. D.. (pHC. 168,6).
B.'1HHHHe YCJ10BHll OTpa:iKeHHH BO.'1HbI A8B.'1eHHH Y BXOAHoro KOH-
a HarHeTaTe.'1bHOli MarHcTpa.'1I1 M01KHO o eHHTb, eC.!JH corrOCTaBHTb
11.aHHbIe pI1c. 168, a n pHC. 168, 6. Opn (J> 0 (pHC. 168, a) Kone-
6aHlIH I1r.'lbI Ha rpaHH e YCTOH1.JHBOCTH B03MO:iKHbI C 1.JaCTOTaMH, 11..1H
KOTOpbIX Be.'1H'.JHHa npOH3Be11.eHHH (OT .1e}KHT B npe11.e.'lax 0 roT
-<....::.; n roT n H T. JI,. YC.loBHe (J < 0 (pHC. 168, 6) no-
2 2. 2
3BO:IHeT no.'1Y'lHTb 1.JaCTOTbI Ko.'1e6aHHii, 11..151 KOTOpbIX (OT
2
3 5 7
-< - n;-;: roT - n H T. JI,. YMeHbweHHe a6C0J1IOTHOrO 3Ha'le-
2 2 2
HHJI (J He OK83bIBaeT cymecTBeHHoro
BJIHHHHH Ha lJ:aCTOTY Ko.7Je6aImH Hr-
JIbI, HO BbI3bIBaeT CHH:iKeHHe nOJI,"be-
Ma Hr.!JbI Ynp H ceKYH11.HOrO paCXOJI,a
Ton.1HBa Q",p lJ:epe3 <POPCYHKY. 1-13
11.aHHbIX pHC. 171 BH11.HO, IJ:TO 11.l!H
O {J 0,85 B03MOlKHbi K0J1e6aHHH
Hr.!JbI C IJ:aCTOTaMH TO.'IbKO nepBOI-!
rapMoHHKIL CJ1e11.OBaTeJ1bHO, C
YMeHbllIeHHeM a MnJ1IlTY.lI.bI BOJ1HbI
JI,aB.leHHH, OTpa:iKaIOIlleHCH OT BXOJI,-
Horo KOH a HarHeTaTeJIbHOH MarH-
CTpaJ1H (YMeHbllIeHHe I (J I), 11.HHa-
MHIJ:eCKaH YCTOll'lHBOCTb CHCTeMb!
nOBbIllIaeTCH.
C e.'Ib1O n011.TBep:iK11.eHHH nOJIY-
IJ:eHHbIX paCIJ:eTHbIX 3aBHcHMocTeii
6bI.la 3KcnepHMeHTaJIbHO onpe11.e.!Je-
Ha IJ:aCTOTa KOJIe6aHHH Hr.!Jb! npH
H3MeHeHHH 11.JIHHbI HarHeTaTeJ1bHO-
1'0 Tpy60npOB011.a Ha CTeH11.e, 06ec-
neIJ:HBalOll.(eM nOCTOJIHHOe 11.aB.'leHHe B aKKYMYJIJITOpe 1 (CM.
pHC. 166). YCJIOBHe oTpa:>KeHHH «(J = 1) BOJ1HbI 11.aB.leHHH Y BX011.-
Horo KOH 8 H8rHeT8TeJIbHOH M8rHCTp8JIH 6uJIO IIOJIYIJ:eHO YCTaHoB-
KOI-I .J:poCCeJ1HpYIOIllero KpaHa 2. .IIBH:iKeHHe HrJlbI pemcTpHpoBa.locb
HH11.YKTHBHbIM .lI.8TIJ:HKOM H IlIJIeH<poBbiM OC HJIJIOrp8<poM. DOJIYIJ:eH-
HbIe 3KCnepl1MeHTaJIbHbIe TO'lKH \'np 11 Ynp 11.J1H rpaHI1 bI nepexoAa
OT YCTOHL[J1BOH K .lI.p06m. eH pa60Te <POPCYHKI1 nOKa3aHU H8
pHC. 168. a H 169 I'PYRmaMH. BH11.HO, IJ:TO .lI.JIH IJ:aCTOT Ko.!Je6aHI1M
OHH .rr.OCTaTOIJ:HO 6JIH3KO COBnaJI,aIOT C paC1.JeTHbIMH KpHBbIMH. Pac-
qeTHble H :1KCnepI1MeHTaJIbHble 3HaLIeHHH Ynp COBn8JI,aIOT MeHbllie
(CM. pl1c. 169), LITO 06"bHCHHeTCH HaJIHLIHeM nOCT05!HHOM COCTaBJIH-
IOIlleH CI1J1b! TpeHHH Me:iK11.Y HrJ10H 11 IwprrYCOM paCIIbIJ1HTe.!JH. 3Ta
CHJIa TpeHHH BJ1HHeT na rr0J10:iKeHHe eHTpa KO.7Je6aImi'I HrJIbI <pop-
CYHKH.
qOl2
YKpCM
0,008
I vKpzl{
2./
2000
0,004
o
I
1000
o
42
41
46
a8 6
PHC. 171. 3aBIJCIIl\10CTb '-IaCTOTbl KO-
.1JC6aHHll H IlO.!J."bCMa Hr.TJbJ Ha rpaHH-
I.\e YCTOll411BOCTil OT YC.l0BIli1 OTpa-
)KCHII5I BO.1HbI .!J.aI3.'ICHH5I Y BXO,QHoro
KOHl.\a TOTI.TJIJBOnpOBO,Qa:
1. 2 - nopfl.l1.KoBbli1 HOMep rapMOHHKH
283
Ha pHC. 168, a HaHeceHbI (KpeCTI:IKaMH) TaKiKe 3KcnepHMeH-
TalIbHbIe 3Ha'leHHH 'laCTOT, nG.TIY'leHHbIe npH IlOCTOHHHOH AJ1lme L
. H H3MeHeHHH pacxoA8 TOIIJIHBa 'lepe3 £pOPCYHKY B 06J1aCTH ee Heyc-
TOH'lHBOH pa60T . 3TH TO'lKH AOCTaTO'lHO 6nH3KO pacnOJ1araIDTCH
OT paC'leTHbIX KpHBbIX, COOTBeTCTBYIDIlI.HX 60nee BbICOKHM CJ1e.a.YID-
llUIM no nopHAKY rapMOHHKaM Ko.lIe6aHHH. HanpHMep, npH A.1HHe
L = 100 CM Ha6nIDAaJ1HCb KO.'Ie6aHHH Hr.1bI C 'laCTOTaMH 675, 1100
H 1600 211, COOTBe'fCTBeHHO paC'leTHbIe 3HaIJeHHH AOCTHraJ1H 698,
1030 H 1500 211. C.TJeAyeT OTMeTHTb, 'lTO C B03paCTaHHeM 'laCTOTbI
Kone6aHHH paCXOLKAeHHe paClleTHbIX H 3KcneplIMeHTanbHbIX AaHHblX
YBeJ1l1IJHBaeTCH. OOCJ1eAHee MOLKHO 06'bHCHHTb TeM, 'lTO npH AaHHOM
paC'leTe He Y'lHTbIBanHCb BOJ1HOBbIe HBneHHH B npYLKHHe TomIHBHOM
£pOPCYHKH.
3KcnepHMeHTa.1bHbIe AaHHbIe no 'laCTOTaM K0J1e6aHHH, npHBe-
,Il,eHHbIe B pa60Te [88] AJ151 £P0PCYHKH C MaccoH ABHLKYIlI.HXCH .a.eTa-
.'IeH, 6J1H3KOH K paCC'lHTbIBaeMoH, H ycnoBHH oTpaLKeHHH BO.1HbI
(j = -1, TaK)Ke cor J1acYIDTcH C paC'leTHbIMH KpHBbIMH (CM.
pHC. 168, 6). Ma"lo OT .J1H'laeTCH H A.'1HHa L, npH KOTOpOH npoHcxo-
AHT nepexoA C OAHOH rapMoHHKH K0J1e6aHHH H8 ApyrYID.
LI.nH Ol(eHKH B.'1H51HHH Y'leTa AHHaMH'leClmX flBneHHH B HarHeTa-
Te.1bHoH MarnCTpa.'1H Ha 'laCToTY K0J1e6aHHH H pefKHMHbIe napaMeT-
pbI £pOPCYHKH Ha pHC. 168, a, 6, 169 H 170 HaHeceHbI nHHHH I H II,
cooTBeTcTBYIDIlI.He paC'leTaM no ypaBHeHHflM (256) H (249B). OpH
Y'leTe BO.JIHbI, HAYIlI.err TO.'1bKO OT £pOPCYHKH K BXOAHOMY KOHl(Y Ha-
rHeTaTe.'1bHOH MarHcTpanH (L CXJ), no ypaBHeHHID (256) noaY'la-
eM V"p = 742 elf, Y"p = 0,00825 CM, Q"p = 26,4 cM 3 /ceK. ECJIH npe-
He6pe<Jb BO.'IHOBbIMH flBaeHHHMH B HarHeTaTe.'IbHOH MarHcTpam1 11
npY)KHHe, perneHHe ypaBHeHHfI (249B) AaeT V"p = 736 211, Y"p =
= 0,0159 CM, Q"p = 35,6 cJo.t 3 /ceK. OOJIY'leHHbIe 3Ha<JeHHH 'JaCTOT H
pe)KHMHbIX napaMeTpoB AJ1H 060HX c.'1Y<JaeB He 3aBHCHT OT AJIHHbI
Ton.J1HBonpOBOAa.
ConOCTaBJ1eHHe npHBeAeHHbIX AaHHbIX C KpHBbIMH Ha pHC. 168, a,
6, 169 H 170 nOKa3bIBaeT, 'lTO AJ1H OTAe.TJbHbIX AJ1HH HarHeTaTeJ1b-
HOH MarHCTpaJ1H OHH COBnaAaIDT C KpHBbIMH, nocTpoeHHbIMH perne-
HHeM ypaBHeHH51 (252). LI..'IH ,Il,Pyrnx A.TJHH paCXO)KAeHHH 1I.0CTHra-
IDT 100 %. B 06.'IacTH HeYCTOHIJHBOH pa60TbI £pOPCYHKH 3TH paCXOLK-
AeHHH MorYT 6bITb ell1.e 3Ha<JHTe.'1bHee.
Ha pHC. 172 H 173 nOKa3aHO B.'1HHHHe K03£p£p H l(HeHTa AeMn£pH-
pOBaHH51 H MaCCbI ABH)J{Yl1.J.HXC51 AeTa.lerr Ha IJaCToTY KO.'Ie6aHHH
HrJ1bI H pefKHMHbIe napaMeTpbI £pOPCYHKH Ha rpaHHl(e YCTOH<JHBO-
CTH. PaC'leT 6bIJ1 BbIDo.'IHeH A.TJ51 £pOPCYHKH AH3eaeH 5IM3 perneHH-
eM ypaBHeHHH (252) npH L = 70 C-1t H (j = 1. C B03paCTaImeM KO-
3£p£pHI:(HeHTa AeMn£pHpoBaHHH <JaCTOTa KOJIe6aHHH HrJ1bI YBe.1H<JH-
BaeTCfI, a BeJIH'lHHa KpHTH<JecKHx 3Ha'lBHHH nOA'beMa Hrabl fI
pacxoAa TOnJ1HBa CHH)KaIDTCfI (pHC. 172). OOCJIeAHee YKa3bIBaeT H8
TO, IJTO YCTOH<JHBOCTb CHCTeMbI nOBbIrnaeTCH H npH {} > 0,24 aBTO-
KOJIe6aHHH Hr.'IbI CTaHOBHTCH HeB03MOLKHbIMH. YBeJ1H<JeHHe MaCCbI
ABH)KYIlI.HXCH AeTaaeH £pOPCYHKH (pHC. 173) CHH)KaeT qaCTOTY KOJIe-
286
6aHlIi'I. KpHTHlJeCKlie 3HalJeHIIfI peLKHMHbIX napaMeTpOB (Ynp II Qnp)
B03paCTalOT.
PaCCMOTpeHH e Ko e6aHlifi Hr W B npouecce HeYCTOHlJIIBOH pa-
60TbI <POPCYHKII npOIICXO.n:5IT C BbICOKOH lJaCTOTOH. Dpli 3TOM lJaCTO-
Ta KO.l1e6aHHH HrJlbI MOLKeT COBna.n:aTb C 'laCTOTOH C06CTBeHHblX
K0J1e6aHIiH npYLKIIHbI IIJIII CTOJI6a LKII.n:KOCTH B HarHeTaTeJlbHOH Ma-
rHCTpaJ1lI. B pe3YJIbTaTe B03HIIKalOT pe30HaHCHbIe 5IB.TJeHIIH, KOr.n:a
BMeCTO rapMOHIIlJeCKIiX CIiHYCOII.n:aJ1bHbIX KOJle6aHHH n05IBJ15IlOTCH
6eCnOpH.n:OlJH e KOJIe6aHII5I C pe3KIIMII II3MeHeHII5IMII aMn IITY.n:W II
Y"p [ 20
CM
0,016 12
0,008 /;,0
0,02 0,06 0,10
it J<FceJ<
CM
0,14 0,18
PIIC. 172. 3aBllcHMoCTb '-IaCTOTb! KO.TJc6a-
HHll IIrJlbI H pCLKHMHbIX napaMcTpoB 1j:J0p-
CYHKH Ha rpaHII c YCTOll'-lHBOCTH OT K031j:J-
Ij:JHI.\HCHTa 1'1':
1 - Y KP; 2 - Q KP; 3 - "II Kp
V"p2U,
1200
1000
800
200
JOO M /07 J<r-ce,,"
eM
PUC. 173. 3aBHcHMoCTb 4aCTOTbI KO-
.lc6aHui1 Hr.1bI H pCLKIJMHb!X napa-
MCTpOB 1j:J0PCYHKII Ha rpaHHI.\C YCTOII-
'-IHBOCTIJ OT MaCCbI .!J.BHLKYII.\IJXC5I
1.\CTaJlCH:
1 - Y Kp ; 2 - QKP; 3 - "II Kp
pa3pbIBOM KliHeMaTlf11eCKOH CBH3H MeLK.n:y .n:BIILKYll\IIMIIC5I .n:eTa,,'IHMII
<POPCYHKH.
Iho6bI OueHIITb pe30HaHCbI LJaCTOT K0J1e6aHIiH IIrJIbI II npYLKHHbI
<POPCYHKH .n:II3eJ1eH 5IM3, Ha pHC. 168, a, 6 HaHeceHbI .'UlHHH nep-
BOH rapMoHIiKH co6cTBeHHoH lJaCTOTbI Ko.'Ie6aHHH npYLKHHbI. Y:acTo-
Ta KOJIe6aHliJI npYLKHHbI onpe.lI.eJIfI.'IaCb no II3BeCTHbIM <popMYJIaM.
1.13 cpaBHeHIIH KpliBbIX LJaCTOT BH.lI.HO, ITO IaCTOTa nepBoH rapMo-
HHKH KOJIe6aHliH npYLKIIHbI '\In] = 1920 Zl{ 3HalJIITeJIbHO npeBbIlllaeT
LJaCTOTY KOJIe6aHliH HrJ1bI Ha rpaHHue YCTOHlJHBOCTIi. B 06J1aCTH
HeYCTOHlJBBOH pa60TbI <POPCYHKH co6CTBeHHaH LJaCTOTa K0J1e6aJIHH
npYLKHHbI MOLKeT COBna.lI.aTb C LJaCTOTOH KOJIe6aHliH Hr.lIbI. HanpH-
Mep, npB L = 16 CM MOLKeT HaCTynHTb HBJ1eHHe pe30HaHca IWJ'1e6a-
HBH BTOpOH rapMOHBKH .lI.JIH IIr.'lb1 H nepBOH rapMOHHKH .lI.J15I npYLKH-
HbI. TaKOH pe30HaHC Ha6J1lO.lI.aJ1C5I npH 3KcnepHMeHTa.ilbHbIX BCC.'Ie-
.lI.OBaHHHX Ha MaJ1bIX pacxo.lI.ax Ton.rIHBa 'lepe3 <POPCYHKY. TOLJKa pe-
30HaHca Ha pHC. 168, a OTMe'leHa 6YKBOH R.
287
I 'I I
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p..5:af- . I
g g: C-::- g
...... := 0.. I. I 1".. ('.,
=s: o2.o I 8
:::f L-. C\3 ;< "-' f'-.. 0' . ct-
O:s:o.. 03U u
:I:S;: o..c. 0 :;.
& ::::'+-8;::lj?
- t: ;g ;> o?
. Q) c::: :::{ i:Q ::
:3 ;, ,II-I
o.. f- _;...11,-')
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288
4aCTOTbI co6cTBeHHbIx I<oJIe6a-
HI1H cTo.'!6a :tKI1)].I<OCTI1 B HarHeTa-
Te.1bHoH MarllCTpaJIH 6bIJIlI paccqll-
TaHbI no lfJopMy.'!e [57]
(VBx-V,p)f r v K
tg vKL = .) .) , (270)
f;;. + VBY ,pv
r.J,e Vex - 06'beM TOnJIHBa Y BXO)].-
Horo I<OH a HarHeTa-
Te.TJbHOH MarHCTpa.TJH.
B OTJ1HIme OT 1fJ0PMYJI, npl1Be-
)].eHHbIX B pa60Te I87], Bblpali\.eHl1e
(270) yql1TbIBaeT 06'beMbI TOnJ1I1Ba
no J{OH aM Ton.TJI1BOnpoBo)].a.
nOcJIe onpe)].eJIeHHH 113 Bwpa-
)KeHI1H (270) 3HaqemIH Un qaCTOTa
c06CTBeHHbIX Ko.'Ie6amIII HaXOLUIT-
CH no 1fJ0pMy.TIe
'V TK = v . (271)
2JT.L
B HarneM cJ1yqae npn YCTaHoBKe
)].pocce.TIlIpYIOIllero KpaHa 2 (CM.
pl1c. 166) 06'beM B IIITy epe KpaHa
co CTOpOHbI HarHeTaTe.'1bHOrO TPY-
60npOBo)].a Vex"'" V!p, Tor)].a 113
1fJ0PMY.'1 (270) 11 (271) no.TIyqaeM
ka k
'V TK = - = - ( 272 )
2L T'
r)].e k = 0, 1, 2, 3, 4, ... - nopH)].I<O-
BbIH HOMep rapMOHHKI1 I<OJIe6aHlIH.
<I>opMy.na (272) COBna)].aeT C
aHaJIOrlIqHbIM BbIpa:tKeHl1eM 113 pa-
60TbI 187].
Dpl1 Henocpej],CTBeHHOM npncoe-
.J:lIHeHIJ TonmIBonpOBo)].a K aI<I<YMY-
JIHTOpy )].aBJIeHlIH I1MeeM Vex =
V a -+ 00, TorAa
f T
tgvKL=-.
V,pv K
(273)
3HaqeHI1H qaCTOT v rn , paCCqlI-
TaHHbIe no 1fJ0pMYJ1e (272), HaHece-
HbI Ha pl1c. 168, a, a no 1fJ0pMYJIe
(271) C yqeTOM BbIpa:tKeHllH
(273) - Ha pl1c. 168, 6. XapaI<Tep
H3l\IeHeHlUI LJaCT01'bI KOJIe6aHHH I1rJ1bI q>OPCYHKH COBna.lI.aeT C H3Me-
HeHHeM C06CTBeHHol'l 'laCTOTbI K0J1e6aHH:H cToJ16a lliH,lLKOCTH B Ha-
rHe1'a1'eJ1bHol'l MarI1C1'paJ1l1. .lXJI5I Ha'JaJ1bHbIX rapMOHI1K Kpl1BbIe LJaC-
TOT K0J1e6aHI1:H I1rJ1bI Ha rpaHl1:o:e YCTO:HLJI1BOCTI1 11 LJaCTOT K0J1e6aHI1:H
\"TH paCnOJ1aralO1'C5I Ha 6J1113KOM paCCT05IHl1lJ O,lLHa 01' ,lLPyrO:H 11 MO-
rYT nepeCeI<aTbC5I. C.TJe.n:OBaTe.'IbHO, npH 6J1lJ3KOM B3aHMHOM pacno-
.TJOIKeHHH 11 nepeCeLJeHl1lJ KpHBbIX LJaCTOT MOrYT B03HI1KaTb pe30HaH-
CbI IWlIe6aHI1H HrJ1bI C C06CTBeHHbIMH LJaCTOTaMH K0J1e6aHl1l'1 CTOo'16a
)KILlKOCTI1 B HarHeTa1'e.TJbHOH MarHCTpa.TJH. npH H3MeHeHHH paCXO,lLa
TOIlJ1HBa 'lepe3 q>OPCYHKY 113MeH5IeTC5I LJaCTOTa Ko.TJe6aHHH HrJ1bI, no-
3TOMY MOllieT Hac1'ynHTb pe30HaHC LJaCT01' pa3.HI1LJHbIX rapMOHI1K.
Ha pHC. 174 nOKa3aHa OC:O:HJ1.TJOrpaMMa K0J1e6aHHl'I I1r.TJbI, nOJ1Y-
'leHHa5I npl1 H3MeHeHHI1 pacxo,lLa TOIlJ1I1Ba LJepe3 q>OPCYHKY (L =
= 70 CM). Ka,lLp 6 cooTBeTc1'ByeT K0J1e6aHI15IM Hr.'IbI Ha rpaHH:o:e
YCTOHLJI1BOCTI1 C 'laCToTol'l VKp = 700 c/.{. DpH YMeHbllIeHI1H pacxo,lLa
'laCTOTa K0J1e6aIII1H I1rJ1bI B03paCTaeT ,lL0 750 c/.{ (Ka,lLp 5). B pe-
3y.lbTaTe .n:aJ1bHe:HllIerO YBe.'lWIeHI15I LJaCTOTbI HacTynaeT pe30HaIIC
Ko.!Ie6aHI1H (Ka,lLp 4), BMeCTO CHHycOH,lLaJ1bHbIX Ko.TJe6aHI1:H B03HI1-
KalOT K0J1e6aHH5I I1rJ1bI C pe3KI1MH 113MeHeHl!5IMI1 aMnlII1TY,lLbI. OHI1
BbI3bIBalOT nOBbIllIeHHbIH 113HOC TPYI11-I1XC5I 11 OIlOpHbIX nOBepxlwcTel'l
.n:BHlliYI11-HXC5I ,lLe1'aJ1e:H q>OPCYHKI1 11 6bICTpoe HapYllIeHHe ee perY.1]I1-
pOB3HH5I. .lXaJ1bHel'IllIee CHHllieHHe pacxo,lLa BbIBO,lLI1T CHCTeMY 113 pe-
30HaHca, I1r.1]a Ha'IHHaeT KO.1]e6aTbC5I C LJaCTOTOH "3 = 1440 c/.{ c.TJe-
,lLYIOI11-eH no nOp5IAKY rapMOHI1KH (Ka.n:p 3).
Ka,lLp 1 cooTBe1'c1'ByeT nOo'IOllieHl-I1O Hr.TJbI Ha Ce.lI..le.
DpH pa60Te q>OPCYHI<H Ha ABl1raTe.1]e neYCTOHLJHBbIe pe)KHMbI
pa60TbI Ha6"'IIO,lLalO1'C5I B 30He Ma.TJbIX LJHce.T1 060pOTOB. Ou:eHHBa5I
pacxo.n: TOn.1]HBa LJepe3 q>OPCYHKY no cpe.n:Hel'l 3a BnpbIcK CKOpOC1'H
nO,lLaLJH, MOlliHO onpe,lLe.1]HTb LJaCToTY KOlIe6sHHH Hr.1]bI C yqeTOM H
6e3 YLJeTa ,lLHHaMHLJeCKI1X 5IBJ1eHHH B HarHeTaTeJ1bHOH MarHCTpaJ1I-I I-I
npYlliHHe q>OPCYHKH. DpH .3TOM llie.laTeJ1bHO, r4T06bI napsMe1'pbI CH-
CTeMbI H pelliHMbI ee pa60TbI 6bI.TJH nO,lL06paHbI TaK, LJTo6bI He B03-
HHKaJIO pe30HaHca K0J1e6aHHH Hr.'lbI, cToJ16a lliH.n:KOCTH B HarHeTa-
Te.'IbHol'l l\IarHCTpa.1H Ii npYlliHHbI q>OPCYHKH.
19 33K33 748
r 11 a B a VI. MEnKOCTb PACnblnJIIBAHJllSI TOnnJIIBA
JII PA3BJIITJIIE CDAKEnA
PaCnbIJ1I:lBaHlle TonJ1IIBa, T. e. np06J1eHHe CTPYH Ha MeJIKHe Kan-
JIH, pe3KO YBeJIlI'.JHBaeT nOBepXHOCTb )J{HnKOCTH, IJ:TO YCKopSIeT npo-
lI.eCCbI TenJ10- H Macco06MeHa Me)J{ny HarpeTbIM B03nYXOM H )J{lfn-
KOCTbro. CHH)J{eHHe pa3MepOB IJ:aCTHlI. 06eCneIJ:HBaeT lfX HarpeBaHHe
H HcnapeHHe B KopOTKHe npOMe)J{YTKH BpeMeHH.
<PopMa KaMepbI cropaHHSI H MeTOn npHMeHSIeMoro cMece06pa30-
BaHHSI npen'bSIBJ1SIroT pa3J1HIJ:HbIe Tpe60BaHHSI K paCnbIJ1HBaHHro Ton-
J1HBa H pa3BHTHro <paKe.,a. OpH 06'beMHOM cMece06pa30BaHHH He-
06xonHMbI Me.TJKOe paCnbIJ1HBaHHe TOnJIHBa H nOCTaTOIJ:HO 60JIbIllaSI
rJ1y6HHa npOHlIKHOBeHHSI <paKeJIa B 06'beM KaMepbI C MHHlI!\WJ1bHbIM
nonanaHHeM KaneJ1b Ha CTeHKH. OJIeHOIJ:HOe cMece06pa30BaHHe He
Tpe6yeT np06JIeHHSI OCHOBHOH Maccu CTPYH Ha MeJIKHe KanJIH, HO
nJ1SI C03naHHSI TOHKOH n.,eHKH He06xonHM BnpbICK Ton.TJHBa H3 con-
JIOBOrO OTBepCTHSI C nOCTaTOIJ:HO BbICOKHMH CKOpOCTSIMH.
)],JISI KaMep, pacnO,,10)J{eHHbIX B nopllIHe, Korna TOnJ1HBO IJ:aCTlfIJ:-
HO nonanaeT Ha CTeHKY, B Ka)J{nOM KOHKpeTHOM CJIYIJ:ae B 3aBlfClf-
MOCTH OT lIHCJIa con.10BbIX OTBepCTHH, paCCTOSIHHH no CTeHKH, na-
npaBJIeHHSI H CKOpOCTH nBH)J{eHHSI ra30Boro 3apHna H3MeHHroTcH
Tpe60BaHHSI K Me.TJKOCTH paCnbIJ1HBaHHH H pa3BHTHro <paKe.TIa. Ha
IJ:aCTHIJ:HUX nOnaIJ:ax B pHne TaKHX KaMep OCYIQeCTBJIHeTCH 06'beM-
Hoe cMeceo6pa30BaHHe.
Tpe60BaHHH K MeJIKOCTH paCnUJIHBaHlfH H3MeHHroTcH TaK)J{e no
Mepe pa3BHTHH BnpHCKa TOnJ1HBa B KaMepy cropaHHH. Oc06eHHO
He)J{e.,aTe.'bHO B 3TOM CJIYIJ:ae 06pa30BaHlle KpynHbIx KaneJIb B KOH-
lI.e BnpbICKa. Heo6xonHMO TaK)J{e nO.'YIJ:eHHe nOCTaTOIJ:Horo tLJIH 6bI-
CTporo BOCITJ1aMeHeHlfH IJ:HCJIa MeJ1KHX KaneJ1b B HaIJ:aJIe nOnaIJ:lf
TOnJIHBa.
t. PACnAA CTPYH H nAPAMETPbl. nPHHSlTblE
AnSI XAPAKTEPHCTHKH MEnKOCTH
H OAHOPOAHOCTH PACnblnHBAHHSI
<POTorpa<pHpoBaHHe CTpYH TOITJ1HBa (52], BbITeKaroIQHX H3 Kpyr-
J1bIX oTBepcTHH C pa3J1lfIJ:HbIMH CKOpOCTHMH B OTHOCHTeJ1bHO Heno-
nBH)J{HbIH B03nyx, nOKa3aJ10, IJ:TO xapaKTep pacnana CTPYH, 3aBH-
CHIII.HH nJ1SI naHHoH KOHCTPYKlI.HH conJ1a II llCITbITyeMoro TOnJ1HBa OT
290
CKOpOC1'l! HC1'e'1eHlUl, pa3,,1H'1eH. DpH 1\1aJIbIX CKOpOC1'flX HC1'elIeHHfI
H3 nOBepXIIOCTl! CTPYH B03HHKalO1' OCeCHMMe1'pHlIHbIe Ko.1J:e6aHHfI,
B03paC1'aHHe aMn,,1H1'Y,lI.bI K01'OpbIX npHBO,lI.HT K 06pa30BaHHIO 01'-
,lI.eJIbHHX KaneJIb. C YBeJIHlIeHHeM CKOpOCTH HCTelIeHHH B03HHKalO1'
BO.:IH006pa3HbIe ,lI.e4>opMaI.{HH CTPYH, OCb ee HCKpHBJIfle1'CfI, lITO npH-
BO,lI.HT K BOJIHOBOMY pacna,lI.Y.
DpH HCTelIeHHH CTPYH C 60.TJblUHMH CKOpOCTHMH pacna,lI. CTPYH
HalIHHaeTCfI HenOCpe,lI.CTBeHHO B6JIH3H ConJIa. DpH 3TOM nepBOHa-
lIa,,1bHO 06pa3YI01'CH HHTH, nJ1eHKH H KpynHbIe KanJIH (06J10MKH
CTPYH), KOTopbIe 3aTeM no,lI. AeilcTBHeM CHJ1 nOBepXHOC1'Horo HaTH-
)!(eHHfI H a3pO,lI.HHaMHlIeCKoro conpOTHBJ1eHHfI ,lI.p06f11'CfI Ha 60.1Jee
MeJ1KHe KanJIH. TaKoH pacnall C1'PYH npHHHTo Ha3HBaTb paCnHJIH-
BaIlHeM.
fp3HHQH nepexo,lI.a 01' O,lI.HOH CTa,lI.HH pacna,lI.3 CTPYH K ,lI.PyroH
;:J.JIH pa3J1HlIHbIX )J{HllKocTeH onpelleJIHJI OHe30pre [91]. 3TH rpaHHQbI
nepexOlla 3aBHCHT 01' HalIaJlbHbIX B03MYIlI.eHHH, B03HHKalOIlI.HX B
nOTOKe TOnJIHBa npH ero ,lI.BH)J{eHHH B pacnbI.1JHTeJIe. C B03paCTa-
HHeM HalIaJIbHbIX B03MYIlI.eHHH rpaHHQbI nepeXO,lI.a CMeIlI.aIOTCH B
30HY MeHblUHX lIHCeJI PeHHOJIb.D,Ca.
AHa_1H3 4>aKTopoB, BbI3bIBalOIlI.HX pacna,lI. CTPYH, nOK33bIBaeT,
lJTO HCXO,lI.HbIMH flBJIHIOTCH HalJa,,1bHHe B03MyIlI.eHHH nOTOKa TOn.11-l-
Ba, B03HHKalOIlI.He npH ero .D,BH)J{eHHH B paCnbIJIHTeJIe. 3TH B03MY-
IlI.eHHH BbI3bIB31OT nOflBJIeHHe nepBOHalJaJIbHbIX HCKpHB.1JeHHH QH-
.1JHH.D,pHlJeCKOH nOBepxHoCTH CTPYH npH oceCHMMeTpHlJHOM HJ1H BOJI-
HOBOM pacna.D,e H pa3pbIBbI CTPYH npH paCnbIJIHBaHHH. DpH 3TOM
O,lI.HH HCCae,lI.OBaTe.1JH YTBep)K,lI.aIOT, lJTO HalJaJIbHbIe B03MYIlI.eHHfI B
nOTOKe onpe.D,e,,1f1IOT Me.1JKOCTb paCnbIJll1BaHHfI TOnJ1HBa, .D,PyrHe )Ke,
YKa3HBafl Ha B03.D,eHCTBHe CHJI a3pOllHHaMHlJeCKOrO conpOTHBJIeHHH
Ha CTPYIO Ton,,1HBa, ClJHT3IOT, lITO OKOHlJaTeJIbHoe .D,p06JIeHHe H, c.'Ie-
llOBaTe,,1bHO, pa3MepbI Kane.1Jb onpe.D,e.1JflIOTCfI B3aHMoneHCTBHeM
CTPYH C ra30BOH Cpe.D,OH.
OnbITbI no B,,1HflHHIO HalJaJIbHbIX B03MYIlI.eHHH B nOTOKe TOnJ1HBa
nOKa3bIBa1OT, lITO npe.D,BapHTeJIbHafl Typ6YJIH3aQHfI nOTOKa YJIYlJ-
lUaeT Me.'IKOCTb paCnbIJ1HBaHl:Ifl Ton.11IBa [58]. DOBbIlUeHHe n.10THOCTH
r330Boi:i Cpe.D,bI He npHBO,lI.HT I( CYIlI.eCTBeHHOMY CHH)J{eHUIO cpellHUX
.D,HaMeTpOB KaneJIb [47, 48]. KaK YCTaHOBHJI B, A. KYTOBOH [47], npH
3TOM HeCKO,,'IbKO CHH)KaIOTCfI pa3MepbI KpynHbIx KaneJIb, HO YMeHb-
maeTCfI lIHC.TIO KaneJ1b Ma.1bIX llH3MeTpoB. DOKa OKa3aJ1HCb 6e3Yc-
nelUHbIMH nOnblTKH llaTb paclIeTHbIH MeTO.D, MeJ1KOCTH paCnbIJIHBaHHH
TOn.'1HBa Ha OCHOBe YlJeTa TOJ1bKO CH.'I a3pOllHHaMHlIecKoro B03.rr.eHCT-
BHfI ra3a Ha TOn.11-IBHYIO CTPYIO. D03TOMY MO)J{HO npe.rr.nOJ1ara1'b, '11'0
npH pacnbI.1HBaHHH pacna.D, CTPYH B6,,'IH3H COnJ10BOrO OTBepCTHfI C 06-
pa30BaImeM HHTeH, nJIeHOK H KpynHbIx KaneJ1b npoHcxo.D,HT no.rr. .D,eH-
CTBHe1\I TaKHX 4>aKTopoB, KaK Typ6y.'IeHTHOCTb nOTOKa, BbI,J:eJIeHHe
pacTBopHMoro B Ton.'IHBe ra3a, BH6paQHH conJ1a H HeTOlJHOCTH 4>op-
MbI oTBepcTHfI paCnbI.1JHTeJ1f1 4>OPCYHKH. DpenflTcTBYIOT HalJa.'IbHoMY
pacna,ny CTPYH npH pacnbwHBaHHH .CHJIbI BR3KOCTH H nOBepxHocTHO-
ro HaTH)J{eHHfI TOnJ1HBa.
19* 291
,lJa.'lbHeihuee Ap06J'1eH11e n.'leHOK 11 H11TeH B OCHOBHOM np011Cxo.n:11T
nOD: .n:eikTB11eM CH.TI nOBepXHocTHOro HanDKeHI-IH. ,lJp06.1JeH11e "pyn-
HbIX KaneJ'1b Ha 60.'lee l\1eJ1K11e BbI3bIBaeTCfI cn.'1aM11 a3po.n:11HaMI1lle-
CKoro COnpOTI1B.leH11H ra30BOH cpeJJ.bI. KpynHbIe KanJ111 {89], nona.n:a-
IDllI,11e B nOTOK ra3a, .n:e<popMI1pYIDTCH C 06pa30BaH11eM TOHKOH nJ'1eH-
KH. coe.n:HmJIDmeikH C YTo.1ll1,eHHbIM KOJ1bQOM. n.'leHKa 3aTeM pa3pbI-
BaeTCH, 06pa3YH 60.'lbIllOe '-l11CJ'10 Me"lK11X Kane.'lb, a KOJ1bQO pacna-
.n:aeTCH Ha HeCKo.'IbKO OTHOC11TeJIbHO 60,,'1ee "pynHbIx Kane.1Jb. Co.n:ep-
)J{a!me TOIW11Ba no Macce B n"leHKe 11 KOJ'1bQe COCTaB.1JfleT COOTBeTCT-
BeHHO 30 H 70%.
nH
0 T ....,... ..... ........
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PIIC. 175. CTPY51 B pa3.1H'-IHbIC lj:Ja3bI BnpbIcKa. TonJlHBH3H annap3Typa 51M3,
de = 0.34 .AUt. q" = 115 .A1.A13, n = 450 06/.AlUfl
Ha .n:eq:JOpl\wQmo KanmI .LI,O ee pacnaJJ.a 3aTpa'-lHBaeTCH onpe.n:e-
JIeHl-lOe BpeMH, KOTopoe, BepoHTHO, 6YAeT B03pacTaTb C YMeHbIlleH11eM
JJ.11aMeTpa I<an,,'111. OT'-laCT11, MOLKeT 6bITb n03ToMY, C YBe.'l11'-leH11eM
nJIOTHOCT11 ra30BoH cpe.n:bI, Bb!3bIBaIOW.11M 6bIcTpoe TopMOllieHI1e Ka-
ne.'lb, He Ha6JIIo.n:aeTCH pe3Koro YJ1Y'-lIlleH11H MeJIIWCT11 paCnbIJ1I1-
eaH115I.
B npoQeCce BnpbICKa '-lepe3 MHoroconJ'10BYID <P0PCYHI<y Ha OCHOB-
HOM Y'-laCTKe no.n:a'-l11 CTPYH BbITeI<aeT l13 pacnbI.;'111Te.'lH C 60.1JbIll11MH
CKOpOCTHl\iH, np11 3TOM 11MeeT MeCTO paCnbIJII1BaH11e TOnJ1I1Ba. OJJ.Ha-
1\0 B KOHQe BnpbICKa CKOpOCTb Ha'-!IlHaeT CH11.1KaTbC5I. I IcTC'-leH11e Ton-
_'mBa B 3TOM CJIY'Iae npol1CXOJI.11T np11 Ma.'!OI\! nepenaJI.e .'IaB.'leH11H no..1
.JI.eikTBHeM JJ.BI1llieHI1H I1r.'1bI JI.O ynopa K CeJI..1Y 11 CI1,'! 11HepQml nOTOKa.
292
B pe3ynbTaTe OTMe aeTCH nOHB eHHe 113 COnJ10BOrO OTBepCTHH He-
paCnaBIlleilcH CTPYH C noC.rIen:YIOIl{I1M 06pa30BaHHeM OCeCHMMeTpH -
HbIX H;r1H BO.TIHOBbIX KO.'Ie6aHHH. CTPYH n:a.'Iee paCnan:aeTCH Ha Kpyn-
HbIe KanJH1 (pHC. 175, 176), Ha HeKoTopbIX <poTorpa<pHHx B KOHu.e
BnpbIcKa (pHC. 175) BHn:HbI HHTI1 Ton.1HBa H KpynHbIe 06JIOMKH. CJIe-
.J.yeT OTMeTI1Tb, TO nOCJIe,'I,HHe nop:u.HH TOnJIHBa Bb!TeKaIOT H3 pac-
nbI.'IHTe.TIH B BH.n.e TOHKHX cTpyeK, He 3anO.'1HHH Bcero ce eHHH con.TIO-
Boro OTBepCTI1H (pI1c. 175, 176).
Ha Ha a.'IbHOM Y JacTKe BnpbIcKa Ton.'IHBO BbiTeKaeT H3 pacnbI.'1I1-
';1"1/'/
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PHC. 176. CTppl B pa3.1H'-IHble lj:Ja3bI BnpblcKa. Ton.1HBHafi annapaTypa 5IM3,
de = 0,34 MM, q.., "'" 115 MM 3 , n = 75006/MUH
TeJIH TaKiKe C MaJ10l1 CKOpOCTbIO. DpH 3TOM MOfKeT B03HHKaTb UH-
.'1HHn:pll'IeCIWH HepaCnaBIuaHCH CTPYH, KOTOpaH COxpaHHeTCH o eHb
KOpOTKHH npOMe1KYTOK BpeMeHH. 3aTeM OHa pa3pywaeTcH nOpu.HHl\1I1
TommBa, CJIe.n.YlOlll.HMH 3a HeH C HapaCTalOlll.HMH CKOpOCTHMH
(pHC. 175).
B pe3y.TIbTaTe pacna.n.a CTPYH o6pa3yeTcH 60.Hbwoe IHCJ10 Ka-
neJIb pa3JIH HbIX pa3MepoB. LL.rIH xapaKTepncTHKH pa3MepoB Ka-
neJIb , T. e. MeJIKOCTH H O.n.HOpO.n.HOCTH paCnbI.TJI1BaHHH, npHHHTo HC-
nOJIb30BaTb cpeJI,HHe JI,HaMeTpbI KaneJIb H KpHBble pacnbI.'1HBaHnH.
Han60.TJbwee pacnpoCTpaHeHne nOJIy nJIn cpen:Hne apH<pMeTn ecKnH,
nOBepxHocTHbIH n 06"beMHbIH JI,naMeTpbI KaneJIb, a TaK1Ke CpeJI,HHH
n:HaMeTp KaneJIb no 3aYTepy. Doc.TIeJI,HHi'I n:aeT o.D.HOBpeMeHHoe pa-
BeHCTBO nOBepxHocTei'I H 06"beMOB Kane.TIb cpe.n.Hero .n.HaMeTpa n Ka-
293
neJIb HCTHHHbI:X pa3MepOB. J11060H 113 YKa3aHHblX CpeJI.HHX JI.l1aMeT-
pOB MOLKeT 6bIlTb nO,lLCtIHTaH no opMy.'le
q- V "'E.N.d f
d =
qp "'E.N.dl? '
L L
(274)
r,lLe q H P - 11 poBbIe I1H,lLeKCbI, cooTBeTcTBYIOllI.lle ,lLaHHoMY cpe,lL-
HeMY JI.llaMeTpy;
N i - o6MepeHHoe tIllCJIO KaneJIb, llMelOllI.llX ,lLHaMeTp d i .
3HatIeHHH q II P H paclIeTHbIe BbIpa:rKeHllH ,lL.'lH HaH60.'lee lllHpOKO
HCnOJIb3yeMbIx Cpe,lLHHx ,lLHaMeTpoB Kane.1b ,lLaHbI B Ta6JI. 7.
Ta6/l11l{a 7
cIIoplMYJlbI lI.JlH paClieTa HaH60Jlee UlHpOKO npHMeHHeMbix
CpCAHHX lI.HaMeTpOB KaneJlb
Cpe)\HHi1 I q I p I d qp II Cpe)],HHi1 I q I p I d qp
)\HaMeTp )],HaMeTp
Kane.nb Kane.nb
K
1:NA y--
ApmpMe- I 06'bCM- K 3
d,o=-
TH'-IeCKHH I 0 .. K HbIH, B3BC- N ;d;
:E N; IlleHHblH 3 I d gl =
I no CYM-
:ENid i
MapHOH I
{- .D:.'1HHe
K 2
nooepx- N;d;
HOCTHblH 2 0 d 20 = -
K
":EN i
I
K 3
- ":EN idi
3/ no 3ayre- I
K 3 d 32 =-
":ENid i py 3 2 K
06'bCMHbIH 3 0 d go = -J! I 1: NidI
- I
K
1:N i
1
He Bce Cpe.JI.Hlle ,lLHaMeTpbI SIBJIHIOTCH He3aBHCllMbIMH. MeLK,lLY HH-
MH CYllI.eCTByelI' COOTHOllIeHHe
1
d = [ d o ] q-p
qp p
d po
KpOMe YKal3aHHbIX cpe,lLHHX .lI.llaMeTpOB KaneJIb, ,lLJIH xapaKTepH-
CTHKH Me.TJKOCll'H paCnbIJIHBaHHH npHMeHHIOT TaKLKe Me,lLHaHHbIH ,lLHa-
MeTp d.TII.co, COQ)TBeTCTBYIOllI.llH Op,lLI1HaTe, paBHoH 50% Ha cYMMapHoH
KpHBOH paCnbIJIHBaHHH.
294
(275)
n([) Cpe,lLHHM ,lLllaMeTpaM Kane.TJb MO)KHO xapaKTepll30BaTb O,lLHO-
pO,lLHOCTb paCnbIJIHBaHHH TOnJIHBa. J],J1H ::noro nO,lLCIJ:IITbIBaIOT pa3HO-
CTI-I M'e)K,lLY Cpe,lLHHMl'I ,lLllaMeTpaMH. YBeJ111IJ:eHlle pa3HOCTell YKa3bIBa-
eT Ha YXY,lLlIIeHlle O,lLHOpO,lLHOCTll paCnbIJ1HBaHIIH. DpH O,lLHOpO,lLHO
paCnbIJ1eHHOM TOnJIIIEe 3Tll pa3HOCTll 6Y,lLYT paBHbI HYJ1IO. MO)KHO llC-
nO.'Ib3:0BaTb TaK)Ke OTHOlliemlH cpe,lLHIIX ,lLllaMeTpOB, HanpllMep a20 =
d 20J d so d S2
= -, a30 = - , a32 =- II T. ,lL., KOTopbIe npll O,lLHOpO,lLHOM pac-
d lOJ d lO d lo
nbI.'IH BaHllll paBHbI eJI.IIHIlu,e.
DOJ1ee IIOJIHO MeJIKOCTb H O,lLHOpO,lLHOCTb paCnbIJIIIBaHIIH xapaKTe-
Pll3Yl<OTCH ,lLll<p<pepeHIJ.HaJ1bHbIMll II CYMMapHbIMll KpllBbIMll paCnbIJ111-
BaHllf'I. Hall6oJ1ee IJ:aCTO llcnO.TJb3YIOT KpllBbIe pacnpe,lLeJ1eHI1H 1IHCJIa
1l.IIH 06'beMa KaneJIb.
ECJ111 113BeCTHa KJPIIBa5I pacnpe,lLeJIeHIIH IJ:IICJ1a Kane.llb no pa3Me-
paM, TO Cpe,lLHlle ,lJI,llaMeTpbI KaneJ1b MO)KHO nO,lLCIJ:IITaTb no BbIpa-
)KeHll IO
d qp =
I
d max -q-p
S d n r d ) ] d(d xn )
d min
d m S ax p [ dNi ]
d xn d(d xn ) d(d xn )
_ dmin
(276)
HpH HaJ111IJ:Hll 061beMHbIX KpllBbIX paCnpe,lLeJIeHHSI
I
-q-p
d m s ax q-3 [ dV xn ]
d xn d(d xn ) d(d Kn )
d min
(277)
d qp =
d m s ax p-3 [ dV Kn ]
d Kn d(d Kn ) d(d xn )
_ d min
1. PAC ET MEnKOCTH H O,AHOPO,AHOCTH p.A.CnblnHUHHSI
K HaCTOSlIIJ.eMY BpeMeHll IIMeeTCH 3HaIJ:IITeJ1bHOe IJ:IICJIO TeopeTll-
qeCKIIIX llCCJIe,lLOBamIiH MeJ1KOCTH paCnbIJIIIBaHIIH. B 60J1bIIIHHCTBe CBO-
eM OHH OCHOBbIBaIOT'CH Ha pelIIeHll1l 3a,lLaIJ:ll B3aHMO,lLellCTBllH CTPYll
Tonm:ma C ra30BOll Cpe,lLOll. GllHaKO CJ10)KHOCTb HBJIeHllll, COnpOBO)K-
llaIOillJ.HX npou,ecc pacna,lLa CTPYH II ,lLaJ1bHelllIIero ,lLp06JIeHH5I KaneJIb,
n03B0J1HJIa nO,,1Y'IIITb y,lLOBJ1eTBOpHTeJ1bHbIe 3aBIICIIMOCTll JIlllIIb llJ1H
Ma.lIbJ[X CKopOCTell HCTeIJ:eHIIH HeBH3KOll IJ BH3KOll )KH):{KOCTH. )IJIH
npou,ecca paCnbIJIIIBaHIl51. ,lLa)Ke B caMbIX IIOCJIe,lLHHX pa60Tax {20, 23,
61] He ,lLaeTCSI TeOpeTIIIJ:eCKIIX 3aBHCHMOCTell, n03B0J151.IOIIJ.Hx ou,eHll-
295
BaTb Cpe.n:HHe .n:HaMeTpbl Kaneo'lb. D03TOMY .n:J"lH paClJeTa Me.'1KOCTH
paCnbI.mmaHHH lJall.{e BCerO npHMeHHIOTCH KpHTepHaJ1bHble ypaBHe-
HHH. 4T06bI nOCTpOHTb KpHBble paCnbIJ1HBaHHfI, He06xo.n:m,w 3HaTb
MaKCHMa.'1bHbIe ..'IHaMeTpbI Kane.'1b, nOnYlJaIOll.{HeCfI B npOu.ecce
BnpblCKa.
Ou.eHKa MaKCHMaJ1bHbIX .ll.HaMeTpOB KaneJlb, 06pa3YIOll.{HXCSI npH
BnpbICKe TOnJ1HBa MHOrOCOnJlOBOH (jJOPCYHKOH 3aKpbITOrO THna. ;J.O-
CTaTOlIHO nO.'1HIbIH aHaJl:H3 3KcnepHMeHTaJ1bHbIX H TeOpeTHlJeCKHX IIC-
c.JIe.n:OBaHHH no YCTOHlJHBOCTH OT.n:e.JIbHbIX KaneJIb .n:aH B pa60Te [20].
YCTOHlIHBOCTb Kane.'1b onpe.n.eJ1HeTCH HX B3aHMo.n.el'lcTBHeM C ra30BoH
cpe.n.oiL B pH.n:e pa60T YKa3bIBaeTcH, lJTO KpHTepHeM YCTOHlJHBOCTH B
dKnU nPl )
3TOM cnYlJae MmKeT C,'IY.iKHTb IJ:HCJl:O Be6epa (We = .
aT
KpHTHlJeCKHe 3Ha l leHHH qHCJ1a Be6epa, onpe.n:e."l5HOll.{He 30HY nepe.
xo.n:a OT YCTOH1!.IHBOrO COCTOHHHH KanJ1H K ee pacna.n.y, HaH.n:eHHbIe
Ha OCHOBaHMH 3KcnepHMeHTaJIbHbIX H TeOpeTHlJeCKHX HCCJIe.n:OBaHHH,
.1e.iKaT B llIHpmmx npe.n:e.l:ax (\Ve KP = 10,7 -7- 20).
PaClJeT M8I<CHMa.'1bHbIX .n:mHvIeTpoB l<ane.'1b no KpHTHQeCKoMY
3HalJeHlHO lIHCJIa Be6epa npHBo.n:HT K MOHOTOHHOMY YMeHbllleHIHo
MaKCHMaJIbHOrO .n:HaMeTpa Kane.'1b no Mepe YBe.mlQeHHH OTHOCH-
TeJ1bHOH CKOpOCTH HX .n:BH.iKeHHH B ra30BoH cpe.n.e. 3TO He COBna..'IaeT
C 3KcnepHMeHTaJIbHbIMH .n:aHHblMH. KOTopbIe YKa3bIBaIOT Ha cTa6H-
J1H3au.HIO Kane.TIb no Mepe YMeHbllleHHH HX pa3MepOB. YlJeT 3Toro
HBJIeHHSI c.n.e.JIaE B pa60Te [611, r.n:e .n.aeTCH <popMy.JIa, CBH3bIBaIOll.{aH
MaKcHMa.1JbHbIH H cTa6HJ1bHbIH .n.HaMeTpbI Kano'IH,
9
P2U pdrnax
\VC Kp
(278)
( 1-11 ) :! '
JI d max
aT
f;lI,e U KP - OTHOCHTeJIbHaH CKOpOCTb KanJIH, COOTBeTCTBYlOlll,aH MaK-
CHMa.'1bHO YCTOHQHBOMY .n:HaMeTpy;
d m : 1X - MaKCHMa.'IbHO B03MO.iKHbIH lI,HaMeTp }<an.m-I npH CKOpO-
CTI-I U"p;
We = 10,7 -7- 20 - KpHTHQeCKOe 3HalJeHHe lJHCo'Ia Be6epa;
d CT - .n:HaMeTp Kan.'1H, He pa3PYlllaIOll.{HHCH npH B3aHMo.n:eHCT-
BHH C ra30BOH cpe.n:OH (cTa6HJ1bHbIH .n:MaMeTp) npH 0'110-
60H OTHOCHTe.'IbHOH CKOpOCTH LIBH.iKeHHH Kamm.
DpM Hao'IHlJMH d CT <popMy.JIa (278) n03BOJIfIeT onpe.n:eJ1fITb lIIaK-
CHMaJ1bHbIH LIH3MeTp KaneJ1b npH .n.aHHoH OTHOCHTeJ1bHOH CKOpOCTH
HX .n:BH.iKeHMfI B ra30BoH cpe.n:e. B pa60Te [61] npMBoLIfITCfI 3HaQeHIffI
d CT TO.'1bKO .n:JIH cnHpTa. ,lJ,J1H d CT ' paBHbIx 59 H 104 MKM, lJHCJ10 Be-
6epa COOTBeTCTBOBa.'IO 10,7 npH pe.iKHMe pa3.n:BoeHHfI H 14 npH pe-
.iKHMe paCnbIJ1HBaHHH KanJ1H.
,lJ,JIfI ou.eHKH H3MeHeHHfI M8KCHMaJ1bHOrO ,lI,HaMeTpa KaneJIb ;{H-
3eJ1bHOrO TOIL,"lHBa OT HaQaJ1bHOH CKOpOCTH HX OTHOCHTe.1JbIIOrO .n.BH-
.iKeHHfI Ha pHC. 177 HaHeceHbI 3KcnepHMelITaJIblIbIe 3HalJeHHH d max ,
296
38MepeHHble npll COOTBeTCTBYIOIl{IlX CKOpOCnlX UnO )1.JIH p8CnbIJIll-
re,;leH C pa3J1HLJHbIM JmaMeTpOM COnJIOBOrO OTBepCTHH. MaJ<CHMaJ1b-
HbIe )1.H8MeTpbI Kane.1Jb 6blJIlJ onpe)1.e.1JeHbI npH HCCJIe)1.0BaHHH B
MA,Z:L11 MeJ1KOCTlJ pac-
nbIJ1HB8HHH TOnJIHB8 )1.H-
3eJIbHblMH 3aKpbITbIMI1
4>OPCYHK8MI1 06bJIIHOrO H
K.rIanaHHO-COrr.'lOBOrO TH-
n8 lI8 cTpo6oCKOnfflIeC-
KOn "yCT8HOBKe DO MeTO-
)1.1IKe HAMil [48]. J1H-
HIlH 1 H 2 (pnc. 177) H3-
MeHeHHH M8KCHM8JIbHUX
)1.MaMeTpOB KaDeJ1b pac-
ClJMTaHbI no 4>0pMy.'le
(278) COOTBeTCTBeHHO
JI,JIH We"KP= 14 M We"KP=
= 10,7 npM aT =
= 0,030 Kr( A! H aT =
= 0,0025 KF I At H d CT =
= 30 -"'[KAt. KpHB85I 3
(pHC. 177) nOJ1.CLJHT8H8
R3 COOTHOllleHMH
1-13 8Ha.'lH3a pHC. 177
BH)1.HO, LJTO H8H60J1blllee
lIllc.no 3KcnepHMeHT8.'1b-
HbIX TOLJeK HaXO)1.HTC5I
Me)!{lI.Y KpHBbIMM 1 H 2.
HeKoTopoe Bbma)1.eHHe
3KcnepHMeHTaJIbHbIX TO-
'lel{ B CTOPOHY YBeJIll'le-
HHH d max no cpaBHeHHIQ
C paclIeTHbIM (KpHBOH
1) MOlliHO 06'bHCHHTb
YBej1ffliemIeM )1.H8MeTp8
OTnelJ8TK8 Kan.'lH npH ee
cOYJ1.ap€HHH C nJ18CTHHOH, 8 T8KLK€ H€o6xO)1.HMOCTbIO YlIllTbIB8Tb
BpeMH JI,e OpM8UllH KanJIH OT Ha'l8JIa ee B3aHMOJI,ellCTBHH C r830BOll
cp€J1.oi-'I JI,O MOM€HT8 p8Cn8JI,8. OTKJIOlI€HHe M8KCHM8JIbHbIX )1.H8M€T-
pOB KaneJ1b no cpaBHeIllllO c paC'leTHbIM (KpI1BOll 2) B CTOPOHY
YM€HbIlIeHHH OTI18CTH 06'bHCHH€TCH T€M, 'lTO LJHCJIO KpyrrHblx K8rr€Jlb
Ha nJIaCTHHKe HeBeJIHKO H OHH He BcerJI,a nonaJI,alOT Ha MHKpOl\JOTO-
rpa4>mo.
W€",p=
u 2 d
Pe KG max
= 14.
aT
(279) 200
d m .. r
HKM
700 o.
500
<9
500 0
o
'too
300
fOO
(
x
ex 2
3
tJ
IPP
JPtJ I/ K () NlceK
2tJP
PHC. 177. 113I'vIC!lC!lHC l'vIaKClIl'vIaJ1bHOro .!J.llaMer-
pa KiiTICab B 3aBHCHI'vIOCT!I OT !IX HaQaJ1bHOH
CKOpOCTH ;J..TJ5! paC!lbl.IHTCJlei1 C pa3JlH'-IHbiM
,J,!JaMCTpOM COTI.TJOBOrO OTBCpCTH51
297
ECJ1H CpaBHHTb 3HaIleHHH d max , onpe}J.eJ1eHHbIe no cpopMYJ1e
(279) (KpHBaH 3), C 3KcnepHMeHT8.lJbHbIMH }J.aHHbIMH, TO BH}J.HO,
"lTO npH U"'O > 50 /u/ceK 38MepeHHbIe 3HaIleHHH 3HaIlHTeJ1bHO rrpe-
BbIlliafOT paCIleTHbIe. 1l0cTaToIlHo 6mI3Koe COBna}J.eHIfe no.IJYIlaeTC5I
}J.JIH }J.HaMeTpOB KaneJ1b d max > 400 MKM.
llJlH nO}J.CIleTa BpeMeHH }J.OCTH:>KeHH5I rpaHHI.J.bI YCT01I'.JHBoro co-
(;T05IHHH Karr lH B pa60Te [61] }J.aeTCH cpopMYJIa
IKP.iJecP = 1,65 d Kn · f P , (280)
U KO V P2
JI3 aHaJ1H3a IWTOpOH CJle}J.yeT, IlTO 6bICTpee }J.ecpopMllpYfOTC5I MeJl-
KHe KanJIIf. nOCJle}J.Hee BP5I}J. JIll cnpaBe}J.J1HBO, TaK KaK no cpH3HIle-
-cKOMY CMbICJlY .popMYJla }J.0J1:>KH8 }J.aBaTb perneHHe npll d"K -+ demo
l"Kp.iJeffi -+ 00.
C I.J.eJlbfO OI.J.eHKH BpeMeHH TopMmKeHH5I e}J.HHHIlHbIX KaneJlb, MMe.
fOllUfX 3a}J.aHHbIe HaIlaJIbHbIe CKOpOCTlI U"KO, }J.O .lI.OCTll:>KeHH5I llMI1
KpHTfIlleCKOH CKOpOCTl! BbJBe}J.eM COOTBeTCTBYfOllI.YfO 3aBHCHMOCTb,
HCrr0J1b3Y5I ypaBHeHHe .lI.HHaMWIeCKoro paBHOBeCH5I KanJlH, npHBe-
JJ.eHHoe B pa60Te [61]. npn 3TOM npeHe6pe:>KeM llCnapem!eM KanJII1
JI npHMeM, lITO IWfI(lI.aJI Kan.IJH nepeMelll.aeTC5I B HenO}J.BH:>KHOM ra-
se, Tor}J.a
M dU Kn = _ P 2 F IIl U 2 c ol. ( We )
K dt 2 Kn 1Il't' ,
(281)
T}J.e F'1.U - nOnepe1JHOe ceIleHlle KpyrJIoii KanJln;
C'1.U = f(Re) - K03cpcpHI.J.lleHT corrpOTHBJleHHH }J.BH:>KeHHfO mapa
B B03.a;yxe;
1jJ (We) = F iJCiJ - CPYHKI.J.HH, YIJ.HTbJBafOllI. a5I H3MeHeHHe rrJ10lll.a}J.M M
FlUcl/l
K03cpcpHI.J.HeHTa cOrrpOTJfB.1IeHllH KpyrJlOH I{an.IJH
BCJ1e}J.CTBHe ee }J.e.popMaI.J.lfH;
F iJ - rronepeIlHoe ceIleHHe }J.ecpopMHpOBaHHOH Kamm.
3KcnepHMeHTaJ1bHaH 3aBllCllMOCTb 'IjJ (We) B pa60Te [61] .a;aeTC5I
II BH.a;e
1lJ(We) = e O ,03We1,5. (282)
O.a;H8KO BBe.lI.eHlle 3aBllCllMOCTll Bll.lI.a (282) .a;a:>Ke npll llcrro.'1b-
30BaHllll ynpOlll.eHHoro BbIpa:>KeHllH C'1.U = f(Re) He n03BOJIHeT no-
JIYIlHTb pellleHllH ypaBHeHIfH (281) B BH}J.e 3J1eMeHTapHbIx CPYHKI.J.lliL
n03TOMY, YIlHTbIBaH npH6J1H:>KeHHOCTb Bcex pacIleToB, BocnoJlb3yeM-
CH cpe}J.HHM 3HaI.J.eHHeM ep. B pa60Te [61] npe}J.JIaraeTCH npHHHMaTb
'I\J(Wc o ) + 'I\J(Wc Kp )
'ljJcp = 2 (283)
TaK KaK rrpe}J.rrOJ1araeTCH, IlTO KanJ1H B HaIlaJ1bHbIH MOMeHT TOp-
MO:>KeHH5I llMeeT KpyrJlYfO CPOPMY, TO 'IjJ(Weo) = 1, a 'IjJ(We"Kp) =
= \jJ ( 10) = 2,56, Tor.a;a 1J- 1 cp = 1,78.
298
B KalJ:eCTBe 3aBHCHMOCTH C w = f (Re) MO)KHO HCnO.lIb30BaTb .lI.O-
CTaT01lHO TOlJ:HYIO annpOKCHMHPYlOllI.YIO <POPMYJIY H3 paOOTbI {61],
KOTOpa5I npHMeHilMa B 111l1pOKOM .lI.Hana30He H3MeHeHI15I lJ:I1Ce.'I PeH-
HOJIb.lI.Ca (10- 3 Re 6.10 3 ):
24 4,4
Cu;=-+ f - + 0,32. (284)
Rc J Rc
. H. B PYOOB HCn0J1b30BaJi .lI.JIH aHaJ10rHlJ:HOrO B BO.lI.a ynpo-
llI.eHHYIO 3aBHCHMOCTb:
"PH 10 Re 1000
12,5
Cu; = V Re .
(285)
O.lI.HaKO npH npHMeHeHHH 3aBHCHMOCTH (285) HeJIb3H BeCTH
paClJ:eT TOpMO)KeHHH KpynHbIx KaneJ1b, HMelOllI.HX OTHOCHTeJ1bHO BbI-
COKHe HalJ:aJIbHbIe CKOpOCTH. B pa60Te [86] npH paClJ:eTe TopMo}J(e-
HH5! KaneJIb npe.lI.JIaraeTCH pa3.lI.eJIHTb YlJ:aCTOK HX .lI.BH>KeHI1H Ha TPH
3T3na, npHMeH5!5! Ha Ka)J{.lI.OM 3Tane cooTBeTcTBYlOllI.He 3aBHCHMOCTH
C w = f(Re), lJ:TO, KOHelJ:HO, HeY.lI.o6HO .lI.J1H pacIIeTa H aH3JIH3a.
TIpeo6pa3yeM ypaBHeHHe (281) C YlJ:eTOM BbIpa)J{eHI1H (283) H
(284), 3aMeHHB TaK)J{e Maccy KanJIIf H ee nOnepelJ:HOe CelJ:eHIfe 3a-
BIfCHMOCTHMIf
M d
K= P;
2
dKn
F =-
Kn 4
TOf.lI.a
_ dU Kn = . . 'l/Jep ( + 4,4 +0,32 ) U n. (286)
dt 4 P d Kn Re YRc
Bblpa3HB CKOpOCTb KanJiH lJ:epe3 lJ:HCJIO PeHHOJIb.lI.Ca U nn =
V V
= Re II dU nn = -2....dRe II, pa3.lI.eJIIIB nepeMeHHbIe, nOJIYlJ:HM
d Kn d"n
.lI.H<p<pepeHl.(IfaJIbHOe ypaBHeHIIe
d Re = _ . . ." dt ( 287 )
0,32 Rc 2 + 4,4 Rc 3 !2 + 24 Rc 4 p d n 'Yep .
38MeHHB nepeMeHHYlO Re B .'1eBOH 'l8CTH ypaBHeHIfH Ha Z2 If
dRe = 2zdz, 6Y.lI.eM IfMeTb
2dz = -kdt,
z(O,32z 2 + 4,4z+ 24)
(288)
r.lI.e
k= . .h
4 P . d 2 'Yep'
Kn
fIpOIfHTerpIfpOBaB ypaBHeHIfe (288), nO.lI.CTaBIfB npe.lI.eJIbI IfHTe-
rpI1pOB8HIfSI If 3aMeHIfB nepeMeHHYlO Z = V Re , nOJIYlJ:I1M BbIpa>Ke-
299
IHIe JJ.J1H BpeMeHH TOpMO:iKeHH5I KanJIH OT HatjaJIbHOH CKOpOCTH .11.0
.'II060H CKOpOCTH U "n:
t = ...!.. f In
hI
4,4 24
0,32+ f - +-
1 Re Rc
4,4 24
0,32+ JI - +-
Reo Rc o
+2,62arctg(O,190V Re + 1,31)-
rJJ.e
-2,62arc!g (0,190 V Re,, + l'31) '
k = 18 .h .
I p'.) 'Yep'
d n
Re, Reo - LJHCJ18 PeHHo"lbJJ.ca .:I.JIH Kan"lH, onpeJJ.eJ1HeMbIe co-
OTBeTCTBeHHO TeKymeH cKopacTbIO U"n H H8LJ8.1b-
HOH CKOpOCTbIO U ,,0.
ECJ1H B <POPMYJ1Y (289) nOJJ.CT8BJ1HTb 3H8'IeHHH LJIICeJI PeHHolIbJJ.-
ca, nOJJ.C'IHTbIB8eMbIX no KpHTwIecKoII CKOpOC'TH U np , TO no.'lYLJHM
BpeMH TOpMO:iKeHH5I Kan.'IH OT H8LJ8JIbHOH CKOPOCTli U"o .11.0 KPHTH-
LJeCKOH U "p (t = tfJeg;).
OYTb, npOXOJJ.HMbIH K8naeH OT H8'WJ18 l 'fOpMO:iKeHHH, M01KHO
nOJJ.C<JHT8Tb no Cpe.lI.HeH CKOpOCTH ee JJ.Bll:iKeHlIH H8 OTJJ.e.'lbHbIX YLJ8-
CTK8X:
(289)
i
S" = (UKCP)J1ti'
...... .
o
(290)
rJJ.e (Un.cP)i - cpeJ],H5IH CKOpOCTb K8nc1H H8 i-oM y'wcTKe;
I1t i - HInepB8JI BpeMeHll i-ro YLJ8CTJ{8 JJ.BH:iKeHH5I K8n"lH.
113MeHeHHe BpeMeHll tfJeg; OT H8LJ8JI8 TopMO:iKeH1l5I K8neJ1b .11.0
LJ:OCTmKeHH5I I1Mll KpHTIILJeCKOH CKOpOCTll npll BnpbIcKe B B03JJ.YX C
p83J1llLJH M npoTHBoJJ.8BJ1eHHeM B 38BllCllMOCTll OT H8LJ8J1bHOH CKO-
pOCTH ,lJ,BH;'KeHI15I nOK838HO H8 pHC. 178. Opfl p8CLJeTe npllH5ITO
'l'cp = 1,78, 3H8LJeHlle KpllTllLJeCKOH CKOpOCTll onpeJJ.e.TJ5IJ10Cb no Kpl1-
BOH 1 H8 pllC. 177. EC.'lll B JJ.8J1bHeHWeM YJJ.8CfC5I C 60JIbWeH TOLJHO-
CTbIO OI.J.eHHTb BpeMH JJ.OCTll:iKeHHSl KpHTI1>J.ecKoH JJ.e<popM8I.J.llH .J.JI5I
K8neJ1b p83J1llLJHOrO JJ.ll8MeTp8, TO, OT.'lO:iKI1B ero no OCH opJJ.llH8r
(pllC. 178), MO:iKHO YTO'IHllTb 3H8LJeHll5J H8LJ8J1bHbIX CKopocTeH H no-
CTpOllTb H8 rp8<pHI<e plle. 177 KPllBYIO M8KCllM8JIbHO B03MO)KHbIX
.lJ.ll8MeTpoB K8neJIb. 38BllCllMOCTb (278), CJ1eJJ.0B8TeJ1bHO, B nepBoM
npll6J1ll:iKeHllll n03 BO.'I 5IeT onpeJJ.e.15ITb 3H8q:eHll5I MaKCllMa.'lbHbIX
JJ.llaMeTpoB I<ane.'Ib Ton.'IllB8 H8 YLJaCTI<e pacn .1JllBaHll5I.
Opll llCTeLJeHllll TOnJIHBa C M8JlbIMll CI<OpOCT5IMI1 Ha OTJJ.eJ1bHbIX
Y'WCTK8X BnpbICI<a, I<aK 6bI.'I0 nOI<838HO, MorYT 06pa30BbIBaTbC5I
JJ.OCT8TO'IHO I<pynHbIe I{8n.1H Ton.'IHB8.
300
DpH OCeCHMMeTpJ-IlIHOM II BOJIHOBOM paCnaJI,e AIIaMeTp KanJ1H
'onpeJI,e.TIHeTCH OnTHMaJ1bHoi'1 AmIHOH BOJIHbI K0J1e6aHHH, 06eCnellH-
BaIOIl1.eH HaH60JIee 6bICTpOe pa3pYllIeHHe CTPYH. LLHaMeTp TaKHX
KaneJ1b npeJI,JIaraeTCH pae-
CllHTbIBaTb no cpopMYJIe [20] ttl'ipCfK
3/ 4
d Kn = de 1/ --;-,
V \\c
K.an.1H MaKCHMa.'IbHbIX
pa3MepoB 06pa3YIOTC5I npH
BbITeKaHHH TOnJ1HBa H3 OT- o.OOJ
BepCTHH noJI, JI,eHCTBHeM CM-
.JIbI THllieCTH (d"n =
= 1 ,89 de). 0,002
OueHIw MaKCHIYIaJlbHbIX
JJ.Ha IeTpoB KaneJ1b no MMK-
pmpoTorpaqYH5IM, nOJ1yqcu-
HbIM JI,J1H 3aKpbITbIX <POPCY-
HOI{. nOKa3aJ1a, llTO B KOHue
BfIpbIcKa nmm.'IHIOTC5I Kan-
.JIM, ,J,MaMeTp I<OTOpbIX pa-
BeH JI,HaMeTpy con.'IOBOrO
OTBepCTMH, XOTH AMaMeTp
BbITeKaIOIl1.eH CTPYHKH Ton-
.JIHBa HaMHoro MeHbllIe (eM.
pHC. 175, 176).
OUNlKa MeJ1J{OCTH pac-
nbI.'HmaHIUI C nOMOlllblO
Cpe)!,HIfX IJ,lfaMeTpoB KaneJIb. TeOpeTHQeCKHIJ 3H3.1li3 p3CnbIJ1HB3UH5I
CTPYH TonJ1HBa [20, 23] He JI,3eT nOKa yJI,OBJleTBOpHTeJIbHbIX paClJeT-
HbiX <POPMYJ1 JI,J1H onpeJI,e.'IeHHH CpeJI,HHX JI,H3MeTpOB K3ne.'Ib. Ha-
npl'E\Iep, 3U3J1H3 pe3YJIbT3TOB paClleTOB, npHBeJI,eHHbIX B p360Te [17],
nOKa3bIBaeT, lJTO JI,J1H de = 0,25 M.lft Bce paccllHT3HHbIe no npeJI,J13r3-
e lOH <popMYJIe CpeJI,I1He JI,H3MeTpbI Kane.'Ib cooTBeTcTBYIOT COOTHO-
meHI1IO
0,004
-j
o
fOO
400 t/xo MiceK
PHC. 178. BpCMH TOpMOLKC!lll51 KanCJlb OT na-
'la.1bHoH )1.0 KpHTII4CCKOH CKOpOCTH HX .D:BHLKe-
!lllH 13 B03.!J.YXC !lpH d",,:
/ - 60 AIK_": 2 - 100 ""K.": 3 - 150 AtK.": 4-
:...'00 'J(KAt; 5 - 30U J1tKJ"t; 6 - 400 Alf(.H; CfTJIOlliHbre
nHHHU - P np = 1 KTjcM'2; llITpXOBbIe - P np =
16 KTiC'"
dqpPBU O
We= :::::::6,5=consL
aT
T 3Koe COOTHOllIeHHe He.1b3H CllHTaTb Cnp3BeJI,.1HBbIM JI,.15I p3ClJe-
TaB CpeJI,HHX JI,H3MeTpOB K3nec1b. OHO 60.1ee npHrO.ll.HO JI,.rIH oueHKH
M3I{CHM3JIbHO B03MOlliHbIX JI,H3MeTpoB Kane.'1b, HO He YlJHTbIB3eT
CT36Hm13aUHH K3ne.1b no lYIepe YMeHbllIeHHH HX p33Mepa.
113-3a CJ10lliHOCHI TeOpeTJ-IlIeCKOro aH3.1H33 npouecca paCn3JI,3
CTPYH Bce lJ3Il1.e JI,JIH p3ClJeT3 cpeJI,unx JI,naMeTpOB K3neJ1b npnMe-
H5IIOT KpHTepHaJlbHbIe yp3BHeHHH. DpH 3TOM B HeKOTopbIX CJ1YlJ35IX
npH COCTaBJ1eHHH YP3BHeHHIi Y<IHTbIB3IOT 60.1bllIoe llHCJIO <p3KTOpOB,
301
KOTopbIe IIWrYT OK838Tb BJIHHHHe H8 p83MepbI rrO.'IYQ8roIII.HXCH K8-
rreJIb, .H8rrpHMep, rrpe.u;JI8r8eTCH <PYHKIJ,HOH8JIbH8H 38BHClIMOCTb BlI.u;a
d qp = f ( Re, We, , , U" , k\, k 2 , k 3 , . . . ) ;
de P I1 T U"o
3.u;eCb QJIeH8MH k(, k 2 , k3 YQHTbIBaroTcH COOTHOIlleHHH reOMeTpHQe-
CKHX pa3MepOB <P0PCYHKH.
B pa60Te [86] B KpHTepHa.HbHoe ypaBHeHHe BBO.u;HTCH yrOJI KO-
Hyca <paKe.'Ia, B pa60Te [93] - OTHOllIeHHe Tel<YIII.eH rro.u;a'lH K HO-
MHHa.1:bHOiL BBe.u;eHHe 60JIbillOrO IlHCJI8 Kpf1TepHeB B yp8BHeHHe
Tpe6yeT illHpOKHX 3KcnepHMeHTaJ1bHWX HCCJ1e.u;OBaHHH H 3aTpy.u;HH-
eT BbI'lHC.'IeHHe rrOKa3aTe.'IeH CTeneHH H K03<p<pHIJ,HeHTOB. D03TOMY
*e aTeJIbHO B KpHTepHaJIbHWe ypaBHeHHH BBO.u;HTb B nepBYro OQe-
pe.u;b HaH6o"1:ee onpe.u;eJIHroIII.He rrapaMeTpbI.
B pa60Tax [20 Ii 23] npeAJ1araeTCH BKJIroIIaTb B ypaBHeHHe tJ:e-
TbIpe KpHTepIIH, YlJIITbIBaroIII.He COOTHOllieHIIH CIIJI CKOpOCTHoro Ha-
nopa II nOBepxHocTHoro H8TH)KeHH5I, BH3KOCTII 11 I1HepIJ,I10HHbIX CHJ1:
d qp _ f ( PP odc . pde(JT . k. )
- '2" t
de U T I1 T P J.t T
pde(JT
me - = Lp - KpHTepl1H JIanJI8ca.
11;
B pa60Te [48] AJ1H llITI1<pTOBOH <POPCYHKH B KpHTepHaJIbHOe ypaB-
HeHHe BK.'IrolJeHbI TOJ1bKO KpHTepHH Be6epa H PeHHOJIbAca. DpH
3TOM B Kpl1TepHH Be6epa BMeCTO nJIOTHOCTH B03.u;yxa BXO.u;HT rrJIOT-
HOCTb Torr"'IHBa. HCK.1rolJeHfle n,;10THOCTH B03.u;yxa, BH.u;HMO, IJ,e"'IeCO-
o6pa3Ho, TaK KaK nOC.TIe.u;HHH MaJIO BJ1HHeT Ha BeJ1HtJ:HHY cpe.u;H!1X
J],HaMeTpoB Kaneo!1b.
A. C. JIbIllIeBcKHH [50] nO.1YtJ:H.'I no.'IY3Mnl1pHtJ:ecKoe KpHTepHa.:lb-
Hoe ypaBHeHHe, cOJ],ep*aIII.ee .1HllIb KpHTepHH Be6epa H J1anJIaca,
H orrpe.u;e.!'IH.n rrOKa3aTe.1H CTeneHH, o6pa6oT8B 60JIbillOe IUICJ1:0 3KC-
nepHlI1eHTa.'IbHbIX .u;aHHbIX:
d
= E We-O. 266 L p . -0.0733 (291 )
de qp
B pa60Te [93] npe.u;JIaraeTCH KpmepIIa.TlbHOe ypaBHeHHe
d qp _ E W -0.36 R --0.4 ( P ) 0.07 ( qt{Ii ) 0.4
-- qp e e - -,
de p" qu,
BHlI,a
(292)
r.u;e qllH - HOMHHaJIbHaH IJ,I1Ko!'IOBaH rrOJ],a1Ia.
YpaBHeHHH (291) H (292) .u;aroTcH .u;JIH paCtJ:eTa cpe.u;HHX lI,Ha-
MeTpOB Karre.!'Ib .u;JI5I scero <p8Ke.!'Ia. A. C. J1bIllIeBcKHH YKa3bIBaeT
TaK)Ke Ha npl1l11eHfIMOCTb ypaBHeHl15l (291) J],JIH paCtJ:eTOB cpe.IJ,HHX
.IJ,HaMeTpOB KaneJIb B pa3J1WIHbIe <pa3bI BnpbICKa.
302
ABTOpbI pa60T [50 H 93] CqHTaIOT, qTa npH onpe.n.e.'IeHHH pa3JIHq-
HbIX Cpe.lI.HHx .lI.HaMeTpoB KaneJIb B KpHTepHaJ1bHbIX ypaBHeHH5JX H3-
MeH5JeTCSI TOJIbKO nocToHHHbIH K034><lmu.HeHT E qp . AHa.'IH3 nOKa3aJt
[69], qTa B KpHTepHaJ1bHOM ypaBHeHHH ,1I}I5J pa3J1HqHbIX Cpe.lI.HHX
.n.HaMeTpoB Kane b 6y.n.YT COOTBeTCTBeHHO H3MeHHTbCH nOCTOHHHHH
K034>4>mXHeHT H nOKa3aTe. r IH CTeneHH. OpH 3TOM, eC.'IH HaH.n.eHbI 3Ha-
qeHlI5J nOCTOHHHbIX II nOKa3aTe.J1ell CTeneHII .lI.JIH Cpe.lI.HlIx apH4>Me-
THqeCKOrO, nOBepxHocTHoro II 06'beMHOrO .lI.HaMeTpoB Kane.TJb, TO A.'IH
OCTa.'IbHbIX CpeLUIllX .lI.IIaMeTpOB, YKa3aHHbIX B Ta6J1. 7, OHH MoryI'
6bITb paCCqIITaHbI TaK:
I
= ( EZo ) q-p .
Eqp ,
E o
qmqO-pmpO
m qp =
q-p
r.lI.e Eqp - nocToHHHbIll K034>4>Hu.HeHT;
mqp - nOK333TeJIb CTeneHH npH JI1060M KpHTepHH, BXO.lI.5!Ill.eM Be
ypaBHeHHe.
OpH 06pa60TKe 3KcnepHMeHTaJ1bHbIX .n.aHHbIX B JIOrapH4>l',mqe-
CKHX Koop.n.HHaTax 19 d qp = f(lg We) H3-3a pa3JIHqHbIX 3HaqeHHH
nOKa3aTeJ15J y KpHTepHH Be6epa .lI.JIH pa3JIHqHNX Cpe.lI.HHX .lI.HaMeT-
pOB ocpe.n.H5JIOII.J.He npSIMbIe nepeceKalOTC5J B O.n.HOll TOQKe. B 3TOH.
TOQKe, c.1elI,OBaTeJ1bHO, paBHbI Bce cpe.n.HHe .n.HaMeTpbI. TaKoe pa-
BeHCTBO HacTynaeT npII 60.'IbIllHX 3HaQeHH5JX KpHTepH5J Be6epa, KO-
TopbIe cooTBeTcTBYIOT BbICOKHM CKOpOCTSIM HCTeQeHHSJ TOnJ1HBa
(450-500 MIceK) H .lI.aBJIeHHHM BnpblcKa (1500-2000 IKF/CM. 2 ). Ha-
.'IHQHe TaKoll TOQKH no.n.TBeplli.n.aeT cTa6H.'IH3aI1HIO KaneJIb no Mepe
YMeHbIlleHH5J HX pa3MepOB.
Ou.eHKa MeJ1KOCTH paCnbIJIHBaHH5J BceH U.HK.10BOll no.n.aQH He no-
3Bo.'I5JeT nO.TIYQIITb .n.aHHbIX, Heo6xo.n.HMbIX .n..'IH paCQeTOB npou.eCCOB
cMeceo6pa30BaHHH B .lI.H3eJ1e H HcnapeHHSI Kanejlb. 3HaQHTe.'IbHO'
60 bIllHll HHTepec npe.n.CTaB.'IHeT onpe.n.e.'IeHHe CpelI,HHX .n.HaMeTpOB.
KaneJIb .n..'I5J nOpu.HH TOnJIHBa, no.n.aBaeMoro B npou.ecce BnpbICKa npH
.11060M rpa.n.yce yr.'Ia nOBopOTa Ky.'IaQKa. HaJIHQHe TaKHX .n.aHHbIX
n03BO.'IHeT paCCQHTbIBaTb 3Ha'IeHIIe Cpe.lI.HHX .n.IIaMeTpOB KaneJIb .n.mI
nopu.IIII Ton HBa, BnpbICKIIBaeMOll OT Ha'IaJ1a .11.0 J11060ro MOMeHTa,
B TOM 'IHCJ1e II Bcell U.HK.'IOBOll no.n.aQH.
3KcnepIIMeHTaJ1bHOe H3YQeHHe MeJIKOCTII paCnbIJIHBaHHH B J11O-
6bIe MOMeHTbI BnpbICKa npOH3Bo.n.IITCH C nOMOIUblO II.J.e.J1eBoro CTpO-
60cKona [48]. J],.'I5J nOJIYQeHHSI ynpOII.J.eHHorO paC'IeTHOrO ypaBHeHHH
ou.eHIIM OCHOBHbIe 4>aKTopbI, B.TJIIHIOII.J.He Ha paCnbJ.'IHBaHHe Ton.'IH-
Ba npH BnpbIcKe 3aKpbIToH 4>opcYHKoll.
KaK OTMeIIa.'IOCb, ra30BaH cpe.n.a MaJ10 B.TJHHeT Ha BeJIHIIHHY
Cpe.lI.HIIx .lI.IIaMeTpoB KaneJIb, n03ToMY H3 paC'IeTHOrO ypaBHeHII
napaMeTpbI ra30Boll Cpe.n.bI J1YQIlle IICK IOIIHTb [48]. OpH BbIBO}le
303
KpHTepfIa.I1bHbIX ypaBHeHHii 3a onpe.l1.eJUIIOIlLYIO Be.1H'lHHY npHHH-
Ma,;lCH ,QHaMeTp C:OnJ10BOrO OTBepCTlUI. O,QHaKO I1MeIOTCH ,QaHHble,
YKa3bIBalOlllHe, 'l1rO JJJJaMeTp COnJIOBOrO OTBepCTHH He3Ha1.JHTe,;lbHO
B.1I151eT na BeJUI1.JH!HY cpe,QHllX ,QI1aMeTpOB KaneJIb. HanpHMep, 3. Ptj-
'Wp,QCOH [62] C1.Jt:I1raeT, 1.JTO B 06.'IaCTH paCnbIJ1HBaHHfI cpe,QHHH pa3-
Mep KanJ1H He 3a!BHCHT OT pa3Mepa ConJIa. Ha pHC. 179, B351TOM II3
pa60Tbl [48], nOK<33aHO H3MeHeHI1e cpe,QHero 06'beMHOrO .l1.IWMeTpa
Kane,,'Ib OT CKOpOCTI1 I1CTe'IemlfI Ton.'II1Ba .l1..'I5I Tpex THnOB Hacoc-
tPOPCYHOK. y!3 pH c. 179 BH,QHO, 1.JTO B 06J1aCTH paCnbIJ1UBaH1I5I
( U KO > 90 .M/ eel{) .3KCnepH-
MeHTaJ1bHbIe T01.JKH ,QJI5I
Bcex Tpex TimOB Hacoc-
OPCYHOK JIelKaT Ha OAHOH
KpHBOH. IhleIOTc5I YKa3a-
Hllfl 0 TOM, 'ITO C YBeJII11.Je-
HIIeM ,QIIaMeTpa ConJ1a npII
de > 0,38.MM B03paCTaHHfI
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6JIIO.l1.aJIOCb.
OnbITbI no IICCJ1e,QOBa-
IHlIO paCnbIJIHBaHH5I TOnJIH-
Ba, npOBe,QeHHbIe B MALHi
?n 'f) 2 't:n Ha w.eJ1eBbIX cTpo6ocKonax
LUI JU lI.:oJolICFX
.ll.J151 3aKpbITbIX MHOrOCOI1-
.'IOBbIX II IwanaHHO-COnJIO-
BbiX tPOPCYHOK I1PII d c =
= 0,32 -7- 0,64 .MJ1-t, TaK)Ke
I10Ka3aJIH, 1.JTO npH paBeH-
CTBe KpilTepHeB Be6epa H
JIanJIaca B KpHTepHaJIbHOM
ypaBHemm K03tPtPiIIIJ,lIeHT, YMHoLKeHHbIH Ha ,QIIaMeTp C0I1J10BOro OT-
Bepcnm, OCTaeTC5I nOCTOHHHbIM. HeKoTopoe HeCOOTBeTCTBHe npu-
Be,QeHHbIX ,QaHHbIX C HCCJ1e.ll.OBaHI1fIMlI paCnbIJ1HBaHI1fI ,Qll51 Bcero
BnpbIcKa B ue.'IOM OT'laCTH 06'b5ICH5IeTC5I TeM, IlTO B nOCJIe,QHeM CJIY-
'lae YJ1aBJ1HBaIOTC5JI TaKLKe Kan.'IH npll OCeCI1MMeTpHIlHoM 11 BO,;'IHOBOM
pacna,Qax CTPYH. 3TH KanJ1H OKa3bIBalOT BJ1HfIHHe Ha xapaKTep no-
.1YIlaeMbIx 3aBHCHlMOCTeH. B03MQ)KHO TaK)Ke, 'ITO IIPH CTpo60CKOI1II-
<IeCKOM HCC,;'Ie.ll.OBaJ.HHH TOHKOCTH paCf1bWBBaHII5I OTceKaeTCH ne3Ha-
'II1TeJlbHaH lYIaCca 'CTPYH H KanJII1 HMeIOT paBHbIe HaIla.'IbHbIe CKOpO-
CTH JI:BHLKeHII5I, n03ToMY npaKTHQeCKI1 HCI<JIIO<IaeTCSI B03MO)l\.HOCTb HX
B3aHMOAeikTBHH H\ ypaBHHBalOTCH YCJIOBI1H ABIiLKeHllH KaneJIb AO UX
nona,QaHI1H Ha YJI<3B.TlHBaIOIlJ,YlO nJ1aCTHHKY. 3TH YCJIOBHH OnblTa
6.TIH3KO cOOTBeTCT!BYlOT YCJIOBHHM pa3BHTHSI aKeJIa B I<aMepe cro-
pamIH, r,Qe npoHoW,QHT 6bICTpoe HcnapeHHe KaneJ1b H HX OTKJ10He-
HHe OT HaQa.1bHbIX TpaeKTopHH ra30BbIM nOTOKOM. D03TO:MY B pac-
'leTHOM ypaBHeHHHI .D:I1aMeTp de COn"TIOBOrO OTBepCTH5I paCIIbWHTeJIH
tP0PCYHI(J1 MO)KHO B nepBOM npI16JIIUKeHlIH BBeCTH B nUCT05lHHbIH
K03tPtPHlJ,HeHT.
d SD
MK/'I. O
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120
tOO
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100
20
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PIIC. 179. 113McHCHIIC MC.1KOCTII pacnhI;IIIBaHiHJ
B 3aBHCIIl\IOCTH OT CKOpOCHI IICTCLJCHHH TonnH-
I3a H3 con.lOBoro OTIJ:CpCTIIH Hacoc-lj:JoPCYIIOK
pa3.1H4Horo THna:
o - AP-2{), de (),!J _ItAt; . - ;\P-2.I, de
0,\32 _'u,; X - AP-2\6 (3aKpblTa>Jj. de = 0,2 ,If."
304
Ha Me.'IKOCTb paCnbIJIHBaHHH cymecTBeHHO BJIHHeT npeLJ:BapH-
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flpe,n:BapHTeJIbHOe YBeJ1WIeHHe Typ6YJ1eHTHOCTH nOTOKa YJ1Y1lrnaeT
paCnbIJ1HBaHHe TOnJ1Haa [58]. flpOXOMn:eHHe Me nOTOKa 1lepe3 ,n:J1HH-
HbIe Y3KHe Il.{eJ1I1 I1J1H KaHaJIbI ,n:eJ18eT Te1leHHe 6oJ1ee .rlaMHHapHbIM
H npHBo,n:HT K YBeJIH1leHHKJ A
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npHMep, npH OTHOCHTeJIbHO
Ma:lblX nOJ\.'be.Max llfAbl pac.-
nbI.1HTeJISI. Y1leT 3TI1X HB.1Je- 250
HHH B paC1leTHOM ypaBHeHHH
CJ10MeH H3-3a He,n:ocTaT01lHO-
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MY nOKa BJ1HHHHe KOHCTPYK-
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06pa6oTKH COnJ10BbIX oTBep-
CTHH, npaBHJ1bHOCTb HX reo-
MeTpH1leCKOH <pOpMbI 6y,n:eM 150
Y'1HTbIBaTb npH BbI60pe BeJIH- {},J
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eHTa.
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pdcU o
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PHC. 180. 3Ha'-lCHIIH K03<p<PIII.\HCHTOB A qp
J.\.15! COmlOBb!X OTBepCTlu'i. pa3JIH'-IHOrO .D:na-
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] - Aw; 2 - A,o; 3 - AD
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crT 11;
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JIII'lHbIe <pa3bI BnpbICI<8 MOMHO n0J1b30BaTbCH BbIpaMeHHeM BH,n:a
d"Pi= A qp ( pdcU o ) a qp ( dcpaT ) bqp . \29 )
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IIeIIHH nOCT05lIIHOH A qp ,n:JI5l 3aKpbITbIX <P0PCYHOK C pa3J1H1lHbIMH
,n:II3MeTpaMH con.TJOBOrO oTBepcTHH, nOJ1Y'leHHbIe 06pa60TKoH 3Kcne-
pHMeHTaJ1bHbIX ,n:aHHbIX MeJ1KOCTH paCnbIJ1HBaHH5l no pa60TaM
MA.LI.I1. DbIJ111 onpe,n:eJleHbI TaKMe 3HaI.JeHMH nOKa3aTeJ1eH CTeTIelH1
y KpHTeplIeB Be6epa H JIarmaca; ocpe,n:HenHbIe 3HaI.JeHH5l npHBen:e-
HbI HIIMe.
B CB5l3H C H3MeneHHeM <pH3HI.JeCKHX KOHCTaHT TOnJ1HBa B Y3KHX
npen:eJlax He yn:aJIOCb TO'lHO onpe,n:eJlHTb H3MeHeHHe 3Ha'leHHH no-
K33aTeJlH b qp npH nepexo,n:e OT o,n:noro cpe,n:Hero ,n:HaMeTpa K n:py-
rOMY, Y1lHTbIBa5l, 1lTO BeJ1HqHHa nOKa3aTeJ15l b MaJ1a, ,n:J15l paC'leTOB
B n:aJIbHeHllleM HcnOJ1b30BaJ10Cb ero cpen:Hee 3Ha'leHHe, KOTopoe 6bI-
JIO npHH5lTO nOCTOHHnbIM n:JI5l Bcex Cpen:HHX AlIaMeTpOB Kane.1Jb.
20 3aI<a3 748
305
JJ:HaMeTp corr- bqp::::::b
JlOBOro OTBCpC- alO °20 °30
THH B AUt
dc=O.32+0,64!-0.21+-0.24! -0,233+-0,263\-0,26+-0.28\-0,082
3KcnepHMeHTa.'IbHbIe .l.I.aHHbIe nOKa3bIBalOT, IlTO npH nO.'IO}KeHHU
HrJIbI Ha Yllope Y 3aKpbITOH MHOrOCOnJ10BOH CPOPCYHKH HJ1H 60.%-
mOM npOXO.l.l.HOM CelleHHH Me}K.l.I.Y K.!lanaHOM H Ce.l.l.JIOM Y KJIanaHHO-
LJq
MM3fzpaiJ Qtp CM%el<
12/1
60
8,0
4,0
fJq 0
MMfcpa8 &tp CM3fcCI<
12,0
6D
8,0
*0
",0 20
o.
4
8 12
8)
16
LJ g.,acp
dIG;
MI<N
o
120
80
4
B
12
16
0)
dIG;
MI<M
PHC. 181. I-!3McHcHHc paC'-ICTHblX H 3KC-
120 ncpllMCHTaJlbHbIX cpeAHIIX apnlj:JMcTlI4e-
CKHX .D:HaMCTpoB KanCJlb B npol.\ccce
BnpblcKa .D:JlH «cTynCHqaTOH» xapaKTe-
pllCTIIKH Ha peLKIIMc:
a - n = 1050 06/MUH, ql{ 12-1,5 MAI 3 ,
perYJIHpOBaHHe pI = 80 Kr;CM'; 6 - n =
40 cp
1050 06/MUII, q I{ 130,4 1.11.1 3 , perY_1Hpo-
BaHHe p I 105 Kr;CM'; B - n =
Cf]
=1050 06/MUH, ql{ = 115,5 1.11.1 3 , perYJIHpo,
BaHHe pI = 125 KT/CM'; 1 - KpHBa>!. no-
cf]
cTpoeHHaSl no 3KcnepHMeHTaJIbHhIM .n.aHHhIM;
2 - KpliBaH. rronyqeHHaH paC1.JeTOM no
q,opMYJIe (293)
I
80
q;O
COIIJ10BOH CPOPCYHKH 3Ha1leHHH IIOCTOHHHbIX K03cpcpHI.1.HeHTOB H 1I0Ka-
3aTeJIeH CTeneHH B paClleTHOM ypaBHeHHU OTJIHllalOTCH He3HaIIH-
TeJIbHO. JJ.J1H Cpe.l.l.He06'beMHOrO .l.I.UaMeTpa KalIeJIb OHH 6J1U3KH aHa-
J10fUIIHbIM 3HaIIeHHHM, peKOMeH.l.I.yeMbIM A. C. JIblmeBcKHM [50].
TaKoe COBlIa.l.l.eHue 06'bHCHHeTCH, BH.l.I.HMO, TeM, 'ITO napaMeTpbI no-
TOKa TOIIJ1HBa onpe.l.l.eJ1HlOTCH IIPH 3TOM xapaKTepOM ero .l.I.BH}KeHH5I
B COIIJIOBbIX OTBepCTHHX.
Ilpu 3Ha'IHTeJIbHOM .l.I.pOCCeJIHpOBaHuH nOTOKa TOIIJIHBa Me)K.l.I.Y
3alIopHbIMH KOHycaMll HrJIbI H ce.l.l..'1a YXY.l.I.maeTCH MeJIKOCTb paClIbI-
JIUBaHIIH. 06pa6oTKa 3KcnepHMeHTaJIbHbIX .l.I.aHHbIX .l.I.JIH Y'IaCTKOB
306
BpeMeHl!, KOTJJ.a HTJIa COBeprnaeT JJ.BH>KeHHe OT ceJJ.J1a K ynopy HJIH
OT ynopa K ceJJ.JIY (!-t"lit"li !-tete), nOKa3aJI8, 1.JTO B ypaBHeHHH (293)
3Ha1.JeHHH nOKa3aTeJ1eH CTeneHH He H3MeHHJ1HCb, HO B03pOCJIH BeJIH-
4HHbI K03q>q>HU:HeHTOB Aqp [69].
llJ1H cpaBHeHH5I paC1.JeTHbIX no ypaBHeHHIO (293) H 3KcnepHMeH-
T8J1bHbIX ,n:aHHbIX Ha pHC. 181, a, 6, 8 nOKa3aHO H3MeHeHI1e cpeAHHX
.ZI.HaMeTpOB KaneJ1b no YTJIY nOBopOTa KYJIa1.JK8 JJ.J1H cTyneH1.JaTbIX
xapaKTepHCTHK BnpbICKa. Y 3THX xapaKTepHCTHK HMelOTCH 1.JeTKO
Bblpa>KeHHbIe Y1.JaCTKH nOJJ.a1.JH TOnJ1HBa C pa3JIH1.JHbIM nOJIO>KeHHeM
HrJIbI B paCnbIJ1HTeJIe. llJ1H paC1.JeTa HCnOJIb30B8J1HCb 3Ha1.JeHlIH KO-
3q>q>HU:HeHTOB H nOKa3aTeJIeH CTeneHH, H306pa>KeHHble Ha pHC. 180,
a TaK>Ke npHBeJJ.eHHbIe Ha CTp. 306
H B pa60Te [69J. BeJ1H1.JHHa KPH- CM ;eK
TepH5I Lp nOJJ.C1.JHTWBaJ1aCb no
cpeJJ.HeH 3a BnpbIcK TeMnepaType 0,04
TOnJIHBa. <PH3H1.JeCKHe KOHCTaH-
TbI TOIJ.TIHBa B 3aBHCHMOCTH OT
OJ
TeMnepaTypbI nOKa3aHbI Ha pHC.
182. 1locTaT01.JHO 6J1H3KOe COB-
naJJ.eHHe pactJeTHblx H 3KcnepH- 0,02
MeHTaJ1bHbIX KpHBbIX YKa3bIBaeT
Ha B03MO>KHOCTb npHMeHeHHH
ypaBHeHHH THna (293) JJ.JIH npH- 0,01
6JIH>KeHHOH ou:eHKH cpeJJ.HHX
JJ.HaMeTpOB KaneJ1b B pa3J1H'lHbIe
q>a3bI BnpbICKa B 06JIaCTH pac-
nbIJ1HBaHH5I.
P8C eT cpe)],HI1X )],l1aMeTpOB
KaneJIb )],JUI nopU:HH TOnJ1HBa 01"
HaIJaJ1a )],0 JlI060ro MOMeHTa BnpbICKa. fIpH HaJ1I-I1.JHH xapaKTepHCTH-
KH BnpWCKa H KpHBWX H3MeHeHH5I cpeJJ.HHX JJ.H8MeTpOB KaneJIb no
yrJ1Y nOBopOTa KYJIa1.JKa MO>KHO paC1.JeTHbIM MeTOJJ.OM ou:eHHTb MeJl-
KOCTb paCnbIJ1HBaHH5I TOnJIHBa, BbITeKlIIero H3 paCnbJ.TIHTeJI5I OT H8-
4aJIa .ZI.O JIIo6oro MOMeHTa BnpbICKa, HanpHMep, nOJJ.aHHoro 3a ne-
pHO,lI, 3a,lI,ep)J{KH Bocn,IJaMeneHlIH H,,'IH BceH U:HKJ10BOH nO.ZI.a1.JH. 1lJIH
"noro Ha Ka}KJJ.OM rpaJJ.yce yrJIa nOBopOTa KYJ1a1.JKa no 3Ha1.JeHHIO
cpeJJ.Hero 06'beMIIOrO ,n:HaMeTpa IWneJ1b H 06'beMY nOJJ.aHHoro TOnJ1H-
Ba nO,lI,C1.JHTbIBaeTCH 4HCJ10 K8neJIb:
6.109 qi
N i = .
n (d 30 i)3
6r Krj,.,
0.0030
O,OD2S
0.0025
0.82
0,81
0,8
to
30
PHC. 182. H3McHcHHe Ij:JH3H'-IeCKHX KOIl-
CTaHT .D:1!3CJlbHOrO TOIlJlHBa B 3aBHCHMO-
CTH OT TeMnepaTypbl
(294)
06III.ee 1.JHCJ10 Kane,,'Ib OT HalJaJ1a no.n.a\lH .n.o JII06oro MOMeHTa
BnpbIcKa
i
N= !.N l . (295)
1=1
Tor.n.a q>OPMYJIbI
( apHq>MeTH'leCKOrO,
20*
,n:JI5I onpe.n.eJ1eHH5I cpe)],HHx .n.HaMeTpOB KaneJ1b
nOBepXHoCTHoro, 06'beMHoro) )J.JI5I TOnJIHBa,
307
paCnbJ.TleHHOro OT Ha1J:aJla nOJ(a1J:H J(O J1I060ro MOMeHTa BnpbICKa.
6Y,lI,F HMeTb BIIll [69]
OCTa.'IbHbIe cpeJ(HIIe J(IIaMeTpbI Kane.TJ:b MorYT 6bITb nO,lI,C1J:HTa-
HbI no aHaJIOrlI'lHO no.'!Y1J:eHI-IbIM <PopMYoi1aM II.'!H Ha OCHOBaHHH co-
OTHOllIeHHH (275). B ypaBHeHII-
SIX (294) H (296) d lOi , d 20i , d 30i -
3Ha1J:eHHH cpeJ(HHx apH<pMeTH1J:eC-
Koro, nOBepxHocTHoro H 06'beM-
Horo ,lI,HaMeTpoB KaneJ1b Ha Ka)K-
):laM i-OM HHTepBaJ1e BnpbICKa.
nO.'lY1J:eHHbIe paC1J:eTOM HJIH ITa
3KcnepHMeHTaJlbHbIM ):laHHbIM.
YXY,lI,llIeHHe Me.'!KOCTH paCITbI-
J1HBaHH5I II3-3a HCTe1J:eHHH TOIlJ1H-
Ba C Ma.l0H CKOpOCTbIO Ha Ha-
QaJ1bHOM H KOHe 1 IHOM Y1J:aCTKaX
BnpbIcKa MO:iKHO Y1J:eCTb, npHHHB,
1J:TO BeCb nO,lI,aHHbIH 3a 3TO BpeM5I
06'beM TOIl.'UIBa pacna,lI,aeTcH Ha
Kan.'lH ,lI,I1aMeTpOM, paBHbIM ,lI,Ha-
MeTpy con.rIOBoro OTBepCTH5I.
l\loxmo TaKx<e ou.eHHBaTb 3Ha-
1JeHHH Cpe,lI,HHx J(HaMeTpOB Ka-
ne.lb no <popMYJ1aM, HanpIIMep.
THna (291). Bo Bcex 3TIIX cJlY1J:a.
HX 01lIII6Ka, BHOCIIMaH B paC1J:el,
He3Ha 1 IlITeJ1eH 06'beM TOnJ1HBa, BbI-
i
NidlOi
d _'=1
10- N
d {
r
3 ;
/
d 30 = J'
qqrpMM 3
d JO MK/1
o
D
120
80
-,-" II 40
;
I I
PI
8
12
16
PI1C. 183. CpaBHCHI1C HlnCrpaJlbHbIX xa-
paKTcpnCTnK BnpNCKa II H3MCHCHllH
CpCl.lHCrO 06'bCMHOrO l.\naMCTpa KanCJlb
)1,.TJH <!>aKc.TJa TOn.TJI1Ba B 3aBllCHMOCTI1 OT
yrJla nOBopOTa Ky.TJa'-lKa .D:. 51 06bI4H0i1
(cn.10IllHbIC .111 HII H ) !J «CTync!l4aTOH»
(IllTpHXOBbIC) XapaKTepHCnIK BnpbICKa
Ha pCLKHMC n = 1050 06/MUH, q'l =
= 115 JftJft3, de = 0,32 .IUt:
1 - d 30 ; 2 - q Ii'"
i
Nidio i
i=l
(296)
N
6.10 9
i
.! ilq i
i=1
:It
N
SfJO
6Y,lI,eT HeCYII.I.eCTBeHHa, TaK KaK
TeKaIOIllIIH C MaJ10H CKOpOCTbIO.
I-hITerpaJ1bHbIe XapaKTepIICTHKII BnpbICKa II paC1J:eTHbIe KpIIBble
II3i\1eHeIIfIH Cpe,lI,HerO 06'beMHOrO ,lI,IIaMeTpa Kane.TJ:b no yrJ1Y nOBO-
pOTa KYJIa1JKOBOrO BaJIa Hacoca H306pa)J(eHbI Ha pHC. 183. YMeHb-
llIeHHe CKOpOCTH HCTe1JeHHH TOnJIHBa II3 COnJIOBHX oTBepcTHH H co-
oTBeTcTBYIoIllee CHIIx,eHIIe TIO,lI,'beMa HrJIbI (CM. «cTyneH1JaTYIO» xa-
paKTepHcTHKY BnpHcKa) npIIBoJ(IIT K YBeJIII1J:eHIIIO cpeJ(Hero 06'beM-
308 "O
Horo JI.HaMeTpa Kane.1.b B KOHl.I,e nepBOH <pa3bI BnpbICKa B 2 pa3a no
cpaBHeHlIlo C 06hI 1 IHOH xapaKTepHcTHKOH nOJI.8lJH. K KOHl.I,Y BnpblcK8
3H8lJeHHH CpeJI.HHX 06veMHhIX JI.HaMeTpoB KaneJb JI.J1H 060HX THnOB
xapaKTepHcTHK BnphIcK8 pa3HHTcH He3HalJllTeJbHO. 3TO YKa3hIBaeT
Ha TO, lJTO onpeJI.e.leHHe pa3MepOB Kane.flb npH pa3J1HlJHbIX xapaK-
TepHCTHKax BnpblCKa 06bIlJHbIMH MeTOJI.aMH Ol.I,eHKH MeJIKOCTH pac-
nbI.1.HBaHHH .!I..1H l.I,HI<.10BOH nOJI.alJIf MO)j{eT npHBeCTH K HenpaBlWb-
JIbIM BbIBO.!I.aM, TaK KaK lIe BCKpbIBa.eT HCTHHHOH KapTHHbI H3MeHe-
HH5J JI.HaMeTpOB Kane.1.b B npOl.I,eCce nOJI.alJH Tonmma.
OpH paClJeTe B HeKOTophIX C.flYlJaHX MO)j{HO npeHe6peraTb HaJ111-
llI1eM OTJI.eJIbHbIX YllaCTKOB, COOTBeTCTBYIOIllHX pa3.1.J1lUIOMY lI,pOC-
ce.1HpOBaHHIO Me)j{JI.Y 3anOpHbIM11 KOHycaM11 Hr.lbI 11 ceJI.JIa, eCJII-I HX
npOJI.o.l)j{I-ITe.1.bHOCTb He npeBblillaeT 1,0°. Ha HeKoTopbIX peMHMax
pa60TbI Ton.1HBHoH CHCTeMbI OT.!I.e.1.bHbIe YlJaCTKH MorYT OTCYTCTBO-
BaTb, HanpHMep, npH MaJ1.hIX lJHC.lax 060pOTOB 11 nOJI.alJax B 06.1.a-
CHI paCnbIJIHBaHH5J 6YJI.eT TOJ1bKO OJI.HH YlJaCTOK C I-1nfn I-1cfe.
K IIcnO.lb30BaHHIO KpIITepHa.lbBbIX ypaBHelIHH JI.J15J paClJeT8
CpeJI.Hl-IX JI.HaMeTpOB KaneJ1b BceH BnpbICHYTOH nOpl.I,Hl1 Ton.'IHBa, KaK
no npeJI.J1araeTCH, HanpHMep, B pa60Tax [50, 93], c.'1eJI.yeT noJI.xo-
lI,HTb C lIeKoTopoD OCTOpO)j{HOCTbIO. OpH TaKOM npl1MeHelII1I1 KpI1Te-
pHa.1.bHOrO ypaBlleHH5J nOCT05JHlIblH K03<P<PHl.I,HeHT 3aBHCl1T OT BHlI,a
3aKOlIa nOJI.alJH Ton.'1HBa. npOH.'I.'IIOCTpHpyeM 3TO nO.'lOMeHHe H8
npIIMepe paClJeTa CpeJI.Hero 06velVIlIoro JI.I1aMeTpa KaneJIb. OpHlVIe-
HHIII JI.J1H paClJeTa CpeD,HerO 06veMlIoro JI.l1aMeTpa Kane.'Ib TOnJIHBa,
nOD,aHHOro OT HalJa.la JI.O .'1!o60ro MOMeHTa BnpblCKa, ypaBHeHHe
(291), TOrD,a
d A . W aoo L b
30 = 30 eep p,
(297)
fJI.e A o = d c E 30 - nOCT05JHHbIH K03<p<PHl.I,IIeHT npI1 paCqeTe cpeJI.-
Hero .!I.HaMeTpa JI..'1H BceD nOpl.I,HI-I BnpbICHYTO-
ro TODJII-IBa;
We - Pzd e U2 - CpeJI.Hee 3HaqelII1e KpHTepH5I Be6epa.
ep - a r ep
CpeJI.HHH CKOpOCTb I1CTelJeHHH TOnJ1I1Ba H3 COnJOBOrO OTBepCTH5J
OT Haqa.rIa nOJI.alJH JI.O .11060ro MOMeHTa BnpbICKa
T
I
U =-
ep Eef c
i
!1q i
i=1
i
Ti
i=l
l .
nOJI.CTaBIIB 3HaqeHH5J Weep 11 U ep B <POPMYJIY (297),
d - A . L b ( / P zde ) aoo U 2a80
30 - 30 p cp .
U r
nOJIYlJHM
(298)
o pHMeM, qTO nOKa3aTe.'1H CTenelII1 OJI.HHaKOBbI npI1 paCqeTe d 30
no CpeD,HHM 11 MrHOBeHHbIM CKOpOCTHM HCTelJeHI1H TODJIHBa. TorJI.a
309
1I3 BbIpa)KeHlIH (297) aHaJIOrlIlIHO JI.J1H paC'leTa CpeJI.HerO 06"beI\tHO-
ro JI.lIaMeTpa Kane.1Jb Ha m060M Y1.JaCTKe BnpbIcKa 6YAervr lIMeTb
d - A L b ( pzd c \ a. o (V ) 2a (299)
30; - 30 P ( - ) ; 30 ,
\ aT /
I M.
rJI.e Vi =- . ---!.-.- CKOpOCTb lICTeqeHlIH TOWIIma Ha i-oM YI.J.aCT-
£ode T;
Ke BnpbICKa.
HaHJI.eM CpeJI.HHH JI.HaMeTp d 30 JI.JIH nOpII.HlI TOnJIHBa, nOJI.aHHOii
OT HaI.J.a.i1a JI.O i-ro yqaCTKa BnpbIcKa, no <popMYJIaM (294)-(296):
3/
d 30 = /
11
i
f'o..q;
;=1
;
l:
i=1 (dBOiP
(300)
OOJI.CTaBHB B BbIpa)KeH11e (300) 3HaI.J.eH11e d 30i , BbItJHCJIeHHOe no
<popMYJ1e (299), 11 np11paBHHB npaBble I.J.aCTH nOJ1YI.J.eHHOrO BbIpa-
)KeHlIH 11 ypaBHeH11H (298), onpeJI.e.'111M 3Ha'IeH11e
. A -2080
A 30 = 30 (V cP )
3(
Y'
;
f'o..q;
i=1
i f'o.. q .
........ ( V . ) 6a.o
.=1 I
(301 )
Ho
/).qi = V;Ec!e Ti
i
f'o.. q '
.....J .
i=I V f
H ----:-- = cpEc e'
.
Ti
i=1
TOrJI.3 OTHOllleHHe K03<p<pHII.11eHTOB
3(
A Bo - V 2a .o }I '
-- ep
A o
i
Ul- 6a .oT;
i=1
;
U ep T;
i=1
(302)
- U.
HJ1H, BBOJI.H 6e3pa3MepHbIe napaMeTphI Vi = ---!:.- Ii
U cp
- T;
T.=-
I . ,
.
T;
i=1
nOJ1)'I.J.Hl\I
3 r .
A Bo _ 1 / i-. V !-6a.o-
---;- - t/ £...,. T i .
A 30 i=I
(303)
310
I-Icn0J1b3yeM ,lJ.J1S1 npHMepa paClJeTa no BbIpa:iKeHHIO (303) Teo-
peTHlJeCKHH CJ1YlJaH J1HHeHHOro HapaCTaHHSI CKOpOCTH HCTelJeHHSI
Ton.'1HBa BO BpeMSI BnpbIcKa. Pa3,lJ.e.TJHB np0,lJ.0J1)KHTe.TIbHOCTb BnpbIc-
Ka Ha k paBHbIx HHTepBaJ10B, onpe,lJ.eJ1HM
T i = :n ; Ti = +.
OpHHHB a30 = -0,265, 6Y,lJ.eM HMeTb
f i (U i )2,59
o = l i=1 k (304)
30
OOCKOJ1bKY CKOpOCTb Vi HapaCTaeT J1HHeIIHo, BocnoJlb3yeMcH
CPOPMYJ10II apHcpMeTHlJeCKOH nporpeccHH ,lJ..'1H onpe,lJ.eJ1eHHH CKOpO-
CTH Ha J11060M y'JacTKe BnpbIcKa:
Vi=Vl+ V(ni-l), (305)
r,lJ.e VI - CKOpOCTb HCTelJeHHSI B HalJa.TIe BnpbICKa;
I1V - npHpaIl1.eHlle CKOpOCTI1 HCTelJeHHH npH nepexo,lJ.e OT 0,lJ.-
HOro YlJaCTKa K ,lJ.pyroMY;
ni = I, 2, 3,...- nOpH,lJ.KOBbIH HOMep YlJaCTKa.
OO,lJ.eJ1HB ypaBHeHHe (305) nOlJJ1eHHO Ha V cp , nOJ1YlJHM
Vi = V 1 + I1 V( ni- 1 ).
(306)
yl3 CPOPMYJ1bI CYMMbI lJJleHOB apHcpMeTlllJeCKOH nporpeccHH H co-
OTHOllIeHHH
i=k i=k i=k f:.q i i=k
Vi = Vi = ""'l= ""'I1Qi=k, (307)
Vcp %, 'riqu,
t=1 t=1 t=] - t=1
Tn
rlOJlYlJHM
2 V I + !1U(k-l) = 2.
(308)
3HalJeHHe BeJ1HlJHHbI VI J1e:iKHT B npe,lJ.eJ1aX 0 VI 1. Opn
VI = 0 HCTelJeHHe TOnJ1HBa HalJHHaeTCH C HYJ1eBOH CKOpOCTH. EC.TJII
VI = I, TO I1J1H I1U = 0, HJ1H k = I. 06a nOCJIe,lJ.HHX C.'1YlJaH COOT-
BeTCTBYIOT I1CTelJeHIIIO TOnJIHBa C nOCTOHHHOii CKOpOCTblO, paBHoi'1
V cp . CJIYlJaH, KOr,lJ.a k -+ 00, COOTBeTcTByeT .'1lmeHHOMY HapaCTaHHIO
CKOpOCTH B npOlLeCCe BnpbICKa.
1-I3 BbIpa}KeHIIlI (306) II (308) HMeeM
V . = U I + 2(I-U\) (n._i). (309 )
I k-I I
311
TIO.l(CTaBHB HaH.l(eHHOe 3HaqeHHe Vi B <POPMYJIY (304), onpe-
.n:eJIHM
ri=k
" 1 sf [ D, +
A 30 JV k
t.IT06bI nOJIyqHTb 3aBHCHMOCTb A3 = f (0 d, .n:JI51 paCCl\IaTpH-
A 30
BaeMoro c yqaH npHMeM nOKa3aTeJIb e npH MHOrOqJIeHe nOCJ1eAO-
2(1 -VI) ] 2.59
(ni- I )
k-I
(310)
J
2 ('=2,5. 0 J
e
o
425
tI,
Ala
A;a
9
t 2
1
f
Pnc. 184. 3aBHcIIMOCTb GTHO-
lIlCHHH K03<jJIj:JHI.\HCHT0I3 KPH-
TCpHaJlbHOrO ypaBllcHHH npH
paC'-IeTe no HCTHHHOll H cpe.D:-
HCll CKOpOCTHM nCTC'-ICHfIH
TonanBa OT nOKa3aTC 51 CTC-
neHfI npn MHOrO'l.TJCHe:
1 - U. I,D; 2 - v: 0,75,
3 - V, = 0,3; 4 - V, 0,25;
5 - V, 0,0
PHC. 185. H3MCHCHIIC OTlto-
IllCllfIH K03<jJIj:JIII.\HCHTOB KPH-
Tcpna.%1I0rO ypaBHcIIHH npli
paC'ieTC no HCTHHHOi\ II cpe,iJ,-
HCll CKOpOCTHM HCTC4CHH!J
Ton.1HBa B 3aI311CIIMOCTH OT
6C3pa3Meplloll lla'-la.1bHOII
CKOpOCTH
BaTe.1JbHO paBHbIM
3TOM PH.l(bI QHCeJ1
MH, nOJIYQHM:
npH e = I A 30 _ 1 .
A o - ,
I, 2, 3, 4. PacKpbIBaH MHOrOQ.leH, CYMMHPYH npHy
H npeHe6peraH 6eCKOHe'IHO MaJlbIMH BeJIHQHHa-
...
npH e = 2
A:o =3./ 1 + (I-U 1 )2
A 30 J 3
o = -:--1 + (1- U 1 )2;
30
A Q = .3/ 1 + 1 2+ (1- V I)2 J (l- U I)2.
A 30 V 5
(311),
npH e = 3
npn e = 4
312
Do BbIpa.>KeHIlHM (311) Ha pIlC. 184 nOCTpoeHbI 3amiCIlMOCTIl
A -
= f(e) AJ1H pa3.'lIlLJHbIX 3Ha L IeHIlH VI. I1cKoMbIe 3Ha L lemHI OT-
A 30
A
HorneHIlH onpeAe.1HlOTcH no KpIfBbIM pIlC. 184 npIl e = 2.59.
A 30
Do 3TH!\! 3HaLJeHIlHM Ha pIlC. 185 nOKa;WHO Il3MeHeHIle Be.1IlLJIfHbI
A -
0THOrneHl1H -2.Q.. B 3aBIlCIlMOCTIf OT VI. ,lJ,mI paCCMaTpIfBaeMoro
A o
c.1Y'laH 3TIl 3Ha 'leHHH .ne)KaT B npeAeJ1aX 1,0-1,2 H 6Y.lI.YT TeM 3Ha-
'IHTe.'!bHee, 'leM 60JIbrne 3aKOH nO.lI.a'lH OT.'lH'laeTCH OT c.1Y'laH HCTe-
'leHHH C nocToHHHOH CKOpOCTblO.
A
B Ta6JI. 8 npllBeAeHbl 3HaLJeHHH , nO.lI.CLJIlTaHHble no .pOPMY-
A 30
J1e (304) .lI..'lH 06bILJHbIX H CTyneH'laTbIX 3aKOHOB nOAaLJH Ha pa3.TJHLJ-
HbIX pe.>KHMaX pa60TbI CIlCTeMbI BnpbIcKa. MaKcIlMa.'1bHOe pa3.'lHLJIle
B BeJIIl'lHHe K03.pqmu.IleHToB A o H A 30 B COOTBeTCTBIlH C 3THMR
.lI.aHHbIMIf AOCTHraeT 22%.
B npoIJ,ecce BnphIcKa Bem1'lIlHa
A
OTHornemUJ MO.>KeT npeBhI-
.4 0
llJaTh 3Ha L leHHH, npIlBe.lI.eIlHhIe B Ta6.1. 8. Ha pRC. 186 nOKa3aHO Il3-
A
MeHeHHe OTHorneHHH no Mepe pa3BIlTHH BnphIcKa .lI..'lH 06bI'lHO-
A 30
ro H cTyncH'laToro 3aKOHOB nO.lI.a'lH.
lb H3.10.>KeHHoro CJ1e.lI.yeT, 'lTO npIl CYI.U.eCTBeHHoH pa3HHIJ,e B
xapaKTepHcTHKax BnpblcKa y O.lI.HOll Il TOll Me Ton.1HBHOll CIfCTeMbI
3Ha'leHHe K03.p.pIlIJ,HeHTa A P' BX0.lI.HIuerO B KpHTepHa.'lbHOe ypaB-
HeHHe, npH paC'leTe no Cpe.lI.Hell CKOpOCTH HCTe'leHHH 3a BeCb BnpbICK
He OCTaeTCH nOCTOHHHhIM. HeJ1b3H TaK.>Ke nOJIb30BaThCH 3Ha'leHHH-
MIl K03£j)£j)HuHeHToB A P' Hall.lI.eHHhIMH no Cpe.lI.HHM CKOpOCTSIM HC-
Te'leHHH, .lI.J1H pac'leTa Cpe.lI.HHx .lI.HaMeTpoB KaneJIb B pa3JIH'lHhIe
£j)a3bI BnphlcKa.
CYMMapHbIe U .lI.u.p.pepeHIJ,UaJ1bHble KpuBbIe paCnbIJ1UBaHlUI Ton-
J1UBa. KpHBble pacnhI.'lIlBaHHH n03BO.1HlOT 60Jlee nO.1HO CY.lI.HTb 0 MeJI-
KOCTH H O.lI.HOpO.lI.HOCTH paCnhIJ1lIBaHHH TOn.1IfBa. DOCTpOHTb TaKHe
KpHBbIe no 3KcnepHMeHTa.lhHhIM .lI.aHHbIM .lI.OBO.'lbHO npocTo. DpIl
3TOM, KaK nOKa3aJl B. A. KYTOBOH [47], IJ,e.'1eC006pa3Hee HcnO.'1b30-
BaTh CYMMapHbIe KpIlBbIe pacnbWIIBaHIIH.. LI.H.p£j)epeHIJ,I1pOBaHHeM
, CYMMapHhIX KpI1BhIX pacnbI.'1I1BaHI1H MO.>KHO nOJ1Y'lI1Tb KpIlBble LJac-
TOT. Ha pIlC. 187 B Ka'leCTBe npIlMepa nOKa3aHbI cYMMapHhIe KPH-
BhIe paCI1hIJIRBaHHH. B pa3JIH'lHhIe .pa3hI BnphIcKa .lI.JIH «cTyneH'la-
Toro» 3aKOHa nO.lI.a'lH, H306pa.>KeHHOrO Ha pI1c. 181,. a.
,QJIH aHaJ1HTlI'IeCKOro pac'leTa KpI1BbIX pacnbIJ1I1BaHHH 6bI.'l
npen:.'10.>KeH pH.lI. annpOKCHl'vmpYlOI.U.HX 3aBI1CHMoCTell. HaH60Jlee H3-
BeCTHhIe H3 HIfX 3TO ypaBHemlH P03eHa - PaMJIepa, HYKHHMa-
313
<>:J
<:j
""
\C
C
f-.
ail
«I
C!\
X
0:
c
o
""'
x
xx
:z: :r
«1«1
""1:
00
c:
0: 'x
00
C..
vo
x 0:
x"
g-a
- 0;
.......x
-:z:
0«1
C>J..
.....x
0:
",'J!
=c:
:z: v
(1.)«1
:co.
..
=
0.""'
:>,V
o
'" ..
-00:
:z:'"
.D:I!:
0:
«1«1
x""'
0.'"
"-' :r
.....v
X«l
0. 0.
..
0;
.. 0:
"1:
x 0;
,,=
0; "-'
"1::r
0,,-,
..
'" v
=
=,:s::
0,,-,
""' ""'
:Cv
"-'0
=0.
::10
x ..
-&v
-S-
. x
.. :c
"1:
0;"-'
xo.
:c v
S=
,0 )<
:c:;;
,,,", :c
.0 :c
"-'
..
o
:c
....
:I!:
:t:
::!
:Oi( ::.;
"" ---.
<=> Ie <:D -
00 - C C'I
t- - {) <=> <:D C'I
- - -
II - ---- U) - -
;:r U) 'I
:t: <:>- a II
::!
---. <:: ci=
\C t ......
.\ '"
C <=>
<=> 00
(io. U) \I
LQ :t:
r' II <> ::!
h -'-' :Oi(
<:: ::.; c:... ---.
Ie
U) M C U) t-
M <=> -
00 C'I "<!' -
- - U) C'I .
- - <=> - -
II - II
;:r II "'"
<:>- <:: <:>-
::.;
:it
::.; C'I
C'I M :t:
M ::.; <=> ::!
<=> ;,; II ---. ;,;
"- ---.
\\ ---. 00 '-' "'- Ie
IC <.D "<:j C "<!' <.D
a t- t- HO <=>
<=> <=> <=> -
<=> - . <i <=> LO M -
rf)- U) - - ..... - <=> - -
:::f; 00 II ::s: II - II
11 "'" ::r: <> II
<:: <:>- -'" <:: ci=
co :::r c:...
::E ""
CD
... ::E
() (!.J
;;:: ..
CJ ()
'" x :!:
;,; () '"
""
:c ::.; '" ;,;
Ci:! fS! ---.
'" <:D C<-I ii3 Ie 00 t-
S I.Q a C<-I
r:: M 0 X - -
00 - to;: :::> "" -
II - t:: U) - -
c U) II
?:: "'" ..... II
<:>- '-'
---. <:: ci=
;0- "-
Ie
a
U)
co C'l
U) -
co II
- :t:
II ::.; co. :::,; 0",
....'-' ;,;
t:: "'- \C :it
u:. "" CJ"]
<:D C U) CJ"]
LO - - CO
- - <=> LO -
- - H") - -
II 0 -
- I:
;:r II
<:>-
<:: ci=
::EO;: :a::Q
x.. x...
s °1 - oj 0
'«r:,M ",\0 «r:,'" '«r:,""
Cl.2:. Cl.i1
TaHacaBa 11 J10rapl1<pMI1lIeCK11 HOpMaJIbHbIH 3aKOH paCnpeAeJleH11H.
OO,lI,p06HbIH aHaJ1113 YKa3aHHbIX TpeX annpOKCI1MaUHH BbInOJIHeH
A. C. JIbUlle.BCK11M [50}. OH >Ke. Bbme.JI aHa.'IHTH'.J.e.CKHe. 3aBMCMMOCTH,
n03B0J1HIOllJ.He paCCqHTbIBaTb cpelUIHe .lI.l1aMeTpbI KaneJIb, Me.lI.HalI-
HbIH .lI.HaMeTp (d.Mea) H HaII60.'Iee qaCTO BCTpeqaIOllJ.HHC5I .lI.HaMeTp
Kane:Ib (d.Moa) np11 11cnO.'IL30BaHHH Ha3BaHHbIX BbIlile ypaBHeH11H.
O.lI.HaKO, KaK nOKa3aJ1H MbIO,lI,>KeJl A JO
II 3BaHc [90], JIyqlllee COBoa,lI,eHlIe Ajo
3KcnepHMeHTaJIbHbIX H paCqeTHbIX
KpHBbIX paCnbIJIMBaHI1H .lI.aeT MC- 1,2"
nO.lb30BaHHe npe.lI.JIO>KeHHOH HMH
3aB11CHMOCTH, KOTOPYKJ OHH Ha3Ba- 1,16
.TIll ypaBHeHHeM BepXHerO npe,lI,eJIa.
OpH HCnO.'1b30BaHIIH J10rapII<p-
MW!eCKH HOpMaJIbHOrO 3aKOHa pac- 1,08
npe,lI,eJ1eHlIH, a TaK>Ke ypaBHeHHH
BepXHero ope.lI.e.rIa npmweHHeTCH 1,00 0
<PYHKUHH HOpMaJ1bHOrO pacnpe,lI,e-
JIeHI151. .1J.JIH 06'beMHOfO pacnpe.lI.e-
JIeHI15I OHa I1MeeT BI1,lI,
16
y;O
dV Kn () -S2y'
dY = Vn e ;
Sy
6 j ' -S'y'
V Kn = --==- e dy,
} n
-00
(312)
Pl!C. 186. I13McHeHlle OTHOIlleHl1H
A 30
. B npOl.tecce BnpblCKa:
A 30
1 - 06bl4HaH xapaKTepHCTHKa BnpblCKa,
n = 1050 06/MUIi, q q = 115,5 flU";
2 - «cTynell'laTaH» xapaKTepncTHKa
BnpbIcKa, n = 550 06/MUIi, q q
I
115.6 -"'-"', perYJlnpoBaHHe PcP
= 80 Kr;CM'
(313)
I
r.lI.e () = - - KOHCTaHTa; 0 2 - .lI.1lCnepCHH.
a 1/2
Opl1 IICnD.'Ib30BaHIlH .1l0rapH<pMllqeCKH HOpMaJIbHOfO 3aKOHa pac-
npe.:.Le.TJeHlI5I npl1HIIMaIOT
y= Ind,w-1ncd'
(314 )
r.lI.e Cd - KOHCTaHTa.
B ypaBHeHllll BepXHerO npe.lI.eJIa yqI1TbIBaeTCH HaJIl1qlle KaneJIb
MaKCHMa.1bHOrO ,lI,HaMeTpa 11 npmIH!\WeTCH
1 adKn
y= n ,
dmax-dKn
(315)
f.n.e a - KOHCTaHTa.
B c.llyqae o6pa6oTKl1 3KcnepHMeHTaJIbHbiX .n.aHHbIX, Kor.n.a HMe-
IOTC5I KpHBbIe pacnpe.lI.eJ1eHHH H HCnOJIb3yeTcH ypaBHeHHe BepxHero
npeLI:e.TJa, 3HaqeHHH KOHCTaHT () H a MorYT 6blTb nO,lI,CqHTaHbI no BbI-
pa>KeHHH!\I, npHBell,eHHbIM B pa60Te [90]:
d max - d MeiJ
a=
d MciJ
(316)
315
6=
0,304
(317)
Ig (d V )90
d max -(d v )90
d.«eiJ
19
dmax-d....eiJ
rlI.e (d,J9o -l/.IIaMeTp KaneJIb, COOTBeTCTBYIOU!.HH 90%-H0l\1Y cO.J.ep-
)IWHHIO no CYMMapHOH 06"beMHOH KprIBOH pacnpe3.e-
.'IeHHSL
3HalJeIIII5I cpel/.HIIX l/.HaMeTpOB Kane.'Ib npH HCn0J1b30BaHHH ypaB-
51 BepxHero npe}J.eJ1a onpe,lJ,e.'I5IIOTC5I ,lJ,JI5I d 3 (J, d 31 II d 3 2 HHTerpfl-
tA no'
-;to
V Kn
80
50
1;0
20
0
fOO
80
60
5 1;0
20
o
1;0
50
120
100
ZOO
2{10 tl xn HKH
PIIC. 187. CpaBHcHHc 3KCHCpHMCHTa.1bHbIX H pac'lcTHbIX cYJl1l\!ap-
Hb]X Kpl1BbIX pacnbI.111I3alIH5! B pa3.TJWIHbIC MOMCHTb! I3npblcKa .J.15J
«CTynClJ'-IaToH;!> xapmncpHcTHKH, nOKa3aHHoH Ha pHC. 181, a:
CnJIOUlHble JII1HHH ---- nOCTpoeHLI no 3KcnepHMeHTa..'1bHbIM .n.aHHbIM; lllTpn-
XOBbie - no ypaBHefIHIO BepXHero npeneJ1a; l1lTpHx-nyttKTHPHhIe - no .TIQ-
rapH<j:)MH4eCKH HopMa.rlbHOMY 3aKOW' pacnpeneJIellHH
116
pOB8HHellf yp8BHeHHH (277) HJIH (276). OCT8JIbHbIe Cpe,iLHHe ,iLH8-
MeTpbI MO:tKHO nO,iLC1.JHT8Tb, HCn0J1b3YH COOTHorlleHHe (275).
npll 06beMHOM pacnpe,iLe eHHH, llcno b3Y ,QaH onpe,QeaeHllH
d 30 (q = 3; P = 0) ypaBHeHlle (277), HlIfeellI
d max
J ' dllKn
d(d Kn ) d(d Kn )
d o = d min
d max
(' -3 dV Kn
J d Kn d(d Kn ) d(d Kn )
d min
(318)
J13 BbIpa:tKeHHH (315) HaXOllHM
d Y
d = max e
KJ!
a+e Y
:. (319)
eY.
d(d Kn ) = dmaxa-dy.
a+e Y
(320)
dV
3aM.e.R.lU! 8 1109M.']Jlax (318) ,d...."f< R iJ (d.........) HX .':lID1ILeHIDl-
d (dKn)
Mn no BblpaLKeHllHM (319) Ii (320), no yqIiM
+00
S dVKn dy
dy
-00
d o=
+00 +00 2 +00 2 +00
S a3 dV Kn d f 3a e Y dV Kn S 3ae y dV Kn d 5 dVKn d
3Y'- d y+ '- d dy+ . d y+ - d y
e y ,e y e y y
oo -00 -00 -00
(321 )
dV Kn u
nO)J.CTaBIiB B ypaBHeHHe (321) 3HaqeHHe "---, Han,QeHHoe no
dy
opMYJIe (312), B n01lbIHTerpaJ1bHbIe BbIpa:tKeH HH Ii npOI1HTerpnpo-
BaB, Ha11,QeM
d 30 =
d max
3,r ! I "9
1/ I + 3a e 4 j;2 + 3a 2 e &2 + a 3 e45'
(322)
AHa.TJ:oru1.JHO 1lJ1H 1lPYrux cpe)J.HHX 1l11aMeTpoB 6Y1leM llMeTb
}1
d 31 =
d max
(323)
-. f ! I
JI 1 + 2 ae 452 + a2e 82
d 32 =
d max
I .
1 + ae 452
(324 )
317
MO.>KeT 6bITb HaHlI,eHO TaKLKe 3JHaqeHHe Me.n.HaHHOrO JUllJ,MeTM
KaneJIb H3 BbIpa.>KeHHH (316):
d .= d max .
."eo a+ I
(325)
JJ.JIH rrocTpoeHHH paCqeTHbIX KpHBbIX 06'beMHOrO pacnpe..n.eJIeHH5I
He06xo..n.HMO 3HaTb BeJ1IllJHHbI a H b. OHH MorYT 6bITb nOJIyqeHbI H3
COBMeCTHoro perneHH5I ypaBHeHHH (3,23) H (324):
I
(326)
()=
-1/2In ( r-2 +1
r ( tdmax -1 ) -
d 32
I
a = ( dmax _ 1 ) e - 4&' .
d 32
(327)
HaJIHlJHe Tpex ypaBHeHHH (322) ,. (323) H (324) n03BO.JIHeT 011-
pe.a.eJ1HTb TPH HeH3BeCTHbIe BeJ1HlJ11HIbI d max , a H b. Ho npB 3TOM
.lI.J151 paCqeTa d max no.TJ:YlJaeTC5I ypaBHeHHe rnecToH CTeneHH, lJTO 3a-
TpY.lI.H5IeT BbIlJHCJIeHH5I. D03ToMY JlY1lJrne BeJIHlJHHY d max ou,eH11BaTb
no q>opMYJIe (278) 11.TJ:11 KpHBbIM, H306pa./KeHHbIM Ha pHC. 177. Me-
TOn. npH6JIH./KeHHOrO onpe.n.eJ1eHH5I d 3I H d 32 6bIJl paCCMOTpeH BbIrne.
PaClJeT KpHBbIX pacnbIlIHBaHH5I no npHBe.lI.eHHbIM COOTHorneHHHM
He npe.a.CTaBJI5IeT Tpyn.a, XOT5I OH HeCKOJIbKO CJIO./KHee, lJeM npH .'10-
rapH<pMH'leCKli HOpMaJ1bHOM 3aKOHe pacnpelJ,eJIeHllH. B nOCJ1elJ,HeM
CJIY'fae BeJIWIHHa () onpen.eJ151eTC5I 113 BbIpa./KeHH5I [50]
q+p-2d
dqp=c# ,
(328)
rn:e d qp - Cpe.a.HHt'I .lI.HaMeTp KaneJIb, HaH.lI.eHI-IbIH 3KcnepHMeHTa.Tlb-
HO HJIH paClJeTOM;
d = 0, 2, 3 - COOTBeTCTBeHHO npH Ko.JIHlJeCTBeHHOM, nOBepx-
HOCTHOM llJIH 06'beMHOM pacnpelI.eJ1eHHH.
BeJIHqHHY Cd MO./KHO onpen.emITb H3 YCJIOBH5I, lJTO nOKa3aTeJlb
CTerreHH rrpH 3KcnOHeHTe paBeH HyJIlO., TOr.lI.a Cd = d qp .
DpH 06'beMHOM pacnpe.n.e.7IeHI1H (d = 3)
q+p-6=O.
(329)
PaBeHcTBo (329) y.n.oB.'1eTBop5leTC5I, HanpHMep, eCJlH q = 4 H
= 2, Tor..n.a C3 = d 42 H BbIpa.>KemIe (328) rrpffHHMaeT DIU!;
q+p-6
----:w-
d qp = d 4Z e
(330)
JJ.JI5I no.a.C<IeTa BeJIH<IHHbI () MO)KHO HCnOJI OBaTb Terrep& JII060H
Cpe.n.HHH .n.HaMeTp Kal1eJIb.
318
HalI60JIee npOCTOe BbIpa2KeHlIe nOJIY'IaeTCH, eCJ11I BbI6paTb cpe -
HUH nOBepxHOcTHbIH lIaMeTp (q = 2; P = 0):
I
l'J=
V / In d 42
d 2 ()
(331)
Ib aHa.11I3a <POPMYJ1bI (331) BU HO, 'ITO nplI 06'beMHOM pacnpe-
eJIeHIIII II HCn0J1b30BaHHII JIOraplI<pMlI'IeCKli HOpMaJ1bHOrO 3aKOHa
D,JIH I10CTpOeHlIH paC'IeTHbIX cYMMapHbIx KpliBbIX He06xoD,lIMO BbI-
[lHC.1fITb CpeD.HHH D.HaMeTp Kane.'lb d 42 .
nO.TJY'IeHHbIe 3aBliCliMOCTli (326), (327) H (331) n03BOJIHIOT D,O-
CTaTOqHO npoCTo paCCqHTaTb cYMMapHwe H D.H<p<pepeH IIaJ1bHWe
KpliBbIe paCnbIJIliBaHlIH, IICnOJIb3YH )J.JIH ::noro 3Ha'IeHlIH cpe)J.HlIx
HaMeTpoB KaneJ1b. nOCJIe HHe MorYT 6bITb onpe eJIeHbI paC'IeTOM
no KplITeplIaJIbHbIM ypaBHeHHflM HJIII HaH)J.eHbI 06pa60TIWH 3KcneplI-
MeHTaJlbHbIX aHHbIX.
PaCqeTHble II 3KcnepHMeHTaJ1bHbIe KpHBbIe paCnbIJ1HBaHlifl B pa3-
JIlI'IHbIe <pa3bI BnpbIcKa 1I306pa2KeHbI Ha pHC. 187. npH paCqeTe 3Ha-
'IeHHH a 1I b HCnOJIb30BaJ11I 3KcnepIIMeHTa.TJbHO onpe)J.eJleHHbIe Be.TJH-
'IlIHbI cpe)J.HlIx II MaKCHMa.!IbHbIX ,n:IIaMeTpOB Kane.TJb.
3Ha'IeHlIe IIHTerpaJ1a (313) onpe)J.eJ15IJIH no rOTOBbIM Ta6J11I aM.
PaC'IeT npoBe,n:eH D,J1H «cTyneH'IaToH» xapaKTeplIcTIIKII BnpbIcKa,
nOKa3aHHOH Ha pliC. 181, a. HCxo)J.HbIe ,n:aHHbIe, a TaK>Ke HeKoTopble
paC'IeTHbIe BeJIlI'IlIHbJ nplIBe)J.eHbI B Ta6.)I. 9. 3Ha'IeHlIH b, YKa3aHHbIe
B 'IlICJ1I1Te.'1e, OTHOCHTCH K JIOraplI<pMll'IeCKli HOpMaJIbHoMY 3aKoHY
pacnpe)J.eJIeHIIH, B 3HaMeHaTeJ1e - K ypaBHeHlIlO BepxHero npe-
)J.eJIa. nplIBe)J.eHHoe Ha plIC. 187 cpaBHeHlIe cYMMapHblx KplIBWX pac-
nbIJIliBaHllH nOKa3bIBaeT, 'ITO JIOrapll<pMll'IeCKII HOpMaJIbHbIH 3aKOH
pacnpe,n:eJIeHlIfI BO Bcex CJIyqafIX ,n:aeT 60.'lbrnee OTKJIOHeHlIe paC'IeT-
HbIX 1I 3KCI1eplIMeHTaJ1bHbIX 3HaqeHllH, 'IeM ypaBHeHlIe BepxHero npe-
e.'la.
BJIUJlHHe KOJIe6aTeJIbHOrO .lI.BH2KeHHJI HrJIbI (j:IOPCYHKH Ha MeJ1-
KOCTb paCnblJIHBaHHJI TOnJIHB8. KOJIe6aTeJIbHOe ;J,BH>KeHlIe HfJ18
<P0PCYHKH cOBeprnaeT Ha nycKoBbIX pe>KHMaX ,n:H3eJ1H, Kor,n:a Me.'1KOe
paCnbIJ1lIBaHlie Heo6xoLIHMO npH Ha.'1ll'lHH JII060H K8MepbI crOp8HII5I.
nplI pa60Te I}:JOPCYHKlI Ha pe>KlIMe aBTOKOJIe6aHliH Me.1KOCTb pac-
nbIJ1IIBaHIIH YJ1Y'IrnaeTCH I10'ITH B 2,5 pa3a [30]. I1cc.7Ie,n:oBaHlUI
10. H. rplI30,n:y6a [28] no BJ1IIHHIIIO K0J1e6aHIIH ,n:aBJIeHHH II CKOpO-
CTII B nOTOKe TOnJIIIBa npli Te'IeHIIlI B TOI1JIIIBOnpOBo,n:ax D,aJ1lI aHa-
JlOflI"lHble pe3Y JIbTaTbI.
M. H. KyxapeB [48] YCTaHOBIIJ1, 'ITO npH Ko.'1e6aHII5IX II rJ1 bI C
H1I3KOH 'IaCTOTOH, npM KOTOpOH 3a neplIOD, BnpblcKa cOBeprnaeT-
CH D,Ba Ko.TJe6aHliH cpe,n:HIIH ,n:lIaMeTp KaneJIb YMeHbrnaeTcH no cpaB-
HeHlI10 co CJIY'IaeM, Kor,n:a CKOpOCTb llCTe'IeHllH nOCT05IHHaH. npll
60JIbrneM 'IlICJIe K0J1e6aHllH llrJlbI MO>KeT YXY.lI.rnHTbCH Me.TJKOCTb pac-
nbUIHBaHIIH 1I3-3a YBeJIlI'IeHlIH "IlIC.TJa KpynHblx KaneJIb B Ha'IaJIe 1I
KOH e Ka>K,n:oro no,n:'beMa lIr J1bI.
319
T a6_Wlja 9
HCXOJ\HblC J\aHHble, npHHHTble .D:JIH paC'IeTa cYMMapHblx KpHBblX paCnblJIHBaHHH
'rOJl DO- MeTo)], ]J.HaMeTpbl KaneJIb B MK.'"
BopOTa V o B
KYJla4Ka" onpeAeJle- M/CCK I d 20 I d.. I d.. I d.. I :0 a
B epaa HHR d 10 d., /d max
OrrblT 59 70,8 81,2 90,5 102,2 112,5 132,5 220 1,429 -
0,7 PaC'-ICT 71,6 80,3 91 102,6 117,9 240 0,88 0,696
- -
OrrbIT 103,4 45,8 52,5 59,2 67,2 72 80,5 135 1,530 -
4,2 PaC'-ICT 43,8 47,8 52,8 58,1 64,6 125 0,787 0,534
- -
Onb!T 92,4 44,4 52,0 59,8 69,4 80 87,9 150 1,380 -
5,7 PaC'-IeT 45,9 50,3 56,0 61,9 69,3 142 0,718 0,500
- -
OnbIT 108 25,8 27,4 29,5 31,6 34 38,2 95 1,735 -
9,7 PaC4cT 30,6 33,4 36,9 40,6 45,7 120 1,173 1,251
- -
Onb!T 248,8 20,7 21,6 22,8 23,9 24,6 26,1 70 2,299 -
13,7 PaC'ICT 21,8 22,9 24,2 25,6 27,2 62 1,869 1,529
- -
OnblT 54 126,5 132 137 142,5 148 153 240 2,603 -
18,7 74,1 83,5 95 107,6 124.3 265 1,080 0,502
PaC'-IeT - -
P8C'leTbI, BbIIIO.J1HeHHbIe HaMIl no BJ1Il5IHIlIO KOJle6aHIlH paCXO.lJ,a
TOnJ1IlBa Ha Be.1Il4I1HY Cpe.lJ,Hero 06'beMHOrO .lJ,IlaMeTpa Kane.fIb, rIO-
Ka3aJ1H, <iTO B pe3YJIbTaTe nepepacnpe.lJ,eJ1emI5I KOJIH<ieCTB8 nO.lJ,8-
BaeMoro Ton.rIHBa B npou.ecce BnpbICKa C pa3J1lf4.HbIMH CKOpOCT5Il'iIH
Cpe.lJ,HIle .lJ,HaMeTpbI K8ne.TJb MorYT YMeHbliIaTbC5I Bcero Ha 20-40%.
C1e]J.oB8Te.TJbHO, OCHOBHoe YJ1Y<ilIleHIle paCnW1I1BaHHH npH .lJ,P06H-
meM BnpblcKe npoIlCxo]J.IlT 6J1aro]J.8p5I nYJ1bcau.H5IM cKopoCTeH H
JI.8BJIeHHit B nOTOKe Ton.1HB8, BbI3bmaeMbIM KOJIe6aHIl5IMIl Hr.fIbI.
B 3aK.fIIO<ieHIle c.1e.lJ,yeT OTMeTHTb, <iTO npOBO.lJ,5ITC5I HCCJ1eJI.OBa-
HIl5I no HcnO.TIb30BaHHIO y.1bTpa3BYKa H 3.fIeKTpWleCKoro nO.TI5I .l1..TI5I
paCnbIJ1HBaHH5I Ton.1HBa [20].
3. PA3BMTME Q)AKEnA TOnnM8A
DpH BnpbIcKe TOnJ1HBa B .l1.H3e.TIe B cJ1Y<iae 06'bel\1Horo HJ1H 06'b-
eMHo-n.leHO'-IHOrO cMece06pa30BaHH5I TOnJIHBO pacnpe]J.eJI5IeTC5I B
06'beMe KaMepbI crOpaHH5I nO.TIHOCTblO HJIH <iaCTH'lHO. P8Cnpe.l1.eJle-
320
HlIe Ton.rnma no KaMepe npOIlCxo.lU1T no.n: .n:eHCTBIIeM KIIHeTlJlleCKOH
3HeprIlIl, nplw6peTaeMOH cTpyei1 B npOl{eCce BnpbICKa, a TaK)J{e CflJI
ra3a. npu 3TOM .n:JI5! nG.'IY1.JeHH5! BbICOKHX 3KOHOMII1.JeCKIIX nOKa3aTe-
J1ei1 lI.BIIraTe.l5! .n:OJI)J{HO 6bITb .n:OCTurHYTO npaBH.TIbHOe C01.JeTaHUe
B3aHM011.ei'IcTBwI KaneJ1b TOn.'II1Ba H ra30BbIX nOTOKOB.
Pa3BHTHe flJaKeJIa paCnbIJ1eHHorO TOnJ1HBa B HenoJl,BH}f{HOH ra30-
BOH cpeJl,e. PaCCMaTpHBa5! pa3BHTue aKe.TJa TOnJIUBa, Ol..{eHHBalOT
np01I.BlDKeHue nepe.n:Hero <ppOHTa <paKeJ1a (.n:aJIbH06oHHOCTb), yroJI
KOHyca II pacnpe.n:eJIeHIIe Ton.TIHBa B <paKeJIe. DpOJl,BlDKeHHe nepeA-
Hero 4>pOHTa 4>aKeJ1a He,rlb35!. paCClJUTaTb, no.'Ib3Y5!.Cb ypaBHeHl1eM
no.leTa eAHHUlJHoi'1 Kan.rm, TaK KaK npIl 9TOM He YlJIITbIBaeTCH cnYT-
Hoe .n:Bl!)KeHIIe ra3a, !\OTOpbIH 3aXBaTbIBaeTCH aJ(e.TJOM II KOTOPOMY
1.JaCTl-l'lHO nepe.n:aeTCH !(l!HeTIIlJeCIWH 3HeprHH TOnJIHBa. KpoMe Toro,
B nepe.n:HeM 4>pOHTe aKeJ1a npIl BnpbICKe 3aTopMO)J{eHHbIe Kan.rm
CMeH5I1OTC5! HOBblMII C .n:OCTaTO IHbIM 3anaCOM KIIHeTII1.JeCKOH
3HeprHH.
I hreeTcH 6o.1bIlloe 'mora 3aBI1CI1MOCTeH .n:J1H paCIJ:eTa npOABHJKe-
HHH nepellHero poHTa aKeJ1a TOnJIHBa. Bce OHH BKJIlOIJ:alOT 3Kcne-
pHMeHTa.lbHbIe K03 I1l{I1eHTbI, II no.LJ:xolI. J( IiX BbIBO.n:y pa3.TJH'leH.
TaK, II. B. ACTaxoB [4] I1Cno.TJb3yeT no.TJY3MnIlpIl'lecKYIO 3aBIICII-
MOCTb .LJ:Bl1>KeHHH aKe.'1a Ton.TJHBa:
dLJ 1,5
-mT-=2pf4'CcjJV '
dt
(332)
r.ll.e fll T - Macca TOnJIHBa B 4>aKeJIe;
UifJ - CKOpOCTb npO.LJ:BII)J{eHII5I nepe.n:Hero <ppoHTa;
fifJ - MaKCI1Ma.TJbHa5! nJ1ow.a.n:b nOnepe'lHorO CeIJ:eHH5! <paKeJIa;
CifJ - K034>4>I1l{lIeHT COnpOTI-lBlIemiH ABI1}KeHHlO 4>aKeJIa.
P. B. PYCHlIOB [63] OCHOBbIBaeT BbIBO.n: <POPMYJ1bI npoJJ.BI1}KeHI1H
nepe.n:Hero poHTa aKe.'1a Ha 6a.laHce KHHeTIIIJ:eCKOH 3HeprnH, 01'-
.n:aBaeMoII TOnJ1HBOM ra3Y. Do.TJY1.JeHHOe HM ypaBHeHHe co.n:ep)KH'T
.n:Ba 3KcnepHMeHTa.TJbHbIX K034><PHl{I1eHTa.
A. C. JIbIllleBCKI1H [50], paccMaTpHBa5I <paKe.TJ: TOnJIHBa KaK CBO-
60!l:HYIO Typ6y.TJeHTHYlO CTPYIO H npHMeHHH TeopeMY 0 KOmI'leCTBe
!l:BH)J{eHHH, nOJIYIJ:H.TJ pacIleTHYIO 4>OPMYJIY .lI..TJH CKOpOCTII Ha ocn 4>a-
Ke.la B .lI060M celIeHHII:
V' _ dcLJ o f P
cjJ- 2 V-2u u xcjJ V Pt/J'
(333)
r.n:e au = kx - Be.1H'lHHa, onpe.n:e.1HeMaH 9Kcnep1lMeHTaJIbHO;
x = dRt/J
dx
; RifJ - YC.l0BHbIH panHY( <paKe.'Ia;
XifJ - paCCT05!HHe B.n:O.lb OCI1 4> a Ke.TJ a .n:o paCCMaTpHBae-
Mora Ce1.JeHH5!;
Va - Ha'laJIbHaH CKOpOCTb TOnJ1HBa Ha OCII <paKeJIa;
pifJ - n.l0THOCTb Cl\reCH B tLaHHOM CeIJ:eHI111 <!JaKeJIa.
21 381(83 748
321
Be.'ll1'IHHa au onpe.lI.e.'lHeTCH no .lI.OCTaTOtJHO C.7IOLKHOMY KpHTepl1-
8JIbHOMY ypaBHeHHlO. OpH BbIBO.lI.e 6bWO T8KLKe npHHHTO, lJTO Ton-
JIHBO B ,,'!106oH MOMeHT BnpblCKa pacnpe.lI.eJI5!.eTC5!. B 06"beMe aKe,\J.a
paBHOMepHO. .3TO npHBO..'l.l1T K p8BeHCTBY KO.1HlJeCTBa .lI.Bl1LKeHI1H B
nOnepelJHbIX CelJeHHHX <p8Ke.1a.
dRt/J
TaK KaK Be.1HlJHHa x B.l1.0,,'!b OCH <paKe:I8 nOCTOHHH8, TO - B
dx
KaLK.lI.bIH MOMeHT BpeMenl1 npe.lI.CTaB.'1HeT C060H TaHreHC nOJIOBl1Hbl
yr,,'la YCJIOBHOrO KOHYC8 <p8KeJla, T. e. x = tg a . ECJ111 npHHHTb .l1.8-
.iIee, lJTO HCTelJeHHe Ton.'IHBa H.n:eT C nOCTOHHHOH (cpe.lI.Heii) CKOpO-
CTblO H yro.'I YC.'10BHOrO KOHYC8 He H3MeHHeTCH, TO 113 BbIpaLKeHHH
(333) MOLKHO no.'IYlJHTb
e 1 dcV cp / P t (334)
q, = ,,/ Y2 . tg (J. V Pq, .
CTPYKTYPHO <pOpMy.'l8 (334) He 0T.1lHlJ8eTCH OT 3aBHCHMOCTH,
npl1Be.l1.eHHOii B pa60Te f17] 11 nO,JI)"lJeHHOii H8 OCHOB8HHH eme 60.'Iee
npocTblx .lI.OnYll.!.eHHH.
HeKOTopbIe Hcc.'Ie.l1.0BaTe.1H npe.l1.JlaralOT .lI..1H pactJeTa npO.lI.BIUKe-
HHH nepe.l1.Hero <ppOHTa <paKeJIa (AaJIbH060HHOCTH) HcnOJIb30BaTb
KpHTepHa.1bHble ypaBHeHHH. HanpHMep, B pa60Te [93] npHBO.lI.HTCH
ypaBl-IeHHe BH.lI.a
Lc}J _ A H O.48 R 0.3 ( P ) 0,35
-- t/J ° e - ,
de PB
r.n:e Ag; - nOCTOHHHaH;
(335)
Ho = Vol .
de '
Re - KpHTepHH PeHHOJIb.lI.Ca.
.lJ.JIH MHorocOnJ10BOH <pOpC)"HKH Ag; = 0,2. YpaBHeHHe (335) pe-
KOMeH.l1.yeTcH npHMeHHTb B .l1.Han830He 4000 < Re < 20 000.
H83BaHHble BbIllie COOTHOllIeHH5!. .lI.JIH paClJeTa npO.lI.BHLKeHHH ne-
pe.lI.Hero <ppOHTa <paKe,l'Ia .l1.alOT Y.l1.0B.'IeTBOpIITe.'IbHbIe COBna.lI.eHIIH C
OnbITHbIMH .lI.aHHbIMH npH npaBHJlbHOM nO.lI.60pe 3KcnepHMeHTaJlb-
HbIX K03<p<PHImeHTOB H TO.'IbKO .l1..'IH CJIYlJaeB xapaKTepHCTHK BnpbIC-
K8 C DJI8BHbIM H3MeHeHHeM CKOpOCTH I1CTeQeHI1H TODJllm8 113 COn,,10-
BbIX OTBepCTHH. B 3THX 3aBHCHMOCT5!.X HCnOJIb3YlOTCH OnbITHbIe
K03<p<pHll.HeHTbI H He YlJHTbIB8eTCH BpeMH Ha .l1.BHLKeHHe KaneJIb BHY-
TPH <p8Ke.'Ia OT con.'10BOrO OTBepCTHH .lI.0 nepe:I,HerO pOHTa. B .lI.eH-
CTBlITeJ1bHOCTH LKe 3aTpatJ11BaeTCH HeKOTopoe BpeMH, nOKa Karr.:1H,
HMelOll.!.He HOBYlO CKOpOCTb. .lI.OrOHHT nepenHHH <ppOHT H npHBe.lI.YT K
COOTBeTCTBYlOll.!.eMY H3MeHeHHlO B ero npO.l1.BHLKeHHH. .3TO OTlJeT.'IlI-
BO BH.lI.HO H3 COnOCT8BJIeHI1.5!. «CTynew.JaToro» 38KOH8 nO.lI.aQI1., KOr.l1.a
CKOpOCTb lICTelJeHHH TOll.'IHBa pe3KO H3MeHHeTCH, H KpHBOH npOj),BH-
LKeHHH nepe.l1.Hero <ppOHTa <paKeJ1a (pHC. 188). CTpeJIKOii Ha PHCYH-
Ke OTMelJe.Ho HalJaJ10 HCTelJeHHH TOnJIHBa C 60JIblIleH CKOpOCTblO.
322
Yro KOHyca aKe a npH HCTe'IeHHH TOn HBa 'Iepe3 Kpyr ue
COnJ10BbIe OTBepCTHSI TaK)Ke 3aBHCHT OT pSI,u:a 4>aKTOpOB. CPOPMY bl
.n SI paC'IeTa yrJIa KOHyca aKe.,'Ia nplIBe.neHbI B pa60Tax [4, 50, 93].
l1.ml oueHKH pacnpe.neJ1eHHSI Tonmma B 4>aKeJIe T. M. MeJIbKY-
MOBbIM B pa60T( [52] npHMeHeHo ypaBHeHlIe HopMa.'lbHOro 3aKOHa
p8cnpe,u:eJleHHSI H npHBe,u:eHbI pe3YJ1bTaTbI Hcc.'Ie.ll.OBaHHll pacnpe-
;rJ.e eHll5l Ton:nma B GJaKeJle, nOJlYlJ.eHHble oT6opOM B3 pa3JlR'.J.HbIX
TO'IeK. Bce OnbITHUe .n:aHHbJe YKa3bIBalOT Ha HepaBHoMepHocTb pac-
npe,u:e.'IeHl1SI Ton.'IHBa B nOnepe'IHbIX Ce'IeHl1SIX cpaKeJ1a 1I no ero .n:JlH-
.1Y'
HH'
l!jJaf}
f6,O
f2,O
8,0
o
() f,0 2,0 10
PHC. 188. iIaJlbH060HHOCTb 4JaKcJ1a H xapaKTepHCTHKlI
Bnpb!CK8 TonJ1HBonoJ.\8!OI1.(CIf annapaTypbl J],H3eJlH 51M3
npH n = 550 06/MUH, q1f = 115 .UM 3 , de = 0.32 MM:
1 - L tjJ npn p np 15 Kr;C.1t'; 2 - L tjJ npH P np = I Kr;C.M';
3 - Aq
He. DpH 3TOM xapaKTep pacnpe,u:e.'IeHHSI Ton.'IHBa no ,u:JIHHe 4>aKeJla
H3MeHSIeTCSI B npol.{ecce BnpbIcK8.
Pa3BlITlIe rpaKeJIa TOnJIIIBa B norOKe ra38. Do p83BHTHlO aKe.'Ia
TOfl.TIHBa B nOTOKe ra3a npOBe,u:eHO nOKa OTHOCHTeJIbHD Ma.'IO Hcc.TJe-
,u:OBaHHH. B pa60Te {52] YKa3bIBaeTCH, 'ITO B03JI.YX, ,u:BH)Kyrn.HHCSI
co CKOpOCTblO .IJ,O 18,3 lrf.lceK, pa3pyrnaeT BO BpeM5I BnpbIcKa TOJIbKO
BHeWHlle C.-lOH 8Ke.la 11 CI10C06cTByeT pacI1pe.n:e.'1eHfHO BnpblcHYTO-
10 TOnm1Ba B 06"beJ\Ie. l1.J1SI pa3pyrneHHH B npol.{ecce BnpbIcKa cep,lI.-
l.{eBHHbI 4>aKeJIa Tpe6yeTcH CKOpOCTb OKOJIO 90 MiceK.
Ha pHC. 189 nOKa3aHa KOH Hrypal.{HSI aKeJIa Ton.1HBa npH
BnpblcKe B HenO.IJ,BH)KHYlO ra30BYlO cpe,lI.y H B nOTOK ra3a npB pa3-
'IJIllHbIX yr.'I8X Me)K.n:y OCblO COllJlOBOrO oTBepcTwr H BeKTopoM CKO-
pOCTH nOTOKa (onbITbI MAl1.11). oTorpa4>HpoBaHHe <paKe.'Ia npo-
BO,lI.HJ10Cb Ha cneUHa.'1bHOll 'CTaHOBKe [77J 06bJ11HbIM <pOToannapa-
TOM npH HcnO.lb30BaHHH HCKpOBoro OCBen-ITe lSI. CKOpOCTb nOTOKa
perYJ1HpOBa aCb nYTeM H3MeHeHHH lJ.HCJI8 060pOTOB 06"beMHorO H8-
rHeTaTe.'IH. Ha pHC. 190 I10K83aHbl <p8KeJIbl T0I1J1HB8 npH BrrpblcKc
'Iepe3 .lI.Ba con.l0BbIX oTBepcTHH no,u: pa3.J'IH'IHbIMH yrJI8MH K BeKTopy
CKOpOCTH nOTOKa. 113 <pOTorpa<pHll BH,u:HO, 'ITO no.ll. .IJ,eHCTBHeM no-
21* 323
Q; !';: 2 0 \ 0" II
C::;>'p.. c
2.:E t::11 1:"''<
'-' 0.. (1) A
Q) E cd . '6 '-
:!O ng,..,
:::: 2..£- i::" to; t:?f5
r=: 5:: .= :
6: Ct) r- L C C I n
..... a c::: I Ii r;.,
. :!: c: J: C'i:i I:'
2 ==f := 2 II r;:@ E::o'.
-cg:;>.Q ::::J I:;::,g
!- i: I 1'1 I
cS c:t' t:. t: li
1;:0'
"-S'
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t:s11
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;
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r--l '.
1 r: .
1- .. f
l-- I
r
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-r--r- r ---r- , I . -r- 7:t I . ,,.
--r- J;j, OJ >-r-'NiioT -.-- 'W'koi .... -+----!7ii/jjj ......
""-
.......
,..
<:::>
<::;".
(
;
t:::::,.
s::.
<:::;,'
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<::::o V .
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I
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<::::0'
<:::>'
TOKa ra3a 3Ha4.HTe.lbHO H3I\1emIIOTCH reOMeTplI4.eCKHe napaMeTpbI
<fJaKe:W.
LI..J1H aHa.1H3a npH:UeM, IITO OCb Y HanpaB.leHa nepneH.J.HKYJ1Hp-
BO, a OCb x - no nOTORV ra3a. Be.1HIIHHY vr.1a Me)j{.lJ.V OCbIO con.10-
Boro OTBepCHIH H Roop.rumaTOH y 0603Ha.iI11\I :!:: uc, -+- OTHOCHTCH K
BnpbICKY no nOTOKY; - OTHOCHTCH K BnpbICKY npOTHB nOTOKa ra3a.
Tor.lJ.a npH U c = 0° Ha:lHIIHe nOTOKa ra3a:
a) YMeHblllaeT npO,!!.BH)j{eBHe nepe.lJ.HerO <fJpoHTa <fJaKe.1a no Ha-
npaBJ1eHHIO Koop,!!.HHaTbI Y;
6) cMeruaeT BHelllHHe C.I0H <fJaKe.la no HanpaB.leHHIO I<00p.lJ.HHa-
TbI x co CI<OpOCTbIO, 6JlH3KOH K CKOpOCHI nOTOKa;
B) YBeJ1H4.HBaeT n Ollla.lJ.b npOeKUHI1 aKe a Ha n OCKOCTb xy.
: $"
fi) I
J
1
j
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1
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5)
" t Mt:el< 0.150
0.240
M40
fl.7f:JO
PHC. 190. Pa.mHTHC lj:JaKc.loB Ton.1HBa npH BnpbJCKe '-ICpe3 .D:Ba con.1OBblX OT-
BCpCTH5I (a c = 30°; ac = -45°):
a - lJ n 0; 6 - lJ n tjO .,,/ eeR
OTKJlOHeHHe yr.J1a BCTpellH aKeJla Ton HBa C nOTOKOM ra3a OT
90° BbI3bIBaeT .lJ.a.TJbHeHlllee YI\IeHbllleHI1e npO.lJ.BH)j{eHHH nepe.lJ.Hero
poHTa aKe.1a B.lJ.O.Jlb Koop.lJ.HHaTbI y. OTMe'laeTCH TaKiKe YMeHb-
IlIeHHe n.lOUWlI.I1 npOeKLI.I1H cpaKeJla Ha n.lOCKOCTb xy.
113 pHC. 190 BH.lJ.HO, IITO npH Ha.1HIIHH .lJ.BY..x con.J10BbIX oTBepcTHH
B YCJlOBHHX 3KcnepHMeHTa no.lJ. .lJ.eHCTBHeM nOTOKa ra3a TOnJ1HBO
nepeHOCHTCH H3 OlI.HOrO cpaKe.la B .lJ.pyrOH. AHa.l0rHIIHbIe cpOTorpa-
<fJHH <fJaKe.la TOn.'lHBa npH BnpbICKe llepe3 IlITHcpTOBYIO <fJ0PCYHKY B
BHxpeBYIO KaMepy rrO.JIY4.H.TJ . L C. XOBax [75] npH HCC.lelI.OBaHIHI Ha
,llIIHal\lH4.ecI<OH MO.J.e.1H.
J{ocTaT04Ho nOlI.p06HOe TeOpeTH4.eCKOe HCCJ1e.lJ.OBaHHe .lJ.BHJKeHHH
e.J.HHH'lHOH Kan.!lH no.lJ. lleHCTBHeM nOTOKa ra3a nOCTOHHHOH H nepe-
MeHHOH CKOpOCTH no nYTH C e.lJ.OBaHHH KanJlH H3JlOR{eHO B pa60Te
{6IJ. OpU6mIR{eHHbIH paCqeT.lJ.BHiKeHlHl elI.HHW1HbIX KaneJlb nolI. lI.eH-
CTBHeM nOTOKa ra3a nOCTOHHHOH CKOpOCTH AaH B pa60Te [77].
325
I DO "
0)8 2 6 f..J.....
II '0 f::!
z...c ct:: ..... __ 055
- g. f= '- <
"'L. t::\.;:: fl 0.::: II g
E = c L.!:::t::::" '- 0 :; r:::+
o g.;;':.::;:: '" 8 I
:= j:. L< C I '-
a. g g I .. I '. '"
cr) = 3" r::: :::Jr:: -
;::9»", :::J» M
. z:=:! I r \
u ::: CJ s:: I
=c>:: c.. ::::::):::r.
c... r::; =:
'
<;:;,
.
......
f
"'-
....-
, .
r-----l
f---.. J l
l-- i
f-
. ,
' - i ;;(JI
c:::
('0,
..,.. .
<:;:"
\;:)
II
:::::,<::
t
, r . .
.
. , , ' .
' , ...... -'- kN(J1
-,
. ,
..
.
:"I ..t
K.
.
j
',.
..
'-tS
<:::::;
f
. t
<::::,,,
-
<:::$
f
,
....,
1(.1' .'
...
"'J,
<:::S
I
c::::,'
.
<:::;)
. .
<:::.
I
. .' , . . ,
.... -+-- }.yHOI
;;:;;-
-;;;-
r . ...,
f .
III.
c
'>:5,
<:::$',
t
.'
'"
«:::;. -
I :
oJ
'-<S
<::::"
I
%:.
""...
. t"'":>
.\
IV
L
<'\j .
. <:::$.
'4-
..... NNOI
c::::,1
'
oil
.
c::::,
c::::,'
.;;t.
c::::,'
"'"5
<:::$'
<'\j
c::::,'
;::;,
....,
TOIia ra3a 3Ha'lHTe.lbHO H31\IeHHIOTCfI reO!\leTpIPIeCKHe napaMeTpbl
cpaKe.1a.
11.'1H aHa.1H3a npH:lIel\l. '1TO OCb Y HanpaB.1eHa nepneH.:U-IKy-JIf!P-
HO, a OCb x - no nOTOKV ra3a. Be.'1H'IHHY \T.1Ja MeLKJI:V OCblO con.'1o-
Bora OTBepCTIHI H KoopllHHaTOH Y 0603HaQUi\I ::!: ac. +- OTHOCHTCH K
BnpbICKY no nOTOKY; - OTHOCHTCH K BnpbICKY npOTHB nOTOKa ra3a.
Tor,lta npH a c = 0° Ha.ll1'1He nOTOKa ra3a:
a) YMeHbillaeT npo.n.BlDKeHHe nepe.n.Hero cppOHTa l}:>aKe.la no Ha-
npaB eHHIO Koop.u.HHaTbl Y;
6) CMel11aeT BHeIllHHe C:Ion tPaKe:la no HanpaB:IeHHlO KOOpJI:HHa-
TbI x co CI<OpOCTblO, 6J1H3KOfI K CKOpOCTH nOTOKa;
B) YBeJIH'IliBaeT n:lOlll.a!l.b npoeKl1.Uu cpaKe:la Ha n."lOCKOCTb xy.
/\
/
1
0)
i
.
1/ 0 "0
t MCPK 0.070 0.160 4*50
1 . \.
r . 5)
Un i
$::> -' I
"'I
l. t MceK 0.150 12240 0.540 a7110
PIIC. 190. Pa3B1ITIIC lj:JaKc.10B Ton.llfBa npll BnpblcKe '-Iepe3 .!J.Ba con.10BblX OT-
BepcTHH (ac = 30°; a c = -45°):
a - V n 0; 6 - U n 60 Miceli
OTKJ10HeHHe yr.la BCTpe'lH l}:>aKe.la TOn.1HBa C nOTOKOI\I ra3a OT
90° Bbl3bIBaeT .n.aJlbHeMillee )"I\IeHbIlleHHe npO,ltBl'J)KeHHH nepe.n.Hero
cppoHTa tPaI{e:la B.n.O.lb Koop.n.HHaTbl y. OTMe'IaeTcH TaK)Ke YMeHb-
IlleHue n."lOlll.a,ltH npOeKl1.HH cpaKe;la Ha n.'10CKOCTb xy.
113 puc. 190 BH.!I.HO, 'lTO npH Ha.1ll'UIH .!I.BYx COnJIOBbIX OTBepCTl-IH
B YCJIOBHHX .3I{CnepI1I\IeHTa nOJI: .'I.eHCTBHeM nOTOKa ra3a TOnJ1I1BO
nepeHOCHTCH 113 OlI.HOrO <fJaKe.la B .n.pyrOH. AHa.TJOrll'lHbIe cpOTorpa-
cplUI cpaKe.la Ton."lHBa npH BnpbICKe 'lepe3 llITHcpTOBYIO cpOPCYHKY B
BHxpeBYIO KaI\Iepy nO.1Y'lIW 1\,1. C. XOBax [75] npH HCC.le.!I.OBaHHH Ha
,ltHHai\Ill'leCKOH I\lO.J.e.1H.
.IlocTaTO'lHO nOJI:p06HOe TeOpeTII'leCKOe HCC.1eJI:OBaHHe JI:BHLKeHI-IH
e.!I.HHH'lHO i Kan.'1H no,lt .n.eflcTBHeM nOTOKa ra3a nOCTOHHHOH H nepe-
MeHHoM CKOpOCTH no nYTII C.1e.n.OBaHI1H Kan.1H I13.10m::eHO B pa60Te
[61]. npH6.1H)KeHHbIfl paC'IeT .'!:BHLKeHHH e.'!:IIHII'IHbIX Kane.1b noJI. .!I.eH-
CTBHeI\I nOTOKa ra3a nOCTOHHHOH CKOpOCTH ,ltaH B pa60Te [77].
325
B pa60Te {61] npHBeJ],eHbI TaK}Ke pe3Y.1bT8.TbI 3KCnepHMeHTa.1b-
HOro llCC.1eJ],OBaHHH pacnpeJ],e.rIeHHfl Kane.'Ib no- - pa3MepaM npH
BnpbICKe B nOTOK ra3a, J],BH}J{yllterOCSI nepneHJ],HKYJ1HpHO OCH conao-
Boro OTBepCTHH. AHa.'1H3 onbITOB n03BO.'1HJ1 CAe.rIaTb BbIBOJ],bI 0 TOM,
qTO MaKCHMYMbI KpHBbIX pacnpeJ],e.1JeHHH COOTBeTCTBYlOT TpaeKTO-
pllHM J],Bll}J{eHllH eJ],IlHllt.JHbIX Kane.lb. Cenapall.HH KaneJIb npOHB-
JIHeTCH cJIa6o. OTHOCHTeJIbHOe paccellBaHHe Kane.'Ib noJ], J],eHcTBHeM
nOTOKa ra3a HeCKO.JlbKO B03pacTaeT C YMeHbweHlleM HX J],llaMeTpa.
3TH .lI.aHHbIe cooTBeTcTBYlOT nO.lI.a'le Tonmma B cpeJ],y C aTMOC<pep-
HbIMH yCJ10BHHMH npH Ma,!10t'1 CKOpOCTH HCTet.JeHHH H3 COnJIOBOrO
oTBepCTllSI.
MCnO.Jlb3YSI .lI.a.Jlee HOpMaJ1bHbIH 3aKOH pacnpeJ],eJIeHHH KaneJ1b,
nO.TIYt.JHJIH Bblpa}J{eHHe J],JIH oll.eHKH pacnpeJ],e.TIeHllH }J{1lJ],KOH l}>a3bI
(TOnJ1HBa) B nonepet.JHoM cet.JeHHll <paKeJ1a npH ero B3aHMOJ],eHCT-
BlllI C nOTOKOM ra3a {61]. OpH BbIBo.ll.e cooTBeTcTBYlOlltHX 3aBHCHMO-
CTeH 6bI.1JO npllHHTO, 'lTO KanJIH B <paKe.'1e He B3aHMOJ],eHCTBYlOT O.ll.Ha
C J],PyroiL
r naB a VII. OCHOBbl npOEKTJofPOBAHJofSI Jof Bbl60PA
nAPAMETPOB TOnI1HBHbIX CJofCTEM Jof nYTJof JofX
YCOBEPWEHCTBOBAHHSI
f. Bbl60P nAPAMETPOB XAPAKTEPHCTHKH BnPblCKA
H npOEKTHPOBAHHE TonnHBHO CHCTEMbl
no .3AAAHHbIM nOKA3ATEnSiM ABJ1fATEnSi
C BocnnAMEHEHHEM OT C>KATHSI
no cYIJJ.eCTBY TOnJIHBHbIe CHCTeMbI npOeKTI1pYlOTCH .lJ}IH HeH3Be-
CTHOH xapaKTepl1CTHIm BnpbIcKa, nOToMY I.JTO OHa MO)J{eT 6bITb pac-
CI.JI1TaHa TOJIbKO LI.JI5I cnpoeKTHpOBaHHOH TOmIMBHOH CI1CTeMbl. DOJIee
l.(e.;leco06pa3HO BHaI.Ja.1Je BbI6paTb xapaKTepI1CTHKY BnpbICKa, a 3a-
Tel\I .lJ,J15I Hee npoeKTHpOBaTb Ton.J1HBHYIO CHCTeMY. Ho LI.JIH TaKoro
nO.lJ,xoLI.a K perneHHIO 3aLI.aI.JH, KOTOpbIH [103BO.'111.1 6bI paCCI.JI1TaTb He
xapaKTepHCTHKY BnpbICKa no napaMeTpaM CIfCTeMbI, a, Ha060pOT,
napaMeTpbI CHCTeMbI no xapaKTepHCTI1Ke BnpbICKa, He06xoLI.HMO pa3-
pa60TaTb COOTBeTCTBYIOIJJ.HH MeTOLI. paCI.JeTa. OCHOBbI TaKoro MeTOLI.a
6bI.1H .lJ,aHbI B pa60Te {6], 3aTeM OHH 6bI.'lIt HeCKOJIbKO pa3BHTbI
JI. K 4e"lnaHOM H A. H. HcaeBbIM. B LI.aHHOH pa60Te MbI TaK)J{e
CLI.e.1aJIH nonbITKY YTOI.JHHTb YKa3aHHbIe Bblrne OCHOBbI 06paTHoro
MeTOLI.a paCI.JeTa nYTeM YI.JeTa npI16.;1I1)J{eHHOH B3aI1MOCB5I3I1 Me)J{LI.Y
xapaKTepHCTHKOH BnpbICKa H pa60IJHM npOl.(eCCOM LI.H3e. T IH. Ehy B3a-
Hl\IOCBH3b MbI BbIpa)J{aeM MeTOLI.OM KOopLI.HHal.(HI1 xapaKTepHCTHKH
Bi1pbICKa C HHLI.HKaTOpHOH LI.Harpal\IMOH llH3e.1H. B CBH3H C 3THM
npellJIaraeMbIH MeTOLI. ueJ1eC006pa3HO 113JIaraTb OLI.HOBpeMeHHO C
paC'leTOM napaMeTpOB CI1CTeMbI KOHKpeTHoro )J.I13eJI5I. BbI6epeM LI..'15I
TaKoro paCI.JeTa LI.113eJ1b 5IM3-236. B OCHOBY KoopJJ.HHal.(HH 6bI.'lH
nO.10)J{eHbI pa60TbI [7, 25, 27, 67], a TaKiKe pa60TbI rpynnbI HCCJIe-
JJ.oBaTeJ1eH XapbKoBcKoro nOJIHTeXHHI.JeCKOrO ItHCTHTYTa, PYKOBOLI.H-
MOH npo<p. 5I. M. MaHepoM. PaCI.JeT 6YLI.eM I1pOBOLI.HTb LI.J15I HOMH-
Ha:IbHoro pe}KI1Ma, LI.JI5I KOToporo q,. = 0,115 2/I{UKJL. COrJIaCHO aHa-
JIH3Y YKa3aHHbIx pa60T 3aKOH nOLI.aI.JH TOnJIHI3a ,aOJ1)J{eH 6bITb Ta-
KHM, I.JTo6bI 3a nepHOlI. 3ana3LI.bIBaHH5I Bocn.'1aMeHeHH5I 6bIJ10 nOLI.aHO
30-40% Q 1 f' 3a nepl1oLI. OT HaI.JaJ1a BOCnJ1aMeI1eHHH JJ.O LI.OCTI1)J{eHlIH
pzmax = 50 + 55% q,., a BCH nOJJ.a'la TOnJIMB3 JJ.OJI)J{Ha OKOH'lHTbCH
B npeLI.e.Tlax 5,0-10° yr.Tla nOBopOTa BaJHi JJ.BHraTeJI5I * noc.Tle B. M. T
nOI.JTI1 Bce cOBpeMeHHbIe TOnJ1HBHbIe CHCTeMbI fIe 06eCneI.JHBa1OT YKa-
3aHHoro pacnpeJJ.eJIeHHH TOnJ1HBa BO BpeMeHH.
YKa3aHHbIH 3aKOH nOJJ.a'lH TOnJII1Ba CJIeLI.yeT CI.JHTaTb nepBbIM
npH6.'1mKeHHeM K Tpe6yeMoH xapaKTepHcTHKe BnpbICKa, KOTopaH B
JJ.a.lbHeHrneM JJ.OJ1)J{Ha YTO'IHHTbCH no Mepe HaKOnJIeHHH 3KcnepHMeH-
'" B I .!J.aHHOH rJlaBbl BpCM5I Ta!{LKC 6YACM BbIpml{aTb B rpa.n:ycax yrJla no-
BopOTa Ba.TJa lIBHraTC.TJH.
327
T3.!IbHOrO M3TepH3.13. OJI:HaKO OTMeqeHHbIe Bblllle TOQKI1 11 $a3bl
Ti - 33na3,!J.bIBaeJVIOe BOCn.laMeHeHHe, pZmax - MaKCHIMa.'IbHOe JI:aB-
.'IeHHe CrOpaHI15I, a TaIOKe MOMeHT OKOH'IaHHH nOD:a'IIli Ton,)lHBa HB-
.J1HIOTCH BnO.'IHe D:OCTaTO'lHbIMH ,lI.:m onpe,'J:eJleHHH npH6. T IHTh':eHHOH
KOOpD:HHaIJ.HH xapaKTepHCTHKH BopbICKa Ha HH,lI.HI{aTOpHO}I ,'J:HarpaM-
Me pa6o'lero npoIJ.ecca JI:H3e:m.
B nepBoM npH6J1HTh':eHHH Be.1H'IHHY nepHo.ll:a 3ana3,lI.bIBaHHH BOC-
n"laMeHeHI15! MO}KHO onpeJI:e.'1HTb no $opMYJ1e [67]
o ,- IT EcO,34
Tj= B.lO-- ; c 1/ -'5....e----w;-; (336)
J' Px
I [ b '
c=- 1+0,5-(B-l) j ;
£'
6 = [ ( I + : ) - ( cos cp + + cos 2cp ) ] ;
v'
f: )=
Vh '
r,lI.e E - 3KcnepHMeHTaJlbHbIH K03$$HIJ.HeHT, 3aBI1CHIIJ.HH OT KaTh':Y-
meikH 3HeprHH aKTHBaIJ.HH H TeMoepaTypHoro K03$$HIJ.H-
eHTa HcnapeHHH Ton.1HBa.
KOOp,lI.IIHHPYH xapaKTepHCTHKY BnpbICI\a no Ti H pzmax, MbI TeM
caMbIM nbITaeMCH COQeTaTb xapaKTepHCTl1KY BnpbICKa C HeKOTopbI-
MH oco6eHHOCTHMH npOTeKaHHH pa6o'lero npOIJ.ecca JI:,H3e.'1H. BeaH-
QHHOH Ti MOTh':HO 3a.ll:aTbCH C ,lI.ocTaTO'lHOH .lI:.'IH npaKTHKH TO'lHOCTbIO.
)1BIIraTe.'lb npoeKTIIpyeTclI Ha onpe.ll:eJIeHHYIO MOm HOCTb II 'IHC-
.10 060pOTOB. 3a.ll:aIOT TaKTh':e Th':e"laTeJIbHbIe TeXHHKO-3KOHOMH'IeCKHe
nOKa3aTeJIII .lI:BHraTe,)llI, B03MO}KHOCTb nOJl !lleHHSJ KOTOpbIX npH6,)lH-
Th':eHHO npOBepSJeTCH npH TenJ1OBOM paC'IeTe pa6o'lero npOIJ.ecca.
B Ka'leCTBe paC'leTHOrO 'lame Bcero BbI6HpaIOT HOMHHla.'IbHbIH pe-
Th':HM. )1JISJ 6bICTPOXO,lI.HOrO .lI:H3e.1H C n = 2000 -7- 2100 o6/.MUIi npH
HOMHHa.'1bHOM peTh':HMe nepHOlI. 3ana31I.bIBaHHH Bocn.'IaM,eHeHHH MmK-
HO npHHHTb paBHbIM 12° yr,)13 nOBopOTa Ba.la ,!J.BHraTe.'1SJ. EC.'IH B
.l1.0nOJIHeHHe K .9TOMY npHHHTb onepe}KeHHe nO.II.a'lH Tonmma paBHblM
22°, TO HHTerpa.'1bHaH xapaKTepHCTHKa BnpbICKa TOI1.1HBa, Y.II.OBJ1e-
TBOpHIOmaSJ YKa3aHHbIM Tpe6oBaHHSJM, .lI:O.'1}KH3 HMeTb BH.lI: npHMep-
HO TaKOIt KaK nOKa3aHO Ha pHC. 191.
KmlwIecTBo TOnJIHBa, KOTopoe Heo6xo.II.Hl\1O nO.II.aTb B O.II.HH IJ.H-
JIHH.II.P .II.BHraTe.l5! 3a pa6o'IHH IJ.HK.l,
ReNe ( 3 37
q'l = 120in ' )
r.II.e i - 'IHC.10 IJ.HJIHH.II.pOB .II.BHraTe,)lSJ.
O.ll:HOBpeMeHHO C H3J10Th':eHHeM MeTO.II.a paCC'lHTaeM, K3KHe napa-
MeTpbI lI.o.1]Th':Ha HMeTb TOnJIHBH3H CHCTeMa 3BTOM06HJlbHOrO D:II3eJIH
HM3-236, QTo6bI 06eCne'lI1Tb xapaKTepHCTHKY BnpbICK3, H306pa)KeH-
HYIO Ha pHC. 191. )1J1H .II.H3eJIII HM3-236 npHMeM q1J 115 .M.M 3 ,
328
<jJn = 30°, P max= 425 liTlcM 2 ; npH IeJ\l B Ka}KJJ,OM c.'Y'Iae 3TH napa-
MeTpbI BbI6HpalOTCSI B 3aBHCHMOCTH OT nma ..'I.BHraTe.TISI. B3aHMO-
CBSI3b Me}J{JJ,Y q1l H rtcfc npH6.'IH}J{eHHO MO}J{HO onpeJJ,e.'IHTb no CJ1e-
JJ,YIOIlI.eH <j>opMYJ1e: %
f t /2 V ' (338
qlj=rtc c en p )/ p Pl/J.cp-P lI , ) 80
OTKYAa 6J
rtcfc =
6nq"
(339) 40
r.n.e
/ 2 ,
n \/ p V Pl/J.cp-p,!
P .cP = +P max [6].
20
o
-40
8.M.m. +20
B <j>opMYJIe (338) t Bnp = .!fu. OpHHSIB .n.J1SI
6n
5IM3-236 P1l = const = 50 Kr;Ot 2 H nOJJ,CTaBHB
3TO 3Ha'IeHHe B Bblpa}J{eHHe (339), HaHJJ,eM, 'ITO
Jtcfc = 0,247 MM 2 . COrJIaCHO OnbITHbIM JJ,aHHbI'\I
rtc = 0,75, TorJJ,a fe = 0,33 MM 2 . B COOTBeTCTBHI1
C pHC. 191 npHMeM, 'ITO 3a rrepI1o.n. 3ana3JJ,bIBaHHSI BOCnJIaMeJ-IeHI1SI
AO.JI}J{HO 6bITb nOJJ,aHO .-- 32,5 % Q1J, MJ1I1 38,5 MM 3 TOnJIHBa. 4T06bI
onpeAeJ1HTb cpeJJ,HIOIO CKOpOCTb BnpbIcKa C'ti 3a 3TOT oTpe30K Bpe-
MeHH, HanHllieM <j>OPMYJIY
q;'i = rtcfcT;CTi,
OTKYJJ,a
Plie. 191. l1HTC-
rpao1bHOC pacnpe,'\e-
.lCHliC TOII.lllBa BO
BpCMCHH .ll:Jl5I .'J,H3C-
.151 5IM3-236
(340)
C <c6n 62 100.0,0385 163 5 j
Ti = - - , l ceK.
!-tcfC 'ti 0,0247.12
Be.1II'II1HY C'ti npI16JIH}J{eHHO MO}J{HO BbIpa3HTb 'Iepe3 cpeJJ,Hee
, I, ,
A3BJIeHI1e BnpbICK3 PtjJ.cp =2 PtjJi' rJJ,e Pl/Ji - JJ,aB.1eHlIe BnpbICKa B
MOMeHT Ha'IaJIa BocnJ1aMeHeHI1SI:
,r2" / I
C.ti=V/ p} 2P' i-PlI'
OTKYJJ,a
, C" 2
P q,i = P ';:i + P II .
(341 )
Ooc.,e nOJJ,CTaHOBKH B <j>OPMYJIY H3BeCTHbIX BeJIH'IHH HaHJJ,eM,
'ITO AJISI paCCMaTpHBaeMoro npHMepa P i = 340,5 KFjCM 2 .
0pHMeM, 'ITO pzrnax JJ,OCTHraeTCSI 'Iepe3 1° nOCJIe B. M. T. EYJJ,eM
C'IHTaTb TaK}J{e, 'ITO P nlax H Pzrnax JJ,OCTHraIOTCH OJJ,HOBpeMeHHO.
329
Tor.na CpelI.Hee lI.aBJ1eHl1e BnpbICKa 3a nepHOLI OT H81.J:8JI8 BOCnJI8Me-
HeHMSl .no pzmax paBHO
. Pt/>i+Pljlmax _ 340,5+425 _ 382 5 r/ 2
Pt/J.cp = 2 - 2 - , K CM.
(342)
KO.Tm1.J:eCTBO TO nJIl1B a , nOlI.8HHoro B 3TOH q>83e,
, · /2 V'
q" = f/Jn/lcfc V p Pt/J.cp-PI{ = 0,247.11.1535.18,2 = 63,2
I{ 6n 6.2100
M.M 2
(343)
.n.O.TDKHO 6bITb nOlI.aHO cor.TJaCHO npHHSlTOMY pacnpelI.eJ1eHHlO 55%
OT q1j, I1JII1 63,5 M.M 3 . TaKl1M 06p830M, npH fP; = 11° 38.n.aHHbIe pa-
Hee YCJ10BHH BnpbICKa TOnJIHBa np8KTH1.J:eCKH 06eCne1.J:HBalOTCSl nOJ1-
HOCTblO. D.onYCTI1M [8], 1.J:TO P max COOTBeTcTByeT F ( t- ) ,KOTO-
, a max
paH 06p83yeTcH B MOMeHT Ha1.J:aJI8 OTCe1.J:KH Y Hacoca. B CBH311 C
HallaJIOM OTcellKll B lI.8JIbHeHllleM 8MnJIllTy.n.bI BOJIH F (t), 8 CJ1e.n.o-
BaTe.TJbHO, II F (t- ) HatlHYT YMeHblllaTbC5!, T. e. TOnJIIIBO 6y.n.eT
BnpblcKIIB8TbCH C YMeHblllalOrn.HMHCH CKOpOCTHMH.
B TOllJIHBHbIX CHCTeM8X 6bICTPOXO.n.HbIX LIH3e.J1err 'Iarn.e Bcero ne-
pHOlI. OT pe3Koro na.n.eHHH lI.8BJIeHHH .n.o MOMeHTa OTXOlI.a HrJIbI OT
ynopa COCT8B.TIHeT 2-2,5° yrJIa nOBopoTa Ba.TJ8 .n.BHraTe.TJ5!. npHMeM
ero paBHbIM 2°. CpelI.Hee .n.aB.TJeHHe BnpbIcK8 B 3TOM ne'pHOlI.e, , co-
. Pt/J max + Pt/J.nn
rJIaCHO npe.n.bIlI.yrn.eMy, npHMeM paBHbIM Pt/J.Hn cp 2
r.n.e P .Hn-lI.8B.TJeHHe BnpbICKa Ton.'IHBa B MOMeHT OTXOlI.a Hr.'IbI OT
ynopa. D.aB.'!eHHe TOnJ1HB8 B 06'beMe V!/j, npH KOTOpOM I1r.'1a H8qH-
HaeT XOlI. nOC8.n.KH Ha ce.n..TIO,
(fu-f ) Pqo-f u
P .H.n=
k
P 'j + (j max
I + k ax
k ax )
I + k ax
( 344 )
f,,-f (1
3a.n.aBlllHCb p!/jo = 150 Kr;CM 2 , d u = 6 MAt, 0' = 200 Kr;CM 11
BbI6paB KOHCTPYKIJ.lIlO p8cnbI.'IHTe.'I5! H IIr.'IbI q>0PCYHKH, MOMeM on-
pelI.eJIIITb 38BI1CHMOCTb k ax OT Ymax. M8KClIM8.TJbHbIH nOlI.'beM lIr.TJbl
q>OPCYHKlI BbI6lIp8eM lI3 YCJ10BlIH [5], QTo6bI f,,, 2fc. D.J1H paccMaT-
plIBaeMoro CJIY1l8H npllMeM Ymax = 0,32 MM. nplI BbI6paHHbIX na-
p8MeTp8X Hr.TJ8 Ha'iHeT onYCKaTbCH npH .n.aBJ1eHI1H
(0,283-0,0282) 150+0,032200-0,0282.50
P .Hn = 0,283-0,282(1-0,85)
155 Kr;CM 2 .
330
Hcno.'Ib30BaB B3aHMOCBH3b Me)K.n.y prfi H P [CM. 4>OPMYJ1Y (43) J,
no.!JYIIHM
, k 2
Pt/Uin = 1 +k2 (Pt/>Hn-Pl{)+ PI! = 0,85(155-50)+
+ 50 = 139,2 KFjCM 2 ,
(345)
Tor.n.a
P ;, = 425 + 139,2 = 282 1 Kr l cM2.
'P.ep 2 '
KOJ1H'IeCTBO TOlwHBa, BnpbICHYToro 3a nOT neprIO.n.,
qU' = Jl f .!::..l( 2 }/ p -P = 0 00247 X
I{ C C 6n JI p .ep 4' 6. 2100
X 1535.15,2 = 0,0091 CM 3 . (346)
Cpe.n.Hee .n.aBJ1eHHe BnpblcKa 3a nepHo.n. noca.n.KH Hr.lIbI Ha ce.n.JIO
p' = PtlJ.n+Po = i39,2+50 -- 94,6 KFjCM2.
t/>.n.ep 2 2
3a 3TOT nepHO.n. .n.O.'I)KHO 6bITb no.n.aHO 115 - 101,7 - 9,1 =
= 4,2 MM 3 TOnJIHBa. 4T06bI o6eCnelJ.HTb 3TO YCJ10BHe, npo.n.OJ1)KH-
TeJ1bHOCTb noca.n.KH Hr.'IbI Ha ce.n..'IO .n.OJ1)KHa 6bITb paBHa
= 0,0042.6n 0,0042.6.2100 =2 1° ( 347 )
Cj)noe V - 0 00247.1535.6 66 ,.
2 V ' ' ,
/-Lefe p Pt/>.n.ep-Pu.
KpHBaH H3MeHeHHH .n.aB.!leHHH P , nOCTpoeHHaH no yrJIY nOBO-
pOTa BaJIa .n.BHraTeJIH, H xapaKTepHCTHKa BnpbICKa nOKa3aHbI Ha
pHC. 192. J],,J1H onpe.n.eJIeHHH KpHBOH H3MeHeHHH .n.aB.'IeHHH prfi .n.OJ1)K-
Ha 6bITb H3BeCTHa BCR KpHBaH .n.BH)KeHHH Hr.'IbI, KOTopaH He06xo-
.n.HM8 .n..'IH nOCTpoeHHH 3aBHCHMOCTeH
k 2 ,
l--,:-k 2 = f(y); fH = f (y).
Dpe)K.n.e Bcero onpe.n.eJIHM xapaKTep .n.BH)KeHHH Hr.!JbI 4>OPCYHKH
Ha yqaCTKe OT MOMeHTa HaqaJ1a no.n.oeMa .n.o conpHKocHoBeHHH Hr-
J1bI C ynopoM. J],aB.;leHHe Ton.!JHBa B 060eMe V rfi, cooTBeTCTBYIOluee
MOMeHTY no.n.xo.n.a HrJ1bI K ynopy, C .n.OCTaTOqHOH TOqHOCTbIO MO)KHO
onpe.n.e,JIHTb no <pop1\1YJIe
pt/J.yn = Pt/Jo + bYmax = 150 + = 172,6 KTjcM 2 . (348)
fu 0,283
J],aB.leHIle BnpblcKa B nOT MOMeHT, onpe.n.eJIeHHOe C YlJ.eTOM CO-
OTHOllleHHH (345), paBHO 153,5 KF/CM 2 . Onpe.n.eJ1HB Ha pHC. 192
TOqKY, cooTBeTcTBYIOIUYIO P .Yfl' HaH.n.eM, IITO npo.n.o.'I)KHTeJIbHOCTb
no.n.oeMa nr.'IbI COCTaB.!JHeT 4,2°. DpeAn0J10)KHM, qTO no.n.oeM H no-
331
Ca,lI,Ka Hr.'IbI npOHCXO,lI,HT no npHI'vIOJ1HHeHHOMY 3aKOHY. norpeWHOCTb
OT noro ,lI,onyru.eHlIH HeBev1l1Ka II He OKafli:eT 3aMeTHoro B.1JHHHHH
Ha xapaKTepHCTHKY BnpbICKa. KpHBaR ,lI,BHfKeHlIH Hr.J1bI, nOCTpoeH-
HaR Ha OCHOBe YKa33HHbIX ,lI,Onyru.eHHH, H306pafKeHa H3 pHC. 193.
COrJlaCHO 3TOH 33BHCHMOCTH CKOpOCTb nO,lI,'beMa Hr.'IbI C u . n =
= const = 0,92 _'<'leeK; CKOpOCTb ee nOCa,lI,KH C u . n = const =
= 1,92 /nleeK. Tenepb
MOfKeM nocTpoHTb 3aBH-
CHMOCTH C u . n = const H
f.. = f'(y) (pIlC. 194),
HCnOJIb3YH KOTopbIe, a
T2.Kfli:e 3aBHCHMOCTlI H3
pHC. 193, onpe,lI,eJIHM H3
Y4acTKe, cooTBeTcTBym-
()CIof*eK
p 60
KrjCl1 Z
400 50
320 40
240 30
,
I
- r . --1---+--+--:-1--
o 0 :,' I i
-22 -f8 .!I; -{f} -6 -28M.m2
80 10
6
PUC. 192. 3aBHCU;\IOCTb p = f((jJ) H 3allaHHaH
xapaKTcpHCTHKa BnpblCKa:
J - P = f(ft): 2 - Q flfjJ)
!lMN
-22
-14 -fO
-4 B.N.fTl. 4 (po
PUC. 193.
KpHBa51 .J.BmKCHH5I m.lbl lj:Jop-
CYHKII
[li'
e
?+k 2
fN /1/12
{j7
t]6
fj5
44
q3
0,2
0,1
o 41 0,2
(j4y"''''
PHC. 194. 3aBHcHMoCTb
k 2
) +k 2 = f(y) H f" = f'(y):
k 2
1 - f (y): 2 -- flY)
n I -1-k2
ru.eM qJ1l, 3aBHCHMOCTb pg, = fUJ (y). 3aBIICIIMOCTb pg, = f (y) nOCTpOe-
H3 no .popMYJIe (43).
LJ:,IIH 3Toro fKe nepHO,lI,a npoll.ecca BnpbIcK3 onpe,lI,eJ1IIM CKOpOCTb
,lI,BHfKeHlUI Ton.1JHBa B BbIXO,lI,HOM ce4eHHII HarHeTaTeJIbHOrO Tpy6o-
npOBo,lI,a H BO.1JHbI lIaB.leHHH F(t- ) II W(t+ ). PaccMoTpHM
ypaBHeHlIe 6a.:1aHCa Ton.1IIBa B BbIXO,lI,HOM ce4eHIIH HarHeTaTeJIbHOrO
Tpy6onpoBo.J.a II pewHM ero, npIIMeHHB I1leTO,lI, KOHe4HbIX pa3HocTeH,
T. e. npe,lI,CTaBHII1 3TO ypaBHeHHe B BH,lI,e
332
Pt/J-Pr/n 2f T ( L ) fT IT
aVt/J - -F t-- --p<jJ-Q-f C +-P, (349)
At ap a ap U U ap 0
;-
f.lI.e Be.'1WIlmy Q = tcfc V +./ P -Pli onpeIJ,e:IHM no pilC. 192.
flpm.leM d r = 2 Jlt.M, V ifJ = 0,5 C.M 3 . 10r11.a 113 ypaBHeHII51 (349)
. nOJ1Y'IIIM
F ( t- ) = apaVtjJ (pq,-pq,d+.£!!:..+
a 2frA/ 2
J- ..!£.. Q , f C _!!E..
1 2fT C -r 2f T U II 2'
(350)
Ll.J151 npHH51TbIX BbIllie napaMeTpOB CHCTeMbI no.'IY'IHM
F (I - ) = 0,71 (P<t,-P<jJI) +0,5P<t,+ 1,61Q + 1,61f"C u -O,5p o ;
npllMeM po = 30 KrjC.M 2 .
, L )
flocne BbI'IIlC.'IeHlifi F ( t - -;; , HCnOJIb3YH 06ll.I.lle ypaBHeHII51
npo ecca, HaH11.eM .lI..TI5I paCCMaTpllBaeI\lOrO nepllO.lI.a npo ecca Ton-
.TIIIBono.n:a'IlI Be.'III'IIIHY W( t + )- l.h06bI onpe.n:e.1I1Tb Ha 1 Ia.1bHYIO
BeTBb KpllBOH PifJ, T. e. onpe11.e.TJIITb, KaK H3MeH51eTC5I 3Ta Be.1H'II1Ha
OT IOMeHTa n011.X011.a OT Hacoca BO.1HbI 11.aB.TJeHl!5I .n:o Ha'Ia.TJa no11.o-
eMa HrJ1bI npe11.no.TJom:I1M, 'ITO np011.0Jl)KI1Te.'IbHOCTb 3Toro nepI1011.a
paBHa 3° II 'lTO .n:aB.TJeHHe pifJ H3MeHHeTC5I no np5IMOJIHHeHHoMY 3a-
KOHY. flp011.0JDKIITe.TJbHOCTblO B 3° 3a11.a.TJHCb Ha OCHOBe aIIa.'IH3a
MHOrO'II1C.'1eHHbIX paC'leTOB pa3.111'IHbIX TOnc1I1BHbIX CHCTeM. floc.TJe
nOCTpOeHH5I KpHBOH .n:8BJ1eHH51 pifJ MmKeM BbI'lHC.1IIfTb F ( t - ). .IJ.J15I
:noro Hcno.'Ib3yeM ypaBHeHHe 6aJIaIICa Ton.1HBa, KOTopoe 3anHllleM
B BH11.e
V Pt/J-Pt/Jt _ 2f T F (t L ) f .' + fT
a </) - -- --P<t> -Po'
At ap a ap ap
(351)
Hcno.'Ib3Y5I ypaBHeHHe (351) H yt HTbIBa5I BbI6paHHbIe HaI\IH na-
paMeTpbI TOnJIHBHOlI CHCTeMbI, no.lyrIaeM
F (I- '\ = 0,71 (Pd>-P</>1)+0,5p<jJ-O,5po'
\ a J
Onpe11.e.1HB no npIIBe11.eHHbIl\I BbIllie ypaBHeHH5IM F(/- ), HaH-
,lI,eM W (t + ). Ha pHC. 195 nOKa3aHbI 3aBI1CHMOCTIi F( t - ) =
,= f(qJ) H W(t+ )= f(qJ).
333
TIpHHHB CKOpOCTb 3BYKa a = 1300 .MIceK, .IJ:.rrHHY nYTH OT o61>e-
Ma V y; J1..0 lllTYl.(epa Hacoca L = 520 .M.M, YCTaHOBHM, 'ITO BO.T1H6
J1..aBJ1eHHH npOXOJ1..HT 3TOT nYTb 3a 5°. C.'leJ1..0BaTe.1JbHO, Y 061>eMa
wTYl.(epa BO.HHa F (t - ) 6wla Ha 5° paHbwe, a BO.JIHa W( t + )
J1..oHJ1..eT J1..0 061>e!\Ia wTYl.(epa Ha 5° n03&e.
Tenepb HaH.n.eM a Mn.JIHTy.n.bI BO,,'lH .n.aB:leHl1R F(t) M W(t) BO
BXO.n:HOM Ce'IeHHH HarHeTaTeJ1bHOrO Tpy60npoBo.n:a, KOTopwe 6y.n:YT
p",
f - )
500
400
w +ft} 300
KileN!
100 200
50 100
0 () 'Po
-50 -(00
-(00 -20()
-(50
-200
L
PilC. 195. 113MCHCHHC ,'\aB.1CHHH Prfj H BO.1H F(t - -) !I
a
L
W (t + -) no vr.TJY nOBopOTa Ba.1a ,!J.BHraTcaH
a .
paBHbI COOTBeTCTBeHHO no Be,,'lWHme F(t- ) H W(t+ ), HO
cMemeHbI no cpa3e, a 3aTeM onpeJ1..e.'1HM 3aBHCHMOCTb p = fUp)
(pHc.196).
1':I3BecTHo, 'ITO nOc,'1e BbIXOJ1..a pa3rpY)J{aJomero n05ICKa H3 KaHa.rra
rHe3J1..a J1..aB.leHH5I p II PH. pa3.'1H'IaIOTC5I no Be"lII'IHHe HeC1Ha'IIue.'Ib-
HO (.n.eOITbIMH J1..0JUlMH aTMoccpepbI), n03ToMY npIIMeM J1...'I5I nepIWJ1..a.
KorJ1..a pa3rpY)J{alOll.\IIH nOHCOK K.'IanaHa Haxo.n.HTCH BHe KaHa.la
rHe3J1..a, P = PH.. MOMeHT Ha'Ia.'la B03pacTaHHH J1..aBJleHH5I py;, co-
r"laCHO CJ1..eJlaHHoMY J1..0nYll.\eHI1IO, II3BeCTeH, 4TO J1..a.lO B03MO)J{HOCTb
onpe.n.e.'1IITb MOMeHT Ha'la.'1a B03paCTamUl .n.aB.leHIUl p , KOTOpbIR
COBrra.n.aeT C MOMeHTOM Ha'Ia.la nOJ],1>eMa HarHeTaTe.'lbHOrO K.'1anaHa.
npHMeM, 'ITO B 3TOT LKe MOMeHT nO,,'lHOCTblO 3aKpbIBalOTcH BcaCbI-
334
B8IOll1.He OKH8 BTy.'IKH rr.'IYHfKep8. ECJIH OKHa BTy.1.KH B YKa3aHHbIii
MOMeHT nO.'IHOCTbIO He 38KpbI.'IHCb, TO fIX npOXO,ll.HaSI nc1.0ll1.a.n:b 6y.n:eT
TaK Ma.na, lJTO KO,;1H11eCTBO I TOnJ1fIBa, nepeTeKaIOlilero lJepe3 HfIX,
MOLKHO npeHe6pelJb. YpaBHeHfIe 6a.'IaHCa Ton.'IHBa B paCCMaTpfIBae-
MOM CelJeHHH npH 3a.n:aHHbIX YCJIOBfISIX
, dp
aV H - = fI(C,,-f,cT'
dt
OTKy.rx.a, HCnOJIb3Y5\ MeTO.II. KOHelJHblX pa3Hocreii, nOJIYlJHM
, .
C f C V . PH-PHI
f"I(=T,.+a H .
D.t
B CBSI31I C TeM, lJTO BeJllIlJlIHbI F (I), W (I), a TaKLKe C T 1I3BeCTHbI,
.n:8B.TJeHHH P II P I onpe.n:eJIHTCH H3 pHC. 196, CJIe.n:OBaTeJIbHO, lJJIeH
f "C" B nepHo.n:e OT HalJa,;1.a rro.n:"beMa HarHeTaTe,;1bHoro K.'IanaHa .n:o
(352)
h".A1H
p'; 2.5
(I/f'H- 2 r
::; t::
20+1,0
100 r [J5
oL 0
-J()-18 -21t -20 -16 -12 -8 -It 8.H.m q/
Puc. 196. I13MCHCHHC .ilaB.1CHII5I p u nYTlI K.TJarraH8
h" no yr.lY nOBopoTa Baaa .D:BHraTC.151:
I - p i(q;J: 2 - hI( i(cpJ
BbIXO,ll.a ero pa3rpYLKaKJw.ero n051CKa 1I3 KaH8.'H] rHe3.rr.a onpe.rr.eJIIIT-
C51 6e3 Tpy.n:a. O.rr.HaIW IlTo6bI BbIlJfIC.1HTb lJJleH f "C", Heo6xo.n.fIMO
3a.n.8TbC5I Be.1HlJHHOII V . DpHMeM V: = 2,5 CM 3 , lJTO cooTBeTcTByeT
Ton lHBHOH CHCTeMe 5lM3-236. DplI B'bI6ope BeJIHIIHH V H V gJ HYLK-
HO YlJHTblBaTb, lJTO lJeM MeHblile 3TH 3HalJeHlI5I, TeM 60Jlee 3aMeTHO
CKa3NBaIOTCH Ha np01I3BO.II.HTeJIbHOCTH OT.n:eJIbHNX ceKQHH .n:e eKTH
H3rOTOB,;1eHl1H npellH3lIQHOHHbIX 3.1eMeHTOB CHCTeMbI. B Ton.TJlIBHbIX
CHCTeM8x 8BTOTp8KTOpHbIX ,lI.H3e.1eH LKec1.aTe.'IbHO, lJTo6bl V =
= 1,5 -7- 2 V T, a V!Ii = 0,25 -7- 0,35 V T'
D0J10LKIIM d" = 6 filM, h" = 2 Mfit. COrc1.aCHO npoBe.n.eHHoMY pac-
lJeTY p83rpYLKaJOll1.HH nOSICOK KJI8naH8 BbIXO.rr.I1T 113 K8Ha.'18 rHe3,l1.8
npH qJ = -20 0 .n.o B. M. T. JJ.8BJleHHe PH .n.JIH paCCMaTpfIB8eMoro
nepHo.n:a npOllecca BnpHCKa orrpe.n.eJIIIM 1I3 ypaBHeHHH .n.BfILKeHI1H
335
HarHeTaTeJIbHOrO KJIanaHa, KOTOpOe, HCno.'Ib3YH MeTO.lI. KOHelJHblX
pa3HOCTeH, npe.lI.CTaBHM B BH;J:e
M C ,,-C"l r 8h . { ( ' )
M ' ,,+t,,:p,,=.. P"-P II '
OTKY.lI.a
_M ( C C ) ,l'>h' + '
p,,- Mt" ,,- ,,1 't: ",P" p,,'
(353)
npHMeM PK = 12 Kr(CM 2 ; () = 8,4 KT/CM. TaKHM oopa30M, MbI
MOLKeM onpe.lI.eJIHTb .lI.aBJleHHe PH OT MOMeHTa HalJaJIa nO.lI."bel\Ia KJIa-
naHa .n:O Ha4a. r Ia OTce4KH. 1I.mI 3Toro LKe nepHO.lI.a no ypaBHeHHIO
6a.'1aHCa TOnJIHBa .n:J1H KaMepbI HarHeTaHl15J, KOTopoe 3anHIueM B BH.n:e
aV" P"-P,, = tn C Il-t"C",
M
onpe.n:eJ1lIM
tncn = aV II PII-P", + {"C". (354)
!1t
npHHHB d n = 9 MM, 1I3 3aBHCHMOCTH f nC n = f{(})) nOJIyQRM 3Ea-
4eHHe Cn. 4TO .lI.aCT B03MmKHOCTb no <PopMYJle
!J.h = Cn-+- C nI !J.t
n 2
onpe.lI.eJIHTb BeJIH4HHbI xO.lI.a n.rIyHLKepa 3a KaLK.lI.bIH rpa.lI.Yc, CYMMH-
PYH KOTopbIe, no.TIY4HM 06U!HH aKTlIBHbIH XO.n: nJ1YHLKepa. BBH.n:y no-
rpeulHOCTeH, KOTOpbJe HeH36em:HbI npH Hcrro.'Ib30BaHHH rpa<pH'leCKHX
3aBHCHMOCTel-I, 3Ha'leHHe C n pe3Ko KOJle6JIeTCH, He n03BOJIHH TeM
caMbIM yCTaHoBHTb onpe.lI.eJIeHHOH 3aBHCHMOCTH. n03TOMY no npH-
Be.lI.eHHOH BbIllIe <popMYJ1e BbI4HCJ1HM .n:.TIH KaLK.lI.oro rpa.lI.yca npOH-
.n:eHHbIH n.nYHLKepOM nYTb, a 3aTeM no 3THM .lI.aHHbIM nOCTpOHM KPH-
BYIO XO.lI.a n.'IymKepa. KaK c.r1e.lI.yeT H3 pHC. 197, B paCCMaTpHBae-
MOM CJIY4ae XO.lI. rr.1YH}Kepa h n onHCbIBaeTCH .lI.BYMH rrpHMO.TIHHeHHbI-
MH Y1JaCTKaMlI. HaqaJIbHOMY Y1JaCTKY rrpo.n:o.'1LKHTeJ1bHOCTbIO 150
cooTBeTcTByeT C n = const = 1.57 MiceK, BTOPOMY Y1JaCTKY rrpo.n:o.TI-
LKHTelIbHOCTbIO 11 0 yrJ1a nOBopoTa BaJIa .lI.BHraTe.'1H cooTBeTcTByeT
C n = const = 2 MiceK. Ha pHC. 197 He nOKa3aHbI paClJeTHbIe TOlJKH
3Ha4eHHH Cn, KOTopbIe TaK pa30pocaHbI, 4TO )'CTaHOBUTb no HUM
KaKYlO-.'1HOO 3aBHCHMOCTb C n OT cp rrpaKTH4eCKH HeB03MOLKHO.
npHHSIB, lITO K MOMeHT)' rrepeKpbITHSI BCaCbIBaIOIUHX OKOH rr.'1YH-
LKep npOXO.J.HT nYTb 3 MM, nOCTpOHM KPHBYIO XOlla nJIYHm:epa .n:.'lSI
h n rnax = II /It-''. (pUC. 198). TqaCTOK, OXBaTbIBaIOuunl aKTHBHblii
XO.n: nJIYHLKepa llJISI qv. = 115 JWM 3 , COCTOHT H3 llBYX YKa3aHHbIX BbI-
llIe npHMbIX. YqaCTKH .lI.0 H noc.TIe h aKm nOCTpoeHbl npHMepHO TaIm-
MH LKe, KaK .lI..'lSI Ton.TII1BHOlf CHCTeMbI 5IM3-236. 3lleCb LKe nOKa3aHa
KpHBaSI H3MeHeHHH C'h a IlITpHXOBOH mmHeH .lI.JIH cpaBHeHHH Ino-
336
6paLKeHa KpHBaH H3MeHeHHH CKOpOCTIi C n cepH1IHOH ToncllIBHOH CH-
CTeMbl 5IM3-236. rpa<j:JUKU Ha pUC. t98 YKa3blBalOT H3 cyw.eCTBeH-
HbIe pa3.TJIPlHH xapmaepa H3MeHe-
HHH CKOpOCTU C n cepUMHOM TOnJ1UB-
HOM CHCTeMbI OT 3aBUCUMOCTU C" =
= f( ), nO YlJ.eHHOM B pe3YJ1bTaTe
pa.CqeTa..
Oco6eHHOCTbKJ paCClJ.UTWBae-
MOH Ton.!IHBHOM CUCTeMbi HB.'1HeTCH
pe3Koe OKOHlJ.3HUe npou.eCC3 BnpbIC-
K3. P3CCMOTpHM KOHeu. npou.ecca
BnpbICK3, lJ.To6bI onpe1I.e UTb, KaK
1I.0J1)KH3 U3MeHHTbCH npu 33113HHbIX
yC.!IOBUHX npOX01I.H3H n.nOlll.31I.b OT-
CelJ.HbIX opraHOB CUCTeMbI. B CBH3H
C TeM, lJ.TO cor.naCHO C1I.e.1aHHOMY
paHee 1I.onYlll.emlIo B MOMeHT HalJ.a-
J1a OTCelJ.KH PH. = P ' pa3rppK8IO-
llI.UM nOHCOK HarHeTaTenbHoro Kna-
naHa 1I.OmKeH HaX01I.HTbC5J OT KaHa-
.na rHe31I.a Ha HeKOTopOM paCCTOH-
HIm. D03TOMY npHMeM, lJ.TO nOHCOK
HarHeTaTenbHoro KnanaHa HalJ.HeT
BX01I.HTb B KaHaJ1 rHe31I.a lJ.epe3 1° nOCJ1e HalJ.aJIa OTce4KH.
hnHH
3,5
.JO
2,5
2,0
1,5
1,0
()
-JO -25
-6 -fO
-5
Iji"
PIIC. 197. PaC'-ICTHaH KpUBa!! ny-
TU HarHeTaTC.1bHoro xOj.\a n.TJyn-
)KCpa
C n /in
MiceK MM
2,0 fO
1,6 8
1,2 6
48 4
q4 2
()
0 5 fO f? 20 2 f /;/} ¥5 50 55 "
\ \
fO 20 JO 40 50 80 90 fOO ffO q;"
PUC. 198. II3J\1cHeHuc n TH II CKOpOCT!1 ,'!Bf!LKCH!1H n.1ymKepa B 3<1-
BIICUMOCTII OT yr.TJa nOBopOTa B2.1a Hacoca:
J - f, n f(1p); 2 - C n flip): - - - J<p>lBaR CKOpOCT>l :\B"",eHIlH
n,TIYH}f{epa I1JHI cepHiIHoro npoq>H 15I TonJIlfBHOrO KYJI3QI';a
YpaBHeHHe 6aJIaHCa Tonmma 1I.. T IH BxollHOrO CelJ.eHHH HarHeTa-
Te.TJbHoro Tpy6onpoBOlla npH PH. = p , HO nOCJle HalJ.3J1.3 OTCelJ.KU
6YlleT HMeTb BIi1I. _
a(VII+V ) dp" = tnCn-tTCT--/!ofo' / V P -P6C. (355)
dt P
22 3aKa3 748
337
OpH HCnO b30BaHHH MeTO a KOHe4HWX pa3HOCTeH H npHHHTWX
napaMeTpaX TOn..1HBHOri CHCTel\IbI .'1H onpe e.leHHH Be.'1H4HHbl
#lot () n0.1Y4H1VI yp8BHeHHe
3,09(p -p I)-L0,632Cfl-0,31 [f (t)+ W(t»)
/-!ofo =
1535 V' P - PBC
(355a)
4epe3 ]0 nOC.le Ha4a.la OTCe4KH fnC n = ]23,5; F(t) + W(t)
= 40; PH. = 22],4 Kr;CAt 2 ; P = 444,] Kr;CM 2 . PewaH C 3THI\IH IWH-
HbIMH ypaBHeHHe (355a), noaY4HM, qTO ,!J,.lH 06eCneqemIH 3a aHHoII
pa3rpY3KH 4epe3 1° nOCJ1e Haqa.1a OTCeQKH npoxo Hoe ce4eHHe OT-
ce'IHbIX OKOH ,!J,O.'1)J{HO 6bITb paBHo f om = 3,5 J tM2. OpH Kpyr.lbIX OT-
ce4HbIX OKHax 06eCneQHTb TaKoe pe31we B03paCTaHHe npOXOJIHOII
n.lorn.a,!J,ll OQeHb TPYJI,HO. Ho ec..1H n.'1YH)J{ep 6Y,Ll,eT HMeTb ,!J,Be OTce4-
HbIe KpOMKH (K8K B Hacoce H3eJIH M-50), a BO BTy.1Ke BMeCTO
Kpyr..1blx OKOH - Be me.1H ,!J,.'lHHOH 12 MM Ka)J{,!J,aH H pacno.101KeH-
Hwe napa.l.1Je.'lbHO OTce'IHbIM KpoMKaM n.'1YH)J{ep8, TO 4epe3 1 ° npH
paCC'Il1TaHHbIx paHee CKOpOCT51X JI,BH)J{eHHH n.'lYH)J{epa npOXOJI,HaH
n.lorn.aJI,b OTCeQHbIX OTBepCTllH 6YJI,eT paBHa 3,5 MM 2 .
Opll JI,a.'lbHeHWeM npOTeKaHHH npoQecca pa3rpY;'KaIOrn.lli1 nOHCOK
K.'Ian8H8 BOfmeT B K8H8.1 rHe3JI,8, rr03TOMY Torr.'1HBO H3 06"beI\w V
B .1HHllIO OTce4KH nepeTeKaTb He 6YJI,eT. JIHHHH HarHeTaHHH 6Y..1eT
pa3rpY)J{aTbCH TO.lbKO B pe3y..'lbTaTe YBe.1H4eHHH 061>eMa, orrHCblBa-
eMoro nOHCKOM K.'1anaHa npn ero noca,!J,04HOM xo e. 11..151 3Tl1X yc-
.10BI:II1 npl1Memnvlbl ypaBHeHI1H (355) H (355a). n pH 3TOM 6Y..1eT
rrpOHCXOJI,HTb pa3rpY3Ka Tpy60npOBOJI,a. HanpmvIep, JI,J1H 2° rrOC:le
HaQa.'la OTce4KH
, dPH
aV H - = fKCK-frC r .
dt
HCnOJIb3YH MeTO..1 KOHe4HWX pa3HocTeH ,!!,J1H paccM8TpHBaeMoro
npHMepa, nOJIY'JHM
2,2 (119,6-221,4) = f,P" + 0,31- 69,6.
oTKy,!!,a HaH eM. 4TO f"C" = -245,6; C" = -8,7 MIceK.
KJIarraH CH,!J,eT Ha fHe3JI,0 4epe3 4° nOC.1e HaQa.1a OTce4KH. 113
aHaJIH3a pllC. 197 CJ1eJI,yeT, 4TO nOCJle rrOCaD.KH HarHeTaTe.lbHoro
K 8rraHa Ha CeJI..l0 K wTYQepy Hacoca 6YJI.YT rrpoJI.o.TIlKaTb nOJI.XOJI.HTb
OTpa)KeHHbIe BO.'lHbI n01l,rropa 3Ha4IITe.'lbHOri Be.1WIl1Hbl, QTO MOiKeT
BbI3BaTb onaCHOCTb nOBTopHoro nOll"beMa HrJ1bl, T. e. nOHB.'leHHH o-
nO,'lHlITe.lbHoro BnpbIcKa. KpOl\Ie Toro, Cl<OpOCTH nOCaJI,KH K anaHa
0'IeHb Be.1HKI1, 'ITO MOiKeT cyrn.ecTBeHHo YXY,!!,IllI1Tb Ha1J.e)J{HOCTb pa-
60TW Y3.'la. B CBH311 C 3THM 60.'lee Qe.leco06pa3Ho I1CnO.'lb30BaTb
K.'lanaH KOHCTPYKQHH N1ALIlI (CM. pHC. 82), KOTOpbIH He TO.'lbKO no-
BbIIllaeT Ha1l,e)KHOCTb pa(JOTbI CI1CTeMbI, HG H cTa6HJ1JI3HpyeT Ha4a..'lb-
338
HbIe YCJ10BIUI npo ecca BnpbICKa. CTa6HJ11I3aIllUI HalJ.a.'IbHbIX YC.'IO-
BlIi'I npouecca BnpbICKa B .lI.aHHOM c.'IYlJ.ae HB.T15leTCH ueJIeco06pa3HoI!,
Tal, KaK Ha.11IlJ.lIe OTplIuaTe.'IbHblX 3HalJ.eHlIH F (t) YIW3bIBaeT Ha B03-
MmKHOCTb 06pa30BaHlIH CB060AHbIX 06"beMOB (nYCTOT) B .TIIUIlIII Ha-
rHeTaHHH.
OplIMepHbIII paClJ.eT nOKa3a.TJ no.'IHYIO B03MO)KHOCTb H 60.1 bIll lIe
npelIIv!Ylll.eCTBa BbI60pa napa1\1eTpOB TOnJIIIBHOH CHCTeMbI no 3a.lI.aH-
HOII xapaKTeplICTIIKe BnpbICKa. OOC.l1e OKOHlJ.aTeJ1bHOrO BbI60pa na-
pallIeTpOB Ton.TJHBHOH CIICTeMbI .lI.J1H npOBepKII npaBII.l1bHOCTH BbI-
opaHHbIX napaMeTpOB MO)KHO npOBeCTII 06bllJ.HbIH paClJ.eT npouecca
BnpbICKa, lJ.TO npH HaJIIIGHH CGeTHO-peIllaIOllI.HX MaIllHH He npe.lI.CTaB-
J1HeT TPY.J:a.
C.1e.lI.yeT OTMeTIITb OO.1bIlloe npeHMYlll.eCTl30 KpllEOI! aKTl1BIIOrO
XO.lI.a n.TJYH)Kepa. COCTOHlll.eH 1I3 .lI.BYX npHMOJIlIHeHHbIX YlJ.aCTKOB C
nOCTOHHHbIMII 3HaGeHHHMH Cn. B CBH31I C TeM. lJ.TO xapaKTepHCTIIKa
BnpblcKa II q1l B OCHOBHOM onpe.lI.e.'IHIOTCH LweHOM fnCn, nplI C n =
= const ,ZI:JIH OT,ZI:eJ1bHbIX paOOlJ.HX YlJ.aCTKOB nplIo.TIII)KeHHO MO)KHO
npm-IHTb. lJ.TO BeJIlI'IHHa C n nplI nOCTOHHHbIX OCTa.'lbHbIX napaMeT-
pax CIICTeMbl oY.lI.eT 1I3MeHHTbCH 06paTHO nponopUIIOHaJIbHO BeJIII-
GIIHe f n. HanplIMep, eCJ1H ObI B paCCMaTpllBaeMOH CHCTeMe .lI.HaMeTp
n.'IYH)Kepa YMeHbIllIIJICH C 9 .lI.0 7,5 .M.M, TO CKOpOCTb nepBoro YlJ.aCT-
Ka 6bI.'I3 6bI
C I =.bL C n I = 0,635 1,57 = 2,26 MIceK,
fn2 0,441
a BTOpOf"O
C 2 2,9 M.lceK.
TaKHe CKOpOCTH .lI.BII)KeHlUI n.TIYH)Kepa BnO.TIHe .lI.OnYCTIIMbI. AK-
TIIBHbIII XO.lI. nJ1YH)Kepa npII 3TOM YBe.TIIIlJ.IITCH Ha 1,8 .M.M II CTaHeT
paBHbIM 5,43 .MM.. TOnJ1I1BHaH CIICTeMa C TaIUlM .lI.lIaMeTpoM 6Y.lI.eT
IIMeTb MeHbililIe ra6aplITHbIe pa3MepbI, MeHbIllIIH Bec H 3HalJ.IITe.TJb-
HO 60JlbIllHH pecypc, TaK KaK .HarpY3KII Ha npIIBo,ZI: nJ1ymKepa YMeHb-
III aTCH 6o.TJee, lJ.eM Ha 40 % .
HaMIl paccMoTpeH paClJ.eT .lI.JIH HOMHHa.'1bHOrO pe)KIIMa pa60TbI
,ZI:1I3eJIH. 4T06bl nplIHHToe pacnpe.lI.eJIeHlIe TOnJIHBa BO BpeMeHH CO-
XpaHHJIOCb II Ha MeHbIllIIX HarpY3Kax, Heo6xo,ZI:IIMO, GTo6bI Ha Bcex
OCTa.'1bHbIX pe)KIIMaX pa60lJ.IIH YlJ.aCTOK npoqJlI.TJH Ky.TIaGKa IIMe.TI .lI.Be
CKOpOCTII. Y.lI.OBJ1eTBOpHTb 3TO Tpe60BaHHe MO)KHO nYTeM pery.'IlIpO-
BaHIIH KO.'IIIlJ.eCTBa Ton.TIHBa H3MeHeHHeM He TO.'1bIW KOHU3, HO II Ha-
lJ.a.1a npouecca BnpbICKa. TaKIIe Ton.TIHBHbIe CIICTeMbl II3BeCTHbI .lI.aB-
HO. Opl1 I1Cn0J1b30BaHI1H .lI.BYXCKOPOCTHbIX KY.l1alJ.IWB 3TI1 CIICTeMbI
Mor;YT no.TIYlJ.HTb Illl1pOKOe pacnpOCTpaHeHl1e.
KOJIIIlJ.eCTBO 11 .lI.HaMeTp pacnbl.TIIIBaIOlll.HX OTBepCTI1H onpe.lI.eJIHTb
paClIeTHbIM nYTeM npaKTIIlJeCKII HeB03MO}KHO, n03TOMY BbIOHpaTb
3TlI napaMeTpbl npIIXO.lI.I1TCH B OCHOBHOM 3KcnepHMeHTaJ1bHblM
nYTeM.
22*
339
2. nPH6nHH<EHHbIE METOAbi OL\EHKH OCHOBHblX nAPAMETPOB
npO ECCA BnPblCKA H TOnnHBHOJ1 CHCTEMbl
)Ke.'IaTeJ1bHO, 'lTo6bl KOlICTPYKTOP pacno.lara.l npOCTbIM MeTO-
.n:OM Ol.(eHKH napaMeTpOB npOl.(eCca BnpbICKa Ton.1HBa, 06eCne'lI1Ba-
IOllJ.IJ:\I npM Ma.l01I TPy.n:OeMKOCTH npHeM.leMYIO ,],.151 npaKTHKM TO'l-
HOCTb. TaKHX MeTo.n:OB npe.n:.1OLKeHO HeCKO.lbK0. 4aCTb 113 HHX, OCHO-
BaHHaH Ha TeOpl111 nOl{06HH H pa3MepHOCTeH, ,.'I.aeT B03MOMHOCTb
orrpe.n:e.1HTb rrapaI\leTpbI npou.ecca (npo.n:0.1MliTe.lbHOCTb BrrpbICKa,
MaKCIIMa.lbHoe .n:aB.leHl1e H .n:p.) B OTpbIBe OT OCTa.lbHbIX napaMeT-
pOB [5IJ, '1TO llCK.lIO'laeT B03I\10MHOCTb ou.eHHBaTb 06llJ.HH xapaKTep
npOTeI<3lIHH npou.ecca no.n:a'lH TOnJIHBa. PaClIeTHbIe cpOPMY.'IbI TaKHX
MeTo.n:OB HOCHT no.1Y3I\IITHpH'leCKHH xapaKTep, rr03TOMY HX 06.'IaCTb
npHMeHeHHH orpaHWIHBaeTCH CliCTeMaMH, 3KcnepllMeHTa.'IbHbIe .n:aH-
HbIe KOTOpbIX nO.l0MeHbI B OCHOBY paC'leTHbIX cpOPMY.'I.
rIpH6m1MeHHbie MeTo.n:bI paClIeTa He MorYT npOTHBonOCTaB.'IHTb-
CH 06IlleH fH.n:po.n:I1HaMI1'leCKOH TeOp1111 npou.ecca BnpblCKa, KaK ;iTO
Ae.laeTCH B pa60Te [5IJ, a .n:O.1JKHbI paCCMaTpl1BaTbCH KaK HeKOTO-
poe BcrrOMoraTe.lbllOe cpe.n:cTBo, C nOI\lOllI.bIO KOToporo MOMHO 6bICT-
po H BeCbMa ripH6.1mKeHHO ou.eHHTb BbJ6paHHbIe napaMeTpbI HOBOH
cHCTeMbI, a TaKMe napaMeTpbI npou.ecca BnpbIcKa 3KCnJIyaTHpyeMoH
CI1CTeI\IbI.
Eo.'Iee cOBepmeHHbI npI16.'IJ1)KeHHbJe MeTo.n:bI, BbIBO.n: paC'leTHbIX
cpOPMYJI KOTOpbIX OCHOBaH Ha 06IllHX nO.10)KeHHHX rH.n:pO.lI.HHaMH'le-
CKOH TeOpHl-I npouecca BnpbICKa Tomnma. PaCCMOTpHM OJ],HH H3 no-
1I.06HbIX MeT01l.0B, ony6.1I1KOBaHHbIH B pa60Te [6]. 06LUeH3BecTHo,
liTO 85-90% Ton.1HBa, nOJ],aBaeMoro 3£1 U.HKJI Ha HOMHlJa.lbHOM pe-
JKHMe, BrrpbICKHBaeTCH B TetIeHHe 3Tarra, BO BpeMH IWToporo Hr JIa
cpOPCYHl{j-J npIUKaTa K ynopy, C:H J],OBaTeJIbHO, Ha npOlJ,ecc He Bmm-
eT; pa3rpYMalOLUHH nOHCOK HarHeTaTe.lbHoro K.'IanaHa Bblme.rI H3
KaHa.'Ia rHe3Aa, n03TOMY ero BJllIHHHeM TaK)Ke MO)'KHO npeHe6pe'lb;
J',caCbIBalOLUHe H OTCe'lHble OKHa BTYJIKH n.'IYHJKepa 3aKpbITbI. Co-
r.'IaCHO YKa3aIlHbII\I YCJIOBHHM B Te'leHHe :>Toro :nana nJIYHJKep rrpo-
XOll.HT npaKTH'leCKH BeCb cBoil aKTHBHblH XO.il., n03ToMy ou.eHKa BbI-
6paHHblx napaMeTpoB Ton,lHBHoH CHCTeMbI no xapaKTepy npoTeKa-
HHH npOu.ecc3 BnpbIcl\a H3 3TOM 3T3ne .il.O.lJKH3 HJ'vIeTb .L(OCT3TOllHYIO
JJ..1H npaKTI1KH TO'lHOCTb.
B JJ.orrO.'IHeHHe K YK33aHHbIM YC.l0BHHM npHHHI\IaeI\I, 'lTO BO"lHa
W (t) He oKa3bIBaeT 3aMeTHoro B.1HHHHH H3 npou.ecc BnpbICK3 H no-
3TOMY He Y1lHTbIBaeTCH. n pellnOJIar3eM, liTO P; max COOTBeTcTByeT
BO"lHe F (t - ), KOTopaH 06pa30B3.'I3Cb y H3coca B I\WMeHT H3q3-
Jla OTKpbITHH OTCe'lHbIX OKOlI. KpoMe Taro, npl1HHMaeM, 'ITO 3aBH-
CHMOCTb C n = f (qJ) !OMHO BbIpa3HTb OJJ.HHM HJIH HeCKOJIbKIIMH
npHMO.:'IHHeHHbIMH YIIaCTK3MH. M3KCIIMa.1bHbIH HMnYJIbC, HJJ.YlllHH
OT HaCOCa K cpOpCYHKe,
F(t)= aPfnCn [ 1- ('l\JfI'-I)e-"'+1 j , (356)
f T \jJ (fI' + 1)
340
r.ne 1j; =
fr(f>aKm
6napAV..
13' == .
!jJaKm
Ec.rn1 0603Ha'lHTb
( W-I)e--w+ I
11.. = 1-
W+I)
TO nOJIY1JIlM
F (t) = YJ" ap :cn . (356a)
AHa.1H3 BbIpa)j{eHlUI (356a) nOK83bIBaeT, 'ITO Be.'1lJIll1H8 flu HB-
JIHeTCH MrHOBeHHbIM K03q>q>IlllJIeHTOM nOAa'lH n8coca. 38BHCHMOCTb
'11" OT 1jJ npH pa3.1H'lHbIX 3Ha IemHIX /3' H306pa)j{eHa Ha pIlC. 199, at
fll
0,8
0,6
0,4
0,2
I
D D,2 D,B '11 0
- !
PHC. 199. 3aBHcHMoCTb 1JM OT 11' npH pa3.TJH'-IHb!X 3Ha4eHIIHX 13'
6, npIl1JeM H8 pIlC. 199, a 38BIlCIlMOCTb '11" = f (1jJ) .naHa B 60JIbillOM
MaCllITa6e .nJIH Ma.J1bIX 3HaqeHHH 1jJ.
B HeKoTopbIX c.TJY'laHX, oco6eHHO UpH HCUOJIb30BaHHH CneIJ.H-
a.rrbHbIX H8rHeT8Te.;rbHbIX K.;ranaHOB,.B HX npOXOJI.HbIX CeqeHMHX B03-
HMKaeT HHTeHCHBHoe 1I.poCCeJIMpOBaHMe, KOTopoe MQ}KHO yqeCTb KO-
3q>q>HIJ.MeHTOM paCXOJI.a 3THX CeqeHHiL f1pH yqeTe 3Toro JI.pOCCemI-
pOBaHJHI JI..151 BXOJI.HOrO Ce'leHHH Tpy6onpoBo.na
F (t) = 'I1"J!K apt Cn ; (3566)
.nJ1H BbIXO.!l.HOrO Ce'leHIIH Tpy6onpOBOJI.a y q>0PCYHKH
F(t- )=[Y}IIJ!K ap :cn] (t_ f
(356B)
341
I1rJIa HalIHeT nOll.HHMaTbC5!. npH prjJ = PrjJO. npeHe6pera5!. o6'be-
MOM <P0PCYHKH, MO)J{HO HamICaTb
P4'O=Po+2F(t- ).
TaK KaK BeJIlI'IliHOM po 3all.aeMC5!., a PrfiO 1I3BeCTHO, TO BOJIHa, CO
OTBeTCTBYlOrn.aH nO;I:ceMY IIr.TIbI,
f (t- ) = P4J O -;Po .
npIlH5!.B, 'ITO B nepllo.n:e 3a.n:aHHoro aKTIIBHoro xo.n:a nJ1YH)J{ep3
BOJIHa f (t) H3MeHHeTCH npHMOJ1I1HeMHO, nOCTpOHM 3aBliCliMOCTh
F (t) = f (qJ), rr03Bo.rrHlOrn.ylO onpe.n:eJ1HTb yrOJI qJnoi'J, npH KOTOpOM
HrJI3 H3'IHHaeT n01l.HIIMaTbCH. TaK KaK BH3KOCTb TOnJIIiBa He Y'I11-
TbIBaeTCH, TO
[F(f}](t_ )= F(t- ).
J(aBJ1eHHe TOnJIIiBa B BNX01l.HOM ce4eHlIli HarHeTaTeJ1bHOrO
60npOBO!Ia pacc4HTbIBaeTC5I no <popMYJ1e
b ...(b 2 ( L )
V Pq,-Plj= -"2+ V 4+ 2F t--;; +PO-PI{'
TPY-
(357)
r!Ie
b= awcfc 1 / 2 1 / k 2 .
f T , p.' 1 + k 2
KaK H3BecTHo, nepeTeKaHHe TOnJIIiBa 'Iepe3 BcaCbIBalOIUlie OKHa
OKa3b1BaeT HenOCpe1l.CTBeHHoe BJIHHHlIe Ha npou.ecc BnpbICKa TOJIbIW
B nepno1l. O!IHOBpeMeHHoro nepeTeKaHHH TOnJIHBa H B HarHeTaTeJIb-
HbIM Tpy60npOBO!I. 3TOT nepllO!I He3Ha4l1TeJIeH (1-2 0 yr.rIa nOBopo-
Ta BaJIa Hacoca), npll4eM npOXO!IHaH n.'lorn.a,.TI.b BcaCbIBalOIUHX OKOH
HenpepbIBHo YMeHbiliaeTcH 11.0 Hy.TJH. n03TOMY npeHe6pe)J{eHlIe 3THM
<paKTOpOM He 1I.0JI)J{HO BHOCHTb B paC4eT 3aMeTHOH norpeiliHOCTH.
nOKa3aHHa5I Ha pliC. 63 1I.lIarpaMMa pacnpe1l.eJIeHlI5I TOnJ1I1Ba no1l.-
TBep)J{!IaeT 3TO.
CJIe1l.oBaTeJIbHO, eC.'l1i neplI01l. HarHeTaHIiH (T. e. neplI01l. qJa"..)
pa311.eJIlITb Ha HeCKOJ1bKO Y4aCTKOB II !IJIS!. KOHua Ka)J{!IOrO 1I3 HHX
oIIpe.n:e.TJHTb W, Cn, '1\1, TO MO)J{HO npH6.TJIUKeHHO paCC411TaTb B03pa-
CTalOrn.ylO BeTBb KpIIBOM !IaBJIeHIIH TOIIJIHBa.
OpHHHB P .cp = O,5p max' MO)J{e M onpe!Ie JIIITb
- /2 _/ '
Cenp.cp = 1-/ P y P4J.cP-Plj' (358)
a 3a'i'eM H3 <POPMYJIbI
q = flcfc!1tC enp . cp
842
HaHTH !!t - npO.ZI.OJDKHTeJIbHOCTb BnpblCKa TOnJIHBa 11 ee 3aBHCHMO-
CTH OT YKa3aHHbIX BbIllle rrapaMeTpOB TOn.1HBHOH CHCTeMbI, Tal< Kal<
q,: H3BeCTHO.
Ol.\eHKa npOH3BO.ZI.HTeJlbHOCTH CHCTeMbI H np0l1,OJI)/(HTeJIbHOCTH
BnpHCKa He HBJIHeTCH CTporo 060CHOBaHHOH, TaK KaK Heo6xo.ZI.HMO
3a.n.aBaTbCH npO.ZI.OJI)K11TeJIbHOCTb BnpWCKa 11JIH np0113Bo.n.11TeJIbHO-
CTb CHCTeMbI. KpoMe Toro, He Y'lllTbIBaeTCH B.l11HH11e TaKoro BaM-
Horo 3.1eMeHTa, KaK HarHeTaTeJlbHbIH K.;18n8H.
11.,'151 YTO'IHeHHH HaH.n.eHHbIX napaMeTpOB onpe.n.e.'1HM no.'IOMeHHe
HarHeT8Te.'IbHOrO K.'I8rraHa B MOMeHT Ha'I8.'1a OTCe'II<H, rrpe.ZI.rrOJIO-
MHB, 'ITO K:JanaH B 3TOT MOMeHT Haxo.n.HTCH B paBHOBeCHOM COCT05J.-
H11H,T. e. 'ITO
_ '..L '"p" + C'Jh"
PH - PH I IK .
npJlHHB, 'ITO Bce Ton.1HBO, rrocTyna lll.ee B HarHeT8TeJ1bHbIH
Tpy6onpOBO.n., rrpoxo.n.HT 'Iepe3 Ce'IeHHe no.n. K.18naHOM, II1000KeM Ha-
nHcaTb ypaBHeHHe Hepa3pblBfIOCTH .ZI.BmKeHH5J. TOrrJIHBa
t - C = f V 2 ./ f"P"+C'JhK
'11" 11 11 ilK " . I '
p "
(359)
r .n.e, COf.'1aCHO npe.n.bI.n.Ylll.eMY,
, t = 2,22d,,(h,,-h,,0).
B ypaBHeHHH (359) 1"J1i H C n Jl3BeCTHbi. C.'Ie.n.oBaTeJ1bHO, H3 :no-
ro yp8BHeHH5J. MO.IKHO BbI'IHC.'1HTb h", a 3aTeM, Tal< KaK Be.'IH'lllH8 h"o
3a.il,aHa, onpe.n.eaHTb l1 h" - h",o - rrO.'10)/(eHHe HHMHeH KpOMKH pa3-
rpYMa lllero rr05J.CK8 Topna Cel1,.'I8 K.1an8Ha. npHl'vleM, 'ITO B MOMeHT
OTCe'lKH HHfKHH5J. Kp01\IK8 pa3rpYMa lll.erO nOHCKa HarHeT8Te.'IbHOrO
K.!I8naHa p8cno.'1araeTCH na He3!Ia'IHTe.1bHOM paCCTOHHHII OT BXO.n.-
HOH KpOMKH KaHa,la rHe3Aa. n03TOMY rrpH M8.'IeHllleM na.n.eHHH
.n.aBJIeHH5J. PH KJIanaH Ha'lHH8eT onYCK8TbC5J. H npH 3TOM p83ne.n.H-
IU.lTb 06neM KaMepbI HarHeTaHHH OT OCTa.;lbHoro 06neM8 CIiCTeMbI.
XapaKTepHbIMH TOIJKaMH B nepHO.n. OTCeIJKH B BbIXO.n.HOM CeIJeHHH
Tpy6onpOBo.n.8 HB:JH TCH MOMeHTbI OTxO.n.a Hf.lbI OT ynopa H no-
CaAKH Hr.;lbI H8 Ce.n..l0.
I1r.'1a Ha'IHeT onYCK8TbCH Ha ce,a:.'IO npH
F u +6'y
Pt/J.1I0C = f
II
(360)
LIaB.'IeHHe BrrpbICKa, COOTBeTCTBY lll.ee MOMeHTY Ha'laJI8 rrocaA-
KH, onpe.n.e.1HeTCH H3 ypaBHeHHH (43). Be.1HIJHHY P cp npHHHMaeM
paBHOH
, ,
Pt/J max + PtjJ.noc
P .cP = 2
343
4T06hI onpeJJ:e.'1HTh MOMeHT lJa4aJIa OnYCKaHHSI HrJIhl $OpCYHlm,
RanmlleM ypaBHeHHH 6a.TJ.aHCa TOnJIl1Ba JJ:.TJ.H KaMephI HarHeTaHHH,
T. e. A.TJ.51 06"beMa HaJJ: n.'1ymKepoM LJ;O HarHeTaTeJlhHoro KJIanaHa H
,!J..'I5I OCTa.TJ.hHOrO 06"heMa CHCTeMhI 3a KJlanaHOM.
11.mI KaMephI HarHeTaHHH
fnl1hn + aV".CPP"1 + fJ1h" = aVII.cpp" + /lofoMCocp. (361)
11..'151 OCTa.TJ.hHOrO 06"heMa CHCTeMhI
aV c Pcl = aVcpc+ f"l1h" + /lcf/1fCBnp.cp.
(362)
CJIO>KHB ypaBHeHHH (361) H (362), nO.TJ.Y4IlM
fn l1h n + aV".CPPIII + aVcPcl = aV".cPPII + a\Tcpc + /lofocpl1tCocp +
+ lcf/).:CBnp.cP' (363)
rJJ:e V c = V + V T + V g;;
Pc - JJ:aBJIeHHe B CHCTeMe 3a HarHeTaTeJIhHhIM K.'1anaHOM.
B ypaBHeHHII (363) f n l1h n - KO.'III4eCTBO TonmIBa, nonaHHoro
IIJ1ymKepoM 3a BpeMH I1t; a V K.CPPK, - KO.'1II4eCTBO Ton.'1IIBa, Haxo-
.n:HII erOCH B KaMepe HarHeTaHH51 B C)KaTOM COCT051HIIH B MOMeHT
HaIIa.TJ.a OTce4KH; a VcPc 1 - KO.'IIlIIeCTBO TOnJIIlBa, Haxo.n:HllJ,erOCH B
OKaTOM COCT051HHH B 06'beMe CHCTeMbI 33 KJlan3HOM B MOMeHT OT-
ceIIKH; 'lL V K.CPPK - KO.TJH'-IeCTBO TOfi.'IIlBa, OCTaBilierOC5I B KaMepe Ha-
rHeT3HHH B cm3TOM COCTOHHHH B IWHL(e npOMemYTKa BpeMemi I1t;
a VcPc - KOJIlI'leCTBO TOTIJIlIBa, OCT3BllIerOC5I L\ 061)eMe CHCTel\Ihl 33
KJ1anaHOM B cmaTOM COCTOHHHH K KOHU.Y npOMen\:YTKa BpeMeHH I1t;
Mofocpl1tCocp - Ko.rm4eCTBO Ton. T IIlB3, BhITeKaIOw.ero 3a BpeMH Ij,t
IIepe3 OTce4HbIe OKHa; McfcL'ltCBnp.cp - KO.'1H'leCTBO TOnm1B3. BhITe-
K3IOllJ,erO 3a BpeMH .!!.t 'lepe3 OTBepCTHH pacnhWHTe lH.
DpIIHHMaeM PH = pc + p".
CpeJJ:HIOIO CKOpOCTh BnphICK3 HaxOJJ:HM no Be.TJ.H41IHe P .cP' KOJ1H'
'leCTBO TOnJIIIBa. BhITeKaIOll1.erO 'lepe3 BcaCbIBaIOll1.He OKHa, paCCIIII-
ThIBaeM no cpe.n:HIIM 3Ha'leHIIHM focp II C Ocp , npII'leM Cocp onpeJJ:eJIH-
eM no Be.'1H mHe
P"I + PtfJ.noc + P"
P".cp =
2
TorJJ:a
C = } / 2 }/ P"I + Pt/J.noc+ P "
l'cp I .
P 2
DpII 3THX .n:Onyw.eHIl5IX 113 ypaBHemIH (363) MOlKHO BhI4IlCJ1HTb
np0JJ:o.'1}KnTe.lbHOCTh nepHOAa OT Ha4a.'1a CHII}KeHIl5I JJ:aB.leHn51 pg; .n:o
MOMeHTa Ha4a.TJ.a OTxo.n:a Hr.'1bI OT ynopa. a TaK)Ke IW.1JH'leCTBO Ton-
.TInBa, BnphIcHYToro 3a 3TO Bpe:.IH 'lepe3 paCIlhIJ1HBaIOWIle oTBep-
CTHSl. 1-13 ypaBHeHHH (363) WIll (361) MomHO onpene.'1I1Tb TaKme
'lJ1eH f",j,h"" a CJle.n:OBaTeJ1hHO, . H I1h", - BeJ1IIQIlHY onycKaHHH KJIa-
344
mlHa 3a paCCMaTpHBaeMblH nepHO.l1. BpeMeHH. TaKaH npOBepKa He-
06XO.l1.HMa, '.JT06bI 3HaTb n0J10meHHe K.lanaHa, TaK KaK HCKlIIO'IeHHe
'1J1eHa f",l1h" paBHOCHJ1bHO Aonyw.eHI-IlO, 'ITO nO.l1.nJ1YHmepHMM 06'b-
eM B 3TOM nepHOAe npOl..{eCca BnpbICKa c006w.aeTCH C 06'beMOM V c .
EC H K MOMeHTY Ha'la a noca.a.KH HI' U K anaH BOllie B KaHa
I'He3.l1.a, TO 3TO 03H8'18eT, '1TO YKa38HHbIe 06'beMbI pa3"beAI-IHeHbI,
C.;le.a.OBaTe.lbHO, .a..1H onpeAe.leHHH npo.a.O.lml-ITe.lbHOCTH onYCK8HHH
H 1'.'1 bI H8 ce.a..l0 .a.OCTaTO'lHO COCTaBHTb yp8BHeHHe 68.18HC8 OTHOCH-
Te.lbHO 06"beM8 V r . Onpe.a.e.1HTb n0J10meHHe KJ1anaHa He06xOAHMO
TaKme .a.mI Toro, '1T06bI 3HaTb HeIfCnOJIb30BaHHYIO '1aCTb pa3rpYnia-
Iow.eI'O XOAa KJ1anaHa.
qaw.e Bcero K MOMeHTY Ha'laJ1a onYCKaHliH HI'.'1bI Ha ce.a..l0 Ha-
rHeTaTe.lbHbIH K.la naJ-I HaxoAIfTCSI B KaHaJIe rHe3.a.a. PaCCMOTpHM
3TOT CJIY'IaM. 3TO I.J.eJleco06pa3HO c.a.e.laTb elI.J.e H nOTOMY, '1TO C.1Y-
'laM, Kor.a.a KJ1anaH Haxo.a.HTCH Ha rpaHHl..{e ce.a. a KJIanaHa, nOAO-
6eH npe.a.bI.a.ymeMY, TO bKO K 6a.TIaHcy .a.J1H 06'beMa V c Heo6xoJIJIMO
.a.06aBHTb '1J1eH fuYu - KOJ1H'IeCTBO TOnJ1HBa, BbITeCHSleMoro HrJIOH
npH onycKaHIfH ee Ha ce.a..l0.
Pac'IeToM YCTaHOBJ1eHO, '1TO npn
d u = 6 MM HI' J1a ca.a.HTCH Ha KOHYC
= 100 KF/CM 2 . CJIe.a.oB8TeJIbHO, .a..;lH
npHHHTb Pifw = 100 Kr;CM 2 .
YpaBHeHHe 6aJlaHCa .a..151 pacnlaTpHBaeMbIx YCJIOBHII:
aVCPH.noc + fuYu = aVCPK.noc + rc!cl1tConp. Cf"
Ptjjo = 150 +- 200 KT/CM 2 H
paCnbIJ1HTeJIH npH Ptjj.n =
YKa3aHHbIx YC.;10BHII MomHO
(364)
r.a.e P"li.noc II p".noc - .a.aBJleHHe pc COOTBeTCTBeHHO B MOMeHTbI Ha-
'1aJ1a H KOHl..{a nocamm Hr.'1bI.
OpII npIIHHToM MeTOJI.e paC'IeTa norpeiliHOCTb He YBeJIIf'lHTC5I,
eC.1II npOl..{ecc pa3rpY3KIf 06"beMa V c pa3JI.eJ1HTb Ha nepHOJI. HCTe'le-
HHS! TOnJIHBa B I.J.HJIHHJI.P JI.BHraTeJI5I H nepHOJI. pa3rpY3KlI Bc eJI.cT-
BHe nocalIKH KJIanaHa Ha ceJI..TIo.
KOml'leCTBO Tonmma, BnpblcHYToro B I.J.HJIHHJI.p JI.BHraTeJI51 BO
BpeMS! nocalIKH Hr.1bI Ha CeJI.,TIO,
aVcPII.noc+ fuyu-nVCPK.noc = q'" = rcfcl1tC onp . cpo (365)
vb ypaBHeHHH (365) CJ1elIyeT, '1TO np0JI.OJI}J{HTe.lbHocTb nocalI-
KH Hr J1bl Ha celI.lO
'H q'" .6n
{}> =
/!cfcConp.cP
B pe3y.TlbTaTe 60JIee YTo'lHeHHoI'o paC'IeTa YCTaHOBJIeHO, '1TO
KO.7UI'IeCTBO TOnJIHBa, BnpbICHYToro 3a UIfKJ1,
q'j = q' + q" + q"', (367)
(366)
rJI.e q' - IWJUI'IeCTBO Ton.;lHBa, BnpbIcHYToro 3a BpeMH OT Ha'laJ1a
BnpbIcK8 JI.O Ha'la..w OTCe'lKIf;
q" - KO.'IH'IeCTBO TOnJ1HBa, BnpbIcHYToro 3a nepHolI OT Ha'laJ13
OTce'IKH 110 MOMeHTa Ha'la.TIa nocalIKH HrJ1bI;
23 3aKa3 748
345
q'" - I\O.llIlfeCTBO nm.1IlB3, BnpbICHYTOrO 33 nepliOLl, IlOC3lJ,KII
lIr.lbl n3 Ce.1.10.
B COOTBeTCTBIIII C 3TII:\I np0.10.1;'!,IITe.lbHOCTb npOlleCC3 BIlpblCK3
TOn.1Im3
<f" = <r' + q;" + <f'''.
(368)
B TpenIii nepIlO.1, B CBH3I1 C nOC3.1IWii II r.l bI H3 Ce.1.10, npHHII-
M3e:\I
:2 k 13X
k noc = 2;
. ,
Pl/J.lln + p"'."n
I't/J.,P = 2
OCT3TOlfHoe Ll,3B.'IeHlIe B CI1CTeMe
IlV c p""-f"h,, I
PO= V '
(l c
( 369)
fLl,e h'iJ = h pn3 - h.. - p33rpY304HbIH XOLl, K.13n3H3 3a BpeM5I <p":
h p<l3 - nO.1HbTii p33rpY304HbIii XOA K.13n3H3;
h.. - p33rpY304HbIri XOl1. K.'13rr3H3 33 BpeMH <p'''.
BeCbM3 B3:tKHO Ll,3Tb OlJ,eHKY TOn.'1lIBHOH CHCTeMe H3 CK.'10IIHOCTb
K Ll,Orr0J1IIHTe.'1bHbI!\1 BnpbICK3M. ::hy OlleHKY rrpOH3BOLl,HM rro Hep3-
BenCTBY [6J
F ( t - ) 3£2,
(370)
fJle
£2 = 2a 2 p ( 11;:," r.
OpH !\I3.J1bIX H3rpY3K3x H 4HCJI3X 060pOTOB lIr.la <POPCYHKH He
JlOXO.ll.lIT JlO ynopa. B 3TO:\1 C.;lY4ae rrOlJ.'beM lIr.J1bI Ha OCHOBaHlIlJ
ypaBHeHHSl (360)
Pt/JIU-F'i
y= 6' .
(371 )
3. nYTH YCOBEPWEHCTBOBAHHSI TonnHBHblX CHCTEM AH3EnEA
KOIICTPYKTlIBHoe 0<poplll.leHHe, a c.leJlOBaTe.'1bHO, 1I YCJIOBlIH
rrpoTeKaHlIH npOlJ,eCCOB C!\IeCe06pa30BalIlIH 1I cropaHlIH B Jl1I3e.'1HX
HerrpepbIBHo 1I3!\1eHSHOTCH. Cneu.lIa.lbHbIe YCTpOHCTBa A.1H 33BlIxpe-
HlIH B03.l.1.yxa B KaMepe crop3mm, n.leH04Hoe cMece06pa30B3HlIe.
H3.l.1.LI,YB H .l.I.p. BIIOCHT 60.1blUoe p33H006p33He B Tpe60B3HHH, rrpe.l.l.'b-
HB.1HeMbIe K pacnpeJle.leHlIlO Ton.'1I1B3 BO BpeMeHII II B npOCTpaHCT-
Be. Y.l.I.OB.leTBopeHIIe 3TIIX Tpe60BaHIII1 HB.1HeTCH C.'IOfKHOH H TPYlJ.-
HOH 3aJla4eH.
BbInO.'lHJlTb I13:\leHHlOllllIeCH Tpe60BaHIIH
EnpbIcKa 1II0;'KIIO B c.'l}!1l3e, eC.'IH KOIICTPYKlJ,lIH
6Y.lJ.eT cooTBeTcTBYlOlllH:\1 06pa30!\1 H3MeHeHa.
K xapaKTeplIcTHKe
Ton.1HBIIOrl CHCTe!\lbl
B nepBYIO olIepeJlb
346
He06xo.'UIMO YCTpaHHTb C)'w.eCTBeHHbIe HeII.OCTaTKH, npHcyw.He CO-
Bpel\1eHHbIM TOn.1HBHbIM CHCTeMaM:
I) HeYllOB eTBopHTe bHoe pacnpeII.e eHHe Ton HBa BO BpeMeHH;
2) HeCTa6H.1bHOCTb HalJa.'1bHbIX YC.10BHH;
3) HeKOTopoe HeCOOTBeTCTBHe npHH Hna II.eHCTBHH OTlle bHWX
3.'JeMeHTOB TOnJHlBHOH CHCTeMbI yc.;IOBHHM npOTeKaHHH pa60lJero
npo ecca .'I.H3e.1H.
COBpeMeHHbIe Ton.1HBHbIe CHCTeMbI 3a nepHoII. 3ana3II.blBaHHH
Bocn.1aMeHeHHH BnpbIcKHBalOT 75-80%, a HHOrII.a H 100% OT q'f.
3TO 06CTOHTe,i1bCTBO npHBOII.HT K nOBbIIlleHHoH fKeCTKOCTH pa60TbI
AH3e.1H, 'ITO BbI3blBaeT HenpHHTHbIe nOCJ1eACTBHH. YCTpaHHTb 3TOT
He..'WCTaTOK :\!OfKHO, eC.1H nOII.06paTb 3.1JeMeHTbI TOnJ1HBHOH CHCTeMbI
no xapaKTepHcTHKe BnpbIcKa, BbI6paHHoH B COOTBeTCTBHH C cOBpe-
MeHHbIMH npeAcTaB.1eHHHMH 0 B3aHMOCBH3H npo eccoB Ton.1HBono-
llalJH, oIece06pa30BaHHH H cropaHHH. B 3THX YCJ10BHHX BeCbMa nep-
cneKTHBHbI Ton.1HBHbIe CHCTeMbI C pery.1JHpOBaHHeM KOJ1HlJeCTBa no-
II.aBaervlOro Ton.1HBa nYTeM H3MeHeHHH Ha a.:1a H KOH a npo ecca
BnpbICKa.
HecTa6H.1bHOCTb HalJa.1bHbIX YC OBHH npo ecca BnpbIcKa C B03-
MOfKHbIM 06pa30BaHHeM pa3.1JHlJHbIX OCTaTOlJHbIX AaB.1eHHH H pa3-
J1HlJHbIX OCTaT01IHbIX 06"beMOB MOfKHO YCTpaHHTb nYTeM nOII.nHTKH
(HaII.llYBa) .1JHHHH HarHeTaHHH TOnJJHBHOH CHCTeMbI [15]. 3TO Tpe6y-
eT pa3pa60TKH II.OnOJ1HHTeJ1bHWX YCTPOHCTB II.J1H ocyw.ecTBJ1eHHH
HaII.llYBa .1HHHH HarHeTaHHH, lJTO HeCKO.1bKO yC.10fKHHeT Ton.1HBHYIO
cHcTeMY, HO cyw.ecTBeHHo y.1JYlJIllaeT pa60lJHH npo ecc llH3e.1H Ha
pefKHMax Ma.1bIX nOllalJ. H lJ.Hce.1J 060pOTOB. MeHee 3<p<peKTHBHbIM
5iB.:1HeTCH npHMeHeHHe nOII.npYfKHHeHHoro KJ1anana KOHCTPYK HH
MAIU1 (CM. pHC. 82). OII.HaKO B 3TOM cJ1YlJae II.pymx II.OnOJ1HH-
TeJ1bHbIX YCTPOHCTB He Tpe6yeTCH.
YCJJOBHH npOTeKaHHH pa60 1 Iero npo ecca B OCHOBHOM B,i1HHIOT
Ha pa60TY <POPCYHKH, KOHe paCnblJ1HTe. I IH KOTOpOH HenocpellCTBeH-
HO BbIXOllHT B KaMepy cropaHHH. Ha xapaKTepHCTHKY BnpbICKa MO-
fKeT B.1JHHTb )l,aB.1JeHHe ra30B B H.1HHII.pe )l,BHraTeJ1H. npHH Hn lleH-
CTBIUI <POPCYHKH II.OJ1fKeH 6bITb TaKHM. lJ.T06bI II.aBJ1eHHe ra30B Y.1JYlJ-
IllaJ10 napaMeTpbI npou,ecca BnpbICKa. O)l,HaKO COBpeMenHbIe
<POPCYHKH 3aKpblToro THna C HrOJJblJaTbIM 3anopHbIM K.1JanaHOM
3TOMY Tpe60BaHHIO He YII.OBJ1eTBOpHIOT. HeII.OCTaTKOM TaKHX <popcy-
HOK HB.1JHeTCH HenpaBH.1JbHOe HanpaBJ1eHHe II.BHfKeHHH Hr.1bI BO Bpe-
MH OTKpbITHH H 33KpbITHH npOXOllHoro CelJeHlIH noII. KOHYCOM. Bo
BpeMH OTKpblTHH npOXOllHOfO CelJeHHH llaBJ1eHHe ra30B B U,H.HHHllpe
II.BHraTe.'1H norvlOraeT nOII."beMY Hr.1JbI H ee )l,BHfKeHHIO, B CBH3H C lJeM
ll.1H 06eCnelJeHHH He06xo)l,HMOrO II.OBOJ1bHO BbICOKoro llaBJ1eHHH IIa-
'WJ1a nOll"beMa Hr J1bI BbIHY)J(II.eHbI YCTaHaBJ1HBaTb fKeCTKYIO npYfKH-
HY, KOTopaH B 3Kcn.'1yaTau,lIlI HHOflla npHHOClIT MHOro HenpHHTHO-
CTeH. Bo BpeMH 3aKpWTHH HrJ10H npOXOllHoro CelJeHHH llaBJ1eHHe
ra30B npenHTcTByeT nOCaII.Ke lIf.1bI Ha ceII.J1o. BCJ1ellCTBHe 3Toro
OKOH'IaHHe npou,ecca BnpbICKa 3aTHrHBaeTCH, CTaHOBHTCH Hepe3-
KHM, BH.1bIM, 'ITO HB.1HeTCH He6J1arOnpHHTHbIM II.J1H pa6olJero npo-
23* 347
u.ecca ;J:H3e.1H II l\IOiKeT npIlBeCTII K 3Ha4HTe.TJbHO IY 33KOKCOBbIBaHljJ{)
H 3arOpaHHIO paCnbI.1HBaIOlUHX OTBepCTl-liL B03MOiKHO, 4TO BH.'lOe
OKOH4aHHe npOu.ecca BnpbICKa HB.'HleTCH OCHOBHOH npH4HHOH, BbI3bI-
BalOlUeH 3aKOKCOBbIBaHHe paCnbI.1HBalOlUHX OTBepCTHH. TaKOe He-
COOTBeTCTBHe HanpaB.leHIIH ;J:BHiKeHHH nr.lbI ;J:aB.leHHIO ra30B 6JIa-
rOnpHHTcTByeT npOHImHOBeHHIO ra30B B 06'beM paCnbI.1HTe.TJH, 4TO
YCH.1HBaeT 3aKOI(COBLIBaHHe paCnLI.:1HBaIOlUHX OTBepCTHII H 43CTO
BLI3LIBaeT neperpeB II 3aBHCaHHe 3anOpHOH Hr.TJL!. npII HCnO.TJL30Ba-
HHH Ha;J:AYBa, KOTOpLII1 B HaCTOHlUee BpeMH npH06peTaeT llIHpOKOe
paCnpOCTpaHeHHe, 3TOT He,a:OCT3TOK 3aKpLITOH 4>0PCYHKH BCJ1e.ll.CTBHe
B03paCT3HHH ,a:3B.leHHH r330B 6YAeT 3Ha4HTeJILHO YUWHB3TLCH, llTO
MOfKeT npHBeCTH K Orp3HHlleHHIO .lI.3B.'leHHH Ha,a:.lI.YBa.
YK333HHbIe He,a:OCTaTKH ycyry6.TJHIOTCH H3COCHLIM ,a:eHCTBHeM
Hr.1LI <POPCYHKH. B Ha 1 I3.'1e BnpLICKa nOA'beM Hr.IILI YCHJ1I1B3eT On3C-
HOCTL npOHHKHOBeHHH ra30B B 06'beM 4>OPCYHKH, 3 B KOHu.e nO.ll.allH
BLITa.1KHB3HHC Hr.l0H TOnJ1HB3 H3 06'beM3, KOTOpLIII OHa OCB060,a:H-
.'Ia npH CBoeM no,a:'beMe, 6y,a:eT elll.e 60.TJbllIe paCTSIrnBaTb KOHeu. npo-
u.ecca BnpbICK3.
50.lIee 6.TJarOnpHHTHbI ,a:.TJH opraHH3au.HH npou.ecca BnpLICK3 I(J1a-
naHHbIe 4>OPCYHKH C Henocpe,a:CTBeHHbIM BLIXO.ll.OM KJ13naHa B K3Me-
py cropaHHH, a TaKiKe K.13n3HHbIe 4>0PCYHKH C MHOroCTPYHHbIMH
pacnbIJIHTe.TJHMH.
K.TJ3naHHble <POPCYHKH H3BeCTHLI ,a:3BHO, HO npHMeHHIOTCH pe,a:-
KO, HanpllMep, B llI13eJIe <pllpMbI Hanz-Endrassik. C HeKOTopbIM no-
nyw.eHJleM K 3TOMY nmy <POPCYHOK MOLKHO OTHeCTH TaKLKe pacnbl-
J1HTe.1H nH3eJ1eH 5IA3-204 H ero Mo,a:Il4>HKau.HH, a T3KiKe ,a:H3eJ1eH
<pHpMbI GN1C.
MHorHe aBTopLI, Y4HTLIB3H Ma.TJYIO LKeCTKOCTL npYiKHHbI K,TJ3na-
Ha, C4HTalOT <P0PCYHKY .lI.H3e.1H <pHpMbI H3nz-Endrassik OTKpbITOH.
B .lI.eHCTBIiTe.TJbHOCTH npH p360Te H3 ,a:BHr3TeJIe 3Ta <POPCYHK3 HB-
JmeTCH 3aKpbJTOH, TaK KaK ra3b! npenHTCTBYIOT ee OTKpbJTlllO, BCJIe.ll.-
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TynaeT ,a:aB.TJeHHIO nonneMa Hr.TJbI llITH4>TOBOH <P0PCYHKH, KOTOpylO
ClJHTalOT 3aKpbITOH. llaB.TJeHHe iKe Ton.1HBa B MOMeHT 3aKpLITHH
I(.lIan3Ha 6y,a:eT He MeHbllIe, lJeM B CHCTeMe C 33KpbITOH <POPCYHKOH
npH nOC3,a:Ke Hf.TJbl H3 ce,a:JIO, a B03MOLKHO H 3H3 1 IHTblbHO 60.TJbllIe.
3nIM H 06'bHCHHeTCH, lJTO H3 .lI.H3e.TJe <pi1pMLI Hanz-Endr3ssik Ton-
.TJHBHbIH H3COC C npYiKHHHLIM npHBo,a:OM, KOTOpblH C03,a:aeT cpaBHH-
Te.llbHO He6oJ1bllIHe ,a:aB.lleHHH BnpbICKa. 06eCnelJHBaeT y,a:OB.lleTBopH-
Te.TJbHbIH y,a:e.TJbHLIH pacxo,a: TomUlBa (no cpaBHeHHIO C ,a:pyrnMH ,a:H-
3e.'lHMH TaKoro LKe THn3).
,.Q.1H ,a:H3e.'leH C Henocpe,a:CTBeHHbIM BnpLICKOM TOn.1JflBa 60J1ee
npHeM.1JeMa K.TJanaHHaH 4>opCYHI(a C MHorOCTpyi1HbIM paCnLI.1Jfne.lleM.
KJ13naHH3H <PopCYHKa (pHC. 200) COCTOIiT I13 Kopnyca 1 C u.eH-
Tpa"lbHbIM KaH3.10M A, K KOTOPOMY no,a:BO.ll.IITCH TOn.1JfmO 1I3 HarHe-
TaTe.'lbHOrO Tpy60npOBO.ll.a. K Kopnycy 1 lJepe3 nepexo,a:HIIK 2 nplI-
LKHMaeTCH BTYJIK3 3, BHYTPH KOTOpOH cOBepwaeT B03BpaTHo-noCTy-
naTe.1bHoe ,a:BIILKeHHe rH,a:paB.TJlIlJeCI\H ynpaB.1JHeMLIH pe6pHcTblH
348
KJ1anaH 4. 0PY)lUIHa 6 C pery.1JIIpyeMoII Ha a.1JbHOH 3anDKKoH npII-
:>KIIMaeT KOlIlI'ieCKliH IWHeu, K.lanaHa 4 K KOHVCV BTV.1Kli 3. MHoro-
CTPYHHbIH pacnbI.1IITe.lb 5 HaBIIH'iliBaeTC5I Ha- nepexo.n:HIIK 2, npII-
)KIDla5ICb HIDKHIIM BHYTpeHHIIM TOpU,OM K TOPUY BTYJ1KII 3.
TonJ1IIBo no KaHa.l)' A no.n:aeTC5I B KaMepy r Kopnyca 1, OTKy.n:a
no KaHa aM Me:>K.n:y pe6paMII K anaHa no.n:Bo.n:IITC5I K KaMepe B
BTy.1Kli 3. Kor.n:a .n:aB.leHlIe TOnJIlIBa B KaMepe B
npeBbIcliT CYMMapHoe .n:aB.1eHIIe Ha l Ia.lbHOH 3a-
T5I:>KKH npY)KHHbI 6 H ra30B B U,H.1HH.n:pe .n:II3e.15I,
K.1JanaH 4 Ha'iHeT nepeMernaTbC5I B HanpaB"leHIIH
.n:BH)KeHIISJ nOTOKa II Ton.;lIIBO 'iepe3 Ce'ieHIIe MeJR-
.n:y KOHycmI K.lanaHa II KOHYCOM BTy.1KIi 3 nOCTY-
nliT B KaMepy E, oTKy.n:a 'iepe3 OTBepCTII5I pacnbI-
J1IITeJI5I 5 6y.n:eT BnpbIcKliBaTbC5I B UII.1JIIHlI.P .n:BII-
raTe.'JSJ.
ll3 pllC. 200 c.le.n:yeT, 'iTO KOHCTPYKU,IHI I{.'Ja-
nmmoH (j:JOPCYHKII nporne 3aKpbITOH II YlI.06Hee B
3Kcn.lyaTaUJIII, TaK KaK K.'1anaH 4, npY)KIIHa 6 II
BTy.1Ka " B c60pe npe.n:CTaB.'1HIOT C060H caMOCTO-
5ITe.'1bHbIH Y3e.'1. C.'1e.n:oBaTe,,'JbHo, npJI Heo6xo.il.JI-
MOCTII MOIKHO OT.lle.'IbHO 3aMeHIITb 3anopHhIH op-
raH JI.'JJI pacnbWIITe.'Ih (j:JOPCYHKJI.
TeXHo.'10rII5I JI3rOTOB.leHII51 K.'IanaHHOH (j:Jop-
C)'HKJI TaIGKe 3Ha l II-ne.lbHO nporne, 'ieM 3aKphITOH.
B K,,'1anaHHOH (j:JopCYHKe JICK.llO'ieHa B03MOIK-
HOCTb OTKphITII5I K.'JanaHa 6e3 BnphICKa Ton.'IJIBa.
B CB5I3II C OTCYTCTBlieM HaCOCHoro .n:eHCTBJI5I 3a-
nopHoro KJlanaHa II npOTJIBo.n:eHCTBlI51 ero .n:BmKe-
HJIIO .n:aB.'JeHI!5I ra30B B UJI.'JIIH.n:pe .'I,BJIraTeJI5I 1\10-
:>KHO npJIHSJTb, 'iTO B K.lanaHHOH (j:JopC)'HKe K.la-
naH 3aKphIBaeTC5I MrHOBeHHO, lITO TaK)I{e 5IBJ15IeT-
C5I ee npemI'I)'rneCTBOM. O.n:HaKO 3TO npe.JIM)'IlLeCT-
BO MO)l{eT 6bITb pea.1JI30BaHO, eC.1JII HarHeTaTe.1JbHbIH K.lanaH 06ec-
ne'iJIBaeT B 06"be:Vle V c pa3rpY3K)' .il.0 .n:aB.leHII5I po :::::;; F ' 3.n:eCb
t",
F n - CIIJla Ha'ia,,'1hHOH 3aT5I:>KKII npY:>KJIHhI K.1anaHa, f - n.;10Ill.a.n:b
K.;lanaHa, Ha KOTOpylO .lleHcTBYIOT ra3bI. EC.'IH 3TO YC,,'IOBlie He BbI-
nO.;lHHeTC5I, TO npH YMeHbrneHHII .llaBJIeHJI5I ra30B B U,H.1JJIHJl.pe .n:BII-
raTe.1H TOnJ1HBO 6y.n:eT BbI.n:aB.;lHBaTbC5I B KaMepy CrOpaHII5I, lITO He
TO,,'JbKO MOlKeT JIJIKBII.n:IIpOBaTb YKa3aHHoe BbIllIe npeliMyrnecTBo, HO
Ii yxy.n:IlIIITb y.n:eJlbHbIH pacxoJl. Ton.1JIBa no cpaBHeHIIIO C 3aKpbITOH
(j:JOPCYHKoif. C'IelI.yeT OTMeTJITb BalKHYIO oc06eHHOCTb B pa60Te
KJIanaHHOH (j:JopCYHIm. KaK II3BeCTHO, npn pa60Te B aTllWc(j:JepHbIX
YCJIOBJI5IX BBn.n:y OTCYTCTBII5I npOTnBo.n:aB eHH5I npOH3Bo.n:JITe b-
HOCTb CJICTeMbI B03paCTaeT no cpaBHeHIIIO C npOJI3Bo.n:HTe.'JbHOCTblO
npJI pa60Te CJICTeMbI Ha .n:BIIraTe.'Ie. OAHaKO npli JICnO.lb30BaHJIJI
3aKpWTOH (j:JOPCYHKJI npOJI3BOAHTe bHOCTb B03paCTaeT He3Ha'iIITeJIb-
34!P
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PHC. 200. KJla-
naHHa51 Ij:J0PCYH-
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nbJ.1HTC.1CM
HO H 3THM 06bILJHO npeHe6peraIOT. B c.1YLJae .IKe npHMeHeHIHI KJIa-
naHHoiJ cpOPCYHKH YKa3aHHOe YBe.TJHLJeHHe npOH3BOLUITe.'lbHOCTH
CTaHOBI1TC51 60.'IbWHM. B CB513H C 3THM TOn.1HBHYIO CHCTeMY C K.'Ia-
naHHOH cpOPCYHKOII He06xo.n:HMO pery.'IHpOBaTb Ha 60.'lbWYIO npOH3-
BO.n:I1Te.'JbHOCTb, KOTopa51 .n:0.1.IKHa YCTaHaB.'IHBaTbC51 3KCnepHMeH-
TaJlbHO. HaLJa.'IbHYIO 3aT51.11my npY.lKHHbI K.TJanaHa cpOpCYHIm TaK.lKe
c.TJe.n:yeTb pery.1HpOBaTb C YlleTOM JI.aB.TJeHH51 ra30B B l.(H.'I.HH.n:pe .n:BH-
raTe.TJ51, COOTBeTCTBYIOru.erO MOMeHTY HaLJa.TJa BnpbICKa. 3TO .n:aB.1eHHe
onpe.n:e.TJ51eTC51 H3 HHAHKaTOpHOH .lI.HarpaMMbI no
3a.LI.aHHOMY onepe.IKeHHIO BnpbICKa Ton.TJHBa.
Ha pHC. 201 nOKa3aHa K.TJanaHHa51 cpopcYHKa,
KOTopa51 B KOHCTPYKTHBHOM H TeXHO.'IOrHLJeCKOM
OTHoweHHH nporu.e onHcaHHOH BbIwe. flpHHl.(Hn
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Te.'IbHO 60JIbWe, LJeM B <PopCYHKe, H306pa.iKeHHOH
Ha pHC. 200.
B nOC e.ll.Hee BpeM51 n051BHJIHCb <POPCYHKH
HeiJTpa.'JbHoro THIIa, B KOTOpbIX .lI.aB.1IeHl1e ra30B
He B.'JH51eT Ha OTKpblTHe Ii 3aKpbITHe 3anopHoro
opraHa (pHC. 202). <I>opcYHKa HMeeT rH,lJ,paB.TJHlJe-
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peHHIOIO nO.TJOCTb <POPCYHKH Ha TPH 06"beMa: VI.
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4 H HapY.IKHoH 06TOlJKOH nJIYH.lKepa 6 30c10THI1Ka. B OIlpe.ll.eJ1eHHbIX
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6Y.lI.eT B03pacTaTb, B TO BpeM5I KaK .lI.aB.'IeHHe TOIIJIHBa B 06"beMe V 2
coxpaHHTC5I HeH3MeHHbIl\I. BCJ1e.ll.CTBHe nepena.ll.a .lI.aBJIeHHH B YKa-
3aHHbIX 06"beMaX BTy.'IKa 4 HalJHeT nepeMeru.aTbc51, YMeHbwaH TeM
caMbIM 06"beM V 2 , B pe3y.1bTaTe lJero .lI.aBJleHHe B nOC.'Ie.ll.HeM TaK./Ke
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lJHHbI, COOTBeTCTBYIOllJ.eH 3a.ll.aHHOMY JJ,aB.'IeHHIO HaLJa.'Ia BIIpbICKa
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nJ1YH./Kepe 30.TJOTHHKa, KOTOpa5I KatJa.1aMH Coe.ll.HH51eTC51 C HH./KHHM
350
PHC. 201. K.1a-
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WilM K KaHa.1Y pacnbwHTemI 8, Kyna BbIxonHT paCnbIJIHBalOw.He
oTBepcTHH.
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BTYJ1KH 4. TaKHM o6pa30M, B 3TOH tPop-
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06'beMe V 2 pe3KO YMeHblllHTCH, 'lTO npl1-
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npoxonHOH n.low.anH OKOH A C BbITOLIIWli
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BeT 3HaLIHTe.TJbHOe B03paCTaHI1e ClWpOCTlI
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113 H3JIO)J{eHHoro c.'IenyeT, LITO 113Me-
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CPOPCYHKI1, 11306pa)J{eHHbIe Ha pHC. 200, 20 I, 202, I1CnbITbIBa.'II1Cb
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4
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'no B03MO.iKHOCTJI HaCOCOB pacnpe.lJ.e.lllTe.'IbHOrO TlIna OrpaHlI'IeHbl
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= 2500 06/_ 1UH). Do.lee ueJleco06pa3Ho npIlMeHSlTb pacnpe.lJ.eJIIl-
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6eHHOCTeH .lJ.EIIraTe.l51 Il YC.10BIlH ero 3Kcn,!lyaTaUIlIl.
Do.'Iee npHe!\I.leMhC\IH 6hI.'I1I 6bI Hacoc-<p0PCYHKlI C ra30BbIM npH-
BO,ZLOM, B KOTOpblX npouecc nO,ZLa411 Ton.ll1Ba onpe1l.e.'I5IeTC5I xapaK-
Tep01\I H3MeHeH1I5I .rr.aB.leHI151 ra30B B U1I.1l1H.lJ.pe .lJ.BJIraTe,;l51. B CBH311
C 3THM npJI lIcnO lb30BaHHlI Hacoc-<p0PCYHOK C ra30BbIM npJIBO..'l.OM
06ecne41IBaeTC51 6.1aronplIHTHoe C04eTaHl1e xapaKTepHcTHKII Bnpblc-
Ka C pa6041IM npoueccOM 1I.1I3eJIH. O.n:HaKo np06JJe1\Ia OX.1a)K.n:eHH5I
Hacoc-<p0PCYHOK C ra30BbI1\I nplIBo.n:oM .n:o CHX nop He peIlleHa.
Oc06bIe Tpe60BaHH5I K Ton.'IHBHbIM CHCTeMaM BbI.n:BHraeT npo-
6.1eMa MHorOTon.'IlIBHOCTH. 1'vlHorOTon.:1HBHbIe ClICTeMhI LIO.1)KHbI 6hITh
MaJI04YBCTBHTe.lbHbJ1\IH K C:iKI1MaeMOCTlI Ton.1HBa. 3TO MO.iKHO 06ec-
ne41ITb nYTeM COKpaweH1I5I 06"beMa ClICTeMbI, a TaK)Ke no.n.a4eH
Ton.1HBa nplI p = const, 4TO .'IY41lle Bcero .n:OCTlIraeTC5I B ClICTeJ\!aX
aKKYMy.15ITOpHOro TlIna.
4T06bI KOMneHClIpOBaTb pa3 11I41Ie B yII.e.1hHhIX Becax TOnJIlIB,
c.1e.n:yeT lIcnO.'lb30BaTb nepe.n.BH:iKHOH OrpaHW-IlITe.lb MaKCI1MaJIhHOH
nOl!.a41I Ton.11IBa. B CJIY4ae nplIMeHeH1I5I .lCrKOlICnap5IIOmlIXC5I Ton-
JIlIB He06xo.n:lIMO npe.n:YCMOTpeTh B03MO)KHOCTh nOBhIIllaTb .n:aBJle-
35L
HHe B .lHHHH BCaCbIBaHH5I C nOl\IOIllblO ..'I.BYX nO..'I.KallIlBalOIllHX HaCO-
COB, O..'I.IIH H3 KOTOpbIX 5IB.151eTC5I HaCOCOM 3aTOn.leHHOrO THna H
yCTaHaBJIHBaeTC5I B HanOpHO!\I TOn,;lHBHO!\I 6a'lKe. B 3aBHCIIMOCTH OT
YC.'IOBHH B Ka)K..'I.OM KOHKpeTHOM c.'IYlIae lIIOrYT 6bITb HCnO.lb30BaHbI
Te H.1H ..'I.p)THe MepbI, a B HeKOTopbIX YC.10BH5IX H BeCb HX KOMnJ1eKC.
Ton.1HBHbIe CHCTeMbI aKKYMy.l51TopHoro THna, B TOM lIHC.1e C B03-
.lI.YWHbIl\I, npYMIIHHbIM H rll.lI.paB.1J11IeCKH1\1 npHBO.lI.al\lH n.1YH)Kepa,
CYIIJ,eCTBeliHO YC.10)KH5IlOT IWHCTPYKUJIlO CHCTeMbI B u.e.lOl\I Ii ee 3KC-
nJ1yaTau.HlO. OCHOBHbIM .lI.OBO..'I.01\1 CTOpOHHHKOB 3TH X CHCTelll 5IBJ151eT-
C5I YTBepM.lI.eHHe, lITO .lI.aBJ1eHHe BnpbICKa He 3aBHCHT OT 'lHCJ1a 060-
pOTOB, COXpaH5I5ICb Ha Bcex pe)KHMaX O.lI.HHaKOBO BbICOKHI\L KOHe'l-
HO, l\Ia.la51 3aBHCHMOCTb OT 'lHC.la 060pOTOB .lI.aB.leHH5I BnpbIcK3
51B.1HeTCH cepbe3HbIl\I npeHMYIllecTBOJ\I 3THX CHCTeM. O.lI.HaKO C.10M-
HOCTb cOBpeMeHHbIx CHCTeM nO.lI.06HOrO THna eIlle Be.1HKa, liTO, no-
BH.lI.HMOMY, Ha HeKOTopoe Bpe'\l5I 3a.lI.epMHT HX WHpOKoe pacnpo-
CTpaHeHHe.
Ton.1HBHa51 CHCTeMa C rH.lI.pOnpHBO.lI.OM n.1YHMepa nepcneKTHBHa
B OTHOIUeHHH HcnO.'1b30BaHH5I ee KaJ, 3KcnepHMeHTa.lbHO-.lI.OBO.lI.01l-
HOH CHCTeMbI, TaK KaK B03.lI.eHCTBHeM Ha xapaKTep H3MeHeHH5I naB-
J1eHHH )KHAKOCTH B rHl!.pOnpIIBO..'I.e MO:rKHO C03.ZJ.aTb 6e3 CYIlleCTBeH-
HbIX KOHCTPYKTHBHbIX H3MeHeHHH CHCTeMbI npaKTH'leCKH 6eCKOHe'l-
Hoe 'lHC O xapaKTepHCTHK BnpNCKa TOn.lHBa. C TaKOH .lI.OBOl!.OllHOH
CHCTeJloIOH 6YAeT nO.lI.6HpaTbC5I TO.1bKO He06xo..'I.HMa51 xapaKTepHCTHKa
BnpbICKa .lI..151 HOBoro .ZJ.BHraTe.l51, no KOTOpOH 3aTeJ\I nO.'1MHa pac-
C'lHTbIBaTbCH H npoeKTHpOBaTbC5I 60.1ee npOCTaH H npHeM.TJ:eJ\Ia51
l!.JI5I 3Kcn.'1yaTau.HH Ton.1HBHa51 CHCTeMa.
Ton.1HBHbIe CHCTeMbI .ZJ.aMe ynpoIlleHHoro HIlla Bce :rKe 51B,;151lOT-
C5I .ZJ.OBO.1bHO C.1mKHbIMH. fl03TOl\IY 6bI.:m Cl!.e.'1aHbI nonbITKH pa3pa-
60TaTb TaK Ha3bIBaeMbII'1 6e3HaCOCHbIH BnpbICK Ton.1HBa. 1VleTo..'I.,
npe..'I..'ImKeHHbIH J}'Opaml\:eM, npe..'I.nO.1ara.;:IH l!.aMe BHe.'J:pHTb B npaK-
TIm:y. Ol!.HaKO 3TOT MeTOl!. He 06ecne4IlBa.1 Tpe6ye1\IbJX napaMeTpOB
npou.ecca BnpbICKa Ton.1HBa. flOnbITKH Hcc.'Ie..'I.oBaTe.'1ell y.'IY'lWHTb
MeTO.ZJ. J}'OpaHMa OKa3a.1HCb 6e3pe3y.1bTaTHbI. Heyna'lH HeCKOJ1bKO
3aTopM03H.1H pa60TbI B 3TOM nanpaB.lellHH, XOT5I OHH H 51B.l51lOTC5I
BeCbMa nepcneKTHBHbIMH. YcnexH B 6e3HaCOCHOl\I BnpbICKe MorYT
nO.1HOCTblO H3J\IeHHTb nYTH pa3BHTH5I TOnJ1HBHbIX CHCTeM .lI.H3e.'1eH.
III-1TEPATYPA
1. A H.D: P e C B C K H i1 H. A. TOn'lI1BOnO.D:alOll\HC CHCTCMbI. LI.1I3C.TJII. CnpaB04-
HOC nOC06HC KOHCTpYKTOpa. M., MaIllfH3, 1957.
2. A H .D: P C C B C K II i1 H. A. H <1> a .D: II H A. A. 3KcncpHMcHTa.1bHoc IICCJlC.l.\O-
BaHHC pa60TbI II paC'-ICT Hacoc-lj:JoPCYHKH 1I.113C.TJ5I «LI.LKcHcpa.TJ MOTOpC 278-A»,
TpY.il.bI Hl1LI.l1. I(H. 5. M.- JI., MaIllfH3. 1948.
3. ACT a x 0 B H. B. Bnll5llIHC B5I3KOCTII II .D:PYfHX lj:JaKTopoB Ha MCJlKOCTb
pacnbl.1I1BaHIUI. «LI.1I3C.1CCTpOCHHC», 1937, N2 2.
4. ACT a x 0 B H. B. npH6.1HLKcHHhIi1 MCTO.D: Ol.\CIIKH KOHyca pacnblo1a, .l.\ao1b-
H060i1HOCTH !J MC.1KOCTII pacnbwa CTPYH TOn.TJHBa occKoMnpeccopHoro .D:H3Cml.
«L!H3c.1eCTpocHlle». 1939..N2 10-11. 12.
5. ACT a x 0 B 11. B. .J,HHaMIIKa npol.\ccca BnpbIcKa Ton.1l1Ba B 6b1CTpOXO,l.\-
HbIX H3Ccl5lX. TPY.D:bl MAn .N2 154. M., 113.i1.. «5IOpO HOBOI! TCXH!1KH», 1948.
6. ACT a x 0 B H. B. fllll.paBclll'-lccKHi1 paC4cT II Bb!OOP OCHOBHbIX napaMcT-
pOB Ton.1HBHbIX CIICTCM .!J.BHraTc.1ci1 C BocnnaMCHCHHCM OT CLKaTl1H. TpYlJ:bl Hl1JIL!
.N2 I. M., MaIllfll3, 1955.
7. ACT a x 0 B H. B. 3aKoH nO.D:a'-lH Ton.1HBa KaK lj:JaKTop nOBbIIllCHH5I Ha-
.D:C)KHOCTH pa60TbI II pccypca Ob!CTpOXO.D:HOrO ,J;H3C.1H. «3HcproMaIllIIHocTpOCHHC»,
1956. .N2 8.
8. ACT a x 0 B 11. B. fpaIj:J0-aHa.1!JTII4cCKIli1 MCTO.!J. OI.\CHKII OCHOBHbIX napa-
MCTpOB Ton.TJHBHoi1 CIICTCMbI !J npol.\ccca BnpbIcKa occKor.mpcccopHoro .D:1I3Co151.
«3HcproMaIllliHocTpOCHHC», 1957, .N2 2.
9. ACT a x 0 B 11. B. H n y r a 'I C B JI. 11. lIcc.1c;\oI3aHllc npol.\ecca nO.!J.a411
Ton.1HBa CHCTCMbl (' B03;\YIllHbIM aKKYMy.1HTOpOM. TpY.!J.bI Hl1l1. 1961, .N2 10.
10. ACT a x 0 B H. B. CLKHMacMocTb MOTOpHbIX TOn.TJHB. «3HcproMaIllHHocTpO-
CHIIC». 1960, .N2 9.
11. ACT a x 0 B 11. B. Bo1l1HHHC ;\!1Har.IIIKH .il.BIDKCHIIH Hr.%I 1j:J0PCYHKII Ha npo-
I.\CCC BnpbIcKa Ton.1HBa ObICTpOXO.D:HOro .!J.H3C.151. «3HcproMaIllHHocTpOCHHC», 1962,
.N2 8.
12. ACT a x 0 B 11. B. B,1!JHHue KOHCTPYKTHBHblX napaMcTpoB HarHCTaTCJlb-
HOro TpyoonpoBo.!J.a II xapaKTcpHcTHK Ton.1l1Ba Ha CKOpOCTb pacnpocTpaHeHHH !J xa-
paKTcp OTpa}KCHII5I BO.1H lI.aBo1CHHH B Tono1l1BHoII CIICTC IC .D:H3C.151. «3HcprOMaIlJHHO-
CTpOCHHC», 1966,.N2 5.
13. ACT a x 0 B 11. B. If r 0 .TJ Y 6 K 0 B JI. H. K ucnO,lb30BaHHIO I.\Hlj:JpOBblX
BbIQ!JC.TJHTC.1bHbIX MaIllHH .!J..TJ5I pac4cTa npol.\ccca BnpbIcKa Ton.TJHBa. TpYll.bl HAM11,
Bbm. 94, 1967.
14. ACT a x 0 B 11. B. H r 0 .1 Y 6 K 0 B JI. H. B.TJH5IHHC Ha npol.\ccc BnpblcKa
Ton.TJIIBa OCTaT04Horo pa3pCiKCHII5I B Ton.TJHBHoi1 CHCTCMC .D:H3C.TJH. «ABToM06IwbHaH
npoMbIIll.1CHHOCTb». 1968, .N2 5.
15. ACT a x 0 B 11. B. H 0 K y.TJ 0 B B. f. B.TJH5IHHC KOHCTPYKTHBHblX napa-
MCTpOB HarHCTaTC.lbHoro K.TJanaHa Ha xapaKTepHcTHKY BnpblcKa II paOO'-lHII npol.\ccc
TpaI<TOpHorO .D:113C.1H. TpY1.\bI nCpMcKoro CC.TJbCKOX03Hi1CTBcHHOro HHcTHTYTa.
nCpMb. nCpMCKOC KHH,KHOC H3.D:aTC.%CTBO, 1966.
16. ACT a x 0 B H. B., n y r a '-I C B JI. 11. II nap Ij:J C HOB 5. n. TOn.TJHBHbIC
CHCTCMb! 6ccKor.mpcccopHbIX Jl-1I3C.'1Ci1 !J TeH.D:CHI.\HH HX pa3BHTI151. M., B11HHTI1,
1959.
354
17. 0 a .1 a K IJ H B. H., E P C M C C B A. <1>., II C C M C HOB O. H. Ton.1JIIBHaH
annapaT)"pa OblCTPOXO.D:HbIX .D:1J3C.1CH. JI., «MaIllIIHocTpOCHI1C», 1967.
18. 0 a III IJ po B P. M. HCKOTOpbIC BOnpOCb! IICC.1C.!J.OBaHH5I Ton.1JIIBOnO aIO!l.!HX
-CHCTCM C n.TJYHLKcpHbIM aKKYMY.TJ5ITOpOM. «3HcproMallIHHocTpOCHHC», 1964, N2 5.
19. 0 C H.:I P II K 0 B r. A. II 1\ 0 H C B <1>. o. nplJMCIICHIIC MCTO.!J.a TpaCKTOpl11J
KOpHCi1 K I1CC.1C.!J.OBaHJ11O .1HHCi1HbIX CHCTCM C 3ana3.!J.blBaIlIICM. BCCTHIJK MfY. <1>>1-
31J4CCKa51 H aCTpOIlOMIJ4CCKa51 CCpH5I, 1967. N2 4.
20. 00 pOll. II H B. A. H .!J.p. Pacnbl.1l1BaHI1C LKIIJ\KOCTCIL M., MallII1HOCTpOC-
HIJC, 1967.
21. 0 P 1J.11J H r H. P., B 11 X CpT M. M., f Y T C P M a H H. H. ObICTPOxoAHbIe
JI,H3C.1II. 1'\1., fHTH, 1951.
22. 0.1 a Y M E. TIpOI.\CCCbI BO BnpbICKI1BalO!l.!IJX CIJCTCMaX OblCTPOXO.D:HbIX AI1-
3C.1Ci1. C6. «]],BllraTc.11J BIIYTpcHHcro cropaHIJ5I». nO.D: pCl!:. c. H. BaCIIJlbCBa. T. V.
1\1.- n.. MaUJr1J3. 1936-1939.
23. B 11 T III a II .rI. A., I\ a 1.\ II C .1 b COli O. D.. IJ n a.1 C C B H. H. PaCnbIJlH-
BaHlJe iKlJ.!J.KOCTCi1 lj:J0pcYHKaMIJ. Moo fOC3I\CprOH3l!:aT, 1962.
24. B hI P Y 6 0 B D.. H. <1>1J311'-1CCKI1C xapaKTCplJCTlIKIJ l!:H3C.'IbHbIX Ton.11\B, on-
PCJ\C.1HIO!l.!IJC np01\CCCbI Ton.1I1I30nOJ\a4H. «D.1I3CJlCCTpOCHI1C», 1935, N2 8.
25. B bI P Y 0 0 B D.. H. CMecc06pa30BaIlllc B .D:BlJfaTC.1JHX .D:H3C.151. B c6. «Pa-
604IJC npol.\cCCbI .D:BllraTc,1ci1 BHYTpcHHcro CrOpaHIJ5I IJ I1X arpcraToB». M., MBTY,
1946.
26. B bl C 0 1\ K II i1 Ill. .rI., f a .TJ b n cpo B II 4 .rI. r. 11 f P IJ H r _1 a 3 .rI. A.
TIpOCKTHpOBaHIIC CIJCTCM BnpbICKa Ton.1lJBa Cyn.OBbIX l!:1J3CJleH. .rI., «CY.!J.OCTpOC-
-EIJC», 1967.
27. f.1 a r 0 .1 C B H. 1\1. Pa60'-lllc npOl.\eCCbI .D:BlJraTC.TJci1 BHYTpcHIIcro cropa-
HHH. M.- KIJCB, MaIllfIJ3, 1950.
28. f p H 30 .D: Y 6 10. H. K HCC.1C.LI.OBaHIJIO BO.1HOBbIX npOI.\CCCOB B Tpy60npo-
BOl!:ax. TpY.D:bI MAH, N2 186, 1960.
29. D.LKOH nO.lb D. C H - f apT 0 r. MCXaHIJ4CCKI!C Ko.TJCOaHHH. M., <1>H3MaTfH3.
1960.
30. D. II T H K II H 10. <1>. H C T P y.'I C B IJ '! H. H. ABTOKO.1COaTc.TJbHbIC PC}({HMbl
lICTC'-ICIIHH 113 1jJ0PCYHKH KaK B03MOLKHbIC CpCl!:CTBa Y.1Y4IllCHIIH paCHbI.1I1BaIlI1H Ton-
.nHBa. TpY.!J.bI lJ.HAM N9 146, 1\1., OoopoHrH3, 1948.
31. D. III H T P C H K 0 B. n. HcC.1Jc.!J.oBaIllJc B.'III5IHII5I KOHCTPYKTIJBHblX 3.1JCMCH-
TOB paCnbI.'lIlTc.1H Ha npoTcKaHHe cro flI.D:paB.111'-1CCKOH xapaKTCpIJCTHKH. Co. «AB-
TOMOOIJ.1bHbIH TpaHcnopT». M., 1\1AD.H. 1970.
32. )I\ Y K 0 B C K IJ i1 H. E. 0 fHl!:paB.1H4cCKOIII Yl!:ape B BOl!:OnpoBo.!J.Hb!X TPY-
oax. Co6p. CO'!., T. II. M., fHTT.rI, 1937.
33. 3 ,. 6 H e T 0 B H. fl I1cc.'!e,'\oBaHl1c HaCOCOB pacnpc.!J.c.'IHTC,lbHoro THna.
TpY.D:bI HATH. Bbm. 127, 1960.
34. H H 0 3 C M 1.\ C B H. B. H K 0 III K IJ H B. K TIp'OI.\CCCbl crOpaHH5I B .D:BH-
raTe.'IHX. M., MaIllfll3, 1949.
35. H C a C B A. H. II 0 K \" .1 0 B B. r. 3KcncpIIMCHTa.1JbHOC HCC.TJC.D:OBaHHC
np01\CCca nOAa'lIJ Ton.TJIIBa B .!J.1J3C.151X. TpY.!J.bl nCpMCKOfO Ce.TJbCKox03Hi1CTBcHHoro
I1HCTHT)'Ta. T. 18. Bbm. 5, TICPMb. TICpMCKOC KHII}({HOC 1J3J\aTc.TJbCTBO, 1962.
36. H C a C B A. H. PaC'-ICT Ton.1I1BHoi1 annapaTypbl C npHMCHCHIJCM 3UBM.
M.. «MaIllIIHocTpOCHHC», 1968.
37. I( a .1 H III f. r. B.1HHHIJC MecTHoro OO"bcnfa B KOHl.\e TonmIBOnpOBO.D:a lIa
OTpaIKCIIIJC BO.1H l!:aB.1CHHH. «D.1J3C.1CCTpOCHIIC». 1938, N2 I.
38. I( a.1 HIll f. r. HCYCTOif'-lHBbIC pCiKlJMbl paOOTbI 1j:J0PCYHOK. TpY.!J.bl HATH.
Ebm. ,12. .\1., MallJflI3, 1945.
39. K a .1 H III r. r. OCHOBHbIC TImbI 1j:J0pC)'HOK II aHaJlH3 IJX fIIl!:pO.!J.HHaMIJ4C-
CKIJX xapaKTcpHCTHK. TpY.J.bI HATH. BbIn. 47. M., MaIllrH3, 1947.
40. 1\ a.1 H III r. r. IJ 3 l!: LK H 0 H H H. <1>. nO.!J.ooHe 1j:J0PCYHOK no IIX xapaK-
TCpHcTHKaM. ITOpIllHCRblC ABllraTC.1H BHYTpcHHcro CrOpaHI151. TpY.!J.bI KOHIj:JCpCHI.\HH
no nopIllHcBblM .!J.BllraTc.1HM. M., AH CCCP, 1956.
41. I( 0 III K H H B. I(. H J:p. ,1BHraTc.1H co CBOOO,J:1I0 lI.BHLKymHMllcH nopm-
H5IMH B Tcn.10CIMOBblX YCTalloBKax. M.. MawfH3, 1957.
42. K p Y T 0 B B. H. ABToMaTH4ccKOC perYJlHpOBaHHc ABHraTCJlCH BHYTPCHHC-
ro crOpaHH5I. M., MaIllrH3, 1963.
355
43. K Y 3 H C 1.\ 0 B T. 11>. TeopcTH'-ICCKHe OCHOBbl H MeTO.D:IIKa paC'-IeTa BITpbICKa
BH3KOrO TOn.1I1Ba B nOpIllIleBblX .LI.BHraTeJlHX BHYTpeHHCrO CrOpaI/HH. TpV.D: bl
XHH)l(T. Bbln. 35, 1960. -
44. K Y 3 H C l.l 0 B T. 11>. ABTOKOJlc6aHHH Hr.1bl Ij:JOPCYHKII. TpY,'\bI XHH)l(T.
Bbm. 68, 1963.
45. K Y IT l.l 0 B C. H. PaC'-ICT npol.\ccca BnpbIcKa TOn.1HBa Hacoc-lj:JoPCYHKOH
.D:BllraTc.1H 5IA3-204. «ABTOMOoH.1bHaH H T p aKTO p Ha51 n p OMbIIllJlCHHOCTb» 1953
J\'!! 8. ' ,
46. K Y IT 1.\ 0 B C. l1. H II II 4 II H a .:\ 3 C B. K. HCC.1C,.WBaHIIC Hacoc-lj:Jopcy-
HOK 6bICTPOXO.il.HbIX .D:1I3eJIci1 C nUl,paB.lII'-1eCKIIM ynpaB.1ellne:\1. M., HAlvU1. Bbm. 14.
1960.
47. K Y T 0 B 0 i1 B. A. PacnbI.1l1BaHlle Ton.1HBa .D:H3C.TJbHbI1\IH lj:JopcYHKa:\IH.
TpY.il.bl HHI1, 1959, .N2 8.
48. K y x a pCB M. H. HCC.1C.rJ.OBaHHe paCIJbJ.1HBaHH5I TOnJ1HBa np!EIICHHTC.lb-
liO K 6bICTpOXO.D:HbIM .rJ.H3C.TJHlIl. «HCC.1C.D:OBaHHC pacnbI.1HBaHH5I II rOpCHII5I .lI,H3C.1b-
HOro TOn.1I1Ba». HAMH. Bbm. 87. M., MaIllrH3. 1959.
49 JI C H H H H. M.. 1\'1 a .TJ a III K III/ O. M. II C a 1\1 0 .1 b r. 11. CHCTClIIbl
Ton.1HBonO.!J.a'-lH aBTOIllOOH.1bHbIX II TpaKTopHbIX .!J.H3C.1Ci1. M.. MaIllrH3, 1963.
50. JI bl III C B C K H II A. C. npOI.\CCCbl pacnbl.1HBaHHH TOnJlHBa ;:J,H3C.TJbHbIlIIlI
lj:JopcYHKallIlI. M., MaIllrH3, 1963.
51. Jl bI III e B C K H M A. C. KpHTCpHl1 nO.D:oomr TOIT.1HBHb!X CHCTCM C 30JlOTHH-
KOBbl;\-1 pcry.1HpoBaHllcM. TpY.il.bI HOB04cpKaccKoro nO.TJHTCXHH4ccKoro HH-Ta.
T. 169, HOBo4cpKaccK, 1967.
52. M C.1 b K Y MOB T. ,'Vl. TcoplISl 6bICTPOXO;l,Horo .J,BHfaTC.151 C caMOBOCIT.la-
MCHCHHC:\1. J"1.. OOOpOHfH3, 1953.
53. M II 4 K II II H. A. PC3y.1bTaTbl HCC.1C.D:OBaHHi1 KOHC4HOH <}Ja3bl npOl.\ccca
BIJpbICKa. TpY.!J.bl HATH, Ebm. 149. 1962.
54. HaT a H 3 0 H S. 5I. 0 .D:HHa IHKe TonmIBHoi1 CHCTClIIbI .D:BHraTc.1ci1 .D:H3C.1H.
TpY.!J.bJ UHAM J','!! 20, 1936.
55. H H K n T II H C. E. Hcc.1c;roBaHHc <}JaKTOpOI3. B.TJII5IIOll.\HX I1a IJpOllCCC
BnpbIcKa B 6bICTpOXO.!J.HOM .il.H3C.1C. «ABToTpaKTopHbIC .il.BHraTC.111 BHYTpcHHcro cro-
paIlH5I». TpYl!.bI MAllH. Bbm. 25. 1\1.. MaIllr1l3. 1960.
56. 0 P .111 II A. C. H .!J.p. ;:I,BllraTC.111 BHYTPCHHCro cropaHHH. T. L lvl., MaIll-
rH3. 1951.
57. naB.l 0 B D. B. HCIJO.lb30BaHHc 3.1CKTpOHllbIX BbI4HC.1HTC.1bHbIX MaIllI1H
.!J..1H HCC.1C.lI,0I3aI/H5I Ton.1HBHbIX CIICTC I ;r113C.1Ci1. 1\\., 1\1 a III fI 13. 1962.
58. no 6 51 P jK H H n. H. HCC.1C.D:0I3aHHC B.1H5IIlIIH BIIYTpCHHcro Bllxpcoopa30-
BaHH5I B Ij:J0PCYHKC Ha Ka4CCTBO pacnbl.TJHBaHIIH H lj:JaKCJI pacnbI.1cHlloro Ton.1I1Ba.
«D.BllraTc.111 BHYTPCIlHCro cropaHlI5I». MBTY. M., MaWrH3. 1958.
59. n 0 H 0 ]II a pCB O. n. COBpCMCHl/a51 Ton.1HBOIJO.!J.aIOlll.a51 aIJnapaTypa
aBTOTpaKTopHbIX .D:H3CJlCH. M., UHHTHMAlli, 1961.
60. n 0 p THO B 1.1.. A. DbICTpOXO.!J.HbIC Typ60nopIllHcBblC .LI.BllraTc.1H C BOC-
n.1aMCHCHHCM OT C.iKaTH5I, M., MaUJfH3, 1963.
61. Pay III a H 0 a x B. B. II Ap. 11>!l3J!1.leCKlle OCHOBb! paoo'lero npou.ecca B
KaMcpax CrOpaHlI5I B03.D:YIllHo-pcaKTIIBHbIX .il.BHraTc.TJci\. lv\., «MaIllHHocTpoclII!e»,
]964.
62. P II '-I a p.:\ C 0 H 3. ..J.HHaMIIKa pca.1bHblX :>K11;I.KOCTCi1. ;'\'1... «MIIP», 1965.
63. P Y C II HOB P. B. KOI/CTPYllpOBaHIIC II paC'-ICT .J,!l3C.TJbHOn Ton.TJHBHOH an-
napaTypb!. M.- Jl., «MaUJHHocTpocHHe», 1965.
64. Clip 0 T K H H A. A. MCTO.D:HKa II annapaTypa .D:.TJH !l3MCpCHHH AaB.TJCHHfI
BnpblcKa Hacoc-<}JoPCYHKoi1 OTKpbITOro nma. ABTOTpaKTopHbIC ,iJ,BHraTC.1H BHYTPCH.
Hcro cropaHHH. TpYlI:bI MAIlH. Bbm. 25. M.. MaIllfll3, 1960.
65. C H Ij:J :1-1 a H D. H. 3KcncpH lcHTa.1bHoc HCC.1C.D:OBaHIIC H MCTO.!J. pac4cTa
Ton.1I1BHblX CHCTCM THna DOlli. JI., HHlll1, 1941.
66. C 0 C K II H J1. r. 51. KTJII5IHIIC n.10THOCTII pacnbI.1Iuc.TJ5I ..'J.1I3CJlbH0i1 <}JOPCYHKH
Ha OCHOBHbIC napaMcTpbl npol.\ccca BnpbIcKa. Ta.1.1HH. TpY.D:bI Ta.'1.TJHHcKoro nO.'1H-
TCXIIH4CCKOro IIH-Ta. J','!! 224, 1965.
67. To.1 C T 0 B A. H. HII,iJ,IIKaTOpIlbIII ncplloA 3ana3;IbIBal/lIH Bocn.TJaMCI/CHHH
H lI:HHaMIIKa lJ,Hl\JIa 6bICTpOXOlI:HOro .J.H3C.151 C Bocn.TJaMCIlCIlIICM OT CLKaTI151. TPYAbI
HHJIIl.N2 I. M., MaWrH3, 1955.
356
68. T p y COB B. 11., M a JI b'-l Y K B. 11. II Maca 51 H b! i1 r. Il.. I1ccJle.llo-
BaHlle .llpoOHll.\eit paooTbl 3aKpbITOH iflOPCYHKII .D:H3e.1eH 51M3. 113BeCTH5I BV30B.
Cepll51 «MaIlJHHOCTpoeHHe», N2 10, 1970. M., MBTY HM. BavMaHa. -
69. T P Y COB B. 11. H P 51 6 H K H H JI. M. 11cc.1e.ll.OBaHHe B.'1H5IHII5I xapaKTe-
pllCTHKH BnpblcK3 Ha TOHKOCTb pacnbI.TJHBallHH TonaHBa 1j:J0pcYHKaMH 3aKpblToro
THna. B co. «ABToTpaKTopllble .!J.BHraTe.1H». TPY.D:bI MAIl.11. M., «MaIlJHIIOCTpoe-
HHe». 1968.
70. <1> a i1 H.l e Ii 6 B. H. CTyneH4aTaH xapaKTepHCTIIKa BnpbICKa - 31j:JIj:JeKTIIB-
Hoe Cpel.\CTBO nOBbIIlJeHH5I MOTopecypca l.\H3e.1eH. «ABTOl\lOOHJlbHaH npOl\lblIlJJlell-
HOCTb». 1965. N2 7.
71. <1> 0 hi fJ H 10. 51. ffJ.!J.pO.ll.HHaMH'-IeCKfJH paC'-IeT Ton.TJfJBHblX CfJCTeM CY.!J.OBblX
..'I,1I3e.1ei1. M.. «MOPCKoi1 TpaHCnOpT», 1959.
72. <1> 0 Mil H 10. 51. Ton,lIIBHa51 annapaTypa CY.lI.OBb!X .D:IBe.1ei1. M., «TpaHc-
nopT», 1966.
73. X a 4 fJ HilA. C. npol.\ecc nnpblcKa TOn.1fJBa Hacoc-lj:JopcYHKaMH OTKpbITO-
ro II 3aKpbITOrO Tllna npH ynpyrml npHI30.D:e. «ABToTpaKToplibIe .llBHraTe.lH». Tpy-
,'J.bl 1\'lAIl.I1. Ebm. 25. M., MaIlJfH3, 1960.
74. X a '-I fJ 51 II A. C. HeKOTOpb!e BonpocbI TeopeTH4ecKoro HCC,1e.!J.OBallll51 npo-
I.\ecca I3npbICKa Ton.'1HBa H npoeKTHpoBaHHH Hacoc-iflopCYHOK Ob!CTPOXOl\HOro .llH-
3e.15I. «CropallHe H cMeceoopa30BaJIHe B ,1,H3eJlHX». TpY.D:bI HaY4Ho-TexHII4ecKoi1
KOHlj:JepeHl.\HH. M., AH CCCP, 1960.
75. X 0 B a x M. C. Hcc.TJe.D:oBaIlHe cl\IeCeOOpa30BaHHH B .lI.BuraTe,1HX C pa3-
.D:e.leHHbII\lH BHXpeBbII\IH KaMepal\lH cropaHHH. CropallHe II cl\IeCe06pa30BallHe B .llH-
3e.TJ5IX. Tpy;rbI HaY4Ho-TexHH4ecKoH KOHlj:JepeHI.\HM. M., AH CCCP, 1960.
76. X 0 B a x M. C. 06 OC06e!!1I0CTHX npol.\ecca cl\IeCeOOpa30BauHH II cropa-
HUS! B ObICTPOXO.llllbIX .lI.H3e,151X C KaMepaMII cropa!!HH pa3.1H'-IlibIX TllnOB. «ABTo-
TpaKTopHbIe .D:BHraTe.1H». TpY.D:bI MAIl.11 , «MamllIlOCTpOeIlHe», 1968.
77. X 0 B a x M. C. H .D:p. Pa3BHTlle lj:JaKe.TJa TOnJIHBa npll BnpbICKe B none-
pe4Hbli1 ra30BbIi1 nOTOK. «TpaKTopb! Ii ce.%X03l\1amHHb!», 1966, N2 7.
78. X 0 B a x M. C. H T P Y COB B. H. CHCTel\lbl nIfTaHIIH aBTOM06u,TJbHbiX
.lI.H3e.lbllbIX .!J.BHraTe,TJei1. M.. «TpaHcnopT», 1967.
79. 4 a p Il bI i1 11. A. HeycTaHOBHBIlJI1eC5I .D:BH)KeIlHH pea.1bHoi1 LKH.lI.KOCTH
B Tpyoax. M., f11TJI. 1951.
80. 4 H P K 1111 A. n. H P e 3 H H K n. n. Il.!13e,lbHaH TOn.TJHBHaH annapaTY-
pa. CnpaI304HIIK. M., Mamrll3, 1963.
81. Bur man P. G., De L u c a F. Fuel Injection and Controls for Internal
Combustion Engines. The Technical Press Ltd. London, 1962.
82. CA V Distribution type fuel injection pamps type DPA. Instruction book
83. Diesel and Gas Turbine Progress N 8. N 9. 1966.
84. Diesel Equipment Superintendent, V. 45. N I, 1967.
85. Gas and Oil Power, v. 63. N 733. 1967.
86. G iff e n E.. .,'vI u r a s z e w A. The atomisation of liquid fuels. Lon-
don, 1953.
87. H 6 f ken. W.. 0 s t e r man n F. Ober die Schnarrirequenzen yon
Einspritzventilen. MTZ. 25. (1964). N 4.
88. H 6 f ken Woo 0 s t e r man n F. Die Bestimmung der Schnarrfrequ-
enzen yon Einspritzventilen. MTZ. 28 (1967), N 3.
89. Lan e W. R. Shatter of drops in streams of air. Industrial and Enginee-
ring Chemistry, v. 43. N 6, 1951.
90. Mug e I e R. A.. E van s A. D. Droplet size distribution in sprays
Industrial and Engineering Chemistry. v. 43, N 5. 1951.
91. 0 h n e s 0 r g e W. Die Bildung von Tropfen aus Diisen aus der Zerta!!
fliissiger Strahlen. Zeitschrift des Vereines Deutscher Ingenieure, v. 81, N 16, 1937.
92. SAE Journal. v. 74. !\J 6. 1966.
93. Sit k e i G. Kraftstoffaufbereitung und Verbrennung bei Dieselmotoren.
Berlin. 1964.
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