Author: Вреина Л.И.
Tags: механическая энергия сохранение механической энергии механика деформируемых тел упругость деформация общетехнические дисциплины механика техническая механика
ISBN: 5-94231-078-5
Year: 2002
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. qHCJIO HeH3BeCTHbIX B 3THX ypaBHeHIHIX TaK)Ke paBHO )),BYM, CJIC)),OBa-
TCJIbHO, 3a)).a1.Ja CTaTHqeCKII onpe)).eJIHMa.
4. 3anHcaTb YCJIOBIiSI paBHoBccHSI B BeKTopHoH (rpa<pH1.JeCKoH) HJIIi aHaJIHTH1.Je-
CKOH <popMe. HaHTH HeH3BeCTHbIe BeJIH1.JIIHbi.
B .aaHHoH 3a)).a1.Je HCnOJIb3yeM aHaJIHTUqeCKHH MeTO)). perneHHSI. 3anHcbIBaeM
ypaBHeHlul paBHoBccHSI nJIOCKOH CHCTeMbI CXO)).SlmIIXCSI CHJI:
3
L,Fix = 0;
;=1
3
L,
y =0;
;=1
-12 cos60° + r. cos30° = 0;
12 cos 30° + r. cos 60° - l11g = O.
PernHB nOJIY1.JeHHYIO clicTeMY ypaBHcHHH, Bbl1.JHCJIIiM HaTSI)KeHIIC HHTCH:
TI = 2,5 H; T 2 = 4,34 H.
MOMeHT CHJlLI OTHOCHTeJlLHO TO
KH. CHJIa, )J;eHcTBYIOll.{aR Ha Teno,
MO)l{eT He TonbKO CMeIl{aTb ero, HO M nOBOpaqMBaTb BOKpyr KaKOH-
HM6Y)J;b TOqKM. IlYCTb CMna F , npMJ10)l{eHHaR B TOqKe A, cTpeMMTcR
nOBepHYTb Teno BOKpyr TOqKI1 0 (PHC. 1.15). 1l0cKonbKY cMny MO)l{HO
nepeHocMTb no JIHHHH ee )J;eHCTBHR, TO Bpall.{aTenbHbIH 3
eKT 3TOH
CHnbI He 6Y)J;eT 3aBHceTb OT Toro, B KaKOH TOqKe 3Ta CMJ1a npHnO)l(eHa,
a 6YJJ:eT 3aBHceTb OT paCCTORHMR h OT TOqKH 0 JJ:O nHHHM JJ:eHCTBHR
CMJIbI.
15
,
,
,
,'
l'
0
momo(F)=-h.F
momc ( Fl )=+h.Fl
i
I:
!I
111
r;
I:
a
6
PlICa 1.15
"
j.:
;!t
,i
i.1
i
f;
MOMellTOM CllJlbI F OTHOCMTeJIbHO HeKOTOpOrO
eHTpa 0 Ha3bIBa-
eTC}! BeJIM'-lMHa, paBHa}! np0l13Be,AeHI1IO CHJIbI Ha KpaT'-lai1:rnee pac-
CTO}!HMe 01' T01.JKM 0 ):(0 JIMHMM ):(eHCTBMSI CHJIbI H B3S1TaSi C COOTBeTCT-
BYIO
I1M 3HaKOM. 3HaK «nJIlOC» COOTBeTcTByeT MOMeHTY CMJIbI, KOTO-
pa}! CTpeMI1TC}! nOBepHYTb TeJIO BOKpyr TO'-lKI1 0 npOTI1B xo)].a 1.JaCO-
BOH CTpeJIKM, a 3HaK «MMHYC» - eCJIM CHJIa CTpeMMTCSI nOBepHYTb TeJIO
no HanpaBJIeHMIO ,ABM)KeHMSI 1.JaCOBOH CTpeJIKM. ECJIM JIMHMSI ):(eHCTBMSI
CHJIbI npOXO):(HT 1.Jepe3 T01.JKY, TO MOMeHT CI1JIbI OTHOCMTeJIbHO 3TOH
T01.JKH paBeH HYJIIO.
llepneH,AI1KYJISIp, ony
eHHbIM H3 TO'-lKH 0 Ha JIMHHIO ):(ei1:cTBMSI CH-
JIbI F, Ha3bIBaeTCSI ee nJleQOM OTHOCUTeJlbHO QeHTpa O.
IIapa CHJI. CMCTeMa )].BYX paBHbIX no MO)].YJIIO, napaJIJIeJIbHbIX If
npOTI1BOnOJIO)KHO HanpaBJIeHHbIX CHJI, npHJIO)l{eHHbIX K TeJIY B .L(BYX
pa3HbIX TOqKaX (PHC. 1.16, a), Ha3bIBaeTCSI napoH CUJI.
I;]
i',
,
F 2
o
x
A
a
6
8
Pnc. 1.16
IIJ1eQoM napbl h (CM. pHC. 1.16, a) Ha3bIBaeTC}! KpaTqaMrnee pac-
CTO}!HHe Me)K,AY JIHHH}!MH )].ei1cTBM}! CMJI, COCTaBJI}!IO
HX napy. Mo-
MeHTOM napbl CHJI Ha3bIBaeTC}! B3}!TOe co 3HaKOM «nJIlOc» I1JIH «MHHYC»
npoH3BeJJ:eHMe MOJ(YJI$I OJJ:HOH M3 CM]] Ha nJIeqo napb!.
16
If
.
,
.
.
I
'i
11
!
.
.
I
I
.
.,
.
.
I
.
5
"-
if
.
.
,
CBOHCTBa napbl CUJI. I. CYMMa npoeKQHH Ha JII06yIO OCb CHJI, 06-
pa3YIO
Hx napy, paBHSleTC}! HYJIIO (PHC. 1.16, 6):
F 2 cos a - FI cos a = o.
CJIe
OBaTeJIbHO, napy CHJI HeJIb3}! 3aMeHHTb paBHo):(eHcTBYIO
eH.
npltMep 1.2
BbItJHCJIHTb MOMeHTbI nap CHJI Fa II F 2 (CM. pliCa 1.16, a Ii 6).
PerneHIIe.
MOMeHT napbI cnn Fi H F2 ' npeIlCTaBneHHbIX Ha plICa 1.16, a:
mom ( f) , f2 ) = +FII1 = +Fh.
MOMeHT napbI ClfJI Fi H F 2 , npe}:(CTaBneHHbIX Ha pUC. 1.16, 6:
mom( Fj , f2 )=-F 1 h=-Fh.
2. CYMMa MOMeHTOB CHJI, 06pa3YIO
MX napy, OTHOCHTeJIhHO JI1060:H
TOqKI1 nJIOCKOCTI1, B KOTOpOM pacnOJIO)KeHa napa, paBH}!eTC}! MOMeH-
TY naphI (PHC. 1.16, 6):
momo(F;) =-F) d=-Fd;
momo(F;) = +F 2 1 = +F I;
- -
momo(F;) + momo(.F;) = -F d + F 1 = -(d -I) F= --F 11.
npHBe
eHHe nJlOCKOH CHCTeMbl CUJI K 3a
aHHOMY ueHTpy. llYCTb H3
- - -
TBep)J;oe Teno ,AeMcTByeT CHCTeMa CHn Pi, F;, ..., F,l (PHC. 1.17, a).
IlpHJIo)KHM B T01.JKe 0 no }J:Be ypaBHoBerneHHbIe CHJIbI, O,l];Ha 113 KO-
TOpbIX 6Y,AeT paBHa H napaJIJIeJIbHa 3a)].aHHOH: Ft' = Pi , ..., F; = Fn , a
):(pyraSi - paBHa, HO HanpaBJIeHa B npOTHBOnOnO)KHYIO CTOPOHY:
FJ " = - Pi , .. . , F ; ' = - Fn .
Tenepb Ha Teno )].ei1cTBYIOT: CHCTeMa CXO.n:SI
HXC}! CHJI F; : F2
..., F,:
-- --
H CHCTeMa nap CI1JI C MOMeHTaMI1 nIl = mom (FlFi"), nI2 = mom (F2.F2" ),...
.o., n1 1l = mom(p"p,,"). CHCTeMY CXO,AHLQI1XC}! CHn 3aMeH}!eM paBHO,AeH-
- - --
CTBYlOll1eH (PHC. 1.17, 6): R = FI't- F/ + F: HJII1 (1.JTO BbITeKaer 113 paBeH-
CTBa Fi = Fi ' H 1'.1.(.) R = F; + F 2 + F" . B COOTBeTCTBHH co BTOpbIM CBOM-
CTBOM napbI CMn HaH)J;eM anre6paHt.JeCKYIO CYMMY MOMeHTOB Bcex CI1JI:
;.
M 0 = n1.+ n12 + 11'1".
, .3
14'1,
tv .
CAXA - H K YTH H
<
6H6AHOTEi
A f7
MPTK .
x
o
- ,
F 2
a
6
PHC. 1.17
i!;
B pe3YJIbTaTe npHBe,neHHSI Bcex CHJI K TOqKe 0 npHxo,nHM K JleMMe
Ilyallco:
ITpOH3B0J1bHYIO nJ10CKYIO CHCTeMY CHJI MOiKHO 3aMeHHTb 0)]-110H CH-
nOH, paBHoH reOMeTpHqeCKOH cYMMe Bcex CHJ1, npHJlOiKeHHbIx B npoH3-
BOJ1bHO BbI6paHHOl\'1 u.eIlTpe, H MOl\1eHTOM, paBllbIM aJlre6paUqeCKOH
cYl\IMe MOMeHTOB npHcoe,nHHeHHbIx nap.
TIonYQeHHa51 B pe3YJIbTaTe npHBe,neHI151 CHna R Ha3bIBaeTC5I pe3YJlb-
THpYIOll\eii CHJ10H (OHa He 5IBJI5IeTC}I paBHo,[(eMCTBYIOIl(ei1 ,nJI}I 3a,naH-
HOM CI1CTeMbl CHJI, TaK KaK He 3aMeH5IeT I1X .n:eMCTBH5I), a M 0 - pe3YJ1b-
TIIPY10Il\Ml\1 MOMeHTOM.
IlpHH5ITbI CJIe,nYlOIl(l1e onpe,neneHH}I:
1. TOllKa 0 Ha3bIBaeTC}I U.eHTpOM npuBe,neHHH.
2. BeKTop R 'I paBHbIM reOMeTpH1.JeCKOM cYMMe Bcex CHJI, 5IBJI5IeTC5I
rJ1aBHblM BeKTopOM. Ero 3Ha1.JeHHe He 3aBI1CHT 01' BbI60pa u;eHTpa
npHBe,lJ,eHH5I, T. e. R - HHBapHaHTHa51 BeJIH1.JHHa.
3. MOMeHT M 0, paBHbIM anre6paHlleCKOH CYMMe MOMeHTOB npH-
coe,nHHeHHbIX nap, Ha3bIBaeTC5I rJ1aBHbiM MOMeHTOM; ero 3HaqeHHe
3aBHCHT 01' BbI60pa u;eHTpa npHBe,neHH5I.
qacTHbIe CJ1YQau npuBe,neHuH.
1. R = 0, Mo *- 0 - CHCTeMa CHJI npHBO,lJ;fITCS! Knape C MOMeHTOM,
paBHbIM anre6paH1.JeCKOM CYMMe MOMeHTOB Bcex CHn OTHOCHTeJIbHO
ueHTpa npHBe,lJ,eHH5I. B 3TOM CJIY1.Jae rJIaBHblM MOMeHT He 3aBHCHT 01'
u;eHTpa npHBe.n:eHH}I.
2. R '* 0, M 0 = 0 - CHCTel'vta npHBo,nI1TC}] K O,nHOM paBHo,[(eMcTBYlO-
II
eH CHne, npHno)J(eHHoH B T01.JKe 0; rnaBHbIM BeKTop B 3TOM cnY1.Jae
S!Bn5leTC5I paBHo,[(eMcTBYlOu
eM, TaK KaK OH O,[(HH 3aMeH5IeT cOBoKyn-
HOCTb ,[(eMcTBYlOIl(HX CHn.
18
--_"".:
1
,
,
I
3. R *- 0, Mo '# 0 - TaKaS! CHCTeMa CHJI MO)KeT 6bITb 3aMeHeHa o,n;-
HOM paBHo.n:eMCTBYIOll.{ei1 CHJIOM, npHJIO)KeHHOM B HOBOM QeHTpe npH- .
Be,n;eHH)], pacnOJIO)KeHHOM 01' npe)KHerO Ha paCCTO}lHHH d = Mol R.
4. R = 0, M 0 = 0 - nnOCKa51 CHCTeMa CHn HaXO,lIJ1TC}J B paBHoBecHH
AHaJlHTUqeCKlte YCJ10BHH paBHoBecHH nJlOCKOH CHCTeMbI CHJ1. He06-
XO,nHMbIMH H Ll-OCTaTOqHbIMH ycnOBH5IMH paBHOBeCH5I SlBn5lIOTC5I: R = 0
HMo = O. CnpoeKTHpOBaB BeKTop R Ha OCH KOOpLl-HHaT, nonY1.JHM
Rx = 0 H Ry = 0, TaK KaK R =
R.; + R;. 3HaH, qTO Rx = ir;x H
;=1
11
Ry = L F;y, nOJIY1.JHM a1-lQJlUmUtleCkue YCJlOBUfl paB1-l0BeCUfl npOU3BOJlb-
;=1
1-l0U nJlOCKOU CUCn'1eMbl CUll:
11
LF;x = 0;
;=1
11
LF;y = 0;
;=1
11
L momo( F; ) = O.
;=1
qacTo 3TH ypaBHeHH5I Ha3bIBalOT OCHOBHblMH ypaBHeHHHMH paBIIO-
BeCHB. B 3aBHCHMOCTH 01' pacnOnO)KeHH5I CHn HHOrLl-a Qeneco06pa3HO
COCTaBJI}lTb YCJIOBH5I paBHOBeCH5I B BH,ne Ll-BYX ypaBHeHHH MOMeHTOB H
OLl-HOrO ypaBHeHH5I npoeKQHH:
11
LF;x = 0;
;=1
n
LmomA( F; ) = 0;
;=1
11
L momB( F;) = o.
;=1
B 3TOM cJIY1.Jae OCb Ox He ,nOJI)J(Ha 6bITb nepneH,[(HKYJI}lpHa AB.
MO)KHO 3anHcaTb ypaBHeHHH paBHoBecHH B BH.n:e Tpex ypaBHeHHH
MOMeHTOB OTHOCHTeJIbHO Tpex T01.JeK A, B H C, He JIe)J(aIl(HX Ha O)];HOM
np5lMoi1:
n
LmomA( F'; ) = 0;
;=1
n
LmomB( F; ) = 0;
;=t
11
L momc( F;) = 0 .
;=1
n plfl\tep 1.3
Ha
epMY BeCOM 100 KH .neHcTByeT BeTep C clinoH F = 20 KH. Onpe)J.enliTb pe-
aKUHH onop.
PeweHlIe.
1. 3a 06'beKT paBHoBecHSI BbI6MpaeM
epMY.
19
...
-
-
2. OCB060)KIlaeMC.H 01' CB
3eH 11 3aMeH
eM liX ,lJ,eHCTBlic peaKUI1
MH (puc. 1.18).
y
x
, I
PHc.1.18
I!
I;
3. B pe3ynhTaTe aHanH3a nonY1JeHHOH CHCTeMbI CHn YCTaHaBnUBaeM, 1.JTO cpepMa
Haxo.n.UTC
B paBHOBeCHH no)). )J,eHcTBueM npou3BonbHoH nnOCKOH CHCTeMbI cun.
Cne.n.oBaTenbHo, cymeCTBYIOT TPH ypaBHcHIISI paBHOBeCHSI. ConocTaBuB '-BlCnO
HeH3BeCTHhIX HCKOMbIX BenlPHIH N B, X A H YA C qHCnOM ypaBHeHHH, .n.enaeM 3a-
KnlO1JeHHe, 1JTO 3aLI,a qa CTaTH4eCKIf onpc.n.enHMa5l.
4. 3anIfchIBaeM ypaBHeHIUI paBHOBeCHSI .n.n51 KOHKpeTHoM 3a)).a 1JU:
5
L
x==O; NBcos600+XA-}
==O;
;=1
:1'
5
L 0, == 0 ; N B COS 30 0 + YA -- 100 == 0;
;
I
5
L n10ffiB (F;) == 0; -- 100. 10+ YA' 20 + 20.4 == 0.
;=1
5. PewaSI nonyqeHHYIO cnC1'eMY ypaBHeluIH, onpe.n.eJISIeM:
YA == 46 KIf, N B = 62,4 KH; XA == -I 1,2 KIf.
PeaKUuSl XA nonyqUnaCh C o1'puuaTenbHhlM 3HaKOM; 31'0 03Ha1.JaeT, 1.JTO cpaKTH-
qeCKOe ee HanpaBnellne npOTlfBOnOnO)KHoe.
1.4. 3JIel\feHTLI TeopllU TpellllH
,[(aBHO 113BeCTHO, 1.J:TO ecnH ,lI.BHraTb O,lI.HO TeJIO no nOBepXHOCTI1
JJ.pyroro, B nnOCKOCTH conpHKOCHOBeHH
B03HHKaeT CHJIa COnpOTI1B-
neHH5I OTHOCI1TenbHO
1Y CKOJIb)KeHI1ID 3THX Ten. BnepBbIe Hccne.n:OBa-
HH
MH SlBJIeHHSI TpeHI1S1 3aHHrvlanc
JIeoHapJJ.O lla BHH'-:IH. TO'-:lHOe
onpe)1eJIeHl1e CI1JIbI TpeHI15I C Y'-:leToM Bcex cpaKTopOB, 01' KOTOpbIX OHa
3aBliCHT, npeJ].CTaBJI}IeT CTOJIb CJIO)KHYIO 3aJJ;a1.JY, 1.JTO [(0 CI1X nop He
Y,lI.aeTC5I HaHTH nOJIHOrO TeOpeTH'-:IeCKOrO peIlleHM5I.
20
;
,
1
IT03TOMY npH H3Y'-:IeHHH 3aKOHOB TpeHH5I
npI1XO,lI.HTCSI OCHOBbIBaTbCSI Ha pe3YJIbTaTaX
3KCnepI1MeHTOB.
HTaK, 3aKOHbI TpeHI1S1 6bIJIl1 Hai1,lJ,eHbI OIlbIT-
HbIM nYTeM H B 1771 r. CcpOPMYJIHpOBaHbI cppaH-
QY3CKI1M yqeHbIM KYJIOHOM.
3aKoHbi TpeHItSl.
1. CI1JIa TpeHH
HanpaBJIeHa B CTOPOHY, npo-
THBOnOJIO)KHYID OTHOCI1TeJIbHOH CKOpOCTH CKOJIb-
)KeHH5I (PHC. 1.19).
2. CHJIa TpeHH5I He 3aBHCHT 01' nnOll{a.l(H
TPY
HXC
nOBepxHocTei1.
3. MO,lI.YJIb CHJIbI TpeHI15I npOnOPQHOHaJIeH HOpMaJIbHOMY ,lI.aBneHHID.
Pa3JII1QaIDT CI1JIY TpeHH
npY) nOKoe H npH .n:BH)KeHHH:
F Tp < ioN - CUJla nlpelfU51 nOK051;
F Tp < fN - CUJla InpelfU51 npu ()BUJlCellUU,
r,lI.e N - CI1JIa HOpl\fanbHOro ,lI.aBJIeHI151, 10 - K03cjJcpul1Uellnl lnpellU51
nOK051, f - K03qJcjJul!Ue1l11'1 lnpellU51 CKOJlbJ-ICellU51. MaKCHMaJIbHa51 BenH-
qHHa CHJIbI TpeHHSI }
p max = foN. 113 3KcnepHMeHTOB H3BeCTHO, '-:11'0
npl1 )J.BH)KeHHH K03cpcpHQHeHT TpeHHSI CKOnb)KeHH5I 3aBI1CI1T 01' CKOpO-
CTI1 CKOnb)KeHHSI TeJI.
K03q)cpHQHeHTbI fo H J' 3aBHC5IT 01' MaTepHana H cpH3H'-:IeCKOrO CO-
CT05lHH
TPY
HXC5I nOBepxHocTei1. 3HaqeHH5I 3THX K03cpcpHQHeHTOB
npHBe,lI.eHbI B Ta6n. 1.1.
PUC. 1.19
Ta6nnu,a 1.1
K03<!J<!JIlu,neHT TpelUIH CKo.rIb
eHIfH
MaTepnan K03cpcpHuueHT TpeHIHI
nOKO
/0 CKOnh)KeHn
f
KaMeHh no KaMHlO 0,6...07 --
EeTOH no rane1.JHHKY 0,5...0,6 -
BepeBKa no .n.epeBY 0,5...0,8 0,5
)].epeBo no IlepeBY 0,4...0,7 0,3
MeTann no )).epeBY 0,4...0,6 0,3...0,5
EeToH no neCKY 0,3... 0,4 -
KaMeHh no .n.epeBY 0,4 -
KO)Ka no MCTanny 0,3.. .0,4 0,3
Ac6eCTOBa51 06Kna.uKa no CTanH (qyrYHY) 0,25...0,35 -
EpoH3a no 1.JyrYHY 0,16 -
EpoH3a no 1.JyrYHY C 06nnhHoH CMa3KOH 0,12 -
CTanh no nhIlY 0,03 0,015
CTanb no 1JyrYHY, CTanh no CTanu, qyrYH no 0,12...0,2 0,1
qyrYHY
21
npnMep 1.4
Ha CTanbHOH Ban (PHC. 1.20, a) .aeHcTByeT KPYTSlIl.{IIH MOMeHT MKP = 500 KH. M.
Onpe.n.enuTb, C KaKoH cHnoM HYlKHO ClKaTb TOpM03HbIe Kono)J.KH, 06TSlHyrbIe KOlKeH,
1.IT06bI OCTaHOBIITb Ban.
J'
1
PerneHHC.
I. 3a 06'beKT paBHOBeCHSI BbI6HpaeM Ban.
2. OCB060)l()J.acMcSI OT CBSl3eH II 3aMeHSleM IIX peaKL{HSlMH: HopManbHoH CHnOH
N H CHnOH TpeHIISI FTP, KOTopbIe 6Y)J.YT )J.CHcTBoBaTb Ha Ban co CTOpOHbI Ka)l()J.OH
KonOJ(KH (PHC. 1.20, 6).
FTp
N
N
FTp
a
6
PHC. 1.20
!
1
".
i
:
i
3. nOCKonbKY 1.JHCnO HCH3BeCTHbIX He npeBbIlllaeT 1.JHCnO ypaBHeHHH paBHOBe-
CliSl nnOCKOH CHCTeMbI CHn, TO C1.JHTaCM, qTO 3a)J.a1.Ja CTaTH1.JeCKH onpe)J.cnHMaSi.
4. 3anHllleM O)J.HO li3 ypaBHcHHH paBHoBecHSI, a HMeHHO:
'
, ,
n
Lmomo(F;) =0; MKp-FTpd=O.
;-::1
M Kp 500
OTclO)J.a FTp = - = - = 1250 (KH).
d 0,4
5. I1CKOMYIO CHJIY N onpel1eJISleM H3 3aBliCHMOCTH FTP = 10' N.
B Ta6n. 1.1 )J.nSl napbI KO)l(a -MeTann K03<pqnuJ,HeHT TpeHHSI nOKOSl peKoMeH.n.y-
eTCSI npHHHMaTb 10 = 0,3. . .0,4. TaKIiM 06pa30M,
N = FTp = 1250 = 4166,6 (KH).
0,3 0,3
Ha rnepoxOBaTOH nOBepxHocTH CHJIa TpeHHSI MO)J(eT KOJIe6aTbCSI 01'
HYJISI ,[(0 MaKCHMaJIbHOrO 3HaI.JeHHSI, T. e. 0 < FTp < FTp max. B 3TOM cJIYI.Jae
peaKQHH CBH3H R 6y,[(eT N < R < Rmax. HaH60JIbllIHH yron <p, Ha KOTOpbIH
nOJIHaSI peaKQHSI R MO)KeT OTKJIOHHTbCH, Ha3bIBaeTCSI yrJloM TpeHHH:
tgcp = F-rpmax/N = ioN IN = 10.
B 3aBHCHMOCTH 01' HanpaBJIeHHSI npHJIO)J(eHHoH K TeJIY CHJIbl MaK-
CHMaJIbHaSI peaKQHSI CBSI3H Rmax MO)l(eT HMeTb pa3JIHI.JHbIe HanpaBJIeHHSI,
o6pa3YH npH 3TOM reOMeTpHqeCKOe MeCTO B npocTpaHcTBe B BH,ne
22
I,
,
j
'"
I
KOHHqeCKOH nOBepxHocTH C BepllIHHoH B TOqKe KacaHHSI TeJIa, Ha3bI-
BaeMOM KOHYCOM TpeHHH. ECJIH nplIJIo)J(eHHaSi K TeJIY CIIJIa npoxo,[(HT
BHYTPM KOHyca TpeHHSI, TO TeJIO HaXO,[(HTCSI B paBHOBeCHH.
TpeHueM KalJeHU51, MJIM TpeHl1eM BToporo po,[(a, Ha3bIBalOT conpo-
TIIBJIeHHe, B03HIIKalOll(ee nplI KaI.JeHI1I1 O,[(Horo TeJIa no ,[(pyrOMY.
PaCCMOTpl1M UI1JIHH.lI.pl1I.JeCKHH KaTOK pa,UHYCOM r H BeCOM mg , JIe-
)l(all(HH Ha rnepOXOBaTOH nOBepXHOCTI1. npIIJIO)J(HM B QeHTpe KaTKa
CHJIY Q (pl1c. 1.21, a), KOTopaSi 6y,[(eT MeHhllIe, qeM F Tp max: Q < F Tp max.
B03HHKHeT CHJIa 1'peHHSI F Tp , npenSl1'c1'BYIOll(aSi CKOJIb)J(eHHIO 1'OQKH A
no nJIOCKOCTH. B 3TOM cJIyqae n 1g M N ypaBHoBellIHBalOTcSI, a FTp H
Q o6pa3YlOT napy CI1JI 11 KaTOK ,[(OJI)J(eH Ka1'HTbCSI no nJIOCKOC1'H.
FTp
Q
Q
a
6
PHC. 1.21
B .neHC1'BH1'eJIbHOCTH, eCJIH Q < Qnpe,lb Ka1'OK OC1'aeTCSI B COC1'OSlHI1H
nOKOSI. )J:JISI 06'bSICHeHI1SI 3Toro SIBJIeHMSI He06xo,[(MMO B paCCY)l(,[(eHHSI
BHeCTH CJIe,nYIOll(l1e KOppeKTI1BbI (pMc.l.21, 6):
QnpeJJ.r = N · AB = Nk.
BXO,[(Slll(MM B 31'0 BbIpa)l(eHl1e K03cpcpHQI1eHT k Ha3bIBaeTCSI K03cjJljJU-
14UeHmOM mpeHU51 KalJeHUR; OH 113MepSIeTCSI B CM. CJIe,[(OBaTeJIbHO, B03-
HHKaeT MOMeHT TpeHHSI KaqeHHSI
MTp = kN.
3HaQeHHSI K03cpcpHQI1eHTa TpeHHSI KaqeHI1S1 npHBe,[(eHhI B Ta6JI. 1.2.
Ta6nHua 1.2
K03c1>cI>IuUfeHT TpeHIfH KaqeHIfH
MaTepHaJI K03<P<PHUlIeHT TpeHHSI KaqeHHSI k, CM
,[(cpeBo no AepeBY 0,05. . .0,08
,[(epeBo no CTanH 0,03...0,04
QyrYH no 1.JyrYHY 0,005
MSlrKaSi CTanh no MSlrKOH CTanH 0,005
3aKaJIeHHaSi CTanb no 3aKaneHHOH CTanH 0,00 1
23
-
1.5. IIpocTpaHcTBeHHaH COCTeMa con
IIpocTpaHcTBeHHoH 6YJJ.eM Ha3bIBaTb CMCTeMY CMJI, JIMHMM JJ.eHCTBMg
KOTOpbIX HMelOT JIlo6bIe HanpaBJIeHHg B npOCTpaHCTBe.
MOMeHT CMJlLI OTHOCIITeJlLHO TOqKM (QeHTpa). BeKTop MOMeHTa
CMJlLI OTHOCMTeJlLHO HeKOToporo QeHTpa eCTL BeKTopHoe npOM3Be
e-
HMe pa
Myca-BeKTopa TOqKIi npliJlOiKeHIiSi CIiJlLI, npOBe
eHHoro If3
3Toro QeHTpa, Ha BeKTOp CIiJlLI (PHC. 1.22). B COOTBeTCTBHM C onpe-
,n:eJIeHHeM
- -
Mo = rxF = momo(F).
113 pHC. 1.22 BH,n:HO, qTO MO.nYJIb BeKTopa MOMeHTa CI1JIbI OTHOCH-
TeJIbHO ueHTpa 0 6y,n:eT paBeH MOMeHTY CHJIbI OTHOCHTeJIbHO TOqKH 0,
HaXO
gl.l\eHCg C 3TOH CMJIOH B O,[(HOH nJIOCKOCTH:
i,
i!
A.
M 0 = hF = rFsin(r,F) = 2 nJIOIIJ;. 6.0AB.
113BecTHo, qTO BCSIKI1H BeKTOp MOJKHO pa3JIOJKHTb no OCgM KOOp-
.nHHaT:
-
Mo = Mxi +Myj +M:k;
TaK )l(e MOJKHO Pa3JIO)l(HTb no OCSIM Koop,[(HHaT pa.nHyc-BeKTop r TOqKH
npHJIO)l(eHHg CMJIbI H CHJIY F:
,
- -
r = xi + yj +zk; F = F.
i +Fyj +F:k.
BbInOJIHI1B JJ.eHcTBHe r x F, nOJIyqHM
';1
,
'.'
- -
M 0 = (yF: - zFy)i + (zF.
- xF=)j + (xF y - yF.
)k.
I'
I ,
z
TaKHM o6pa30M, npoeKUHH BeK-
Topa MOMeHTa CHJIbI Ha OCH KOOp-
J];HHaT 6y.nYT CJIe.nYIOI1.(He:
B
I
I
HanpaBJIglOI1.(He KOCHHYCbI BeKTO-
pa MOMeHTa CHJIbJ onpe)J.eJIglOT ero
HanpaBJIeHHe B npocTpaHcTBe:
Mx = yF= - zFy;
My = zF.
-xF:;
"
, I
; ,
y
M: = xF;. - yF.
.
PliC. 1.22
24
11.
1
I
,
I
I
,
I
tII
A
( M 7 ) M x
COS 1 =--=.-'
0, Mo '
_A. _ M
c os ( M J . ) =
.
0, Mo '
A
- - M-
cos(M o,k) =----=:-.
Mo
llpoeKUlIH BeKTopa MOMeHTa CI1JIbI Ha OCb qHCJIeHHO paBHbl 1\-10-
MeH111Y CUJlbl olnHOCUmeJlbHO OCU:
momx(F) = Mx = y.F= -z.Py;
mom y(F) = M y = z . F.
- x . F=;
mOffi=(F) = M= = _"'(.Fy - y.F.
;
Mo =
M.
+M; +M;.
nepBbIe TpH ypaBHeHHg gBJIglOTCg aHaJIHTHQeCKI1M BbIpa)f(eHHeM roUI
onpe)J.eJIeHHR MOMeHTOB CHJIbJ OTHOCllTeJIbHO oceM Koop,[(IlHaT.
n plfMep 1.5
- -
Onpe.aenlITb MOMeHTbI Clin Q, T II P OTHOCHTenbHO oceH Koop)J.IIHaT, ecnH
113BeCTHbI TOQKH npHnO)KeHHSI 3TliX CHn (PHC. ] .23).
PellieHue.
1.0npe,lJ,enSleM MOMeHTbl CHnbI T OTHOCH-
TenbHO oceii KoopllHHaT:
mom.,.(T) = -Ta;
mom y (T) = 0 (TaK KaK CHna T nepeceKaeT
OCb Oy);
mom:(T) = 0 (TaK KaK CHna T napan-
nenbHa OCli Oz).
2. Onpe,lJ,enSleM MOMeHTbI CHnbI P OTHOCH-
TenbHO oceii Koop.aHHaT:
mom.
(P) = +Ph;
x
momy(P) = 0 (TaK KaK Clina P napan-
nenbHa OCli Oy);
mom:(P) = -Ph.
z
T
p
y
ClIJIa Q - B nJIOCKocm ABCD
PHC. 1.23
25
3. BbItnICn
eM MOMeHTbI CHnbI Q OTHOCIiTenbHO oceH Koop)J.HHaT:
mon1x(Q) = 0 (TaK KaK CHna Q nepeceKaeT OCb Ox);
n10m y (Q) = -Q sin a b;
mom;(Q) = +Qcosab.
TeopeMa ° nplfBetJ,eHIfIf npocTpaHCTBeHHOU CHCTeMLI CIfJI K 3atJ,aH-
HOl\1Y L\eHTpy. BC5IKa51 npocTpaHcTBeHHa51 CHCTeMa cHn, ,Z:(eHCTBYIOll.{HX
Ha a6conlOTHo TBep,Z:(oe Teno, MO-
)f(eT 6bITb 3aMeHeHa OD;HOH CHnOH,
reOMeTpHqeCKH paBHOH CYMMe Bcex
.n.eHCTBYIOll.{HX CI1JI, npHJIO)l(eHHbIX
B npOH3BOJIbHO BbI6paHHOM QeHT-
pe, H BeKTopOM-MOMeHTOM, paBHbIM
reOMeTpHqeCKOH CYMMe MOMeHTOB
y Bcex CHJI OTHOCHTeJIbHO QeHTpa npH-
Be,Z:(eHH5I (PHC. 1.24).
/{oKa3al1zellbcmBo. TIYCTb Ha TBep-
.n.oe TeJIO ,Z:(eHcTByeT CHCTeMa CI1JI,
npOH3BOJIbHO pacnOJIO)KeHHa
B
npocTpaHcTBe. 3a L{eHTp npHBe,Z:(e-
HH5I BbI6HpaeM npOH3BOJIhHYIO
TOqKY O. IIpHJIo)KHM B 3TOH TOqKe ypaBHoBerneHHYIO CI1CTeMY CI1JI:
F( == - Fj' ; F{ == - F{' 11 TaK .n.aJIee, npl1qeM F;' == FI ,..., P,; == P" . 3aMe-
z
PHC. 1.24
- -
HI1M CXO
51ll{YJOC
cHcTervlY CHJI paBHo,[(eHCTBYIOIT(eH R == Fa' + F;' + ...
... + p,;. 3aTeM BblQHCJIHM MOMeHTbI Bcex OCTaBlllI1XC5I CHJI OTHOCH-
TeJIbHO ueHTpa npI1Be,n;eHI151 O. MOMeHTbI CI1JI Ft': F{: ..., F,:' OTHOCH-
TeJIbHO QeHTpa 0 paBHbl HYJIlO, TaK KaK I1X nJIeqo paBHO HYJIlO. BeK-
TOPbI-MOMeHTbJ 3a.n.aHHbIX CI1JI OTHOCI1TeJIbHO QeHTpa np HBe .n.eHH5I
6Y,Z:(YT paBHbI:
lTI01TIO(FJ) == 111 1;
lTIomo(F 2 ) == 1112 ;
mOI110(!:,) == 111" .
HaHJI.eM reOMeTpHQeCKYIO CYMMY 3TI1X BeKTOpOB 11 nOJIyql1M I'JIaB-
HbIH BeKTOp-MOMeHT:
" 11
Mo == Lmomo( F; )== L /11; .
;=1 ;=1
26
I
J
.
h
_
"
-
""i" .,:-_:
_'"
1
I
I
TaKHM 06pa30M, Ha TBep.n.Oe TeJIO Tenepb ,neHcTByeT O.n.Ha CHJIa R
H O,[(HH MOMeHT M 0, T. e. CHCTeMa npOCTpaHCTBeHHbIX CHJI, npOH3-
BOJIbHO paCnOJIO)KeHHbIX, CBe.n.eHa K O,[(HOH pe3YJIbTHPYlOll.{eH CHJIe R
H O.n.HOMY pe3YJIbTl1pYlOIT(eMY MOMeHTY Mo. TeopeMa ,nOKa3aHa.
AHaJllfTlfqeCKOe Bblpajf\eHHe .LJ.JIH onpetJ,eJleHHH r JlaBHOrO BeKTopa H
rJIaBHOrO 1\10MeHTa. rJIaBHbIH BeKTOp R 11 rJIaBHbIH MOMeHT M 0 6bIJIM
HaH.n.eHbI reOMeTpMqeCKHM nYTeM (nOCTpoeHHeM BeKTopHbIX MHoro-
yrOJIbHHKOB). j::(JI5I npOCTpaHCTBeHHOM CI1CTeMbI CHJI HX npOIT(e onpeJI.e-
JI5ITb aHaJIHTHqeCKH. TIpHHHMaeM QeHTp npHBe,lJ;eHM5I 3a HaqaJIO KOOp-
.n.MHaT. Tor.n.a, npoeKTMpY5I Ha OCH KOOp.n.HHaT BeKTopHbIe paBeHCTBa,
nOJIYQaeM:
11
Rx == L
x;
;=1
11
Ry == L
y;
;=1
11
R: == L
:;
;=1
i
--II
"
11
Mx == L l1 '1;x;
;=1
11
M)' == Ll11;y;
;=1
11
M: == LI11;:.
;=1
"
. :
qacTHble cJlyqaH npHBeJ].eHHH. JI106a51 npOH3BonbHa
npOCTpaHCT-
BeHHa51 CHCTeMa MO)KeT 6bITb 3aMeHeHa rJIaBHbll\l BeKTopOM H rJIaB-
HbIM MOMeHTOM. PaCCMOTpMM B03MO)l(HbIe qaCTHbIe CJIyqaH:
a) clly
au paBIl0BeCUJl:
R == 0; M 0 == 0;
6) cucmeMa CUll c600ulncR Knape (TBep,[(oe TeJIO BpalliaeTC
):
R == 0; M 0 * 0;
6) cucmeMa CUll C60du111CR K pa6HodeUC1116YIOU/eu:
I-H CJIyqaM - R * 0, M 0 == 0 - paBHO,lJ;eMCTBYlOIT(a51 npoxo.n.HT qe-
pe3 ueHTp I1pHBeJI.eHH
(TOQKY 0);
2-M CJIyqai1 -. R * 0, M 0 * 0 - npH 3TOM 11 pe3YJIbTMpYIO
a51 CHJIa
- -
M pe3ynbTHpYIO
a
napa JIe)l(aT B O,lJ;HOH nnOCKOCTM, T.e. Rl.Mo.
31'0 qaCTHblM CJIyqaM nJIOCKOH CHCTeMbI CHJI. PaHee 6bIJIO nOKa3aHO,
qTO TaKOH cJIyqai1 MO)f(eT MMeTb paBHO,lI.eMcTBYIOll\YlO, npHJIO)l(eHHYIO
He B QeHTpe npHBe.n.eHM
, a B ,lI.PyroM TOQKe, OTCT05lIT(eM 01' Hero Ha
paCCTO
HI1H, paBHOM MoIR. TaKMM o6pa30M npOCTpaHCTBeHHa
CHCTe-
Ma 3aMeHeHa O,[(HOM paBHo,[(eMCTBYIOll.\ei1, He npoxo.n.
ll.{ei1 Qepe3 L{eHTp
npHBe,lJ;eHM5I;
2) CUC111e.kta CBO()UI1"lCJl K ()U1-lQA;tU
eCKOJvtY BU1-l11ZY:
R * 0; M 0 :;t: 0 ,
H OHM He nepneH,lI.HKYJI5IpHbI.
-
1
AHaJlHTHQeCKHe YCJlOBHH paBIIOBeCHH npOCTpaHCTBeHHOii CHCTeMbl
CHll. He06xo,lI.HMhIMH 11 ,lI.OCTaT01JHhIMH ycnoBH
MH paBHOBeCH
npo-
H3BOJIhHOM npOCTpaHCTBeHHOM CHCTeMhI CHn
Bn
eTCSI paBeHCTBO
HYJIIO rllaBHoro BeKTopa H rJIaBHOrO MOMeHTa:
R = 0; M 0 = o.
:,
'I:
nOCKonbKY R =
R; + R; + R; = 0, TO R.n Ry J1 R= .lJ,OmKHbI 6bITb
paBHhI HYJIIO. AHanOrHqHOe paCCY)J(JJ;eHHe cnpaBe.nJIHBO H JJ;JISI BeKTO-
pa rJIaBHOrO MOMeHTa. CJIeJJ;OBaTenbHO, ,lI.llSl paBHOBeCH
npOH3BOJIb-
HOM npOCTpaHCTBeHHOM CHCTeMhJ CHll He06xo,lI.HMO H J(OCTaTOqHO:
11
L
x = 0;
;=1
11
LF;y = 0;
;=1
II
LF;= = 0;
i=l
n
L momx( F; ) = 0;
i=l
II
LlTIOffiy( F; ) = 0;
i=l
II
L lTI 0 lTI = ( F; ) = O.
;=1
nplfMep 1.6
OnpeJ],enuTb, KaKOH rpY3 CMO)l(eT nO)J.HSlTb 1.JeJIOBeK, npHKJIaLI.bIBaSl YCHJIHe K
BepeBKe P=60 11 (PHC. 1.25); onpeLI.enlITb TaK)I(e peaKI
HH onop.
y
x
PHC. 1.25
PemeHl1e.
I. 3a 06'beKT paBHOBeCIUI BbI6HpaeM Ban A B.
2. OCBo60)l()].aeM Ban 01' CB5I3eH H 3aMeH5IeM nx lIencTBHe peaKl{H5IMH. OnopbI
o 11 B npeLI.CTaBn5llOT c060n l{IiJIHHLI.pIPfecKHe IlJapHHpbI, KOTopbIe npen5l1 CTBYIOT
nepeMeli{eHHIO TonbKO B pa;UlanbHoM HanpaBJIeHIIH, n03ToMY npOCTaBJI5IeM B
28
.
I
I
pa)J.HaJIbHbIX HanpaBneHH5IX peaKl{IUf X 0, Zo, X B H ZB. BepeBKY «06pbIBaeM»
YTb
BbIIlle ponHKa C H 3aMCH5IeM HaT5I)I(CHHCM HHTH T.
3. I'cnepb MO)l(HO paccMaTplIBaTb paBHoBecHe cB06o)].Horo Tcna no)]. .D.eHCTBH-
eM aKTHBHbIX H naCCIiBHbIX CHJI. 113 IlIeCTH ypaBHeHHH paBHOBeCH5I npOH3BonbHOH
CIiCTeMbI npOCTpaHCTBeHHbIX cun OCTaeTC5I TonbKO n5lTb, TaK KaK cyrvlMa npOeKl{HH
Ha OCb Oy TO)l(LI.eCTBCHHO paBHa HYJIIO. 3aJ],a lJa npe)].CTaBJI5IeTC5I CTaTH1.JeCKH onpe-
.D.CJIHMOH:, TaK KaK HeU3BCCTHbIX BeJIHlJHH TO)l(e n5lTb: X 0, XB, Q, Zo Ii ZB.
4. COCTaBJI5ICrvt ypaBHeHII5I paBHOBeCIi51 npOCTpaHCTBeHHoH CHCTCMbI CHJI:
f-.: = Xo + X B + T cos300= 0;
F =0;
J
F: =-Q+Zo +ZB -Tcos600=0;
Mx = +ZB .1,5 - Q.l + 7'cos60°.0,5 = 0:
A1)' = -Qr + TR = 0;
M: = -x B .1,5 + Tcos30°.0,5 = O.
5. Ilo)].cTaBHB B npe)].nocJIc.D.Hee ypaBHeHHc r = 0,2 M, R = 1,2 M Ii 7' = 60 H, nOJIY-
1.JIiM, 1.JTO BCC rpY3a Q = 360 H.
113 nocne)J.Hero ypaBHCHH5I onpe):(eJIUM pcaKIUflO XB:
X B = 60cos 30°.0,5 = 17 (H).
1,5
nO.D.CTaBn5l51 nonY
CHHbIe 3HalJeHH5I Q = 360 H,
¥B = 17 H B OCTaBliHICC5I ypaB-
HCHII5I, HaH:.D:CM ZB, 20 Ii X 0:
ZB = 360.1- 60.0,5.0,5 = 230 (H);
1,5
Zo = 360 - 230 + 60 . 0,5 = 160 (H);
x 0 = -(17 + 60 . 0,85) = -68 (H).
PCaKIJ.IUI X 0 6Y.D.CT IIMCTb npoTHBOnOJIO)l(HOC HanpaBJICHIie, TaK KaK B PC3YJIb-
TaTe BbILHICJICHHH: nOJIYlJHJ1C5I OTplIIJ.aTCJIbHbIH: 3HaK.
1.6. OnpeJJ;eJIeHUe l(ellTpa TH
eCTU
QellTp THiKeCTII TBepAoro TeJIa. CHJIbI npHTSI)KeHHSI OT,lI.enbHhlX
qaCTHQ TeJIa HanpaBJIeHhJ npH6nH3HTellbHo K U.eHTpy 3eMJIH. 'I'aK KaK
pa3rvlepbI paCCMaTpl1BaeMbIX Ten MaJIbI no cpaBHeHHIO C pa,nHYCOM
3e11JIH, TO 3TH CHJIhI MO)f(HO C1JHTaTb napaJIJIenbHhIMM. PaBHOJJ;eHCT-
BYlOlI(a
3THX napanneJIbHhIX CHJI, paBHa
HX CYMMe, eCTb Bee TeJIa, a
U.eHTp 3TOH CHCTeMbI napaJIJIenbHbIX CHll, B KOTOpOM npHnO)l{eH Bec
TeJIa, Ha3hIBaeTC
l1eHl1'lpOJH 111R:HCeC111U lneJlQ.
29
QT06bI HaHTM nOnO)J(eHMe QeHTpa T$I)J(eCTI1 Tena, He06xo
HMO 113Y-
QI1Tb, KaK CKJIalIbIBaIOTC$I napaJIJIeJIbHbIe CI1JIbI H Onpe
eJI$lIOTC$I KO-
Op,nHHaTbI T01.JKH npHJIO)J(eHH$I HX paBHO,neHCTBYIO
eH.
CJlOil\eHHe nap3JIJleJlbHblX CHJI. ,ZJ;OnYCTI1M, 4TO Ha TenO
eHcTByeT
CI1 CTeMa napannenbHbIX CHn Pi , F 2 , F3 11 F4 (pl1c. 1.26), npH1.JeM Fi H
F2
eHcTBYIOT B O,nHY CTOPOHY, a F3 11 Ft - B npoTMBonono)J(HYIO.
,aJI$I CMJI Fi H F 2 HaH
eM TaKOH QeHTp npI1Be
eHI1}}, OTHOCHTeJIbHO
KOToporo pe3YJIbTHPYIOI..QHH MOMeHT 6YJJ:eT paBeH HynIO:
2
L InomBI (r:) = f2 . A2B, - F; . AIBI = o.
;=1
O A2BI F;
TCIOJJ:a = -. Mo
ynb pe3YJIbTHpYlOl..Qei1 CHnbI, npHJIo)J(eHHoi1
A I B, F 2
B T01.JKe B., 6y,n;eT paBeH R, = F; + F 2 .
AHaJIOrM1.JHO Hai1
eM R 2 H ee T01.JKY npMJIo)J(eHM}} B 2 .
3aTeM npMBe,ne
1 CHnbI RI H R 2 K QeHTpy npHBe
eHH$I C, nono)J(e-
HMe KOToporo onpe
eJIMTC$I H3 COOTHOIlleHH}}
B 2 C = RJ
BJC R 2
z
Pe3YJIbTHpYlOl..Qa}} CHJI R, M
R 2 6y
eT paBHa HX reOMeT-
pM1.JeCKOH CYMMe, T. e.
R= RI + R2 .
TIocKonbKY JIMHM}} J(eHCT-
BH}J y aHTMnapanneJIbHbIX CHn
O
Ha M Ta )Ke, TO MOJJ:ynb R
6y,neT paBeH R = R 2 - RJ .
ECJIM R :;t 0, TO Bcer,na
Y MO)J(HO HaHTH TaKYIO T01.JKY, B
KOTOpOH 6y,n;eT npl1J10)KeHa
paBHo
eHCTBYIO
a$l R Bcex
napaJInenbHbIX CMJI.
x
PliCa 1.26
30
.
.
,
3Ta TOQKa Ha3bIBaeTC}J ijeflmpOM napaJUleJlbflblX CUll.
KOOpAHHaTbl QeHTpa napaJIJlCJlbHblX CHJI. nOJIO)l(eHHe u;eHTpa na-
paJIJIeJIbHbIX CMJI OTHOCMTeJIbHO Ha1.JaJIa KOop,nMHaT Onpe
eJI}JeTC$I
pa
MYCOM-BeKTOpOM f MJIM ero npOeKI..JJ1RMM Ha OCM Koop,nMHaT, 1.JTO
paBH03Ha1.JHO Koop,n;MHaTaM u;eHTpa napaJIJIeJIbHbIX CMJI xc, Yc H Zc.
TeopeMa 0 MOMeHTe paBHOAeHCTBYIOw;eH (meopeMa BapUflbOlla).
npHJIOJKI1M B T01.JKe C CI1JIY R I = - R (CM. pl1c. 1.26). Tor,n;a CHCTeMa
6y,n;eT Haxo,n;HTbCSI B paBHOBeCHI1.
Tenepb onpe,n;eJIHM MOMeHT OTHOCHTeJIbHO T01.JKM O. 01.JeBI1,ZJ;Ho,
OH paBeH HynlO, TaK KaK CHCTeMa CHII HaXOJlHTCSI B paBHoBecHH:
11+ 1 II
L momo ( F; ) = L momo ( F'; ) + mOITIo ( R ') = o.
;=1 ;=1
Ho TaK KaK R I = - R , TO
Il
L fi x F; -
x R = 0,
;=1
HnH
n
L'ix F; =fcx R .
;=1
B npaBOM 1.JaCTM paBeHCTBa 3anHcaH MOMeHT paBHo,n;eMcTBYIOIll.eM, a B
neBOM 1.JaCTH - reOMeTpl11.JeCKaR CYMMa MOMeHTOB Bcex CM]] OTHOCM-
TeJIbHO TOM JKe T01.JKM.
OTCIO,L(a cne,L(yeT, QTO 1\10MeHT paBHOAeHCTBYIOIIJ.eH OTHOCnTCJlbHO
JlI06oro QeHTpa paBeH reOMeTpn1.JeCKOH cYMMe BeKTopOB-MOMeHToB cJla-
raeMblX CHJI OTHOCHTeJlbHO Toro )Ke u.eHTpa. 3Ta TeopeMa 0 MOMeHTe
paBHO,L(eMCTBYIOI..QeH Ha3bIBaeTCSI TeopeMOM BapHHbOHa.
II
CnpoeKTMpOBaB BeKTopHoe paBeHCTBO
x R = L r; x F; Ha OCH
;-1
KoopJJ.MHaT, nonY1.JI1M cpopMynbI ,n;nSI onpe,L(eneHHSI MOMeHTOB paBHO-
,L(eMCTBYlOll1ei1 OTHOCMTeJIbHO oceM Koop,ZJ;MHaT:
II _____
momx (R) = L'no'nx(
);
;=1
II _
Inomy (R) = LlnOffiy(F';);
;=1
II
mOffi:( R ) = LITIOffi:( F'; ).
;=1
31
BeJIMqMHa p aBHO .n:ei1cTBYlOlQei1 napannenbHbIX CMn He M3MeHMTC
,
eCJ1Ii Bce CIiJ1bJ nOBepHYTb napannenbHO OCM Oz. B 3TOM cnyqae MO-
MeHT paBHo,n;eifcTBYlOlQeif OTHOCMTeJIbHO OCM 0»)
11
Rx c =
F.x.
.L.J I I'
;=1
n
F:x.
.L.J I I
oTKy,n;a Xc = ;=1
R
AHaJ10rMQHbIM 06pa30M BbIQMCJlMM M ,n;pyrMe KoopduHambl lI eH111 pa
napaJlJleJlbHblX CUll:
n 11
LF:x. LRx.
I I I I
Xc = ;=1 ;=1
R 11
L
;=1
n n
LF;y; L 1; )J;
)J c = ;=1 ;=1
-
R 11
Lfi
;=1
11 11
LFzo LFz.
I I I I
Zc = ;=1 i=t
R 11
LF;
;=)
KOOp
"HaTbl ueHTpa TB
eCT" TBepAoro TeJIa. EcnM B cpopMYJIaX
,n;nH onpeJJ:eJIeHMH KOOp)JYIHaT QeHTpa napaJI11enbHbIX CMJI B1vfeCTO Fi.J"
F;y, F;z H R nO,[(CTaBHTh Illig:", nl;gy, 111 i g: H lng, TO n011YQMM 3aBMCMMO-
CTH
n
onpe,n;eJleHHSI Koop,n;HHaT QeHTpa T
)I(eCTM TeJIa:
L111;g
.}:;
Xc =
mg
v.x.
.L.J I I
- .
V
m. g . ) ".
V y .
.L.J I)' I .L.J II
Yc = mg = V ;
L 111 ig: .Zi
Zc =
n1g
Vz.
L.J I I
V
rile m i , Vi - COOTBeTCTBeHHO Macca Ii 06'beM Ka)l(,n;OH qaCTHl..{bI TBep-
oro Te11a, a n'l Ii V - BCH Macca H 06'beM O,l(HopO,l(Horo TeJla.
,[(JI
nnocKOH cpHrYPbI nno
a,n;bIO l.S, I1MelO
eH OlIHHaKoBYIO Ton-
l.QHHY 11, 3J1eMeHTapHhIe 06'beMhI f/; MO)l(HO BbIpa3HTh Qepe3 3neMeH-
TapHbIe fIJIOlQa,n;H Si: Vi = IzS i .
32
'I
I
Tor,n;a Koop,nMHaTbI QeHTpa T
)I(eCTH 3TOM cpHrypbI onpe,n;en
TC
cne,nYlOlQHM 06pa30M:
S.x.
L.J I ,
Xc = S ;
LSiYi
Yc = S ;
S'Z.
L.J ' I
S
Zc =
CYI.QeCTByeT TaK)I(e nOH
THe l1eHn1pa Macc, KOTopoe cnpaBe,nJlHBO
,[(11H JlI06oro CIi110Boro n011
:
m.x.
L.J ' ,
Xc = ;
m
LmiYi.
Yc = ,
m
111'Z'
L..J I'
Zc = .
m
TaKHM 06pa30M, QeHTp TH)KeCTM (H11M QeHTp Macc) - 3TO reOMeT-
pMqeCKa
TOqKa C, KOTopaH B QaCTHhIX cJlyqaHX MO)I(eT Jle)I(aTb BHe
npe,ne110B caMoro Tena; HanpMMep, QeHTp TH)I{eCTM KOJlbQa ne)l{MT Ha
nepeCeqeHHH ero oceM CI1MMeTpI1H, T. e. BHe Tena.
8CM
x
o
N
a
6
PHC. 1.27
nplfMep 1.7
HauTH KOOp.D.HHaTbI QeHTpa TSI)I(eCTH O.D.HOpO.D.HOH nnacTHHbI, H306pa)l(eHHOH
Ha pHC. 1.27, a. TOnll(HHa nnaCTHHKH nOCTOSlHHaSi.
PellleHHe.
I. nOCKonbKY O)J.HopO)J.HaSi nnaCTHHa HMeeT O)J.HHaKOBYIO TOnll(HHY, TO MO)l(HO
BOCnOflb30BaTbCSI <pOpMynaMlI )J.nSl onpeJJ.eneHHSI nOnO:>KeHHSI u,eHTpa TSDKeCTli
nnor.ua)J.lI.
2. Pa36HBaeM nnaCTIIHKY Ha TPH npOCTeHlllHe reOMeTpH1.JeCKHe <PHrYPbl
(PIiC. 1.27, 6), ¥OOp.D.HHaTbI QeHTpOB TSI:>KeCTU KOTOpblX H3BeCTHbi.
3. Bbl6npaeM CHCTeMY Koop)J.HHaT, KaK YKa3aHO Ha 1.JepTejf(e.
2 JI. 11. BepeHH3
33
t
4. 3aHocHM B Ta6n. 1.3 pe3ynbTaTbI BbI1.JHCneHHH; Ka)f()J.OMY npjlMoyronbHHKY
cooTBeTcTByeT O
Ha cTpoKa Ta6nHQbl.
5. CYMMHpyeM Si, S;' Xi, Si. Yi H 3annCbIBaeM pe3ynbTaTbI B HH)f(HeH CTpOKe.
6. Bbl1.JHCnSleM Koop)J.HHaTbI QeHTpa TSI)f(eCTH nnaCTHHKH:
LS; .X; 76 1 LS;. Yi 212 8
Xc = - -=2-(CM). Yc = =-=5-(CM)
S 36 9' S 36 9 .
7. no BbI1.JIICneHHbIM Koop)J.HHaTaM QeHTpa TjI)f(eCTH nnaCTIIHKH CTpOHM ee
QeHTp TSDKeCTI1 c.
Ta6nuua 1.3
HOMep 3JleMeHTa S. CM2 Xi, CM Y i, CM S.. X' CM3 S..y. CM3
I , I " I "
I 12 5 9 60 108
2 20 I 5 20 100
.., 4 -1 1 -4 4
-'
L 36 76 212
Cnoco6LI onpe):(eJIeHHH ....eHTpoB THiI\eCTH.
Cnoco6 pa36uelluJl lla tjJU2YPbl, nOnO:>KeHHe IJ;eHTpoB TSI:>KeCTI1 KOTO-
pbIX 113BeCTHO. llpHMeHSleTcSI B cnyqaSlx, Kor,na Teno MO:>KHO pa36HTb
Ha KOHe1.II'loe LJHCnO 3neMeHTOB.
Cnoco6 dOnOJlUeHUR SlBnSleTCSI LJaCTHbIM cnyqaeM cnoc06a pa36l1e-
HHSI Ha npocTeMIliHe clJHrYPbI. llpHMeHSleTcSI, Kor,na Teno pa36HBaeTcSI
Ha npocTeMIllHe cpHrYPbI, nOnO:>KeHI1S1 IJ;eHTpOB TSI:>KeCTH KOTOpbIX
H3BecTHbI, HO HeKoTopbIe H3 reOMeTpHqeCKHX cpl1ryp npe,ncTaBnSlIOT H3
ce6S1 nycTOTbI.
npltMep 1.8
HaHTH ueHTp TjI)I(eCTU nOnepelJHOrO CelJeHIUI (PHC. 1.28) Bana JI,lIaMe-rpoM 12 CM,
B KOTOpOM BblCBepneHO OTBepCTHe )J.HaMeTpoM 2 CM.
PerneHHe.
I. nOCKOJlbKY HY)f(HO HaHTH UeHTp TSI)I(eCTH nOnepe1.JHOrO CelJeHHSI, TO BOC-
nonb3yeMcSI <tJopMynaMH )J.nSl onpe)J.eneHHSI ueHTpa TSI)I(eCTH nnomallH.
2. ,l].onOJIHSleM nOnepe1.JHOe Ce1.JeHHe OTpHuaTeJlbHOH
nn 0 ll\aJI,blO
PHC. 1.28
34
S2 = -rcr 2 = -rc .}2 = -rc (CM 2 ).
3. Ha1.Jano cnCTeMbI Koop)J.HHaT paCnOnO)l(HM B ueHT-
x pe OKPY)f(HOCTH paJI,ltyca R, T.e. B T01.JKe Ct.
4. 3anOJlHjleM Ta6n. 1.4.
5. CYMMHpyeM S; II S;. Xi, nOCJle 1.Jero 3anlICblBaeM pe-
3YJlb TaTLI B HII)f(HCH CTpOKe.
6. BbI1.JIICnSlCM Koop,n,IIHaTbI ueHTpa TSI)I(eCTH none-
pelJHOrO Ce1.JeHIISI:
_ LS;.x; _ -3rc -_2- ( )
Xc - - - CM ,
S 35rc 35
a Yc = 0, TaK KaK OCb C t SlBJlSleTCjI OCblO CHMMeTpHH 3Toro CeqeHHSI.
7. no BbI1.JIICJleHHbIM KoopJJ.HHaTaM nOnepelJHOrO Ce1.JeHHSI CTpOHM ero QeH'Ip
TSI)f(eCTH C.
Ta6nuua 1.4
HOMep 3neMeHTa Si' CM2 Xi, CM Yi, CM S;. Xi, CM3 S,'y. CM3
I I'
1 36rc 0 0 0 0
2 -n 3 0 -3n 0
L 35n -3n 0
Cnoco6 U1-lme2pUp06a1-lUJl npHMeHSleTcSI B cnyqaSlx, Kor,na )InSl onpe-
,neJIeHMSI IJ;eHTpa TSI:>KeCTM He MorYT 6bITb npMMeHeHbI nepBbIe ,[(Ba
cnoco6a.
3KCnepUMe1-lmaJlb1-lblii cnoco6 oCYI..QeCTBJISleTCSI ):(BY1\1S1 MeTo):(aMM -
no,nBeIliMBaHHSI M B3BeIllHBaHMSI.
MeT O)J; n 0,[( B e III M B a H 11 SI 3aKJIIOQaeTCSI B TOM, '-ITO nJIOCKOe
TeJIO, KOTopoe Henb3S1 pa36HTb Ha npOCTeH:IllHe cpHrypbl C H3BeCTHbIM
nOJIO)KeHMeM IJ;eHTpa TSI)KeCTH, nO)J;BeIllHBaIOT Ha HMTM. llpOqepqH-
BalOT nHHMIO B)J;onb 3TOM HMTH Ha nJIOCKOCTH TeJIa. 3aTeM 3TY nJIO-
CKYIO cpMryPY OTKpenJISlIOT M nO,[(BeIllHBaIOT 3a ,[(pyrylO TOqKY, nOCJIe
qero BHOBb npOBo,nSlT BepTHKaJIbHYIO nHHMIO (B,nOJIb JIHHHM nO,[(Beca).
IlepeceqeHMe 3TMX JJ.BYX nHHMH: JJ.aeT TOqKY, B KOTOpOH Haxo,nMTCSI
IJ;eHTp TSI)KeCTM.
MeT 0)]. B 3 B e III H B a H M SI. 06bIQHO npHMeHSleTCSI JJ.JISI KpynHbIx
113,[(eJIMM: CaMOJIeTOB, BepTOJIeTOB M ,[(PyrMx MaIllMH. ECJIM H3BeCTHa
Macca, HanpMMep, CaMOJIeTa, TO CTaBSlT Ha BeCbI 3a,nHMe Koneca (PHC.
1.29) 11 no nOKa3aHHIO BeCOB onpe,nenSlIOT peaKQl110 N B. 3aTeM co-
CTaBnSlIOT O,[(HO H3 ypaBHeHHH: paBHOBe-
CHSI; y,[(06Hee COCTaBMTb CYMMY MOMeH-
TOB OTHOCHTenbHO TOQKH A:
3
L ffiOffiA ( F'; ) = 0; mga - N B 1=0.
;;::1
-
N B
OTCIO,na HaXOJISlT MCKOMYIO BenMqM-
HY a, T. e. nOnO)KeHMe QeHTpa TSI)KeCTM
NBI
caMoneTa: a =
mg
I
PUC. 1.29
35
---.-
.
1.7. KHHeMaTHKa TOIJKH
OCHOBHble nOHHTHH. KMHeMaTMKOM Ha3bIBaeTCH pa3JJ:en MexaHMKM,
B KOTOpOM H3yqaeTCH JJ:BM)I(eHHe MaTepHanbHbIX Ten B npOCTpaHCTBe c
reOMeTpMqeCKOH TOqKM 3peHMH, BHe CBH311 C CMnaMM, BbI3bIBaJOI..l.{I1MM
3TO ,lJ;BH)KeHl1e.
B TeOpeTMqeCKOH MexaHMKe H3yqaeTCSI npOCTeHrnaSl cpopMa JJ:BM-
)f(eHHH - MeXal-lU1leCKOe d6U:JICel-lUe. MeXaHMqeCKOe JJ:BM)I(eHMe Bcer,na
paCCMaTpHBaeTCSI OTHOCHTeJIhHO BbI6paHHOM CI1CTeMbI OTC1.J:eTa, KOTO-
paH MO)KeT 6bITb no,nBH)I(HOM I1JIM YCJIOBHO HenO,lJ;BH)KHOM. HanpMMep,
npM paCCMOTpeHMH MeXaHMqeCKOrO JJ:BH)I(eHMSI Ten, HaXOJJ:SlI..l.{HXCSI Ha
3eMne, 3a l-len006U:JICl-lYlO cucnrzeMY oceu KOOpOUl-lanrz BbI6MpaeM CMCTeMY
oceM, HeM3MeHHO CBH3aHHbIx C 3eMJIeM.
Cnoco6bl 3aAaHHH ABHiKeHHH MaTepHaJIbHOH T01JKH. )]:BM)KYll.{aSlCSI
TOqKa onHCbIBaeT B npOCTpaHCTBe HeKOTOpyJO JIHHMJO, MJIM mpaeKmo-
PUlO n101lKU.
)];BI1)1(eHl1e T01.J:KH 6y,neT 3a,naHO ecrecrBeHHblM cnoco60M (pHC. 1.30, a),
eCJIH 6y,nYT M3BeCTHbI: 1) TpaeKTopMH T01.J:KM; 2) 3aBHCHMOCTb M3MeHe-
HHH ,lJ;JIHHbI ,nyrl1 OT BpeMeHH: OM; = S = f(t) (3Ta 3aBHCMMOCTb Ha3bI-
BaeTCH ypa6l-lel-lUeM 06U:JICel-lUJl A1-amepUaJlbl-lOU m01lKu); 3) HaqaJIO JJ:BH-
)l(eHHSI; 4) HanpaBJIeHHe OTCqeTa.
nOJIO)l(eHl1e T01.J:KI1 B npocTpaHcTBe O)];H03HaqHO onpe,nenSleTCSI pa-
,lJ.MycoM-BeKTopoM r, npOBe,neHHbIM M3 HeKoToporo Heno,nBH)I(HOrO
L\eHTpa B ,AaHHYJO T01.J:KY M (PHC. 1.30, 6). TaKoM cnoco6 3a,naHMH
,lJ.BM)I(eHHSI Ha3hIBaeTCH BeKTopHbIM:
f = f(t).
nOnO)l(eHMe T01.J:KM B npocTpaHcTBe B 3TOM cnyqae 6y,neT onpeJJ:e-
JIHTbCSI reOMeTpMqeCKHM MeCTOM KOHL\OB BeKTopoB r, T. e. 2ooo2pa-
rjJOM ee pa,nMyca-BeKTopa.
y
x
a
6
8
PHC. 1.30
npH KoopAHHaTIiOM cnoco6e 3aJJ:aHMH JlBM)I(eHMSI (PHC. 1.30, 6) ,nOJI)I(-
HbI 6bITh H3BeCTHbI 3aBHCHMOCTH, no KOTOpbIM MO)l(HO onpe,neJIMTb,
30
l'
KaK co BpeMeHeM H3MeHHIOTCH KOOp-
)J.HHaTbI TOqKH B npOCTpaHCTBe:
y
x = 11 (t); Y = !2(t);
x
x =11 (t); Y = h(t); z = h(t).
3TH ypaBHeHI1H Ha3bIBaIOTCSI ypa6-
l-lel-lURMU 06U:JICellUR nrzOllKU 6 oeKapn10-
6blX KOOpOUl-lanlQX, C I1X nOMOIQblO J(JISI
Ka)l(,noro MOMeHTa BpeMeHH MO)l(HO
onpe,neJII1Tb nOJIO)l(eHl1e TOqKM B npo-
CTpaHCTBe. ECJII1 TOqKa 06U:JICen1CR l-la
11JlOCKOClnu, TO ee nOnO)l(eHl1e onpe,ne-
I1HTCSI ,lJ.BYMjI ypaBHeHMSlMM
I v
I
eCJIH TOqKa 06UJlCemCR no npRMOU, TO
ee ,lJ.BI1)1(eHMe onpe,neJIMTCSI TOJIbKO
O)J.HHM ypaBHeHl1eM x = I(t).
nplfMep 1.9
BH)f{eHHe TOIlKli B nnOCKOCTH 3a)J.aHO ypaBHeHHSlMH
x=2+4t;
y=--3+8t,
PUC. 1.31
I
r)J.e x H Y -. B CM, a t - B C. OnpeJJ.enHTb TpaeKTopHIO )J.BH)I(yIl{eHCSI T01.JKH.
PemeH He.
YpaBHeHlie TpaeKTopliH nonY1.JHM, liCKnlO1.JHB BpeMSI t H3 3a)J.aHHbIX ypaBHeHIIH
)J.BH)I(eHHSI. H3 nepBoro ypaBHeHHSI t = (x -- 2)/4, li3 BToporo t = (y + 3)/8. llpHpaB-
HSIB npaBbIe llaCTH 3TH X paBeHCTB, nonYIlUM
x-2 y+3
---
4 8
nnH 2x - y = 7.
TpaeKTopuSI JJ.BII)I(eHHSI - npSlMaSl JUIHHSI, nOCTpOIiM ee. llonaraSl x = 0, HaH)J.eM
T01.JKY nepeCe1.JeHHSI nlIHIUI TpaeKTopHH C OCblO Oy: Yl = -7.
lloJIaraSl Y = 0, HaHJJ.eM TOIlKY nepecelleHuSI TpaeKTopHII C OCblO Ox: X2 = 3.5.
npoBellSl 1.Jepe3 3TH T01.JKH npSlMYIO, nOJIY1.JHM JIHHIIIO TpaeKTopHH JJ.BH)I(eHIUI
MaTepHanbHOH TOIlKU (puc. 1.31). Ha 3TOH JIIIHHH He06xo)J.HMO HaHTH Ha1.JanO
.l1.BHlKeHIUI TOlJKH.
B MOMeHT Ha1.Jana IIBII)I(eHHSI, T. e. Kor)J.a t = 0, TOQKa HMena KoopJJ.HHaTY XA =
= 2 + 4.0 = 2 CM, a Koop)J.HHaT)' YA = - 3 + 8.0 = -3 CM. OCTaeTCSI onpe)J.eJlHTb, KaK OT
T01.JKH A )J.BII)I(eTCSI MaTeplIanbHaSl T01.JKa. C YBenH1.JeHHeM BpeMeHH KoopJJ.HHaTbI x H
y 6Y)J.YT B03pacTaTb. Cne)J.oBaTenbHo, MaTepHanbHaSl TOIlKa Ha1.JHeT lIBH)I(eHlIe H3
T01.JKII A H )J.anee 6YJI.eT )J.BuraTbCSI BBepx no c1penKe )J.O 6eCKOHe1.JHOcTH.
I1TaK, TpaeKTopuSI JJ.BH)I(eHUSI MaTepHanbHoH T01.JKII HaH)J.eHa; OHa nOKa3aHa eCTe-
CTBeHHbIM cnoc060M: ee Ha1.JanO -. B T01.JKe A, HanpaBneHHe )J.BH)I(eHHSI - no cTpenKe.
37
:
CKOpOCTb TO
KH. CKOpOCTb TOqKM XapaKTepM3yeT 6bICTpOTY M Ha-
npaBJIeHMe ,nBM)I(eHMSI TOqKM. llpM BeKTOpHOM cnoc06e 3a,naHMSI ,nBM-
)l(eHMSI nOJIO)l(eHMe TOqKM B Ka)l(,nbIM MOMeHT Bpe
1eHM onpe,neJISIeTCSI
pa,nMYCOM-BeKTOpOM if = r(t).
llYCTb B MOMeHT BpeMeHM t TOQKa 3aHMMaeT nOJIO)KeHHe M, onpe-
.n:enSleMOe pa.n:HYCOM-BeKTOpOM ,= ,(t) (PHC. 1.32, a). B MOMeHT Bpe-
MeHH t + /1t TOqKa 3aM
leT nOnO)KeHHe Mt, onpeL(enSieMOe pa,n;HycoM-
BeKTopOM 'i. 3TOT pa,n;Myc-BeKTop 6y,neT paBeH CYMMe: 'i = r + 1:1, .
OTHollIeHHe I:1r / I:1t SlBnSleTCSI BeKTopoM cpe,n;HeH CKOpOCTH, a BeKTop-
HaSi npOM3Bo,nHaSi 01' r no BpeMeHH t M 6y,n;eT BeKTopO
1 CKOpOCTM B
,lIaHHbu1 MOMeHT BpeMeHM:
v = df / dt .
,
!
!
1l0cKonbKY v eCTb npOH3Bo,n;HaSi 01' £}>YHKQHH r = r(t) , TO BeKTOp
CKOpOCTH v Bcer,n;a HanpaBneH no KacaTenbHOM K TpaeKTOp1111 )1BH-
)KeHMSI MaTepl1aJIbHOM TOqKH.
M
v
A
r
°1
a
6
V z
V y
y
x
8
PlICa 1.32
ECJIH )Ke ,nBH)KeHHe TOtIKM 3a,naHO eCTeCTBeHHbIM cnOC060M, TO 113-
BeCTHbI ee TpaeKTOpHSI AB, HaqanO )].BH)KeHHSI, HanpaBneHl1e H ypaB-
HeHMe ,n;BH)KeHHSI S = S(t). BOCnOJIb3yeMcR nonytIeHHOM 3aBHCHMO-
38
-
.
I
,
\
CTblO,WISI CKOpOCTH V = dr/dt. BBe,n;eM npOMe:>KYTOIIHYIO nepeMeHHYIO-
,nyrOBYIO Koop,n;MHaTY s:
df ds
v =--.
ds dl
fIoCKOJIbKY dS - BeJIHqHHa CKaJISIpHaSl, TO BeKTOp df / ds 6y,neT
MMeTb HanpaBneHHe KaCaTeJIbHOM K TpaeKTopHH B TOqKe M; 31'01'
BeKTOp 0603HaqaeTCSI 't (PHC. 1.32, 6) H SlBJISleTCSI OpTOM HanpaBJIe-
HHSI, MO,n;YJIb ero paBeH e,n;HHHQe. OpT
Bcer,n;a HanpaBJIeH B CTOPOHY
B03paCTaHHSI S.
TaKHM 06pa30M, npH eCTeCTBeHHOM cnoc06e 3a):(aHHSI TpaeKTopHM
BeKTOp CKOpOCTM
ds-
v = -'t.
dt
npOH3Bo,n;HaSi ds/dt npe,n;CTaBJISIeT C060M aJIre6paHqeCKOe 3HaIIe-
HHe CKOpOCTH. ECJIM ds/dt > 0, TO B 3TOT MOMeHT BpeMeHH TOqKa
,lJ:BH)I(eTCSI B CTOPOHY YBenHIIeHHSI ,n;yrH S H, CJIe,n;OBaTeJIbHO, HanpaB-
JIeHHe ee CKOpOCTI1 COBna,n;aeT C HanpaBJIeHl1eM opTa 't o ECJIM )l(e
dsjdt < 0, TO CPYHKQHSI S y6bIBaeT, 11, cne,n;OBaTenbHO, BeKTOp CKOpO-
CTI1 HanpaBJIeH B CTOPOHY, npOTHBOnOJIO)KHYIO BeKTOpy 'to
Onpe,nenHM CKOpOCTb TOqKH npH Koop,n;HHaTHOM cnoc06e 3a,n;aHHSI
,l(BM)KeHHSI. llYCTb 3a,n;aHbI ypaBHeHHSI ,n;BH)KeHHSI TOtIKM M (PHC. 1.32, 6):
x = /I(t); Y = h(t); z = h(t).
Ee nOJIO)KeHMe B npocTpaHcTBe onpe,neJISIeTCH pa,lI,HycoM-BeKTopoM
-
r = i X + j y + k z.
Ha OCHOBaHHM npe,n;bIAYI..QHX BbIBO,l(OB BeKTop CKOpOCTM MO)KHO
3anHcaTb cJIe,n;YIOI.QHM 06pa30M:
_ dr d -:- -: - -:- dx -: dy - dz
V =-=-(XI + Yl+zk)=Z-+ }-+k-.
dl dt dl dl dl
Cne,nOBaTeJIbHO,
- -
v = iv x + jv y +kv:_
1l0CTpOHM naparrJIeJIenHne,n; Ha npoeKQMSlx
\:, v y M v: (CM. pMC. 1.32, 6)
H onpeAeJIHM MO,n;YJIb BeKTopa CKOpOCTH:
2 2 2
V = V x + v y + v: .
39
Y CKOpeHUe TO"KU. BeKTOp YCKOpeHMSI T01:lKM a = d v / dt = d 2 v/ dt 2 .
EcnM M3BeCTHbI npoeKQMM ax, a y Ii a::; 3Toro BeKTopa Ha OCM KOOp-
)1I1HaT, TO MO)KHO onpe,[(enMTh Mo,[(ynb YCKopeHMH:
2 2 2
a = ax + a y + a::; .
IIpH eCTeCTBeHHOM cnoco6e 3a.n:aHMH TpaeKTopHH ,[(BH)KeHHH MaTe-
pHaJIhHOH TOqKH ee BeKTop YCKopeHHSI MO)l(HO pa3JIO)l(MTb no eCTeCT-
BeHHbIM OCHM Koop,[(MHaT 'r M n (PHC. 1.33):
;"
a = aT 'r + an n.
fipoeKQHR YCKopeHHR Ha OpT
Ha3bIBaeTCR KaCameJlbHblM YCKoIe-
J-lUeM, KOTOpOe M3MeHHeT MO.n;YJIb CKOpOCTH:
dv
aT = -.
dl
KacaTenbHoe YCKopeHMe cYI1..\eCTByeT TOJIbKO npM HepaBHoMepHoM
KpHBonMHeMHoM ,lJ.BM)KeHMM.
HopManbHoe YCKopeHMe an = v 2 /p M3MeHSleT HanpaBJIeHMe BeKTO-
pa CKOpOCTM v, n03TOMY MaTepManhHaH T01:lKa ,[(BM)KeTCH no KpMBO-
JIHHeHHOM TpaeKTopMM (p - pa,lJ.MYC KpMBM3HbI TpaeKTopMM).
qacTHLle cJly..au ,[(BHjKeHHH 1\1aTepUaJlLHOH TO"KH.
1. all = 0; ar; = O. Cne,[(oBaTenbHo, nonHoe YCKopeHMe a = O. TOqKa
J(BH)KeTC}J paBHOMepHO no npHMoH JIHHHH. 3aKOH ,ZJ;BH)KeHHH B 3TOM
cJIY1:Iae
S = So + Vol,
r,ne So - ,n.yroBaH Koop,nMHaTa B HaqaJIbHbIM MOMeHT BpeMeHM; Vo -
CKOpOCTb .I1.BM)I(eHMH TOqKI1 B HaqaJIbHbIH MOMeHT ,l(BM)KeHMH (CKO-
pOCTb He H3MeHMTCH M B nlO6oM ,l(pyroM MOMeHT BpeMeHM l, TaK KaK
,l(BM)I(eHMe He YCKopeHHoe).
2. all '* O
aT = 0 - paBHOMepHoe KpMBOJIH-
HeMHoe ,[(BM)KeHMe. BeKTOp CKOpOCTH MaTe-
pllaJIbHOH T01:lKH H3MeHSIeTCSI JIHllIb no Ha-
npaBJIeHMIO. 3aKOH ,[(BM)KeHMH no KPMBOJIM-
HeMHOM TpaeKTopMM 3anHllIeTCSI aHaJIOrHIIHO
nepBOMY cnyqalO:
:'
an
PlICa 1.33
40
5'=So+vol.
3. all = 0; ar; '* 0 - npHMOnMHeMHOe YCKO-
peHHOe ,l(BM)I(eHMe no 3aKOHY
I
I
at 2
S = So + vol + -.
2
Vo
4. all '* 0; ar; '* 0 - KpMBOJIMHeHHOe YCKO-
peHHoe ,[(BIi)KeHMe no 3aKOHY
(2
S = So + vot + llr; -- .
2
npllMep 1.10
noe3
)J.BIDKeTCSI paBH03aMenneHHo no 3aKpyrne- a'[
HIiIO palll1ycoM r = I KM. B Haqane Y1.JaCTKa noe3)J.
lIMeJI CKOpOCTb 36 KM/1.J II nOJIHOe YCKopeHl1e ao =
= 0,125 M/c2. Onpe,D.eJIHTb CKOpOCTb Ii YCKopeHHe
nOe3,D.a B KOHu,e KpHBonliHeHHoro Y1.JaCTKa, eCJII1
)J.nHHa Y1.JaCTKa 560 M.
PeuleH nee
I. EY)J.eM paCCMaTpHBaTb )J.BH)I(eHlIe O)J.HOH li3 TOqeK noe3)J.a, HanpHMep ero
u,eHTpa TSI)I(eCTH. COBMecTIiM Ha qaJIO OTC4eTa )J.yroBoH KOOp,D.HHaTbI 0 C Ha 4aJIbHbIM
nOJIO)l(eHHeM T01.JKII M 0, HanpaBJIeHl1e ,D.BI1)1(eHI1S1 npl1HIIMaeM 3a nOJIO)l(l1TeJIbHOe
(PIiC. 1.34). B 3TOM cnY1.Jae BenlI1.JI1Ha So 6Y,D.eT paBHa HynlO.
2. 3anl1WeM 3aKOH paBH03aMe)J.JIeHHOrO )J.BH)I(eHI1S1 MaTepHanbHoH T04KH
a'[t 2
S=vot--
2
PlICa 1.34
II <l>OPMYJIY ,D.JISI onpe,D.eneHI1S1 CKOpOCTI1 B 3TOM )J.BH)I(eHHH
v = v() - a'[t.
3. OnpeL(enliM HopManbHoe YCKopeHl1e T01.JKI1 B Ha1.Jane Y1.JaCTKa:
v
I 00 ( I 2 )
a () =-=-=01 M C
n R I 000 '
(vo = 36 KM/4 = 10 M/c; R = I KM = 1000 M).
4. 3HaSl MO,D.YJlb nonHoro YCKopeHI1S1 T01.JKII B Ha1.Jane nYTH, onpeL(enliM ero Ka-
caTenbHYIO COCTaBJISIIOIll.YIO:
2 2 + 2.
an = an(} a'[ ,
a'[ =
a
- a;,o =
0,1252 - 0,1 2 = 0,075 (M/c2).
5. nO)J.cTaBJISljI B 3aKOB ,D.BH)I(eHI1S1 KaCaTeJIbHYIO COCTaBJUIIOIll.YIO YCKopeHI1J1 a'[,
onpe)],eJIHM BpeMSI t, B Te4eHI1e KOToporo noe3)], nporneJI yqaCTOK ,D.JII1HOH 560 M:
560 = lOt _ 0,75t 2
2
O 10:!: .J I 00 -1120.0,075 IO:t 4 ( )
TCIO,D.a t = = C .
075
075
41
14 6
Cne.n.oBaTenbHo, I. = 00 (c); 1 2 = ° (C).
, 75 ,075
3Ha qeHHe t 1 oT6paCblBaeM KaK HepeaJIbHOe, TaK KaK 3TO BpeMjI npeBbIIllaeT BpeMjI
10
I. = 0,075 c, 1.Jepe3 KOTopoe nOe3.II. OCTaHOBliTCSI (npH Vk = 0). n03TOMY npHHHMaeM
BO BHHMaHl1e TonbKO BTOpOH KopeHb ypaBHeHHSI 1 2 = 6 = 80 (c).
0,075
6. Onpe)J.enHM CKOpOCTb B KOHL{e nYTH:
Vk = 10 - 0,075 Ik = 10 - 0,075.80 = 4 (M/c).
7. BblQHCnlIM HopManbHoe YCKopeHHe B KOHL{e nYTU:
vi 4 2
a,t!.. = - = - = 0,016 (M/c 2 ).
\ R 1000
8. Onpe)J.enHM nonHoe YCKopeHHe B KOHue nYTH:
ak = Ja
+a; = J O,016 2 +0,075 2 =O,0767(M/c2).
113 paC1.JeTOB BU)].HO, t.JTO nOJIHOe YCKopeHHe YMeHblllunOCb 3a C1.JeT YMeHbllle-
HHjI HopManbHoro YCKopeHIUI, B TO BpeMSI KaK KacaTenbHoe YCKopeHlIe OCTanOCb
HeH3MeHHbIM.
1.8. I1pocTeumHe ,nBHjKeHHH TBep,noro TeJIa
I1ocTynaTeJlbHoe ,[(BUiKeHue. II ocn'lynameJlbllblAt lla3bleael1'1Cfl lnaKoe
oeUJlCellue m6epi)020 l1'1eJla, npu KomopOM Jl106aJl npJlMaR, e3JllnaJl J-lQ
melle, eo epeMJl oeUJlCeJ-lUJl OCI1'1aenlCJl napaJUlellbJ-lOU CeOeAl,y J-la1.JaJlbJ-lOMY
nOllOJICeHUIO.
npH nocTynaTeJIbHOM ,[(BH)I(eHHH Bce T01.JKH onHCbIBaIOT O,[(I1HaKO-
Bble TpaeKTopHH H B Ka)l()J.bIH MOMeH1' BpeMeHH HMelOT reOMeTpH1.JeCKH
paBHbIe CKOpOCTI1 11 YCKopeHI1SI. 31'0 OCHOBHoe CBOHC1'BO nocTyna-
TeJIbHOrO ,[(BH)I(eHI1SI ,[(aeT B03MO)l(HOCTb H3Y1.JaTb ,[(BH)I(eHHe no O,[(HOH
113 ero T01.JeK. IIpl1MepOM nocTynaTeJIbHOrO ,lJ;BH)I(eHHSI SIBJISIeTCSI ,[(BI1-
>KeHHe nopIllHSI napOBOM MalliHHbI, n0113YHa C pe3QOM B nOnepeQHO-
CTpOraJIbHOM CTaHKe. B 3THX CJIY1.JaSIX TpaeKTopHH T01.JeK TeJIa npSIMO-
11MHeHHbIe. B cnapHHKe JU3YX KOJIeC (PHC. 1.35) TpaeKTopHH TOt.IeK npe,[(-
CTaBJISIIOT OKPY)l(HOCTb; caM cnapHMK AA 1 ABM)I(eTCSI nocTynaTeJIbHO,
a KOJIeCa BpalI..(aIOTCSI. CYlI..(eCTBYIOT elI..(e 60JIee CJIO)l(HbIe TpaeKTopHH
ABH)I(eHI1SI T01.JeK npH nocTynaTeJIbHOM ,[(BM)I(eHHH TeJIa. fIpH BbInYCKe
maCCH y HCTpe6MTeJISI MMf'-21 Koneca COBepmalOT nocTynaTeJIbHOe
)U3I1)1(eHl1e, npM1.JeM TpaeKTopHM TOlIeK KOJIeCa MMeIOT npocrpaHcTBeH-
HYIO KPMBYIO.
42
,.
W
:,j
,
A
PHC. 1.35
Bpall(aTeJlbHOe L1BUiKellHe OTHOCUTeJlbHO HenO,lJ.BHjI\II0H OCIf. Bpa-
U{amellbHblM lla3bleaemCJl maKoe i)eUJlCeflUe meepi)o20 mella, npu Komo-
pOM n101.JKU mella i)euJlCymCJl 6 nllOCKOCmJlX, nepnefldUKYllJlpflblX flenoO-
eUJlC1l0U npJl.iHOU, fla3bleaeA10U OCblO epaU{eflUJl mella, U onUCb16QIOm
OKP)JJlCflOCmU, lJeflmpbl K01110pblX JleJICa111 fla 31110U OCU. )111$1 OCYlI..(eCTB-
neHMSI 3Toro ,[(BH)I(eHMSI cne,[(yeT HenO,[(BM)I(HO 3aKpenMTb ,[(Be 1'Ot.IKI1
TBep,[(oro Tena A Ii B (PMC. 1.36). Tor,[(a npSIMaSI, npoxo,[(SIlI..(aSI 1.J:epe3
3TM TOt.IKM, SIBJISIeTCSI OCbIO Bpa
eHMSI.
IIpM BpalI..(eHMH Tena yron nOBopoTa Tena MeHSIeTCSI B 3aBMCMMOCTM
01' BpeMeHM:
3Ta 3aBHCI1MOCTb Ha3bIBaeTCSI ypaefleflueM epaU{amellbfl020 i)euJlCe-
flUR mella.
BeJIMlIHHa, xapaKTepM3YIOlI..(aSI 6bICTPOTY H3MeHeHMSI yrna nOBopo-
Ta <p C TeqeHHeM BpeMeHM, Ha3bIBaeTCSI Y2ll060U cKopocmblO nlella. Ee
3HalIeHMe onpe,[(eJIReTCR no <popMYJIe
d<p
F., -
UJ - dt .
<p = f(t).
'{' *. 'C
S
YlIMTbIBaSI, lITO S = r<p H, cne.n:OBaTeJIbHO, <p = -.,
r
nOJIY1.JI1M
_ dS _ V M
(0----.
rdt r
OTCIO,[(a HaH,[(eM llU1leU1lYIO CKOpOC111b 11101.JKU 6pa-
U{aIOUle20CJl mella
VM=mr.
BenMlIHHa, xapaKTepH3YIOlI..(aSI 6bICTPOTY 113-
MeHeHMSI yrnoBoH CKOpOCTH C Te1.JeHMeM BpeMe-
HH, Ha3bIBaeTCSI Y2ll06bVvl YCKopeHueM
_ dO) _ d 2 <p
E----
dt dt 2 ·
-'j ,
- .
.
E{Z
ro
PHC. 1.36
43
ECJIH dro/dt > 0 Ii dcp/dt> 0, TO
BH)J(eHl1e YCKOpeHHOe; eCJIH
dro/dt < 0, a dcp/dt> 0, TO
BI1)J(eHHe 3aMe
JIeHHOe.
qacTHble cJly
aH Bpall\aTeJlbHOrO ABHa\eHHH TeJla.
1. ro = const - paBHoMepHoe Bpall\aTeJIbHOe
BH)I(eHl1e no 3aKoHY
cp = <Po + rot.
2. E = const - paBHonepeMeHHoe Bpa
aTenhHoe
BH)J(eHHe (paBHo-
YCKopeHHoe HJIM paBH03aMe,lJ.JIeHHoe). Ero 3aKOH ,lJ.BI'DKeHM
:
Et 2
cp = CPo + root +2.
IIJlocKoe ABHa\eHHe TBepAoro TeJla. IIJloCKUM, UJlU nJlOCKO-napQJl-
JleJlbflbLM, ()BU:JICeflUeM m8epoo2o meJla fla3bZ8aemC51 maKoe 08U:JICeflUe,
npu KomopOM Ka:JICOa51 mO'-lKa meJla 08U:JICemC51 8 nJlOCKOCmu, napaJl-
JleJlbflOU fleKomopou nen008UJICflOU n.JlOCKocmu. IlpHMepaMH nJIOCKOrO
BH)KeHH
SlBJI
IOTCSI ,ABH)KeHHe rnaH6bI no JIb,AY, KOJIeCa noe3
a no
npSlMonHHeHHOMY yqaCTKY nYTH.
I1nocKoe ,lJ.BH)J(eHHe Tena MO)J(HO pa3JIO)l(HTh Ha nocTynaTenbHoe H
BpaIIJ.aTenbHoe OTHOCHTeJIbHO BbI6paHHoro l..{eHTpa. Ha pHC. 1.37 nOKa-
3aHO, 1.JTO TeJIO H3 nOJIO)l(eHI1
I MO)l(HO nepeMeCTI1Tb B nOJIO)l(eHl1e II,
HCnOJIb3YSI ,lJ.Ba Bapl1aHTa.
1. BapHaHT. IIepeMeIl.\aeM TeJIO nocTynaTeJIbHO TaK, qT06bI np
MaSl
AB, nepeMell\a
Cb napanJIeJIbHO caMOH ce6e, 3aH
JIa B npOCTpaHCTBe
nOJIO)KeHHe A2Bl. nOcne 3Toro nOBepHeM TeJIO BOKpyr T01.JKH Bl Ha
yrOJI cp].
2 BapHaHT. fIepeMecTHM Teno nocTynaTenbHO 113 nOJIO)J(eHH
I TaK,
qT06bI np
MaSl AB COBMeCTHJIaCh C np
MoH A ]B 2 , eM napaJIJIeJIhHoH.
llocne 3Toro 6Y,lJ.eM Bpa
aTb TeJIO BOKpyr TOqKH A I )];0 Tex nop, nOKa
TOQKa B 2 He nOna,lJ.eT B TOqKY B]. lloCKOJIbKY A]B 2 11 A 2 B}, TO yrJIbI
cp I = <P2. CJIe,lJ.OBaTeJIbHO, QT06bI 3aH
Tb nOJIO)l(eHl1e II, TeJIO MO)l(eT
B 2
I
II
PHC. 1.37
44
t
COBeprnHTb pa3JIHqHbIe nocTynaTeJIhHbIe ,ABH)I(e-
HH
(B 3aBI1CHMOCTH OT BbI6paHHoro nOJIlOca),
a BpaIIJ.eHl1e, KaK B nepBoM, TaK 11 BO BTOpOM
Bapl1aHTe, 6Y,lJ.eT O,lJ.I1HaKOBbIM.
Cne,lJ.OBaTenbHO, Jl1060e nJlOCKOe OBUJlCeflUe
MOJICflO pa3JlOJICUmb fla nocmynameJlbflOe 08UJlCe-
Hue meJla 8Mecme C 8bz6paHHbUvt nOJllOCOM U 8pa-
UjameJlbflOe omHOCUmeJlbflO nOl110ca. qa
e Bcero
3a TaKoH nonlOc BbI6MpalOT QeHTp Macc TeJIa. PHC. 1.38
MrHoBeHHblH QeHTp CKopOCTeH. Hel13MeHHO
CB
3aHHaSl C TeJIOM TOqKa, CKOpOCTb KOTOpOH paBHa HYJIIO, Ha3bIBaeT-
CSI M2H08eHHbLM l1eHn1poM cKopocmeu. MrHoBeHHbIH QeHTp CKopocTeH
(M:QC) JIe)l(HT Ha nepneH.nI1Kyn
pax K CKOpOCT
M TOQeK Tena, ony-
I.QeHHbIX H3 3THX TOlleK (PHC. 1.38). Pa3JIHQHbIe cnyqaH onpeJ1eneHH
MrHOBeHHoro QeHTpa CKopocTeH nOKa3aHbl Ha pHC. 1.39, a-B.
(M
C)
00
a
6
8
PlfC. 1.39
IIpeo6pa30BaHHe ABHa\eHHu. B MaWI1HaX OqeHb QaCTO npOI1CXOJ1HT
npe06pa30BaHI1e o
Horo ,lJ.BH)KeHH
B ,[(pyroe. HanpHMep, B KpHBO-
rnHnHo-rnaTYHHoM MexaHH3Me (PHC. 1.40) KpHBornHn OA cOBeprnaeT
BpaIl.\aTeJIbHOe ,[(BH)I(eHHe, KOTopoe npe06pa3yeTc
B nocTynaTeJIbHOe
nepeMeIl.\eHHe nOJI3YHa B. IIpH perneHMH npaKTH1.JeCKHX 3a,lJ.aQ 6bIBaeT
He06xo,lI-liMO HaHTM 3aKOHhI 3Toro ,lJ.BH)I(eHMSI MJIM CKOpOCTM. PaccMoT-
pHM npHMep.
VB
MLJC600
a
6
PHC. 1.40
45
DpltMep 1.11
B KpHBollilinHo-rnaTYHHoM MexaHH3Me (CM. pHC. 1.40) 3a O)J.liH 060POT KpHBO-
llIHna non3YH npOXO)J.HT nYTb, paBHbIH 400 MM. KaKOH nYTb npOH)J.eT 3a 3TO BpeMSI
T01JKa A? r)J.e 6y.n;eT HaXO)J;HTbC
Ml(C 3BeHa AB, Kor.n;a KpHBOllIHn OA 3aHMeT
BepTI1KanbHOe nOnO)KeHHe?
PellIeHHe.
]. PaCCMOTpIIM, KaKlie TpaeKTopHIf )J.BIDKeHII
HMelOT T01.JKII A, B If KaKlfe
.nBH)KeHII
OCYll(eCTBn
IOT TeJIa, K KOTOpbIM OHIi npIIHa)J.ne)KaT. T01JKa A C01JneHSI-
eT )J,Ba TeJIa, COBeplllalOll(Ue pa3JIII1JHbIe )J.BII)KeHIISI. C O)J.HOH CTOpOHbI, T01.JKa A
Y1.JaCTByeT BO BpaIl{aTenbHOM )J,BUlKeHIII1 KpliBOlllHna OA, a C )J,pyroH CTOpOHbI,
OHa npHHa)J.nelKHT Teny AR, KOTopoe COBepllIaeT nnOCKoe )J,BII)KeHHe. T01.JKa B
TaKlKe C01.JJIeHSIeT )J.Ba TeJIa: llIaTYH AB H nOJI3YH B. nOCKOJIbKY T01.JKa B npIIHaI(-
JIe)KHT non3YHY, COBepllIalOll(eMY nocTynaTenbHoe )J.BIDKeHHe C npSlMonlIHeHHOH
TpaeKTOpHeH Bcex ero T01JeK, TO ,lI,JUI Hee Bcer)J.a H3BeCTHa TpaeKTopliSI )J.BHlKeHH
-
3TO ropH30HTaJIbHaSi npSlMaSi. TaKIiM 06pa30M, 3HaSi HanpaBneHIISi CKopOCTeH
T01.JeK A H B, MOlKHO HaHTH nonOlKeHlIe MrHOBeHHoro u:eHTpa CKopocTeH )J.nSl
KpHBOllIHnHO-lliaTYHHoro MexaHH3Ma, Kor)J.a KpHBOIlJlIn OA 3aHHMaeT BepTHKanb-
Hoe nonOlKeHlIe. 113 pHC. 1.40, 6 BI1)J.HO, 1JTO MUC JIelKHT B 6eCKOHe1.JHOcTH. CJIe-
,lJ,OBaTenbHO, Bce T01.JKII 3BeHa A B I1MelOT O)),IIHaKOBbIe CKOpOCTIi.
2. 3a O)J.IIH 060POT KpliBOlllHna TOt.JKa A npoxo)),IIT nYTb S = 2nr. non3YH B 3a
O)J.MH 060POT npoH)J.eT nYTb, paBHblH 4r. CJIe)J,oBaTeJIbHO, MOlKHO HaHTH pa)J.HYc
KpuBolllHna, eCJIH H3BeCTeH npoH)J.eHHbIH nYTb T01.JKII B:
4r = 400 MM; r = 100 MM.
3. 3HaSl paJJ.HYC r KpHBOIlJHna, MO)KHO onpe)J.enHTb npoH)J.eHHbIll T01JKOH A nYTb
3a O)J.HH 060POT KpHBollIHna:
S = 2nr = 2n. 100 = 628 (MM).
1.9. 3aKOHbI AHHaMHKH H ypaBHeHHH ABH
eHHH TO"KH
HHaMHKO" Ha3bIBaeTCSI pa3,lJ,eJI MexaHHKH, B KOTOpOM M3yqaeTCSI
,nBH)I{eHHe MaTepMaJIbHbIX Ten no,lJ, ,lI,eMCTBMeM npHnO)l{eHHbIX K HHM CHJI.
B OCHOBe .n:MHaMMKH JIe)KaT 3aKOHbI, C<POPMYJIHpOBaHHbIe HbIOTOHOM.
IIepBblu 3aKOH - 3aKOH HHepQHH, YCTaHOBJIeHHbIH raJIMJIeeM, rJIaCMT:
Man1epUaJlbHaR n101lKa coxpaHRen1 cocnlORHue nOKOR UJlU pa6HoMepHo2o
npJlMOJlUHeUH02o 06U:JICeHUR, nOKa 6030eucm6ue OPY2UX nzeJl H.e U3MeHum
3nlO coem051l-lue.
BTOpoii 3aKOH - OCHOBHOM 3aKOH )].HHaMHKM - YCTaHaBnHBaeT CB$I3b
Me)l(,ny YCKopeHMeM, MaCCOH M CMJIOH: YCKopeHue MamepUaJlbHOU nl01lKU
nponoPlluoHa.nbHo npUJlO:JICeHHOU K Heu CUJle U UMeen1 oi)uHaKo60e C Heu
Hanpa6JleHue. 3anMllleM 3TOT 3aKOH B cpopMe, KOTOpylO npM,naJI 3TOMY
3aKOHY 3MJIep (PHC. 1.41):
n1 a = F.
46
J
I
II
1
,
B KJIaCCMqeCKOM MexaHMKe Mac-
ca n1 npHHSlTa 3a nocToSlHHYIO Be-
JIMqMHY. M acea S1BJISleTCSI MepoM
HHepTHocTH MaTepMaJIbHbIX TeJI B
HX nocTynaTeJIbHOM JJ.BH)I{eHHM.
3anHllIeM OCHOBHOM 3aKOH JJ.HHa-
MHKH B BH.l{e CKaJISlpHbIX paBeHcTB,
npoeKTHpySI BeKTopHoe paBeHcTBo
Ha OCM Koop,lJ,HHaT:
z
y
lna x = F'.y;;
x
PHC. 1.41
n1a y = Fy;
ma_ = F,".
.:. -
TpeTHu 3aKOH c}JopMynMpyeTcH cneJJ.YIOll\MM 06pa30M: 6CRKOMY oeu-
cm6UlO eOOn'16en1cn16yem pa6Hoe U npol11U60nOJlO:JICHO Hanpa6JleHHOe npo-
mU600euen16ue. 3TOT 3aKOH YCTaHaBJIMBaeT, qTO npH B3aMMO,lJ,eHCTBHM
,lJ,BYX TeJI, B KaKOM 6bI KHHeMaTHqeCKOM COCTOSlHHI1 OHI1 He HaXO,lJ,I1JII1Cb,
CMJIbI, npMJIO)KeHHbIe K Ka)KJJ.OMY M3 HMX, paBHbI no MO.nYJIIO 11 HanpaB-
neHbI no OAHOM np$IMOM B npoTHBOnOJIO)l{HbIe CTOpOHbI.
qeTBepTblH 3aKOH He 6bIJI CCPOPMYJIl1pOBaH HblOTOHOM KaK OT,lJ,eJIb-
HbIM 3aKOH MeXaHI1KI1, HO TaKOBbIM MO)KHO CqMTaTb c,nenaHHoe HM
0606I.I.1;eHl1e npaBMJIa napaJIneJIOrpaMMa CI1JI: fleeKOJlbKO OOH06peMeHHO
i)eucn16YlOUjUX CUll coo6UJa1Om lnOllKe maKoe YCKopeHue, KaKoe coo6UJQJla
6bl OOHa CUJla, pa8Hafl UX 2eOMen1pUlleCKOU CYMMe.
BeKTopHoe BbIpa)KeHMe OCHOBHoro 3aKOHa ,nI1HaMI1KH MO:>KHO cnpo-
eKTl1pOBaTb JII160 Ha ,neKapTOBbl, JII160 Ha eCTeCTBeHHbIe OCI1 KOOp,nM-
HaT. B nepBOM CJIyqae nonyql1M )Jpa6HeHU51 06U:JICeHUR Man'1epUQJlbHOU
mOtiKU 6 npRMOY20JlbHOU i)eKapn1060U cucmeMe KoopOUHam:
mx = F'.y;;
my = Fy;
n'zz = F=,
.. ..
r.n:e X' = ax; y = a y ; Z = a=.
Bo BTOpOM cnyqae nOJIyqMM ecmeCm6eHl-lble ypa6HeHUfl d6UJlCeHUfl:
mall = P',;
nla'[ = Fe;
mab = F b ,
rJJ.e an = v 2 /p; a'( = d 2 S/dt 2 .
47
I1poeKQHSI YCKOpeHHSI Ha 6HHOpMaJIb BCer,na paBHa HYJIIO ab = 0,
n03TOMY Fb = O.
nplfMep 1.12
YpaBHeHHe )).BJDKeHIISI MaTepHaJIbHOH TOqKH M C MaccoH m HMeeT BH)).:
x = rcoskt; y = rSInkt.
Onpe,aeJIIITb paBHo,neHcTBYIOIl{YIO npliJIO)KeHHbIX K T01.JKe CliJI Ii TpaeKTopli1O
):(BHJKeHIHI MaTepHaJIbHOH T01.JKH.
PerneHlie.
I. Onpe)).eJISleM npoeKUIiH YCKopeHHSI Ha OCIi Koop)).IIHaT. }1.nSl JTOrO CHa1.Jana
onpe)).enliM npoeKuHH CKOpOCTII Ha Te )f(e OCII:
V x = X = -krsinkt; v y = y = krcoskt.
C Y1.JeTOM JTOrO nonY1.JaeM
ax = vo\O = -k 2 rcoskt; a)' = v y = -k 2 rsinkt.
2. Onpe)).enSleM npoeKUHH paBHo)).eHcTBYlOllieH CHJIbI. nOCKOJIbKY fy = Inx;
F;, = my, TO F'.\o = -mk 2 rcoskt; F'..,. = -mk 2 rsinkt.
3. Onpe)).enSleM Mo ,nynb paB Ho,neHcT BYIOIl{eH:
F=
F}+F/ = mk 2 r .J cos 2 kt+sin 2 kt =mk 2 r.
4. Onpe)).enSleM HanpaBneHlIe paBHo)).eHcTBYlOll.{eH:
F\o x
cosa = --.:..- = -coskt = __a
F r'
F,. . Y
cosr3 = --=-- = -sin kt = --a
F r
o 1.JeB H)).H 0 , 1.JTO yron HaKJIOHa paBHo,neHCTBYIOIl{eH CHnbI no OTHOllleHlI1O K
OCSIM Koop)).IIHaT
leHJleTCSI.
5. Onpe)).enJleM TpaeKTopHIO ,[(BIIJKeHHSI MaTepHaJIbHOH T01.JKH. )];nSl IICKnlO1.Je-
HHSI BpeMeHH B03Be)).eM B KBa,npaT H CnO)KIIM ypaBHeHlul ,nBII)KeHIIJI. B pe3ynbTaTe
nonY1.JHM ypaBHeHl1e OKPYJKHOCTH C pa,alIycoM r: x 2 + y2 = r 2 .
ECJIH nOCTpOHTb npoeKUIUI paBHo.n.eHcTBYIOll{eH CHJIhI, npHJIOJKeHHOH K MaTe-
puanbHoH T01.JKe, TO nonY1.JHTCJI, 1.JTO Clina Bce BpeMSI MeHSleT HanpaBJIeHne, OCTa-
BaSlCb nOCTOSlHHO HanpaBJIeHHOH K ueHTpy OKPYJKHOCTH pa)).lIyca r.
1.10. CHJlbI, .aeHCTBYIOUlHe H3 TOIJKH MeX3HHIJeCKOH CHCTeMbI
MexaJ-lUl{,eCKOU cucmeMOU Ha3bIBalOT MblcneHHO BbI,neJIeHHYIO COBO-
KynHocTb MaTepHanbHbIX TOqeK, B3aHMo,neMcTBYIO
HX Me)l(,ny C060M.
MeXaHHqecKYIO CHCTeMY HHor,na Ha3bIBalOT MaTepHaJIbHOH CHCTeMOH
I1nH CUCn'leMOU MamepUaJlbJ-lblX mOlleK. Cy
ecTBYIOT CI1CTeMbI c606oo-
48
"
.
,
,
.
'.
II
.
.
.
i,
,
..
.
I
r
...
,
I
J-lblX TOqeK (HanpHMep, COnHeqHa» cHcTeMa) 11 J-lec606ooJ-lblX MaTepl1-
aJIbHbIX TOqeK (HX ,[(BH)KeHMSI OrpaHMqeHbI CBSl3SIMH). llpMMepoM CMC-
TeMbI HeCB06o,lJ:HbIX TOqeK MO)KeT C11Y)KHTb 111060M MexaHM3M M11M
MaIlIHHa.
Bce CMJIbI, J(eHcTBYIO
He Ha CMCTeMY HeCB060,ZJ;HbIX TOqeK, MO)KHO
pa3,nenMTb Ha 3aoa6aeMble CUJlbl M peaKl/UU C6R3eu.
110 npyrOMY npH3HaKY CM11bI, JJ,eMcTBYIO
Me Ha TOqKM 111060M Me-
XaHMqeCKOH CHCTeMbI, MO)KHO pa3,lJ:enMTb Ha 81leUlJ-lUe U 8J-lyn'lpellllUe.
-E -J
YC110BHMCSI 0603HaqaTb BHeIlIHMe CHJIbI F , a BHYTpeHHMe CHJIbI F .
BHeIlIHMMH Ha3bIBaIOT CMnbI, ,n;eHcTBYIO
He Ha TOqKM CMCTeMbI co
CTOpOHbI MaTepHa11bHbIX TOqeK, He BXO,ZJ;SI
MX B COCTaB ,n;aHHOH
CMCTeMbI.
BHYTpeHHHMH CHnaMH Ha3bIBalOTCSI CH11bI B3aHMOJJ,eMCTBHSI Me)K,ZJ;Y
MaTepHaJIbHbIMH TOqKaMH ,naHHOM MeXaHHqeCKOM CHCTeMbI. IIpHMepoM
BHYTpeHHI1X CHJI MorYT CJIY)I(MTb CHJIbI ynpyrocTH, ,neMcTBYIO
He Me)l(,ny
qaCTHQaMH ynpyroro Te11a, npHHSlToro 3a MeXaHMqecKYIO cMcTeMY.
O,nHa H Ta )Ke CHJIa MO)KeT 6bITb KaK BHelllHeM, TaK M BHYTpeHHeM B
3aBMCHMOCTH OT Toro, KaKaSl MeXaHHqeCKaSl CHCTeMa paccMaTpHBaeTcSI.
HanpHMep, peaKQHl1 no,nlllHnHHKOB BaJIa SlBJ1S1IOTC
BHelllHHMM CHJ1aMH
no OTHOlIleHHIO K BaJIY. 3TM )Ke peaKQHM MO)KHO OTHeCTH K BHYTpeHHHM
CMJ1aM, eC11l1 paccMaTpHBaTb BCIO YCTaHoBKY BMeCTe co CTaHHHOM.
TaKl1M 06pa30M, B 3aBHCHMOCTH OT TMna KJ1aCcMcpMKaQHH CHJI JIIO-
6aS! CI1JIa MO:>KeT 6bITb BHelllHeM I111H BHYTpeHHeM, B TO )Ke BpeMSI OHa
MO)KeT 6bITb 3aJ(aBaeMOM HJIH peaKQHeM CBSl3H. ,[(BH)I(eHHe TOqeK
CMCTeMbI 3aBHCI1T KaK OT BHelllHHX, TaK H OT BHYTpeHHMX CI1JI.
no 3aKOHY paBeHCTBa ,neMCTBMSI H npOTMBo,neMCTBMSI Ka)K,[(OM BHYT-
peHHeM CH11e COOTBeTcTByeT ,npyraSl BHYTpeHHSlS! CMna, paBHaSl eM no
MOJJ,YJ1IO 11 npoTHBOn0J10:>KHaSl no HanpaB11eHHIO.
Ha OCHOBaHHM 3Toro MO)KHO CJJ,eJ1aTb c11e,nYIO
Me BbIBO,[(bI:
1. rnaBHbIH BeKTop Bcex BHYTpeHHMx CHJ1 CHCTeMbI paBeH HynlO:
-J -J
R = L F i = O.
C11e,[(OBaTeJIbHO, H CYMMbI HX npOeKUI1M Ha Koop,[(MHaTHble OCM
TaK)I(e paBHbI HYJ1IO:
-)
LFix = 0;
-J
LFiY = 0;
-J
LFi: = O.
2. rnaBHbIM MOMeHT Bcex BHYTpeHHHx CHJI CMCTeMbI OTHOCMTeJIbHO
JII06oro QeHTpa H Koop,nHHaTHblx oceM paBeH HYJIIO:
'
I
-J k_}
Mo = LMiO =0 MJ1"
;=1
49
-J
Lmomx(Fi) = 0;
-J
Lmomy(Fi) = 0;
-J
Lmornz(Fi) = O.
XOTSI 3TH ypaBHeHHSJ HMelOT BH,n ypaBHeHHH paBHOBeCHSI CHn, npo-
H3BOJIbHO npMnO)l(eHHbIX B npOCTpaHCTBe, HO BHYTpeHHHe CMJIbI He
ypaBHoBeIlIHBaIOTCSI, TaK KaK OHM npMnO)f(eHbI K pa3HbIM TOIlKaM
CHCTeMbI H MorYT BbI3BaTb nepeMelQeHHe 3THX TOqeK OTHOCHTenbHO
,n;pyr ,Apyra.
1.11. l'eopeMa 0 JlBHjf\eHHIt l(eHTpa Macc
MeXaHHl.JeCKOH CHCTeMLI
I1pe,n;CTaBHM, IlTO MexaHHlleCKaSl CHCTeMa COCTOHT H3 k MaTepHanb-
HbIX TOlleK (PliC. 1.42).
z
m2
E
-J
F 2
ml
c
m , " "
-!
I
-E
F i 0
m
Zc
y
Yc
x
PHC. 1.42
H3BeCTHO (CM. no,npa3,[(. 1.6), IlTO MO)f(HO HaHTH QeHTp Macc TaKOM
CHCTeMbI, ecnH 3a,AaHbI MaCCbI m; H Koop,nHHaTbI QeHTpoB TSI)f(eCTH
TOlleK:
k
m"x.
L.J ' ,
X - ;=1
e-
m
k
Lm;y;
Ye = ;=1
k
L nl,i Z ;
Z i=1
e=
,
m
m
JillM, lITO TO )f(e caMoe,
50
T
w
,
!
t
.
..
I
II
,
,
,
k
nl, X c = L IniXi;
;=1
k
myc = L m;y;;
;=1
k
mzc = L In;z;.
;=1
)]:Ba:>KllbI npO.lJ.M<p<pepeHIJ.MpOBaB 3TH paBeHCTBa, nonyqHM
k
mxc = Lm;x;;
;=1
k
myc = Lm;y;;
;=1
k
mzc = L n1;z;.
;=1
npaBbIe llaCTH nonYlleHHbIX ypaBHeHHH B COOTBeTCTBHH C OCHOBHbIM
3aKOHOM ,n;HHaMHKH npe,n;CTaBnSlIOT C060H CYMMY BHeWHHX F; E H BHYT-
peHHHX F; J CMJI., ,n;ei1cTBYlOlU;I1X Ha 3TH MaTepHanhHble TOIlKH, B npo-
eKQMSlX Ha COOTBeTCTBYIOI.QHe OCM Koop,n;MHaT. Cne,nOBaTenbHO, no-
cne,nHHe ypaBHeHMSI MO)f(HO nepenHcaTb TaK:
k k
..
DE
DJ.
mxc = L-i r;x + L-i F;x,
;=1 ;=1
k k
..
DE
DJ.
lnyc = L-iF;y + L-i F;y,
;=1 ;=1
k k
mzc = LF;; + LF;
.
;=1 ;=1
YqHTbIBaSl, qTO rnaBHbIM BeKTOp BHYTpeHHMX CMn paBeH HYlllO
( R J =0), nonYIlMM
k
..
DE
mxc = L-iFix;
;=1
k
..
F E
myc = L-i ;y;
;=1
k
..
DE
mzc = L.J .1';= .
;=1
3TH ypaBHeHHSI BbIpa)f(alOT TeopeMY 0 ABHiKeHH" QeHTpa Macc CHCTe-
MbI, KOTopa
opMynHpyeTcSI cne,n;YIOIl{HM 06pa30M.
QeHTp Macc MeXaHIf'leCKOH CHCTeMbl ABHiKeTCH KaK MaTepHaJIbHaH
TO'lKa C MaCCO", paBHOH Macce CHCTeMbI, K KOTOpOH npHJlOiKeHbl Bce
BHemHHe CHJlbI, AeHCTBYlOll\He H3 3TY CHCTeMY.
OTCIO,n;a cne,n;yeT, qTO BHYTpeHHMe CMJIbI He OKa3bIBalOT BnMSlHHSI Ha
,n;BM:>KeHHe QeHTpa Macc MexaHHlleCKOH CHCTeMbI.
npltMep 1.13
Onpe)J.enHTb nepeMew.eHue nnaBY1.JerO KpaHa, nO)J.HIIMalOw.ero rpY3 MaCCOH
2000 Kr, npH nOBopOTe CTpenbI KpaHa )J.O BepTHKanbHoro nOnO:>KeHHSI (PHC. 1.43).
Macca KpaHa 20 T. ,L{nHHa CTpenbI AB paBHa 8 M. ConpoTHBneHHeM BO,Z:(bl npe-
He6pelJb.
51
y
x
x
a
6
PHC. 1.43
Pell1eHHe.
I. BbI6HpaeM CHCTeMY OTC1.JeTa (PHC. 1.43, a).
2. n pOCTaBn
eM Bce BHell1HlIe CHnbI, .neHCTBYIOll.{He Ha MaTepHanbHbIe Tena
)J.aHHOH MeXaHIP-IeCKOH CHCTeMbI. Ha nnaByqHH KpaH )J.eHCTBYIOT CHna T
)I(eCTn
mlg (3a)J.aHHa
CHna) H CHJIa N (peaKUHH, T. e. naCCHBHa
CHna); K rpY3Y npHJIO-
)l(eHa TonbKO O)J.Ha BHell1HSI
CHna - ero Bec In2 g.
3. 3anHweM ypaBHeHHSI JI.BH)I(eHHSI ueHTpa Macc MeXaHH1.JeCKOH CHCTeMbI:
2 2
n1Xc = Lfi;; Inyc = L.F;ff,
;=1 ;=1
HJIH
mxc =0; Inyc =-lnlg-n12g+N.
4. Ey.neM Hccne.nOBaTb nepBoe ypaBHeHHe, TaK KaK Hac IIHTepecyeT .nBH:>KeHHe
ueHTpa Macc no ropH30HTanH. nOCKOJIbKY 11IXc = 0, TO CKOpOCTb QeHTpa Macc
B.nonb OCH OX Vxc = const. 3TO 03Ha 1.JaeT, 1.JTO CKOpOCTb QeH'rpa Macc B 3TOM HanpaB-
JIeHHl1 B 1I1060H MOMeHT BpeMeHH HeH3MeHHa, T.e. CnpaBeJI.JIHBO paBeHcTBo VxC Hail =
= VXCJ<OH.
B Ha 1.JaJIbHbIH MOMeHT CHCTeMa HaXO)J.HJIaCb B nOKOe CJIe"OBaTeJIbHO V C -
,
J X Hail-
= VxC J<OH = O. A TaK KaK VxC = dxcl dt J TO Xc = const.
TaKHM 06pa30M, aHaJlH3 ypaBHeHHSI )J.BI1)1(eHH
ueHTpa Macc B)J.OJlb OCli Ox no-
Ka3an, qTO Ha 1.JanbHaSl H KOHet.JHaSl Koop)J.HHaTbI ueH1pa Macc COBna)J.aIOT: Xc Hail =
= XCJ<OH.
5. 3anHIlleM cl>opMyny )J.nSl onpeJI.eneHII
nOJIO)f(eHHSI QeHTpa Macc MeXaHH1.Je-
CKO" CHCTeMbI nplIMeHHTeJIbHO K ee Ha 1.JaJIbHoMY nOJIO:>KeHlilO
x InlXI Hail+ 1112 X 2 Half
C Hail =
ml + 1112
i
j"
52
,
,
,
.1
t
1
f
t
\
H KOHe1.IHOMY nOJIO)I(eHHIO
mIXIJ<oH + m2 x 2J<OH
XCJ<OH =
ml + m2
6. BbIpa3HM Ha1.JanbHbIe If KOHe1.JHbIe Koop)J.HHaTbI MaTepHanbHbIX TeJI CHCTeMbl
B COOTBeTCTBHH C BbI6paHHOH CHCTeMOH OTC1.JeTa (CM. pHC. 1.43):
XI H" = b; X2 H" = -ABsin 30 0 = - 8.
= -4 (M);
Xl )(OH = b -I; X2 J<OH = -I.
7. Onpe.neJISleM nepeMeIl{eHHe I nJIaByqerO KpaHa. fIpHpaBHHBaSl Xc Hail = Xc )(OH,
nonY1.JIIM
mixi Hail + m2 X 2 Hail = mixi J<OH + In2x2 J<OH
HJIIi
In,b+ m2(-4) = ml(b-/) + m2(-/);
n1lb- m2 .4 = mlb- nl)l- m2 / ;
- 2000 .4 = -200001- 2000 I.
OI11eem: I = 0,36 M.
1.12. Pa60Ta CHJIbI
BblqMCnMM pa60TY CMnbI, nOCTOSlHHOH no MOJJ;ynlO H HanpaBneHMIO
(pwc. 1.44). ITpe,nnonO)l(HM, qTO TOqKa M nepeMeID-aeTCSI B TOqKY MI.
BeKTop CHnbI F C BeKTopoM nepeMeI.QeHHSI COCTaBllSieT yroll a. B 3TOM
cnyqae pa60TY BbInonHSleT TonbKO Ta COCTaBllSlIOll.{aS1 CHllbI, KOTopaSl
COBna,naeT C HanpaBneHHeM BeKTopa nepeMemeHHSI U :
A
A = FU cosa = FU cos(F,U).
113 BeKTopHOH anre6pbI M3BeCTHO, 1.JTO CKanSipHoe np0l13Be,n;eHHe
A
,n;BYX BeKTopOB FU = FU cos( F , U ). Cne,nOBaTeJIbHO, pa60Ta nOCTOHH-
HOH no MO,nYJlIO H HanpaBJleHHIO CHJlbI Ha npHMO-
JlHHeHHOM nepeMel.l(eHHH onpe,neJlHeTCS1 CKaJ1Hp-
HblM npOH3BeJ(eHHeM BeKTopa CHJlbl Ha BeKTOp
nepeMel.l(eHHH ee T01.JKH npHJ10iKeHHH:
F
U
M.
A = FU .
PHC. 1.44
53
PaCCMOTpHM qaCTHbIe CnYlJaH onpe,n;eneHHSI pa60TbI nOCTOSIHHOH
CHllbI.
1. CHlla F ,[(eHcTByeT Ha Teno B HanpaBlleHMIi BeKTopa nepeMelQe-
HMSI U:
A = FU.
2. CMna F HanpaBlleHa nepneH)].HKYJISIpHO BeKTopy nepeMelQeHHSI U:
A = O.
3. CMlla F HanpaBlleHa B CTOPOHY, npoTHBonono)J(HYIO BeKTopy
nepeMelI..\eHHSI U:
A = -FU.
4. Pa60Ta CHnbI TSI)J(eCTH He 3aBHCHT 01' BH,n;a TpaeKTopHH, a onpe-
,[(ellSIeTC
TOllbKO paCCTOSIHHeM no BepTHKarrH Me)J(
Y HalJallbHOH Ii
KOHelJHOM TOlJKaMH nepeMelQeHliSI:
eCJIH TOlJKa nepeMelI..\aeTCSI cBepxy BHH3, TO pa60Ta CMJIbI T5I)I(eCTH
nonO)J(MTellbHa5l:
A = mgH,
r.L(e H - nepena
BbICOT;
eCllH TOlJKa nepeMelI..\aeTC
CHH3Y BBepx, TO pa60Ta CHnbI T5I)J(eCTH
OTpHuaTenbHaSI:
A = -lngH.
113 3Toro cne
yeT Ba)J(HbIH BbIBO,[(: pa60Ta CHJIbl TH
eCTH Ha 3aMK-
HYTOM nYTH paDHa HY JIIO.
npnMep 1.14
llpeHe6peraSl conpOTHBneHHeM B03.ayxa, onpe.aenHTb pa60TY ClinbI TSI)J(eCTH
npn nnaHHpOBaHIUi caMoneTa Maccoi1: 1200 Kr
A H3 T01.JKH A B T01.JKY B (PHC. 1.45).
PerneHHe.
IIa nJIaHep, KOTOpblH Mbl npHHHMaeM 3a
MaTepHanbHYIO TOt:IKY, )J.ei1:cTByeT TonbKO CHna
TSDKeCTH. Pa60Ta CHnbl TSDKeCTH npH nepeMe-
ll(eHHH ee T01.JKH nplInO)J(eHHSI cBepxy BHlI3
o npe.aenlITCSI TaK:
25KM
PUC. 1.45
A = /ngH = 1200.9,8.2800 = 32828000 H. M =
= 32,82 MH. M.
54
T
iii
i
I
,
t
.
I
1.13. MO
IIOCTb
O
Ha 11 Ta )l(e pa60Ta MO)J(eT 6bITb BbInOllHeHa 3a pa311MlJHbIe npo-
Me)KYTKH BpeMeHH. n03TOMY BBOl1SIT nOHSITHe MOmHOCTH N, KOTopaSI
onpe
eJISIeTCSI OTHOllleHHeM pa60TbI KO BpeMeHH.
ECJII1 B BbIpa)J(eHl1e MOlQHOCTH nO,[(CTaBI1Tb BMeCTO nepeMemeHHSI
V = vt, TO npH paBHOMepHOM npSIMOllHHeMHOM
BI1)KeHHH MOlQHOCTb
MO)J(HO onpe.L(eJISITb 1.Jepe3 CI1JIY 11 CKOpOCTb ,[(BH)I(eHHSI:
N = Fvcos cx.
IlpH pa60Te MalllHH lJaCTO 6bIBaeT He06xo.L(HMO BbIpa3MTb MOm-
HOCTb Qepe3 yrJIOBYIO CKOpOCTb BpalQeHHSI roo )J;JISI paBHOMepHoro Bpa-
l.I.{aTeJIbHOrO
BH)I(eHI1SI CnpaBe.L(JII1Ba CJIe.L(YlOlQaSI cpopMYJIa:
11
N = MxpU> = M Kp -,
30
r
e M Kp - KPYTSImHH MOMeHT OTHOCHTellbHO OCH BpalQeHHSI; n -
QaCTOTa BpameHHSI, 06/MHH.
1.14. K034>4>uQuell'I' nOJle3HOrO ,neucTBHH
qT06bI npOH3BeCTH nOlle3HYlO pa60TY, He06xo.L(HMO 3aTpaTHTb He-
CKonbKO 60JIbIlIYlO pa60TY, TaK KaK lJaCTb ee paCXO.lI,yeTcSI Ha npeo.lI,O-
neHHe CHn conpOTHBneHHSI (CHll TpeHHSI B 3y6lJaTbIX nepe,n;alJax H ono-
pax, conpOTHBneHHSI B03,n;yxa 11 ,n;pyroM cpe,n;bI, B KOTOpOM nepeMelQa-
eTCSI MaTepHanbHaSI TOQKa). 3cpcpeKTHBHoCTb pa60TbI KaKOH-nH60
YCTaHOBKH HJIH MaIllHHbI oueHHBaeTCSI K03<P<PHl(HeHTOM none3Horo
.L(eHCTBI1SI 11.
K03fjJif! u llueHn'10.kt nOlle3H020 {)eucmBUJl (Kn,lJ) MallIl1Hbl Ha3bIBalOT
OTHOIlIeHHe nOlle3HOH pa60TbI K nOJIHOH 3aTpaQeHHOH pa60Te:
A
11 = none3 < 1.
A nonH
KOHmpOJlbl'ble BOllpOCbl U 3a
a1lUH
1. qTO Ha3bIBaeTCSI a6conlOTHo TBep,n;bIM TenoM?
2. KaKHe CHCTeMbI CHJI Ha3bIBalOTCSI 3KBHBaneHTHbIMH?
3. B QeM COCTOHT npl1Hl{l1n oCBo6o)l(,n;aeMocTH TBep,n;oro Tena OT
CBSI311?
4. qeM OTJII1LJalOTCSI aKTHBHbIe CI111bI 01' naccHBHbIX?
5. qTO Ha3bIBaeTCSI nnOCKOH Ii npocTpaHcTBeHHoH CHCTeMOH cHn?
55
6. tICM OTJIM1.JaIOTCg CXO,n;gr.u:HCCg CHJIbI OT npOH3BOJIhHO paCIIOJIO-
)l(CHHbIX B npocTpaHcTBc?
7. KaK onpCJICngeTCg MOMeHT CMnbI OTHOCHTeJIbHO T01.JKH?
8. 3anHlIIHTc OCHOBHhle ypaBHeHHg paBHOBeCMSI npoM3BoJIhHOH
npocTpaHcTBeHHoH CHCTeMhI CHJI.
9. qTO TaKoe rJIaBHbIM BeKTop CMJI H 1.JeMY OH paBcH? 3aBMCHT JIM
rJIaBHhIH BeKTOp CMJI OT BbI60pa QeHTpa npHBe,n;eHMSI?
10. IIepeqHcJIHTe cnoco6bI onpe;:J;eJIeHHSI nOJIO)l(eHHSI QeHTpa TSI)I(e-
CTH TBep;:J;oro TeJIa.
11. HMeeT JIH MaTepHaJIbHaSI T01.JKa YCKopeHHe npH paBHoMepHoM
,l(BH)I(eHHH no KpHBOJIMHeMHOH TpaeKTopMH?
12. MorYT JIM T01.JKM Tena, ,n;BM)I(YllJ.erocSI nocTynaTeJIbHO, HMeTh
KpMBOJIHHeHHbIe TpaeKTopHH?
13. qTO TaKoe MrHOBeHHbIM QeHTp CKopocTeM nJIOCKOM cpHrypbI?
14. 3anHlllHTe OCHOBHOH 3aKOH ,[(HHaMHKH.
15. qeMY paBHa pa60Ta CHJIbI TSI)I(eCTH? 3aBHCMT JIM OHa OT BM)J;a
TpaeKTopMM T01.JKH npMnO)l(eHHg CMJIbI?
16. )];aMTe onpe,[(eJIeHHe K03cp<pHQHeHTa none3Horo J(eMcTBHSI. )];JISI
1.Jero BBe,n;eHO 3TO nOHSITHe?
17. KaK onpe,n;eJIHTh QeHTp Tg)l(eCTH rpY30BHKa?
I
t
L
1
I
Pa3,L(eJI 2
OCHOBbI COIIPOTHBJIEHHg MATEPMAJIOB
2.1. OCHoBHbIe nOHHTHH
B ,n;aHHOM pa3;:J;eJIe paCCMaTpHBalOT TeJ1a, KOTopbIe no,n; J(eMCTBH-
eM BHelIIHHX CHJI MeHSIIOT CBOIO CPOPMY H pa3MepbI, T. e. fJeipopMUPY-
lOmCR.
ecpopMaQHH MorYT 6bITb y'npY2UMU, eCJIH Teno nOCJIe YCTpaHe-
HMSI HarpY3KH, T. e. BHelIIHHX CMJI, BOCCTaHaBJ1MBaeT CBOI1 pa3MepbI M
CPOPMY. EClIH )l(e nOClIe CHSITHSI HarpY3KM TeJIO He BOCCTaHaBJIHBaeT
npe)l(HeH cpOpMbl, TO B03HHKalOr.u:He npM 3TOM ,n;ecpopMaQHM Ha3bI-
BalOTCSI OCmam01JHblMU. 3,n;eCb 6YJ(eM 113YQaTb TOJIbKO oiJ1l0poiJHble
U30mponHble TeJIa, Y KOTOpbIX no BceM HanpaBJIeHMgM CBOHCTBa O,[(M-
HaKOBbIe.
B conpOTMBJIeHHH MaTepHaJIOB TeJIa KJIaCCH<pHQHPYIOT CJIe,n;ylO-
IJJ;HM 06pa30M:
. nJIaCTMHa - Y Hee ,[(JIHHa M lIIHpHHa HaMHoro 60JIblIIe TOJIll.{HHbI;
. 060JI01.JKa - B OTJIH1.JHe OT nJIaCTHHbI OHa OrpaHH1.JeHa KPMBOJIH-
HeHHbIMM nOBepXHOCTSlMM;
. 6pyc - Y Hero J(JIHHa TeJIa 3Ha1JMTeJIbHO 60JIbllle ero BbICOTbI H
lIIHpHHbI. ECJIH JIHHHSI, coe,n;MHglOIJJ;aSl QeHTpbI TSI)I(eCTM OT,n;eJIbHbIX
nOnepeQHbIX Ce1JeHHH 6pyca, npSlMaSl, TO TaKOH 6pyc Ha3bIBalOT
npgMbIM;
. CTep)l(eHb - 6pyc, pa60TalOll.{HH Ha paCTSI)I(eHHe HJIll C)I(aTHe;
. 6anKa - 6pyc, K KOTOPOMY npHJIO)l(eHbI CMJ1bI nOJ( yrJIOM. B 3TOM
CJ1YQae 6pyc no,n; ,n;eHCTBHeM TaKHX CHJ1 6y,n;eT pa60TaTb He TOJIbKO Ha
C)I(aTHe (paCTSI)I(eHHe), HO H Ha H3rH6, T. e. 6y,n;eT H3rH6aTbCSI.
B 3aBHCHMOCTH OT Toro, KaKHe CHJIbl npHJ10)l(eHbI K 6pycy, OH 6y-
,n;eT no-pa3HOMY ,n;ecpopMHpOBaTbCSI. QT06bl onpe,n;eJIHTb HanpSl)l(eH-
Hoe COCTOSlHHe, npHMeHSlIOT MemoiJ Ce1JeHUU. MeToJ( CeQeHHH n03BO-
JISleT BbISlBHTb BHYTpeHHHe CHJ1bI H 3aKJIIOQaeTCSI B TOM, QTO TeJIO MbIC-
JIeHHO pacceKalOT nJIOCKOCTblO Ha ,n;Be nOJIOBHHbI (PHC. 2.1, a) M pac-
cMaTpHBalOT paBHoBecHe KaKOH-JIH60 OTCe1.JeHHOH qaCTH. CqHTaIOT,
57
N
a
6
PliC. 2.1
qTO BHYTpeHHHe ..£HnhI pacnpe,AeJIeHhI paBHOMepHO, HX paBHo,n;eMCT-
BYIOIl.(a
paBHa N (PHC. 2.1, 6). COCTaBHM ypaBHeHHe paBHOBeCH
CHJI, ,neHCTBYIOIl{HX Ha OTCeqeHHYIO qaCTb 6pyca:
-E
-J
LiP; + L.JF; = 0 HJIH F - N = O.
OTCIO,na
N=F.
BeJIH1.JHHa 0', xapaKTepH3YIOIl.(a
HHTeHCHBHOCTb pacnpe,n;eJIeHHH
BHYTpeHHHX CHn no nOnepe1JHoMY Ce1JeHHIO, H33hIBaeTCSlHanpRJlCenueM:
a=N/S,
r,n;e S - nnOIl.(a,n;h nOnepe1.JHOrO Ce1JeHH
. Hanp
)I(eHMe cornaCHO Me)l(-
,n;YHapo,n;HoM CHCTeMe e,n;MHMQ H3MepSleTcH B ITa (H/M2), a Ha npaKTHKe
qaIl.(e HCnOJIb3YIOT H/CM2, H/MM2.
B paccMoTpeHHOM npHMepe BHYTpeHHI1e CHJIbl HanpaBJIeHhI no
HOpMaJIH K nOnepeqHoMY CeqeHHIO, n03TOMY HanpH)I(eHHe Ha3bIBaeTCH
HOpMaJlbllbw.
y
z
Mx
PHC. 2.2
58
I
,
f
,
B 06Il.(eM cnY1.Jae HarpY)KeHHH Tena (PHC. 2.2) Bce BHYTpeHHHe CHJIhI
MO)KHO npHBeCTM K rJIaBHOMY BeKTOpy R M rJIaBHOMY MOMeHTY M .
BhI6MpaeM CMCTeMY KOOp,lJJIHaT TaK, 1JTo6bI OCh Z 6bIJIa HanpaBneHa
no HOpMaJIM K Ce1JeHMIO, a OCM x H y paCnOnO:>KHM B ero nnOCKOCTH.
CnpoeKTHpOBaB rJ1aBHbIH BeKTOp M rnaBHhIH MOMeHT Ha Koop,n;MHaT-
HhIe OCM, nOJ1YQHM llleCTb ypaBHeHHH )].JISI onpe,neneHMSI 6HympeHHux
CWl06blX paKmop06. COCTaBJ1HlOIl.(aSl BH)'TpeHHMX CMJ1 no HOpMaJIH K
CeqeHMIO N - HOpMaJIbHa
CMJIa; CMJIbI Qx H Qy SlBJISlIOTCSI COCTaBJ1S1lO-
Il.(HMH nOnepe1JHOH CMJIhI Q. MOMeHT OTHOCMTeJ1hHO OCM Z Ha3hIBalOT
KPYTSlI1.\MM MOMeHTOM (M Kp ), a MOMeHThI Mx H My - M3rM6alOI1.\MMM
MOMeHTaMM OTHOCMTeJIbHO oceM x H y. I1pM 3a.n:aHHbIX BHelllHMX CMJIaX
Bce llleCTb BHYTpeHHMx CHJIOBbIX <paKTopOB MorYT 6bITb onpen.eJ1eHbI M3
rneCTH ypaBHeHHH paBHoBecHSI, COCTaBJ1eHHbIX J(J1S1 OTCe1JeHHOM 1JaCTH
6pyca. ECJ1M B nOnepeqHOM CeqeHMM B03HMKaeT TOJ1bKO BHYTpeHHSISI
HOpMaJIhHaSl CMJ1a N , a np01.JMe BHYTpeHHMe CMnOBbIe <paKTopbI 06pa-
Il.(alOTCSI B HYJ1b, TO I1MeeT MeCTO paCTSI)KeHMe MJIM C)I(aTMe, B 3aBHCMMO-
CTM OT HanpaBneHMSI CMJIbI N. ECJIM B nOnepe1JHOM CeqeHI1M B03HMKaeT
TOJ1bKO MOMeHT M Kp , TO 6pyc B J(aHHOM CeqeHMI1 pa60TaeT TOJIbKO Ha
KpYQeHl1e. B CJIyqae, KorJ(a BHelllHMe CHJIb] npMJIO)l(eHbI K 6pycy TaKMM
06Pa30M, 1JTO B nOnepe1JHbIX Ce1JeHMSlX B03HMKaeT TOJIbKO H3rM6alOlI.J;MH
MOMeHT Mx (MJIM My), MMeeT MeCTO 1JHCTbIH M3rM6 B nJIOCKOCTM y=
(MJIM x=). ECJII1 B nOnepe1JHOM CeqeHHH HapHJ(Y C M3rH6alOIl.(I1M MOMeH-
TOM, Hanpl1Mep Mon B03HHKaeT H nOnepeqHaSl CMJIa Qy, TaKOM CJIyqaM
HarpY)I(eHMSI Ha3bIBaeTCSI nOnepeqHbIM H3rH6oM (B nJIOCKOCTH yz). B03-
MO:>KHbI H .n:PyrMe CJIyqaH, KorJ(a B nOnepeqHOM CeqeHHH ,neMCTBYIOT Pa3-
J1MqHble CMJIOBble cpaKTopbI; npM 3TOM 6pyc HcnbITbIBaeT CJIO:>KHOe Ha-
npSl)KeHHOe COCTOSlHMe. nOMHMO HOpMaJIbHOrO HanpSl)KeHMSI B CeqeHHH
6y,neT B03HMKaTb KaCaTeJ1bHOe HanpH)I(eHMe 't' B nJIOCKOCTH 3Toro CeqeHMSI
2.2. PaCTH)KeHUe u c
aTue
TIOJ( paCTSI)I(eHMeM nOHMMaeTCSI TaKOH BM,n HarpY)I(eHHSI, npM KO-
TOpOM B nOnepeqHbIX CeQeHHSlX 6pyca (CTep)l{HSI) B03HMKalOT TOJ1bKO
HOpMaJIbHbIe CHJ1bI, a Bce np01JMe BHYTpeHHMe CHJIOBbIe cpaKTopbI (no-
nepeQHbIe CMJIbI, KPYTSlIl.(MH M M3rM6alOlI.J;Me MOMeHTbI) paBHb
YJIIO.
C)I(aTHe OTJIMqaeTCSI OT paCTSI )I(e HMSI TOJIbKO 3HaKOM CMJIbI N: npH
paCTSDKeHHH HOpMaJIbHaSl CHna N HanpaBJIeHa OT CeqeHHSI (CM. pHC. 2.1),
a npl1 C)f(aTMH - K CeqeHHIO. n03TOMY npH aHaJIM3e BHYTpeHHMx CMJI
coxpaHSleTcSI e.lU1HCTBO no.n:xo.n:a K BonpocaM paCT.H)f(eHHSI H C)J(aTHSI.
HCKJIIOIIeHHe COCTaBSlT ,nJIMHHbIe TOHKMe CTep)l(HH, ,nJISI KOTOpbIX c)I(a-
THe COnpOBO)l(.n:aeTCSI H3rM60M (CM. no.n:pa3.n:. 2.7).
.59
__ I>i/;i
/
3aKOH rYKa. MHOrOqHCneHHbIe Ha6nIOJJ:eHHH 3a nOBe,n;eHHeM TBep-
,n:bIX Ten nOKa3bIBaIOT, qTO B no.naBnSllOlQeM 60JIbllIHHCTBe CJIyqaeB
nepeMem;eHHSI B onpe,n;eneHHbIX npe!(enax nponOPQMOHaJIbHbI J(eHCT-
BYIOm;MM CMnaM. BnepBbIe B 1676 r. rYKOM 6bIn ccpopMynMpoBaH
3aKOH 0 TOM, qTO «KaKOBa CMJIa, TaKOBa M ,n;ecpopMaQMSI».
B COBpeMeHHOM TpaKTOBKe 3aKOH rYKa onpe,n:enSleT JlUHeUHYIO 3Q-
6UCUMocmb Me:JICdy llanpR:JICeHUeM U oeljJopMa'4 u eu:
j:
(j = EE.
3)1;eCb K03<p<p M QMeHT nponOPQMOHanbHOCTM E eCTb MOOYllb ynpY20cmu
nepe020 poda, E - ,n;e<popMaQMSI, KOTOpyIO ,n;JISI O,[(Hopo,n:Horo CTep>KH.sI
MO)I(HO onpe)1;eJIMTb KaK
111
E=-.
I
BeJIMqMHY € MHor,n:a Ha3bIBaIOT omHocumellbHblM yOllUllellUeM CTep>KHH
,n;JIMHOM I, YJ(JIMHeHMe KOToporo no.n .l1eHCTBMeM npMJIO:>KeHHOM CMnbI
COCTaBHJIO !11.
MO,n;YJIb ynpyrocTM nepBoro po,n;a SlBJISleTCSI cpM3MqeCKOH KOHCTaH-
TOM MaTepHarra; OH onpe,n;eJIReTCH 3KCnepI1MeHTaJIbHO. ,ZJ:JISI HaH60JIee
1.JaCTO BCTpeqalOI.l.{MxcSI MaTepHaJIOB ero 3Ha1JeHHSI npHBe,neHbI B Ta6n. 2.1
(CM. no,n;pa3,n:. 2.3).
YMHueHue cTepa\HH. ECJIM B 3aKOH rYKa BMeCTO HanpSI:>KeHMR nO)1;-
CTaBI1Tb 0' = N IS, a BMeCTO !(e<}JopMaQI1I1 E = f),.lll, TO L(JISI CTep)J(HSI, Y
KOToporo Ha ,lJ;JII1He I BHYTpeHHSISI HopManbHaSI CMJIa nOCTOHHHaSl Ii
nOnepe1JHOe CeQeHI1e He 113MeHSIeTCSI, nOJIyqMM BbIpa)J(eHI1e ,D;JISI onpe-
,n;eJIeHMSI y,n;JIMHeHMSI CTep:>KHSI:
!11= NI .
ES
llpH pellIeHMH MHorMX npaKTM1JeCKMX 3a,n;aq B03HHKaeT Heo6xo-
,lJ;I1MOCTb HapSI,n:y C y,n;JIHHeHHeM, o6ycnOBJIeHHbIM HanpSI)I(eHHeM 0',
Y1JMTbIBaTb TaK)I{e y,n;JIHHeHI1S1, CBSl3aHHbIe C TeMnepaTypHbIM B03-
,lJ;eMcTBHeM.
B 3TOM cJIY1.Jae .ne<popMaQHIO paccMaTpHBalOT KaK CYMMY CHJIOBOl1
11 1JHCTO TeMnepaTypHoH ,n:ecpopMaQHH:
E = alE +at,
r.n:e a - K03<P<P H L{HeHT TeMnepaTypHoro paclliHpeHHSI MaTepHaJIa. L(JISI
O,n:Hopo,n;Horo cTep)I(HSI, HarpY)KeHHOrO no KOHQaM 11 paBHoMepHo
HarpeToro, HMeeM
60
...,'
'!:
,
NI
l = -+alt.
ES
ITocTpoeHHe 3nlOp. rpaqH1K 113MeHeHHSI HOpMaJIbHOH CMJIbI, HanpSl-
:>KeHHH H nepeMem;eHHH CTep:>KHSI B,n;OJIb ero OCH Ha3bIBaeTC}) 3n1Opou
COOTBeTCTBeHHO HOpMaJIbHbIX CMJI, Hanp}J)I(eHHH H nepeMem;eHHH.
3nlOpbI ,[(alOT HarJISI,[(Hoe npe,[(CTaBJIeHHe 0 3aKOHax H3MeHeHHSI pa3-
JIHlIHbIX HCCJIelI.yeMbIx BeJIHlIHH. llOCTpoeHHe 3nlOp paCCMOTpHM Ha
KOHKpeTHOM npHMepe.
nplfMep 2.1
,l(nR 6pyca, H306paJKeHHOrO Ha pHC. 2.3, G, nOCTpOHTb 3nlOpbI BHYTpeHHHX cnn,
HanpSl)KeHHH H nepeMell\eHHH no ,llJ1HHe 6pyca.
No
@
@
@
N 2
N l F
F1=F
z
e
St=S
6
z
a
PHC. 2.3
PerneHHe.
I. BbI6upaeM Ha1.JanO OTC1.JeTa B HenOLIBIDKHOM CeqeHUli (T01.IKa 0); nOnO)l(H-
TenbHoe HanpaBneHHe ocn Z HanpaBHM no OCH 6pyca T.e. BHH3.
2. Onpe)J.enHM peaKl{HIO, COCTaBHB O,lJ.HO ypaBHeHHe paBHoBeclf
:
Lfi: =0;
i
No -3F +F =0.
OTCIO)J.a No = 2F .
61
3. nOCTpOHM 3nlOpy BHYTpeHHHX CHn N. ,lI;nSl 3Toro Ha paCCTOSlHHIi Zt paCCeqeM
6pyc H paccMol]JIIM paBHoBecHe HH)f(HeH 1.JaCTH (PIiC. 2.3,6):
Hnii
F F
U 2 =U t +-(z -I); npli Z = 2/ U 2 = --I.
2
2
{
...
L F;; = 0 ;
- N. + F = 0 .
t(nSl 2/
ZI
31
OTCIO)).a N. = F , qTO CnpaBe)J.JIHBO ;J:nSl I
Z.
3/. B 3TlIX npe)).enax B 6pyce B03HH-
KaeT paCTSI)f(eHlIe, TaK KaK Nt HanpaBneHa OT Ce1.JeHIISI.
Ten:pb BbI6epeM BTOpOH yqaCTOK 6pyca 0::; Z2 ::; 1 Ii paccMoTpHM paBHOBeCHe
BepxHeH 1.JaCTH (PIiC. 2.3, e):
L,Fi: = 0;
No-N 2 = 0;
2F - N 2 = o.
F F
U 3 =U 2 +-(z.-2l); npli z.=31 U 3 =-I.
ES 2ES
OTKna.nbIBaeM BbI1.JI1CneHHbIe nepeMell{eHHSI Ha 3nlOpe @(PHC. 2.3, e).
t(HarpaMMa pacTHiKeHHH. HaH60nee HarnSl,n;HO oc06eHHocTH ,n;Ha-
rpaMMbI paCTSI)KeHHSI MO)KHO nOKa3aTb Ha npMMepe HcnbITaHMSI
06pa3u a H3 Manoyrnepo,n;HCTOM CTanH (PMC. 2.4).
HarpaMMa BbI-
tIeptIeHa B Koop,n;HHaTax F, 6./. Ha KpHBOM MO)KHO BbI.nenHTb tIeTbIpe
30 HbI.
30Ha OA HOCHT Ha3BaHHe 301lbl ynpY20cmu. 3,l(eCb MaTepHan no,n;-
FI
QMHSleTCSI 3aKOHY fYKa H 6./ = -. Ha pHC. 2.4 31'01' ytIaCTOK ,n;nSl
ES
66nbIlleM HarnSl,n;HOCTI1 nOKa3aH C OTcTynneHMeM 01' MaCllITa6a. Y,n;-
nMHeHHSI Ha YllaCTKe OA OlleHb ManbI, M npSlMaSi OA, 6y,n;YllH BbIqep-
qeHHOM B MaClllTa6e, COBna,n;ana 6bI B npe,n;enax IllMpMHbI nMHMH C
OCblO 0P.lJ.HHaT. 3HaqeHHe CHnbI, ,n;nSl KOTOpOM cnpaBe,[(nHB 3aKOH
fYKa, 3aBMCMT 01' pa3MepOB 06pa3Qa H cpM3HtIeCKMX CBOMCTB MaTe-
pHana, n03TOMY npM .lJ.anbHei1llleM paCCMOTpeHMI1 J.(HarpaMMbI paCTSI-
)KeHMSI ee nepeCTpaHBalOT B Koop,n;MHaTax cr H E.
30Ha AB Ha3bIBaeTCSI 301l0U o6UJeu n1eKYlleCmU, a ytIaCTOK AB -
12.JlOUJadKOU n1eKYlleCn1U. 3,n;eCb npOHcxo,n;HT cy
ecTBeHHoe H3MeHeHHe
J.(JIHHbI 06pa3Qa 6e3 3aMeTHoro YBeJIM1.J:eHI1S1 HarpY3KM. He Bce MeTan-
JIbI MMelOT nno
aJ-(KY TeKYllecTH. HanpMMep, y anIOMI1HHSI, OTO)l()I(eH-
HOM Me,n;M, JIerHpOBaHHbIx cTanei1 nnOlI.\aJ.(Ka TeKytIeCTI1 He 06Hapy-
)KI1BaeTCSI .
30Ha BC Ha3bIBaeTCSI 301l0U ynpOIl1-le1-lUJl. 3,n;eCb y,n;nMHeHMe 06pa3u. a
COnpOBO)l(.lJ.aeTCSI B03paCTaHHeM HarpY3KH. B CTa,n;MM ynpOqHeHMSI Ha
06pa3Qe HaMeqaeTCSI MeCTO 6Y.lJ.y
ero pa3pbIBa 11 HatIMHaeT 06pa30BbI-
BaTbCSI TaK Ha3bIBaeMaSl UleUKa - MeCT-
Hoe CY)l(eHHe 06pa3Qa. TIpH ,naJIbHei1-
UleM paCTSI)I(eHHH 06pa3Qa UleHKa 6bICT- F C
po nporpeccMpyeT. HatIHHaSl C TOllKH C
y,nnHHeHHe 06pa3Qa npOHcxo,n;HT C
YMeHbllIeHHeM CHnbI, HO cpe.lJ.Hee HanpSl-
:>KeHHe B nOnepe1.J:HOM CeqeHHH lIIeHKH
B03paCTaeT. Y,n;JIHHeHHe 06pa3Qa HOCHT
B 3TOM cnyqae MeCTHbIM xapaKTep, no-
3TOMY yqaCTOK CD Ha3bIBaeTCSI 301-l0U 0 f:,.l
MeCn11l0U 11'1eKYlleCn1u. TOtIKa D COOTBeT-
cTByeT pa3pyrneHHlO 06pa3Qa. Plic. 2.4
: I
OTCIO)).a N 2 = 2F. nOCKonbKY N 2 HanpaBneHa K CeqeHHIO, TO 6pyc no)). )).eHCT-
BlieM Clin No II N 2 C)f(IIMaeTCSI.
nOcne Toro KaK onpe)).enl1nl1 Bce BHYTpeHHl1e HopManbHbIe ClinbI, nepeXO)).HM
J( nOCTpOeHl11O 3nlOpbI HopManbHbIX clin (PHC. 2.3, 2). BnpaBO 6y)).eM oTKna)).bI-
BaTb nOnO)f(HTenbHbIe 3Ha1.JeHIISI, a BneBO - OTpuuaTeRbHbIe 3Ha1.JeHIUI HopMaRb-
HbIX CHn.
AHanH3lIpySl nOCTpoeHHYIO 3nlOpy @, 3aMeTI1M, lITO BHYTpeHHHe ClInbl He 3a-
BHCSlT OT pa3MepOB nonepet.J:Horo CeqeHHSI, a 3aBlICSlT TonbKO OT nplInO)f(eHHbIX
BHeIllHHX CIiR. n03TOMY )).RHHY 6pyca pa36lIBalOT Ha TaKOe QHCnO Y1.JaCTKOB
CKOnbKO CHn Ha ero )).nHHe npHnO)f(eHO. B )).aHHOM cnY1.Jae 6bIno )).Ba Y1.JaCTKa. '
n pH npOBepKe npaBHRbHOCTH nOCTpoeHIISI 3nlOpbl @ cne)).yeT 06paTHTb
BHHMaHlie Ha TO, 1.JTO Ha 3nlOpe BHYTpeHHHX CHn B Tex Ce1.JeHHSlX, r)).e 6bInH
npHnO)l(
HbI BHeIllHHe CHnbI, 1l0n)l(HbI 6bITb CKaqKH, paBHbIe npHnO)f(eHHOH
BHelllHeH CHne.
4. nOCTpOHM 3nlOpy HanpSl)f(eHIIH @. Epyc cne)).yeT pa36lITb Ha Y1.JaCTKII. no-
cKonbKY 0' = N / S, TO yqaCTKOB Ha 3nlOpe 6y)).eT CTonbKO, CKonbKO pa3 MeHSleTCSI
nOne
e1.JHOe Ce1.JeHHe; npli 3TOM cne)).yeT 06pall\aTb BHHMaHHe, 1.JT06bI npH nOCTO-
SlHHOH nnOIl{a)).1I nOnepe1.JHOrO Ce1.JeHHSI HopManbHaSl Clina Ha 3nlOpe N OCTaBa-
naCb HeH3MeHHOH. C yqeTOM 3Toro Ha 3nlOpe@ 6Y)).YT TPIi pa3nlI1.JHbIX 3Ha1.JeHHSI
0' (PHC. 2.3, 0): 0'. = NI/S. = FjS; 0'2 = N./S 2 = F/2S: 0'3 = N 2 /S 2 = - 2F/2S =
=-F/S.
5. CTpOHM 3nlOpy nepeMeIl{eHHH @. Ha1.JIIHaTb cne)).yeT OT HenO)).BH)f(HOrO ce-
1.JeHHSI, T. e. OT Ce1.JeHIISI O. BbIpa3HM nepeMeIl{eHHe Ce1.JeHHSI, HaXO)).51Il{erOCSI OT
HenO,[{BH)f(HOrO Ha paCCTOSlHHH Z2:
cr
V =-Z2'
E
EcnH 0 ::; Z2 ::; I, TO )).nSl Z2 = I nepeMell{eHlIe
-F
VI =-1
ES .
JHI I ::; z ::; 21
a
V 2 =V . +-z
E'
62
63
PlICa 2.5
OTHOCUTeJIbHaB nOnepeqHaH ,[(e4>op-
MaI.(HH. llpH paCTSI)KeHHH (C)KaTHH)
np
MOrO 6pyca KpOMe npO
OnbHOM
e<pOpMau.HH E npOHCXO,l(I1T H3MeHeHHe
nOnepeqHbIX pa3MepOB 6pyca (PHC.
2.5). I11HpHHa 6pyca npH paCTSI)KeHHH
YMeHbllIaeTC
Ha I1b. EcnH I1b OTHeCTH
K nepBOHaqanbHOM IllHpHHe, TO nony-
Onpe,l(eneHI1S1 OTHOCHTenbHOM nOnepeqHOM
e-
F.-o --- --
--- --I F
<]
. I .
1+l11 )
ql1M Bblpa)KeHl1e ,l(JISI
cpOpMaUHH EI:
EI = I1b/b.
OTHOIlleHHe OTHOCHTenbHOM nOnepeQHOM ,l(ecpOpMaQHH K OTHOCH-
TenbHOM npO,l(OnbHOM ,l(e<pOpMaQHH Ha3bIBalOT K03fjJfjJul1ueHmOM JIyac-
COlla 11 0603HaqaIOT J.l:
J.l = EI/E.
K03<P<P H QHeHT llyaccoHa, TaK )Ke KaK 11 MO,[(YJIb ynpyrocTH E, xa-
paKTepH3yeT <p11311qeCKHe CBoMcTBa MaTepHana; ero 3HaqeHl1e Kone6-
neTCSI ,l(JISI MeTannOB B npe
eJIax OT 0,25 J].O 0,35. HeKoTopbIe 3Haqe-
HHSI K03<P<PI1Ql1eHTa Jl npHBe
eHbI B Ta6n. 2.1.
2.3. OCHoBHbIe MeXaHHqeCKHe xapaKTepHcTHKH MaTepHaJIOB
MeXaHI1QeCKl1e CBOHCTBa MaTepl1anOB YCTaHaBnHBalOT onbITHbIM
nYTeM, I1CnbITbIBaSl 06pa3IJ.bI Ha paCTSI)J(eHl1e. 3aTeM .aHarpaMMY paCTSI-
)KeHI1S1 nepeCTpal1BaIOT B KOOp,l(I1HaTaX 0" H E. KaK BI1,nHO 113 pl1c. 2.6,
OHa HMeeT TaKOH )Ke BH,[(, KaK H B Koop.aI1HaTaX F, 11/ (CM. pHC. 2.4),
HO :Ta Kpl1Ba51 6y,[(eT xapaKTepH30BaTb y)Ke He CBOMCTBa 06pa3Qa, a
CBOI1CTBa MaTepHaJIa. OTMeTI1M Ha 3TOH ,[(HarpaMMe xapaKTepHbIe
TOQKH.
HaH60Jlbmee 3HaQeHUe HanpHiKeHuH, ,[(0 KOToporo MaTepHaJI CJIeAY-
eT 3aKoHY rYKa, Ha3bIBaeTCH npeAeJlOM npOIlOpIJ.UOHaJlbHOCTU O"n.
YnpyrHe CBoMcTBa l\1aTepl1ana coxpaHSlIOTc
,[(0 3HaqeHl1M HanpSl-
)f(eHI1S1, Ha3bIBaeMoro npe,[(enoM ynpyroCTI1. IIOA npeAeJlOM ynpyrocTu
O"y nOHUMaeTCH TaKoe Hau60Jlbmee 3HaqeHHe HanpHiKeHHH, AO KOToporo
MaTepUaJI He nOJIyqaeT OCTaTOqHbIX .ne4JopMaIJ.HH.
Ha npaKTI1Ke npe
en nponopUHOHaJIbHOCTM II npe,[(en ynpyroCTI1
TIJY,l(HO nO,l(,naIOTCSI 3aMepy, n03TOMY 3HaQeHHSI O"n M (jy B CnpaBOqHbIe
J{aHHble no CBOHCTBaM MaTepManOB 06bIqHO He BKnIOt.laIOTCSI.
Eonee onpe,[(eJIeHHOH xapaKTepHcTHKOH HBnHeTCSI npe,[(en TeKyqe-
CTI1. IIOA npe,[(eJlOM TeKyqeCTH nOHUMaeTCH TaKoe 3HaqeHHe H3npHiKe-
64
'"
.
C1
E
PliCa 2.6
t
HUH, npu KOTOpOM pOCT Ae
OpMau.HU npOUCXOAHT 6e3 3aMeTHoro YBe-
JlHqeHHH HarpY3KU. B Tex cnyqaSlX, Kor,[(a Ha ,[(l1arpaMMe OTCYTCTByeT
SlBHO BbIpa)l(eHHa51 nno
a,nKa TeKYQeCTH, 3a npe,nen TeKyqeCTI1 ycnoB-
HO npl1HI1MaIOT TaKoe 3HaqeHIIe HanpSl)KeHI1S1, npH KOTOpOM OCTaTOq-
HaSl ,ne<popMaQI1S1 COCTaBJISleT 0,20/0. B 3TOM cnyqae YCl106HblU npedell
n'1eK) J1 ieCn1U 6YAeT 0603HaqaTbCSI qepe3 0"0.2. ECJII1 Heo6xo,[(HMO OTnH-
ql1Tb npe,[(en TeKYQeCTI1 npM pacTSI)J(eHHH OT npe,[(ena TeKYQeCTI1 npl1
C)J(aTHM, TO B 0603HaQeHl1e BBO,[(HTCSI ,[(onOJIHI1TenbHbIH MH,[(eKC «p»
I1nH «C» «jTP 11 (jTC). Ilpe)].eJI TeKyqeCTI1 JIerKO onpe,[(eJISleTCSI 3KCnepl1-
MeHTanbHO, n03TOMY OH SlBJISleTCSI O,[(HOH 113 OCHOBHbIX MeXaHHQeCKI1X
xapaKTepHCTHK MaTepHaJIa.
OTHorneHHe MaKCHManbHOH CHJIbI, KOTOpyIO cnoc06eH BbI,[(ep)KaTb
06pa3eQ, K ero HaQanbHOH nno
a,[(11 nOnepe1.JHOrO CeQeHHSI Ha3bIBaeT-
CSI npedellOM npOl.J1l0cmu, MJIM 6peMellllb
t conpOmU611ellUeM pa3pb16Y - O"BP
(C)I(aTHIO - O"BC). Cne,[(yeT 3aMeTHTb, QTO O"Bp He SlBnSleTCSI TeM 3HaQeHH-
eM HanpSl)J(eHH
, npM KOTOpOM pa3pyrnaeTcSI 06pa3eQ. <DaKTI1QeCKOe
HanpSl)J(eHl1e, npM KOTOpOM 06pa3eu pa3pyrnaeTcSI, 6Y,l(eT 60JIbrne, TaK
KaK nJIO
a)],b nOnepeQHOrO CeqeHHSI B 3TOT MOMeHT MeHbllle nepBOHa-
qanbHOH nnOll.(a,[(H BCJIe,[(CTBHe 06pa30BaHI1S1 rneHKH (Ha )],HarpaMMe
HanpSl)l(eHMe nO,[(CQMTbIBaeTCSI OTHOCHTeJIbHO nepBOHaQanbHOH nJIOlQa-
)],M nOnepeQHOrO CeQeHH51 06pa3Qa). 3HaqeHMe (jBP SlBJlSleTCSI cpaBHM-
TeJlbHOM xapaKTepHCTHKOM npOQHOCTHbIX CBOHCTB MaTepHaJIOB H qaCTO
I1CnOnb3yeTcH npM paCQeTax.
npH HcnbITaHlfSlX Ha paCTSI)KeHl1e onpe,n:enSleTCSI elQe o,n:Ha xapaKTe-
pHCTI1Ka MaTepl1aJla - TaK Ha3bIBaeMoe YAJII1HeHl1e npM pa3pbIBe 80/0
Y,nJlUHeHHe npu p33pbIBe npeACT3BJlHeT C060H 3HaqeHHe cpeAHeH
OCT3TOQHOH .nel!>0pMaQuu, KOTOp3H 06pa3yeTcH K MOMeHT)' pa3pblBa H3
onpeAeJleHHOH cT3HAapTHoH AJ1HHe o6pa3u.a. 3a CTaH,[(apTHYIO ,D;JIHHY
06pa3Qa npl1HI1MalOT JIM60 10 = 10d, nl160 10 = 5d, r,l(e d - ,[(MaMeTp
06pa3I.1a.
3HaQeHI1S1 MeXaHI1QeCKHX xapaKTepMcTHK HeKoTopbIX HaM60JIee
qaCTO BCTpeQaIOlQHxc}J MaTepHaJIOB npHBe.aeHbI B Ta6JI. 2.1.
I
i
j
3 J1. H. BepeHHC:i
6S
"
, \
. I
Ta6JIl1ua 2.1
MeXaHlfqeCKlIe xapaKTepnCTIiKIt MaTepltaJIOB
MaTepl1an HanpSDKeHl1e, H/MM2 E, S 0/0 Jl
(jTP (jTC Usp asc H/MM2 /0 = 5d
CTanb Manoyrnep0)).H- 250 250 390 2 0.10 5 42
,
CTaS{
CTanb 30 He3aKaneHHaR 330 330 530 2,0.10 5 28
CTanb 30 3aKaneHHaSi 1030 900 1100 2,0.10 5 11 0,25...
...0,35
CTaJIb 45 He3aKaJIeHHaSl 370 370 620 2,0.10 5 24
CTanb 45 3aKaneHHaSi 1040 970 1080 2,0.10 5 13
CTanb Y8 He3aKaneH-
HaSi 250 430 630 2,0.10 5 25
CTanb Y8 3aKaneHHaSl 700 700 1100 2,0.10 5 16
CTanb 30xrc 3aKa-
neHHaSi 1400 1400 1620 2,0.10 5 10
CTanb 40XHB 3aKa-
neHHaSl 1720 2100 2050 2,0.10 5 10
qyrYH cepbIH C1I28 140 3]0 150 640 o 7. 10 5 0,6
,
TI1TaH TeXHH1.JeCKHH 520 520 600 I , 1 . I 0 5 23
Me)).b OTO)IOKeHHaSl 55 55 220 1 , 1 . 1 0 5 46 0,34
Me)).b npYTKOBaSl 250 250 320 1 , 1 . 1 0 5 15
J1aTYHb 330 330 450 1 ,2. I 0 5 17
EpoH3a 110 110 136 1,2.10 5 7,5
AnlOMHHIIH 50 50 84 0,7.10 5 35 0,26...
... 0,36
)])opanb 340 340 540 0,75.10 5 13
TeKcTonHT 75 115 127 168 0,03.10 5 1,5
2.4. PaCIJeTbI Ha "POIJIIOCTb "PH paCTH)KeHHH H CiKaTHH
Pa3MephI 3neMeHTOB KOHCTPYKQI1H cne,nyeT no,n6HpaTb TaK, IIT06hI
06eCneqHTb HX np0'-IHOCTb B pa60Te npH HaHMeHbllIeH 3aTpaTe MaTe-
pHaJIa. Ha OCHOBaHHH aHaJIH3a KOHCTPYKQHI1 BbHIBJI$leTC$I Ta TOIIKa,
r,l:(e B03HHKalOT HaH60JIbIllHe HanpSDKeHH$I O"H31t6. HaH,l:(eHHOe 3HaqeHI1e
HanpSDKeHHSI conOCTaBJISIeTC$I C ,l(OnYCTHMbIM 3HaqeHI1eM HanpSI)I{eHH$I
,l:(JI$I ,l(aHHOrO MaTepHana H KOHCTPYKQI1I1.
Kor,na KOHCTPYKI
I1H HaXO,nI1TCSI B CTa,l(HH npOeKTl1pOBaHI1SI, TO 3a-
,naIOTCSI K03ppUl1ueHn10A1 3anaca n. OH Ha3HaqaeTC$I 113 KOHKpeTHbIX
ycnoBHH pa60TbI paCCIII1TbIBaeMOH KOHCTPYKQI1I1. B Ka)K,nOM 06naCTH
66
TeXHI1KI1 Y)Ke CnO)KI1JIHCb CBOH Tpa,lIHQHH, CBOH Tpe60BaHH$I H cne-
QHQJHKa paCQeTOB. HanpHMep, np" npoeKTHpOBaHHI1 CTpOI1TeJIhHhIX
coopY)I(eHHH, paCC1.JHTaHHbIX Ha ,nOJIrHe CpOKH 3KCnJIyaTaQHH, 3anaCbI
npHHHMalOTCSI ,[(OBOJIbHO 60nbllIHMH (n B = 2...5). HH,n;eKc «B» nOKa3bI-
BaeT Ha TO, qTO 3anaC BbP.JHCJISIeTC$I OT npe,nena npOQHOCTH O"B.
B aBl1aQHOHHOH TeXHHKe, r,ne Ha KOHCTPYKQHIO HaKJIa,nbIBaIOTC$I or-
paHHQeHHSI no Macce, K03cpcpHQHeHTbI 3anaca TaK)I(e onpe,l(en$lIOTCSI no
npe,neJIY np01.JHOCTH, HO COCTaBJI$lIOT nB = 1,3...2,0.
3HaQeHHe K03cpcpHQHeHToB 3anaca 3aBHCI1T H OT CBOHCTB MaTepHaJIa.
B cJIYQae nJIaCTI1QHOrO MaTepl1aJIa K03<}JqH1QHeHT 3anaca 6epeTc$I OT
npe,neJIa TeKYIIecTI1 (n T = 1,5...2,0), a ,nJISI xpynKHx MaTepHaJIOB 3anac
paCCQI1TbIBaeTcSI OT npe,l(eJIa npO'-IHOCTI1I1 npHHHMaeTcSI n B = 2,5... 4,0.
Ha3Haql1B K03cpcpHltHeHT 3anaca, ,Z:(JI$I ,naHHoro 3JIeMeHTa KOHCTpYK-
QI1H paccIIHTbIBalOT donycKaeMoe HanpRJlCeHUe
,
t ,"
I >
j,
',-,
"'. .
- .
;0- .
[cr]= crT wnw [cr]=
.
n T ns
j-:
-j::
BbI6paB ,nonYCKaeMoe HanpSl)l(eHHe, COCTaBJI$lIOT YCJIOBHe
O"H31t6 < [0"],
i-
H3 KOToporo onpe
eJISIIOT pa3MepbI npOeKTl1pyeMoro 3JIeMeHTa.
UpltMep 2.2
Onpe)).enHTb llHaMeTpbI nOnepe1.JHbIX Ce1.JeHIIH 6pyca (MaTepHan - He3aKaneH-
HaSl CTanb 30), Harpy)KeHHOrO no cxeMe, npHBe)).eHHoH Ha pHC. 2.3, Q. CHna F =
= 1000 H.
PemeHHe.
1. CHa1.Jana He06xo,nI1MO nOCTpOI1Tb 3nlOpbI @ 1I@. MeTO)).I1Ka II nOCne,lIOBa-
TenbHOCTb nOCTpoeHHSl3nlOp npe)).CTaBneHa B npliMepe 2.1.
2. OnpeJJ:enSleM K03<P<PHUHeHT 3anaca. nOCKonbKY MaTepHan nnaCTH1.JHbIH,
npHHHMaeM K03<pQJHQHeHT 3anaca n T = 1,5.
3. BbI1.JHCn
eM ,nonYCKaeMoe HanpSl)l(eHlIe. 113 Ta6n. 2.1 JJ:nSl CTanH 30 BbInHCbI-
BaeM a Tp = a TC = 330 H/MM2. nocne 3Toro MO)l(HO onpe,neJII1Tb )).onYCKaeMoe Ha-
npSl)KeHl1e npH paCT
)KeHI1H 11 C)KaTHI1:
,
380
[U]p = [a]c =- = 220 (H/MM2).
1,5
4. npOaHanl13HpOBaB 3nlOpy HanpSl)l(eHI1H (CM. pHC. 2.3, 0), YCTaHOBl1nl1. 1.JTO
Ha )).BYX yqaCTKaX B03HHKaeT O)).IIHaKOBoe HanpSl:>KeHIie a HaH 6 = F / S. nOCKonbKY
)).aHHbIH MaTepHan pa60TaeT O)).IIHaKOBO Ha paCTSI:>KeHlIe Ii C)I(aTlle, TO MO)l(HO )).nSl
JII060ro H3 3THX ):(BYX Y1.JaCTKOB 3anHCaTb ycnoBHe UHaH6 ::; [a]:
1000 = 220.
S
67
5. OnpellenSleM )).liaMeTpbI Kpyrnoro 6pyca li3 nonY1.JeHHOrO ypaBHCHIUI: S =
= 4,55 MM2. 3Hajl, lITO S = n,2, onpe)).en
eM 'I = 1,2 MM; d l = 2,4 MM. Ha Y1.JaCTKC,
r)).e nnOll\a)).b S2 = 2S, ,[{liaMeTp d 2 6y)).eT paBeH 3,35 MM.
2.5. Cpe3 H CMHTHe
HanpHiKeHHH H Ae
OpMaI.(HH npH CABHre (cpe3e). B no,npa3,n. 2.1 Y)I(e
ynoMMHanocb, qTO B nOnepeqHOM CeqeHMH MorYT B03HHKaTh KaK
HopManhHbIe 0', TaK M KacaTenbHbIe HanpSl)l(eHMSI 'to EcnH K KOPOTKOMY
6pycy, )l(eCTKO 3aJ(enaHHoMY O,nHHM KOHQOM B cTeHY (PHC. 2.7, a),
nepneH,nMKynSlpHo K OCM 6pyca npHJIO)l(HTb cHny F, TO B nOnepeqHbIX
CeqeHMSlX B03HHKHeT BHYTpeHHSI.H nOnepeqHaSl CMna Q B nnOCKOCTM
CeqeHHSI, a cne,nOBaTenhHO, H KacaTenbHoe HanpSl)l(eHHe 't = Q/ S.
T;
n
'f=Lt j
;=1 '
a
6
PUC. 2.7
napannenbHbIe CeqeHM.H 6pyca CJ(BMraIOTCSI OTHOCHTenbHO )].pyr
,npyra (PHC. 2.7, 6) TaK, qTO BepXHSISI rpaHb 06pa3yeT yron y C ropH30H-
TallblO. YCTaHOBneHO, qTO KacaTenbHoe HanpSl)l(eHHe 't npSlMO nponop-
QMOHanbHO Y2110BOU oefjJopMal1UU y:
't = Gy.
3Ta 3aBHCMMOCTb BbIpa)l(aeT 3aKOll TYKa OIlR COBU2a. .5IBneHHe cpe3a
MO)l(HO Ha6nlO,l(aTb, ecnH CTanbHYIO nonocy HnH 6YMary nepepe3aTb
HO)l(HHQaMM, a TaK)I(e B cnyqae, ecnM K KnenaHOMY coe,nHHeHHIO npl1-
nO)l(eHa CHna, 66nbllIaSl, qeM Ta, Ha KOTOPYIO ,l(aHHOe COe,l(HHeHHe
6bIno paCCqHTaHO. Ha pHC. 2.8 nOKa3aHO, qTO CHnbI F npHnO)l(eHbI
B nnOCKOCTM CeqeHHM; OHH BhI3hIBalOT ,l(e<popMaUHIO c.n.BHra, 11 MO-
68
T
t
)l(eT npOH30MTH cpe3 3aKnenKH. BOT nOqeMY c,nBHr qaCTO Ha3bIBalOT
Cpe30M.
MO,l(YJIb ynpyrocTI1 npM C,l(Bl1re 3aBMCHT OT MO,nynSl ynpyrocTM
I po.n.a E:
t
G= E
t 2(1 +
)
EcnM M3BeCTHbI E H
, TO MO,l(ynb ynpyrocTM npM C,l(BMre MO)l(HO
onpeJ(enHTb. HanpMMep, ,l(nSl CTMH 30 E = 2.10 5 H/MM 2 ,
= 0,3, cne-
,nOBaTenbHO,
- ,
)
.
> .'
£1
:...,.
...
':-
G == 2.10 5 == 0,77 .10 5 (H/MM 2 ).
2. (1 + 0,3)
i
I' .
_! .
Ilo,l(qepKHeM, qTO C,l(BHr - 31'0 HanpSl)l(eHHOe COCTOSlHHe. ECnH B03-
HHKlllHe npH C,l(Bl1re ,l(ecpOpMaQI1I1 HaXO)].SITCSI B npe,l(enaX ynpyrocTH,
TO nocne CHSITHSI HarpY3KH pa3MepbI M <pOpMa ,l(eTanH BOCCTaHaBnH-
BaIOTCSI. ECnH )l(e ,l(ecpOpMaI.(HM npeBhICMnM npe,l(en ynpyrocTM, TO
Ha6nlO,na1OTCSI nnaCTl1qeCKl1e ,l(ecpOpMaQMI1. Ilocne CHSITHSI HarpY3KH
OCTaeTCSI HaMeqeHHOe MeCTO cpe3a. no ,nOCTH)I(eHHH npe,nenhHbIX Ha-
npSI)I(eHMH npOM30H,l(eT cpe3.
npliMep 2.3
npOBCpUTb np01.JHOCTb 3aKncnOK (CM. pliCa 2.8), cenli [T]cp = 100 H/MM2.
PcrnCHlie.
I. OnpeAenSleM ct>aKTli1.JCCKOC KaeaTcnhHoe Hanp
)KeHlie, B03HliKalOll{ee B none-
pC1.JHbIX Ce1.JeHH
X 3aKnenOK no)). AeHcTBlIcM 3aJ(aHHbIX Clin. nOCKonbKY 1.JIICnO
3aKncnOK i = 2 li OHli epC3alOTCSI no O)).HOH nnOCKOCTli (1.JliCnO cpe30B k = I), TO
:
1
'}
- i
1
_ F _ F _ 50000 _ 2
'(4)'''"1 - - - . 2f - ? 2 - 79,6 (H/MM).
S (lk) . nd 4 2 . I . 1t _0
4
F
A
Plie. 2.8
69
2. OCYlQeCTBnSleM npoBepKY npOIJHOCTH 3aKnenOK: cpaKTHIJeCKOe KacaTenbHoe
Hanp
)f(eHHe B nOnepe1.JHOM Ce'-leHHH 3aKnenKH )J.on)f(HO 6bITb MeHbllle HnH paBHo
J(onycKaeMoMY KacaTenbHoMY HanpjI)f(eHHIO Ha cpe3. )J:eMcTBHTenbHo, 79,6 < 100.
Cne)J.oBaTenbHo, 3aKnenKH no)J. )J.eHcTBHeM F = 50 KH He Cpe)f(YTCSI.
CMHTHe. OpH C)KaTHH ,nBYX TeJI B03HHKaeT OnaCHOCTb CMSlTHSI 3THX
nJIOCKOCTeH. HanpHiKeHHH, B03HUKalOII(He Ha KOHTaKTupYlOlI(UX no-
BepXHOCTHX, Ha3bIBaIOTCH HanpHiI\eHUHMU CMHTHH. CM5ITHe HMeeT MeCTO
B 3aKJIenOQHbIX H 60JITOBbIX cOe,nHHeHHSlX. Hanp5l)KeHI1e CMSlTI151 onpe-
,nenSlIOT no cpopMyne
0CM = F/S CM ,
r,ne F - CHJIa, C KOTOpOH c,naBJIHBaIOTC5I KOHTaKTHpYIOll\He nOBepx-
HOCTH, SCM - nJIOll\a,nb CM5ITH5I. ECJlH nOBepXHOCTb CMHTHH HBJlHeTCH
KpHBOJ1HHeHHOH, TO nJ10II(a.lJ.b CMHTHH TaKOH nOBepXIIOCTU BLlqUCJlHeTCH
KaK nJIOlI(a.lJ.b npoeKQHU 3TOH nOBepXHOCTU Ha nJlOCKOCTb, nepneH.lJ.U-
KYJlHPHYIO K JlUHUU J.(eHCTBHH CMUHalOlI(eH CUJlbl.
IIpHMep 2.4
npoBeplITb np01.JHOCTb 3aKJIen01.JHOrO coe)J.IiHeHlIjI (CM. pHC. 2.8), eCJIH ['t']cp =
= 100 H/MM2; [cr]CM = 240 H/MM2; [cr]p = 140 H/MM2.
PellleHHe.
1. npoBepSleM np01.JHOCTb 3aKJIenKli Ha cpe3 (MeTo)J.HKa paC1.JeTa npHBe)J.eHa B
npHMepe 2.3).
2. npoBepKa Ha CM
THe CTeHOK oTBepcTHH B COe.ll.IIH
eMbIX nHCTax:
F 50000 2
cr4>aKT. CM = . = - 125 H/MM .
I DnHcrd 2.10.20
Cne)J.OBaTenbHO, CMjITII
CTeHOK OTBepCTIiH He npOll30HlleT.
nonY1.JeHHOe 3Ha1.JeHHe <paKTII1.JeCKOrO CM
TH5I MeHbllle )J.onYCKaeMoro, TaK KaK
no ycnoBHIO [cr]CM = 240 H/MM2.
3. npoBepKY npOIJHOCTH nHCTOB Ha paCT
)f(eHHe BblnonH
eM no cpopMyne
crcjJaKT. p = F / S ::; r cr]p.
njI onpelleneHHSI onaCHoro Ce'-leHH
B CnO)f(HbIX cnY1.JaSlx 06bIIJHO CTpO
TC
3nlO-
pbI @. a 3aTeM @. B )J.aHHOM cnY1.Jae 3alla1.Ja 60nee npocTaSl.51cHo, LITO onaCHbIM
Ce1.JeHHeM SlBnSleTC
Ce1.JeHHe A -- A. nnOlQa)J.b B 3TOM nOnepe1.JHOM celleHlI1i S =
= 10. (120 - 2.20) = 800 MM2, a cpaKTHIJeCKOe HanpSl)f(eHHe
_ 50000 _ 2
(j 4>aKT. p - 800 - 63,3 (H/MM ),
1.JTO MeHbllle JJ.onYCKaeMoro: 63,3 < 140.
Omeem: MO)f(HO C1.JHTaTb, 1.JTO np01.JHOCTb coe)J.HHjIeMbIX nliCTOB )J.OCTaT01.JHa.
70
2.6. KpyqeHHe
IIo.lJ. KpyqeHUeM nOHHMaeTCH TaKOH BHIt HarpYiKeHHH, npH KOTOpOM
B nOnepeqHblX CeqeHUHX B03HHKaeT TOJIbKO KpYTHll{U" MOMeHT. llpo-
qHe BHYTpeHHHe CHnOBbIe cpaKTopbI (HopMaJIbHaSl H nonepelIHbIe CHJIbI,
H3rH6alOll\He MOMeHTbI) paBHbI HynlO.
PaCCMOTpI1M KpYlIeHHe Kpyrnoro 6pyca (PHC. 2.9). K KpyrnoMY
6pycy, )KeCTKO 3a,neJIaHHoMY B CTeHKY, Ha cBo6o,nHOM TOPQe npHJIO-
)KeH KPYT5Ill\I1M MOMeHT M. B pe3YJIbTaTe 3Toro 6pyc ,necpopMHpyeT-
C5I: CMe)l(HbIe CelIeHI1S1 nOBopalIMBalOTC5I OTHOCHTellbHO ,npyr ,npyra,
o6pa3YIOll\a51 OB MCKpHB1l5leTC5I M 3aHMMaeT nOJIO)KeHMe OC. IlpH
onHcaHHH KpY1.JeHH5I npHHHMalOTCSI cne,[(YIOl.QHe ,[(onyu.(eHHSI 11 npa-
BMJIa:
OCb 6pyca He ,necpopMMpyeTc5I;
nOnepe1.JHbIe CeqeHH5I, nJIOCKI1e D.O D.ecpopMaIJ.HH, nOCJIe .ae<popMaUMH
TaK)Ke OCTaIOTC5I nJIOCKHMH;
npo,nOJIbHbIe BOJIOKHa He H3MeH5IIOT cBoeH MHHbI (yrOJI Y HaCTOJIbKO
MaJI, qTO H3MeHeHHeM ,[(JIHHbJ MO)KHO npeHe6peqb);
pa,nHYCbI r nOnepeqHbIX CeqeHHH OCTaIOTC5I np5lMbIMH nOCJIe ,ne-
cpOpMaI..\HH, nOBOpaqHBaSlCb Ha HeKOTopbIH yron <p;
,nJI5I BHYTpeHHHX KPYT5Ill\HX MOMeHTOB npHHSlTO CJIe,nYIOll\ee npa-
BHJIO 3HaKOB: eCJII1 Ha6JIIO,naTeJIb CMOTpI1T Ha nonepelIHoe CeqeHHe co
CTOpOHbI BHellIHeH HOpMaJIH 11 BH,[(I1T BHYTpeHHHH KPYT5Ill\I1H MOMeHT
M Kp HanpaBneHHbIM npOTHB xo,[(a qaCOBOH CTpeJIKI1, TO MOMeHT C1JH-
TaeTC5I nOJIO)KHTeJIbHbIM.
TaKHM 06pa30M, npH KpYlIeHHH B nOnepeqHOM CelIeHl111 6pyca B03-
HI1KalOT KaCaTeJIbHbIe Hanp5l)KeHHSI
(QHCTbIH c,nBHr).
CYI..QeCTBYIOT nOHSlTI1S1 yrna 3a-
KpY1JMBaHH
M OTHOCMTeJIbHOrO
yrJIa 3aKpyqI1BaHHSI 8:
8=
/1.
KaCaTeJIbHble Hanp5I)I(eHM
't npM
KpY1JeHMH pacnpen.eJISlIOTC5I no ce-
qeHHIO HepaBHoMepHo: B QeHTpe
OHI1 paBHbI HYJIIO, a Ha MaKCH-
ManbHoM OKPY)KHOCTH nOnepeqHO-
ro CeqeHI151 - MaKCMMaJIbHoMY 3Ha-
LJeHHIO 't max . Ilo3ToMY paCqeT Be-
,[(eTCSl no 't max . 3HalIeHHe KaCaTeJIb-
Horo HanpSl)KeHI1S1 3aBHCHT OT BHYT-
I
I
M
A
B .
. .-
q>
M
PliCa 2.9
-
71
peHHero KpYT5I
erO lvfOMeHTa H reOMeTpHqeCKOM XapaKTepHCTHKH no-
nepeqHOrO CeqeHH5I:
't max = Mxp/W p ,
r,ne W p eCTb nOJl51pllblU MOMe1lm conpOmU6Jle1lU51.
,[(JISI CnJIOllIHOrO nOnepeqHOrO CeqeHHSI ,D;HaMeTpOM D W p = O,2D 3 ;
M5I KOJIbQeBoro CeQeHH5I (nOJIbIM BaJI) W p = 0;2D 3 (1- d 4/ D 4 ), r,ne d -
BHYTpeHHHH ,D;HaMeTp (,D;HaMeTp OTBepCTHSI), D - BHellIHHH ,D;HaMeTp
BaJIa. IIoKa)l(eM, qTO BaJIbI CnJIOllIHOrO nOnepeqHOrO CeqeHH}) HCnOJIb-
30BaTb He3KOHOMHqHO.
UplfMep 2.5
Ban nepe)).aeT MOMeHT M = 10000 H . M. Tpe6yeTcSI no
06paTb pa3Mepbl none-
pe1.JHOrO Ce1.JeHHSI Bana
nSl cnY1.JaeB: a) cnnOlllHoro KpyroBoro Ce1.JeHIISI II 6) KPy-
rOBoro Ce1.JeHIISI C oTBepcTHeM d = (7/8) D. CpaBHIITb 06a Ce1.JeHHSI no pacxo
y
MeTanna. ,[(onycKaeMoe HanpSl)J(eHHe [-r] = 6000 H/CM2.
PellleHHe.
I. Onpe.u.enSieM MOMeHT conpOTHBneHIISI )).nSl 060HX nOnepe1.JHbIX Ce1.JeHHH:
JV = M Kp = 10000.100 - 167 (CM 3 ).
p T 6000
2. Onpe.u.enSieM )).HaMeTp Bana )).nSl cnnOlliHoro CeqeHHSI:
167
D 3 = - = 833 (CM 3 ); D = 9,43 (eM).
0,2
3. OnpelienSleM llHaMeTp Bana llnSl nonoro nOnepe1.JHOrO CeqeHHSI:
3 167
D = ( 74 ) = 12,7 (CM).
O J 1 _-
,- 4
8
4. Onpe
enSleM pacxo.u. MeTan.TIa. ,[(nSl 3Toro BbI1.JHCnHM nno
a)).H nOnepe1.JHbIX
CeqeHHH cnnOlliHoro Ii nonoro BanOB:
)J.JISI cnnOlliHoro Bana
nD 2
S=-=698 ( CM 2 ) .
4 ' ,
)J.JI$I nonoro Bana
TtD 2 ( d2 J
S=T 1- D 2 =29.4 (CM 2 ).
nOCKonbKY pacxo)). MeTanna 6y)).eT npOnOpIJ.HOHaneH nnOma)).H nOnepe1.JHOrO
CeqeHHSI, TO nonoe CeqeHlIe SlBnSleTcSl 60nee 3KOHOMH1.JHbIM H B .n.aHHOM cnyqae
,naeT 60nee 1.JeM JJ.BYKpaTHoe CHH)J(eHHe Beca Bana.
IIocTpoeHHe JUlOp. IIpI1 KpyqeHHH, KaK H npH paCT5I)I(eHHH, CTp05IT
3nIOpbI BHYTpeHHHx CI1JIOBbIX cpaKTopoB (KPYTSI
HX MOMeHToB), Hanp5I-
)KeHHH ('t Max ) 11 nepeMe
eHHH (yrJIOB 3aKpyqHBaHHSI cp).
72
I
I
I
M 2 =M M}=2M
+
M
16d 3
,
;.
M
8
..,
30,6 Ml
O.d 4
MI 10.6 MI
G .1,6d 4 Gd 4
PlICa 2.10
y 'I
,
r,
f
II ocmpoel-lue 3nlOpbl M Kp. BclO ,nJIHHY 6pyca (PHC. 2.10) pa306beM Ha
,n;Ba yqaCTKa. Ha 3nlOpe BHYTpeHHHX CHJIOBbIX <}JaKTopOB B CeqeHHSIX,
r,n;e npHJIO)l(eHbI BHellIHHe CHJIbI, 6y,n;YT CKaqKH, paBHbIe npHJIO)l(eH-
HbIM HarpY3KaM (B ,n;aHHOM CJIyqae - KPYT5I
HM MOMeHTaM). npHMe-
HSI5I MeTO)]. CeqeHHH C yqeTOM npaBHJIa 3HaKOB ,D;JISI KPYTSI
HX MOMeH-
TOB, CTpOHM 3nlOpbI M Kp . Ha pHC. 2.10 .l(JI}) H306pa)l(eHHSI BHellIHHX
MOMeHTOB npHMeHeHO YCJIOBHOe 0603HaqeHI1e B BH,ne KPY)l(KOB: KPY-
)l(OK C TOqKOH 0603HaQaeT CHJIY, HanpaBJIeHHYIO Ha Ha6JIIO,naTeJI5I, a
KPY)I(OK C KpecTHKoM - CHJIY, HanpaBJIeHHYIO OT Ha6JIIO,D;aTeJISI.
llocmpoe1lue 3nlOpbl 't max . BclO .l(JIHHY 6pyca pa36HBaeM Ha TPH yqa-
CTKa; Ha Ka)l(,nOM H3 HHX M Kp H W p coxpaHSIIOT nOCT05IHHOe 3HaqeHHe.
3aTeM no,nCTaBJI5IeM B <}JOPMYJIY Tmax =MI<p/Wp cooTBeTcTBYIO
He 3Ha-
qeHHSI M I<p H W p :
M
Ha I YlJ.acTKe M Kp = +M; W p =0,2_(2d)3 = 1,6d 3 ; 't'max = 16d 3 ;
,
--
..
;
73
J'C
,;
5M
Ha II yqaCTKe M"" = +M; W p = 0,2d 3 ; 't rnax = d 3 ;
.. 10M
Ha III yqaCTKe M J(p = +2M; W p = O,2d"'; 't rnax = 3 .
d
II0CKOJIbKY Bce BHYTpeHHHe KPYTSlll\He MOMeHTbI IIMeJIH nOJIO)l(H-
TeJIbHbIH 3HaK, TO H Bce KaCaTeJIbHbIe Hanp5l)l(eHII5I 6y,nYT nOJIO>KH-
TeJIbHbI npH nOCTpoeHHH HX Ha 3nlOpe t max .
Ilocmpoenue 311lOpbl <p. ITpe>K,ne Bcero He06xo,nHMO YCTaHOBHTb 3a-
BIICMMOCTb, no KOTOpOH 6y,neM onpe):(eJI5ITb yrJIbI 3aKpYQMBaHHSI <po Ha
OCHOBaHHH 3aKOHa rYKa ,nJISI c,nBHra 3anHllleM BbIpa>KeHHe .n;JISI MaK-
CHMaJIbHOrO KaCaTeJIbHOrO Hanp5l>KeHHSI B nOnepeqHOM CeqeHHM
KpyrJIOro 6pyca:
J p = O'ID{I-
:J
Tenepb yrOJI 3aKpyqHBaHHSI <p 3anHllleM B BII,ne
= MJ(p I
<P GJ .
p
't max = Gy.
fIpoH3Be.n;eHHe GJ p Ha3bIBalOT JlCeClnKOcmblO 6pyca npu KpYllellUU
I1TaK, nOJIyqeHa 3aBIICMMOCTb, no KOTOpOH MO)l(HO onpe;J;eJI5ITb
yrJIbI 3aKpYQHBaHHSI 6pyca. OnpeAeJlHTb YfOJI 3aKpY-IOBaHUH no 3TOU
3aBUCUMOCTU MOiKHO TOJlbKO npo YCJlOBOU, -ITO Ha MOHe I Bce BXOAH-
"-,-oe B 3TY 4>OPMYJlY BeJlU-IOHbl- M Kp , J p 0 G - nOCTOHHHble.
IlepexO.lIJIM K nocTpoeHMIO 3nlOpbI yrJIOBbIX nepeMeI..QeHMM. BaJI no
.l(JIHHe 3nlOpbI pa36MBaeM Ha qeTbIpe yqaCTKa. TaK )l(e, KaK II npM no-
cTpoeHHH 3nlOpbI nepeMeI..QeHHM npH paCT5I>KeHHH, HaqMHaeM CTpOHTb
3nlOpy OT HenOLIBM>KHOrO CeQeHHSI, T. e. OT >KeCTKOM 3a,neJIKH. B KOHQe
nepBoro yqaCTKa yroJI 3aKpYQHBaHHSI 6y.n;eT
113 pHC. 2.9 BH.n;HO, qTO npH KpyqeHHH 06pa3YIOll.{aSl QHJIHH.n;pa DB
nOBOpaQMBaeTCSI Ha yrOJI y H 3aHHMaeT nOJIO)l(eHI1e DC. fIpM 3TOM
.n;yra BC paBHa yl; rJISIJI,S1 Ha nOnepeqHOe CeQeHHe no cTpeJIKe A, MO)l(HO
3anHcaTb, qTO Ta >Ke .n;yra BC paBHa cpr. CJIe,aoBaTeJIbHO,
yl=cpr,
oTKy.n;a
MJ(pl
<PI = GJ
pI
Ml
G. 0,1. (2d)4
Ml
-
4 .
G.16.d
,
<pr
'\I-
I -T.
B KOHQe II yqaCTKa yron 3aKpyqMBaHM5I
llO,L(CTaBJISISI HaM)I.eHHOe 3HaqeHHe y B 3aKOH I""'YKa, nonyqHM
t=G <P r.
l
en _ en + M J(pIIl
't'll - 't'I GJ -
pII
Ml Ml IO,6Ml
+ -
1,6Gd 4 0 IGd 4 Gd 4 .
M Kp
C )::(pyroH CTOpOHbI, '[ = . CJIe,lJ.OBaTenbHo,
W p
B KOHQe III YIJaCTKa
J
M Kp =G <P r.
W p I
M J(pIlIl IO,6Ml 2Ml
en - en + - +
't'III - 't'll GJ pIlI - Gd 4 O,IGd 4 -
Ha IV yqaCTKe yrOJI 3aKpYQHBaHM5I 6y.n;eT paBeH yrny 3aKpyqI1BaHM5I
<PIlI, TaK KaK Ha 3TOM YQaCTKe OTCYTCTBYIOT BHYTpeHHHe KpYTSII..QHe MO-
MeHTbI.
BbILJI1CJIeHHble yrJIOBble rrepeMeI.l(eHI1S1 OTKJIa;J;bIBaeM Ha 3nlOpe <po
30,6Ml
Gd 4 .
MKpl
BbIpa3HM OTCIO):(a yron 3aKpYIJI1BaHH5I <p = .
GWpT
D
BemlqHHY Wpr (HJIH W P "2) Ha3bIBalOT nOllRpllblM MOMellmOM Ullep-
14uu CellellUR H 0603HaQalOT J p .
II0JISlpHbIM MOMeHT MHepQHM J'(JISI CnJIOlliHOrO KpyrJIOro 6pyca
J p = O,ID4;
.l(JISI nOJIoro Kpyrnoro 6pyca
2.7. IlpHMOH nOnepeQHbIH H3rH6
IIOA H3fH60M nOHHMaeTCH TaKOH BHj.:( HarpYiKeHHH, "PH KOTOpOM B
nOnepe-IHblX CeqeHHHX 6pyca B03HHKalOT U3fU6alOIl\Ue MOMeHTbl (CM.
nO)I.pa3)I.. 2.1). EcnH H3rH6alOI..QI1H MOMeHT SlBnSleTCSI e):(HHCTBeHHbIM
CHJIOBbIM cpaKTopoM, a nOnepeLJHble 11 HOpMaJIbHhIe CHJIbI OTCYTCTBYIOT,
74
7
-
TO TaKOH H3rH6 Ha3bIBaeTCSI l.JUCnlblM.
B 60nbllIHHCTBe cnyqaeB B nOnepeqHbIX
B CeqeHHSIX 6pyca HapSIJJ.Y C H3rM6alO
M-
MH MOMeHTaMH B03HHKalOT nOnepeqHbIe
CMJIbI. B 3TOM CJIyqae M3rH6 Ha3bIBalOT
"/ nonepettHblM. 6pyc, pa60TalOIl\UH B OC-
HOBHOM Ha H3rH6, Ha3bIBaeTCH 63JIKOH.
Ha 6anKY MOrYT ,l(eHCTBOBaTb cocpe-
dOmOtteHHbze CHnbI M MOMeHTbI, a TaK)Ke pacnpedeJlellllble no ,l(JIHHe.
HanpMMep, Ha pMC. 2.11 F - cOCpe,l(OTOqeHHaSl CHna, M - cOCpe,l(OTO-
qeHHbIH MOMeHT; Ha yqaCTKe a npHnO)KeHa pacnpe,l(eneHHaSI HarpY3Ka
OT HynSI ,no qrnax.
OpM onHcaHHH SlBneHHSJ M3rM6a Hcnonb3YlOT reOMeTpU'IeCKUe xa-
paKTepucTuKH nOnepe'IHOrO Ce'IeHHH, yqHTbIBalOll1Me pacnpe.aeneHMe
MaTepMana no BbICOTe CeqeHMSI: 1.,< - MOMeHT MHepQMH CeqeHHSI OTHO-
CHTenbHO rnaBHoH OCM, nepneH)J,HKynSlpHoM K nJIOCKOCTH H3rH6alO-
ero MOMeHTa; w.
- MOMeHT conpOTHBneHMSI CeqeHMSI npH H3rM6e,
W = J Iy r)J,e Y max - Koop.n;MHaTa TOqKM, HaH60nee y.n;aneHHOH OT
x x max ,
HeMTpaJIbHOM nMHMM 6pyca (CM. pHC. 2.12, 6).
HanpMMep, ,n;JISI npgMoyrOJIbHOrO CeqeHMg
qmax
F
PHC. 2.11
bh 3 bh 2
J --. W =-
x - 12' x 6'
r)J,e b - lllHpHHa; h - BblCOTa CeqeHHSI;
)J,JISI KpyrJIOro nOnepeqHOrO CeqeHHSI
nD 4
J = .
x 64
nD 3
W x = = 0,ID3,
. 32
r,l(e D - ,[(MaMeTp CeqeHMSI.
AHaJIH3 BHYTpellHHX CHJ10BbIX 4>aKTopoB HaqHHaeTCSI C onpe)J,ene-
HMSI nOJIHOH CMCTeMbJ BHelllHMX CMJI. PaccMoTpMM HeKoTopbIe xapaK-
TepHbIe npMMepbI H YCTaHOBHM npaBHJIa onpe,lI.eJIeHMSI H3rH6alO
Mx
MOMeHTOB H nOnepeqHbIX CMn.
Ha pHC. 2.12, a nOKa3aHa npOCTeHlllag ,lI)3yxonopHaSi 6anKa, Harpy-
>KeHHaSI CMJIOM F. OCBo6o)l(.n;aeM 6anKY OT CBSI3eH M 3aMeHSIeM MX ,lI.eHCT-
BMe peaKQMSlMH. Onopa A npe,l(CTaBJISIeT C060M HeBeCOMbIM CTep)l(eHb,
n03ToMY peaKQHSI R A nOM,lI.eT B,lI.onb Hero. B rnapHMpe B peaKQHIO
paCKJIa,lI.bIBaeM Ha ,nBe COCTaBnSIIO
Me. HeCMOTpSI Ha TO, qTO BbI60p
CHCTeMbI KOOp,l(MHaT, 6e3ycnoBHo, npOM3BoneH, B conpOTHBneHHH
MaTepManOB npMHSlTO OCb Z HanpaBnSITb B,lI.Onb 6pyca; OCM x H Y
,[(on)KHbI ne)KaTb B nnOCKOCTM, nepneH,lI.HKynSIpHoM K 3TOH OCM, npHqeM
nOBopOT OT OCM X KOCH Y ,lI.On)KeH npOHcxo.n;MTb npOTHB XO,lI.a qaCO-
76
,
I
I
l
F
A
a
I
a
A-A
y
Y
6
z
A
x
M H3r
B
II
A
I-a
B
PHC. 2.12
BOM cTpenKH, eCJIH cMOTpeTb C KOHQa OCH Z (PMC. 2.12,6). Haqano
OTCqeTa ,l(nSI oceM pacnonaraeTCSI B QeHTpe TSI)I(eCTH nOnepeqHOrO
CeqeHMSI. B 3TOM cnyqae OCM X M Y Ha3bIBaIOTCSI 2Jla8HblMU l1el-lmpaJlb-
HbLMU OCRMU nonepe1.l1l020 Ce1.lellUR.
COCTaBHM ypaBHeHMSI paBHOBeCI1SI ,lI.JISI nnOCKOH CHCTeMbI CHJI H on-
pe,n;enMM HeH3BeCTHhIe peaKQHI1 CBSl3eM. HeH3BeCTHhIx BenMqHH TpM -,
RA' Y B , ZB. YpaBHeHMH CTaTMKM TO)Ke TpM, cne)J,OBaTenhHO, 3a.n;aqa
CTaTMqeCKM onpe,lI.enMMaSl:
L F iy = 0;
L F i : = 0;
LmomB( F ;) = 0;
+ R A - F + Y B = 0;
+ZB =0;
- RAI + F(l- a) = O.
"
,
,
77
(
f
'
I
" '1
. a
OTCIO,n;a HaXO,n;MM peaK:QMM onop:
ZB = 0;
R A = F(/-a)/I;
Y B = Fa/I.
Tenepb npMcTynMM K BbHIBJIeHMIO BHYTpeHHMX CMJIOBbIX $aKTOpOB B
nOnepeQHbIX CeqeHMSlX 6pyca. L{JISI 3TOrO Me)J{,n;y TOQKaMM npMJIO)J{e-
HMSI BHeWHHX CHJI Ii MOMeHTOB, BOCnOJIb30BaBllIMCb MeTO,lIOM Ceqe-
HMM, COCTaBJISlIOT ypaBHeHHSI paBHOBeCI1H OTCeqeHHbIX qaCTeH. TaK, B
KOHKpeTHOM npHMepe Heo6xo,[(HMO ,[(eJIaTb CeqeHI1SJ ,[(Ba)J{,[(bI: Ha pac-
CTOSlHHM Z] H Z2 OT neBOH OnOpbI. Ha pMC. 2.12, 6 nOKa3aHO, KaK pac-
CeqeH 6pyc Ha paCCTOSlHMH ZI. CJIe,[(yeT 06paTMTb BHMMaHMe Ha TO,
QT06bI BHYTpeHHMe CHJIOBbIe cpaKTOpbI B nOnepeqHOM CeqeHMM neBOH
M npaBoH qaCTeH 6bInH 06S13aTenbHO npOTMBononO)J{HbI no HanpaB-
JIeHMIO.
113 npe,lJ.bI,lJ.YlQerO MaTepMaJIa Y)J{e H3BeCTHO, qTO BHYTpeHHHe CH-
nOBbIe cpaKTopbI onpe,[(enSJIOTCSJ H3 ypaBHeHHH paBHOBeCHSI OTCeqeH-
HbIX qaCTeH:. Cne,[(yeT YCJIOBMTbCSI 0 3HaKax nOnepeqHbIX CMn M MO-
MeHTOB.
.r;
(j)
( op
HHaTa )
BBepx
)
BHH3
o
z
a
6
PHC. 2.13
CymecTByeT HeCKOJIbKO cnoc06oB onpe,n;eJIeHHSI 3HaKa M3rM6alO-
mero MOMeHTa B nOnepeqHOM CeqeHMM. 1. ITo 3HaKY KpHBM3HbI H30-
rHYToro 6pyca (PHC. 2.13, a). OqeBH,n;Ho, 3HaK 6y,n;eT 3aBHceTb OT
BbI6paHHOH: CHCTeMbJ Koop,Z:(HHaT. ECJIH OCb Y HanpaBMTb B npOTHBO-
nOJIO)J{HYIO CTOPOHY, TO 3HaKH M H3r M3MeHSlTCSJ Ha npOTMBOnOJIO)J{-
HbIe. 2. qalQe Bcero npM nocTpoeHHH 3nlOp H3rM6alOlI(Hx MOMeHTOB
3HaK MOMeHTa He 3aBMCHT OT BbI6paHHOM CMCTeMbI OTCqeTa, a Op,lJ.M-
HaTa OTKJIa,lJ.bIBaeTCSJ Ha CJlCamOM 60JlOKHe, T. e. B CTOPOHY BorHYTOCTI1
H30rHYTOH OCH 6pyca (PMC. 2.13, 6). 3. EcnM TPY,Z:(HO npe,lJ.CTaBHTb, KaK
6YJJ:eT BbIrJISJ,lJ.eTb H30rHYTaSl OCb 6pyca, TO COCTaBJISlIOT CYMMY MOMeH-
TOB CHJI, ,lJ.ei1:cTBYlOlQHX Ha JIeBYIO OTCeqeHHYIO qaCTb 6pyca. ECJII1 paB-
78
I
Ho,n;eHCTBYIOlI(HM MOMeHT Bcex CHn, ,n;eHCTBYIOlI(HX Ha neBYIO qaCTb,
6y,Z:(eT HanpaBJIeH no qaCOBOH CTpeJIKe, TO op,lJ.HHaTa H3rH6alOlQerO
MOMeHTa OTKna,lJ.bIBaeTCSJ Ha 3nlOpe BBepx, T. e. MOMeHT B nOnepeqHOM
CeqeHMM ,n;eMcTByeT npOTMB qaCOBOM CTpenKH, a 6pyc M3rH6aeTcSI
BorHYTOCTblO BBepx, Cne,lJ.OBaTeJIbHO, Op,lJ.HHaTa 6Y,lJ.eT OTnO)J{eHa Ha
C)J{aTOM BonOKHe. ECJIM )J{e CYMMa MOMeHTOB, ,n;eMcTBYIOlI(MX CJIeBa OT
ce
eHHH, HanpaBneHa npOTHB
aCOBOH CTpeJIKH, TO u3ru6awIl\u" MOMeHT
OTKJIa.z:I.bIBaeTCH BHU3 (PMC. 2.13, 6).
t:(JISJ CMJI, JIe)J{alI(HX cnpaBa OT CeqeHMSJ, I1MeeT MeCTO o6paTHaSJ 3a-
BI1CI1MOCTb.
IIpaBuJlo onpeAeJIeHHH 3HaKa )l.JIH nonepe
Hblx CUJI: eCJIU paBHoAeH-
CTBYIOID-aH BHeUJHUX CWI, JleiKaID-DX no JleBYW CTOPOHY OT CeqeHUH, Ha-
npaBJIella BBepx, TO nonepe
HaH CUJIa B ce
eHHU C
UTaeTCH nOJIOiKHTeJlb-
Hoil, a eCJID BHU3, TO nOnepe'lHaH cuna OTpun:aTeJIbHa.
B CeqeHI1H Ha paCCTOSlHHI1 ZI OT Haqana KOOp,lJ.HHaT (T. e. B neBOM
qaCTH 6pyca OT CeqeHI1S1, CM. pHC. 2.12, 6) nonepelfHaSl CMJIa Q HMeeT
nOnO)KHTeJIbHbIM 3HaK 11 Ha 3nlOpe 6Y,lJ.eT OTKJ1a,lJ.bIBaTbCSJ BBepx. IlpH
paCCMOTpeHI1M paBHOBeCHSJ npaBOM OTCeqeHHOM qaCTH ):(JISJ CHn, ne)l(a-
ll..\HX cnpaBa OT CeqeHHSI, I1MeeT MeCTO 06paTHaSl 3aBMCMMOCTb. QTo6bI
J1erqe YCBOHTb npaBMna onpeJJ:eJIeHMSJ 3HaKOB, )KenaTeJIbHO paCCMaT-
pHBaTb paBHOBeCl1e, HanpliMep, BCer,lJ.a neBOM QaCTI1 6pyca. IlpM
nOCTpoeHMM 3nlOp M3rI16alOlI(MX MOMeHTOB M nOnepeqHbIX CMn 6Yl1eT
nOKa3aH cnoc06 npOBepKM npaBMJIbHOCTM BbI60pa 3HaKOB nonepeq-
HbIX CMJI.
I1ocTpoeHue 3nlOp u3ru6alOID-HX I\fOMeHTOB H nonepe
HblX CUJI oCYlI(e-
CTBJISIeTCSI B cneAYIOI.l\eH nOCJIeAOBaTeJ1bHOCTM: 1) onpeAenSIIOT peaK:QMM
onop; 2) BbISlBJISJIOT B nOnepeqHbIX CeqeHHSJX 6pyca Bce BHYTpeHHMe
CHJIOBbIe cpaKTopbl (HX 3HaqeHMe M 3HaK); 3) CTpOSIT 3nlOpbI. IlocTpoHM
3nlOpbI AJISI 6aJ1KM, npe,Z:(cTaBJIeHHOH Ha pMC. 2.12, Mcnonb3YSJ nOJIY-
qeHHbIe paHee BbIQI1CneHMSI.
1. Onpe,n;eJISIeM peaK:QMM onop.
COCTaBJISJeM ypaBHeHMSJ paBHoBecMSJ nJIOCKOM CI1CTeMbI CMn:
II
R A = F(/-a)jl; Y B = Fa/I.
2. Onpe,[(enSieM BHYTpeHHMe M3rH6alOlI(He MOMeHTbI B nOnepeqHhIX
CeqeHHSIX 6aJIKH.
JISJ 3Toro paccMaTpMBaeM paBHoBecHe OTCeQeHHOM
neBO" QaCTI1 (pl1c. 2.12, 6):
B CeqeHMI1 Z I
Lmomc( F i) = 0; - R A Zl +M H3r = 0;
F(l-a)
M lur = +RAz l = Zl J(JISJ 0 < z] < a;
I
79
:iIII
B CeqeHMIi Z2
Lmomc( F i) = 0;
-R A z 2 +F(Z2 -a)+M H3 [. =0;
M H3f = +R A z 2 - F(Z2 - a) ,nnSI a < Z2 < I.
3. OnpeIleJISIeM nOnepeqHbIe CHJIbI.
B CeqeHMH ZI
L
y = 0;
R A - Q = o.
OTCID,na Q = R A = F(I - a) II;
B Ce1.IeHI1M Z2
L
y = 0; R A - F + Q = o.
OTCIO,n;a Q = Fa / I.
4. CTpOMM 3TIIOpbJ H3rM6aIOI1J;IiX MOMeHTOB.
3nlOpa M H3f B npe):(eJIax 0 < ZI < a HMeeT nMHeMHYIO 3aBHCHMOCTb.
3a,n:aeMcSI Zl = 0, npM 3TOM M lf3f = o. OTKJIa,nbIBaeM 3TY TOqKY Ha
3nlOpe (PHC. 2.14). ,[(aJIee npM ZI = a M H3f = F(l-a)ajl.
B npe,n;enax a < Z2 < I nonyqaeM: npH 22 = a M H3f = F(l- a) a/I; npH
Z2 = I M H3f = O. OTKJIa):(bIBaeM 31'11 op):(HHaTbI (OHH nOCTpoeHbI Ha
C)KaTOM BOJIOKHe) H COe,1JJ1HSIeM nHHI1SIMH. Cne,1J.yeT 3aMeTHTb, 1.ITO Ha
BTOpOM yqaCTKe MO)l(HO 6bIno op,nI1HaTbI He BblqMCnSITb, TaK KaK B
rnapHMpHOH onope B MOMeHT He MO)l(eT B03HMKaTb, H n03TOMY Ha
3nlOpe HY)KHO cpa3Y OTJIO)Kl1Tb O.
5. CTpOHM 3nIOpbJ nOnepeqHbIX CI1JI.
KaK 6bIno BbISIBTIeHO B n. 3, nOnepeqHbIe CMTIbI nOCTOSIHHbI Ha Ka-
)I(,n:OM H3 ):(BYX yqaCTKOB, n03TOMY OTKJIa,1J.bIBaeM nO):(C1.II1TaHHbIe 3Ha-
QeHI1SI C Y1.IeTOM 3HaKOB. HY)KHO 06paTI1Tb BHI1MaHl1e, qTO B TOqKe
npI1JIO)KeHI1SI BHelIlHeM CMnbI ):(on)KeH 6bITb CKaqOK, paBHbIM npl1JIO-
jl(eHHOM CHJIe.
KpoMe Toro, MO)KHO npoBepliTb npaBHJIbHOCTb YCTaHOBJIeHHbIX
3HaKOB TIOnepeqHbIX CI1JI. TaHreHC yrna HaKJIOHa JII1HHI1 M H3f Ha 3nlO-
pe H3rM6aIO
Hx MOMeHTOB nOKa3bIBaeT Ha 3HaK nOnepeqHOM CHnbI.
EcnH yrOJI OCTpbIM, TO TaHreHC nOJIO)l(HTenbHbIH, a CJIe,nOBaTenbHO, 11
nOnepeQHaSI CI1JIa HMeeT 3HaK nJIlOc. ECJIH yron HaKJIOHa JIHHHI1 C
OCblO Z TynoM, TO nOnepeqHaSI CHna OTpH
aTenbHaSI. ConOCTaBbTe
nOCTpoeHHbIe 3TIIOpbI M lf3f Ii Q (CM. pHC. 2.14).
80
. _t.
- ;:.., - . .
I
! I
RAtA
F
a
@
@
Fa
I
PliCa 2.14
HanpHiKeHHH B 6pyce npH npHMOM IJHCTOM H3rH6e. QI1CTbIM H3rH6
B 6pyce MO)KeT HMeTb MeCTO no BceH ,[(JIHHe 6pyca ab (PHC. 2.15, a)
HJIH TOJIbKO Ha ero qaCTH ab (PHC. 2.15, 6). npl1 qHCTOM H3rl16e B
6pyce B03HI1KaIDT HanpSI)KeHI1SI, HenOCTOSIHHbIe no BbICOTe nonepeq-
Horo CeqeHI1SI. 113 pHC. 2.16 BI1):(HO, QTO npl1 113rl16e 6pyca HanpSI)Ke-
HHe MeHSIeTCSI 01' +O'max ):(0 -O'max. Cne):(oBaTeJIbHO, B nOnepeqHbIX
CeqeHI1SIX eCTb He):(e!}JopMl1pyeMble TOqKI1, KOTopbIe o6pa3YlOT Heu-
mpaJlbHYlO JlUHUlO, npoxo):(SI
YIO Qepe3 QeHTp TSI)I(eCTI1 nOnepeQHbIX
CeQeHI1H. ECJlH H3MeHeHHe KPHBH3Hbi 6pyca npOHCXOAHT B nJlOCKOCTH,
B KOTOpOU AeucTByeT H3rH6aIOII(H" MOMeHT, H 3Ta nJlOCKOCTb npo-
XOJl.HT lJepe3 fJIaBHble OCM CelJeHMH, TO TaKOH M3fH6 Ha3blBaeTCH
npHMbiM.
npl1 npSIMOM qHCTOM H3rl16e
II
0' max = M H3f /W.'!( .
PaClJeT lIa npOIJHOCTb npH H3rH6e no MeTO,l],I1Ke aHaJIOrHqeH paCQe-
TaM Ha npOQHOCTb npl1 paCTSI)KeHl111 11 KpyqeHI1I1. llOIlCQI1TbIBalOTCSI
HanpSI)I(eHI1SI B CeqeHMSIX no n.JII1He 6pyca 11 113 HI1X (no 3nlOpe HanpSJ.-
)KeHI1H) BbI611paeTCSI Hal160JIblIlee. nOCJIe qero 113 YCJIOBI1SI
0' max Han6 < [0' ]p,C>K
onpe,neJISIIOTCSI reOMeTpHqeCKHe pa3MepbI nOnepeqHOrO CeqeHI1SI
6pyca.
81
a a
6
M
+
@
b
F
+O'max
a
-O'max
HeHTpaJILHLIH CJIOH
Fi
PHC. 2.15
PHc.2.16
IIplfMep 2.6
Onpe)J.enHTb Jl.HaMeTp Kpyrnoro nOnepe1.JHOrO Ce1.JeHIUI 6pyca, Harpy)l(eHHoro
H3rH6alO1l{HM MOMeHTOM M = 600 KH.M (CM. pHC. 2.15, a), ecnH )J.onYCKaeMoe
HanpSl)l(eHHe [cr]p = 160 H/MM2.
PellleHlIe.
I. nOCKonbKY JnlOpa H3rH6alO1l{HX MOMeHTOB Y)I(e H3BeCTHa, a 6pyc HMeeT no-
CTOSlHHoe nOnepe':lHOe Ce1.JeHHe, TO onpe)J.enSleM MOMeHT conpOTHBneHHSI
w = W, = M H3r = 6000000.100 = 375 000 ( MM 3 ) .
x J [ cr]p 160
2. Onpe.nenSieM .nHaMeTp Kpyrnoro 6pyca:
w
= 0,1 D3; 375000 = 0,ID 3 ; D = IO ;J3750 == 155 (MM).
2.8. Y CTOH'IHBOCTL "PH OCeBOM Harpy*eHHH CTep*HH
I10)]; )JcmOU1JU60CmblO nOHHMaeTCSI CBOMCTBO CI1CTeMbI caMOCTOSl-
TeJIbHO BOCCTaHaBJIHBaTb CBoe nepBOHa1.JanbHOe COCTO
Hl1e nOCJIe Toro,
KaK eM 6bIJIO c006ll.\eHO HeKoTopoe OTKnOHeHl1e OT nOJIO)l(eHI1
paBHo-
BeCHSI. ECJIM CHCTeMa TaKI1M CBOMCTBOM He 06na.n;aeT, TO OHa Ha3bIBa-
eTCSI neycmOUllU60U (rOBopSlT, 1.J:TO npOH30IllJIa nOTepR YCTOM1iHBOCTH).
82
"
i
't
I
I
1
CHCTeMa, nOTepSiBIllaSi YCTOH1.J:HBOCTb, MO>KeT BeCTH ce6R no-
pa3HOMY, HO nepexo.n; K HOBO MY nOJIO)KeHHIO paBHOBeCH
COnpOBO)l(-
):(aeTCSI 60JIbIllHMM nepeMe
eHMSIMM. KJIaCCHqeCKMM npMMepOM Heyc-
TOMQI1BOrO paBHOBeCI1S1 SlBJI5IeTCSI paBHOBeCMe rnapHKa Ha BblnYKJIOH
nOBepXHOCTI1 (PHC. 2.17, a). MaJIeHrnee OTKJIOHeHHe OT 3Toro nono-
)l(eHI1S1 npl1Be,n:eT K TOMY, QTO rnapl1K CKaTHTCSI BHI13 (pl1c. 2.17, 6, 6).
nonaB B BorHYTYIO nOBepXHOCTb, rnapl1K 6YJXeT HaXOJ1JITbCSI B COCTOSI-
HI1H YCTOH1.JHBOrO paBHOBeCHSI. ECJIH Tenepb ero BbIBeCTI1 113 3Toro
COCT05lHI1S1, OTKJIOHHB BJIeBO I1JII1 BnpaBO, OH BepHeTCSI B nepBOHa-
1.JaJIbHOe nOJIO)l(eHl1e.
JIBneHHe nOTepH YCTOH1.JHBOCTH MO)l(HO Ha6JIIO)].aTb ,l:(JISI ynpyrHx
TeJI Ha QeJIOM pR
e npMMepOB. HaH60JIee npOCTbIM CJIYQaeM RBJIReTCR
nOTepR YCTOHlJHBOCTH QeHTpaJIbHO C)I(aTOrO CTep)l(HSI (PHC. 2.18). TIpH
):(OCTaT01.JHO 60JIbrnOH CHJIe CTep)KeHb He CMO)l(eT coxpaHHTb npSlMO-
JIHHeMHYIO CPOPMY H H30rHeTCSI. npOH30M,l:(eT nOTepSl YCTOH1.JHBOCTH.
I
F IF
I
I
I
{()!i
6
8
PHC. 2.17
PHC. 2. 18
TOHKOCTeHHaSi TPy6a, HarpY)I(eHHaSi BHernHHM
aBJIeHHeM, TaK)I(e
MO)l(eT nOTepSlTb YCTOMlJHBOCTb. TIpH 3TOM KpyroBaSi <popMa CelJeHHSI
nepexo,nHT B 3JIJIHnTHQecKYIO, H Tpy6a cnnlO
HBaeTc}J.
BnepBbIe 3a.n;alJa 06 YCTOMQHBOCTH CTep)l(HR 6bIJIa nOCTaBJIeHa If
perneHa JI. 3MJIepOM B cepe,nHHe XVIII B. TI03TOMY, Kor,na pe1.Jb H
eT
06 YCTOM1.JHBOCTH C)I(aTOrO CTep)KHSI, ynOTpe6JISlIOT Bblpa)l(eHHe «YCTOM-
1.JHBOCTb CTep>KHSI no 3HJIepy». 3HJIep OnpelIeJIHJI 3Ha1.JeHHe nepBoM
KpHTH1.JeCKOM (3HnepoBoM) CHJIbI JXJISI npo.n;OJIbHO C)I(aTOrO CTep)l(HSI C
lllapHHpHbIM onHpaHMeM (PHC. 2.19):
n 2 EJ
FJ<p = 2
I
I
IIo ,nOCTH)I(eHMH KpHTHt.JecKoM CHJIbI
F Kp np}JMOJIHHeMHaSl <popMa paBHo-
BeCHSI CTaHOBHTCSI HeycTOM1.JI1BOM.
TIpo,nonbHo C)I(aTbIe CTep)l(HH He-
06XO
HMO npoBepSlTb Ha YCTOM1.J:H-
%
PUC. 2.19
83
2.9. PaCIIeT 6pyca lla COBMeCTHoe lIeHcTBHe KpYIJeHUH H u3ru6a
14. qTO TaKoe cMSlTMe? KaK onpel(eJISleTcSI HanpsDKeHHe npM CMSlTHH?
15. qTO TaKoe nOJISlpHbIM MOMeHT conpOTHBJIeHHSI?
16. KaKHe BHYTpeHHHe CHJIOBbIe <paKTopbI B03HHKalOT B nonepeq-
HOM CeqeHHH 6pyca npH ero H3rH6e?
17. qeM OTJIHqaeTCSI qHCTbIH H3rH6 OT nOnepeQHOro?
18. KaK onpel(eJISlIOTCSI 3HaKH H3rH6alOll.\HX MOMeHTOB H nonepeq-
HbIX cHn?
19. KaKHe HanpSDKeHI1S1 B03HMKalOT B nOnepe'IHOM CeqeHMM npM
H3rH6e?
20. qTO TaKoe YCTOHQHBOCTb?
21. ITo KaKoMY HanpSl)I(eHMIO Be,neTCSI paC'IeT 6pyca, Ha KOTOpbIH
l(eiicTBYIOT O)1HOBpeMeHHO M3rM6alOllI.HH H KPYTSlllI.HH MOMeHTbI?
22. KaKHe CTpoHTeJIbHble KOHCTpYKQHH MO)l(HO npM paCqeTaX npe,ll,-
CTaBHTb B BH,ne )J;ByxonopHoM 6aJIKH?
BOCTb. Oco6eHHo onaceH 3TOT BM,l]; ,lI,e<popMaQHM npM C)I{aTHI1 l(JIMH-
HbIX CTep)l(Hei1 C He6oJIbIlII1M oceBbIM MOMeHTOM MHepl\MH J.
,[(eTaJIH MallIHH OqeHb qaCTO pa6oTalOT npM COBMeCTHOM )J;eHCTBI1H
H3rM6alOll.\I1X 11 KPYTSlLQI1X MOMeHTOB (HanpHMep, BaJ1bI pe,nYKTopOB Ii
Kopo6oK CKopocTeii) QTo6bI MO)l{HO 6bIJIO cpaBHHTb ,lI,Ba CJIO)l(HbIX
HanpSI)I{eHHbIX COCTOSlHHSI, BBOl(HTCSI nOHSlTHe 3KBHBaJIeHTHOro Ha-
np.H)KeHI1S1.
3KBHBaJIeHTHOe HanpH*eHHe 0"3KB - 3TO TaKoe HanpH*eHHe, KOTopoe
cJleAyeT C03AaTb B pacTHHYTOM 06pa3Qe, QTo6bl ero HanpH*eHHoe co-
CTOHHHe 6blJlO paBHoonacHo C 3a)J.aHHbIM.
EcnH 3HaqeHMe 0"3KB HaHl(eHO, TO 3al(aqy 0 Mepe onaCHOCTH CJIO)l(-
Horo HanpSl)l(eHHOrO COCTOSlHHSI MO)l{HO C1.JHTaTb perneHHOH. K03<P<PH-
QHeHT 3anaca 11 = (JT/cr)KB.
TIpH COBMeCTHOM .n.eHCTBHM KpY1.JeHHSI H H3rH6a 3KBHBaJIeHTHOe
HanpSl)l(eHHe
,
0" 3KB = .J (J2 + 4't 2 =
( M li3r ) 2 + 4 ( MKP ) 2
w\: W p
KOll111pOJlbHbie 60llpOCbl U 3adaHUH
1. qeM OTJIM1.JaIOTCSI ynpyrHe l(ecpopMaQHH OT OCTaTOqHbIX?
2. PaCCKa)KHTe 0 MeTO,ll,e Ce1.JeHHH.
3. 3anMlllHTe 3aKOH rYK3 npM paCTSI)I(eHMH (C)I(aTMM).
4. qTO TaKoe OTHOCHTeJ1bHOe yn;JIMHeHMe?
5. KaKMe 3nlOpbI Heo6xo,ll,HMO nOCTpOHTb, qTo6bI BbInOJIHMTb pac-
qeT Ha np01.JHOCTb npM paCTSI)I(eHHH?
6. qTO o6I..Qero M B 1.JeM pa3JIM1.JHe y l(HarpaMMbI paCTSI)KeHHSI 06-
pa3Qa If MaTepHana?
7. qTO TaKoe npe,ll,en ynpyroCTH?
8. IlpHBel(HTe 0603Ha1.JeHHSI MO.n.YJISI ynpyrocTH I po,na H K03<P<PH-
QHeHTa TIyaccOHa.
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10. JJ:JISI qero BBOJJ;HTCSI nOHSlTHe l(OnYCKaeMoro HanpSl)KeHHSI?
11. KaKHe HanpSl)l(eHHSI B nOnepe1.JHOM CeqeHHH B03HHKalOT npH
KpyqeHHH o6pa3Qa?
12. 3anMllIHTe 3aKOH rYKa ,l.(JISI Cl(BHra.
13. YKa)KHTe 3aBHCHMOCTb Me)K.n.y Mo.n.YJIeM ynpyroCTH I po,na H MO-
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86
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TeJIbHO, Ha T01.JHOCTb KOOp.ll.HHaTHO-paCT01.JHOrO CTaHKa (T.e. MallIMHbI)
OKa3bIBaeT BJIMSIHHe )KeCTKOCTb Y3JIOB. KpoMe Toro, T01.JHOCTb M3MepM-
TeJIbHbIX H OTC1.JeTHbIX YCTpOHCTB 3Toro CTaHKa, npe,n;Ha3Ha1.JeHHbIX .lI.JISI
nepeMemeHMSI CTOJIa C M3.l1.eJIHeM OTHOCMTeJIbHO MHCTpYMeHTa, 6Y.lI. eT
OKa3bIBaTb 60JIbllIOe BJIMSIHHe Ha T01.JHOCTb 06pa60TKH. CJIe,[(OBaTeJIb-
HO, M 3TOT <paKTOp 6YJI.eT BJIHHTb Ha T01.JHOCTb CTaHKa.
HeT01.JHOCTb 06pa60TKH Ha CTaHKe MO)l(eT B03HHKHYTb B pe3YJIbTa-
Te TeMnepaTypHbIX ,[(ecpopMaQI1H Y3JIOB H ,neTaJIeH CTaHKa, a TaK)Ke
BCJIe,n;CTBHe CHH)I(eHHSI Ka1.JeCTBa 3y61.JaTbIX KOJIeC Ii XO,[(OBoro BHHTa,
KOTopoe BnHSIeT Ha T01.JHOCTb KHHeMaTM1.JeCKOH QenM CTaHKa. Oc06eH-
HO 3TO aKTyaJIbHO ,n;JISI 3y60pe3Hblx cTaHKoB, BHHTope3Hblx, 3y60- H
pe3b60llIJIH<poBaJIbHblx. KHHeMaTH1.JeCKaSl T01.JHOCTb B 3y60pe3HbIX
CTaHKax cymecTBeHHo 3aBHCHT OT T01.JHOCTH 113rOTOBJIeHHSI Ii MOHTa-
)l(a 1.JepBSIKa M 1.JepBSl1.JHOrO KOJIeCa B ,n:eJIMTeJIbHOH I..(enM.
llpH KOHCTpYHpoBaHMM .npyrl1x MallIl1H (aBTOM06MJIeH, CaMOJIeTOB,
no,n:'beMHbIX KpaHoB) ,n:OJI)I(Hbl 6bITb Y1.JTeHbI KOHKpeTHble cpaKTopbl,
KOTopbIe MorYT CHl1)1(aTb T01.JHOCTb npoeKTl1pyeMoH MalllHHbI.
)KecTKocTb. Kpl1Tepl1H )l(eCTKOCTH B MallIl1HaX SIBIIHeTCH O,n;HHM 113
Ba)l(HeHllIHX. Oc06eHHO 60IlbllIoe 3Ha1.JeHMe OH HMeeT B CTaHKOCTpoe-
HI1Ii. HanpMMep, npeI..(H3HOHHble CTaHKI1 npI1Xo,n;I1TCSI npOeKTl1pOBaTb
3Ha1.JHTeJIbHO 60Ilee MaCCI1BHbIMH, 1.JeM .lI.pyrHeMaIlIHHbI.l1I1S1 Tex )l(e
HarpY30K Ii MOll(HOCTeH.
)l{ecTKocTb CTaHKa BJIHSIeT Ha T01.JHOCTb o6pa6oTKH, BM6poYCTOH-
1.JI1BOCTb 11 ,n;OJIrOBe1.JHOCTb.
)KecTKocTblO Y3J1a Ha3blBaeTCH ero cnoco6HOCTb conpOTHBJlHTbCH
nOHBJleHHIO ynpyrHx OTiKaTHH noJ.( .neHCTBHeM HarpY3KH. aHa MO)l(eT
6bITb onpeJJ:eJIeHa KaK OTHOllleHHe CHIIbI F(H), npHJIO)KeHHOH K Y3I1Y B
3a.naHHOM HanpaBIIeHHH, K ynpyrOMY OT)I(aTHIO 3Toro Y3I1a B (MM):
j = F18.
M3HOCOCTOHKOCTb. B pe3YJIbTaTe nOCTeneHHoro H3MeHeHHH no-
BepXHOCTeH TpeHHSI npM B3aMMo.neHCTBMI1 .lI.BYX COnpH)I(eHHbIX ,n;eTa-
JIeH npOHCXO,lJ;MT H3HOC. H3HaIlIHBaHHe npe,nCTaBJIHeT C060H npo-
95
Qecc nOCTeneHHOrO YMeHbllIeHHSI pa3MepOB H cpOpMbI JJ;eTaJIeH. no
CTaTHCTHKe 60JIbllIHHCTBO JJ;eTaJIeM MallIHH BbIXOJJ;HT 113 CTpOSl H3-3a
H3Hoca. TIpH H3Hoce B MHHHaTlOpe npOHCXO)I;SlT Te >Ke pa3pYlleHHSI:
nnaCTHqeCKHe H ynpyrHe JJ;ecpopMaQHH, C,lJ,BHr, YCTanOCTHbIe pa3py-
rneHHSI.
)J:JISI 60JIbllHHCTBa )I;eTarreH HaH60JIee xapaKTepeH a6pa3HBHbIH
H3HOC. A6pa3HBHble qaCTHubI MorYT nOna)I;aTb H3BHe B CMa3KY HJIH
HenOCpe,lJ,CTBeHHO Ha TpYI.QHecSI nOBepXHOCTI1; 3a CqeT pe3aHI1S1 HJIM
QapanaHHSI C OTJJ;eJICHHeM MHKPOCTPY>KKH OHH pa3pYllialOT 3TH no-
BepXHOCTH. KpOMe Toro, npH OTHOCHTeJIbHOM nepeMell\eHHH ,nBYX
nOBepXHOCTeH MHKpOBbIcTynbI I1CnbITbIBalOT nepeMeHHbIe HanpSl)f(e-
HHSI, BCJIe,nCTBHe qero B ,n;aJIbHCHllIeM HacTynaeT YCTaJIOCTHOe pa3py-
rneHMe. nOSlBJISlIOTCSI MHKpOTpe
HHbI, qTO cnoc06cTByeT OT)].CJIeHHIO
qaCTHqeK MaTepHaJIa. TaKHM 06pa30M, H3HOC npH nepeMeIl{eHHH .D.BYX
nOBepXHOCTeH conpOBO)J{,AaeTCR a6pa3HBHbIM H3HOCOM 3a ClIeT OT,Ae-
JIHBllMXCSI qaCTHQ.
B 60nbllIHHCTBe cnyqaeB MO)f(HO Ha6nlO,n;aTb TPH CTa,n;MM H3Hoca
(PHC. 3.4): I - nCpHO,A npHpa60TKH; II - YCTaHoBHBIlIHHCR (HJIH HOp-
MaJIbHbIH) H3HOC; III - KaTacTpocpHqeCKHH H3HOC.
II
t
JISI KOHKpeTHbIx nap MO>KHO 3KcnepHMeHTaJIbHO onpe)I;eJIHTb KO-
3<p<PHQHeHT k H B )I;aJIbHeHlleM nporH03HpoBaTb )I;OJIrOBeqHOCTb pa60-
TbI MHorHX ,neTaJIeH: HanpaBJISlIOIl{HX CKOJIb>KCHHSI CTaHKOB, KYJIHCHbIX
MexaHH3MOB, ,nHCKOB CPpHKQHOHHbIX MYCPT, XO,nOBbIX BHHTOB 11 raeK
CKOJIb)J{eHHR.
113Hoc BbI3bIBaeT pe3Koc y,nopO>KaHMe 3KCnJIyaTaI..{MH MallMH B CBSI3H
C Heo6xollJiMOCTblO nepHo)J.HqeCKOH npOBepKI1 HX TeXHMqeCKOrO co-
CTOSlHMSI, a TaK)I(C pCMoHTa. 3To, B CBOIO 01JCpCJIb, CBSl3aHO C npocToSlMH
H CHH)I(CHMCM npoH3Bo,nHTeJIbHOCTH MallI1H.
CYI.QCCTBYIOT CJIC)I;YIO
l1e MCpOnpl1S1TMSI no nOBbIllCHl11O M3HOCO-
CTOHKOCTI1: CMa3Ka TPY
I1XCSI nOBcpxHOCTCH; npHMCHCHI1C 113HOCO-
CTOHKMX MaTCpl1aJIOB; 3a
MTa nOBcpxHOCTCH OT 3arpSl3HeHI1S1; ncpcHoc
YCI1JIHH C OTBeTCTBCHHbIX MexaHH3MOB Ha MCHee OTBCTCTBeHHbIe (Ha-
npHMcp, 06TaqHBaHMe HapY>KHOH nOBepxHocTM Ha TOKapHoM CTaHKe
npoH3Bo,nRT npM BKJIlOlIeHHOM XO,nOBOM Barre, a XO,nOBOH BHHT OTKnlO-
qaIOT); BBe)I;CHHC pa3rpY3KH H3HallIHBaCMbIX nOBcpxHOCTci1 H )I;p.
CTOHKOCTb K TenJ10Bb1M B03AeHCTBHHM. Pa60Ta MallIHHbI conpOBO-
)l(I(aCTCSI TCnJIOBbI.D.CJICHMCM, BbI3bIBaCMbIM pa60qHM npOQCCCOM MalllHH
H TpeHHCM B MX
tCXaHH3Max. TCnJIOBbIJICJICHHC, CBSl3aHHoe C pa60qH
npOI..{eCCOM, SlBJISIeTCR oco6eHHO MHTeHCHBHbIM Y TenJIOBbIX JIBl1raT:JICI1,
3neKTpHqeCKHX MaIlIHH, nMTeMHbIX MallIMH H MaruHH AJISI rOpSlqeM 06-
pa60TKI1 MaTCpl1aJIOB.
B pC3ynbTaTc TCnJIOBOrO B03)I;CHCTBHSI B03HI1KalOT TeMncpaTypHble
)I;ecpopMaQMI1, KOTopbIe MorYT oTpMQaTCJIbHO BJIHSlTb Ha pa6oTocno-
C06HOCTb MalllMH, a HMCHHO:
nOHM)I(aTb 3all\MTHYIO cnoc06HoCTb MaCJISlHOrO cnoSl B TpYIl{HXCSI
nOBcpxHOCTSlX 11, CnC)I;OBaTeJIbHO, BbI3bIBaTb nOBbIlllcHHbIH 113HOC HJIH
3ae,naHMe;
M3MCHSlTb 3a30pbI B no,nBM)I(HbIX COe)I;HHeHHSlX;
nOHH)I(aTb TOqHOCTb MaruHH (HanpHMep, B MCTaJIJIOpC>KYIl{HX CTaH-
Kax B pC3ynbTaTc HarpcBa nepe)I;HeH onopbI llInMH)I;enSI MO>KCT npo-
H30HTM OTKJIOHCHMe ero OCH, 1JTO npHBe)I;eT K CHH)I(eHMIO TOqHOCTH
o6pa6oTKH).
PaCqCT TeMncpaTypHbIX .necpopMaUMH Y3JIOB MallIMH MO)l(eT npoH3-
BO)I;HTbCSI, ecnH M3BeCTHbI TeMncpaTypHbIe nOJISI B ,nCTaJISlX MallIHHbI.
npH 3KCnJIyaTaI..{HM MeTaJIJIOpe>KY
Mx cTaHKoB, KOHTpOJIbHO-H3Me-
pHTenbHbIx MalllHH H ,n;pyroro npcQH3MoHHoro 060pYJ10BaHHSI npH-
MCHSIIOT CJIC,nYIOIl{HC MCTO,nbI 60pb6bI C TCMncpaTypHbIMI1 ,n;C<popMa-
I..(HSlMM:
BbIHOC MexaHH3MOB C TCnJIOBbI,lJ,enCHHCM 3a npe)I;CJIbI TCXHOJIOrHqe-
CKoro o6opy,nOBaHHSI (HanpHMCp, rH)I;pOCTaHQMH M rH)I;pOCHCTCM);
I1CnOJIb30BaHHe CMa30qHO-OXna)l()I;aIOI.QCH )I(H,nKOCTM (CO)l() B 30-
He pC3aHHSI MCTaJIJIOpe)l(YIl{HX CTaHKOB;
npHHYJJ;HTeJIbHOe OXJIa)f(JJ;eHHe Y3nOB;
:1
Co
U
U max
PliC. 3.4
[lCPMOJJ. HopManbHOM 3l<CnnyaTal.J.MM MaWMH (II CTa,nMSI H3Hoca)
xapaKTcpM3YCTCSI JIHHCHHOH 3aBMCHMOCTblO Me)I(,ny BpCMCHCM H3Ha-
lllHBaHHSI t H BCJIH1.fHHOH H3Hoca U (MKM). CKOpOCTb H3HalliMBaHMR Y B
3TOH CTa)I;HM OCTaeTCSI nOCTOSlHHOH: y = U / t. [(JISI a6pa3HBHoro M
YCTanOCTHoro H3Hoca BenHqHHY 113HOCa MO)f(HO onpe.neJIMTb no cne-
,lJ,YlOl.QeH 3aBMCHMOCTH:
U = kpVOTHt,
r,lJ,C k - K03<P<P M l.J.HCHT, 3aBMCSlI.QHH OT MaTepHana nap TpeHMSI, CMa3-
KI1, MI1KpOHepoBHocTei1 11 ,npyrl1x cpaKTopoB; p - y,neJIbHOe ,naBJICHl1e;
V OTH - CKOpOCTb OTHOCHTcnbHoro CKOJIb)f(eHHSI.
I1CKJIlOlIl1B BpeMR t, nOJIY1.fI1M
y = kpV OTH .
96
4 J1. H. BepeHH3
97
C03,n;aHMe TepMOKOHCTaHTHbIX QeXOB, B KOTOpbIX nOMep)l(MBaeTCS!
nOCTOSlHHaS! TeMnepaTypa;
BbIpaBHMBaHMe TeMnepaTypHoro nonS! nYTeM MCKYCCTBeHHoro no-
,n;orpeBa MnM OXna)l(lIeHMSI OT)1enbHbIX Y3nOB;
aBTOMaTHQeCKaSI KOMneHca:QMSI TeMnepaTypHbIX ,n;ecpopMa:QMH - npM-
MeHeHMe KoppeKQMOHHbIX nHHeeK, Hcnonb30BaHMe npe,n;bICKa)l(eHMSI
nporpaMMbI B CTaHKax C qIIY.
BH6poYCTOH
HBOCTb. IIo,n BM6poYCTOMqMBOCTblO nOHMMalOT cno-
C06HOCTb KOHCTpYKQHM pa60TaTb B 3aJ,(aHHoM ,AMana30He 6e3 He,AOny-
CTMMbIX Kone6aHMM. B CBSl3M C YBenMqeHMeM CKopOCTeH MaIllHH Kone-
6aHI1S1 CTaHOBSlTCSI Bce 60nee onaCHbIMM. EcnH qaCTOTa co6CTBeHHbIX
Kone6aHMM Y3nOB MaIllMHbI COBna,neT C qaCTOTOH BbIHY)l()J.eHHbIX Kone-
6aHMM, HacTynHT pe30HaHC. 3TO caMoe onaCHoe COCTOSlHMe MarnMHbI B
QenOM, TaK KaK MO)l(eT npOM30MTM pa3pYIlleHHe. BI16paQMM TaK)I(e
He)l(enaTenbHbI. B MeTannOpe)l(Yll{eM CTaHKe, HanpMMep, BM6paUMM
YXYlIIllalOT o6pa6aTbIBaeMYIO nOBepXHOCTb, YMeHbIllalOT ,nonrOBeq-
HOCTb CTaHKa, OrpaHI11.JMBaIOT ero TeXHOnOrH1.JeCKHe B03MO)l(HOCTI1.
OCHOBHoe pacnpOCTpaHeHMe B MaIllHHax MMelOT BbIHY)I(,AeHHbIe, napa-
MeTpH1.JeCKHe KOJIe6aHHSI 11 aBTOKOne6aHI1S1.
BblllY:JI-Cdellllble KOfle6allUR B03HMKalOT no,n )1eMCTBMeM BHeIllHeH ne-
pHo,nH1.JeCKI1 H3MeHSllOll
eHCSI CHJIbI no CJIe,nYIOI..QHM npH1.JHHaM:
,AI1C6anaHc BparQalOrQHXCSI ,neTaneM (pOTopa 3neKTpo,nBMraTenSl,
Illnl1H,AenSl C paCT01.JHbIM pe3QOM);
OIllH6Ka B 3y6qaTbIX nepe,Aa1.Jax (BXO,A B 3aL(enneHMe 6Y,AeT conpo-
BO)l(,n;aTbCSI y,n;apOM);
HanM1.Jl1e npepbIBHCTOH Cl1nbI pe3aHHSI npH cppe3epOBaHHH, lI-oJI6-
neHMM, 3aTbIJIOBaHMM, npOTSlrMBaHMM;
HaJIH1.Jl1e BHellIHI1X I1CT01.JHHKOB Kone6aHHM.
IIapaA-tempullecKue KOJle6allUR B03HHKalOT npM HanHqHM KaKoro-
nM60 nepeMeHHoro napaMeTpa, HanpMMep MOMeHTa MHepUMM none-
peqHOrO CeqeHMSI. IIpe,nnono)l(MM, 1.JTO Ha Bpall{alOll.{MHCSI Ban ,n;eHCT-
ByeT nOCTOSlHHaSI CMna. EcnM nOnepeqHOe CeqeHMe Bana - OKPY)I(-
HOCTb, Y KOTOpOM MOMeHTbI MHepQHH OTHOCHTenbHO Bcex oceM O,n;M-
HaKOBbIe, TO HMKaKMX KoneGaHHM He B03HMKaeT. EcnM )l(e nonepeq-
Hoe Ce1.JeHMe - npSIMoyrOJIbHMK, TO Ban no,n ,neHCTBMeM nOCTOSlHHOM
CMnbI 6y,n;eT nporM6aTbC}J no-pa3HOMY, TaK KaK MOMeHThI MHepQMH Y
npSIMoyrOJIbHMKa OTHOCHTenbHO B3aMMHO nepneH,nMKYJISIpHbIX oceM
pa3nHqHbI.
A6mOKOJle6aflUR, MnM He3aTyxalOrQHe caMOnOMep)l(HBalOrQMe KO-
ne6aHMSI, xapaKTepM3YlOTCSI TeM, 1.JTO B03MYrQalOll\Me CHJIbI B03HMKalOT
B caMOM npOL(eCce Kone6aHI1S1. fIpM aBTOKone6aTenbHOM npoQecce B
cnY1.Jae npeKpaI..QeHMSI Kone6aHMH CMCTeMbI nepeCTalOT cymecTBoBaTb
H nepeMeHHbIe CHnbI, no,n;,n;ep)J(HBalOI.l(He 3TH KOJIe6aHHSI. IIpHMepOM
MorYT cnY)l(MTb aBTOKone6aHMSI npM TpeHMM (cppMKL(MOHHbIe Kone6a-
98
HMSI npM Me,n;neHHOM nepeMell\eHMM CTonOB, cynnopToB CTaHKa no
HanpaBnSIIOll\MM CKOJIb)l(eHHSI). fIpMqMHOM 3TMX Kone6aHMM SlBnSIeTCSI
nepeMeHHocTb CMnbI TpeHMSI B 3aBMCMMOCTM OT M3MeHeHMSI CKopocTeM.
}J.pyrMM npMMepoM aBToKone6aHMM HBnSlIOTCSI caMoBo36Y)I(,n;alOll\MeCSI
Kone6aHHSI B MeTaJIJIOpe)J(YI.l(HX CTaHKax npH pe3aHMM.
IIoBbIIlleHl1e )l(eCTKOCTI1 Y3JIOB MaIllHHhI 6Y,AeT cnoc06cTBoBaTb
CHM)I(eHHIO aBToKOne6aHI1M. HanM1.JMe Kone6aHMM B MaIllMHe qall\e
Bcero cOnpOBO)l(.[{aeTcSI rnYMoM. lllYM CBSI3aH C coy.napeHMeM ,[{BM)I(Y-
ll\HXCSI ,n;eTaneM MaIlII1H. HanpMMep, norpelllHocTM lllara H npocpMnSI
3y6beB 3y61.JaTbIX Konee npMBO,ASlT K coy,napeHHIO npM Bxo,n;e B 3aL(en-
neHHe. IIoBbIIlleHHbIH ypoBeHb lllYMa nOBbIIllaeT YToMnSleMocTb nep-
COHana 11, cne,nOBaTenbHO, Bpe,neH ,l(nSI 3,nOpOBbSI. YpOBeHb IllYMa
M3MepSIeTCSI B ,n;eQM6enax (JJ;E), ero npe,AeJIbHOe 3Ha1.JeHl1e OrpaHM1.JI1-
BaeTCSI CaHI1TapHbIMM HopMaMH.
OCHOBHble MepbI 60pb6bI C IllYMOM: nOBbIllIeHMe T01.JHOCTM M 1.JMC-
TOTbl 06pa6oTKI1, YMeHbIlleHl1e CHJIbI y,n;apa KOHCTpYKTMBHbIMM MeTO-
,n;aMH, npMMeHeHMe ,n;eMncpepOB M MaTepManOB C nOBbIllIeHHbIM BHYT-
peHHMM TpeHMeM.
H3!l.e
HOCTb. IIp06neMa Ha,n;e)J(HoCTM SIBnSleTCSI O,n;HOM M3 OCHOBHbIX
np06neM B MaIllMHocTpoeHMM. CBoiicTBO H3J.J.eJIHH coxpaHHTb CBOIO
pa60Tocnoco6HOCTb B Te
eHHe 33J(aHHoro npoMe
yrKa BpeMeHH, o6yc-
JIOBJIeHHOe 6e30TKa3HOCTbIO H AOJIrOBe
HOCTblO H3AeJiHii, Ha3blBaeTCH
HaAe
HOCTblO.
113BeCTHbIM aBMaKOHCTpYKTOP A. H. TynoneB rOBopMn: «qeM ,Aanb-
Ille OT JJ;OCKM KOHCTpYKTopa 06HapY)J(MBaeTCSI HeHa,[(e)l(HOCTb, TeM
OHa ,n;opo)l(e 06XO,[(MTCSI». HeHa,n;e)l(HaSl MalllMHa He CMO)l(eT 3cpcpeK-
TI1BHO cpYHKQI10HMpOBaTb, TaK KaK Ka)l(,[(aSI ee OCTaHOBKa M3-3a no-
Bpe)l(,n;eHMSI OT,n;enbHbIX 3neMeHTOB MnM CHM)I(eHMSI TeXHM1.JeCKMX
xapaKTepMCTMK HM)Ke ,nonYCTMMoro ypOBHSI Bne1.JeT 3a C060M MaTe-
pManbHbIe y6bITKM, a B oT,[(enbHbIx cnyqaSlx M KaTaCTpocpM1.JeCKMe
nOCJIe,nCTBHSI .
113-3a He,nocTaT01.JHOH Ha,[(e)l(HOCTH npoMbIlllneHHocTb HeceT or-
pOMHbIe nOTepH. TaK, 3a BeCb nepMo,n; 3KcnnyaTaQMM 3 aTpaTbI Ha
peMOHT H TeXHM1.JeCKOe 06cnY)KHBaHMe MalllMH B CBSl3M C MX M3HOCOM B
HeCKonbKO pa3 npeBbIIllalOT CTOMMOCTb HOBOH MaIlIMHbI: ,nnSl aBTOMO-
6MneH - 110 6 pa3, ,[(nSl caMoneTOB - 110 5, J{nSl CTaHKOB - J{O 8, J{nSl
pa,n;MoTeXHM1.JeCKOM annapaTypbI -,lI0 12 pa3. 113-3a KOpp03HM e)l{e-
ro,n;HO TepSleTcSI,no 100/0 BbInnaBnSIeMoro MeTaJIna.
Ha,n;e:>KHOCTb 3 a K n a,n; bI B a e T C SI npM npoeKTHpOBaHMM 11 paC1.Je-
Te MaIllMHbI. OpM M3rOTOBJIeHMI1 Mall1HHbI 0 6 e C n e 1.J M B a e T C SI Ha-
,ne)l{HOCTb; OHa 3aBHCHT OT KaqeCTBa H3rOTOBneHHbIX ,neTaJIeH, Kaqe-
CTBa C60PKM Y3JIOB MallIMHbl, MeTo,n;OB KOHTpOJISI If McnbITaHMSI rOTO-
BOM npo,nYKQMM M ,n;PyrHx nOKa3aTeneM TeXHOJIOrMqeCKOrO npoQecca
IlpH 3KcnnyaTaQHM MaIllI1HbI pea JI H 3 yeT C SI ee Ha,ne)l(HOCTb.
,
I
99
nOKa3aTeJIM 6e30TKa3HOCTM H .n;OJIrOBeqHOCTH npOSIBJISIIOTCSJ TOJIb-
KO npM 3KCnJIyaTaQMH, 3aBHCSIT OT YCJIOBMM MCnOJIb30BaHMSI MalIIMHbI,
CMCTeMbI ee peMOHTa M TeXHMqeCKOrO 06CJIYJKMBaHHR.
Ee30mKa31l0Cnlb - 3TO CBOHCTBO M3,neJIMSI HenpepblBHO COXpaHRTb
CBOIO pa60TOCnoc06HOCTb B TeqeHMe 3a,naHHOrO nepMO,na BpeMeHI1. B
3TO nOHRTMe He BKJIIOqaeTCR TeXHMqeCKOe 06cnYJKMBaHMe, peMOHT,
no,nHaJIa,nKa. H3,neJIl1e ,nOJIJKHO coxpaHRTb CBOM HaqaJIbHble napaMeT-
pbI B )].onYCTMMbIX npe,[(eJIax.
01l206el/,1l0Cmb - CBOMCTBO H3,[(eJIMR coxpaHSITb CBOIO pa60Tocno-
C06HOCTb B TeqeHMe Bcero nepMo.na 3KCnJIyaTaQMH .no npe,nenbHoro
COCTOSIHHR. 3,neCb yqHTbIBaIOTCR Bce peMOHTbI, no.nHana.nKM.
IIoJIHaH HJIH "IaCTH"IHaH YTpaTa pa60Tocnoco6HOCTH H3.aeJIHH Ha3bl-
BaeTCH OTKa30M. TIo CBoeM npHpo.n:e OTKa3bI MorYT 6blTb CBR3aHbI C
pa3pYlIIeHMeM nOBepXHOCTeH MJIH caMMX ,[(eTaJIeM (BbIKpalilMBaHHe,
H3HOC, KOPP03M}!, nOJIOMKM) MJIM He CBR3aHbI C pa3pYlIIeHMeM (ocJIa6-
JIeHMe npe,lU3apHTeJIbHOrO HaTSIra no,nlIIMnHMKOB, 3acopeHMe KaHaJIOB).
OTKa3bI 6bIBalOT nonHble MnM qaCTMqHble, BHe3anHble (nonOMKM) HJIH
nOCTeneHHbIe (M3HalilMBaHHe, KOpp03MR), onaCHbIe ,lUISI )l(M3HM qenOBeKa
HJIM HeT, YCTpaHMMbIe H HeYCTpaHHMbIe.
TIoKa3aTenM 6e30TKa3HOCTM M ,[(OJIrOBeqHOCTH M3,[(eJIMSJ onpe,[(eJISI-
IOTCR B COOTBeTCTBMI1 C TeopMeM BepORTHOCTM. BepORTHOCTb 6e30T-
Ka3HOM pa60TbI P(t) B TeqeHMe 3a,naHHoro BpeMeHM t (HnH 3a,naHHOH
Hapa60TKM) H BepORTHOCTb OTKa3a F(t) - B3aMMHO npOTHBOnOJIOJK-
HbIe C06bITHR. Hx CYMMa Bcer.na paBHa e,n:MHML(e. BepORTHOCTb 6e30T-
Ka3HOM pa60TbJ Haxo,n:HTCR B npe,n:enax 0 < P( t) < 1. HanpHMep, 3a
BpeMR t = 100 1I BepoRTHoCTb 6e30TKa3HoH pa60ThI COCTaBnReT P(t) =
= 0,99. 3TO cne,n:yeT nOHMMaTb TaK: 3a YKa3aHHoe BpeMR pa60TbI 113-
.neJIMSI BepOSITHOCTb OTKa3a COCTaBHT 1 0/0, T. e. F(t) = 0,01.
OCHOBHbIM nOKa3aTeJIeM ,[(onrOBeqHOCTM 3neMeHTa H3,[(eJIHR SIBJISI-
eTCSI CpOK cllY:JIC6bl (1lapa6omKa) t ,[(0 OTKa3a.
npM oueHKe Ha,n:e)l(HOCTM M3,l1.eJIHR 01IeHh Ba)l(HbI 3KOHOMMQeCKMe
nOKa3aTeJII1. lloBbIlIIeHHe 6e30TKa3HocTM M ,n:OJIrOBeqHOCTM MalIIMH
CBSI3aHO C ,[(onOJIHMTeJIbHbIMM MaTepHaJIbHbIMH 3aTpaTaMH.
3.3. MamHHocTpOHTeJIbHbIe MaTepHaJIbl
)::(eTanM MallIl1H Qpe3BbIQaHHO pa3Ho06pa3HbI, n03TOMY JJ:JIR HX M3-
rOTOBJIeHMSI He06xo.nHMbI MaTepMaJibI C pa3JIHqHbIMH CBOHCTBaMM.
Pa3JIMqalOT KOHCTPYKQHOHHble MaTepMaJIbI, KOTopbIe HCnOJIb3YlOT
,[(JISI H3rOTOBJIeHHR JJ:eTaneM MalIIMH, H HHCTpYMeHTaJIbHble MaTepHaJIbI,
H3 KOTOpbIX nonYQalOT peJKYII(He MHCTpYMeHTbI.
OpH M3rOTOBneHMM M3.nenMH H3 KOHCTpYKQHOHHbIX MaTepMaJIOB
OJJ:HM JJ:eTaJIM .n;onJKHbI o6na.naTb nOBbIlIIeHHOH KOpp03HHHOH CTOHKO-
100
,
,
CThlO, ,[(PyrMe - MMeTb CBepxnpOBO,l(MMOCTb, TpeTbM - 06JIa,L(aTb OC06hI-
MM MarHHTHbIMH CBOMCTBaMH.
B KalIeCTBe KOHCTpYKQMOHHbIX MaTepMaJIOB HCnOJIb3YlOT pa3nHlI-
HbIe MeTaJIJIbI (aJIIOMHHHH, JKene30, Me,l(b, THTaH), CnJIaBbI MeTaJInOB
(JKene30yrnepo.nMcTbIe - qyrYH, CTanb; MarHMeBbIe; Me,[(HOQMHKOBhIe -
naTYHH; Me,nHoonOBRHHbIe - 6pOH3bI; CnnaBhJ aJIIOMHHHSI M ,np.), He-
MeTanJIbI (nnacTMaccbl, J(peBeCI1HY, TeKCTonHTbI, CTeKJIOTeKCTonHTbI)
H KOMn03HQHOHHbIe MaTepMaJIbI.
KOMn03ul1U01l1lble MamepUa.Jlbl SIBJISIIOTCSI HOBbIMM KOHCTPYKQHOH-
HbIMH MaTepHaJIaMM. JI:JIR HX nonyqeHMSI B OCHOBHOH MaTepHan ,[(0-
6aBJISIIOT HanOJIHHTeJIH, KOTopbIe M onpe.nenSIIOT CBOHCTBa KOMn03H-
L(HOHHOro MaTepMaJIa. Pa3MepbI BXO,n:RI.l(I1X KOMnOHeHTOB Kone6nIOT-
CR OT J(oneH MHKpOMeTpa (,anSI nopOlllKOBbIX HanOnHHTeJIeH) ,l(O He-
CKonbKHX MMnJIMMeTpOB (y BOJIOKHHCTbIX HanOnHHTeJIei1).
ITopolilKoBaSI MeTaJIJIyprHSI n03B0J1SIeT nOJ1yqaTb KOMn03Hl{HOH-
HbIe MaTepHanbI, xapaKTepH3YIOID-HeCSI JKapOnpOQHOCTblO H M3HOCO-
CTOHKOCTbIO, cTa6MnbHbIMM MarHMTHbIMH H J(pyrMMM CBOHCTBaMH.
OOpoliKoBaSI MeTaJInyprHSI ,[(aeT B03MOJKHOCTb nonYQaTb nceB,[(O-
CnnaBbJ H3 TaKMX HecnnaBnSIIOlI(MXCSI MeTaJIJ10B, KaK MeJ(b-Bonb<ppaM,
cepe6po- B0J1b <ppaM, KOTopbIe 06J1a,[(aIOT BbICOKOi1 3neKTpHQeCKOM npo-
BO,n:MMOCTbIO Ii CTOHKOCThlO K 3neKTp03p03MOHHOMY M3HalliMBaHHIO;
113 HMX M3rOTaBJIMBalOT 3neKTpOKOHTaKTHbIe ,n:eTanH.
KOMn03HQHOHHble MaTepHanbI Ha OCHOBe nnaCTMacc xapaKTepM-
3YlOTCSI BblCOKOM XHMMQeCKOM M KOpp03110HHOM CTOMKOCTblO. OHH C
ycnexoM 3aMeHSIIOT J(oporOCTOSIID-Me QBeTHbIe MeTannbI.
KOMn03MUMOHHbIe MaTepManbl Ha OCHOBe pe3MHbl CYlI(eCTBeHHO
OTnMQalOTCSI OT MeTannOB. OHM xapaKTepH3YlOTCSI cnoc06HOCTblO
BbI,[(epJKHBaTb 3HaQMTeJIbHhIe lle<popMalJ.HH 6e3 pa3pYlIIeHHSI, BbICOKOM
conpOTMBnSIeMOCTblO K H3HalIIHBaHI1IO, ra30- H Bo.n:OHenpOHMl{aeMO-
CTblO, ,nH3neKTpHQeCKMMH CBOMCTBaMM.
CTeKno, KepaMMlIeCKMe, ,n:peBeCHhIe 11 .n:pyrMe HeMeTaJIJII1QeCI<Me Ma-
TepManbI MMelOT CBOM CneQH<pMqeCKHe <pM3HKO-MeXaHHQeCKHe M 3KC-
nJIyaTaQHOHHbIe CBOMCTBa.
Oco6oe MeCTO B KOMn03MQHOHHbIX MaTepHaJiaX 3aHMMalOT BonOK-
HMCThIe MaTepManbI. B KaqeCTBe BOJIOKHMCTbIX HanOJIHHTeneH HC-
nOJIb3YlOT npOBOJIOKH 113 BOJIb<ppaMa, MOJIM6,[(eHa, BOJIOKHa OKCH,[(OB
aJIIOMHHMSI, 60pa, Kap6H,[(a KpeMHHSI, rpa<p HTa .
BhI60p TMna KOHCTpYKQMOHHoro MaTepMana 3aBHCHT OT <pM3MKO-
MeXaHMQeCKHX M 3KCnJIyaTal{HOHHbIX CBOMCTB, Ha KOTophle BJIHSleT
TeXHOJIOrMQeCKHM npoQecc nonYQeHHR KaK caMMX MaTepManOB, TaK M
)leTaneM M3 HMX.
Pa3nMqHhle <pOpMhI JJ.eTaJIeM MaliMH H3 3arOTOBOK nonYQaIOT npM
nOMOW:M peJKYW:HX HHCTpYMeHTOB. Pe)l(YIIJ.Me MHCTpYMeHTbI pa60TaIOT
B ycnoBMSlX 60JIbliHX HarpY30K, BblCOKHX TeMnepaTYP, TpeHHSI M H3-
!
,
t
I
101
Hoca. TI03TOMY HHCTpYMeHTanbHbIe MaTepHanbI .nOn>KHbI HMeTb OCO-
6bIe 3KCnnY
TaQHOHHbIe 11 <pH3HKO-MeXaHHqeCKl1e CBOHCTBa. MaTepH-
an pe)l(y
eH qaCTH HHCTpYMeHTa .nOn)KeH HMeTb 60nblIlYIO TBep.nOCTb
H BbICOKHe .nOnYCKaeMbIe HanpR>KeHHR Ha paCTR>KeHHe, C>KaTHe, KPY-
qeHHe I1H3r
6. KpoMe TOrO, pe)l(Y
HH HHCTpYMeHT .nOn)l(eH 06na.naTb
J(OCTaTOqHOH BR3KOCTblO, qT06bI BOCnpHHHMaTb y.napHYIO HarpY3KY
npH 06pa60TKe 3arOTOBOK H3 xpynKHx MaTepHaJIOB H C npepbIBHCTOM
nOBepXHOCTblO pe3aHHR. Pe)KY
HH HHCTpYMeHT .nOn)KeH COXpaHSlTb
CBOIO TBep.nOCTb, a TaK)Ke pe)J(YIl{He CBOHCTBa npH BbICOKHX TeMnepa-
Typax, n03TOMY HHCTpYMeHTaJIbHbIe MaTepHaJIbI .non)J(HbI HMeTb BbI-
COKYIO TennOCTOHKOCTb.
Ba)f(HeHIlleH
apaKTepHCTHKOH pe)J(y
eH qaCTM HHCTpYMeHTa RBnR-
eTC}I 113HOCOCTOHKOCTb. B 3TOM cnyqae .neTaJIH, 06pa60TaHHbIe O.nHHM
H TeM )Ke HHCTpYMeHTOM, 6y-nYT HMeTb MHHHManbHbIH pa36poc Pa3-
MepOB. B QenRX nOBbIlIleHHR H3HOCOCTOMKOCTH Ha pe)KYIl{YIO qaCTb
HHCTpYMeHTa HaHOCRT Cnel.{HaJIbHbIMH MeTO)IaMH O-nHO- H MHorocnOH-
HbIe nOKpbITHR H3 Kap6HJJ.OB Bonb<ppaMa HJIH HHTpH-nOB TI1TaHa.
B KaqeCTBe HHCTpYMeHTaJIbHbIX MaTepHanOB Hcnonb3YlOT HHCTpy-
MeHTaJIbHbIe CTaJIH, TBep-nbIe cnnaBbI, CHHTeTHqeCKHe CBepXTBep.nbIe H
KepaMHqeCKHe HHCTpYMeHTaJIbHbIe MaTepHaJIbI, a6pa3HBHbIe MaTe-
pl1anbI.
K HHCTpYMeHTanbHbIM CTanRM OTHOCRTCR:
- y r n e p 0 -n H C T bI e H H C T P Y M e H T a JI b H bI e C T a JI H C co-nep-
)f(aHHeM yrJIepo.na 1...1,30/0; npHMeHRIOT MapKM YI0A, YI lA, YI2A.
,[(onycTHMhIe CKOpOCTM pe3aHM
3THX CTaneH - 15... 18 M / MHH. 113
3THX CTaJIeM H3rOTOBnRIOT MeTqHKH, nnaIllKH, HO)l(OBOqHhIe nonOTHa,
CBepJIa, 3eHKephI MaJIbIX pa3MepOB;
- JI e r H p 0 B a H H bI e H H C T P Y M e H T a JI b H hI e C T a JI H; If X no-
JIyqalOT Ha OCHOBe HHCTpYMeHTanhHhIX CTaneH C -n06aBneHHeM xpOMa
Bonh<ppa
la, BaHa.nHSI, KpeMHH
11 .npyrHx nerHpYlOlUHX JJ.06aBOK
JIerHpoBaHHhIe CTanH no cpaBHeHl110 C yrJIepO,[(HCThIMH HMelOT no-
BhIIlleHHYIO BR3KOCTh B 3aKarreHHOM COCTORHI1H, 60nee BhICOKYIO npo-
KaJIHBaeMOCTb, MeHbllIYIO CKJIOHHOCTb K nORBJIeHHIO TpeIl{HH npH
3aKaJIKe. .D:onYCTHMaR CKOpOCTb pe3aHI1R - 15...25 M/MI1H. npHMeHR-
IOTCR ,n;nR H3rOTOBneHHR npOTR)I(eK, CBepn, MeTqI1KOB, nnaIlleK, pa3Bep-
TOK (MapKH 9XBr, XBr, 6XC H ,n;p.);
- 6 hI C T pop e )I( y
11 e C Tan 11; OHM co.nep)l(aT Bonb<ppaMa .no
190/0, n03ToMY nocne TepMo06pa60TKH ,[(0 TBep.nOCTI1 HRC 3 62...65
HMelOT TennOCTOMKOCTb 600...650 °C. .D:nR 113rOTOBneHMR pe)l(YlQl1X
HHcTpYMeHToB HCnOJIb3YlOT CTanH P9, P12, PI8 - pe3QbI, <ppe3hI,
-nOJI6RKH. bbICTpOpe)l(YlQl1e CTanH C -no6aBneHl1eM K06anbTa (P9K5
P18KIO) npH
emnoT )1,ml o6pa6oTKH TpY.D.Hoo6pa6aTbIBaeMblx KOP
p03HOHHO-CT0I1KHX 11 )l(apOnpOqHbIX CTaneM H cnnaBOB B ycnoBI1RX
TR)KeJIOrO npepbIBI1CTOrO pe3aHI1R.
102
"
I
BaHa,LJJleBhle 6hICTpOpe)l(YlQHe CTanH (P9<1>5, P14<1>4) peKoMeH-
-nYIOT ,[(nR HHcTpYMeHToB, npe,lJ,Ha3HaqeHHbIX ,n:nR qHCTOBOH o6pa-
60TKH (npoTR)J(KH, pa3BepTKH, llleBepbI). I1x TaK)J(e npMMeHRIOT ,n:nR
o6pa6oTKM Tpy-nHoo6pa6aTbIBaeMbIx MaTepManoB npH cpe3aHMM
CTPY)I(KM He6onbliioro CeqeHHSI. Bonb<ppaMoMonM6-neHoBhIe CTanH
(P9M4, P6M3) Mcnonb3YIOT ,IJ;nR MHcTpYMeHToB, npMMeH}leMhIX ,[(nR
qepHOBOH o6pa6oTKH, a TaK)J(e ,[(nR 113rOTOBJIeHHR npoTR)J(eK, ,[(on-
6RKOB, lIIeBepoB.
TIocKonbKY 6bIcTpope)J(YlQHe CTanll ,[(oporMe, TO .nnR 3KOHOMlIH
pe)KYIl{MH HHCTpYMeHT H3rOTOBJIHIOT C60PHbIM HnH CBapHhIM. XBO-
CTOBMK BhInonHSlIOT 113 KOHCTPYKl.{HOHHOM CTaJII1 45, 50, 40X. qacTo
I1CnOnb3YIOT nJ1aCTlIHKH H3 6hlcTpope)J(yweH CTanH, KOTophIe npHBa-
pllBalOT K ,lJ.ep)KaBKaM HnH KopnycaM HHcTpYMeHToB.
EhIcTpope)J(Y
He CTanH 06na,lJ,alOT BhICOKOH H3HOCOCTOMKOCTblO,
MorYT pa60TaTb co CKOpOCTHMM pe3aHHR ,n:o 100 M/MMH;
- T B e p .n hI e c n JI a B bI npHMeHRIOT B BM.ne nnaCTHHOK onpe.n e -
JIeHHbIX cpOpM M pa3MepOB, H3rOTOBnReMbIX MeTO,lJ,OM nopOlliKOBOM
MeTaJInyprHH. nJIaCTHHKM npe.nBapMTenbHO npeCCYIOT, a 3aTeM cne-
KalOT npM TeMnepaType 1500...1900°C. TBep.nhIe cnnaBhI .nenSlT Ha TPH
rpynnbI: BonbcppaMOBYIO (BK2, BK3, BK4 M T.A.), TMTaHO-Bonhcp-
paMOBYIO (T30K4, T15K6 H T..n.) 11 THTaHOTaHTanOBonb<ppaMOBYIO
(TT7KI2, TTIOK8E). ITnacTHHKI1 M3 TBep.noro cnnaBa 06naJJ.alOT npl1
HRC 3 86... 92 BbICOKOM H3HOCOCTOHKOCThlO M TennocToHKOCThlO
800... 1250°C. 3TO n03BonReT BeCTM 06pa6oTKY co CKOpOCTRMM .no
800 M/MHH. TInacTHHKH 113 TBepJJ.oro cnnaBa npHnaMBalOT K ,lJ,ep)J(aB-
KaM Me,[(HhIMM HnM naTYHHbIMI1 npMnOSlMH. HeJJ.OCTaTKaMM TBep,n:hIX
cnnaBOB HBnHeTCR HH3KaR nnaCTHqHOCTh.
TBep-n bIe cnnaBhI rpynnbI BK npMMeHRIOT ,IJ;nR o6pa6oTKM xpynKMx
MeTaJInOB, nJIaCTMaCC H .npyrHx He
teTaJInMqeCKMX MaTepHaJIOB. Cnna-
BbI rpynnbI TK MCnOJIh3YIOT npM 06pa6oTKe BSl3KHX MeTanJIOB M cnna-
BOB. CnJIaBbI rpynnhI TTK OTnMqalOTCSI nOBhIlIIeHHOM H3HOCOCTOHKO-
CThlO, n03TOMY I1X npMMeH}lIOT ,n;nSl o6pa60TKM CTaneH aYCTeHHTHoro
KJIaCCa ('rpy.nHo06pa6aThIBaeMhIX);
- C M H T e T H q e C K M e C B e p x T B e p JJ. bI e M K e paM M q e C K M e
MHCTpYMeHTanbHhle MaTepMaJIbI. Cy
ecTByeT 60nbIlloe pa3-
Hoo6pa3Me CBepXTBep,lJ,hIX MaTepHaJIOB (CTM) Ha OCHOBe Mo,n;McpHKa-
QHH HMTpH)Ia 6opa: 3nh6op (KoMn03MT 0,1), reKcaHMT-P (KoMno3MT 10)
M JJ.p. Oco6eHHocTh nJIaCTMH CTM COCTOMT B TOM, qTO OHM MorYT
o6pa6aTbIBaTb TBep,n:bIe cnnaBhI, qyrYHbI nlO60M TBep.nOCTM, HO B
OCHOBHOM He BhI.nep:>KMBaIOT y,n;apHOH HarpY3KM.
HHCTpYMeHTaJ1bHbIe KepaMMqeCKMe MaTepl1aJIbI (QM332, CI1JIMHHT P
M ,np.) I1cnonb3YlOTCR ,lJ,nSl QI1CTOBOM 11 nonyqMCTOBOM o6pa60TKI1
He3aKaneHHbIX CTaneM Ii cepbIX qyrYHOB co CKOpOCTSlMH pe3aHHSI JJ.O
900 M/MMH, a «qepHYIO» KepaMMKY (BOK-60) npMMeHSlIOT
JIR qHCTO-
t
1
I
I
I
J
,I
1
,
103
BOM Ii nOnY1JHCTOBOM 06pa60TKH KOBKHX, BbICOKOnp01JHbIX, oT6eneH-
HbIX qyrYHOB H 3aKaneHHbIX CTaneH;
- a6pa3HBHbIe MaTepHaJIbI - 3TO MenK03epHMCTbIe nOpOlllKOBbIe Be-
l.QeCTBa, KOTOpbIe HCnOnb3YIOT MSI H3rOTOBJIeHMSI a6pa3MBHbIX MHCTpY-
MeHTOB: lllnM<p0BaJIbHbIX KpyroB, rOnOBOK, CerMeHTOB, 6PYCKOB. ECTe-
CTBeHHbIe a6pa3MBHbIe MaTepManbI (Ha:>K,naK, KBapQeBbIH neCOK, KO-
PYH,n) npHMeH$lIOT BeCbMa OrpaHHqeHHO H3-3a HeO,nHOp0,[(HOCTH HX
CBOHCTB. B npOMbIlllneHHOCTM npHMeHSlIOT HCKYCCTBeHHbIe a6pa3HBHbIe
MaTepManbI: 3JIeKTpOKOpYH,[(bI, Kap6M,[(bI 60pa, OKCM,[( XpOMa, CMHTe-
TM1JeCKHe aJIMa3bI, 60pCHnOKap6H,n:, CnaBYTHq, 3nb6op, reKCarOHHT.
A6pa3MBHbIe MaTepMaJIbI HMelOT BbICOKYIO TBep,n:OCTb, H3HOCOCTOM-
KOCTb H TennOCTOHKOCTb (1200... 1800°C). HHCTpYMeHTbI H3 a6pa3HB-
HbIX MaTepHaJIOB n03BonSllOT 06pa6aTbIBaTb 3arOTOBKH CO CKOpOCTblO
pe3aHHSI 15... 100 M/C; B OCHOBHOM MX HCnOJIb3YIOT ,n:nSl <pHHMlllHOH
o6pa6oTKH ,n:eTaJIeM, Kor,n:a npe,n:'bSlBnSlIOTcSI nOBbIllIeHHbIe Tpe60BaHHSI
K TOqHOCTM H llIepoxoBaTocTM 06pa60TaHHbIx nOBepxHocTeH.
n$l npHTHpOqHbIX H .n;OBO.n;OqHbIX pa6oT, HanpMMep ,[(nSl ,nOBO,nKI1
MHcTpYMeHToB H3 TBep,n:bIx cnnaBOB, a TaK:>Ke ,n:nSl llInHcpoBaHMSI 3aro-
TOBOK 113 OqeHb TBep,nbIX MaTepl1anOB (Py6MHOB, KBapQa, KOPYH,[(a),
Hcnonb3YIOT UJJIMcpOBanbHbIe nopOlliKH H3 Kap6H,n:a 60pa. ,[(nSl H3ro-
TOBJIeHI1$1 lllJIHcpOBanbHbIX 11 nOnHpOBaJIbHbIX naCT npHMeHSlIOT OKCM,n
xpOMa, BeHCKYIO 113BeCTb, Tpenen.
bopCHnOKap611,n: I1cnonb3YIOT ):(nSl o6pa60TKI1 3arOTOBOK 113 TBep-
,n:bIX cnnaBOB, Py6HHa 11 ,n:pyrHx CBepXTBep):(bIX MaTepHanOB. 3nb60p
(Ky60HI1T) npHMeH$lIOT .n;JISI o6pa60TKH 3arOTOBOK M3 BbICOKOTBepJJ.bIX
MaTepManOB H KOHCTPYKQMOHHbIX CTaJIeH. HHCTPYMeHTbI H3 cnaBYTM-
qa He YCTynalOT anMa3HbIM no M3HOCOCTOMKOCTI1 11 npeBOCXO):(SlT HX
no np01JHOCTM.
B npOMbIllIneHHOCTI1 Mcnonb3YIOT npHpo,n:HbIe (A) H CHHTeTI11Je-
CKl1e (ACO, ACP, ACM M T. ):(.) anMa3bI. AJIMa3 SlBnSleTCSI caMbIM
TBepllbIM MaTepHa.nOM, HMeeT BbICOKYIO TenJIOCTOHKOCTb H H3HOCO-
CTOHKOCTb, Y Hero npaKTMqeCKI1 He npOI1CXO):(MT CJIMnaHMSI co MHorMMM
MaTepHaJIaMM. He,n:OCTaTKOM anMa30B SlBnSleTCSI nOBbIllIeHHaSl xpyn-
KOCTb. KpHCTaJIJIbI a.nMa30B npMMeHSlIOT ):(n$l OCHalQeHH$I pe3QOB, CBepJI;
aJIMa3bI MCnOJIb3YIOT L(JISI M3rOTOBneHHSI HHCTpYMeHTOB (KpyroB, nMn,
neHT,6pYCKOB).
AnMa3HbIH HHCTpYMeHT I1CnOJIb3YlOT npM TOHKOM TOqeHMM ,n:eTa-
JIeM 113 cnnaBOB anIOMI1HHSI, 6pOH3, naTYHeM, HeMeTannl11JeCKHX MaTe-
pHanoB; npMMeH$lIOT ):(JI$I o6pa60TKI1 3arOTOBOK M3 TBep,nbIx MaTepMa-
JIOB, repMaHH
, KpeMHHSI, nonynpOBo,n:HI1KOBbIX H KepaMH1JeCKHX MaTe-
pHanOB, :>KapOnpOqHbIX CTaneH 11 cnnaBOB. 06pa6oTKY Be,n:YT co CKO-
pOCTSlMI1 pe3aHH$I .n;o 20 M/c. fIoBepxHocTM, o6pa60TaHHbIe aJIMa3aMH,
HMelOT HM3KYIO rnepoxoBaTocTb H Manoe OTKJIOHeHMe pa3MepoB, TaK
KaK aJIMa3bI HMelOT BbICOKYIO pa3MepHYIO CTOHKOCTb.
104
'If
..
I
3.4. )J:cTaJIH BpatnaTeJIbHOrO ABHjKeHHH
B MallIHHax MHoro pa3Ho06pa3HbIx ,n;eTaJIeH BpalQaTeJIbHOrO ):(BI1-
)l(eHI1S1: 3y61JaTbIe Koneca, llIKMBbI peMeHHbIX nepe,n:aq, 6apa6aHbI, 3Be3-
,n:OqKI1 QenHbIX nepe,naq, MaXOBMKH, llInHH):(eJII1 CTaHKOB, Koneca aBTO-
Mo6HJIeH M rM,npoTyp6lfH. Bce 3TM Bpall(alOll(MeCSI ,neTanM YCTaHaBJIM-
BalOT Ha BaJIaX MJIH oc»x.
OCLIO Ha3bIBaeTCSI ):(eTanb, npe,n:Ha3HaqeHHaSl TonbKO ,n:nSI nOJl[(ep-
)l(aHMSI Bpall(alOIl.(MXCSI ,n:eTaJIeH; OCM He nepe,n;alOT KpYTSlll.{erO MOMeHTa.
qalQe Bcero OCI1 lf3rOTOBnSIIOTCSI npSlMbIMI1 11 MorYT 6bITb lI.BYX THnOB:
HeBpalQalOlQHMHCSI H no,n:BM)I(HbIMlf, T. e. BpalQalOll(MMI1CSI BMeCTe C
YCTaHOBneHHbIMH Ha HMX ,[(eTanSlMM. Ha paC1JeTHbIX cxeMax OCM npen;-
CTaBJISlIOT 6aJIKaMI1, HarpY)I(eHHbIMM M3rH6alOIl.(HMI1 MOMeHTaMI1, T. e.
npl1 paC1JeTaX He Y1JI1TbIBaIOT KPYTSlIl.(MH MOMeHT H CMnbI TpeHI1S1.
BaJlLI, B OTnl11JHe OT oceM, He TOJIbKO nOMep)l(l1BalOT BpalQalO-
lQMeCSI ,n:eTanl1 Mallll1H, HO M nepe,n:alOT KpYTSlIl.(l1e MOMeHTbI, n03TOMY
HX paCCqMTbIBalOT Ha COBMeCTHoe ,n;eHCTBHe KpyqeHHSI 11 113r116a. EcnH
3Ha1JeHMSI KPYTSllQMX MOMeHTOB Ha Bany 3Ha1JMTenbHO 60JIbllle 3Ha1Je-
HI1M M3rl16alOlQI1X MOMeHTOB, TO BaJIbI CqHTalOTCSI nerKO HarpY)I(eH-
HbIMM M HX paCCqMTbIBalOT Ha KpyqeHMe, npeHe6peraSl M3rM60M.
no <popMe reOMeTpMqeCKOll OCM BaJIbI pa3,nenSlIOT Ha npRMble 11 KO-
JleH1Jamble. KOneHqaTbIe BMbI npMMeHSlIOT npl1 He06xo,lIMMOCTM npe-
06pa30BaHMSI B MalIIMHe B03BpaTHo-nocTynaTeJIbHOrO ,n:BM)I(eHMSI BO
BpalQaTeJIbHOe M Ha06opOT. B TaKMX BaJIaX COBMelQalOTCSI <PYHKQHM
BaJIOB C <PYHKQMSlMM KpMBOlllMnOB B KpMBOlIIMnHO-lliaTYHHbIX Mexa-
HM3Max. Oc06yIO rpynny COCTaBnSlIOT 2u6Kue BanbI, nonO)J(eHlfe reo-
MeTpMqeCKOH OCM KOTOpbIX MO)l(eT M3MeHSlTbCSI B npOCTpaHCTBe.
qall(e Bcero OCM M BaJIbI MMelOT ,[(Be onopbI, HO CYll(eCTBYIOT M MHO-
roonopHbIe TpaHCMI1CCI10HHbIe BanbI, OT,n:eJIbHbIe QaCTI1 KOTOpbIX
coe,[(MHSlIOTCSI MY<PTaMM. bonee no,n:po6HbIe CBe,n:eHI1S1 0 MY<P Tax 6y,n:YT
.n;aHbI B nOL(pa3JJ:. 3.11.
OnopHbIe qaCTM BanOB M oceH Ha3bIBalOT ijanfjJaMu (1 Ha pMC. 3.5),
npH1JeM npoMe)l(YTOqHbIe QancpbI Ha3bIBalOT llleMKaMH, a KOHQeBbIe -
UJMnaMM. Qan<pbI nepeJJ;alOT Ha onopbI pa):(ManbHYIO HarpY3KY; JJ;nHHa
QancpbI no,n: nOJJ;lllMnHI1KI1 Ka1JeHMSI MeHbIIle, 1JeM no,n: nO,[jJIIHnHHKH
2
3
4
5 6
PMC. 3.5
105
CKOIlbJKeHMSI. LJ:I1$I COe,lJ;MHeHMSI BaIla MIIM OCM C ,lJ;PyrMMM ,lJ;eTaJISIMM Ha
nOBepXHOCT$IX )];enalOT IllnOHOqHble na3bI 4, OTBepCTM$I 3; HapC3alOT
pe3b6y 2 M IllJIMQbl 6 (eM. pMe. 3.5). Pe3KMe M3MeHeHMSI eeqeHMH BaJIa
CHM)KaIOT ero yeTaJIOCTHYIO npOqHOcTb. n03TOMY nepexo)]; OT O)];HOrO
CeqeHMSI K .n:pyroMY J10n)KeH BblnOJIHSITbCSI nnaBHO, B BM.[(e raJITeJIeH 5.
llpM BepTMKaJIbHOM paenOJIO)KeHMM BaJIa oeeBble eMnbI BaJIa )J.aBSlT
Ha no,[(n}lTHMK. B 60nbIllHx rM.n:poarperaTax (TMna BOn)KCKOH r3C)
no.[(n}lTHMKH McnbITbIBalOT oceBYIO HarpY3KY, ,n:oeTMralO
YIO 34 MH.
3.5. KopnycHbIe JJ:eTaJIH
KopnYCHbIe ,n:eTaJIH MorYT MMeTb pa3Hoe Ha3HaqeHMe. OHH 3aKJIIO-
qalOT B ce6e MexaHH3MbI MaruMH, nO,lJ;,lJ;epJKMBaIOT MX, CJIY)KaT 6a30H
)];n}l B3aMMHoro pacnOJIO)KeHM$I OCHOBHbIX Y3I10B H, HaKOHeQ, 06pa3Y-
lOT KOHTYP MaIllMHbI MJIM OT,lJ;eJIbHbIX ee Y3I10B.
KopnYCHble )];eTaJIH B 3HaqHTeJIbHOH CTeneHH onpe.[(eJI}lIOT pa60TO-
cnoc06HOCTb M Ha,n:e)KHOCTb MaIllMH no KpMTepMSIM TOqHOCTM pa60TbI
no,lJ; HarpY3KOH, BM6poYCTOHqMBOCTM, ,lJ;OnrOBeqHOCTM. B CTaQHOHap-
HbIX MaIllMHax KopnYCHbIe ,n;eTaJIM COCTaBJISlIOT 70...85 % OT BceH MaCCbI
MaIllHHbI. n03TOMY Bonpoc CHM)KeHH}l MaCCbI KopnycHblx ,[(eTaneH
Beer)]:a }lBJISIeTC}l 3n060J1HeBHbIM, oc06eHHo ,n:JISI T}l)KenbIX CTaHKOB.
Ha
Me. 3.6 nOKa3aH T}l)KenbIH ,llByxcTOeqHbIH np0J10JIbHO-CTpO-
raJIbHbIH CTaHOK. CTaHHHa 1, CTOHKa 2, nOnepeQMHa 3, nepeKna)];MHa 4
11 CTon 5 - 3TO Bce npHMepbI KopnycHbIx ,n:eTaneH.
PHc.3.6
106
I
I
I
K KopnycHbIM ,[(eTaJISIM OTHOC}lTCSI TaK)Ke Kopnyca Kop060K eKopo-
cTeM (aBToM06HJIeM), nnMTbI, paMbI, OCHOBaHMSI, Kopnyca Kop060K
nepe.[(aq, <PYH.[(aMeHTHble nJIMTbI.
baJOBOH ,[(eTaJIblO CTaQMoHapHoM MaIllHHbI HBJISleTC}l CTaHHHa. Ha
CTaHMHe 3aKpennSIIOTcSI Bce Y3nbI, npH 3TOM 06eCneqI1BaeTCSI TOqHOCTb MX
B3aMMHoro pacnOnO)l(eHHH. Y MeTaJIJIOpe)l(y
ero CTaHKa (CM. pMC. 3.6)
Ha CTaHMHe MMelOTCSI HanpaBJI}lIO
He 6, no KOTOpbIM nepeMellJ.aIOTC}l
Y3JIbI, HecYIl.\Me pe)l(YIl.\MH MHcTpYMeHT MJII1 3aroToBKY. CTaHMHa SIBn}l-
eTC}l O.[(HOM M3 HaM60nee OTBeTCTBeHHbIX ,[(eTaneH CTaHKa, KOTOpa}l
onpe)J.en}leT MHorMe ero 3KcnnyaTaQMOHHble KaqeCTBa. K KOHCTpYKQMH
CTaHHHbI npe)];'b}lBJI}lIOTC}l CJIe.[(YIO
Me Tpe60BaHMSI: OHa ,[(OJI)I(Ha HMeTb
BbICOKYIO )l(eCTKOCTb M BM6poYCTOHqMBOCTb, .[(JIMTeJIbHOe coxpaHeHMe
TOqHOCTM, TeXHOJIOrMqHOCTb KOHCTPYKUMM M MMHMMaJIbHYIO Maccy,
y,[(06Hoe B3aMMHoe pacnOJIO)KeHHe OT,[(eJIbHbIX Y3JIOB, HaJIMtlHe pe3ep-
ByapoB ,lJ;JISI CMaJKM M OXJIa)l()];eHMSI, Y,lJ;06CTBO OTBo.[(a CTpY)I(KM, HaJIM-
QMe HMIll .[(JISI 3JIeKTpO,[(BMraTeJISI H 3JIeKTpoannapaTypbI.
.An}l KopnYCHbIX ,n:eTaneM KpumepURMU pa6omocnoco6l-locmu H l-la-
i)e:JICl-locmu }lBJISlIOTCSI npOqHOCTb, )KeCTKOCTb M ,[(OJIrOBeQHOCTb.
ITpOqHOCTb SlBJI}leTC}l OCHOBHbIM KpMTepHeM pa60Tocnoc06HOCTli
,lJ;JISI KopnYCHbIX ,[(eTaJIeM, no.n;Bep)l(eHHbIX 60JIbIllI1M HarpY3KaM, rnaB-
HbIM 06pa30M y,n:apHbIM 11 nepeMeHHbIM.
)l{ecTKocTb CJIY)I(MT OCHOBHbIM KpHTepMeM pa60Tocnoc06HOCTM
60JIbIlll1HCTBa KopnYCHbIX .[(eTaJIeM. OOBbIIlleHHble ynpyrMe nepeMe-
eHMSI B KopnYCHbIX ,lJ;eTaJISIX npMBO,[(}lT K HenpaBMJIbHOH pa60Te
MexaHM3MOB, CHM)KeHMIO TOqHOCTM pa60TbI MaIllHHbI, cnoc06CTBYIOT
B03HMKHOBeHMIO KOJIe6aHHM.
LJ:onrOBeQHOCTb no M3HOCY MMeeT OQ)OMHoe 3HaqeHMe ,l])I}l KopnYCHbIX
.n;eTaJIeM, MMelOllJ.MX nJIOeKMe MJIM Ul1nMH.apHqeCKMe nOBepXHOCTM CKOJIb-
,\
)l(eHM}l, BbInonHeHHbIe 3ao.n;HO C KopnYCOM (6e3 npOKna.n;OK M BTynOK).
MaTepHaJlbl KopnYCHblX ,neTaJleu. KopnYCHbIe ,lJ;eTaJIM ,lJ;OJI)I(HbI
M
feTb 60JIbIllYIO )l(eCTKOCTb; I1X 113rOTOBJI}lIOT 113 MaTepl1aJIOB C BbICO-
KMM Mo.n;yneM ynpyroCTI1 (M3 qyrYHa 11 CTaneH 6e3 TepMl1qeCKOH 06-
pa60TKH, nocKonbKY TepMMqeCKaSI 06pa60TKa ,lJ;n}l KopnycHbIx ,[(eTa-
neM 3aTPYJIHeHa).
KopnycHbIe .n.eTanl1 B TpaHcnopTHbIX MallIMHax, HanpMMep KapTe-
pbI ,ABMraTeneH, a TaK)Ke no.n;BM)KHbIe .n;eTaJIM CTaUMOHapHbIX MaIllMH,
HanpMMep nopIllHM, HarpY)KaeMble 60JIbIllMMM HHepQMOHHbIMI1 Macca-
MI1, qa
e Bcero BblnOnH}lIOT M3 nerKMX cnnaBOB, 06na,[(alOllJ.MX nOBbI-
lIleHHOM npOqHOCTblO, OTHeceHHOH K e.n;I1HMUe MaCCbI ,[(eTanM. bonb-
lIlMHCTBO KopnYCHbIX .n;eTaneM OTnMBalOT M3 qyrYHa, QTO n03BOn}leT
nonYtlaTb CnO)KHbIe reOMeTpMqeCKMe <pOpMbI.
CBapHbIe KOHCTpYKQMM npMMeH}lIOT .n.n}l YMeHbIlleHM}l MaCCbI M ra-
6apMTHbIX pa3MepOB, a B e,[(MHMqHOM M MenKocepMHHoM npOM3BO,[(CT-
Be CBapHble KopnYCHbIe .[(eTaJIM 6y Jl.YT ,n:eIlleBne, qeM JIMTbIe.
I
107
t
B TSI)J(enOM MallIHHOCTpoeHHM npHMeHSlJOT CBapHo-nHTbIe KOHCT-
PYKQHH, TaK KaK OHH 3Ha1.1HTenbHO ynpOlQaJOT H3rOTOBneHHe KpynHbIx
OTnHBOK (HanpHMep, CTaHHHbI npo,[(onbHO-CTporanbHbIX CTaHKOB, y
KOTOpbIX ,n;nHHa HanpaBJISlIOI.l{HX ,n;OCTHraeT ).:{Ba}JJ!aTH MeTpOB).
[{JISI KpynHbIx KopnYCHbIX .n:eTaJIeH B nocnen;Hee BpeMSI CTaJIM npH-
MeHSlTb 6eTOHHbIe H )J(eJIe306eTOHHbIe KOHCTPYKQHH. EeTOH XOpOlliO
raCMT BH6paUHH, 1.11'0 YBenH1.1MBaeT )J(eCTKOCTb MallIHHbI B QeJIOM.
KpOMe Toro, no cpaBHeHMIO C qyrYHOM 6eTOH MeHee 1JYBCTBMTeJIeH K
Kone6aHHSIM TeMnepaTypbI. XOTSI MO,[(YJIb ynpyrocTM 6eTOHa MeHb-
we, qeM MO,[(YJIb ynpyrocTH 1.1yrYHa, TaKYIO )J(e )J(eCTKOCTb MO)J(HO
nonY1.1HTb 3a C1.1eT YBeJIH1.1eHHSI TOJIlQHHbI CTeHOK. Macca KopnYCHOH
)I.eTanM npM 3TOM OCTaeTCSI B npe,[(enax HOpMbI, TaK KaK y,[(eJIbHbIH
Bec 6eTOHa COCTaBJISIeT TOJIbKO TpeTb 01' y)].eJIbHOrO Beca ceporo
qyrYHa.
O,AHaKO 6eTOH HMeeT He,AOCTaTOK: nOCJIe CXBaTbIBaHMSI OH norJIO-
LQaeT BJIary, 1.11'0 BJIe1.1eT 3a C060H 06'beMHbIe H3MeHeHMSI. KpoMe Toro,
nona,naHHe MaCJIa Ha 6eTOH nOBpe)l(,naeT ero. 1l03TOMY CJIe,nyeT npH-
HHMaTb He06xo,l(HMbIe MepbI no 3aI.QHTe 6eTOHa 01' BJIarH H nona,na-
HHSI MaCJIa.
JISI H3rOTOBJIeHHSI CTaHHH TSI)J(enbIX CTaHKOB Hcnonb3YlOT )J(ene-
306eTOH. llpHMeHeHMe )l(eJIe306eTOHa ,naeT 3KOHOMHIO MeTaJIJIa Ha
40...600/0, npM 3TOM 06eCne1.1HBaeTCSI TaKaSI )l(e )J(eCTKOCTb, KaK 11 npM
npMMeHeHHH 1.1yrYHa.
IIepcneKTHBHbIM MaTepHanoM SIBnSIeTCSI nOJIHMepHbIH 6eToH, KO-
TOpbIH HMeeT BbICOKHH MO,n;YJIb ynpyrocTH (E = 40 KH/MM2) M JIHllleH
He,n;OCTaTKOB, npHcYI.l{MX 6eToHY.
KopnycHble ,AeTaJIM C MHHHMaJIbHOH MaccoH, KOTopble He McnbI-
TbIBalOT 60nbllIHX HarpY30K H He Tpe6YlOT cTa6HJIbHOCTH pa3MepOB,
H3rOTaBnHBalOT H3 nnaCTMacc. K TaKHM ,neTaJISIM OTHOCSITCSI Kopny-
ca npM60pOB, nepeHOCHbIX MallIMH H HHCTpYMeHTOB, KpbIlllKM, KO-
)J(YXH Ii T.,n;.
3.6. llpY
HHLI H peccopLI
TIpY)I(HHbI H peccopbI - 31'0 ynpyrHe 3JIeMeHTbi. 06JIaCTb HX npH-
MeHeHMSI O1.1eHb llIHpOKa:
C03,naHHe 3a,naHHbIx nOCTOSIHHbIX CHJI - Ha1.1aJIbHOrO C)I(aTHSI MJIH
HaTSI)J(eHMSI - B nepe,l(a1.1ax TpeHHeM, cppHKQHOHHbIX MY<PTax, TopM03ax,
npe,l(OXpaHMTeJIbHbIX YCTpOHCTBax, nO)I.llIMnHHKax Ka1.1eHHSI;
CHJIOBOe 3aMbIKaHHe MexaHM3MOB ,AJISI HCKJII01JeHHSI BJIHSIHHSI 3a30-
pOB Ha T01.1HOCTb nepeMeI.l{eHMH;
BbInOJIHeHMe CPYHKQHH ,nBHraTeJISI Ha OCHOBe npe,n;BapMTeJIbHOrO
3aKpY1.1HBaHHSI npY)I(HHbI, HanpMMep B qaCOBbIX MeXaHH3l\laX;
108
I
1
BH6pOH30nSlQHSI B TpaHcnopT-
HbIX MalllMHax - aBTOM06HJISIX, F
)J(ene3Ho,[(opO)J(HbIX BarOHax, npH-
60pax, BH6pOH30JISIQI10HHbIX ono-
pax MallIHH;
rallIeHHe 3HeprHH y,napa, Ha-
npMMep C nOMOIQblO 6ycpepHbIX
npY)l(MH, npMMeHSleMbIX B apTHn- PHC. 3.7
nepHHcKHX 0pYAHSIX. DJIaro,napSI
ynpyrHM 3JIeMeHTaM Ha 60JIbllIHX nepeMeIQeHHSIX 3HeprHSI y,n;apa raCMT-
CSI Ii CMJIa y,napa YMeHbllIaeTcSI. B OTJIM1.JHe 01' nepBblx Tpex CJIyqaeB,
6ycpepHbIe H BH6pOH30JISIUHOHHble npY)J(MHbI aKKYMYJIHPYIOT Bpe,n;HYIO
,l(JISI pa60TbI MallIHHbI 3HeprMIO;
H3MepeHHe CHJI B H3MepHTeJIbHbIX npH60pax Qepe3 ynpyroe nepe-
MeI.QeHHe BHTKOB npY)l(HHbI.
Peccopbl (PHC. 3.7) nonyqalOT 113 JIHCTOBOro MaTepHana; ,[(JISI YBeJIH-
1.1eHMSI rH6KOCTH HX c06MpalOT 113 JIMCTOB pa3HOM ,[(JIMHbI, 1.11'0 npH-
6nM)J(aeT MX K TenaM paBHoro conpOTHBJIeHI1SI nOnepeqHOMY H3rM6y.
TpeHHe Me)J(,[(Y nHCl'aMH 06eCneQHBaeT ,[(eMncpl1pOBaHl1e KOJIe6aHMH.
JIHCToBble peccopbI npHMeHSIlOl' B OCHOBHOM ,AJISI BH6pOH30JISIQHH (yn-
Pyrl1e nO,[(BeCKH aBTOM06MJIeH, )J(eJIe3Ho,n;op0)J(HbIX BarOHOB) M BocnpH-
SITI1SI y,n;apa (B KY3HeQHO-npeCCOBOM 060Py,n;OBaHHI1). )J;JISI 06eCne1.1eHI1SI
nnOTHoro KOHTaKl'a Me)J(,n;y nl1Cl'aMH H HeKOl'opOH pa3rpY3KI1 )I.JIHHHbIX
JIHCTOB (nOJIOMKa KOl'OpbIX 60nee onaCHa, QeM KOpOTKHX) KopOTKHe
JIHCTbI BbInOJIHSIlOl' C 66nbllIeH KpI1BM3HOH. PeccopbI H3rOTaBnl1BalOT H3
KpeMHI1CTbIX CTaJIeH, KpeMHeHHKeneBbIX 11 xpOMOMapraHQOBHCl'bIX.
ITpH ynpOIQeHHOM paC1.1eTe Ha H3rH6 peccopbI paCCMaTpHBalOT KaK
KOHCOJIbHYIO 6aJIKY, liMelOlQYIO l'peyronbHYIO CPOPMY B nnaHe, pa3pe-
3aHHYIO Ha nonOCbI M c06paHHYlO B naKeT. )J;onYCKaeMble HanpSI)J(eHI1S1
BbI6HpalOT B npe,[(eJIax 40...60 MH/CM 2 .
IIpYiKHHbl - Hal160JIee YHHBepCaJIbHble ynpyrHe 3JIeMeHTbI; OHM
npMMeHSIIOTCSI BO Bcex llIeCl'H CJIyqaSIX, nepe1.1HCJIeHHbIX BbIIlle. llpY)J(M-
HbI Moryl' pa60TaTb Ha paCTSI)J(eHHe (PHC. 3.8, a), C)I(aTHe (PHC. 3.8, 6) H
KpYQeHHe (PMC. 3.8, 6). E,n;I1HCTBeHHO, OHH He BocnpMHHMalOl' none-
peQHbIH H3rM6. B 3TOM CJIY1.1ae MX 3aMeHSIIOl' peCCOpaMI1.
c
o
a
6
o
8
z
PI1C. 3.8
109
i
110 cpOpMe npY:>KHHbI OqeHb pa3H006pa3HbI: Q H n H H,n; P If q e -
C K H e (pHe. 3.8, a-e), n n 0 C K H e C n H pan b H bI e (PHC. 3.8, 2),
Tap e n b qaT bI e (PH C. 3.8, a), <p H r y p H bI e If,n;p.
MaTepManbJ ,n;nSI npY:>KMH ,n;on:>KHbI MMeTb BbICOKMe M cTa6HnhHhIe
ynpyrHe CBOHCTBa. TI03TOMY OCHOBHbIMH MaTepHanaMH
BJI
IOTC
BhIcoKoyrnepo,n;MCTbIe CTaJIH 65, 70, MapraHQOBHCTaSI CTaJIh 65r, KpeM-
HHCTbIe CTaJIM 60C2A, xpoMoBaHa,n;HeBa
CTaJIb 50X<I>A M ,n;p.
3.7. Hepa3'LeMHLle coe
HHeHHH
eTaJIeii
K Hepa3'beMHbIM OTHOCSITC
coe,n;HHeHH
, He ,n;onYCKalOI.QMe OTHO-
CHTenbHoro nepeMeI.QeHH
,n;eTaneH MaruMH. 3TO CBapHbIe, 3aKJIenOq-
HbIe M KneeBbIe coe,n;MHeHM
; HenO,LJ;BM)I(HbIe coe,n;MHeHM
, nOJIyqeHHbIe
apMMpOBaHMeM nnaCTMaCCOBbIX ,n;eTaneH. CIO,n;a MO)l(HO OTHeCTH H
HenO,nBI1JKHbIe coe)].MHeHMSI )].eTarreM no noca)].KaM C HaTSlroM.
CoapHble COeL(HHeHHH - 3TO Hepa3'beMHbIe coeJ],HHeHM
, OCHOBaH-
HbIe Ha MCnOJIb30BaHMM CMJI MOJIeKYJISIpHOrO CuenJIeHMSI M nOJIyqae-
MbIe nYTeM MeCTHoro HarpeBa M3,n;enMH. CBapKa (3JIeKTpOJ],yroBa
,
3JIeKTpOlIlJIaKOBaSI) OCYI.QeCTBJISleTCSI HarpeBOM ,n;o paCnJIaBJIeHHOrO
HnM TeCTo06pa3Horo COCTOSlHMSI, HO C npMMeHeHMeM MeXaHMqeCKOrO
YCMnMSI (KOHTaKTHaSl CBapKa).
CBapHbIe coe,n;MHeHMSI SlBnSIIOTCSI HaM60JIee COBeplIleHHbIMH Hepa3'b-
eMHbIMM coeJ],MHeHHSlMM. CBapKOH MO)l(HO H3rOTaBJIHBaTb J],eTaJIM Heor-
paHMqeHHbIX pa3MepOB. TIpOqHOCTb CBapHbIX coe,n;HHeHHH )].OBe)].eHa
npH CTaTHqeCKHX If y)].apHbIX HarpY3Kax )].0 npOqHOCTH QeJIoro MeTaJI-
na. B HaCTOSII.Qee BpeMS! OCBoeHa CBapKa Bcex KOHCTpYKQMOHHbIX Me-
TannOB, BKJIlOqaSl BbICOKOJIerHpOBaHHbIe, a TaK)I(e QBeTHbIX cnnaBOB H
nJIaCTMacc.
KaqeCTBO CBapKH 3aBHCHT OT qHCTOTbI no)].rOTOBKH If cpOpMbI CBa-
pHBaeMbIX nOBepXHOCTeH, KBanH<pHKaQHH CBapI.QHKa H ycnoBHH npo-
H3Bo,n;CTBa pa60T. TIpOqHOCTb CBapHbIX lllBOB 3aBMCMT OT B3aMMHoro
npOHMKHOBeHHSI paCnJIaBJIeHHOrO MeTaJIJIa H MeTanJIa CBapHBaeMbIX
,n;eTaneM. EcnH rny6HHa lllBa MeHee 1,5 MM, TO B03MO)l(eH HenpOBap, a
ecnM OHa 60JIblIle 3 MM, TO MO)l(eT 6bITb nepe)l(or MeTaJIJIa CBapMBae-
MbIX ,n;eTaJIeH. 06a ,n;ecpeKTa npHBe,n;YT K CHH:>KeHHIO npOqHOCTM lIlBa.
TIo B3aHMHOMY pacnOnO)l(eHHIO coe,n;HHSIeMbIX 3neMeHTOB CBapHbIe
coe)].HHeHHSI MO)l(HO pa3,n;eJIHTb Ha cne)].YIOI.QHe rpynnbI:
coe)].HHeHHSI BCTbIK (coe)].HHSleMbIe 3neMeHTbJ CBapHBalOT no TOp-
QaM, PMC. 3.9);
coe)].HHeHHSI BHaXJIeCTKY (nOBepXHOCTH coe)].MHSleMbIX 3JIeMeHTOB
qaCTHqHO nepeKpbIBalOT )].pyr ,n;pyra);
coe)].HHeHMSI TaBpOBbIe (coe)].HHSleMbIe 3JIeMeHTbI nepneH)].HKYJISlp-
HbI O)].HH K )].pyrOMY, npM 3TOM O)].HH 3JIeMeHT npMBapMBaeTCSI TOPQOM
K 60KOBOH nOBepXHOCTM ,n;pyroro);
110
.,.
t
I
V///
tw
a
6
- f
II
z
i)
PlICa 3.9
coe,nMHeHMSI yrnoBbIe (coeJ],MHSleMbIe 3JIeMeHTbI pacnOJIO)l(eHhl no)].
yrJIOM )].pyr K )].pyry, npHBapHBalOTcSI no KpoMKaM).
CBapHbIe CTanbHbIe KOHCTPYKQHM nerqe qyrYHHbIx JIHTbIX HHor)].a
].(0 500/0, a CTaJIbHbIX JIHTbIX - )].0 30%. KpoMe Toro, CTOHMOCTb cBap-
HbIX KOHCTPYKQHH H3 npoKaTa nOqTM B ,n;Ba pa3a MeHblIle, qeM CTOH-
MOCTb CTanbHoro JIHTbSl HJIM nOKOBOK.
He.aocTaTKoM cBapKH SlBJISleTCSI HeCTa6MJIbHOCTb KaqeCTBa lllBa, 3a-
BHCSlm.aSl OT KBaJIH<pMKaQHM CBapI.QMKa. 3TOT He)].OCTaTOK YCTpaHSleTCSI
nYTeM npMMeHeHMSI aBTOMaTMqeCKOH CBapKM.
TIpH npoeKTHpOBaHHH CBapHbIX coe,n;HHeHMM He06xo,n;HMO BbInOJI-
HSlTb YCJIOBHe paBHOnpOqHOCTH lllBa If coe,n;HHSle
bIX 3JIeMeHTOB.
lllOB eCmblK. "MeeT HeCKOJIbKO pa3HOBH)].HOCTeH, 3aBHCSlI.QHX OT Ton:
m.HHbI coe,n;HHSleMbIX 3JIeMeHTOB (Ta6n. 3.2). ,L(JISI 3JIeMeHTOB ManOH
TOJIIl\HHbI npHMeHSlIOT cBapKY C oT6opTOBKOH (CM. pHC. 3.9, a); ,[(JISI
3JIeMeHTOB cpe)].HeM TonIQHHbI - cBapKY 6e3 CKoca KpOMOK (CM. pHC.
3.9, 6) H co CKocaMH KpOMOK (CM. pHC. 3.9, e); ,[(JISI 3JIeMeHTOB 6onb-
mOM TOJIll(HHbl - cBapKY C KpHBOJIHHeHHbIMH CKocaMH (CM. pHC. 3.9, 2)
H C qeTbIpbMSI CKOCaMH (CM. pHC. 3.9, d).
Ta6nHua 3.2
T OJlIUIfHa JJleMeHTOB
, MM, "PH COeLl.HHeHHH BCTblK .nyroBoH CBapKOH
BM,L( CBapKM <l>opMa lllBa no PMC. 3.9
a 6 e 2 j)
PY1.JHaSl 1...3 3...8 3 . .. 26 20 . . . 60 12 .. . 60
ABTOMaTM1.JeCKaSi 1,5...3,0 2 . .. 20 14 . .. 24 24...160 20 . .. 60
no,L(
nlOcoM
Bce BH,[(bI IIlBOB BCTbIK npH BbICOTe HannaBJISleMOrO MeTaJIJIa h
MorYT BbInOJIHSlTbCSI HOpMaJIbHbIMH (h = 8), YCHneHHbIMH (h ::::; 1,28)
"nH 06JIerqeHHbIMH (8 > h).
I
III
F
o
......
CTbIKOBbIe IlIBbI paCCqHTbIBalOT
Ha npOqHOCTb no HOMHHaJIbHOMY
CeqeHHIO coe
HH
eMbIX 3JIeMeHTOB
(6e3 yqeTa YTOJI
eHH
llIBOB). Ha-
npSl)f(eHMe paCT
)f(eHHSI (C)f(aTHR) (J
onpe,l(eJI
eTC
no cpopMyne
F
_F< [ / ]
0' p(C>K) - - - cr p(C:iK),
18
F
r.n;e 1 -. paCqeTHaR ,l(JIHHa IlIBa B MM,
paBHaSJ ,l(JIHHe IllBa 3a BbIQeTOM
10 MM Ha HenpoBap. JJ:onycKaeMbIe
HanpR)KeHHR [0"] B cBapHblx IlIBax BbI6Hpa1OTc
no Ta6JI. 3.3.
onyc-
KaeMaR pacTSlrHBalO
aSI (HJIM C)I(HMalOIl{a
) CI1JIa
[F] = [0"]p(cJK)18.
PHC. 3.10
nplfMep 3.1
,l].Be nOJIOCbI H3 CTaJIH CT3 ([a]p = 160 H/MM2) CBapeHbI BCTbIK H HarpYJKeHbI
paCTSlrHBalOllJ.eH CHJIOH (PHC. 3.10). Onpe)).eJIHTb )).onYCKaeMYIO CHJIY, eCJIIi ocy
e-
CTBJUIeTC
PY1.JHa
CBapKa 3JIeKrpo)).aMH 342.
PellleHHe.
I. no Ta6JI. 3.3 BbI6lIpaeM [a']p = 0,8 [a]p = 0,8. 160 = 128 (H/MM2).
2. OnpeneJISleM paC1.JeTHYIO ,nJIHHY lllBa I = 180 - 10 = 170 (MM).
3. Onpe)).eJISleM )).onycKaeM)'IO paCTRrlmalO
CHJI)' [F] = 128. 170 . 10 = 217,6 (KH).
ECJIH B nJIOCKOCTH COe,l(HHSJeMblx 3JIeMeHTOB ,l(eHcTBYIOT H3rH6alO-
lI.\HM MOMeHT M H pacT
rHBalOIl{a
(C)I(HMalOIl{aR) CHJIa, TO HanpR)I(e-
HMe onpe,l(eJISlIOT no cpopMYJIe
M F [ I ]
--+-<
a - W c - /8 - a p'
r,n;e W c - MOMeHT conpOTHBJIeHH
paCQeTHOrO CeqeHHSlIlIBa.
CoedUllellUR 6IlQXJleCmKY, KaK npaBHJIO, Bbln011H
IOTC
Y r 11 0 B bl-
M H, HJIH B a 11 H K 0 B bl M 11
IlIBaMH (PHC. 3.11). ITo paCn0110)l(eHHIO K
HarpY3Ke yrJIOBbIe IlIBbI pa3,l(eJI
IOT Ha: JI060BbIe, pacnOJIO)l(eHHbIe
nepneH,l.(HKYJISlpHO HanpaBJIeHHIO CHJIbI (PHC. 3.12, a); cpnaHroBbIe,
pacnOJIO)l(eHHble napaJIJIeJIbHO K HanpaBJIeHHIO CHJIbI (PHC. 3.12, 6);
KOCble, pacnOJIO)l(eHHble no,l( yrJIOM K HanpaBJIeHHIO CHJIbI (PHC. 3.12, 6),
H KOM6HHHpOBaHHble.
JIHHY yrJIOBbIX lllBOB BbI6HpalOT He MeHee 30 MM
H3-3a HeH36e)l(HbIX J(ecpeKToB no KOHQaM LIlBOB. JI060BbIe WBbJ HaKJIa-
,l.(bIBaIOT C ,l(BYX CTOpOH, BeJIHqHHa nepeKpbITH
,l(OJI)I(Ha 6blTb He Me-
Hee 48. MaKCMMaJIbHYIO .n:JIHHY JI060BblX H KOCbIX lllBOB He orpaHlfllH-
BaIOT. )J,JIHHY cpJIaHrOBbIX llIBOB peKOMeH,l(YIOT BbI6HpaTb He 60JIee
112
(50...60)k , rJ(e k - KaTeT TpeyrOJIbHHKa nOnepeqHOrO CeqeHHSI IllBa.
Pa3Mep k, KaK npaBHJIO, paBeH TOJIIl{MHe JIHCTOB o. PaCqeT Bcex yrJIo-
BbIX llIBOB npOH3BO,l(HTCSI no e)lHHbIM <popMYJIaM
1:' = F < [ 1:'/ ] . [ F ] < 0,7 k/ [ 1:" ]Cp .
0,7 kl - cp ,
Ta6JIHQa 3.3
JJ:onYCKaeMLle HanpH*eHHH 0 coapHLIX moax npH CTaTHQeCKOH HarpY3Ke
Cnoc06 CBapKH Ii CTbIKOBbIe lllBbI YrJIOBbIe
Tlin 3JIeKTpo)).a npH paCT
- npH CJKaTHH (BaJIHKOBbIe) lllBbl
JKeHHH [a']p [0"] C)K npH cpe3e ['t'] cp
KOHTaKTHbIH T01.Je1.JHbIH - - 0,50 [a]p
PYQHOH 3JIeKTpo)).aMH 334 0,60 [a]p 0,75 [a]p 0,50 [a]p
PY1.JHOH 3J1eKTpo)).aMH 342 0,80 [a]p 0,90 [a]p 0,60 [a]p
ABTOMaTH1.JeCKHM no)). CJIOeM 0,90 [a]p [alp 0,65 [a]p
JIIOCa, KOHTaKTHbIH CTbI -
KOBOH C OnJIaBJIeHHeM, Pyq-
HOM 3J1eKTpo)).aMH 342A II
350A B cpe)).e 3aIl{HTHOrO
ra3a
n p H M e 11 a H M e. [a]p -- .n;onYCKaeMoe HanpR:>KeHHe J1.]Ul OCHOBHoro MeTaJlJIa KOHC-rpYKQHH
npH paCTSI>KeHMM; [cr']p' ['t']cp - lI.OnYCKaeMble Hanp5DKeHHSI COOTBeTCTBeHHO npH paCTSI)I(eHHH
J1.]Ul CTblKOBoro llIBa M cpe3e .1J.,1UI yrJIOBOrO lllBa.
I
I
II
a
6
6
PH c. 3. 11
5 11. 11. BepeHH3
113
!
a
to
F
F
6
F
6
,
"
F
Puc.3.12
nplfMep 3.2
PaCT5IHYTbIH pacKoc cpepMbI COCTOIiT Ii3 l1BYX paBH060KIiX yronbHHKoB 75 x 75 x 6,
npIiBapeHHbIX K KOCbIHKe n060BbIMIi Ii cpJIaHrOBblMH lIlBaMH C KaTeTOM k == 5 MM.
MaTepHaJI yrOJIbHIiKOB - CT3;'[crJp == 160 = H/MM2; CBapKa pYQHaSI 3neKTpoJ:(aMII
342A.
Onpe,nenlITb ,nnHHbI cpnaHroBblx lllBOB 14>1 Ii 14>2 II3 ycnoBlul paBHOnpO
nIOCTH
paCKOCa Ii ero COe,D.liHeHHSI C KOCblHKOH (PHC. 3.13).
PerneHIie.
I. Onpe.rr.enSIeM )J.onycKaeMYIO BenH1.JHHY pacTSlrHBalOll\eH ClinbI [F] == [a]pSmin =
= 2S yr [alp = 2.8,78.10 2 '160 == 281-10 3 (II).
nnOll(aJ:(b nOnepe1.JHOrO Ce1.JeHIUI yrOJIbHHKOB 6epeTcSI no CnpaB01.JHIIKaM, B
J:(aHHOM cnYQae OHa paBHa 8,78 CM2.
2. Onpe
enSieM )J.onYCKaeMoe ycnnHe Fn ,[(nSi n060Boro lllBa. npelK,ne Bcero on-
pe,nenSIeM ['t']cp = 0,65 [alp = 0,65. 160 = 104 (H/MM2) (CM. Ta6n. 3.3).
3aTeM BbI1.JHCnSleM [Fn] = 2.0,7 kin [t"]cp = 2'0,7.5.75.104 = 52.10 3 (H).
3. OnpeJ:(eJISleM YCHJIHe F4>' KOTopoe l10JIlKHO 6bITb BocnpHHSITO cpJIaHrOBbIMH
IllBaMH:
114
F(p = [F]-[F]n =281.10 3 -52.10 3 =229.10 3 (H).
4. Bbl1.JHCJI5IeM CYMMapHYIO )J.nHHY
naHrOBbiX lIlBOB
FcfJ 229 . I 0 3
/4> = 2(/4>1 + /4>2) = [ ] = = 630 (MM).
0,7 k '[' 0,7 .5.) 04
cp
Cne,n:OBaTenbHO, )J.JISI O)J.Horo yrOJIbHHKa /4>1 + 14>1 == 630/2 == 315 (MM).
/cfJl + /4>2 = 630 /2 = 315 (MM).
5. Onpe)J.eJI5IeM pa3MepbI 14>J II 1$2'
3aMeTHM, 1.JTO u.eHTp TSllKeCTII yronKoB HaXOJ:(HTCSI Ha paCCTOSlHIIH 20,6 MM. nO-
JTOMY cpJIaHrOBbIH 1ll0B /4>J )J.OJIlKeH 6bITb 60JIbllle, 1.JeM 14>2' OTClOl1a
I = /(pl + 1(p2 ( 75 - 206 ) == 75 - 20,6 315 = 228 ( MM ) .
4>1 75 '75 '
TaKHM 06pa30M, 1
2 == 315 -- 228 == 87 (MM).
YCJlOBHOe u306pa*eHue U 0603Ha
eHue lllBOB CBapHbIX COe,lI.HHeHHH
YCTaHaBJIHBaeT rOCT 2.312-72*. He3aBHCHMO OT cnoco6a CBapKH BH-
,lI.HMbIH lllOB H306pa:>Ka1OT cnnOIllHOH JIHHHeH, a HeBH,lI.HMbIll - nYHK-
THpOM; OT H306pa:>KeHH
lliBa npOBO,lI.
T JIHHHIO-BbIHOCKY, 3aKaHqH-
BalO
YIOCSI O,lI.HOCTOpoHHeM CTpeJIKOll (CM. pHC. 3.12). I1pH TOqeqHOH
KOHTaKTHOH CBapKe BH,lI.HMYIO O,L(HHOqHYIO CBapHYIO TOqKY H306pa)Ka-
lOT 3HaKOM +, HeBH,lI.HMbIe O,lI.HHOqHbIe TOqKH Ha qepTe)Ke He H306pa-
:>KaIOT. Pa3Mep KaTeTa WBa YKa3bIBaeTC
3HaKOM
, a cTo
a
cnpaBa
QH<ppa 03HaqaeT BbICOTY KaTeTa B MM (CM. pHC. 3.12).
Coei)Ul-lel-lU51 na51l-lble, XOT
H
BJISIIOTCSI pa3HOBH,lI.HOCTbIO CBapHbIX,
0603Haqa1OTC
Ha qepTe:>KaX HHaqe. YcnOBHbIH 3HaK naHKH HaHOC
T
\0
o
C"'I
F
14>1
PHC. 3.13
I
115
,1
:j1
'-""'/PO
-=-
Ha nMHMM-BbIHOCKe: ,)L - TaK YKa3bIBmOT Ha BM)J,M-
MbIH mOB; a npH YKa3aHHI1 HeBH.lJJIMbIX nOBepXHO-
P 3 14 cTeH CT p eJIKa He CTaBHTC5I - <I. , llIBbl , BblnOJIHeHHbIe
HC. . r
no nepHMeTpY, OTMeqalOT Ha JIHHHH-BbIHOCKe KPY)l(-
KOM - ,;t; npH He06xo,[(I1MOCTH Ha qepTe)l(e npOCTaBJI5IIOT pa3MepbI
WBa H mepOXOBaTOCTb nOBepXHOCTH; 0603HaqeHHe npHno
YKa3bIBa-
101' B TeXHHqeCKHX Tpe60BaHH
X qepTe)l(a 3anHCblO no THny: «IIOC 40
rOCT ....».
IlpH BbInOJIHeHHH IllBOB npHnoSlMH pa3JIHQHbIX MapoK BceM IllBaM,
BblnOJIH5IeMbIM O,[(HHM H TeM )l(e MaTepHanoM, npHcBaHBalOT O,[(HH
nOp5llI;KOBbIH HOMep, KOTOpbIH HaHOC
T Ha nHHHI1-BbIHOCKe, HanpH-
M ep: < ( Ng 1 .
3aKllenOtL1lbZe coedU1le1lUfl 06pa3YIOT nOCTaHOBKOH 3aKJIenOK B COBMe-
l.QeHHbIe OTBepCTHSI coe,[(I1HSleMbIX 3JIeMeHTOB H paCKJIenKOM C OCa)l(H-
BaHHeM CTep)l(H5I (PHC. 3.14).
3aKJIenKa npe,[(cTaBJI
eT C060H QHJIHH,[(pHqeCKHH MeTanJIHqeCKHM
CTep)l{eHb C rOJIOBKOiL B 3aBHCHMOCTH 01' THna rOJIOBKH pa3JIHqalOT
3aKJIenKH C nOJIYKpyrJIOH (PHC. 3.15, a), nOTaHHOH (PHC. 3.15, 6) 11
nOJIynoTaHHoH (PHC. 3.15, 6) rOJIOBKaMH. 3aKJIenKH C nOJIYKpyrJIbIMH
rOJIOBKaMH npHMeH
IOT B CHJIOBbIX I1 nJIOTHbIX CHJIOBbIX IlIBax; 3a-
KJIenKH C nOTaHHOH rOJIOBKOH HCnOJIb3YlOT Tor,[(a, Kor,[(a BbIcTynalO-
!UHe rOJIOBKH He)l(enaTenbHbI; 3aKnenKH C nonynoTaHHOH rOJIOBKOH
npHMeH
IOT ,[(JI
coerU1HeHH
TOHKI1X (no 4 MM) CTanbHblX JIHCTOB. L{n51
coe)J;HHeHH5I TOHKHX JIHCTOB H HeMeTanJIHqeCKHX J{eTaneH npHMeH5IIOT
nycTOTeJIbIe 3aKJIenKH.
""-
<!
.......
<!
o 5d
a
6
8
PHc.3.15
Pa3MepbI 3JIeMeHTOB 3aKJIenOK npHBo,[(
TC5I B rOCT 10299-80,
fOCT 10300-80, fOCT 10301-80.
06bIQHO 3aKJIenKH H3rOTOBJI
IOT H3 yrnepo,nHcTOH CTaJIH MapoK
CT2 H CT3. ,[(onycKaeMble Hanp5l)l(eHH5I Ha cpe3 H CM5ITHe npHBe,[(eHbI B
Ta6n
3.4.
JIIiHY 3aKJIenKH paCCqHTbIBalOT no <popMyne
116
I
t
I
I
I = It + 111 = It + (1 ,3 ... 1,7) d,
r,[(e II - cYMMapHa51 Ton
HHa CKnenbIBaeMblX ,neTaJIeH; 111- 3anac ,[(JIHHbI
Ha 06pa30BaHHe 3aMbIKalO
eH rOJIOBKH; d - ,[(HaMeTp 3aKJIenKI1.
-1
. i
I
I
I
i
Ta6nHua 3.4
)].onYCKaeMLle HanpHjKeHltH" H/MMz, lI.JlH 3aK.TlenOQHLIX COell.l-IHeHI-IH CTaJlbHLIX
KOHCTPYKl(IIH nplt CTaTIIQeCKOM HarpYiKeHlui
)::(onYCKaeMbIe MaTepHaJI 3aKJIenOK
HanpSllKeHHSI CT2 CT3
Cnoc06 nO)J.rOTOBKll oTBepcTHH
[ II I II
Ha cpe3 ['t'] cp 140 100 140 100
Ha CMSlTHe [cr]CM 280 240 320 280
IT pH M e 1.J a H II SI.
I. )::(onYCKaeMbIe HanpSllKeHHSI Ha paCTSllKeHHe )J.JI$l OCHOBHoro MaTepHaJIa KOH-
CTpYKUIUf: .lI.nSl CT2 [cr]p = 140 H/MM2, .lI.JISI CT3 [cr]p = 160 H/MM2.
2. Cnoco6bI nOJIrOTOBKII oTBepcTHH: I - oTBepcTHSI npocBepneHbI IIJIH npOlIaB-
JIeHbI (Ha MeHbllIHH )J.HaMeTp) C nOCJIe)J.YIOllJ,eH paCCBepJIOBKOH; II - npo.n.aBJIeHHbIe
OTBepCTHSI.
Ta6nHua 3.5
PeKOMeHLl.yeMLle Ll.lfaMeTpLI oTBepcTnii noLI. 3aKJlenKY
nplt TOQHOii 1-1 rpy60ii c6opKax, MM
HOMHHaJIbHbIH C60pKa HOMHHanbHbIH C60pKa
JIHaMeTp .n.naMeTp
3aKJIenKH TOQHaSl rpy6aSl 3aKJIenKH TOQHaSl rpy6aSl
10 10,5 11,0 19 21 21
11,5 12,5 12,5 22 23 24
13 13,5 14,0 25 26 27
16 16,5 17,0 28 29 30
OTBepCTHSI ,[(JI5I 3aKnenOK np06HBalOT HJIH npOCBepJIHBalOT no pa3-
MeTKe. MO)l(HO o,[(HoBpeMeHHo CBepJIHTb 06e CKnenbIBaeMble ,[(eTaJII1,
31'0 nOBbIlllaeT TOQHOCTh coe,[(HHeHH
. CBepneHHe OTBepCTHH 51BJI
eTC5I
60JIee Tpy,noeMKOH 11 ,[(oporOH onepaQHeH, QeM np06l1BKa. lIlHpoKoe
pacnpOCTpaHeHHe nOJIYQHJI KOM6HHHpOBaHHbIH cnoc06 06pa60TKH
MaTepHaJIa nOJ{ 3aKnenKI1: BHaQaJIe np06HBaJQT OTBepCTH5I MeHhlllero
J{HaMeTpa, a 3aTeM paCCBepJIHBalOT HX no HY)l(Horo pa3Mepa. Pa3MepbI
oTBepcTHH no)]; 3aKJIenKI1 peKOMeHLJ;yeTcH 6paTb 113 Ta6JI. 3.5.
117
I1pH Heo6xoJJ;HMOCTH nonyqHTb oco60
npOQHble COeJJ;HHeHH5I, ,nOnYCKalOlQHe npOH3-
BOJIbHYIO HarpY3KY, BKJII01.Ja51 HepaBHOMepHbIH
OTpbIB, BH6paQHOHHYIO HarpY3KY, npHMeH5IIOT
KOM6HHHpOBaHHbIe COe)J:HHeHH5I: KJIeeBHHTO-
BbIe, KJIee3aKnen01.JHbIe, KneeCBapHbIe. HCnbI-
TaHH5I Ha Cpe3 nOKa3bIBaIOT, 1.JTO npOQHOCTb
KJIeepe3b6oBbIX COen;HHeHHH 60JIee qeM B )1Ba
pa3a BbIllIe np01.JHOCTH npOCTbIX KJIeeBbIX
COe)J:HHeHHH.
Y CnelliHO npl1MeH5IIOT KJIeH )J:JISI nOBbIllleHHSI np01.JHOCTI1 COnp5l)l(e-
HI1H 3y6qaTbIX KOneC C BaJIOM; npH YCTaHOBKe HapY)I(HbIX KOJIeQ nO)J:-
lllHnHHKOB B Kopnyc, B qaCTHOCTH nOCJIe nOTepH pa3MepOB paCT01.JeK;
JJ;JI5I ynJIOTHeHHSI 11 CTOnOpeHHSI pe3b60BbIX COe)J:HHeHHH.
llIBbI Hepa3'beMHbIX COeJJ;HHeHHH, nonyqeHHbIX CKJleHBaHHeM, OT-
MeqalOT Ha qepTe:>Ke 3HaKOM «K», npOCTaBJIeHHbIM Ha JlHHHI1-BbI-
HOCKe: ,tf; MeCTO KJIeeBOrO COe,[(MHeHH5I H306pa)l(alOT CnJIOlllHOH
JIHHHeH, KOTOpa51 ,[(OJI)I(Ha 6bITb B ,[(Ba pa3a TOJII.IJ:e OCHOBHOH. B TeX-
HH1.JeCKI1X Tpe60BaHHSIX 1.JepTe)l(a He06xo,[(HMO YKa3aTb, KaKHM KJIeeM
OCYI.IJ:eCTBJIeHO Hepa3'beMHOe COeJJ;I1HeHHe, HanpHMep «KJIeH E<I>- 2
rOCT ...».
B MallIHHocTpoeHHH ,[(JI5I C03,[(aHH5I HenO,[(BH)I(HOrO coe,[(HHeHHSI,
HanpHMep JJ;JlSI JJ;eTaJleH «BaJI-llleCTepHSI», MO)l(HO HCnOJIb30BaTb no-
cadKu c Han'15120M. OHM XapaKTepH3YIOTC5I HaJII11.JHeM rapaHTl1pOBaH-
HOrO HaTSIra He3aBHCHMO 01' cnoc06a COe,lIHHeHH5I .neTaneH (no.n npec-
COM, pa30rpeBaHHeM OXBaTbIBalOIIleH ,lIeTaJIH, OXJIa)l(.neHHeM OXBaTbI-
BaeMOM ,neTaJIH HnH KOM6HHHpOBaHHbIM cnOC060M). BbI60p nOCaJJ;KH
npOH3BOJJ;HTC5I 113 ycnoBHSI, 1.11'0 npH HaHMeHbllleM HaT5Ire 06eCne1.JHBa-
eTC5I np01.JHOCTb COeJJ;HHeHH5I H nepe,na1.Ja HarpY3KH, a npH HaH6oJIb-
llIeM - np01.fHOCTb ,neTaJIeH.
COnp5l)l(eHHe ,neTaJIeH no,n npeCCOM - HaH60nee H3BeCTHbIH H He-
CnO)l(HbIH npoQecc. Ero He)].OCTaTKOM 51BJI5IeTC5I HepaBHOMepHa51
,ne<popMal(H5I TOHKOCTeHHbIX ,neTaJIeH 11 B03MO)l(HOCTb nOBpe)l(JJ;eHH5I
TOPQOB.
Cnoco6 COnp5l)l(eHI151 nYTeM HarpeBa OXBaTbIBalOI.l\eH ,neTaJIH ,no
200...400°C H 3anpeccoBKH B Hee XOJIOJJ;HOH OXBaTbIBael\10H ,neTaJIH
TaK)I(e llIHpOKO pacnpocTpaHeH. He,nocTaTKH 3Toro cnoc06a - B03-
MO)KHOCTb H3MeHeHH5I CTPYKTypbI MeTaJIna, n05lBJIeHHe OKanHHbI H
Kop06JIeHHe.
XOpOlllHM cnoc060M cOnp5l)KeHHSI .n;eTaJIeH C HaT5IrOM 51BJISIeTCSI oxna-
:>KJ(eHHe oXBaTbIBaeMoM ,neTaJIH. B 3aBHCHMOCTH OT Ha3HaQeHHSI coe.n;HHe-
HHM BbI6HpalOTcSI T5I)I(eJIbIe, cpe,nHHe H JIerKH noca,[(KH C HaT
)TOM.
T 51)1( e JI bI e n 0 C a,[( K H npHMeH5IIOTC5I B coe,[(HHeHH5IX C 60nblllHMH
HarpY3KaMI1, HanpHMep B BarOHHbIX KOJIeCaX Ha OCSIX, YCTaHOBOqHbIX
tr
C60pKa coe,nHHeHH5I oCYI.QeCTBnSIeTcSI cne,n;YIOI.QHM 06pa30M. B ro-
TOBbIe OTBepCTH5I CTaB5IT 3aKJIenKH. 3aTeM no,n HH)I(HIOIO (3aKna,nHYIO)
rOJIOBKY no,n;CTaBJI5IIOT no,[(,n;ep)l(KY C yrny6JIeHHeM, cooTBeTcTBYIO-
lQHM OqepTaHHIO rOJIOBKH. Ilo,nJJ.ep:>KKa ,non)KHa onHpaTbcSI Ha Mac-
CHBHYIO HaKOBaJIbHIO, nocne qero oCYlI.\ecTBJISIeTC5I KJIenKa (BpyqHYIO
I1JII1 MeXaHHqeCKH).
B 3aBHCHMOCTH 01' ycnoBHH pa60TbI npHH5ITa cJIe,nYIOI.l\a51 KnaCCH-
<PHKaQIISI 3aKnenOqHbIX IllBOB:
npOQHbIe - 06eCne1.JHBa1OT paC1.JeTHYIO npOqHOCTb coe,nHHeHH5I (cpep-
Mbl, 6aJIKH, KOJIOHHhI);
np01.JHOnJIOTHbIe - 06eCne1.JHBa1OT He TOJIbKO paC1.JeTHYIO npOQHOCTb,
HO H repMeTH1.JHOCTb coe)J:HHeHHSI (napOBbIe KOTJIbI, pe3epByapbI no)];
JJ.aBJIeHHeM);
nJIOTHbIe - 06eCne1.JHBa1OT repMeTH1.JHOCTb coe,nHHeHHM (pe3epByapbI
11 'fPy6onpOBO)];bI C He60JIbIllHM H36hIT01.JHbIM )J:aBJIeHHeM).
3aKJIenOqHhIe lllBbI MorYT BbInOJIHSITbCSI BHaxneCTKY (CM. pHC. 3.14),
C O,nHOH (PHC. 3.16, a) HJII1 ,[(BYM5I (PHC. 3.16, 6) HaKna,nKaMH, npH 3TOM
cxeMbI 3aKJIen01.JHbIX cOe,lIJIHeHHH MorYT BbInOJIH5ITbCSI C p}l)];HbIM pac-
nOJIO)l(eHHeM 3aKJIenOK (CM. pHC. 3.16, 6) HJIH C llIaXMaTHbIM (PHC. 3.17).
[d::
!
:[]
a
6
PIiC. 3.16
IlpHMepbI paC1.JeTa 3aKJIenOK 6bIJIH paccMOTpeHbI B pa3,n. 2 (npH-
MephI 2.3, 2.4).
Hepa3'beMHOe coeJ(HHeHHe )];eTaneH 113 pa3JIH1.JHhIX MaTepHaJIOB MO)K-
HO ocymecTBHTb KJIeSlMH Ha OCHOBe CHHTeTHqeCKHX CMOJI. ,L(OCTOHHCT-
BaMH Kllee6blX coei)U1ie1iUU 51BJI5IIOTC5I: B03MO)l(HOCTb coe,nHHeHH}I ,neTa-
nei1 113 pa3HopOJ(HbIX, a TaK)I(e TOHKOJIHCTOBhIX MaTepHaJIOB; xopOIllee
conpOTHBneHlIe YCTanOCTII; B03MO)l(HOCTb 06eCneQeHlISI repMeTH1.JHO-
CTH. B nOCJIe,nHHe rOJ(hI CKJIeHBaHHe HallIJIO lllHpOKoe npHMeHeHHe
)J;a)J(e B OTBeTCTBeHHbIX MallIHHax M coopY)l(eHH5IX (caMOJIeTaX, MOCTax),
B MeTannOpe)KymHx CTaHKax (J(JISI nOBbIIlleHHSI 113HOCOCTOMKOCTH Ha
HanpaBJI}lIOlI.\l1e npl1KJIeHBalOT cpTopOnJIaCT). OCHOBHbIM HeJJ;OCTaTKOM
KJIeeBbIX coeJJJIHeHHH 51BJI5IeTC5I I1X cJIa6a51 pa60Ta Ha HepaBHOMepHbIM
OTpbIB.
118
.
-+-.
-.-.
'
I
. 1
.--+- 1
. 1
.-+1
1
PI1C. 3.17
119
IlITM<pTax B CTaHOqHbIX npMcnoco6neHHSIX, HeC'beMHbIX MycpTaX Ha
KOHQaX BanOB npOKaTHhIX CTaHOB, ce,nne KnanaHa B rOnOBKe 6noKa
QMnHH,npOB rpY30BOrO aBTOM06HnSl.
C p e,A H Men 0 C a,n K 11 peKOMeH,nyercSI npl1MeHSlTh ,[(JISI 3anpeCCOB-
KI1 BTynoK B llIKHBhI M 3y61.JaThIe Koneca, coe,nI1HeHMSI KOH,nYKTOPHhIX
BTynoK C KopnYCOM KOH,nYKTopa, 3aKpenneHMSI 3y6qaThIX Konec Ha Banax
Kopo6oK CKopOCTeM, YCTaHOBKI1 6pOH30BhIX BeHQOB qepBSlqHhIX Konec.
n e r K Hen 0 C a A K 11 C HaTSIrOM npMMeHSIIOT AnSI coe)].HHeHHSI
TOHKOCTeHHhIX BTYJIOK C KopnycaMI1, 3aKpenneHHSI YCTaHOB01.JHhIX
KOnel..\ Ha BaJIY 3neKTpoJ(BMraTeJISI, coeJ(HHeHMSI BTynoK C 3y6qaTbIMM
KonecaMH MeTaJIJIOpe)l(YlQI1x CTaHKOB.
O,nHHM 113 cnoco6oB c03,naHI1S1 Heno,nBH)I(HhIX coe,nI1HeHI1M SlBnSleT-
CSI a p M H P 0 B a H Hen n aCT Mac COB bI X .L{ eTa JI e Ii. B pa.L{HO- 11
3neKTpOTeXHMqeCKOH npOMbIlllJIeHHOCTI1 npeCCOBaHMeM H JIMTheM no.l1
,naBJIeHHeM nOJIyqalOT 3JIeKTpH1.JeCKl1e pa31>eMHMKH, Kono,nKM, naHeJIH.
3TO n03BOJISleT B 10... 100 pa3 cOKpaTHTh Tpy,noeMKocTh H3rOTOBJIe-
HI1S1 TaKI1X ,AeTarreH no cpaBHeHl110 C Tpy,noeMKOCThlO nonY1.JeHHSI aHa-
nOrHqHhIX KOHCTPYKQHH nYTeM C60PKH M3 OT,nenbHbIX 3JIeMeHTOB C
nOMO
hlO MeXaHH1.JeCKOrO KpenJIeHI1R. ,[(JISI C03
aHHSI Heno,nBH)I(HhIX
coe
I1HeHI1M apMaTYPY B BI1,ne BI1HTOB, raeK, lIIThIpeii (PHC. 3.18, a, 6)
a
6
B
z
o
PH c. 3. 18
120
I
3aKpenJISIIOT C nOMOlQblO KOJIhQeBbIx 6YPTHKOB Mnl1 KaHaBOK. ,L(n.sI
npe,noTBpa
eHI1S1 npOBOpa1.JI1BaHI1S1 Ha HapY)I(HhIX nOBepxHocTSlX 3TI1X
eTarreM BhInOJIHSlIOT pHcpJIeHI1S1, HaCe1.JKY I1JII1 nJIOCKl1e rpaHI1. MenKl1e
,AeTaJII1 B BI1,ne nJIaCTI1HOK (KJIeMMhI 3JIeKTpH1.JeCKHX pa31>eMOB) 3aKpe-
nJISlIOT C nOMOlQblO BbIpe30B HJII1 OTBepcTHM (PHC. 3.18, 6, 2). IIpoBO-
JI01.JHYIO apMaTYPY paCnJIlOlQl1BalOT (pl1c. 3.18, 0).
3.8. Pa3'beMHLIe coeAHHeHHH AeTaJIeU
K pa3'beMHbIM COe,AI1HeHI1S1M )J.eTarreH OTHOCSlTCSI: pe3b6oBbIe, CPPI1K-
QI10HHbIe C KOHI11.JeCKHMH KOJIbQaMH, KJII1HOBbIe, lllTl1cpToBbIe, lllnOH01.J-
HbIe, IlIJII1QeBbIe 11 npo<pI1JIbHbIe (6ecrnnOHOqHbIe). Pa31>eMHbIe coe.L{l1-
HeHI1S1 MO)l(HO HeO,llHOKpaTHO pa36l1paTb 11 BHOBb co6l1paTb. PaCCMOT-
pl1M Hal160JIee qaCTO BCTpeQalOlQl1ecSi B Marnl1HOCTpOeHHM pa3'be
iHbIe
COe.L{I1HeHI1S1 ,neTaJIeH.
Pe3b6oBbie coe
HHeHHH - 3TO pa3'beMHhIe coe,nHHeHI1S1, BbInOJIHeH-
HbIe c nOMOlQblO pe3b6oBbIX Kpene)l(HbIX ,neTaJIeH - BHHTOB, 60JITOB 2
(pl1c. 3.19), lllnl1JIeK, raeK 1 (pl1c. 3.19) I1JII1 pe3b6bI, HaHeceHHOM He-
nocpe,nCTBeHHO B coe
I1HSleMoii J(eTaJII1.
Pe3b6a 06pa3yeTcSI nYTeM HaHeCeHI1S1 Ha nOBepxHocTb ,neTaJIeH
BI1HTOBbIX KaHaBOK C Ce1.JeHl1eM COrJIaCHO npocpHJIIO pe3b6hl. 06pa30-
BaHHbIe TaKI1M 06pa30M BhIcTynbI HOCSIT Ha3BaHI1e BMTKOB. B03MO)l(-
HbI CJIe
YIO
l1e npocpl1JII1 pe3b6, npl1MeHSleMhIX ,AJISI BI1HTOBhIX nepe-
J(a1.J: TpeyrOJIbHhIH (PHC. 3.20, a), npSlMoyrOJIbHbIH (PHC. 3.20, 6) H
Tpaneuel1JJ.aJIbHbIH (pl1c. 3.20, 8).
TepMI1H «6U1-lm» npl1MeHSlIOT KaK B 06l.l.(eM (o6'be.l1HHSllOlileM TaK)I(e
60JIThI 11 rnnI1JIbKI1), TaK 11 B 1.JaCTHOM (BI1HT, Bpa
aeMbIM npM 3aBI1H-
1.JI1B aH 1111 11 OTBI1H1.JI1BaHI1I1, T. e. BBI1HqI1BalO
I1HCSI B
eTaJIb) CMhICJIax.
OT 3Toro Ha3BaHHSI B03HI1KJIM ,n:pyrHe TepMHHhI: BHHTOBoe J(BI1)KeHl1e,
BI1HTOBaSl JII1HI1S1, BI1HTOBaSl nOBepXHOCTb. TepMI1H «pe3b6a» np01130-
meJI OT TeXHOJIOrl1QeCKOrO npoQecca ee H3rOTOBJIeHI1S1 - Hape3aHI1S1.
raUKa - 3TO J(eTaJIb C pe3b6oBhIM OTBepCTl1eM,
HaBI1HQI1BaeMaSi Ha BI1HT 11 I1MelO
aSl cpOPMY,
npl1cnOC06JIeHHYlO ,n:JISI 3aXBaTa rae1.JHbIM KJIIO-
'-10M I1JII1 PYKOH.
Pa3JII1'-1alOT npaBYIO H JIeBYIO pe3b6y. ECJIH co
CTOpOHbI TOPQa BI1HTa Ha HapY)KHOH QaCTI1 BI1H-
TOBaSi JII1HHSI no,n:HHMaeTCSI CJIeBa HanpaBO, TO
pe3b6y Ha3bIBalOT npaBOH, eCJII1 cnpaBa HarreBO -
JIeBOM.
He3aBI1CI1MO OT npocpl1JISI Bce pe3b6bI I1MelOT
CTaHJJ:apTI130BaHHhIH mar BI1HTa P (CM. pl1c. 3.20).
3TO OCHOBHaSl xapaKTepHCTI1Ka BI1HTa, KOTopaSl
1
2
PI1C. 3.19
121
a
6
6
PHC. 3.20
nOKa3bIBaeT, Ha KaKoe paCCTO$lHHe (B MM) nepeMemaeTCSI raHKa (HJIH
60JIT) B,[{OJIb CBoeH OCH 3a O,l(HH 060pOT.
ECJIH B pe3b6oBOM H3}J;eJIHH BbInOJIHeHa MHor03aXO}J;HaSl pe3b6a, TO
3a O}J;HH 060POT raHKa B}J;OJIb CBOeH OCI1 nepeMeCTI1TC
Ha BeJII1IJI1HY
xo
a S = kp , r
e k - 3aXO
HOCTb pe3b6bI.
Pe3b6oBbIe COe)JJ1HeHHSI nOJIY4HJIH 60JIblIlOe paCnpOCTpaHeHHe B
MaIIlHHOCTpOeHHH. B COBpeMeHHbIX MalIlHHaX }J;eTaJIH, HMelOW;He pe3b-
6y, COCTaBJISlIOT CBbIlIle 60 % 01' 06w;ero 1.II1CJIa ,n:eTaJIei1.
KJIHHOBOe coe
HHeHHe -- 3TO pa3'beMHOe coe}J;HHeHHe, 3aTgrHBaeMoe
MJIM perYJIMpyeMoe C nOMOIll.blO KJIMHa. TMnM1:IHbIM npMMepOM KJII1HO-
Boro coelIJiHeHHSI SlBJIgeTCSI COelI.HHeHHe BaJIa co BTYJIKOH.
B KJIHHOBbIX coe}J;I1HeHI1S1X npl1MeHSlIOT n01.ITI1 HCKJII01.IHTeJIbHO OlI.-
HOCKOCHble KJIHHbSl, TaK KaK J(BYXCKOCHbIe SlBJISlIOTCSI 60JIee CJIO)l(HbIMH
B H3rOTOBJIeHI1H, a npeHMymecTB nepe,n; O,n;HOCKOCHbIMH He HMeIOT.
Pa601.IHe nOBepxHocTH KJIHHbeB BblnOJIHSlIOT QHJIHH,[{pH1.IeCKI1MH HJIH
nJIOCKHMH C cpaCKaMH (pHe. 3.21). B CHJIOBbIX KJIHHOBbIX coe}J;I1HeHI1S1X
BbI6HpalOT YKJIOHbI 1: 100, 1 :40, 1 :30. Y CTaHOB01.IHbIe KJIHHbSl HMelOT
YKJIOHbI I: 10, 1 :6, 1 :4.
ECJIH KJIHH COe,l(HHgeT co BTYJIKOH BaJI J(HaMeTpOM d, TO TOJIW;HHa
KJIHHa (H3 YCJIOBHSI paBHOnp01.IHOCTH BaJIa Ha paCTg)l(eHHe H Ha CMSI-
THe KJIHHOM) b = (0,25... 0,30)d; BbICOTa CeIJeHHSI KJIHHa h > 2,5 b.
QT06hI KJIHH He BbI,l(aBJIHBaJICSI H3 rHe3,n:a, He06xoJ(HMO C06JIIO,l(aTb
COOTHOlueHHe Me)l(.ny yrJIOM TpeHH5I <p H yrJIOM HaKJIOHa a: a < 2<p, r
e
tga = (hi - 11 2 )/1 (,n;JISI O,l(HOCKOCHoro KJIHHa).
A-A
I
b
h 2
A
PlICa 3.21
122
I
I
!
-/
!
CoeAHHeHHH IllTU4JTaMH. IIlTH<pTbI npe,l(Ha3Ha1JeHbI B OCHOBHOM
}J;JISI B3aHMHOrO
HKCHpOBaHHSI ,n:eTaJIeH, a TaK)I(e ):(JI$I nepe):(a1JH
OTHOCHTeJIbHO He60JIblllHX HarpY30K. npHMeH$lIOTCH H cneQHaJIbHbIe
Cpe3alOllJ;HeCSI lIlTHCPTbI, CJIY)I(allJ;He npe,n;oxpaHHTeJIbHbIM 3JIeMeHTOM
B MY<PTax.
IIlTH
TbI pa3,l(eJISlIOT Ha rJIa,l(KHe C HaCeqeHHbIMH HJIH BbI}J;aBJIeH-
HbIMH KaHaBKaMH, npY)KHHHbIe. no
opMe lIlTH
TbI pa3}J;eJISlIOTCSI Ha
I..{HJIHH,npHqeCKlie H KOHH1JeCKHe. rJIa,nKlie lllTH<pTbI 1I3rOTaBJIliBalOT H3
CTaJIH 45 H A 12, lllTH
ThI C KaHaBKaMH H npY)I(HHHbIe - H3 npY)I(HH-
HOM CTaJIH.
a
PUC. 3.22
6
l.{HJIHH,l(pHQeCKHe lllTH
ThI CTaBSlT B OTBepCTH$I C HaTSlrOM (PHC. 3.22,
a); HHor}J;a KOHI..{bI llITHcpTOB paCKJIenbIBalOT (PHC. 3.22, 6). B ,neTa-
JI5IX, KOTopbIe nOCTOSlHHO nOlI.JIe)l(aT pa360pKe, oTBepcTHe pa3BepThI-
BaIOT, QTO n03BOJISleT pa3'belI.HHSlTb COelI.HHeHHe 6e3 BhIKOJIa1.IHBaHH$I
lllTH cpTOB.
HaH60JIblllee pacnpocTpaHeHlIe nOJIYQI1JII1 rJIa}J;KI1e KOHHQeCKHe
llITHcpThI; HX BbInOJIHSlIOT C KOHYCHOCTblO 1: 50. ITpocThIe IIlTHCPTbI, 3a-
6HBaeMbIe B oTBepcTHSI (PHC. 3.23, a), HCnOJIb3YIOT TOJIbKO }J;JI$I CKB03-
HbIX oTBepcTHH, KOr,l(a C npoTHBonoJIo)l(HoM CTOpOHbI HX MO)l(HO
a
6
PHC. 3.23
6
123
BbI6MTb. IlITM
TbI C pe3b60H .[{n51 M3BneqeHM5I npM pa360pKe (PMC. 3.23,
6) npMMeHSlIOTC5I )1n51 YCTaHoBKM B rnyxMe oTBepCTM5I. Il1TM
TbI C pe3b-
60H, 3aT5IrMBaeMOH raHKOH (PMC. 3.23, 6), MCnOnb3YIOTC5I B COe.[{MHe-
HM5IX, nOJJ;Bep>KeHHbIX TOnqKaM M y,napaM, a TaK>Ke B 6bICTpOBpalI(alO-
lI(MXCSI coe.[{MHeHM5IX. )J;n51 nepe.[{aqM HarpY3KH, a He ,n:n51
MKCMpOBa-
HM5I B3aHMHoro nOnO>KeHH5I ,n:eTaneH, Mcnonb3YIOT lllTM
Tb] C KaHaB-
KaMH.
UInOHOIJHbIe coe)J.HHeHHH - 31'0 MHoropa3MepHbIe coe.[{HHeHH5I .[{e-
TaneM, npe,nHa3HaQeHHble ,nn51 nepe.[{aqH, rnaBHbIM 06pa30M, BpalI(a-
TenbHoro
BH>KeHH5I (Bana co lllKHBOM, C 3y6qaTbIM KoneCOM). 3TH
coe.[{MHeHM5I npHMeH5IIOT B Tex cnyqa5lX, ecnH K T01.JHOCTI1 QeHTpM-
pOBaHH5I coe.[{HH5IeMbIX .[{eTaneM He npe,zJJ)51Bn5leTC5I OC06bIX Tpe60-
BaHMH.
A-A
1
AJ
PliCa 3.24
Coe,nHHeHHe llInOHKaMH 1 MO>KeT 6bITb Heno,nBH>KHbIM (PHC. 3.24)
MnM nO.[{BH>KHbIM B.[{onb OCM Bana 2. B nocne.[{HeM cnyqae HanpaB-
n5l1Orn:a51 IllnOHKa npHT5IrHBaeTC5I K BaJIY BHHTaMH. IllnoHKa npH-
MepHO HanonOBHHY BhICOTbI BXO.[{HT B na3 Bana H HanonOBHHY - B
na3 cTynHQbI Koneca. EOKoBbIe (pa60qHe) rpaHM IlInOHKH nepe.[{alOT
BpaI.QeHHe 01' Bana K Konecy H o6paTHo. <l>opMa l1 pa3MepbJ 60nb-
llIHHCTBa THnOB lllnOHOK cTaH.[{apTH30BaHbI H 3aBHC5IT 01' ycnoBHM
pa60TbI coe.[{HH5IeMbIX .[{eTaJIeH M ,nHaMeTpa Bana. ITo cpopMe CTaH-
,napTHble lllnOHKH pa3.[{en5lIOTC5I Ha npH3MaTHqeCKHe, KnHHOBhle, cer-
MeHTHble H TaHreHQHanbHble C np5lMoyronbHbIM nOnepeQHbIM ceqe-
HMeM.
Ha npOL(OnbHbIX pa3pe3ax Bce lllnOHKH nOKa3bIBalOT HepaCCeqeH-
HbIMH. Pa3MepbJ CeqeHHM lllnOHOK H na30B BbI6HpalOT B 3aBHCHMOCTH
01' .[{HaMeTpOB BanOB.
MaTepHaJI - CTanb qHCToT5IHYTa51 ,nn51 UlnOHOK C BpeMeHHbIM co-
npOTHBJIeHHeM pa3pbIBY He MeHee 590 MIla.
UIJ1Hl..{eBble coeAHHeHHH npHMeHSlIOT .[{n51 60nee T01.IHOrO QeHTpH-
pOBaHHSI .[{eTaneM Ha Banax; OHH nepe.[{aIOT, no cpaBHeHHIO co lllno-
HOqHbIMH coe.[{HHeHHSlMH, 66JIbIlIHe KPYTSlll
He MOMeHTbl, HMelOT 66JIb-
124
I
I
i
rnylO YCTMOCTHYIO npOqHOCTb. Ha Banax .[{enalOT BbIcTynbI, a Ha neTa-
nM - Bna.[{MHbI cooTBeTcTBYlOrn:MX £pOpM 11 pa3MepoB.
HaH60nbllIee pacnpocTpaHeHHe nonyqHnH lllnHQeBbIe coe.[{HHeHHSI
C npSlM060qHbIM, 3BonbBeHTHbIM H TpeyronbHbIM npoQJHn5lMH 3y6beB.
IllnMQeBbIe coe.[{HHeHH5I BbInonHSlIOT C pa3HbIM lJHCnOf..1 3y6beB (01' 6
.[{O 20 - Y npSlM060tIHbIX, 01' 12.[(0 50 - Y 3BonbBeHTHbIx).
IIlnHQeBbIe coe.[{HHeHHSI BblnonHSlIOT nO)J;BH>KHbIMH H HenO.[{BH>K-
HbIMH. KaK npaBMno, npM OrpaHHlJeHHbIX .[{HaMeTpaJIbHbIX ra6apHTHbIX
pa3Mepax BbInonHSlIOT HenO.[{BH>KHbIe lllnHQeBbIe coe.[{HHeHHSI Tpe-
yronbHoro npocpMJISI C Mo.[{yneM 01' 0,2 .[{O 1,5 MM H tIl1CJIOM llIJIlIQeB
01' 20 .[{O 70.
i.
3.9. nOJ.{IllHDHHKH CKOJIb
eHHH
IIo,lImHnHHKH CKOJlbiKeHHH - 3TO onopbl BpautalOll(HXCH JJ:eTaJleH,
pa60TalOIl(He B YCJ10BHHX OTHOCHTeJ1bHOrO CKOJ1biKeHHH nOBepXHOCTH
I..{an(j>bl no nOBepXHOCTH no
mHnHHKa, pa3AeJ1eHHblX CJlOeM CMa3KH.
ITo HanpaBJIeHlIlO HarpY30K, .[(eHcTBYlOrn:I1X Ha nO.[{llIMnHI1KI1
CKOnb>KeH1I5I, nOCne,l1.HHe nO,l1.pa3,l1.enSllOT Ha paOUaJlbllble H ynOpllble.
Pa,l1.HaJIbHbIe nO,LJJlll1nHHKl1 BOCnpHHI1MalOT HarpY3KH, HanpaBneHHble
nepneH,[(HKYJISlpHO KOCH Bana, a ynopHble nO.[{lllHnHHKH - oceBbIe
HarpY3KH.
Pa3nHqalOT HeCKonbKO THnOB nO.[{lllMnHHKOB:
a) rHApO)J.HHaMHIJeCKHe nO)J.mHnHHKH CKOJlbiKeHHH, B KOTOpbIX cnOM
CMa3KH 3aXBaTbIBaeTCSI nOBepXHOCTblO QanQJbI B npoQecce BPall(eHHSI
BaJIa. B TeXHlIqeCKOH nHTepaType HX qaCTO Ha3hIBalOT npOCTO no.[{-
llIHnHHKaMH CKOnb>KeHHSI. 110 cpaBHeHHIO c )J;pyrHMH nO.[{IllHnHHKaMH
CKOJIb>KeHH5I OHH Hcnonb3YlOTCSI qall{e Bcero;
6) rH
pOCTaTHIJeCKHe nOJJ:mHnHHKH CKOJ1biKeHHH - B HHX MaCJI5IHbIH
CROM Me>KL(Y TPYlUHMHCSl nOBepXHOCTSlMl1 C03JJ.aeTCSI HaCOCOM )].0 Ha-
qana Bpall{eHHSI Bana. B rHL(pOCTaTHlJeCKHX nOJJ.lllHnHHKax YMeHbllla-
eTCSI BnHSlHHe norpelllHOCTH llleeK BanOB H nO.[{IllHnHHKOB Ha T01.J-
HOCTb Bpal.I.\eHHSI (.[{O 5-10 pa3). OHl1 npHMeHSlIOTcSI B onopax TSI>KenbIX
THXOXO,[(HbIX 6apa6aHoB (lllapoBblx MenbHHQ, BpalI(alOll
HXcSI nelJeM);
onopax C MMHlIManbHbIM TpeHHeM HcnbITaTeJIbHbIX MalllHH M npM60-
pOB; onopax .[{JISI MexaHH3MOB, Tpe6YlOlIJJ1X TOlJHbIX nepeMelI(eHHM (no-
BOpOTHbIX YCTPOHCTB TeneCKonOB, .[(eJIMTenbHbIX CTOJIOB); onopax
rnnMH.[{eJIeH npeQH3MOHHbIX CTaHKOB. llpM nYCKe napOBbIX Typ61IH,
rM.[{poreHepaTopOB lICnOJIb3YlOT rH.[{pOCTaTMqeCKYIO pa3rpY3KY. IIe.[{o-
CTaTKaMlI rM.[{pOCTaTlItIeCKlIX nO.[{llIlInHMKOB SlBJISlIOTC5I 60JIbllIMe nOTe-
pH MOIl
HOCTH Ha npoKpyqHBaHHe Bana .[{a>Ke Ha xonOCTOM Xo.[{y, a
TaK>Ke CJIO>KHOCTb KOHCTPYKQHH nO,l1.IlIHnHHKa, He06xo.[{HMOCTb c60pa
MaCJIa, BbITeKalOll(erO H3 onopbI;
j
t
125
.II!
.1
II
B) nO,[(UJUnHUKII C B03,[(YUJHOU CMa3KOU. CKOpOCTb BpameHI151 Bana B
TaKHX nOJJ:llIl1nHI1KaX npaKTHqeCKI1 He orpaHl1ql1BaeTC5I - onopbI C B03-
)J.YllIHOM CMa3KOH pa60TalOT C MaJIbIMH nOTep5lMI1 11 HI1QTO)l(HbIM Harpe-
BOM, B5I3KOCTb C
1a3KI1 nOQTH He MeHSleTC5I OT 113MeHeHI1S1 TeMnepaTypbI
(B5I3KOCTb B03JJ:yxa B 100 pa3 MeHbllie B5I3KOCTI1 Hal1MeHee BSl3KOH H3
npl1MeH5IeMbIX IKI1,nKI1X CMa30K - KepOCI1Ha). KpoMe Toro, pecypc B03-
)J.yxa He OrpaHI1IIeH, He Tpe6yeTc5I c0611paTb CMa3KY 11 no Tpy60npoBO-
)J.aM OTnpaBn5lTb 06paTHO B MacnSlHbIM 6aK. )J;n51 3TI1X no,nllIl1nHI1KOB
)J;l1aMeTpanbHbIe 3a30pbI Ha3HaQalOT B npe)J.enax 10... 30 MKM.
OnopbI C B03,nYiliHOM CMa3KOM MorYT 6bITb a3poi)uHaJUUlleCKUAlu Ii
a3pOCman'1UllecKUMu. B a3po)J.I1HaMI1IIeCKI1X nO)J.Illl1nHI1KaX B03,nyx MO-
)l(eT caM03acaCbIBaTbCSI B 3a30p 113 aTMoccpepbI qepe3 TOPQbI nO)J;llIl1n-
HI1KOB, B a3pOCTaTI1QeCKI1X B03,nyX no,naeTCSI no)J. )J.aBneHl1eM 113BHe elI.{e
,no HaQana BpaIQeHI151, TaKI1M 06pa30M Ban nOMep)KHBaeTC5I B0311YIll-
HOM no,nYlliKOM. no 3KcnnyaTaQI10HHbIM CBOMCTBaM 3TI1 onopbI 6nl13KI1
K rl1,npOCTaTI1QeCKHM, HO HMelOT MeHbIlIl1e CHJIbI TpeHI151. B03,nYIlIHble
onopbl I1cnonb3YlOT B npeQH3110HHbIX MeTaJIJIOpe)KYW;I1X CTaHKax, B
3JIeKTpOIllnI1H,neJISlX BHYTpl1111nl1cpOBanbHbIX CTaHKOB (c qaCTOTOM Bpa-
IQeHH5I 40 000 ... 300 000 06/MHH).
He,nocTaTKH B03,nYlllHbIX onop: He,nonYCTI1MOCTb neperpY30K, npH-
BO,l(»
I1X K CYXOMY TpeHI1IO; BbICOKa51 TOqHOCTb 113rOTOBJIeHI151; He06xo-
)J.HMOCTb no,n)J.ep)l(aHI151 3a)J.aHHoro )J.aBJIeHI1S1 B nHeBMoceTH, TaK KaK
npl1 na,neHHI1 ,naBneHH51 B a3pOCTaTI1QeCKI1X onopax B03HHKaeT aBapl1H-
Ha51 cHTyaQI1S1;
r) 3JIeKTpOl\farHIITHbIe 6eCKOHTaKTHbIe onopbI - I1cnonb3YlOT npM
OIIeHb 60JIbllll1X CKOpOCTSlX. nOTepl1 B TaKI1X onopax HI1QTO)l(HbI H
,[(onYCTI1MaSl CKOpOCTb 06bIqHO onpe,nen5leTCSI npOqHOCTblO pOTopa.
He,l(OCTaTKOM SlBJISleTCSI BbICOKaSl CTOI1MOCTb 113rOTOBJIeHI1S1.
I10JJ:Illl1nHI1K CKOnb)l(eHI151 COCTOI1T 113 Kopnyca, BKnaj1-bIIlleM, no,n-
,lIep)KI1BaIOIQI1X Ban, a TaK)Ke CMa3bIBalOIQHX 11 3aIQI1THbIX YCTPOMCTB.
Kopnyc nOlIJIll1nHHKa MO)l(eT npe)J.cTaBnSlTb C060H oT)J.eJIbHYIO JII1-
TYIO HJII1 cBapHYIO ,neTanb, npI1Coe)J.I1H5IeMYIO K MaIlII1He, I1JII1 MO)l(eT
BbInOJIH5ITbC5I KaK O,nHO Qenoe C Heno,nBI1)KHOH 4aCTblO MaIllI1HbI I1nl1 C
nO)J;BI1)1(HOH ee )J.eTaJIblO, Hanpl1Mep C lllaTYHoM. Kopnyca nOj1-Illl1nHI1-
KOB BbInonHSlIOT QeJIbHbIMI1 Hnl1 pa3'beMHbIMI1.
Pa3beMHblu l1oi)UJUnHUK (pl1c. 3.25) COCTOI1T 113 Kopnyca 2, npHKpe-
nJI5IeMOrO K CTaHHHe 1 6onTaMI1 3, KpbIlllKH nO)J.llll1nHI1Ka 4 co CMa-
30QHbIM YCTpOHCTBOM 5 11 CMeHHbIX BKnaj1-bIllleM (nOJIYBTynoK) 6.
KpbIlllKa no,nllll1nHI1Ka coe,nI1H5IeTCSI C KopnycoM 60nTaMI1 7. 3a30p
Me)f(,[(y BanOM 11 BKna,nbIlllaMI1 perynl1pyeTc5I npoKna,nKaMI1, a no Mepe
M3Hoca BKna,nbIllleM - no,nT5IrI1BaHl1eM 60JITOB 4.
Pa3'beMHbIe Kopnyca 06nerQalOT MOHTa)l( BanOB, 110nycKalOT pery-
JIHpOBKY 3a30poB B nO)J.llll1nHI1Ke. OCHoBHoe npl1MeHeHl1e pa3'beMHble
Kopnyca HallIJII1 B TSI)I(enOM MaIllI1HOCTpOeHI1I1.
, I
! !
.,i
'i:
, .
Ii
i
126
T
.
a
5
7
PUC. 3.25
BKllaOblUlU npl1MeH5IIOT ,nJISI Toro, lIT06bI He BbInonHSlTb Kopnyca
no,nllll1nHI1KOB 113 ,noporl1x aHTl1cppl1KQHOHHbIX MaTepHaJIOB, a TaK)I(e
j1-JISI 06JIerQeHI1S1 peMoHTa nOj1-111l1nHHKOB nOCJIe H3Hoca. B Hepa3'beM-
HbIX nO)J.lllHnHI1KaX BKna,nbIlllH BblnOJIHSlIOT B BHJJ:e BTynoK, a B pa3'b-
eMHbIX - B Bl1l1e nOJIYBTynOK. BKJIa,nbIIlII1 3a BeCb CpOK cnY)K6bI H3Ha-
IlII1BalOTCSI Ha l'JIy6HHY, 113MepSleMYIO, KaK MaKCHMYM, B j1-eC5ITbIX j1-0-
JI5IX MHnJIHMeTpa. Ol1HaKO BbInonHSlIOT BKna,nbIIlII1 l'Opa3j1-0 60JIbllleH
TOnlI.{HHbI, TaK KaK 3Toro Tpe6YlOT YCJIOBI1S1 npOQHOCTH. BKna,nbIlllH
QalI.{e Bcero BblnonHSlIOT 6HMeTanJII1QeCKHMH: Ha CTanbHYIO (qyrYHHYIO
I1JIH 6pOH30BYIO) OCHOBY HannaBJI5IeTCSI TOHKHM aHTH£ppI1KQI10HHbIH
CJIOH.
B MenKOCepl1HHOM 11 I1Hj1-I1BI1)J.yanbHoM npOH3BO,UCTBe HapSlj1-y C
6HMeTanJII1QeCKI1MI1 BKna)J.bIlllaMI1 npl1MeH5IIOT 60nee npOCTbIe B 113-
rOTOBneHl111 cnnOllIHble BKJIaj1-bIllll1 113 aHTI1cppl1KQI10HHbIX MaTepHa-
nOB cpe)J.HeM 11 BbICOKOM npOIIHOCTI1. BKJIa,nbIIllI1 H3 aHTHcppHKQHOH-
HbIX QyrYHOB, TeKCTOJIHTa, npeCCOBaHHOH )J.peBeCHHbI 06bIQHO H3ro-
TaBJII1BalOT cnnOllIHbIMI1.
TOJIIQI1Ha nHToro BKJI a,nbI III a, YCTaHaBnHBaeMoro B Kopnyce, 8 B =
= (0,035... 0,05) d + 2,5, rj1-e d - )J.l1aMeTp QancpbI, MM. TOnIl{I1Ha 3a-
nl1BKI1 npHHHMaeTCSI
1 = 0,01 d. Y MeHbIlleHl1e TOJIIl{I1HbI 3aJII1BKH
6narOnpl1S1THO CKa3bIBaeTCSI Ha nOBbIllleHI1H YCTaJIOCTHOH npOQHO-
CTH cnoSl. HanpHMep, YMeHbIlleHl1e TOJIlI.{I1HbI cnoSl C 2)J.0 1 MM YBe-
nl1QI1BaeT YCTanocTHYIO npOQHOCTb 6a66HToBoro cnoSl B j1-Ba pa3a.
TOJIIl{HHa nOnl1aMHj1-HOrO BKnaL(bIllIa
B = (0,04... 0,05)d + 1, Ton-
lI.{I1Ha nnaCTMaCCOBoro nOKpbITI1S1
2 = (0,015...0,020) d. B MaCCOBOM
npoH3Bo,ncTBe BKna)J.bIIllH IllTaMnYIOT 113 neHTbI, Ha KOTOpylO HaHeceH
aHTl1cppHKQHOHHbIH MaTepl1an. 3TO npHBOj1-I1T K 3HaQl1TenbHoM 3KO-
HOMI1H QBeTHblx MeTaJIJIOB (j1-0 3-10 pa3), cOKparn:eHI1IO TpYj1-0eMKOCTH
(j1-0 10 pa3) H nOBbIIlleHl11O KaQeCTBa nOj1-111l1nHI1KOB.
127
npMBe,neM OnTMManbHOe OTHOllIeHMe ,nnMHbI BKna,nbIllia I K ero
BHYTpeHHeMY ,nMaMeTpy d:
B KOpOTKMX no,nllIMnHMKax CKOnb)l(eHMSI
I = (0,3... 0,4)d,
B no,nllIl1nHHKaX 6bICTpOXO,nHbIX nopllIHeBbIx ,nBHraTeneM BHYTpeH-
Hero cropaHHSI (aBHa:QHOHHbIX M aBTOM06MnbHbIX)
1= (0,5... 0,6)d,
B nO
llIMnHMKax ,nM3eneM
1= (0,5... 0,9)d,
B nO
llIMnHHKax )l(H
KOCTHoro TpeHHSI npoKaTHbIx CTaHOB
1= (0,6... 0,9)d,
B no,nllIMnHMKax 06
ero MallIMHOCTpoeHMSI MHHa MHor,na .nOXOJI:HT
J{O 1,5d.
MaTepHanbI JJ;nSl nOJJ;llIHrIHHKOB BbI6HpalOT npHMeHHTenbHo K pa-
GOTe B nape co CTaJIbHbIMM :QancpaMH BaJIOB. Hx no,npa3,nenSlIOT Ha cne-
,n;YIO
He rpynbI:
a) MeTannHlJeCKHe - 6a66HTbI, 6pOH3bl, cnnaBbI Ha QMHKOBOH oc-
HOBe, CnJIaBbI Ha aJIIOMHHHeBOM OCHOBe, aHTI1<PPI1KQHoHHbIe QyrYHbI;
6) MeTaJIJIOKepaMHlJeCKHe;
B) HeMeTannHlJeCKHe - nnaCTMaCCbI, ,npeBeCHbIe nnaCTI1KM, pe3M-
HbI H ,np.
JISI no,nlIIl1nHI1KOB )l(11,nKOCTHoro TpeHHSI ocy
ecTBnSlIOTC5I CJIe-
,n;YIO
He paClJeTbI.
PaCqeT no AonYCKaeMblM AaBJIeUHHM B nOAIUH"UHKax. KaK npaBHno,
paClJeT Be,nYT no HarpY3Ke Ha onopy (no peaKQHI1 R), oTHeceHHoM K
npoeKQHM u:ancpbI:
R
p=- < [p].
dl
B no,nllIl1nHI1KaX 60JIbllll1HCTBa CTaQI10HapHbIX MaIllHH p = 1...4 H/MM 2
B 3aBMCHMOCTM OT ycnoBMM pa60TbI H MaTepHaJIOB; B KopeHHbIx no,n-
IllHnHHKax )J,BHraTeJIeM BHYTpeHHero cropaHHSI p = 4...20 H/MM2; B
nOJ(IlIHnHHKax BanKOB npOKaTHbIX CTaHOB p = 15...50 H/MM2.
PaClJeT Hcnonb3yeTcSI KaK npOBepOlJHbIM, TaK KaK JI:MaMeTp QancpbI
Y)Ke onpe.n.eJIeH KOHCTPYKTMBHO nocne paCqeTa Bana.
PaC'lJeT no npOH3BeAeUHIO AaBJIeUHH B nOAIUH"UHKe Ha CKOpOCTb
CKOJlbiKeUHH:
pv < [pv].
128
i
i
t
I
(
npOH3Be,neHMe pv xapaKTepH3yeT B HeKoTopoM CTeneHM Tenno06pa30-
BaHHe B nOJ].lIIHnHHKe, a TaK)I(e H3HOC.
B nOJ].llIMnHMKax CTaQMOHapHbIX MallIMH pv = 2...10 H.M/(MM 2 .C).
B onopax CKOJIb)l(eHHSI 6bICTPOXOJ].HbIX H TSI)I(eJIOHarpY)I(eHHbIX Ma-
llIHH npM xoporneM OXna)l(JI:eHHM 3HalJeHI1e P v MO)l(eT 6bITb 3HaQM-
TeJIbHO BbIllie. B nonllIMnHHKax aBTOM06MJIbHblX )J,BHraTeneH p v =
= 25...35 H. M/(MM 2 .C), noplIIHeBbIx aBl1aQHOHHbIX J].BHraTeJIeH 30...50,
npoKaTHblx CTaHOB 40...200, napoBbIx Typ6MH 100 H.M/(MM 2 .C) M BbIllie.
n pltMep 3.3
Ha pHC. 3.26 nOKa3aH Ban qep-
BSl1.JHOrO pe)J.YKTopa, BocnpHHIIMalO-
ero palIHanbHbIe HarpY3KII R I =
= 9000 H H R2 = 7000 H H oceBYIO A =
= 3000 H. Ban Bpa
aeTcSI c yrnOBOH.
CKOpOCTblO ffi = 7,65 paJJ:1 c. Uancpbl
Bana HMelOT o)J.HHaKoBbIH )J.HaMeTp d =
= 60 MM, a d l = 65 MM. BKnaJJ:bIlllH
BbInonHeHbI B BIIJJ.e BTynoK H3 6pOH3bI
npOQC6-6-3. o npeJJ:enHTb )J.nHHY
BKnaJJ:bIllleH I H JJ:HaMeTp D TOPUOBOM
qaCTH BKna)J.bIwa, BocnpHHHMalOIUeH
oceBYIO HarpY3KY.
PeweHlIe.
PHC. 3.26
I. B COOTBeTCTBHII C peKOMeH)J.aUHSlMM [8], H3nO)KeHHbIMH BbIwe, )J.nSl MexaHH3-
Ma CTaUMOHapHOH MaWMHbI npHHHMaeM (P] = 3 H/MM2.
2. PaCqeT no JJ:onycKaeMoMY )J.aBneHMIO npoBo)J.HM )J.nSl neBoH onopbI, TaK KaK
OHa IIcnbITbIBaeT 66nbllIYlO HarpY3KY, 1.JeM npaBaSi. 113 3aBHCHMOCTII R J :::; [p]
dl
onpeJJ:enSleM )J.nHHY BKna)J.bIwa:
Rt 900
I
- = - = 50 (MM).
[p] d 3 . 60
3. npoBepSieM napy uancpa -- BKna)J.bIW Ha .n:onYCKaeMoe npOH3BeJJ:eHHe )J.aBne-
HHSI Ha CKOpOCTb pv:::; [pv]. BHa 1.Jane onpeJJ:enliM OKPY)KHYIO CKOpOCTb
d 60
v = ffi"2 = 7,65 2 = 230 (MM I c) = 0,23 (M/c).
KpHTepHH pv = 3.0,23 = 0,69 H .M/(MM2.C). JJ:onycKaeMoe 3Ha1.JeHHe 3Toro KpliTepHSI
)J.nSl CTaUHOHapHbIX MallIHH HaXO)J.HTCSI B npe)J.enax 2... 10 H'M/(MM2.c), LITO 3Ha1.JH-
TenbHO BbIwe cpaKTHLIeCKoro.
129
4. 113 YCJIOBH5I H3HOCOCTOHKOCTH TOPUOBOH 1.JaCTH BKJIa)J.bIll1a <t>aKTH1.JeCKOe
)J.aBJIeHHe Ha ero TopeQ
A
. = 1t(D 2 _d 2 )
4
)J.on:>KHO 6bITb MeHbllle ,[(onycKaeMoro, cne)J.OBaTenbHO
A
[p)o
1t (D2 -d. 2 )
4
113 3Toro ycnoBHSI onpe.n.enliM )J.HaMeTp
D '? 4A + d. 2 = 4.3000 + 65 2 = 75 (MM).
n[p] 1t . 3
5. npoBep»eM Ha HarpeB TOPQOBYIO 1.JaCTb BKJIa)lbIllIa npH JIHHeHHOH CKOpO-
CTH, cooTBeTcTBYIOll{eH cpe)J.HeMY )J.HaMeTpY onopHoH nOBepXHOCTH:
D +d 75+65
v cp = w · - 7,65. = 267 (MM/c) = 0,276 (MM/c).
2 2
npli 3TOM KpliTepHH pI Vcp = 3.0,267 = 0,80 I H .M/(MM2.C), I.JTO 3Ha1.JHTeJIbHO HH:>Ke
.nonycKaeMoro: [pv] = 2... 10 H .M/(MM2.C).
IIoltnHTHHKH. OnopLI CKOJILiKeHHH Bep-
THKaJlLHO paCnOJlOiKeHHLlx BaJlOB Ha3LI-
BalOTCH nOAnHTHHKaMH (PHC. 3.27). B KOp-
nyce 2 no,n:nSlTHMKa pa3Me
aeTcSI 6pOH-
30BaSi HJIH CTaJIbHaSi JIHH3a 3, KOTopaSi no
Mepe H3Hoca 3aMeHSleTCSI HOBOH. B pSl,n:e
CJIyqaeB, B 3aBHCHMOCTH OT BH,n:a CMa3-
KH, BKJIaJ(bIlIlH H3rOTOBJISIIOT H3 J(epeBa,
TeKCTOJIHTa, BHHHnJIaCTa, pe3HHbI M ,n:p.
BTynKa 1 BocnpHHHMaeT pa)].HaJIbHWe
HarpY3KH. Kopnyc no,[(nSlTHHKa BblnOJI-
PHC. 3.27 HSiIOT H3 ceporo qyrYHa HJIH CTaJIbHOrO
JIHTbSI.
3.10. IloJ(mHnHHKH Ka1JeHHH
IIOAmHnHHKH Ka-JeHHH - 3TO onopLI Bpa
alO
HXCH AeTaJleii, HC-
nOJIb3YIO
He 3J1eMeHTLI Ka-JeHHH (IllapHKM HJIH pOJIHKH) H pa60TalOID:He
Ha OCHOBe TpeHHH Ka-JeHHH. OHM COCTOSIT (PHC. 3.28, a) 113 BHYTpeH-
Hero 1, HapY)l(Horo 2 KOJIeQ, Ten KaqeHHSI 3 11 cenapaTopa 4, pa3J(e-
130
-
II
e
n
II!
I
,_
t:
R
1
.1
-
A
4
3
3
.1.
3
2
a
6
6
PlIC. 3.28
I
I
JISlIO
ero H HanpaBJISlIO
erO TeJIa KaqeHHSI. ITo qHCJIY TeJI KaqeHHSI
no,n:IllHnHHKH MorYT 6bITb Odl-lOpRdl-lble (PHC. 3.28., a) H d6YXpRdl-lble
(PHC. 3.28, 6).
ITo xapaKTepy BocnpHHMMaeMbIx HarpY30K nOJJ;IllHnHHKH KaqeHHSI
JI,eJISlTCSI Ha p
H3JlLHLIe (PHC. 3.28, a), BocnpMHHMalO
He TOJIbKO pa,n:H-
aJIbHbIe HarpY3KH; ynopHLIe (pHC. 3.28, 6), BocnpHHHMalO
He TOJIbKO
oceBbIe HarpY3KH, H P
"3JlbHo-ynopHble, BocnpHHHMalO
He pa,n:HaJIb-
HbIe n oceBble HarpY3KH.
no cpopMe TeJI KaqeHHSI no,n:IllHnHHKH pa3,n:eJISIIOT Ha wapUK06ble
(PHC. 3.28) H pOJlUK06ble. B pOJIHKono,n:IllHnHHKax TeJIa KaqeHHSI MorYT
HMeTb cpOPMY KOpOTKHX QHJIHH,n:pHqeCKHX pOJIHKOB (PHC. 3.29, a),
J.{JIHHHbIX l..\HJIHH,n:pHqeCKHX pOJIHKOB (plIC. 3.29, 6), KOHHqeCKHX POJIH-
KOB (PHC. 3.29, 6), 60qKOo6pa3HbIX pOJIHKOB (PHC. 3.29, 2), HrOJIbqa-
TbIX pOJIHKOB (PHC. 3.29, d).
-E3 +- . -t -E3- 8 H I
a 6 6 2 i)
.'
PIiC. 3.29
1
IllapHKonOJJ;IllHnHHKM 60JIee 6bICTPOXO,n:HbI, a pOJIMKono,n:I.llMnHH-
KH MMelOT 66JIblllYIO rpY30no,n:'beMHocTb. QMJIHH,n:pHQeCKHe pOJIHKO-
no,n:lllHnHHKH, 6JIM3KHe no 6bICTpOXOJ(HOCTH K lllapHKoBbIM, nJIOXO
BocnpHHHMalOT oceBble HarpY3KM. KOHHqeCKl1e pOJII1KOno,n:llll1nHI1KH,
06JIa,n:alO
l1e OJ(I1HaKOBO BbICOKOH pa,n:MaJIbHOH Ii oceBoH rpY30no,[('b-
eMHOCTblO, J(onycKalOT MeHee BblCOKHe qaCTOTbI Bpa
eHHSI.
131
Bee BI1
bI nO
llIMnHMKOB cTaH
apTI130BaHb] 11 B 3aBl1Cl1MOCTH OT
pa3MepOB, ,n;eHcTBYIOmHX Ha HHX HarpY30K H ,[(onrOBeqHOCTH 06'be,n;H-
HeHbI B cepHH: n e r K He, C p e,[( H H e 11 T H )I( en bI e nO,[(llIHfIHHKH.
PaCqeT Ha AOJlrOBeqHOCTb. Ilo,n:llIMnHHKH KaqeHHH TepHIOT pa60TO-
cnoc06HOCTb 113-3a YCTanOCTHoro pa3pYllleHHH nOBepXHOCTHbIX cnoeB
,n:opO)l(eK KaqeHMH H Ten KaqeHMH. l103TOMY OHH paCCqHTbIBaIOTCH Ha
):(OJIrOBeqHOCTb pa60TbI. Ha OCHOBe MHOrOqMCJIeHHbIX 3KcnepMMeH-
TOB 6bIJIa YCTaHOBJIeHa 3aBMCl1MOCTb Me)l(,n:y HarpY3KOH Q 11 pecypCOM
(CYMMapHbIM qHCJIOM L 060pOTOB AO nOHBJIeHHH npH3HaKOB YCTa-
JIOCTM):
(
r =L,
r,n:e a - nOKa3aTeJIb CTeneHM; ,[(JISI lllapHKonO,[(WHnHHKOB a = 3, ,n:nH
pOJII1KOno,n:llIHnHHKoB a = 3,33; C - ,n;HHaMMqeCKaSI rpY30no,[('beM-
HOCTb, KOTOpylO nOAlllHllHHK MO)l(eT BbIAep)l(aTb B TeqeHHe 10 6 060-
pOTOB.
nOCKOJIbKY nO,[(lllMnHMKH KaqeHMSI nO,[(BepraIOTCSI COBl\tleCTHOMY
,[(eHCTBHIO pa,n:HaJIbHOH H oceBOH HarpY30K, TO BMeCTO Q nO,[(CTaBJISI-
101' npHBeAeHHYIO HarpY3KY, KOTopa
AJI5I pa3JIH1.JHbIX THnOB nOAlllHn-
HHKOB BbIqHCJIHeTCH no-pa3HOMY. KpoMe Toro, HMeeT 3HaqeHHe COOT-
HOllIeHHe Me)K,n:y oceBOH H pal1HanbHOH HarpY3KaMH [8].
llOl1WHnHHKH KaqeHHSI B HaCTOSI
ee BpeMSI HBJISIIOTCSI OCHOBHbIM
BM110M onop B MallIHHOCTpoeHMM. OHM 06JIa,n:a1OT pSI,[(OM npeHMymeCTB.
Bo-nepBbIX, 3TO CTaH,[(apTHbIH Y3en, HaH60JIee CTaH,[(apTH30BaHHbIH B
Me)l(,n:YHapo,n:HOM MaCll1Ta6e H
eHTpaJIH30BaHHO H3rOTaBnHBaeMbIH.
B CHJIY 3Toro nOAll1HnHHKH KaqeHHSI ,n:ellleBJIe, qeM nOAlllHnHHKH
CKOJIb)KeHH5I. BO-BTOpbIX, nOAlllHnHHKI1 KaqeHH
XOpOlllO pa60TalOT
npM M3MeHeHMH HarpY30K, npH pa3JIHqHbIX qaCTOTax Bparn;eHH.SI H pe-
Bepcax, qero HeJIb3
CKa3aTb 0 nO)J:lllHTIHHKaX CKOJIb)l(eHH
. B-TpeTbHX,
y TIO,n:lllHTIHHKOB KaqeHH5I M:eHbllle, qeM y nO,[(lllHnHHKOB CKOJIb)l(eHHH,
nYCKOBbIe MOMeHTbI, TaK KaK MeHbllle MOMeHTbI CH]] TpeHHSI, a CJIe,[(OBa-
TeJIbHO, H MeHbillee TenJIOBbIAeJIeHHe. ,ZJ:aJIee, nOCKOJIbKY nOAlllHnHH-
KH KaqeHHH LJarn;e Bcero CMa3bIBalOT rYCTOH C
1a3KOH, TO MMeeT MeCTO
MeHbllll1H pacxoJ]. CMa30QHOrO MaTepHaJIa no cpaBHeHMIO C nOl1lllMn-
HMKaMH CKOJIb)l(eHHSI. ,[(JIH nO)J:lllHnHHKOB KaqeHHSI He HY)I(HO pacxo-
,lJ;OBaTb )J:oporOCTOSILUHe l.{BeTHbIe MaTepHaJIbI Ii TIpe,lJ;'b5J:BJIHTb oc06bIe
Tpe60BaHH.SI K MaTepHaJIY M TepMo06pa60TKe Qancp BaJIOB.
K HeAOCTaTKaM nO,lJ;IllHnHHKOB KaqeHHH OTHOC5ITCSI: orpaHHLJeHHbIH
CpOK CJIY)l(6bI; nepeMeHHa
)l(eCTKOCTb, BbI3bIBalOrn;aH B03HHKHOBeHHe
napaMeTpHqeCKHX KOJIe6aHMH; 60JIbllIMe ,lJ;naMeTpaJIbHbIe pa3MepbI;
MeHbllIa
, qeM y no,n:IllHTIHMKOB CKOJIb)l(eHHH, cnoco6HOCTb ,n:eMncpHpo-
BaHM$I KOJIe6aHHH.
132
T
,
I
3.11. My4JTLI
Ha3HaqeHHe My<pT - COel1HHHTb OT,n:eJIbHbIe BaJIbI, HBJI5J:IOII.(HeC.SI
OAMH npo,n:OJI)KeHHeM JIpyroro, H nepe,[(aBaTh npH 3TOM KpYTHrn;HM
MOMeHT. TaKHe MY<PTbI Ha3bIBaIOTCSI npu8oi)J-lblMU. KpoMe HHX B Ma-
llIHHOCTpoeHHM cyrn;eCTBYIOT My<pThI )InH COel1HHeHHSI: Tpy6 T5J:r 11 ,[(PY-
rMX ,n;eTaJIeH (OHM B 3TOM YQe6HMKe He paCCMaTpMBaIOTC5J:).
B Ta6JI. 3.1 npe,[(cTaBJIeHbI YCJIOBHble 0603HaQeHMSI Hepacu:enJI.SIe-
MbIX, ynpaBJISleMbIX H aBTOMaTHqeCKH ,n:eMcTBYIOII.(HX MY<P T .
HepaCL\enJ1HeMble (HeynpaBJlHeMble) MycpTbI MCnOJIb3YIOT B CJIY-
qae, Kor,[(a BaJIbI no YCJIOBH.SIM TeXHOJIOrHH H3rOTOBneHM.SI H C60PKH
npHxo,n:HTC.SI ,[(enaTb COCTaBHbIMH, npHqeM COCTaBHOM BaJI ,n:OJI)KeH
pa60TaTb KaK QeJIbIH. K 3TOH KaTerOpl1H OTHOCSlTC.SI: a) 2Jlyxue MyljJ-
mbl 1 (PHC. 3.30), KOTopbIe coe,[(MH.SIIOT COOCHbIe BaJIbl 2 H 3; 6) ynpY2ue
Mypmbl, Ha3HaqeHHe KOTOpbIX - CM5J:rqaTh y,n;apHbIe HarpY3KH, a TaK)I(e
KOMneHcHpoBaTb HeKoTopylO HeTOqHOCTb B3aHMHoro nOJIO)KeHH.SI Ba-
JIOB. llpHMepoM rH6KoM My<pTbI 5J:BJIHeTCH CHJIb<poHHaH MY<P Ta 2
(PHC. 3.31), KOTOpa5J: HCnOJIb3yeTcH ,[(JIH coellHHeHH5J: Barra BbICOKOMO-
MeHTHoro 3JIeKTpO,D;BHraTeJISI 3 CTaHKa C qIlY MO,D;eJIH HP 500 <1>4 C
XO,n:OBbIM BHHTOM KaqeHHSI 1; OHa KOMneHcHpyeT HeKOTopbIe nepeKOCbI
H HeCOOCHOCTb oceM BaJIa 3JIeKTpO)J:BHraTeJISI H onopbI lllapHKOBoro
BHHTa. B TO )l(e BpeMSI B03MO)KHOCTb YBeJIHqeHHSI )KeCTKOCTM coe,[(HHe-
HH.SI Ban ,n:BMraTeJISI - XO,[(OBOH BHHT HCKJIIOQaeT ,[(a)Ke He6oJIbllIOH OTHO-
CHTeJIbHbIM nOBopOT coe,n:HHSleMbIX BaJIOB, H OHM pa60TaIOT KaK e,[(HHoe
ueJIoe; 8) KOMneJ-lCupYI014ue MyfjJmbl npe,[(Ha3HaqeHbI ,[(JISI coe,[(HHeHHSI
BanOB C HeTOqHO coe,[(HHeHHbIMH OCSlMM; 3TH MY<PTbI ,[(on)KHbl KOMneH-
CMpOBaTb pa.D:HanhHble, oceBhIe M yrJIOBbIe CMell\eHHSI BaJIOB.
3 A-A
PliCa 3.30
YnpaBJlHeMble, HJlH C",enJlHeMble, MY<PTbI npHMeHSlIOT B MallIMHaX
MJIH HX OT,n:enbHbIX Y3naX, B KOTOphIX He06xo.D:HMO OCyrn;eCTBJISlTh
qaCTbIe OCTaHOBbI 11 nYCKH, HanpHMep B MeTannOpe)KYll\HX CTaHKaX H
aBTOM06HnSlX. CQenJISleMbIe MY<PTbI MOrYT 6bITb MeXaHMQeCKHMH, 3JIeK-
TpHqeCKHMH, rH.apaBJIHqeCKHMH H nHeBMaTHqeCKHMH. K MeXaJ-lUlle-
CKUM ClJe111l51eMbl.kl MyfjJmaM OTHOCSITCH K Y n a q K 0 B bI e (HnH 3y6qa-
133
TbIe) Ii cp pH K Q H 0 H H bI e. Ha pHC. 3.32 nOKa3aHa cQenn5IeMa5I Kynaq-
KOBa5I My<pTa, KOTOpa5I COCTOHT H3 ,nBYX nonYMY<PT 1 H 2 C TOPQOBbIMH
KynaqKaMH, BXO,n5ILQHMH BO Bna,nHHbI Me:>K,ny Kyna4KaMH COnpSl:>KeH-
HOM nonYMYCPTbI. IIonYMy<pTa 2 MO:>KeT nepeMeLQaTbC
no wnHuaM
B,lJ;Onb Bana, a nonYMYCPTa 1 :>KeCTKO coe,nHHeHa C BanOM. B uen5IX
YMeHbllIeHH.SI H3Hoca MexaHH3MOB BKnIOQeHH5I nepeMeIltaeMOM llenalOT
nonYMY<PTY Ha Be,nOMOM Bany. EcnH coe,nHHSlIOTCSI llBa Bana, TO KY-
nallKOBbIe MYCPTbI Tpe6YIOT TOllHOrO l.{eHTpHpOBaHH
BanOB, KOTopoe
MO:>KeT ,nOCTMraTbC5I UeHTPHPYIOLQMM KonbQOM. qaLQe Bcero 3TH MYQ>-
TbI npHMeH5IlOT ,l.J.n5I coellHHeHHSI Bana H CH,n5ILQeH Ha HeM llIeCTepHH; B
3TOM cnYllae o6e nonYMY
TbI CH,nSlT Ha O,nHOM Bany (KaK nOKa3aHO
Ha pHC. 3.32) M QeHTpMpoBaHHe coe,nHH5IeMbIX ,n;eTaneH 06eCneqeHo.
01leHb llaCTO nonYMYQ>TY 2 3aMeH5IIOT KynaqKaMH Ha TOPQe llIecTepHH
HnM ,n;pyroH coe,n;HHSleMoH C BanOM ,n;eTanH. )J;n5I KynaqKOBbIX MYQ>T
xapaKTepHbI OTCYTcTBHe npOCKaJIb3bIBaHH5I H MaJIbIe ra6apHTHbIe pa3-
MepbI. He,nocTaTKoM 5IBnSleTCSI HeB03MO)l(HOCTb BKnIOQeHH5I Ha 6bICT-
pOM xo,n;y. BKnlOlleHHe npOHcxo,n;HT C y,n;apOM ,n;a:>Ke npH BKnlOqeHHH
Ha TMXOM Xo,n;y co CKOpOCT.SIMH MeHee 1 M/c.
<I> p H K U H 0 H H bI e cue n n SI e M bI e MY<PTbI nepe,nalOT KPYTSlLQHM
MOMeHT CHnaMH TpeHHSI, 06ecne4HBaSl nnaBHoe coe,n;HHeHHe Be,n;YLQero
3BeHa C Heno,n;BH)I(HbIM BanOM. 3TO
n03BonSleT H36e:>KaTb L(HHaMH4eCKHX
HarpY30K H WYMa npH nYCKe, a B
TpaHcnopTHbIX MaIlIHHax HenpH5IT-
HbIX )I.JI5I llenOBeKa 60nbIllHx YCKope-
HHM. KpoMe Toro, <PPHKUHoHHwe
MYQ>TbI MorYT cnY:>KHTb npe,noxpaHH-
TenbHbIM YCTPOMCTBO
1. ITo Q>opMe
pa60QHX nOBepxHocTeH Q>PHKQHOH-
I
i
I
,1
i
,.
1
it
Ii
!.
j
!
i
i -
!
2
Plic.3.32
134
3
2
PUC. 3.31
I
,
I
:It
HbIe MYQ>TbI pa3,n;en5IIOTC5I Ha ,n H C K 0 B bI e,
K 0 H Y C H bI e H Q H n H H ,n P H q e C K Ii e ( C
pa311BH:>KHbIMH KonOJJ:KaMH).
CQennSleMbIe MYQ>TbI 311eKI1'1pU1J.eCKUe,
2ui)pa611UlJeCKUe H lZHe6A1Ql1ZU1J.eCKUe - 3TO Te
lKe Q>PHKUHOHHbIe MYQ>TbI, HO ynpaBnSle-
MbIe He MeXaHHqeCKH (qepe3 pbIqa)l(HbIe 3
cHcTeMbI), a C nOMoLQblO 3neKTpHqeCKOM
3HeprHH, rl1JJ:paBnl1KI1 Hnl1 nHeBMaTHKI1.
Ha pHC. 3.33 H306pa)l(eHa 3neKTpH4e- 1 2
CKaSl ynpaBnSleMa5I MYQ>Ta. O,nHaKo y 3TOM
MY<P TbI ,npyroe <PYHKQHOHaJIbHOe Ha3Halle-
HHe - He nepe,naBaTb KPYT5Ill
HM MOMeHT, a, Pl1c. 3.33
Ha060pOT, OCTaHaBnHBaTb BpaLQeHHe, T.e.
OHa BbInOnH5IeT ponb TopM03a. ITpH BKnIOlleHI1H 3neKTpHqeCTBa Heno,n-
BH)I(HbIH naKeT MarHHTonpOBo,nSlLQHX )JJICKOB 3 3aTOpMa)l(HBaeT naKeT
2, 3aKpenneHHbIH C 3y61laTbIM KoneCO
1 1, H OHO OCTaHaBnHBaeTCSI.
ABTOMaTUqeCKHe (caMoJJ.eiicTBYIOIl(He) My4>TbI cpa6aTbIBalOT B on-
peJJ:eneHHbIx ycnOBH5IX 6e3 BMernaTenbCTBa llenOBeKa. K HHM OTHOC5IT-
C5I: a) 0620HHble A-typnlbl, KOTopbIe nepell.alOT MOMeHT B O,nHOM Ha-
npaBneHHH 11 ,l.J.OnycKalOT cB060,nHoe OTHOCHTenbHoe BpaIll,eHHe B npo-
THBOnOnO)l(HOM. IT03TOMY HX Ha3bIBalOT MycpTaMH cB060,nHoro xo,na.
TepMHH «06rOHHa5I MYQ>Ta» B03HHK B CB5I3H C TeM, 4TO OHH ,n;onYCKa-
lOT 06rOH Be,l.J.YLQero Bana Be,nOMbIM, ecnH nocne,nHHH nonYllaeT 60nee
6bICTpOe BpalQeHHe OT JJ:PyroH KHHeMaTHlleCKOH uenH; 6) l1 eH1n po6eJIC-
1-lble A1J J cjJnzbl cnY)I(aT ,l.J.JI5I aBTOMaTHqeCKOrO COe,l.J.HHeHHSI (HnH pa3'bell.H-
HeHH5I) BanOB npH ,l.J.OCTH)I(eHHH Be,n;YLQHM BanO
1 3a,naHHoH qaCTOTbI
BpaLQeHHSI. 3TH MY£PTb] }lBn5IIOTC5I caMoynpaBn5IIOIl
HMHC
no CKOpOCTH;
6) npeiJoxpaHulnellbHble MycjJnZbl, KOTopbIe BbInonHSlIOT <PYHKUHIO npe,n;o-
xpaHHTenbHoro 3BeHa npH neperpY3Ke MallIHHbI HnH ee OT,nenbHbIX
MexaHH3MOB.
ITo npHHUHny pa60TbI MexaHH4eCKHe npe,noxpaHHTenbHbIe MYQ>TbI
,nenSlTCSI Ha MYQ>TbI C pa3pyrnalOmHM 3neMeHTOM, npY)l(HHHo-Kynaq-
KOBbIe, <pPHKUHOHHble.
IT p e,l.J. 0 x p a H H Ten b H bi e M Y <P T bI cpa 3 p Y rn a 10 LQ H M 3 n e -
M e H TOM. ilx npHMeHSlIOT npH pe3KHX neperpY3Kax. He,nOCTaTKOM
3THX MY<P T 5IBnSleTCSI He06xo,nHMOCTb 3aMeHbi pa3pyrnalOLQHX 3neMeH-
TOB nocne cpa6aTbIBaHHSI MYC])TbI. 113 MYCPT 3Toro THna B OCHOBHOM
npHMeHSlIOT MYQ>TbI co cpe3HbIMH LlITHcpTaMH 1 (PHC. 3.34). "
IllTHcpTbI 06bIllHO H3rOTaBnHBalOT H3 cpe,nHeyrnepO,l.J.HCTOH CTanH
(ynyqrneHHOH HnH 3aKaJIeHHoi1). B npe,l.J.nOnaraeMoM MeCTe pa3pyrneHHSI
Ha WTI1Q>Tax ,n;enalOT BbITOqKY, KOTopaSl nOBblrnaeT TOllHOCTb cpa6a-
TbIBaHI1S1, o6nerQaeT H3BneQeHHe IlITHcpTOB nocne I1X pa3pyrneHHSI, a
TaK)I(e YMeHbillaeT onaCHOCTb nOBpe)l(,n;eHHSI T
PUOBOi1 nOBepxHocTH
135
1
A-A 1
1
,
t,!
J
PUC. 3.34
, i
My<p T . IlITHcpThI Heo6xo
HMO YCTaHaBnHBaTh BO BTynKI1, 3aKaneHHhIe
O BhICOKOH TBep
OCTI1, 1.JT06hI 1136e)KaTh nOBpe)K
eHI1
I1X nOBepXHO-
cTeH. PacnonaralOT IIITI1<pThI B Y,[(06HOM ,[(n
3aMeHhI MeCTe.
Il P Y )I( 11 H H 0 - K Y n a 1.J K 0 B hI e n p e ,[( 0 x p a H 11 Ten b H bI e M Y <P -
T bI 111l1pOKO npMMeH
IOT npH He60JIhlllMX CKOpOCT
X 11 nepe,[(aBaeMbIX
KPYT
MX MOMeHTax. OHI1 06ec-
1 ne1.JMBalOT BbICOKYIO T01.JHOCTb cpa-
6aThIBaHM
, TaK KaK ynpyrMe CBOH-
CTBa npY)KMH ,[(OCTaT01.JHO CTa-
2 6MnbHbI. IlpM BbICOKI1X CKOpOCT
X
3TH MY<PTbI He npHMeH
IOT. B npy-
IKMHHo-Kyna1.JKOBbIX MY<PTax KYJIa-
LIKH MorYT 6hITb 3aMeHeHbI rnapM-
Ka
1M 1 (PHC. 3.35). TaKHe npy-
PliCa 3.35 )KMHHO-rnapMKOBbIe My<p TbI MMelOT
npeHMy
ecTBa: OHM 60nee TeXHO-
nOrM1.JHbI, HMelOT MeHblllHH M3HOC H Ha Ka)K,[(bIHrnapI1K B KOHCTpYKQMH
MO)l(HO nOCTaBHTb OT,[(eJIbHYIO npY)KI1HY 2, LITO nOBbIlliaeT paBHOMep-
HOCTb HarpY3KH. TaKMe MY<PTbI nOnY1.JMnM lIlMpOKOe pacnpOCTpaHeHMe
cpe,[(11 npY)I{MHHO-KY JIa 1.IKOBbIX MY CPT .
<D P H K Q H 0 H H hI e n p e,[( 0 x p a H H T e JI b H bI e M Y cp T hI npHMe-
H
IOT npM 1.JaCTbIX KpaTKOBpeMeHHhIX neperpY3Kax B OCHOBHOM y
ap-
Horo TMna. I1x BbInonH
IOT !{MCKOBbIMM MnM KOHYCHbIMM; no KOHCT-
PYKQHH OHM aHaJIOrM1.JHhI cppI1KQI10HHhIM My<pTaM, OTJIM1.JaIOTC
JIMlllh
OTCYTCTBMeM MexaHM3Ma ynpaBJIeHMSI.
3.12. <l>PUKQUOHHLIe nepe,L(aQU
0611(He CBeAeHHH 0 nepeAa
ax. MeXaHM1.JeCKM
1M nepe
a1.JaMM MJIM
npOCTO nepe,[(a1.JaMH Ha3bIBalOT MexaHM3MbI, CJIY)I(a
Me ,[(JISI nepe,[(aqM
136
I
I
I
I
MeXaHH1.JeCKOH 3HeprHH Ha paCCTO
HHe, KaK npaBHJIO, C H3MeHeHHeM
CKopocTeH H MOMeHTOB, a I1Hor,[(a H C npeo6pa30BaHHeM BH,[(OB H 3aKO-
HOB .n-BH)I(eHH
.
B MarnHHOCTpoeHHH WHpOKO npHMeH
IOTC
pa3JIHqHbIe
epe.n-aqH.
B TaKI1X MarnMHax, KaK aBTOM06HJIb HJIH MeTaJIJIOpe)l(YI.l(HH CT
HOK,
HMeeTC
no HeCKOJIhKO Ll-eC
TKOB 3y6qaThIX nepe)J.aq, a MHpOBOH BbI-
nYCK 3y6qaTbIX KOJIeC HCqHCJI
eTC
MHJIJIHOHaMH IIITYK B .n-eHb.
ITo npMHQI1ny pa60TbI nepe)J.aqH
eJI
TC
:
Ha nep e .n- a 1.IH TpeHHeM C Henocpe.n-CTBeHHhIM KOHTaKTOM TeJI Kaqe-
HH
(<1>PHKQHOHHbIe) H C rH6KOH CB
3hlO (peMeHHbIe);
nepe.n- aqH 3aQenJIeHHeM C Henocpe.n-CTBeHHbIM KOHTaKTOM (3y6qa-
TbIe H qepB
qHbIe) H C rH6KOH CB
3blO (QenHhIe).
HapSlLl-Y C MeXaHHqeCKHMH nepe
aqaMH llIHpOKO npl1MeHSlIOT rHLI-
paBJIHqeCKHe, nHeBMaTHqeCKHe H 3JIeKTpHQeCKHe nepe,[(aqH. 3
eCb
6Y!{YT paCCMOTpeHbI TonbKO MeXaHHqeCKHe nepe
aql1.
<l>pHK
"OHHbIe nepeAa
" - 3TO nepe!{aqH, B KOTOpbIX !{BH)KeHHe OT
Be.n-YI.l(ero Tena K Be.n-OMOMY nepeLIaeTCSI CHnaMH TpeHH
. Ha ",pHC. 3.36
nOKa3aHa npocTeHrna
<1>PHKQHoHHaSl nepe!{a1.Ja. Be)J.YI.l(HH .n-HCK 1
no.n-)I(HMaeTC
CHJIOM Q K TOPQOBOM nOBepxHocTH !{HCKa 2. lIpH Bpa-
eHHH !{HCKa 1 B T01.JKe M B03HI1KaeT CHna TpeHHSI FTp = hpQ, KOTopa
npHBo.n-HT BO BpaI.l(eHHe Be.n-oMbIM .n-HCK 2. MO)KHO '-" onpe!{eJIHTb, C
KaKoM yrJIOBOM CKOpOCThlO 6y.n-eT Bpa
aTbc
Be.n-OMhIH LIHCK. 113BecT-
HO, qTO nepei)amolllloe Om1l0Ule1lUe onpei)eJlJlemcJl OmIl0Ul
IlUeM Y2JlO-
6blX cKopocmeu 6ei)oMo2o 36e1la K 6eoYUleMY.
JI
!{aHHOH nepe.aaqH
OHO onpeLl-enHTC
TaK:
. 002 _ V M . V M _ ". T. e. 1 . = !l. = 'Bill .
l=---.---,
00. '2 1i'2 '2 'Bll
. 1j
Cne
OBaTenbHO, yrnoBaSi CKOpOCTb Be!{OMOrO 3BeHa ro2 = lro} = rot
.
2
ECJIH .n-HCKY 1 C006
HTb nocTynaTeJIhHOe nepeMeIl.\eHHe B.n-OJIh OCH
N - N, TO Y Be)].OMoro !{HCKa 2 6y
eT
6eccTyneHqaTO MeH
ThC
yrJIOBaSi CKO- Q
pOCTb, TaK KaK pa)J.HYC '2 MO)KeT H3Me-
H
Tb CBoe 3Ha1.JeHHe OT 0 !{O R.
TaKHe <PpHKQHOHHbIe nepe
aqH, KO-
TopbIe n03BOJI
IOT 6eccTyneHqaTO 113-
MeH
Tb qaCTOTY BpaIl(eHH
Be!{OMOrO
3BeHa, Ha3bIBalOTCSI eapuamopaMu.
HaH60JIblllHM )J.Hana30H perYJIHpO-
BaHHSI QaCTOT Bpall(eHHSI D = nmaxfnmin: 00)2
Y n060BhIX BapHaTOpOB - 3...4, Y TOpO-
BbIX H KOHYCHO-llIKHBHbIX - 8... 10. Plic.3.36
137
):(OCTOHHCTBa rPPHKL(HOHHbIX nepeLIa1J: npOCTOTa Ten Ka1JeHH
; 6ec-
cTyneHqaTOCTb perynHpoBaHH5I CKOpOCTH; B03MO)KHOCTb H3MeHeHMR
CKOpOCTM Be,nOMoro 3BeHa 6e3 OCTaHOBKM Be,n:yIl.{ero, LITO 01JeHb Ba)K-
HO B npHBo,n:ax MeTannOpe)KY
HX CTaHKOB; HH3Kag CTOHMOCTb H3ro-
TOBneHH
B cHny npOCTOTbI KOHCTPYKL(HH.
!le,n:OCTaTKH: HeB03MO)KHOCTb (B OTnH1JHe OT 3y61JaTbIX 3aL(enne-
HHM) nonY1JeHH5I T01JHbIX nepe
aT01.JHbIX OTHOlIleHMH; nOBbIlIleHHbIH
M3HOC; Heo6xo,n:MMOCTb cneQHaJIbHhIX Ha)KHMHhIX YCTPOMCTB (qero He
Tpe6yeTcR 3y6qaTbIM nepe
a1JaM); 60nblIlHe HarpY3KH Ha nO,D:lIlHnHH-
KI1. B cl1ny YKa3aHHbIX He,[(OCTaTKOB npl1MeHeHHe BapMaTopOB B Ma-
111I1HOCTpoeHI1M orpaHM1JeHO. OHM MCnOJIh3YlOTCR B BMHTOBhIX npeccax
npM60pax, npMBo,[(ax rnaBHoro
BM)KeHI1R HeKOTophIX CTaHKOB (HanpH
Mep, MO,n:. 1810 -- TOKapHo-3aThIJIOB01JHhIH cTaHoK).
3.13. PeMeHHbIe nepe,n;a..u
PeMeHHa
nepe,n:a1Ja (pHC. 3.37, Q, 6) lIlMpOKO npHMeHReTCg ,[(nR ne-
pe,n:a1JH ,n:BI1)KeHM
Me)K,[(y y,[(aneHHhIlvfM ,n:pyr OT ,n:pyra BanaMM. OHa
ocymecTBngeTCSI nocpe,[(CTBOM UIKMBOB 2, 3aKpenneHHbIx Ha Banax, M
Ha,n:eThIX Ha 3TM lIlKMBbI O,[(Horo nnOCKoro 1 11H60 HeCKOnhKI1X KnMHO-
BbIX peMHe
3. IIepBa
Ha3hIBaeTCH nnocKopeMeHHoH, a BTopa
KnM-
HopeMeHHoH nepeLIa1JeH.
3
1 2
8
a
6
z
PHC. 3.37
npeHMYI.I.1eCTBaMM peMeHHbIx nepe,n:a1J
Bn
IOTCSI B03MO)KHOCTb
oCYIl{ecTBJIRTb nep e .n.a1JY Ha 3Ha1JMTenbHbIe paccTo
HHH; 3naCTH1JHOCTb
138
T
t
I
npMBo,[(a, CMRr1JalO
aSI Kone6aHMSI H HarpY3KH 11 npe,n:oxpaHSIIOI.l{a5I OT
3Ha1JHTeJIbHbIX neperpY30K (3a CqeT npOCKaJIb3bIBaHMSI); nJIaBHOCTb
xo,[(a H 6eclllYMHoCTb pa60ThI.
K He,n:ocTaTKaM OTHOC5ITCSI 60JIbIlIHe ra6apHTbI, HenOCTOSIHCTBO ne-
pe,n:aT01.JHOrO OTHOllleHHSI (H3-3a npOCKaJIh3bIBaHHSI peMHSI Ha IllKHBax),
60JIbIlIOe ,[(aBJIeHHe Ha BanbI Ii no,n:lIlHnHHKH.
llJIOCKHe peMHH H3rOTOBJISIIOT H3 KO)KH, xJIonqaT06YMa)KHbIX H
npope3MHeHHblx TKaHeH. JJ:JISI c03,n:aHMSI 3al\lKHYTOH rM6KoH CBSI3M MX
ClllHBaIOT. KnHHoBhIe peMHH H3rOTOBJISIIOT 3aMKHYTbIMH - L(eJIbHbIMH
onpeJ].eneHHoH J].JIHHbI. TaKHe peMHM 06eCneqliBalOT XOpOlIlHH KOHTaKT
co lllKHBOM B )l(en06e 11 nJIaBHYIO 6e3y,n:apHYIO nepe,[(aqy.
nepe,[(aqa YCHJIHH 06eCneqHBaeTCSI TOJIhKO npH HOpMaJIbHO HaTSIHY-
TbIX peMHSIx. JJ:JISI 3Toro peMHH nepMo,[(HqeCKH nepelIlHBalOT HJIH yc-
TaHaBJIHBalOT cneQHaJIbHble YCTpoHcTBa, KOTopbIe perynHpYIOT HaTSI-
)l(eHHe pelvlHeH.
llJIOCKOpeMeHHa5I nepe,[(aqa 6bIBaeT OTKphITaSI (PHC. 3.37, 6), Ha-
npaBJIeHHe Bpa
eHHSI BeJ].OMoro BaJIa npli KOTOpOH COBnaJ].aeT C Ha-
npaBJIeHHeM Bpa
eHI1SI Be,n:y
ero lllKHBa, H nepeKpeCTHaSI (PHC. 3.37, 2),
H3MeHSIIO
aSI HanpaBJIeHl1e Bpa
eHH5I Be,[(OMoro BaJIa Ha 06paTHoe.
Ha npo,n:OJIbHO-CTpOraJIbHbIX CTaHKax HeKOTophIX TMnOB npMMeHSIIOT
OTKPbITYIO H nepeKpeCTHYIO peMeHHbIe nepe,n:aqH.
BCJIeJ].CTBHe HeH36e:>KHOrO CKOJIb:>KeHIiSI OKpY:>KHaSI CKOpOCTb Ha Be-
,[(OMOM BaJIY V2 MeHbIlIe CKOpOCTH VI Ha Be,n:y
eM BaJIY: V2 = (1 -
) VI.
OTCIO,n:a nepeJ].aTOqHOe OTHOllIeHHe
i == n Bl1 == W Bl1 == (1-1;)v( . 2 : VI · 2 == (1-1;)dI ; T.e. i =
I (1-1;).
I1Bll1. w B ll1. d 2 d} d 2 2
B CnpaBOqHHKaX npHBe,n:eHbI CJIe,n:YIO
He 3HaqeHHSJ OTHOCHTeJIbHO-
ro CKOJIb)l(eHI1SI
: npope3HHeHHhIe, TeKCTMJIhHhle M CMHTeTMqeCKMe
peMHH - 0,01; KO)l{aHhIe peMHIi - 0,015; KopJ].TKaHeBhIe KJIHHOBbIe
peMHH - 0,2; KOp,n:IlIHypoBbIe KJIHHOBbIe peMHH - 0,01.
3.14. 3y6
aTbIe nepe,n:a
H
3y6qaTaSI nepe,n:aqa SIBJISIeTCSI MexaHM3MOM, KOTOpbIH C nOMO
hlO
3y61JaTOrO 3aL(enJIeHHSI nepe,n:aeT MJIH npe06pa3yeT ,n:BM:>KeHl1e C H3Me-
HeHMeM yrJIOBbIX CKopocTeM M MOMeHTOB.
3,n:ecb 6y,n:YT paCCMOTpeHhI 3y6qaThle nepe,n:aqM, COCTaBJIeHHhle Ii3
QHJIHH,n:pl1qeCKMX (PHC. 3.38, a) M KOHMqeCKHX (PMC. 3.38, 6) 3y6qaTbIX
KOJIec. 3y6qaTbIe nepeJJ.aqM, B KOTOpbIX npe06pa3yeTcSI BpamaTeJIbHOe
,n:BM)I(eHHe B nocTynaTeJIbHOe H Hao60poT, 6y,n:YT paccMoTpeHhI B
no,n:pa3
. 3.19.
139
,lInH nepen:atIH Bpa
eHH5I Me)l(,ny napaJIJIeJIbHbIMH BanaMH HCnOJIb-
3YlOT lJ.HnHHn:pHqeCKHe 3y6qaTbIe KOJIeCa (PHC. 3.38, 6-0). )];JISI npe06-
pa30BaHHH H nepe,n;aqH BpaIl(eHHH Me)l(,n;y BanaMH C nepeCeKalOIl(HMHcH
OCgMH Hcnonb3YlOT KOHHqeCKHe 3y6qaTbIe Koneca (pHC. 3.38, 6), a Me)l(,n;y
nepeKpeIl(HBalOIl(HMHcH OCHMH - 3y6qaTOBHHToBbIe (PHC. 3.38, 0).
no cpaBHeHHIO C paccMoTpeHHbIMH BbIllle 3y6qaTbIe nepe,naqH
I1MelOT cYIl(ecTBeHHbIe npel1MYIl(ecTBa: MaJIbIe ra6apHTbI, HaL(e)l(HbI B
pa6oTe, ,n;onrOBeI.JHbI, BbICOKHH Kn)];, nOCTOHHHoe nepe,naTOqHOe
oTHoIlleHHe, 60JIblllOH nepe,n;aBaeMbIH KPYTSlIl(IIH MOMeHT. KpoMe
Toro, OHH MorYT npHMeHSlTbcH B lllHpOKOM ,n;Hana30He CKopocTeH H
MOMeHTOB.
K He,[(OCTaTKaM MO)l(HO OTHeCTH: lIlYM, cTyneHqaTOCTb perYJIHpo-
BaHH5I CKopocTeH, HeB03MO)l(HOCTb nepeKJII01.JaTb CKOpOCTH Ha xo,ny.
OCHoBHble 3JIel\leHTbl 3y6QaTOrO KOJIeca. OCHOBHbIM KHHeMaTHqe-
CKI1M ycnoBHeM, KOTOPO
1Y ,nOJI)I(eH y,noBJIeTBOpSlTb npocP HJIb 3y6beB,
SlBnHeTCH nOCT05IHCTBO MrHOBeHHoro nepe,naTOqHOrO OTHOlIleHH5I.
IlpocpHnb 3y6beB ,n;OJI)I(eH o6eCneqHBaTb MaJIbIe CKOpOCTH CKOJIb)l(e-
HI1R, qTo6hJ nepe,naqa HMeJIa BbICOKHH KIT)];, npOqHOCTb H ,lIOJIro-
BeqHOCTh. ITpOcpHJIb J-I:OJI)I(eH ,no-
nycKaTb JIerKOe H3rOTOBneHHe (Ha-
pe3aHHe O,lJ.HHM HHcTpYMeHToM He-
3aBHCHMO 01' I.JHCJIa 3y6beB). 3THM
BceM YCJIOBHSlM y,n;oBneTBOpSleT 36011b-
6ellnlHoe 3al/el111eHue, KOTopoe lIlHpO-
KO npHMeHSleTcSI B MaIlIHHocTpoe-
HHH. 3JIeMeHTbI 3BOJIbBeHTHbIX 3y6-
1.JaTbIX KOJIeC cTaH,napTH30BaHbI. 3a
OCHOBHOH napaMeTp npHHSlT MOOYllb
6
I
Pnc, 3.39
140
6
z
d
PUC. 3.38
I
JI
3y6be6 m - BenHIIHHa, npOnOPQHOHanbHaH mary P no ,n;enHTenbHoMY
p
QHnHH,npy: m = -.
n
B o6Il(eM cnyqae, B TOM qHCne H ,nJISI KOC03y6bIX KOJIeC, paCCMaT-
pl1BalOT OKpY)l(HbIe marH P, 11 HopManbHbIe Pn:
Pn = P, cos (3,
r,ne (3 - yrOJI HaKJIOHa 3y6beB no ,neJII1TeJIbHOMY IJ.HJII1H,n.PY.
JISI n!'5I-
M03y6bIX Konec B = 0, cne,n;OBaTenbHO, Pn = Pr = p, T.e. OKPY)I(HOH
HopManbHbIH warM COBna[(aIOT. H3MepSleTCSI mar no ,n;enHTen!>HOH
OKPY)l(HOCTH (PHC. 3.39) H onpe[(enSleTCR ,n;eneHHeM .n;nHHbI 3TOH OK-
PY)I(HOCTH Ha L(HCnO 3y6beB z:
P = nd/ Z .
3HaSl, 1.JTO m = pin, MO)l(HO BbIpa3HTb LIJlaMeTp ,neJIHTeJIbHOH OKPY:>KHO-
CTH qepe3 MO,n.YJIb 3y6beB:
d = mz.
I h "
BbICOTa 3y6a h CKJIa,n;bIBaeTCSI 113 rOJIOBKH h = m 11 HO)l(KH =
= 1,25 n1. OTcIO,n;a BbICOTa 3y6a
h = h' + h" = 2,25m.
Yql1TbIBaSl 3TH 3aBl1CHMOCTH, 3anl1WeM ,[(HaMeTp OKPY)l(HOCTI1 BbI-
cTynoB
d e =nl(z+2)
11 Bna[(l1H
d; = (z - 2,25)m .
PaCCTOHHHe Me)l(,n;y QeHTpaMH ,n;BYX 3y6IIaTbIX KOneC (pI1C. 3.40),
Haxo,n.SlIT(l1XCSI B 3aQenJIeHHH, onpe,n.eJIHTC5I CJIe,n.YIOIT(HM 06pa30M:
d . d 2 mlz. m2 z 2 Zt + Z2
A=-+-= + = m
2 2 2 2 2
r,n;e Zl 11 Z2 - 1.JHCna 3y6beB 3Tl1X Konec; ml = m2 = n'1, TaK KaK B 3aQen-
JIeHHH MorYT 6bITb 3y6qaTbIe KOJIeCa TOJIbKO o,nHoro MO.nYJISI.
TIepe,naT01.JHOe OTHomeHHe HaH.neM 113 YCJIOBH5I OTCYTCTBHSI npo-
CKaJIb3bIBaHHSI B T01.JKe KOHTaKTa npocpHJIeH 3y6beB, T. e. paBeHCTBa
OKPY)l(HbIX CKopOCTeH VI = V2. nYCTb yrJIOBaSl CKOpOCTb Be.nYIT(ero
3y61.JaTOrO KOJIeCa 6y,[(eT (01, a Be,n;OMoro (02.
141
,
I' :
"
d'
h
, I
:: i
Torrra d , (Olmlzl (02 ,n 2 z 2
po. VI = WI - = . V2 = . YqHTbIBaSl, qTO In. =
222
(OtmZI _ (f)2,nz 2
= m2, nOJIyqMM 2 2 MJIM O)IZI = 0)2 Z 2. OTclOna nepe
aTOq-
Hoe OTHorneHMe 6y
eT paBHO
m. e. nepei)amOllll0e om1l0we1lue 3y6llamou nepeiJallu pa61l0 Om1l0WeHUlO
1.JUCell 3)J6be6 6edyU/e20 3y6llamo20 KOlleca K llUCllY 3y6be6 6eiJoM020.
MaTepU3J1bI WIH U3rOTOBJIeHUH 3y6qaTbIX KOJlec. ,L(JISI TMXOXO
HbIX
nepenaq, npeMMYI.QeCTBeHHO KpynHora6apMTHbIX Ii OTKpbITbIX nepe
aq,
npMMeHSlIOT qyrYHbI. OHM OTHOCHTeJIbHO XOp0ll10 conpOTHBJISlIOTCSI
3ae]1.aHHSlM, n03TOMY MorYT pa60TaTb npH CKy,n:HOH CMa3Ke. I1pMMeHSI-
IOTCSI qyrYHbI Cq 21-40, Cq 24-44, MO
H<PHQHpOBaHHbIe qyrYHbI
Cq 28-48, Cq 32-52, Cq 36-56, a TaK)f(e BbIcOKOnpOqHble MarHHe-
Bble qyrYHbI C ll1apOBH
HbIM rpacpMToM.
,L(JISI 60JIbll1HX
HaMeTpOB HCnOJIb3YIOT CTaJIbHOe JIHTbe (CTaJIH
35JI - 50Il), a TaK)f(e JIHTeHHbIe MapraHQoBHcTbIe H HH3KOJIerHpOBaH-
HbIe CTaJIH 40XJI, 30XrCJI, 50r2.
B CJIa60HarpY)l(eHHbIx nepe
aqax npMMeHSlIOT nJIaCTMaCCOBble
3y6qaTbIe KOJIeCa B nape C MeTaJIJIHqeCKHMH; OHH 6eCll1YMHbI B pa60-
Te, XHMHqeCKM CTOMKHe M 06eCneqMBalOT ca
10CMa3bIBaeMOCTb. 3y6qa-
TbIe KOJIeCa H3rOTaBJIHBalOT H3 TeKCTOJIHTa,
peBeCHO-CJIOHCTbIX nJIa-
CTHKOB, KanpOHa, KanpOJIOHa, nOJIH<popMaJIb,n;erM
a. If3 cyr.u;eCTBYIO-
l.QHX MapOK TeKCTOJIMTa CJIe,n;yeT peKOMeH.l{OBaTb MapKM TIT M TITK;
M3 LI-peBeCHO-CJIOMCTbIX nJIaCTMKOB - ,L(CTI-r co 3Be3LI-006pa3HbIM
pacnOJIO)l(eHMeM lllnOHa (BOJIOKHa Ka)l(,n;oro CJIOSI ll1nOHa CMel.QeHbI Ha
25...30 0 ). 3y6qaTbIe KOJIeCa M3 KanpoHa E npM qHCTOM CMa3Ke nOCJIe
HeKOToporo BpeMeHM pa60TbI nepeCTalOT M3HaIIIMBaTbCSI. KanpOJIOH M
nonHcpopMaJIb,n;erH
B HaCTOSll.Qee BpeMSI SlBJISlIOTCSI HaH60JIee nepcneK-
TMBHbIM MaTepHaJIOM MSI 3y6qaTbIX KOJIec.
L(JISI cpenHeHarpY)l(eHHbIx KOJIeC, OCO-
6eHHo B CTaHKocTpoeHMH, MCnOJIb3YIOTCSI
CTaJIH 40X, 40XH C nOBepXHOCTHOM 3a-
KaJIKOH TOKaMH BbICOKOH qaCTOTbI.
B MaCCOBOM H KpynHocepl1MHOM npo-
113BO
CTBe npHMeHSlIOT 3y6qaTbIe KOJIeCa
BbICOKOH TBep,n:ocTH, KOTopbIe OT
eJIOq-
HbIM onepaQHSlM nO
BepralOT nOCJIe Tep-
MMqeCKOM 06pa60TKH.
PaHee OCHOBHbIM BM
OM TepMMqeCKOM
o6pa60TKM SlBJISlJIaCb 061>eMHaSl 3aKaJIKa.
,Ii!
J;
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PlIC. 3.40
142
. _ O)BJI _ 0)2 _ ZI
1------
,
O)Bllt CO I Z2
.
KOJIeca M3rOTOBJISlJIM M3 CTaJIeM MapKI1 Tl1na 40X, a B 60nee OTBeTCT-
BeHHbIX cnyqaSlX 113 CTaJIeM MapOK 40XH, 40XH2MA H ,n:p. O,[(HaK
061>eMHaSl 3aKaJIKa He coxpaHSleT BSl3KYlO cep,n;QeBI1HY npl1 BbICOKOI1
TBep,n;OCTI1 nOBepXHOCTM (06bIqHO HRC 3 45... 55). I103TOMY B Ha-
CTOSll.Qee BpeMSI 06'beMHaSl 3aKaJIKa YCTynaeT MeCTO nOBepxHocTHbIM
TepMl1qeCKI1M 11 XI1MI1KO-TepMl1qeCKMM MeTo,n;aM ynpOqHeHI1S1 (60nee
no,n;po6HO 3TO 6y,n;eT paccMoTpeHo B pa3Ll. 4).
An51 OTBeTCTBeHHbIX 3y61.J:aTbIX Konec, oco6eHHo pa60TalOl.QI1X C
neperpY3KaMH H y,n;apHbIMH HarpY3KaMI1, peKoMeH,[(yeTcSI npl1MeHSlTb
XpOMOHI1KeJIeBbIe CTaJII1 MapoK 12XH3A, 18X2H4MA, 20X!H4A 11
6e3HI1KeneBbIe CTanl1 18XrT, 25XfT H 15X<l> c nocne,AYIOIUel1 QeMeH-
TaQl1eHH3aKaJIKoM.
3.15. qepBHqHble nepeLtaqu
lJepBSlQHaSi nepe,[(aqa (PHC. 3.41) COCTOHT H3 llep65lKa, T. e. BI1HTa C
TpaneQel1,n;aJIbHOH pe3b6oi1:, 11 3y6'-IaTOrO (qepBSlqHOro) KOJIeca.
OCHoBHbIe 3neMeHTbi qepBSlqHOrO Koneca TaKl1e )l(e, KaK y QI1JII1H,n;-
pHQeCKOrO 3y61.J:aTOrO Koneca. OTnHqHe COCTOI1T B TOM, 1.J:TO Y qepBSlq-
Horo Koneca HaqanbHbIH KOHTaKT npOI1CXO,[(HT He B T01.J:Ke, a no JII1-
HHM. 3y6b51 qepBSlqHbIX KOJIeC I1MelOT
yrOBYIO cpOPMY, nonyqaeMYIO
B pe3YJIbTaTe B3aHMHoro Or116aHI1S1 C BI1TKaMI1 qepBSlKa. OCb qepBSlq-
Horo KOJIeCa nepneH,n;I1KYJISlpHa OCI1 qepBSlKa, n03TOMY qepBSl1.J:Hble
nepe,AaqI1 I1lVielOT xapaKTepHble qepTbI 3y6qaTbIX H BI1HTOBbIX nepe-
.n.aq. If306peTeHHe qepBSlqHbIX nepe,n;a'-I npl1nl1CbIBalOT ApXHMe,n;y.
qepBSI'-IHaSl nepe,n;aqa ,n;aeT B03MO)l(HOCTb nOJIyqaTb OqeHb MaJIble
nepe,n;aTOqHbIe OTHOIIleHI1S1 (HanpHMep, 1 :400, 1 :500, B npHBo,nax
CTonOB 60JIbIllOrO ,n;l1aMeTpa CTaHKOB BCTpeqalOTCSI 1: 1000).
TIepe,n;aTOqHbIe OTHOIlleHI1S1 qepBSlqHOM nepe,n;aql1 paCCqHTbIBaIOTC51
no cpopMyne i = I(/z, r,n;e I( - ql1cno 3axo,nOB qepBSlKa; z - ql1cno 3y6beB
1.J:epBSlqHOrO Koneca.
He,n:ocTaTKoM QepBSl1.J:HOM nepe,[(a1.J:H 51BnSleTC5I
MaJIbIH K03Q)cpI1QHeHT nOJIe3HOrO ,n;eMCTBI1S1, npel1-
MYl.QeCTBOM - KOMnaKTHOCTb, 6ecIIIYMHoCTb, nJIaB-
HOCTb xo,[(a, B03MO)l(HOCTb 60JIblIlOrO pe'[(YQHpo-
BaHI1S1. Illl1pOKOe npl1MeHeHl1e qepBSlqHbIe nepe,[(a-
qH I1MelOT B no,n;'beMHO-TpaHcnopTHbIX MaIllI1HaX,
B MeTaJIJIOpe)l(Yl.QHX CTaHKax, aBToM0611nSlx. MaTe-
pl1aJIbI BbI611palOT C yqeTOM oc06eHHocTeH pa60TbI
qepBSlqHOM napbI. 110 cpaBHeHl110 C 3y61.J:aTbIMI1
qepBSI'-IHbIe nepe,n;aql1 n
1elOT 60JIbllll1e CKOpOCTI1
CKOJIb)l(eHI1S1 B KOHTaKTHoM 30He H He6JIaronpl1-
SlTHble ycnoBHSI AnSI rl1,npo,n;I1HaMl1qeCKOH CMa3KI1. PHC. 3.41
143
j:{n» YMeHbIIleHMSI M3HOCa 06bII.JHO l.JepBSlI.JHOe KOneCO BbInOnHglOT M3
aHTM<PPMKQMOHHOrO MaTepl1ana (OTHOCMTenbHO MgrKoro), a l.JepBgK _
113 TBepn;
IX MaTepHMOB. B CHnOBbIX nepe,n;aqax HCnOJIb3YlOT tJepBgKH
M3 CTaJIeH, TepMMtJeCKI1 06pa60TaHHbIX ,n;o 3HaqMTeJIbHOM TBep,n;OCTM.
HaMJIYtJllIYIO M3HOCOCTOHKOCTb nepe,n;aq 06ecnetJMBalOT qepBgKM 113
QeMeHTMpyeMbIx CTaJIeH 20X, 12XH3A, 18XrT, 15X<I>, MMelO
He
TBep,n;OCTh nOCJIe 3aKaJIKM HRC 3 56...63. llIHpoKo npHMeHglOT qepBg-
KH 113 c
e,nHeyrJIepO)].I1
TOH CTanl1 45, 40X, 40XH, 35XrCA C nOBepx-
HOCTHOI1I1JII1 06'beMHOM 3aKaJIKOH .lI0 TBep,n;OCTM HRC 3 45... 55, nocne
qero qepBgK llIJII1<pYIOT 11 nOJIl1pYIOT. ,L(JISJ H3rOTOBJIeHMg tJepBgKOB
npHMeHglOT TaK)Ke aJoTl1pyeMhIe CTaJIM 38X2MIOA, 38X21O M ,n;pyrl1e,
Tpe6YIO
He TOJIhKO nOJIMpOBaHMg.
,[(JIg nepe,n;aq C KonecaMM OtJeHb 60JIbIlIHX ,n;HaMeTpoB QeJIecoo6-
pa3Ho npl1MeHgTh 6pOH30BbIe l.JepBgKH, npH 3TOM tJepBSlqHbIe Koneca
BbITIOnHglOT 113 qyrYHa.
!lPH BbICOKI1X CKOpOCTJlX CKOnb)KeHHg (OT 5 .lIO 25 M/c) 11 ,n;JII1TeJIb-
HOI1 pa60Te 6e3 nepepbIBa BeHeQ y qepBgqHOrO KOJIeCa BbInOJIHglOT
113 OJIOBgHMCTOH 6pOH3bI EpO<l> 1 0-1, OnOBgHO-HMKeJIeBOH 6POH3bI
EpOH <I> 10- 1- I, a TaK)Ke CypbMgHO-HMKeneBoH 6pOH3bI.
,L(ng TMXOXO,nHbIX nepe,naq npl1MeHglOT aJIIOMMHMeBO-)Kene3MCThIe
6pOH3bI npA)K 9-4. llpl1 3TOM qepBgK ,nOJI)KeH 06g3aTeJIbHO MMeTh
BbICOKYIO TBep,n;OCTb, He HH)Ke HRC 3 45.
3.16. QenHLIe nepe
a"H
061I(He CBe
eHHH. UenHbIe nepe,n;aI.JM, KaK M peMeHHbIe, npMMeHg-
IOTCg ,n;ng nepe,n;aq Me)l(,n;y BanaMH, y,n;aneHHbIMH ):(pyr OT ,n;pyra. Qen-
HaSi nepe,n;aqa COCTOI1T (PMC. 3.42) 113 Be,n;y
eH J M Be,n;oMoH 2 3Be3):(0-
qeK M Qenl1 3, oXBaTbIBalO
eH M Bxo,n;g
el1 C HMMM B 3aqenneHMe.
KpoMe nepeqMCneHHbIX OCHOBHbIX 3neMeHTOB L(enHhIe nepe,n;atJH BKnlO-
qalOT HaTg)l(HbIe M CMa301.JHbIe YCTpoHcTBa.
1
3
PHc.3.42
144
T
j
a
6
Plic.3.43
QenHbIe nepe,n;aI.JH llIHpOKO npHMeHglOTCg B TpaHcnopTHbIX MaIlIH-
Hax (MOTO[(HKJIaX, BenOCHne,nax, aBTOM06HngX, TpaHcnopTepax), B
CeJIhCKOX03S1HCTBeHHbIX MaIlIHHax, B MeTaJInOpe)KYIl\MX CTaHKax. )J;JISI
[(enHbIX nepe.lIaI.J CTaHKOB Hcnonb3YIOT [(enH ,nBYX KOHCTPYK[(HH: BTY-
JIOqHO-pOJIHKOBble (PHC. 3.43, a) 11 6ecIlIYMHble (PHC. 3.43, 6); nOCJIe,n-
HHe peKOMeH.lIYIOTcSI .lIJISI nepelIaqH 60JIbllIHX KPYTSlIl\HX MOMeHTOB.
)J;OCTOI1HCTBa [(enHbIX nepe,naq: B03MO)KHOCTb nepe,naBaTb ,nBH-
)KeHHe Ha y,naJIeHHble )J.pyr OT ,n;pyra BaJIbI; MeHbIlIl1e, qeM y peMeHHbIx
nepe,n;aq, ra6apHTHble pa3MephI; BbICOKI1H Kn,[(; B03MO)l(HOCTb ne-
pe,n;aBaTb BpaIl\eHHe HeCKOJIbKHM 3Be3,n;OqKaM; MaJIble CHJIbI, ,n;eHcT-
BYIOIl\He Ha BaJIbI, TaK KaK OTCYTCTBYIOT nepBOHaqaJIbHble HaTSI)KHbIe
YCTpoHcTBa; OTCYTcTBHe CKOJIb)l(eHHSI; B03MO)KHOCTb JIerKOH 3aMeHbI
L(enl1.
He,n;ocTaTKI1: nOBbIllIeHHbIH H3HOC (pa60Ta1OT B YCJIOBHSlX OTCYT-
CTBHSI )l(H,n;KOCTHoro TpeHHSI); [(enH BbITSlrHBalOTCSI BCJIe)J.CTBlfe H3Hoca
rnapHHpoB, n03TOMY B npo[(ecce 3KCnJIyaTa[(HI1 npI1Xo,n;HTCSI npHMe-
HSlTb HaTSI)KHbIe YCTpoHcTBa; npH He60JIbllIOM tJl1CJIe 3y6beB 3Be3-
lIOI.JKIf CKOPOCTb BpaIl\eHl1g npHBO.lIHOH 3Be3.lI0QKH If L(enl1 HepaBHo-
MepHaSl.
6 II. H. BepeHH3
145
ITepe,n:aT01.JHOe OTHOIlleHHe 6yneT onpe,n:eJUITbCR, KaK 1I ,n:JISI 3y61.Ja-
TOM nepe.n.a1.JH, cpOPMYJIOH
. Z 1
1 =-
,
7
....2
r,n;e ZI - 1.JHCJIO 3y6beB Be)J.ymei1 3Be3,L(01-1KH, a 22 - 1.JHCJIO 3y6beB Be,n;o-
MOM 3Be3,D;OQKH.
BeJlIIQIfHa, 06paTHaH nepe
aTOqHOMY OTHomeHIIIO, Ha3bIBaeTCH ne-
peL\aTOqHLIM qHCJlOM:
u = I /i.
Ilepe,n;aT01.JHoe 1.JHCnO OrpaHH1.JHBaeTC5I ,L(OnYCTHMbIMH ra6apHTHbIMH
pa3MeparvfH, yrJIaMH 06XBaTa Ii 1.JHCJIal'vIH 3y6beB 3Be3,L(01.JeK; 06hI1.JHO
OHO 6bIBaeT
1eHbIlle 7. B OTL(eJIbHhIX CJIY1.JaRX, eCJIII n03BOJIRIOT ra6a-
pHTHbIe pa3rvlepbI, B THXOXO,L(HbIX nepe,n;a1.Jax
onYCKaeTC5J 6paTb nepe-
aT01.JHOe 1.JHCJIO,lI,O 10.
qHcna 3y6beB 3Be3
OQeK. MHHHMaJIbHOe QHCJIO 3y6beB OrpaHM1.JH-
BaeTCSI H3HOCOM LIlapHHpOB, ,L(HHaMH1.JeCKHMH HarpY3KaMH H llIYMOM
nepe,na1.J. qeM l\1eHbilie 1.JHCJIO 3y6beB 3Be3,L(01.JKH, TeM 60JIbllIe H3HOC,
TaK KaK yrOJ1 nOBopoTa 3BeHa QenH npM Ha6eraHMM Ha 3Be3,lI,01.JKY H
c6eraHHH C nee paBeH 360 0 /z.
C Yl'vleHbWeHHeM LJHCJIa 3y6ben B03paCTaeT HepaBHoMepHocTb CKO-
pOCTH ,L(Blf}KeHH$I QenH II CKOpOCTb y,a;apa QenH 0 3Be3,L(OLJKY. MHHH-
MaJIbHOe 1.JHCJIO 3y6beB 3Be3,L(01.JKH B CHJIOBbIX nepe,L(a1.Jax pOJIMKOBbIMH
QenSlMH CJIe,L(YIOmee: npH MaKCHMaJIbHbIX 1.JaCTOTax BpameHMR Z lmin ==
= 19...23; npH Cpe,L(HHX 17... 19 H npM HH3KMX 13... 15. MaKCHMaJIbHOe
LJMCnO 3y6heB 3Be3,L(01.JeK .n.JI5I pOJIHKOBbIX QeneH BbI6MpaIOT paBHbIM
100... 120
a JJ.JIR 3y6LJaTbIX 120... 140.
MaKCHMaJIbHOe Me)l(OCeBOe paccToSlHHe onpe,neJI5IIOT no YCJIOBHIO,
npH KOTOpO
1 yroJI 06xBaTa QenbIO MaJIOM 3Be3,n;01.JKH ,n;on)l(eH 6bITb He
MeHbwe 120°:
npM U < 3
A min = (D 1 + D 2 )/2 + (30.. .50);
npH U > 3
A . == DI + D 2 9 + u
Il1m 2 1 0 '
r,n;e DI M D2 -- HapY)J(HbIe
HaMeTpbI 3Be3):(01.JeK.
OnTMManbHble Me)l(OCeBble paCCT05lHM5I
A == (30...50) ]J,
rJ].e J) -- mar QenH.
146
I
,
llIar QenH (paccTOSlHl1e Me)l(,[.(y ee 3BeHbSlMH) SlBJISleTCR OCHOBHbIM
napaMeTpo
1 QenHoM nepe,L(a1.JH; 06bI1.JHO A/80 < P < A/25.
no npe,[.(BapHTeJIbHO BbI6paHHoMY paccToRHHIO A, llIary p M 1.JHCJIaM
3y6beB 3Be3,n;01.JeK onpe,n;eJIRIOT nOTpe6HOe 1.JHCJIO 3BeHheB u:enM W:
W Z. +Z2 2A (Z2 _ZI)2 P
- + +
- 2 P 2n A .
Cne,L(yeT OTMeTMTb, qTO 3Ta
opMYJIa SlBJIReTCR npM6JIH)I(eHHoM.
MaTepUaJlLI uene". rIJIaCTHHbI BbInOJIHSlIOT H3 XOJIO)IHOKaTaHoH
JleHTbI, H3rOTaBJIMBaeMOM 113 CTaJIeM 45, 50, 40X, 40XH, 30XH3A.
B 3aBHCI1MOCTli OT Ha3Ha1.JeHH5J nJIaCTlIHbJ 3aKaJIHBaIOT ,L(O TBep,n;ocTM
HRC 3 40...50. ,[(eTanH lllapHHpoB - OCM, BTynKH, BKJIa,nbIlllH - BbI-
nonHRIOT npeHMy
ecTBeHHO H3 QeMeHTupyeMbIx CTaJIell 15, 20, 15X,
20X, 12XH3, 20XH3A, 20X2H4A, 30XH3A H no,n;BepraIOT 3aKaJIKe
)].0 HRC 3 50... 65.
B llIapHMpax pOJIHKOBbIX QeneH ,[.(JIR pa60TbI 6e3 CMa3KM npMMeHR-
101' nJIaCTMaCCbI.
Pecypc uenei1 B cTaQMoHapHblx MalIlMHax ,L(On)l(eH COCTaBJIRTh He
MeHee 3. . . 5 TbIC. 1.JaCOB pa60TbI.
3.17. BHHT-rauKa CKOJIb)KeIIHH
nepe,n;a1.Ja BMHT-raHKa npellHa3Ha1.JeHa JJ.JIR npe06pa30BaHMR Bpa-
maTeJIbHOrO ,n;BM)I(eHMR B npSlMOJIHHeHHOe nocTynaTeJIbHoe. nepe-
,n;a1.JM BMHT-raMKa CKOJIb)l(eHHR 06eCne1.JHBa1OT 60JIbllIOM BbIMrpbIlll
B CHne, B03MO)KHOCTb nOJIY1.JeHMR Me,n;JIeHHOrO ,n;BH)I(eHHR, 60JIhllIYIO
HeCYLQYIO cnoc06HOCTb npM MaJIbIX ra6apHTHbIX pa3Mepax, B03MO)l(-
HOCTb ,n;OCTM)I(eHHSI BbICOKOM T01.JHOCTH nepeMe
eHMR HCnOJIHMTeJIh-
Horo opraHa, )l(eCTKO CBSl3aHHoro C raMKoM, M npOCTOTY KOHCT-
PYKQI1M.
He,n;ocTaTKaMH RBJIRIOTCR 60JIbillMe nOTepM Ha TpeHHe, HH3KHM
Kn,l];, HeB03MO)l(HOCTb npHMeHeHHR Ha 60JIblllHX CKOpOCTRX nepeMe-
l1..(eHHM. CKOpOCTb CKOJIb)l(eHHR npocpHJIeM pe3b6bI BMHTa OTHOCHTenb-
HO npocpMJIeM raMKM B 10-40 pa3 npeBbIlIlaeT CKOpOCTb oceBoro ne-
peMeLQeHMR Y3JIa, )l(eCTKO CKpenJIeHHOrO C raMKOM.
06JIaCTb npMMeHeHMR nepe,n:a1.J BMHT-raHKa CKOJIb)l(eHMSI: no,n;HRTMe
rpY30B (,noMKpaTbI), HarpY)l(eHHe B HCTIbITaTeJIbHbIX MalllHHax, Mexa-
HM1.JeCKaR 06pa60TKa Ha MeTaJIJIOpe)l(ymMX CTaHKax M BI1HTOBbIX
npeccax; ynpaBJIeHMe onepeHHeM caMoneTOB; T01.JHbIe ,[.(enMTeJIbHbIe
nepeMemeHMR B M3MepMTeJIbHbIX M ,L(eJIHTeJIbHbIX MalllHHax, B MeTaJIJIO-
pe)l(YlQMX CTaHKax; YCTaHOBOqHbIe nepe
1emeHMR ,n;JIR HacTpoMKM M pe-
rYJIMpOBaHMSI MallIMH.
147
300
BHHTbI, He nO,L1;BepraeMbIe 3aKanKe, Ii3rOTaBnHBalOT H3 CTaneM 45,
50 IinH A45, A50 H A40r (c cO,L1;ep)KaHHeM 0,15...0,500/0 CBHHQa);
nO)J.BepraeMbIe 3aKanKe - H3 CTaneM 651", 40X; a30THpyeMbIe - H3
CTaJIeM 40X<I>A, 18xrT. A30THpoBaHHe 06eCne1.JHBaeT BbICOKYIO H3HO-
COCTOMKOCTb M MHHHManbHoe ,L1;eMn
MpoBaHMe npM ynp01.JHeHMM
(CM. pa3,L1;. 4). I103TOMY ,L1;nSl XO,L1;OBbIX BHHTOB MeTannOpe:>Kym Mx CTaH-
KOB peKOMeH,L1;yeTcSI npMMeHSlTb a30THpoBaHHe.
MaTepHanbI raeK - 6pOH3bI onOBSlHHCTbIe (EpO<D 10-1, EpOQC
6-6-3) H UHHKOBbIM cnnaB DAM 10-5; npH ManbIX CKOpOCTSlX H
HarpY3Kax - qyrYH. faHKM 60nblllHx H cpe,L1;HHX )J.MaMeTpoB 3anHBalOT
aHTH
pHKUMOHHbIM cnnaBOM.
KOHCTPYKTuBHLle oco6eHHocTu BUHTa U railKH. KOHCTPYKIJ.MH BMH-
TOB
On)l(HbI y
oBneTBOp5ITb 06mHM Tpe6oBaHI15IM, npe
D5IBn5IeMbIM K
BanaM: He I1MeTb pe3KHX nepeXO
OB
l1aMeTpOB, 6YPTHKOB 60nbllloro
JJ;HaMeTpa, LIT06bI He npeBpamaTb B CTPY)I{KY MeTann Ii T. n. ,[(nHHHble
BHHTbI BbInonHSlIOT COCTaBHbIMH, HX YCTaHaBnHBalOT Ha
BYX onopax
(KopOTKl1e YCTaHaBnHBalOT Ha O,nHOM, BTOpOM onopOM cnY)I{HT raMKa).
O,L1;HH KOHeu xo,nOBoro BHHTa 06bI1.JHO
HKcHpyeTcSI B onope, 1.JTO
n03BonSleT BocnpHHHMaTb oceBbIe YCl1nHSI.
raMKH xo,nOBoro BHHTa BblnonHSlIOT
enbHbIMI1 H pa3'heMHbIMH;
HX ycnoBHble 0603Ha1.JeHHSI npHBe,neHbI B Ta6n. 3.1. B npeUH3HoH-
HbIX MeTannOpe:>KYllI.HX CTaHKax ocyrn:ecTBnSlIOT 6e3nlOcpToBYIO nepe-
,naqy «BI1HT-raMKa CKOnb)KeHH5I». 3TO LlOCTHraeTC5I npHMeHeHHeM
c,nBoeHHbIX raeK, pacnOnO)l{eHHbIX B O,nHOM Kopnyce 3. OHM CMern:a-
IOTC5I o,nHa OTHOCHTenbHO ,npyroH B oceBOM HanpaBneHHH, T.e. no-
BOpOTOM raeK 2 H 4 (PHC. 3.45, a) BOKpyr xo,nOBoro BHHTa 1 B npo-
THBOnOnO)l(HbIX HanpaBneHHSlx, nocne LIero HX nOnO)l(eHHe CPHKCH-
pyeTcSI KOHTpraMKaMH 5. Tenepb npH BpameHHH xo,nOBoro BHHTa B
O,nHOM HanpaBneHHH nepeMellI.eHIie cynnopTa 6 6Y,L1;eT npoHcxoLlHTb
OT neBoH raMKH 2; ecnH )l(e XO,nOBOH BMHT H3MeHHT HanpaBneHHe
BpallI.eHHSI, TO npaBaSl raHKa 4 cpa3Y nepe,nacT ,nBH)I(eHHe cynnopTY B
a
6
6
z
i)
PHc.3.44
B OTnHqHe 01' Kpene)KHbIX pe3b6 B XO,nOBbIX Ii rpY30BbIX BHHTax
HY)KHO HMeTb HaHMeHblllee TpeHHe
Il03ToMY Iicnonb3YIOT pe3b6bI C
ManbIMH yrnaMH npocpHn5I, qame Bcero TPaneueH,naJIbHbIe (PHC. 3.44, a),
npM'-IeM OCHOBHoe npMMeHeHMe MMeeT pe3b6a co cpe,nHMMI1 rnaraMI1.
MenKYIO pe3b6y npHMeHSlIOT ,nnSl nepeMellI.eHI1M nOBbIIlleHHOH T01.JHO-
CTH H OTHOCHTenbHO Me,nneHHbIX nepeMemeHI1M. KpynHYIO pe3b6y
npHMeHSlIOT B TSI)I(enbIX (no H3HOCY) ycnoBHSlx pa60TbI.
IIpHMoyrOJILHLIe pe3L6LI (PHC. 3.44, 6) Hcnonb3YlOT ,nnSl oCYllI.eCTB-
neHHSI OqeHh TOqHhIX nepeMellI.eHHH, nocKonhKY nOTepH Ha TpeHHe H3
Bcex THnOB pe3b6 (PHC. 3.44, a-d) y npSlMoyronhHbIX MeHhIlle, a KpO-
Me Toro, y 3Toro npO
HnSl HaHMeHblllee BnHSlHl1e HeH36e)l(HbIX pa,nH-
anhHhIX 6HeHHH Ha TOqHOCTh nepeMellI.eHI1}1 raHKI1, a cne,nOBaTenbHO,
H HcnonHHTenhHoro MexaHH3Ma.
He,nOCTaTKOM npSlMoyronhHoH pe3h6bI SlBnSleTCSI TPY,lI.HOCTb H3ro-
TOBneHH5I - HeB03MO)KHOCTh OKOHqaTenhHoH 06pa60TKH lllnH
OBaHM-
eM, LITO OrpaHHqHBaeT ee npHMeHeHHe.
B Kpene)l(HbIX pe3h60BbIX coe,nHHeHHSlX LIallI.e Bcero npHMeHSlIOT
MeTpH
eCKHe (PHC. 3.44, 6) H
lOilMOBLIe (PHC. 3.44, 2) pe3b6bI.
)J:n51 TOlJHbIX BI1H1'OB ,[(eJIH1'eJIbHbIX H H3MepH1'eJIbHbIX MallIHH npH-
MeHSlIOT TpeyroJlLHLle pe3h6hI C yrnoM npocpHnSl 30° H lIa)l(e 60°, KOTO-
phIe MO)KHO H3rOTOBHTh C ManbIMM lllaraMH.
,lJ;JI5I BHHTOB, nOl(Bep)KeHHbIX 60JIbllll1M O,[(HOC1'OpOHHHM oceBbIM
HarpY3KaM (B npeccax, Ha)l(H
IHhIX YCTpoHcTBax npoKaTHhIx cTaHoB),
npHMeHSlIOT ynopHYIO pe3b6y (PHC. 3.44, 0).
MaTepHanbI BHHTOB ,lI.on)l(HbI 06na,lI.aTb BbICOKOH H3HococToHKo-
CThlO H xoporneH o6pa6aThIBaeMocThlO; TSI)I(enoHarpY)l(eHHbIe BHHTbI
He06xo,lI.HMO H3rOTOBnSlTh Ii3 BhIcOKOnpOqHbIX MaTepHaJIOB.
1
2
4
2 3
4
a
6
PUC. 3.45
1
148
149
npOTHBOnOJIO)J(HOM HanpaBJIeHHM. B TaKO" KOHCTPYKQHH JIIOflJT He
BbI6HpaeTCSI, TaK KaK raMKH pa60TaIOT Ka)J(,n:aSI Ha CBoe HanpaBJIeHHe.
Ha pHC. 3.45, 6 HarJISI,n:HO nOKa3aHO, KaK conpHKacaroTC5I npocpHnH
neBOH H npaBoH raeK C npocpHJISIMH xo,n:OBoro BMH1'a.
OCHOBHOH npM1.JMHOM BbIxo,n:a M3 C1'pO
nepe,n:a1.JH BMHT-raHKa
B-
JISIe1'CSI H3HOC. )J;nSI 06eCneqeHHSI Heo6xo,n:MMOH 113HOCOC1'OMKOCTH ,n:aB-
neHHe B pe3b6e He ,n:on)J(HO npeBbIIllaTb ,n:onYCTHMoe:
= F < [ ]
P dl -p,
'It cp lZ
r,n:e F -. paCqeTHa51 OCeBa5I CHna, ,n:eHcTByrom:aSI Ha BHHT; d cp - cpe,n:HHH
}J;HaMe1'p pe3b6bI; Jz - pa60QaSI BbIC01'a npocpl1nSI (AnSI 1'paneueHL{aJIb-
HOM pe3b6bI Jz = 0,5pX.B; PX.B - llIar pe3b6bI xO}J;oBoro BHH1'a); Z - qHCJI0
BHTKOB pe3b6bI Ha BbICOTe raHKH H (z = H/PX.B).
2F
I10,n:CTaBJISI5I B cpopMyny 3HalJeHHSI h HZ, nonyqM
f p = < [p].
ndcpH
O1'clO,n:a MO)KHO onpe,n:eJIMTb cpe,n:HMM
MaMe1'p pe3b6bI
d > f2i?
cp-V
'
r}J;e \If = H / d cp ; }J;JUI QeJIbIX raeK \If = 1,2... 2,5; }J;nSI pa31>eMHbIX raeK
'V = 2,5... 3,5. EOJIbllIMe 3HaqeHH5J \If npHHMMaIOT
JI5I pe3b6 MeHblIlHX
,lJ;I-IaMe1'poB. )J;onycKaeMbIe
aBJIeHMSI B pe3b6e npMHMMaIOT }J;JISI nap:
3aKaneHHa
CTaJIb - 6poH3a [P] =12 H/MM 2 ,
He3aKaneHHaSI C1'aJIb - 6poH3a [P] = 9 H/MM2,
He3aKaneHHaSI C1'aJIb - QyrYH [P] =5 H/MM 2 .
,L(aBneHMe B pe3b6e ,[(JISI TOlJHbIX pe3b6 (,neJIMTenbHbIe MallIHHbI) ,n:OJI)J(-
HO 6bITb B 2-3 pa3a MeHbllIe.
CIIJIbHO HarpY)KeHHbIe BMH1'bI npOBep5IIOT Ha npolfHocTb npH co-
BMeCTHOM ,neMcTBMH C)J(aTHSI H KpyqeHHSI; 3KBHBaJIeHTHOe HanpSI-
)l(eHHe
OJI)I(HO 6bITb MeHbllIe ,nonYCKaeMoro Hanp
)I(eHH}] Ha pac1'
-
)l(eHHe:
:j
'!
cr, =
(F/SI)2 +3(M KP /W p )2 < [cr]p,
:1
r,n:e M Kp - KPYT
m:HM MOMeHT, cKpyqHBalOm:MM BHHT; 8 1 M W p - COOT-
BeTCTBeHHO nJIom:a,nb M nOJISIpHbIM MOMeHT conpoTHBneHM51 CeqeHMSI
BHHTa, B35JTble no BHYTpeHHeMY ,n:MaMeTpy pe3b6bI.
L(onycKaeMoe HanpSI)J(eHMe 6epeTcSI [cr]p < cr T /3 BO H36e)J(aHHe Me-
CTHbIX nJIaCTMlJeCKHX ,neQJopMau.MH.
150
Ii
It
I
,[(JIHHHbIe BHHTbI npoBepSIIOT Ha nOTeplO YCTOHqHBOCTH no 3MJIe-
PY, 3a paCqeTHOe npHHHMalOT KpaHHee nOJIO)KeHHe raMKH, Kor,na BHHT
no,n:BepraeTcSI C)KaTMIO Ha MaKcHManbHoH ,LJ)IMHe:
F< n 2 EJ np
- n(Jl/)2 '
r,n:e JlI - npHBe,n:eHHaSl ,n:JIHHa; / - pacc1'oSIHHe Me)l(,n:y onopaMH ,n:JISI
L{ByxonopHbIx XO,nOBbIX BMHTOB, a ,nJISI KOpOTKMX BHHTOB - 31'0 pac-
C1'OSIHMe Me)l(,[{Y onopOH Ii cepe,n;HHOM raMKH; n = 2,5...4,0 - K03<P<PH-
nd 4 ( d J
QHeHT 6e30nacHocTM; J"P =
0,4 + 0,6- - npMBe,n:eHHbIM MOMeHT
64 d.
MHepUIiM; d M dl - COOTBeTCTBeHHO HapY)J(HbIH M BHYTpeHHMH ,n:MaMeTpbI
pe3b6bI; E - Mo.nynb ynpyrocTH I-ro po,n;a.
3.18. BUHT-raHKa KaIJeHUH
llepe,n;alJM BMHT-raMKa KaqeHM5J npHMeHSIIOTCSI B MexaHM3Max, r,n;e
Heo6xo,n;MMa nJIaBHOCTb nepeMem:eHHSI, B CJIe,n;SIm:HX CHCTeMax, CTaHKax
C 1.JHCJIOBbIM nporpaMMHbIM ynpaBJIeHMeM. KI1t( TaKHX nepe,n:alf ,n:oc-
1'Mrae1' 0,9. B pe3b6e MO)l(e1' 6bI1'b BbI6paH nOJIHOC1'blO 3a30p M C03.n:aH
npe,n;BapHTeJIbHbIH Ha1'SIr, o6eCneqHBalOl.l.\HH BbICOKYIO oceBYIO )J(eCT-
KOCTb. B KalJeCTBe TeJI Ka1.JeHHSI npHMeHSIIOTC5I rnapMKH 11 pOJIHKH, HO
lfa
e npMMeHSIlO1'cSi IllapHKoBbIe nepe,n;alfH. B JIMTepaType qaCTO BCTpe-
qaeTCSI a66peBHaTypa BrK (BMHT-raMKa KaqeHHSI) M llIBII (IllapMKo-
BMHTOBaSI nepe.n:alJa).
Ha BHHTe H B raMKe BbII10JIHSIeTC5I" BHHTOBaSI KaHaBKa (qarue nOJIY-
KpyrJIOro npoQ>MJI5J), no KOTOpOM nepeKaTbIBalOTcSI TeJIa KaqeHHSI
(llIaplfKIf MJIH pOJIHKH). )]:lfaMeTp rnaplfKa Dill = 0,6 PX.B.
I1plf HCnOJIb30BaHMM IllBII B MallIHHax T01.JHbIX nepeMeIQeHIfM He-
,n;onycTMM oceBOM 3a30p. B 3TOM CJIyqae BrK BbInOJIHSIIOT no aHaJIO-
rHH C paCCMOTpeHHOH Ha plfC. 3.45 nepe,n;aqeH BHH1'-raHKa CKOJIb)J(e-
HM
. B e,ZJ;I1HOM Kopnyce 5 (PMC. 3.46) pa3Mem:alOT
Be raHKH 2 M 4,
CMem:eHHbIe o,n;Ha OTHOCM1'eJIhHO .n:pyroM no BHHTOBOM JII1HHM. 31'0
TaK)f(e C03,[(ae1' 6e3JIIO<pToBYIO nepe,n;aqy.
B OTJIHlJHe 01' BHHTOBOM rrapbI CKOJIb)J(eHH5I B lllBII ,n;OJI)KeH 6bITb
C03,naH npe.n:BapM1'eJIbHbIM HaTSlr: eIQe .n:o npMJIo)J(eHI15J pa60qei1 Ha-
rpY3KI1 B KOHCTPYKQHM IllBTI C nOMom:blO npOKJIa,n;oK MJIH npY)KHH
nYTeM 3aTSIrMBaHMSI pe3b60BbIX coe,nHHeHHM C03,n;aIOTC5I npe,n;BapHTeJIb-
HbIe oceBbIe YCMJIHSI. Tenepb TeJIa KaqeHIfSI 3 BMeCTO TOqeqHOrO KOH-
TaKTa C !!OpO)KKOM KaqeHM
HMelOT KOHTaKT no He60JIblIlOM nOBepx-
HOCTM (B CIfJIY ynpyroro nepeMem:eHI1SI no!! lI.ei1cTBHeM npI1no)J(eHHbIx
CHJI). TaKHM 06pa30M nOBbIllIalOT oceBYIO )J(eCTKOCTb IlIBII.
151
B 60nblIll1HCTBe KOHCTPYK.QHH lIlapl1KI1 B
raHKe nepeMelQalOTCg no 3aMKHYTOM TpaeK-
TOpHH. KaHanOM B03BpaTa cnY)KHT cne.Ql1-
anbHag BCTaBKa 6 (CM. pl1c. 3.46), coe,[(HHglO-
ag ,[(Ba COCe.l(HHX BHTKa raHKH, KOTOpag 3a-
CTaBngeT .QHpKynHpoBaTb lIlapHKH TonbKO B
npe,[(enax O,[(Horo rnara XO,[(OBoro BHHTa 1.
B cTaHKocTpoeHl111 HOpMaJII130BaHHbIe rna-
pHKoBbIe napbI BI1HT-raHKa H3rOTaBnHBalOT
Ha cnel(l1anH3l1poBaHHbIx 3aBO.l(ax.
LI:onycTI1MYIO CTaTI11.JecKYIO HarpY3KY pac-
C1.JHTbIBaIOT HCXO.l(g 113 ,[(onYCKaeMbIX ynpyrl1x KOHTaKTHbIX Hanp5I)Ke-
HI1H 250...300 KH/CM 2 .
,L(onycKaeMag HarpY3Ka Ha O.l(I1H rnapl1K npl1 Hanp
)KeHHH 250 KH/CM 2
[F}] = 20d
H, r,[(e dill - ,[(HaMeTp lIlapl1Ka, MM. 06I.Qa
,[(onYCTI1MaSJ
oceBa
CTaTI11.JeCKag HarpY3Ka Ha BHHT
4
3
5
PHC. 3.46
p= 1t m
""
PlICa 3.47
PIiC. 3.48
[F] = zp[fl] sin a cos\V,
Horo Koneca ,n:o 6eCKOHe1.JHOCTI1 nonY1.JalOT TaK Ha3bIBaeMYlO OCHOBHYIO
peHKY, 01.Jep1.JeHHYIO I1CXO.l(HbIM KOHTypOM. OCHoBHa
peHKa nonHOCTblO
onpe,n:enSieT npo
l1nl1 3y6beB Bcex Konec HopManbHoro 3al(enneHl1g.
I1apaMeTpbI I1CXO,[(Horo KOHTypa (PHC. 3.48) cTaH,[(apTH30BaHhI; yron
npO
Hng ex = 20 0 , rny611Ha 3axo,[(a 3y6beB B peHKY h 3y 6 = 2m, pa,[(HaJIb-
HbIM 3a30p Me)K,[(Y 3y6bgMH B l(l1nHH,[(pH1.JeCKHX nepe,[(aqax c = 0,25m
(npH Hape3Ke .l(On6gKaMI1 - ,[(0 0,35m), pa,[(I1Yc BbIKPY)KKH Y KOpH5I 3y6a
,[(ng .QMnMH,n:pM1.JeCKMX Konec r = 0,4n1 (nl - HOpMaJIbHbIM Mo,n:ynb).
PeeqHag nepe,[(aI.J:a MO)KeT 6bITb BbInOJIHeHa C npSlM03y6bIM H KOCO-
3y6bIM 3al(enJIeHl1eM Koneca C peHKoH. 3a O,l.I:MH 060POT npgM03y6oro
Koneca C 1.JI1CnOM 3y6beB z peHKa nepeMeCTHTCg Ha HI = pz = 1tlrlZ, a 3a
n 06/MHH 3y6qaTOrO Koneca - Ha H = 1tnlzn.
PeeqHbIe nepe.n:a1.JH 01.JeHb qaCTO Hcnonb3YlOT B MeTaJIJIOpe)KyI.QHX
CTaHKax, HanpHMep B TOKapHbIX, .n:JIg OCYll.1eCTBJIeHHSI ,lJ.BH)KeHHSI npo-
,n:onbHoii no,n:a1.J11 cynnopTa C pe3l(OM OTHOCMTenbHO o6pa6aTbIBaeMoH
3arOTOBKM. B 60JIee KpynHbIx CTaHKax, TaKHX KaK npo,n:onbHo-crpo-
ranbHbIe, He06xo,lJ.HMO nepe,n:aBaTb 66JIblIll1e YCI1JII1S1. TaM npl1MeHSlIOT
1.JepBSlqHO-peeqHYIO nepe,n:aqy. Ha pl1c. 3.49 nOKa3aH BM,[( CHI13Y Ha CTOJI
npo,n:onbHo-cTporaJIbHOrO CTaHKa; K cTony 3 HenO)J.BM)KHO npl1Kpenne-
HbI peHKH 2. BpalQeHl1e 1.JepBgKOB J npe06pa3yeTCg B nocTynaTenbHoe
npSlMOJII1HeHHOe nepeMeI.QeHHe peHKI1, a CJIe,lJ.OBaTeJIbHO, 11 CTOJIa C YCTa-
HOBJIeHHbIM Ha HeM o6pa6aTbIBaeMbIM H3,lJ.eJIl1eM. IIepeMeI.QeHHe peHKH
(cne,n:OBaTenbHO, 11 CTona) 3a O.l(HH 060POT 4epBgKa C 3axo,n:HocTblO Z
6y,n:eT paBHo HI = nmz, a 3a n 060pOTOB 1.JepBgKa H = nmzn. 06bI1.JHO
B TaKMX nepe,n:aqax 3aXO,[(HOCTb 1.JepBgKa MO)KeT 6bITb Z = 8...10.
JIg yrvteHblIleHl1g TpeHHg B nape qepBgK-peHKa Me)K,n:y npO
I1JISlMH
I1X 3y6beB no.n:aeTCg no.n: .n:aBJIeHHeM TOHKI1H CJIOH MaCJIa. TaKl1e 2uiJpO-
cmalnUlleCKue llep6RllHo-peellHble nepeiJallu HCnOJIb3YlOT B npl1BO,lJ.e
nO.l(aq Tg)KeJIbIX CTaHKOB. Ha pl1c. 3.50 npe.l(CTaBJIeHO YCTpOHCTBO rH.n:-
pOCTaTl1qeCKOH qepBSl1.JHO-peeqHOH nepe)IaqH MHorO.QeJIeBOrO CTaHKa
MO.l(eJIM 6620M<D4 YJIbgHOBCKOro 3aBO.l(a Tg)KenbIX H YHI1KaJIbHbIX
r,[(e Zp = 0,7z - paC1.JeTHOe qHCJIO rnapHKoB; z - qHCJIO rnapHKoB, Haxo-
,[(Slll(MXCSI B KOHTaKTe, T. e. TonbKO B O,[(HOH 113 raeK - neBoM HnM npa-
BOH; a - yrOJJ KOHTaKTa rnapHKa, 06bI1.JHO a = 450; \V - yroJI nO,[('heMa
BI1HTOBOH nl1HI1M pe3b6bI (\V = 2. . .5 0 ).
TaK paCC1.JHTbIBaIOT HarpY3KY, ,[(onycKaeMYIO Ha BI1HT .[(JISI TI1XOXOI(-
HbIX nepe,[(aq. ECJIH )Ke 06lQee qHCJIO l(HKnOB HarpY )KeHHH N> 10 7 , TO
HarpY3KY CHH)j(aIOT, YMHO)j(aSi ee Ha K03<}JqmL{HeHT V 107 IN.
MaTepl1anbI J(nSl lllBn: BHHTbI H3rOTaBnl1BalOT H3 CTaneH XBr 11
7xr2BM C 06'heMHOH 3aKaJIKOH, 8XB C 3aKanKOH npH HH.[(YKUI10HHOM
HarpeBe 11 20X3MB<D C a30Tl1pOBaHl1eM. )J:nSl raeK npl1MeHSlIOT CTanH
9xrc, IIIXI5, XBr C 06'heMHOH 3aKaJIKOM H u:eMeHTHpyeMbIe CTaJII1
18xrT, 12XH3A. Pa601.JHe nOBepxHocTH 3aKanHBalOT ):(0 TBep):(oCTI1
HRC 60 H BbIllie.
3.19. PeelJHbIe nepe
alJH
PeeqHaSl nepe.l(a1.Ja, KaK H nepe,[(a1.Ja BI1HT-raMKa, cnY)KHT .[(JISI npe06-
pa30BaHHSI BpaLQaTenbHoro .l(BH)KeHI1S1 B nocTynaTeJIbHOe npSlMOJII1HeH-
Hoe 11 Hao6opOT. Pee1.JHaSl nepe,n:a1.Ja (pl1c. 3.47) COCTOI1T 113 3y61.JaTOrO
KOJIeCa 111 3y6qaToM peHKI1 2. PeHKa SlBnSleTCSI 1.JaCTHbIM CJIyqaeM 3y6-
qaTOrO Koneca, KOr.l(a pa,[(HYC Koneca YBeJIHqeH ,[(0 6eCKOHeqHOCTI1. TIpH
3TOM KOJIeCO npeBpaLQaeTCSI B peHKY, a 3BonbBeHTHbIM npoQn1nb 3y6a -
B npSlMonHHeMHbI1L I1pl1 YBenHqeHI1H 1.JI1CJIa 3y6beB HeKOpperl1pOBaH-
152
153
3.20. KpHBomHnHo-maTYHHbIe MexaHH3MbI
B no,[(pa3,[(. 3.17-3.19 6bIJIH paccMoTpeHbI MexaHH3MbI, npe06pa-
3YIO
He Bpa
aTeJIbHOe ,[(BH)f(eHl1e B nocTynaTeJIbHoe. lIpH 3TOM 06ec-
neLII1BaJIaCb nOCT05lHHa51 CKOpOCTb nepeMe
eHH5I pa601.fl1x opraHOB.
KpHBomHnHo-maTYHHble I\1eXaHH3Mbi (CM. pl1C. 3.3) TaK)f(e npe,[(Ha-
3HaqeHbI ,[(JI5I npe06pa30BaHH5I Bpa
aTeJIbHOrO ,[(BH)f(eHH5I B nocTyna-
TeJIbHOe, HO OHI1 06eCneQl1BalOT nepeMe
eHHe no onpe,[(eJIeHHOMY
3aKOHY. CKOpOCTb pa6oQero opraHa He OCTaeTC5I nOCT05lHHOll BO BpeM5I
ero JJ.BH)f(eHH5I. B 3TOM eCTb CBoe npeHMy
ecTBO: npH H3MeHeHHH Ha-
npaBJIeHH5I CKOpOCTH He B03HHKaeT YJJ.apOB H 60JIbllIHX HarpY30K, TaK
KaK K MOMeHTY peBepCHpOBaHH5I D.BH)f(eHH5I CKOpOCTb pa601.fero opra-
Ha nOCTeneHHO na,n;aeT, npH6JIH)f(a5lCb K HYJIIO. KpoMe Toro, B03BpaTHo-
nocTynaTerrbHoe ,n;BH)f(eHHe B KpHBollIHnHo-lliaTYHHbIX MexaHH3Max
ocy
eCTBJI5IeTC5I 6e3 npHMeHeHI151 ,[(onOJIHHTeJIbHbIX peBepCI1BHbIX Me-
xaHH3MOB.
KpHBollIHnHo-lliaTYHHbIe MexaHH3MbI HMelOT 1lII1pOKOe pacnpocT-
paHeHHe: B nopllIHeBbIx ,[(Bl1raTeJI5IX, Hacocax, KOMnpeccopax, CTaHKax
C np5lMOJII1HeHHbIM ,[(BI1)f(eHl1eM pe3aHI151.
3.21. KYJlHCHbIe MexaHH3MbI
KpI1BOllIl1nHO-KYJIHCHbIll MeXaHI13M (B ,n;aJIbHeHllIeM 6y,n;eT COKpa-
eHHO Ha3hIBaTbC5I KYJlHCHbll\t MexaHH3MoM) CJIY)f(I1T ,[(JI5I npe06pa30Ba-
HI151 Bpa
aTeJIbHOrO ,[(BI1)f(eHI151 B nocTynaTeJIbHoe. Cy
ecTByeT ceMb
pa3JIH1.fHhIX cxeM KYJIHCHhIX MexaHH3MOB. B O,n;HHX KYJIHCa Ka1.faeTC5I, B
,n;pyrHx Bpa
aeTC5I HepaBHOMepHO, B TpeTbHX Bpa
aeTC5I paBHOMepHO
H T.,l(. ECTb KYJIHCHhIe MeXaHI13MbI C ,l(BYM5I nocTynaTeJIbHbIMI1 napaMH,
npl11.feM caMa KYJII1Ca nepeMe
aeTC5I nocTynaTeJIbHO. Hal160JIbllIee pac-
npOCTpaHeHHe nOJIY1.fI1JIH KYJIHCHbIe Mexa-
HH3MbI C KaQalOll1eHC5I KYJIHCOH (B npHBo,[(e
nOnepe1.fHO-CTpOraJIbHhIX cTaHKoB) H C Bpa-
alO
eHC5I KYJIHCOll (B npHBOJJ.e ,[(oJI6e)f(-
HbIX cTaHKoB).
Ha pHC. 3.51 npe,l(CTaBJIeHa cxeMa npH-
Bo,[(a C KaQalO
ellC5I KYJIHCOH. KYJIHCHOe
KOJIeCO 1 nOJIyqaeT Bpa
eHHe OT Be,l(y
ero
KOJIeCa ZBllt. Ha KYJIHCHOM KOJIeCe 3aKpen-
JIeB naJIeu. 2 C Ba,[(eTbIM Ha Hero KaMHeM 3.
KaMeHb BCTaBJIeH B npope3b KYJIHCbI 4 H
MO)f(eT CKOJIb3HTb B,[(OJIb npope3H. BepxHHH
KOHeu. KYJIHCbI Qepe3 cepbry 5 CB5I3aH C
nOJI3YHoM 6.
PUC. 3.49
CTaHKOB. C nOMO
hlO rH.npopacnpeJ
eJIHTeJI5I B KaHaJ1hI 1.fepB5IKa 1 OT
HaCOCOB 3 no
,[(aBJIeHHeM nO,l],aeTC5I MaCJIO. OHO C03,[(aeT MaCJI5IHhIH
cnoM Me)f(,[(Y 3y6b5lMI1 QepB5IKa H peHKI1, 3y6b5I 2 KOTOpOH apMHpOBaHhI
nnaCTMaCCOH. B oceBble 3a30pbI COe,l],HHeHH5I MaCJ10 HarHeTaeTC5I Haco-
CaMI1 4. Bce HaCOCbI HMelOT O,[(HH 06
HH npHBO,[( OT 3J1eKTpO,lJ,BHraTeJ151 5.
4
PHC. 3.50
154
5 6
PUC. 3.51
155
)
2
#
_ ;..
{.1 1 i
.: 1"
..
PliCa 3.52
J(nl1Ha xo,[(a nOn3YHa L 3aBI1CI1T 01' aMnnl1TY,[(bI KaqaHI151 KYJII1CbI. Ee
MO)KHO perYJIl1pOBaTb 113MeHeHI1eM Benl1ql1HbI pa,[(l1yca R Bpa
eHI151
nanbQa 2. B cnyqae, Kocn.a A > R, KYJII1Ca KaqaeTC5I 11 npl1 R/ A < 0,5
yron KaqaHI151 2a = 60°; ecnl1 A < R, TO Kynl1ca Bpall.{aeTC5I HepaBHO-
MepHO; npl1 A = R KynHca paBHOMepHO BpamaeTC5I.
KynHcHbIH npHBO,lJ; nOnepeqHO-CTpOraJIbHOrO CTaHKa C KaqalOll.{eH-
C5I KYJII1COH (pI1C. 3.52) cnpOeKTl1pOBaH B COOTBeTCTBl111 C KHHeMaTI1-
qeCKOH cxeMOH, H306pa)KeHHOH Ha pHC. 3.51. KYJII1CHbIH MeXaHI13M
06eCneqHBaeT nnaBHOCTb XOlla npl1 CTpOraHHI1 nOBepXHOCTH 3aro-
TOBKH 11 6bICTpbIH OTBOll npl1 06paTHOM xonOCTOM XO,lJ;e. B 3TOM npe-
I1My
ecTBo Kynl1cHbIX MeXaHI13MOB. Kynl1ca 4 COBeprnaeT KaqaTenb-
Hoe )];BI1)1(eHl1e, KOTopoe C nOMOIl{blO Cepbrl1 3 npe06pa3yeTcSI B no-
cTynaTeJIbHOe npSlMOJII1HeHHOe ,lJ;BI1)1(eHl1e non3YHa 5 CTaHKa. Kynl1cHoe
Koneco 2 nonyqaeT BpaIl{eHl1e 01' Kop06KH CKopocTeH qepe3 rnecTep-
HIO 1. BMeCTe C KaMHeM KynHcHoe Koneco BpalQaeTC5I BOKpyr OCI1 01,
a KYJII1Ca KaqaeTC5I BOKpyr OCI1 O. Pa,lJ;I1Yc Bpall.{eHI151 KaMH5I YCTaHaB-
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3. Y3JIbI 11 ,lJ;eTaJII1 Marnl1H, KaKa51 Me)l(.ny HI1MH CBSl3b 11 pa3nl1ql1e?
4. PaCCKa)l(I1Te, KaKl1e BbI 3HaeTe KI1HeMaTl1qeCKl1e napbI?
5. Ha30BHTe KpHTepl1H pa60Tocnoco6HoCTH MaIlII1H.
6. KaK YCJIOBHO 11306pa)l(alOT Ha cxeMax KI1HeMaTI1QeCKl1e napbl 11
MYCPTbI?
7. KaKHe COe,lJ,HHeHH5I ,lJ,eTaneH MallIHH OTHOC5ITC5I K Hepa3'beMHbIM?
8. llepeQHCnl1Te pa3'beMHble COe,lJ,HHeHH5I.
9. 3a CqeT qero nepe,lJ;aeTC5I ,lJ;BI1)1(eHl1e B cppI1Kl.(HOHHbIX nepe,lJ,aqax?
10. KaKHe 3y6qaTbIe nepe,lJ,aqH BbI 3HaeTe?
11. Ha30BHTe npel1MYll.{eCTBa H HeJJ;OCTaTKH 3y6qaTbIX nepe,lJ,aq.
12. qTO TaKoe MO,lJ,ynb 3y6qaTOrO Koneca?
13. qeM OTnl1qaeTC5I QepB5IQHOe KOJIeCO 01' QI1JII1H,lJ;pHQeCKOrO np5l-
M03y60ro?
14. QenHbIe nepe,naQI1 - HX ,nOCTOHHCTBa 11 HeL!OCTaTKI1.
15. fIepe,lJ;aTOQHOe OTHOllleHHe 11 nepeJJ;aTOqHOe QHCJIO. B qeM pa3-
HHl.(a?
16. qeM OTJIHqaeTC5I Ban 01' OCH?
17. KaKl1e BbI 3HaeTe nO)J.llll1nHI1KI1 CKOJIb)KeHMSI?
18. qTO TaKoe nO,lJ,n5lTHHK?
19. KaKl1e onopbI Bpal.l{aIO
HXC5I JJ;eTaneH BbI 3HaeTe?
20. Ha3HaqeHHe MYCPT.
21. Ha30BHTe npl1MepbI HepacQenJI5IeMbIX 11 pacQenJI5IeMbIX My<p T .
22. KaKI1e BbI 3HaeTe npe,lJ,OXpaHHTenbHbIe MYCPTbI?
23. qeM OTJIHQaIOTC5I npY)I(HHbl 01' peccop? qTO Y 3TI1X ,lJ,eTaJIeH
06ll.{ero?
24. qTO TaKoe 6e3JIlOcpToBa51 nepe
aqa? llpHBe,lJ.HTe npHMepbI.
25. KaKl1e nepe)J.aQH BI1HT - raHKa BbI 3HaeTe? qeM OHI1 OTJIHqaIOTcSI?
26. KaKl1e npocpl1JIH pe3b6bI I1CnOJIb3YIOT B nepe,lJ.aqax BHHT - raHKa?
27. qTO TaKoe IllBfI? Kor,lJ,a 3Ta nepe,naqa npI1MeH5IeTC5I?
28. Ha30BI1Te npl1MepbI KopnycHbIx ,lJ,eTaneH.
29. r,lJ;e 11 ,lJ;JI5I qero I1CnOJIb3YIOTC5I KYJII1CHbIe MeXaHI13MbI?
30. KaKl1e peeQHbIe nepe,lJ,alll1 BbI 3HaeTe? 06nacTb HX npHMeHeHH5I.
31. qTO TaKoe KpI1BoIlIHnHo-lllaTYHHbIH MeXaHI13M? )];JI5I KaKoH l.(e-
JII1 OH npHMeH5IeTC5I?
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33. Ha30BI1Te 113,lJ;eJII151, B KOTOpbIX I1CnOJIb3YIOTC5I npY)l(HHbI.
34. IlpI1Ben.HTe npHMepbI I1cnonb30BaHH5I peccop.
4.1. lloHHTHe H OCHOBHLIe cnoco6LI H3MeHeHHH
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nOKpbITHH )J;n51 nOBbIllleHH5I conpOTHBJIeHH5I MeXaHHqeCKoMY H3HO-
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nOKpbITH5I )])151 BOCCTaHOBneHHH pa3MepOB ,l(eTMeM - XpoMoBbIe (Pa3-
MepHoe XpoMHpoBaHHe C nocne,a:YlOlQeH 1I0BOl(KOH), )J(ene3HbIe, Me,a:HbIe.
PaccMoTpHM nO)J;p06Hee nOKpbITH5I, KOTopbIe H3MeH5IIOT cpH3HKO-
MeXaHHqeCKHe CBoHcTBa H31IenHH, T. e. nOKpbITHH, OTHOC5IlQHeC5I K nep-
BOM H TpeTbeH rpynnaM.
[{HHKoBoe nOKpbITHe ,a:enaeT nOBepxHocTb KOpp03HOHHOCTOMKOM.
OQMHKoBaHHbIe CTanhHhIe JIMCTbI, Kpene)l(, npoBonoKa, pa60TalOll.(Me
B pa3nHqHbIX KnHMaTHqeCKHX ycnoBHHx, 3aKpbITbIX nOMelQeHH5IX C
YMepeHHoM Bna)J(HocTblO, aTMoccpepe, 3arp5l3HeHHOH cepHHcTbIM
ra30M, He nO)J;BepralO1'CH KOpp03HH. [(HHKOBoe nOKpbITHe npHMeH5I-
eTC5I TaK)J(e AnSI 3aI..IJ:H1'bI H3,a:enHH H3 qepHOrO MeTanna 01' ,a:eHcTBH
6eH3HHa H Macna (6eH306aKH, 6eH30- H MacnonpoBo,a:bI), BOllonpo-
BO,l(HhIX Tpy6 H )J;p.
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KOpp03HH XHMHQeCKOM H 3neKTpOXHMHQeCKOH annapaTypbI, COnpl1KaCa-
IOlQeHC5I C lQeJIOQHOH cpe,n;OH, a TaK)J(e }J.n51 MeAHl{HHCKOro HHcTpYMeHTa.
L{n51 3aIT(HTbI 01' KOpp03HH CTaJIbHbIX H3}J.enHM, HCnOJIb3YIOIT(HXC5I B
3aKpbITbIX nOMeIT(eHH5IX C HearpeccHBHoi1 KOpp03HOHHOM cpe,nOM,
npHMeH5IIOT OKCH)J;HpOBaHMe.
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XHMHqeCKaSl
annapaTypa),l(JIS! nOBbIllleHHSI 3neKTponpOBo)J;HlQHX CBOHC1'B nOBepx-
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H npO)l(eKTopOB.
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cnoc06HoCTH H3)J;eJIHH.
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Me}J.blO, onoBoM, Ka}J.MHeM YMeHb-
lllalOT MHKponepeMelQeHH
B CBSI3H C pe3KHM YBeJIHqeHHeM K03cpcpH-
UHeHTa TpeHHSI. Il03ToMY OHH npHMeHSlIOTc
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TOB H noca}J.OqHbIX nOBepXHOCTeH: coe)J;HHeHHi1 C HaT5IrOM, nY)I(eHHSI
onopHhIx nOBepxHOCTeH BKna)],bIllieH.
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TaneH; npHMeH5IeTC5I ,[(JI
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conpOTHBJIeHHSI MeXaHHqeCKOMY H3HOCY npMMeH5IIOT TaK)I(e HHKeJIe-
Boe nOKpbITHe cTanei1 (6e3 no)],cno51 Me)],H).
llJIaCTMaCcoBble nOKpbITH5I 06eCneQHBalOT B03MO)l(HOCTb Hcnonb-
30BaHH5I BbICOKI1X aHTH<PPHKQHOHHbIX HnH <PpHKQHOHHbIX, KOMneH-
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aCC C YMeHbllleHHbI
BJIHSlHHeM HX He)],OCTaTKOB, a HMeHHO xono)],HOH nOJI3YQeCTH, HH3KOH
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BbIllIeHHe 113HOCOCTOHKOCTH If KOpp03110HHOM CTOHKOCTH, a B HeKOTO-
pbIX CJIYQaSlX H YCTaJIOCTHOH npOQHOCTH ,a:eTaneH MallIHH )],OCTHraeTCSI
elQe H XHMHKo-TepMHQeCKOH o6pa60TKoi1. PaccMoTpHM HaH60nee
llIHpOKO npHMeH
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16S
llpolJ ecc a30mUpOBaHUR (npOqHOCTHOii) npl1MeHSIeTCSI ,n;JISI ,n;eTaneM
Marul1H, pa60TalO
I1X B ycnoBI1SIX TpeHI1SI 11 3HaKOnepeMeHHbIX Ha-
rpY30K H3rH6a (WeHKM KOlleHqaTbIX BarrOB 6bICTpOXO,lJ:HbIX ,lJ:BHraTelleH,
pa60qee 3epKaJIO rl1nb3 Ql1nMH,lI.pOB, KnanaHbI, ce,lI.na KnanaHOB, TonKa-
Tenl1 ,n;Bl1raTeJIeM BHYTpeHHero CrOpaHI1SI, ruecTepHI1 aBMaQMOHHbIX
,lU3l1raTeneii, TOQHbIe ,lI.eTaJIl1 TonnMBHOH: annapaTypbI, Illnl1H,lI.enl1 6bI-
CTpOXO)].HbIX CTaHKOB). A30TI1pOBaHI1e npl1MeHSIeTCSI TaK)I(e )].nSl nOBbI-
rueHHSI M3HOCOCTOHKOCTM MepMTeJIbHbIX MHCTpYMeHTOB (pe3b6oBbIe
11 rna)].Kl1e npo6KI1 11 KOJIbQa, nJIOCKl1e KaJIH6pbI, CK06bI, rna6nOHbI).
Pa3HOBI1)].HOCTblO npoQecca SIBnSIeTCSI aHTHKopp03110HHoe a30Tl1pO-
BaHl1e, npMMeHSleMoe J1llSl MaJIOHarpy)KeHHbIX ,neTaJIeH, 113rOTaBlll1Bae-
MbIX H3 yrnepOI(I1CTOM 11 HI13KOnerHpOBaHHOH CTMH. OpH 3TOM B no-
BepXHOCTHOM Clloe JJ;Oll)KHa 06eCneqMBaTbCSI MaKCMMaJIbHaSI KOHQeH-
TpaQMSI a30Ta. YrJIepo,nHCTaSI CTaJIb nOClle a30TMpOBaHHSI npM 650°C
B TeqeHl1e 3 q He KOppo3HpyeT B Bo,ne B TeqeHHe 720 lJ.
lJuallUpOBQHUe - npoQecc XHMHKo-TepMHqeCKOM o6pa6oTKH, o6yc-
nOBnI1BaIOIL(MM HaCbII.QeHl1e nOBepXHOCTHoro cnoSl CTaJIH O)I.HOBpeMeH-
HO yrnepO)].OM l1 a30TOM. QHaHl1pOBaHl1e ocy
ecTBnSlIOT nocne 3aKan-
KH 11 HH3Koro OTnYCKa, B pe3ynbTaTe nOBbIIllaeTCSI TBepL{OCTb H npoq-
HOCTb nOBepXHOCTHoro cnoSl, H3HOCOCTOHKOCTb 11 YCTMOCTHaSI npoq-
HOCTb. IlpHMeHSIeTcSI L{nSI HHCTpYMeHTOB 113 6bICTpOpe:>Ky
eM CTaJIH
(npOTSI:>KKI1, CBepna, 3eHKepbI, MeTqI1KH, pa3BepTKI1, <ppe3bI) 11 )].J1SI L{eTa-
JIeH MaWMH (60llTbI, raHKI1, BMHTbI, BallHKM, lIIeCTepHM, pbIqarH).
Pe3Koe nOBbIllleHHe conpOTHBneHI1SI CXBaTbIBaHI1IO, 113HOCOCTOM-
KOCTH 11 npHpa6aTbIBaeMOCTH CTaneH: H QyrYHOB )].OCTHraeTCSI CYJlbfjJO-
lJUQHUpOBQHUeM, T. e. HaCbII.QeHl1eM nOBepXHOCTHbIX cnoeB a30TOM,
yrJIepo,n;OM 11 cepOM. CYJIbcpOQHaHl1pOBaHHe npl1MeHSIIOT J(JISI CPPI1KQI1-
OHHbIX ,nHCKOB, QI1JII1H,npOB, XO)J;OBbIX BI1HTOB.
qyrYHHbIe rl1J1b3bI QI1J1I1H)].pOB M nopIIiHeBbIe KOJ1bQa nO)].BepralOT
CYJlbljJuiJupoeaHUIO (HaCbIlI.\eHHIO nOBepXHOCTHbIX cnoeB cepOM).
B pe3YJIbTaTe TaKOM o6pa6oTKI1 nOBbIlllaeTCSI 113HOCOCTOMKOCTb 11
npl1pa6aTbIBaeMOCTb. CYJIb<Pl1,lJ.I1pOBaHl1e pe:>KYlI.\l1x I1HCTpYMeHTOB
nOBhIIllaeT CTOHKOCTb pe)KylI.\HX I1HCTpYMeHTOB 113 6bICTpOpe)KY
HX
CTaneM P9 11 PI8 B 2-3 pa3a.
/(UrjJrjJY3UOHHQJl Alen1QJlJlU3al1UJl - HaCbIIl.(eHHe nOBepxHocTHoro CJIOSI
CTaJII1 aJIIOMHHMeM, XpOMOM, KpeMHMeM, 60pOM C QellblO npM,[(aHMSI
CTaJIH BbICOKOH )l(apOnpOqHOCTH, aHTHKopp03HOHHbIX CBOMCTB H
H3HOCOCTOMKOCTI1. Hal1BbICillaSI no cpaBHeHl110 C ,n;pyrl1MI1 BH,n;aMH
ynpOqHeHHM TBep,n;ocTb HV = 1500...1800 H 113HOCOCTOMKOCTb ,n;OCTM-
ralOTCSI 60PUpOBQHUeM. YKa3aHHa
TBep,n;ocTb 3HaQHTenbHO BbIllle, qeM
TBep,n;ocTb KBapQa. BOpl1pOBaHHe HCnOJIb3yeTcSI ,n;nSl KOH,[(YKTOPHbIX
BTYJIOK H pe:>KYI.I{MX I1HCTpYMeHTOB Ero BeCbMa 3<p<peKTMBHo npMMe-
HSITb B a6pa311BHbIX cpe,[(ax; HHcTpYMeHT MO)KeT pa60TaTb npH TeMne-
paType 800°C, He TepSISI TBep,n;OCTH H He H3HaIllHBaSICb.
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BbICOKYIO :>KapOnpOqHOCTb nOJIyqalOT nOBepXHOCTHbIe CJIOH ,[(eTa-
JIeH nOCJIe aJlUmUpOBQHUR ()I(apOnpOqHOCTb ,l.XO 850... 900°C). 06JIaCTb
npl1MeHeHI1SI aJIHTMpOBaHI1SI: qeXllbI TepMonap, peTopTbI ,[(JISI QHaHHpo-
BaHMSI, TMrJIH COJ1SIHbIX BaHH, TOnJIMBHMKM ra30reHepaTopOB, QyrYHHbIe
KOJIOCHMKH, Tpy6bI ,[(.TISI KpeKI1Hra He<pTH, BbIXJIOnHbIe Tpy6bI.
4.6. Ynpo..ueUHe XO,lJ;OBLIX BHUTOB
K XO,n;OBbIM BHHTaM npe:>K,n;e Bcero npe,n;'bSIBJISIIOTCSI BbICOKHe Tpe6o-
BaHHSI no H3HOCOCTOHKOCTH, KOTopa
06bIqHO 06eCneQl1BaeTCSI BbI-
COKOM TBep,n;OCTblO nOCJIe 3aKaJIKI1. O,lI.HaKO COBpeMeHHbIe
eTo,n;bI
ynpOQHeHHSI XOAOBbIX BllHTOB n03BOJIHJ111 nOBbICI1Tb H3HOCOCTOHKOCTb.
O,[(HI1M 113 TaKI1X MeTO)],OB ynpOqHeHHSI XO)],OBbIX BHHTOB SIBllSIeTCSI
a30mupoBaHue. A30THpOBaHHbIe XO,l!OBbIe BI1HTbI 06JIa,n;a1OT CYIQeCT-
BeHHO 60JIee BbICOKOM ll3HOCOCTOMKOCTblO, qeM 3aKaJIeHHbIe; B HcnbI-
TaHHSlX npM pa60Te C 3arpSI3HeHHOH: a6pa3HBOM CMa3KOH a30THpo-
BaHHbIe BHHTbI H3 CTaneH 40X<I>A H 30X3BA H3HaIllHBaJIHCb B 1,75
pa3a MeHbIlle, qeM 3aKaJ1eHHbIe BI1HTbI, H3rOTOBJIeHHbIe H3 CTaJIH XBr
(HRC 54...58). llo3ToMY 06'beMHaSI 3aKaJIKa MO)l(eT 6bITb peKoMeH,l!O-
BaHa ,[(JISI XO,lI.OBbIX BHHTOB nOHH:>KeHHOH )l(eCTKOCTI1, BHHTOB C MaJIbI
rnarOM pe3b6bI H npl1 Heo6xo,lI.I1MOCTI1 ynpOQHeHHSI BI1HTa Ha KaKOH-
JII160 qaCTI1 ,[(JII1HbI BI1HTa. YnpOQHeHHbIe XO,lI.OBbIe BMHTbI Heo6xo,n;H-
MbI J1JISI MeTaJIJIOpe)l(YlI.\HX CTaHKOB, B TOM ql1CJIe cneQl1aJIbHbIX, npe,n;-
Ha3HaQeHHbIX JI.JISI Hape3aHI1SI pe3b6.
pyroM MeTOJI. ynpOQHeHHSI XO,[(OBbIX BI1HTOB - 3JleKmpOMeXQHUlleC-
KUU. npH 3JIeKTpOMeXaHHQeCKOM MeTo,n;e ynpOqHeHllSI pa60QHX no-
BepXHOCTeH pe3b6bI BllHTOB COBMeI.I{aeTCSI 06KaTKa pe3b6bJ (HaKJIen) C
TepMI1QeCKOM o6pa6oTKOM TOHKHX nOBepXHOCTHbIX CJIOeB npl1 Harpe-
Be 3JIeKTpOTOKOM.
a:>Ke B ycnoBllSIX a6pa311BHoro 113HaIllHBaHHSI nOCJIe 3JIeKTpOMe-
XaHI1QeCKOrO ynp01..fHeHI1SI H3HOCOCTOHKOCTb XOJJ:OBoro BMHTa MO)l(eT
YBeJII1QHTbCSI B 2-5 pa3 (B 3aBI1CI1MOCTH OT MaTep"aJIa
HHTa). ,
CoxpaHeHHe T01.JHOCTM nepe,n;aQH XO,[(OBOH BI1HT-raHKa
B 60J1bllIeH
Mepe 3aBI1CMT OT 113HOCOCTOHKOCTH pe3b6bJ BI1HTa, a He raHKI1. n03TO-
MY raHKI1 peKOMeH,n;yeTcSI H3rOTOBJISITb 113 6pOH3 MJIH QI1HKO
Oro cnJIa-
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TOKapHbIX CTaHKOB ,n;JISI qHCTOBbIX OnepaQMH MorYT H3rOTOBJISITbCSI 113
TeKCTOJII1Ta MapOK IlT MJII1 nTK.
KOHmpOJlbHble 60llpOCbl U 3aoaHuR
1. KaKHe cnoc06bI H3MeHeHHSI MeJ.CaHHQeCKI1X CBOMCTB MaTepl1aJIOB
BbI 3HaeTe?
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2. JJ:JISI qero npM
leHSIeTcSI o6KaTbIBaHMe HapY)J(HbIX nOBepxHocTeM
Tell Bpa
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bI ynpoLfHeHMSI nJIaCTMqeCKMM L{ecpopMMpoBa-
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4. KaKMe cnoco6bI nOBbIlIleHMSI M3HOCOCTOHKOCTM nOBepxHocTeH
TpYl.QMXCSI ,neTaneM BbI 3HaeTe?
5. Ha30BMTe XMMMKo-TepMMQeCKMe npOl.{eCcbI, Mcnollb3yeMbIe ,nJISI
nOBbIIlIeHMSI )J(aponpOqHOCTM ,[(eTaneH.
6. KaKMe MeTO,[(bI nOBbIllleHMSI M3HOCOCTOHKOCTM XO,[(OBbIX BMHTOB
BbI 3HaeTe?
7. KaK MO)KHO nOBbICMTb KOpp03MOHHYIO CTOHKOCTb MaTepMana
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3TOM cnYQae HOBbIe H3,QeJIMSI 6Y,QYT KOHKypeHTocnoc06HbI.
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napaMeTpbI TenbHOCTb, Kn)J., Ha- cpOpMHpOBaHHH BbIXOJJ.HbIX napa-
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167
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napaMeTpbI Y3na CKOpOCTb nepeMerneHlul CTHK Y3na, 06ecnet.JHBalOllUIx BbI-
XO)J.HbIe napaMeTpbI MaIllHHbI B
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pa60Tocnoc06- )l(eCTKOCTb,BH6poCTOH- KpliTepliSI B o6eCne1.JeHHII pa6oTo-
HOCTH MallIHHbI KOCTb,H3HOCOCTOHKOCTb, cnoco6HoCTH Y3na
np01.JHOCTb
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TexHHKo- CTOHMOCTb, TeXHOnOrlfl-:l- 3TH ,[(aHHbIe Hcnonb3YlOT KaK
3KOHOMH1.JeCKlie HOCTb, Y)I06CTBO 06cnY)I(II- OCHOBHbIe KpHTepHH npH cpaB-
nOKa3aTenH BaHIISI, Macca HeHIUI B03MO)KHbIX BapliaHTOB
KOHCTPYKUHH
COBepllIeHCTBO 3MnHpH1.JeCKUe )J.aHHbIe, OueHHBalOT B03MO)KHOCTb
MeTO,[(OB paC1.Je- aHanHTH1.JeCKHe paC1.JeTbI, npHMeHeHIISI pa3nHt.JHbIX peliC-
TOB nporpaMMbI CAnp HHH H BbI60p onTHManbHoro
BapHaHTa
XapaKTepHCTHKa )J;aHHbIe Ii xapaKTepliCTIiKIi CpaBHeHHe pa3pa6aTbIBaeMoro
CYW.eCTBYIO ll{HX nY1.JliHX KOHCTpYKUHH BapliaHTa KOHCTpYKUHII C cYll{e-
KOHCTpYKl{HH aHanOrH1.JHOrO Ha3Ha 1.JeHHSI CTBYIOll{HMII
llpH nOHCKe HOBbIX KOHCTpYKTHBHbIX perneHHH }J;JI
pa3JIHqHbIX Y3-
nOB M MeXaHM3MOB MalllMH, HeCMOTp
Ha pa3Hoo6pa3Me MX <PYHKQH",
npO
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l1e 06
He TeH):(eHQl1H.
1. Ilpl1MeHeHl1e HOBbIX MexaHH3MOB, CKOHCTpy"poBaHHbIx C yqe-
TOM ,L(OCTM)I(eHMH MexaHMKM, rHD.paBnI1KH, nHeBMaTHKM, a TaK)Ke KOM-
611HHpOBaHHbIX MeXaHI13MOB (nHeBMOrH,lJ.paBnHqeCKHX, 3neKTpOMexa-
HMqeCKHx).
2. llpMMeHeHMe MexaHM3MOB, nocTpoeHHbIx H3 HOBbIX <p 113MIJ e-
CKI1X npMHQl1nax: MarHI1TOCTPMKQHoHHbIe npHBO,lJ.bl, MarHI1THbIe 11
ra30CTaTI1qeCKHe onopbI; I1X Hcnonb30BaHHe n03Bon
eT C03,lJ.aBaTb
KOHCTpYKQHM c 60nee BbICOKM
1H xapaKTepMCTMKaMI1. MarHHTOCTpHK-
QHOHHbIe npHBO):(bJ ,lJ.alOT B03MO)J(HOCTb ocy
ecTBnSlTb MHKponepe-
Mell.\eHH
.
3. I1cnonb30BaHHe ,lJ.ocTM)I(eHHM CMe)l(HbIX 06nacTeH. Hanpl1Mep,
B cTaHKocTpoeHl1H CTanH npHMeH
Tb rH,lJ.pOCTaTI1QeCKl1e 11 ra30CTaTI1Qe-
CKl1e onopbI .nn
BpalQaTenbHoro 11 nocTynaTenbHoro nepeMell{eHI1H.
168
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4. TIpHMeHeHHe MexaTpoHI1KH, T. e. CI1CTeM Ii MeXaHI13MOB, COQeTalO-
I.UI1X MeXaHI1KY M 3JIeKTpoHMKY; 3TO xapaKTepHo ,lJ.nSl CTaHKOB C CHCTe-
MaMH QI1CnOBOro nporpaMMHoro ynpaBneHI1
. BHe):(peHl1e MexaTpo-
HI1KH KopeHHbIM 06pa30
1 MeH
eT Tpa,lJ.I1QMoHHbIe perneHM
. Hanpl1Mep,
B 3y6006pa6aTbIBalO
Mx CTaHKax KI1HeMaTI1QeCKMe QenM, COCTO
l1e
113 cOBoKynHocTM 3y6QaTbIX Konec, 3aMeHeHbI 3neKTpOHHbIMI1 CB
3
MII.
5. 3aMeHa pYQHOrO ynpaBneHI1
C nOMOlQblO MeXaHHqeCKHX CI1CTeJ\11
H3 3JIeKTpoHHYlO CHCTeMY.
6. COBeprneHcTBoBaHMe 3neKTpOnpl1BO,lJ.a n03Bon
eT cy
ecTBeHHo
cOKpaTMTb MeXaHHQecKYIO qaCTb; npHMeH
5I 3JIeKTpOnpMBO,L( C 6eccTY-
neHQaTbIM perYJIHpOBaHHeM QaCTOTbI BpaI.UeHI1
BaJIa 3JIeKTpO,L(BMra-
TeJI
, MO)l(HO HCKJIlOqaTb 113 KOHCTPYKQI1I1 Marnl1HbI Kopo6KM CKOpO-
CTeM, Kop06KH no):(aq H ,lJ.pyrHe nepe,lJ.aTOqHble MexaHM3MbI. TaKoe
pe3Koe COKpaII(eHHe QHCJIa KHHeMaTIIQeCKHX nap ,lJ.aCT B03MO)KHOCTb
nOBbICMTb KllL{ II ynpocTMTb KOHCTPYKQMIO B QenOM.
7. ArperaTHO-MO,lJ.ynbHbIM npMHQMn npoeKTHpoBaHH
Y3noB MarnHH
BnSleTC
HaM60nee 06
l1M, oTpa)J(alOII(MM nporpeccHBHYIO TeH,lJ.eH-
QMIO KOMnOHOBKM H3 Y3JIOB, ocpopMJIeHHbIX B caMOCT05ITeJIbHbIe e):(M-
HIIU,bl. HanpMMep, BblnOJIH5IeTC5I aBToHoMHbIH npMBO,lJ. C pa3nl1qHblMI1
<PYHKQM5IMM HJIM pa3JIMIJHOH TOqHOCTM II MOl.I.\HOCTM. 3TOT npMHQMn
KOMnOHOBKI1 n03BOJISleT He TOJIbKO M0611JIbHO 113MeH5ITb Ha3HaqeHI1e
Ii ,na)l(e KOHCTPYKQI1IO BceM Marnl1HbI, HO 11 COBeprneHCTBOBaTb MnM
M3MeH5ITb KOHCTPYKQMIO OT,L(eJIbHOrO Y3JIa, He 3aTparHBa5I KOHCTPYK-
U,HIO MarnMHbI B Qen0J\11, coxpaH
nHrnb Tpe6oBaHI1
npMCOe,lJ.MHM-
TenbHblX H ra6apMTHbIX pa3MepoB.
8. I1cnonb30BaHHe pa3nHQHbIX MeTO,lJ.OB ,nn5I YMeHbrneHM
Hnl1 YCT-
paHeHM
H3Hoca ,lJ.eTaJIeM Marnl1H: npIIMeHeHl1e a3pocTaTMKM II rl1,npo-
CTaTI1KM B onopax II HanpaBn
IO
HX, M3HOCOCTOMKMX nOKpbITI1M,
HaKna,nHbIX HanpaBn
lOlQMX, pa3rpY3Ka HanpaBn
IO
MX (B MeTanno-
pe)KYlU MX CTaHKax), 3aII(IITa Y3JIOB MalllMH OT 3arp5I3HeHM5I (nona-
,lJ.aHI1Sl B TpYll{MeC
nOBepXHOCTM a6pa3MBHoro MaTepl1ana).
9. IToBbIllleHMe KaQeCTBa Y3noB, '-ITO
BnSleTC
nOCTO
HHbIM cpaKTo-
pOM, onpeJJ;en5IIOII(MM KOHKypeHTocnoco6HOCTb KOHCTPYKU,HM.
,[(JI
,lJ.OCTM)J(eHM
Tpe6yeMoro ypOBH
KaqeCTBa II Ha,L(e)J(HOCTI1
npMMeHSlIOT pa3nMQHbIe cpe.n.CTBa, CBSl3aHHbIe KaK C KOHCTpYKI..\Mei1
Y3JIa, TaK M C MaTepHaJIaMH M TeXHonorMeH, npHMeH5IeMbIMH npM ero
H3rOTOBneHMM. BbI60p OnTMMaJIbHbIX cpOpM H pa3MepOB KOHCTPYKQMM
CB5I3aH B nepBYIO Oqepe,nb C MX paCQeTOM. B nocne.n.HMe rOJJ;bl paCllIM-
p
eTC5I HOMeHKJIaTypa npMMeH
eMblX MaTepIHUIOB, oco6eHHO HeMeTan-
JIMqeCKMX, qTO n03Bon
eT nonyqaTb HOBbIe xapaKTepMCTMKH Y3na.
YqMTbIBa
CnO)l(HBlllMeCSl TeH,neHQMM pa3BMTM
KOHCTPYKQI1H Ma-
rnMH, He CTOHT y,nHBn
TbC
, ecnM B HOBOM BeKe MbI BCTpeTMM nOe3,lJ.a
6e3 KOJIeC, KOTopbIe 6y,nYT MQaTbC5I C 60JIblllOM CKOpOCTblO, HO He no
peJIbCaM.
-169
B MeTaJIJIOpe)J(ymMX CTaHKax He 6y,neT Kopo60K CKopOCTeM M KO-
P060K nOJJ;aq (CKOJIbKO MeTaJIJIa 6YJJ;eT C3KOHOMneHO!). BpameHMe C
nepeMeHHOM yrnoBoM CKOpOCTblO 6YJJ;eT co06
aTbCg HenocpeJJ;CTBeHHO
HCnOJIHHTeJIbHOMY opraHY (mnHHJJ;enlO CTaHKa); pOTOp 3neKTpOJJ;BM-
raTeJIg CTaHeT lIInHHJJ:eneM.
113 aB1'OMamHH y6epy1' ,l(BHra1'eJIH BHYTpeHHero crOpaHHg - )f(H1'enH
Bcex ropOJJ:OB CKa)f(YT cnacH60 KOHCTpYKTopaM HOBoro nOKOneHHg.
MexaHM3MbI, npe06pa3YIOmHe Bpa
eHHe B noc1'yna1'enbHoe nepe-
Me
eHMe (KpHBOlIIHnHo-ma1'YHHbIe, KYJIMCHbIe M ,np.), ,nO)J(MBalO1' CBOM
BeK. Y)f(e CeMqaC B 3KcnepMMeH1'aJIbHbIX pa3pa601'Kax nocTyna1'enbHoe
,n;BM)f(eHHe coo6
alO1' HenocpeJJ;c1'BeHHo McnonHM1'enbHOMY opraHY
(cynnop1'Y HJIM CTOJIY cTaHKa, noe3,ny).
Ha nepBbIM B3rng)J., 31'0 cpaH1'aC1'MKa. Ho 31'0 Harne 6y,nymee. B Ma-
IlIHHe OC1'aHeTC51 npMBO,n M HCnOJIHMTeJIbHbIM MexaHM3M, HnM pa601.JHM
opraH, MC1.Je3HeT nepe,naT01.JHbIH MexaHM3M.
A ,l(BMraTenb? MO)J(HO nM y6pa1'b 3JIeKTpO,l.(BMraTenb? MbI 3HaeM, q1'O
y)f(e ceiiqac B MMpe TeXHHKH HCnOJIb3YI01' COJIHeQHbIe 6aTapeH, a B HeKO-
1'OpbIX crpaHax MCTOqHMKOM 3HeprMM 5lBJI51eTCg 3HeprMg BonH H BeTpa.
TaK 1.J1'O YJJ:MBM1'enbHoe - p51,nOM, B HOBOM 1'bICgqene1'HM, B HOBOM
1'eXHH1.JeCKOM 3pe.
!oj:.,'
,r'
CI1MCOK JIMTEP A TYPbI
I. Ea2peee B. B. U Ope C60pHHK 3a,na1.J no TeXHH'-IeCKOH MexaHHKe. - JI.: Cy-
,nOCTpoeHHe, 1973. - 496 c.
2. EeflJlee H.M. ConpoTMBneHHe MaTepManoB. - M.: HaYKa, 1976. -- 607 c.
3. JI:eTanH H MexaHH3MbI MeTannOpe)f(YllU1X CTaHKOB: B 2 T. T. I. 663 c.
T. 2. 520 c. I no,n pe)J.. )J.. H. PellleToBa. - M.: MalllHHocTpoeHHe, 1972.
4. HZ/KOBUlJ r. M. U Ope C60pHHK 3a.n.aIJ M npHMepOB paCIJeTa no KYpCY .n.e-
TaneH MalllMH. - M.: MalllHHocTpoeHHe, 1975. - 286 c.
5. MeulepcKliu H.B. C60pHHK 3a.n.aIJ no TeOpeTH1.JeCKOH MexaHHKe -- M.:
HaYKa, 1986. --- 447 c.
6. M06HUH M.C. U Ope OCHOBbI TeXHHIJeCKOH MexaHHKH. - JI.: MalllHHO-
CTpoeHHe. JIcHMHrp. OT,n-HHe, 1982. -- 287 c.
7. naUIKoe H.H., KWZb H.A. TeXHM1.JeCKaSl MexaHMKa .n.nH CTpOHTeneH. -
M.: BbICIlI. lllK., 1977. - 144 c.
8. PeUlel110e p.H. JJ:eTanl1 MalllHH. - M.: MalllI1HOCTpOeHl1e, 1989. -.496 c.
9. Py6UHUH M.B. PYKOBO.n.CTBO K npaKTM1.JeCKHM 3aH
TH
M no conpOTHB-
neHHIO MaTepHaJIOB. -- M.: POCBY3H3.n.aT, 1963. -- 488 c.
10. (/JeooocbeB B.N. ConpOTMBJIeHHe MaTCpHaJIOB. - M.: HaYKa, 1986. --
512 c.
11. Jl6flOHCKUU A.A., HUKurjJopoBa B.M. Kypc TeOpeTHIJeCKOH MexaHHKH. -
M.: BbICIil. lllK., 1984. - lJ:. I. - 343 c.
12. J/6flOHCKUii A.A. Kypc TeOpeTHIJeCKOH MeXaHI1KH. - M.; JI.: BbIClll. lllK.,
1977. - q. 2. -- 430 c.
CO
EPjKAHME
BBC):{CHHe .................................................... 3
........ ........... ............ ................. ... ............
Pa3J{eJI 1. l'eopeTuqecKaH MexaHUKa . ................ ...... ......... ....... ............ ...... ......... 6
1.1. OCHoBHbIe nOH$lTIiSI H aKCHOMbI CTaTHKH .................................................... 6
1.2. CB$l3 H Ii I1X peaKLl.lIli .................................................................................... 9
1.3. nnOCKa$l CIiCTeMa CHn ................................................................................ 13
1.4. 3neMcHTbI TeopHH TpeHI1$1 ................. ........................................................ 20
1.5. n pocTpaHcTBeHHaSl cnCTeMa cnJI............................................... ........ ........ 24
1.6. Onpe)J.eJIeHHe QeHTpa T$lJKeCTII .................................................................. 29
1.7. KHHeMa THKa TO 1.JKH .................................................................................... 36
1.8. npocTeihuHe )J.BHJKeHII$I TBep.n.oro TeJIa .................................................... 42
1.9. 3aKoHbI J].IIHaMIiKII II ypaBHeHnSl ABI1JKeHIUI TOt.{KH ................................... 46
1.10. CMnbl, .n.CHCTBYIOll{IIe Ha T01.JKII MeXaHII1.JeCKOH CI1CTeMbI ........................ 48
1.11. TeopeMa 0 )J.BIIJKeHIIH Ll.eHTpa Macc MeXaHUlJeCKOH CIiCTeMbI .................. 50
1.12. Pa60Ta CHJIbI.................................................................................... . 53
I 13 M ........
. . 0 I..IJ.H OCTb . . . . . . . . . . . . . . . . . .. . .. . . . . . ... . 5 5
1.14. K03cpcpIIQneHT none3Horo .n.eHc
.
55
KOHTpOJIbHbIe BonpOCbI H 3a)J.aHH$I ............................ ...................................... 55
Pa3;::teJl 2. OCHOBbl conpOTHBJleHHH MaTepHaJlOB ............................................ 57
2.1. OCHoBHbIe nOH$lTHSI.................................................................................... 57
2.2. PaCT$lJKeHHe H CJKaTHe ................................................................................ 59
2.3. OCHoBHbIe MeXaHI11.JeCKHe xapaKTepliCTIiKH MaTepHanOB.......................... 64
2.4. PaC1.JeTbI Ha npOlIHOCTb npli paCTSI)f(eHHU H CJKaTHH.................................. 66
2.5. Cpe3 H CM$lTlIe............................................................................................ 68
2.6. K P Y1.J e H He. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71
2.7. n pSlMOH nOnepe1.JHbIH H3ru6...................................................................... 75
2.8. YCTOll1.JI1BOCTb npH oceBOM HarpYJKeHIIU CTepJKH$I.................................... 82
2.9. PaC1.JeT 6pyca Ha COBMeCTHoe )J.eHcTBHe KpY1.JeHHSI H H3rH6a .....................84
KOHTpOJIbHbIe BonpOCbI H 3anaHHSI .......................... ............................. ........... 84
Pa3J{eJI 3. )J;eTaJiU U MexaHU3Mbi MaWUH.......................................................... 86
3.1. MallllfHbI H HX OCHOBHbIe 3JIeMeHTbI.......................................................... 86
3.2. OCHoBHbIe KpliTepHI1 pa6oTocnoc06HOCTI1II paC1.JeTa JIeTaneH MalllHH .... 93
3.3. MallluHocTpOIITeJIbHbIe MaTepUaJIbI....... ....... .................. .......... ....... ....... 100
3. 4.
eTanl1 Bpall{aTenbHoro )J.BHJKeHIISI......................................................... 105
3.5. KopnycHbIe )J.eTaJIH .................................................................................. 106
3.6. n PYJKHHbI Ii peccop bI ............................................................................... 108
3.7. Hepa3'heMHbIe coe)J.IIHeHH$I )J.eTaJIeH .........................................................110
3.8. Pa3'heMHbIe coe.[(HHeHHSI )J.eTaJIeH............................................................. .121
172
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3.9. n O)J.lllHnHHKH CKOJIbJKeHH$I....................................................................... 125
3.10. nO)J.lllHnHHKH Ka lIeHHSI........... ... .................................................. .... ........ 130
3. II. M YCPTbI .................................................................................................... 133
3.12. <l>pHKQHOHHbIe nepe)J.a 1.JH ........... .................................. ..... ...................... 136
3.13. PeMeHHbIe nepelI.a 1.JH................................................................................ 138
3.14. 3y61.JaTbIe nepe):{a1.JH ................................................................................139
3.15. q epBSl1.JHbIe nepe)J.a 1.JH.............................................................................. 143
3.16. QenHbIe nepe;:(a 1.Jn ................................................................................... 144
3.17. BHHT-raHKa CKOJIbJKeHHSI.......................................................... ............... 147
3.18. BlfHT-raHKa Ka1.JeHH$I...............................................................................151
3.19. PCC1.JHbIC ncpc.n.a 1.JM .................................................................................. 152
3.20. KPHBollulnHo-lllaTYHHbIe MexaHH3MbI ... ....... ..... ...................... ............... 155
3.21. KYJIIiCHbIe MexaHII3MbI ............................................................................155
KOHTpOJIbHbIe BonpOCbI H 3a)J.aHH$I .................................................................157
Pa3,neJl 4. H3MeHeHue MeXaHUqeCKUX CBOHCTB MaTepUaJIOB ........................158
4.1. nOH$lTHe H OCHOBHbIe cnoc06bI H3MeHeHI1S1 MeXaHII1.JeCKI1X CBOHCTB .......158
4.2. Ynp01.JH$lIO
a$l 06pa60TKa nnaCTII1.JeCKHM .ne
OpMl1pOBaHl1eM ..............158
4.3. nOBbIllleHHe H3HOCOCTOHKOCTH nOBepxHocTHbIX CJIOeB ...........................161
4.4. OOBepxHocTHbIe nOKpbITH$I...................................................................... 162
4.5. Ynp01.JHeHl1e nOBepxHocTHbIX CJIOeB XI1MHKO-TepMlf1.JeCKOH
o6pa 60TKO H .............................................................................................. 163
4.6. Y np01.JHeHHe XO)J.OBbIX BHHTOB ....................................... ....... ................... 165
Ko HTpOJIbHbIe BO npOCbI H 3a.n.aHH$I ................................................................. 166
Pa311eJI 5. TeH,neHUuu pa3BuTuH KOHCTpYKUUH MaruuH U MexaHU3MOB ......167
C nH co K JIHTepa TYP bI . . . .. . . . . . . . . . . . .. . . . .. . . . . . . ... . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . .. ... . ... 171
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