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134Vol.13No.4199712TransactionsoftheCSAEDec.1997:1996-08-281997-08-15,,142,130025()(),,,,ReliabilityDesignofBack-AxleHousingLiuQiao2ling(JilinUniversityofTechnology,Changchun)ZhangYi2minWenBang2chun(NortheasternUniversity)AbstractTechniquefromperturbationmethodandreliabilitydesigntheoryareemployedtopresentthepracticalandeffectivemethodforthereliabilitydesignofback2axlehous2ing.Thetheoryformulaeofreliabilitydesignofback2axlehousingareobtained.There2spectiveprogramcanbeusedtoobtainthereliabilitydesignparametersofback2axlehous2ingaccuratelyandquickly.KeywordsBack2axlehousingReliabilitydesignPerturbationmethod,,,,,,,,,,,,1R=g(X)0fX(X)dX(1)fX(X)X=(X1,X2,Xn)T,©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.g(X),g(X)0g(X)0(2)g(X)=0n,Xg(X)X=Xd+EXp(3)g(X)=gd(X)+Egp(X)(4)E,d,p,E(X)=E(Xd)+EE(Xp)=Xd=X{(5)E[g(X)]=E[gd(X)]+EE[gp(X)]=gd(X)=g(X{)(6),,Kronecker12,Var(X)=E[(X-E(X))2]=E2[X2p](7)Var[g(X)]=E[(g(X)-E(g(X)))2]=E2E[(gp(X))2](8)X2p=XpáXpKronecker,áKroneckerTaylor,,gp(X)E(X)=Xd,gp(X)=9gd(X)9XTXp(9)(8),Var[g(X)]=E2E[(9gd(X)9XT)2X2p]=(9gd(X)9XT)2Var(X)(10)Var(X),B=E[g(X)]Var[g(X)](11),X,,R=5(B)(12)5()g(X)X,,,,BRg(X),Taylorg(X);,,BR2011997©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2,,,,,2.1R=MWn(13)M,Wn,3Wn=bh26(1-0.59d4bh3)(14)d,bh,g(X)=r-R(15)r,X=(r,M,b,h,d)TE(X)Var(X),g(X)X,5g(X)5XT=[5g(X)5r5g(X)5M5g(X)5b5g(X)5h5g(X)5d](16)5g(X)5r=1(17)5g(X)5M=-6hbh3-0.59d4(18)5g(X)5b=6Mh4(bh3-0.59d4)2(19)5g(X)5h=12Mbh3+3.54Md4(bh3-0.59d4)2(20)5g(X)5d=-14.16Mhd3(bh3-0.59d4)2(21)(6)(10)E[g(X)]Var[g(X)],(11)(12)2.2R,B,B=E[g(X)]Var[g(X)]c1dq16+c2dq12+c3dq8+c4dq4+c5=0(22)c1=0.12117361(rl2-B2Var(r))(23)3014:©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.c2=-0.821516blhq3(rl2-B2Var(r))+2.464548rlM{hq(24)c3=2.0886bl2hq6(rl2-B2Var(r))-12.5316rlM{blhq4+12.5316hq2(M{2-B2Var(M))-B2M{2(12.5316Var(h)+0.00501264hq2)(25)c4=-2.36bl3hq9(rl2-B2Var(r))+21.24rlM{bl2hq7-42.48blhq5(M{2-B2Var(M))-84.96B2M{2blhq3Var(h)(26)c5=bl4hq12(rl2-B2Var(r))-12rlM{bl3hq10+36bl2hq8(M{2-B2Var(M))-144B2M{2bl2hq6Var(h)-36B2M{2hq8Var(b)(27)3R,Var(d)=0.005E(d)(28)(22),E(R)E(r),,(28),350450,,d=(120,0.6)mm,b=(160,0.8)mm,h=(164,0.82)mm,M=(53371061.13,4851429.456)Nmm,r=(433,27.5)MPa,,:B=11.94R=1.0000R=0.9999,B=3.72,d=(148.9136,0.7446)mm4,,,,,1WJVetter.MatrixcalculusoperationsandTaylorexpansions,SIAMRev.,1973,15(2):3523692FMa.Extensionofsecondmomentanalysistovector2valuedandmatrix2valuedfunctions,Int.J.Non2LinearMechanics,1987,22(3):2512603,,:,1981.36374..,1984,6(2):174011997©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.