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1、92 FTM 8 The Role of Reliabilityfor Bearingsand Gears by: Charles A. Moyer The Timken Company AmericanGearManufacturersAssociation TECHNICALPAPER Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Res
2、ale, 04/18/2007 12:15:32 MDTNo reproduction or networking permitted without license from IHS -,-,- The Role of Reliabilityfor Bearingsand Gears Charles A. Moyer (retired) The Timken Company, Canton, Ohio The statements and opinions contained herein are those of the author and should not be construed
3、 asan official action or opinion of the AmericanGear ManufacturersAssociation. ABSTRACT: Life prediction or performance assessment is primarily done for bearings or gears with recognition of the significant role of stress level to such assessments.Reliability or probabilityof performanceis known to
4、relate to the stress-life relationshipbut the details as to how these interact are not often clearly defined. This paper details the experimental basis for the relationship between stress (load), life and reliability for bearings and gears considering the similarity and differences of their respecti
5、ve systems.The role of stress level and life scatter in terms of the Weibull distribution will be addressed.The background and equations to calculate the reliability factors, as included in both bearing and gear standards, are then developed. Copyright 1992 American Gear ManufacturersAssociation 150
6、0 King Street, Suite 201 Alexandria,Virginia, 22314 October,1992 ISBN:1-55589-588-3 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 12:15:32 MDTNo reproduction or networking perm
7、itted without license from IHS -,-,- TheRoleofReliabilityforBearingsand Gears byCharlesA.Moyer Withinanyvitaloperatingequipment,theS_ reliabilityofthecomponentsthatmake_ up the unit must be known if any sound_2 predictionsoflifeorstresscapability _retobemade.Reliabiltyofcourseisk_.t_ notanindependen
8、tqualityorfactorof_ any component, whether it be bearing or_._ gear. The interdependenceof these three_:_-_k factors,life,stress(or load leveland“ reliabilitywasdemonstratedyearsago_. interlinkingplotsinwhatWeibullN calledthecompletefatiguediagram. p _.Eo Section1onthefigureisthetypical-I 00._s(;00.
9、2s S/NcurvewithSrepresentingstressona._/./_J_/y_D2_4_0b linearscaleandNrepresentinglifein stresscyclesonalogscale.Thecurveso-,0z labeledParethefullrangeof/_/ ,7._._/j probabiltythatcantheoreticallyoccur/ fromPrO(100%reliability)toP=I(zero/,_. _-_ _ /./_04 reliability).Alltestingorreallife_“ ,_,_ com
10、ponentoperationsfallwithinthese extremes. For a given stress and expected,n_ or determined life, a probability ori_N reliabilityvaluemustexist.For bearingsandgearsonetendsto considerFig.1 TheCompleteFatigueDiagram(i). onlya fewspecificcurvesrepresentedby sectioni ofthediagram. Insections2and3ofFig.i
11、,othereventuallyusedingearandbearing representationsofthestress-life-standards,theyhavebeendevelopedfrom reliabilityrelationshipareillustrated,tests.TheS/Ncurvesarebasedon Forthisfigurethespacingofthecurvesfatiguetestsandthereliability-lifeor andthelogorlinearscalesarereliability-stressrelationships
12、depend arbitary.Inactualitytheunderlyingonrelatedoradditionaltesting,usually distributionsorscalesaredeterminedbywithmultipletestsateachofseveral experiment.Andwhencurvesaredrawnandstresslevels. Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Em
13、ployees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 12:15:32 MDTNo reproduction or networking permitted without license from IHS -,-,- Reliability-LifeforBearings70)leof 22985mmbore Thereliability-liferelationshipfor bearingshasbeengeneratedfrommultiple testsrunonalltypesofrollingelemen
14、t bearings.Bearinglifehasbeenexpressed asB-IOorL-IOforyearsandisL-IOin thelatestbearingstandards(2)(3)(4). L-IOis definedasbasicratinglifein millionsofrevolutionssothatfora(-_ groupof apparentlyidenticalrollingZ bearings,operatingunderthesame_ conditions,90percentare expectedto meetorexceedratinglif
15、eandtencr99 percentareexpectedtofailearlier. Thus,reliabilityinthebroadersenseisO0 thepercentageofanidenticalgroupthatE- willreachorexceedaspecifiedlife.ZI LJJ Foranindividualbearingitsreliability0 is theprobabilitythatit willreachorrr exceedthespecifiedlife.LU O_99._ Ithasbeendeterminedthatlivesof
16、identical bearing groups could beI representedbytheWeibulldistribution asshowninFig.2.In1972thebearing loadratingsandfatiguelifestandards (5)(6)incorporatedtheconceptoflife adjustmentfactorssothatapplication life(L-na)couldbemoreclosely assessedratherthanratinglife(L-IO)0.01.02.04.06.I.2.4 .61.02.0
17、thatassumedoperatingconditionsthat wouldonlyleadtoclassicalsubsurface rollingcontactfatigue.ThereliabilityRELATIVELIFE factora(1)asgiveninthereferences wasbasedonaWeibulldispersionFig.2 TypicalWeibullDistributionPlot. parameterorslopeof1.5.Itcanbe determinedwiththeequation: extensiveWeibullanalysisp
18、resentedby 4.483,in(lOO/R)i/l.5Tallian(7)in1962.Talliansdatawason a(1) =i93 test groups of 2520 bearings covering where,about 30 years of testing,of which 91 a(1)=aliferatiogivingvaluespercentwereballbearings.Inthe otherthan1.0forotherreliabilities;surivalrangeof40to90percent,the a(1)=l.OforL-IOlife
19、.fatiguefailuresfittheWeibull R=reliabilityasexpressedindistributionverywellwithaWeibull termsofpercentsurvival,slope(m)of1.0,veryclosetothe1.125 m=Wsibullslope=1.5for(9/8)valueof mthatisusedinthe equation i.standard ball bearing rating equations. However,inthesurvivalrangeof95to Ageneralizedequatio
20、nforanyvalueof99.9percentadeviantline,showing Weibullslopemayalsobeusefulandis:excesslifeheldfortheearlyfailures, wasputthroughthelowestlifebearings a(1)=9.4912*in(lOO/R)I/m2givingaWeibullslopehereof1.5.Fig. 3 fromreference(7)showsa Weibullplot WithaWeibullslopeof1.5a(1)values from90to99.97percentsu
21、rvival.Thus, arenormallypresentedintabularformas foratleastballbearings,a Weibull takenfromreferences(2)(3)forballand slopeof1.5seemedsuitableforequation rollerbearings:2orwouldjustifyequationiabove. Tablei:Reliabilitya(1)Values Reliability%L-haa_l)Asizeablegroupoftaperedroller 90L-IO1.00bearings,re
22、presentingstandard 95L-50.62productionlotsoverafiveyearperiod, havebeenfatiguetestedwithSAE20 96L-40.53 97L-30.44mineraloilofcloselycontrolled 98L-20.33viscosity and inlet oil temperature controlledat38C(I00F).Thetest 99L-I0.21 bearingsrangedinsizefrom12.0to85.0 mmboreConsideringthesimiliarityof AsT
23、able1indicates,reliabilitywas onlyconsideredforvaluesgreaterthanthetestconditions,itwaspossibleto 90percentThiswaspartlyfromtheexpressthebearings“livesasaratioof “experimentallife to expected life or as Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA License
24、e=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 12:15:32 MDTNo reproduction or networking permitted without license from IHS -,-,- 90._a /70Composite sampleof 3465 95 “80_Tapered RollerBearings 2095bearingsspalled Jj90m=1“6r=O99(crrcef) 99-o _95 .-/-/.dZ98 -,/_ _ rr 99.9“_JO
25、 99.5 - /1:“ 99 97 “,././!.0 oX_l_1QOl_1 LO_r“ W Fig.3LifeDistribution:EarlyFailures95_J*I Tallian,Reference(7)/1l z relativelife.Theexpectedlifeforeach198/ii:I, ! r sizebearingwasdeterminedusingthat99.99. I_I,I bearingsspecificratinganditstest0.01 .02,04.06.I.2.4 .61.02.0 loads.TheresultingWeibulld
26、istribution isgiveninFig.4(8).ThisisaportionRELATIVELIFE ofaWeibullplotfrom70to99.99 percentsurvival. Fig.4CompositeWeibullDistributionof Thecompositesampleconsistedof34653465TaperedRollerBearings. bearings,ofwhich2095spelledtothe laboratorycriteriaoffatiguelimitof 6.5squaremm.TheWeibullslopeis1.6 w
27、ithlittleindicationofdeviationfrom thecalculatedpopulationline.Thus,m(orloadlevel)isknowntocausea equalto1.5maybeconsideredacceptablereductionoflifescatterforgeneral foruseinequation2forrollerformsofhigh-cyclefatigue(9). bearingsandisperhapsslightly conservative.ForrollerbearingsandforAnexampleofthi
28、sfromfatiguetestsof linecontact,forreliabilitieslessthanalargesampleof19mmboretapered 90percent,mequalto1.5mayberollerbearings,testedassevensub- considered.For50percentreliability(L-groupsisgiveninFig.5.Thesetests 50),a(1)wouldhavea valueof 3.51.Forwererunwiththesameinletoil pointcontact(asballbeari
29、ngs)withmtemperatureandoilflowrateforall equalto1.0,reliabilityof50percentsevenstresslevels.ThetestHertzian wouldgivea(1)equalto6.56.contactstressesrangedfrom1420 HPa (206KSI)to2365HPa(343K6I)andas can Althoughthebearingstandardsacceptthebeseen,theWeibullslopeshoweda reliabilityvaluesas givenin Tabl
30、ei,generalincrease(decreasein life itispossiblethatotherWeibullslopesscatter)withincreaseinstress.The mayoccur,especiallywithsmallerlinethroughthepointsisbasedona samples.Valuesof mfrom1.39to 3.34regressionthathasa correlation weregiveninreference(8)fortaperedcoefficientof0.83.Thecorrelation rollerb
31、earings.Theaveragevalueofmindicatesasignificanttrendtothe calculatedforallthetestgroupsindata,butislowenoughthatother reference(7)was1.3 withplusandminusfactorsnotclearlyidentifiedalsohave onesigmalimitsof1.6to0.95giveninaninfluence.Therefore,atpresent Talliansclosuretodiscussionsofhisreliabilityfor
32、bearingsisprimarily paper.Differingoperatingconditions,computedfromequationIandinfluences especiallythose,suchaschangesinthethatcouldchangethisinactual lambdaratio,thatcausechangesinapplications,includingstresslevel,are failuremodearerecognizedtocontributenotusuallyconsidered. tochangesofm.Increaseo
33、fstresslevel Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 12:15:32 MDTNo reproduction or networking permitted without license from IHS -,-,- 1381172520702415(MPA)Table3:Expres
34、sionsofProbability 3,0, RequirementsofFailureSurvival _95percentconfidencebandApplicationProbabilityProbab. onWeibullslopei/i00000.000199.99 I/I0000.001099.90 LU2.5-/i/i000.010099.00 O./i/I00.i00090.00 qITi/2050o050 00 O0One can assumethat the two parameter -,J2.(Weibulldistributionshouldrepresentth
35、e -Joriginalreliabilityfactorvaluesin Table 2. Using Weibullprobability paper _-the reliabilityfactorvalues C(R),K(R) h_can be plottedversussurvival I._probabilityas illustratedon Fig. 6. The linecanberepresentedbya simple equationin thegenreofequationias follows: 1.0_fIC(R),K(R)=0.68/in(I/S)I/II43
36、200250300350(KSI) HERTZIANCONTACTSTRESS Theequationisnotexactbutdetermines Fig.5 Relationof HertzianContactreliabilityfactorswithin2 percentas Stressto WeibullSlope“m“.shownon Table2,the secondcolumnfrom theright.Itmayalsobepossibleto considerthereliabilityfactorsaslife factorsratherthanstresssincel
37、ife Reliability-Lifefor Gearsscattermaybeeasierto determinefrom testingthanthevariabilityofstress Reliabilityforgears,asgiveninthelevel.If oneassumes,forpitting ANSI/AGMA2001-B88Standard(I0),isfatigue,thattherelationshipoflife reallyin termsofreliability-stress,factorC(L)versusnumberofloadcycles Tab
38、le17-1fromthestandardgivestheN canbe usedfromStandard2001-B88 C(R)times10/3or6.667.However,forhigher G(I)=I.0forL-Ilife.reliabilityvaluesthe“lines,“for R=reliabilityintermsofpercentexample,of95percentor99percent, survival,would have smaller stress-life exponents. Thisfactmayneedtobetakeninto Recogni
39、zingthelinkbetweenlifeandaccountifthelifescatteractually stresstheC(R),K(R)factorvaluesfordecreaseswithhigherstressand reliabilitycanbedeterminedbytheincreaseswithlowerstress. followingversionofequation7: Forgears,thesameassumptionistaken C(R),K(R)=i/99.50,1n(100/R)I/II48for99percentreliabilitythatt
40、his valueholdsforthestress-lifeexponent Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 12:15:32 MDTNo reproduction or networking permitted without license from IHS -,-,- of1/0.0
41、58or17.86forpittingfatigueReferences asillustratedintheAGHAStandardin Fig.16-1.However,iflifescatterI. Weibull,W.,“AStatistical decreaseswithincreasedstressasFig.7RepresentationofFatigueFailuresin indicatesthenthestress-lifeexponentSolids,“Trans.RoyalInstituteof woulddecreaseforreliabilitiesgreaterT
42、echnology,Nr27,Stockholm,Sweden, than99 percent(forexample,99.9or1949. 99.99percentreliabilities).This interrelationofstress-lifeand2._,“LoadRatingsandFatigueLife reliabilitywillneedto betakenintoforBallBearings,“AmericanNational accountforimprovementtobothgearandStandard,AFBMAStd.ANSI/AFBMAStandard
43、 bearinglifepredictionandthisconcept9-1990,July17,1990. impactstheunderstandingofendurance limitorinfinitelifeatlowerstresses3. _,“LoadRatingsandFatigueLife wherelifescatterwouldbegreatest,forRollerBearings,“AmericanNational InfinitelifewithreliabilityofperhapsStandard,AFBMAStd.,ANSI/AFBMAStandard 5
44、0 percentconfidencewouldnotbe very11-1990,July17,1990. helpfulin.fatiguelifeprediction. 4._,“RollingBearings-Dynamicload Thisdiscussionhascenteredprimarilyonratingsandratinglife,“International pittingfatigueforbothbearingsandStd.ISO281,FirstEd.,1990-12-01. gears.ThatK(R)wasin someofthe tablesimplies
45、thatthelifefactors5. _,“LoadRatingsand FatigueLife wouldbethesame.However,theexponentsforBallBearings,“AFBMAStandard9, onthestress-lifecurvesonFig.16-2June1972. (AGMAStandard2001-B88),forthebending strengthlifefactor,K(L)aredifferent6. _,“LoadRatingsandFatigueLife thanforpittingfatigue.ForcaseforRol
46、lerBearings,“AFBMAStandardii, carburizedsteeltheexponentis0.1192.June1972. ThusiftheWeibullslopefromFig.6is raisedbythisexponent,thatis7. Tallian,T.,“WeibullDistributionof (ll.4)exp0.1192,it willequal1.34.TheRollingContactFatigueLifeand implicationofthisisthatthefatigueDeviationsTherefrom,“ASLETrans
47、.5, lifeWeibullslopeof1.34,beinghigherpp183-196,1962. thanthe1.15Weibullslopeforpitting fatigue,thatlifescatterforbending8.Moyer,C.A.,“TheStatusandFutureof fatigueislessthanforpittingorRollerBearingLifePrediction, surfacefatigue.IfthisistruethentheProceedingsInt.Ind.Tribology inclusionofK(R)insomeof
48、theSymposium,NorthwesternUn.,Aug.1990, equationsconsideredinthispapermaySTLESP-31,Advancesin Engineering notbevalid.AdditionalbendingfatigueTribology,Ed.Y.Chung&H.S.Cheng, scatterdatais neededtoexplainthispp89-99,April1991. lifescatterdifference. 9.Rice,R.C.,“FatigueDataAnalysis,“ SummaryStatisticsand Data Analyses. Metals Handbook,Vol8MechanicalTesting,pp695- Theexperimentalbasisofthereliability713,NinthXdition1989. lifefactorsusedforbearingshasbeen giyen_Theequivalentfactorshavebeeni0. _“FundamentalRatingFactorsand develope