外文翻译--行星齿轮装置动态载荷的齿廓磨损.doc

1附录A中英文翻译DynamictoothloadsofplanetarygearsetshavingtoothprofilewearC.Yuksela,A.Kahramanb,*aTheUniversityofToledo,Toledo,OH43606,USAbDepartmentofMechanicalEngineering,TheOhioStateUniversity,Room255,650AckermanRoad,Columbus,OH43202,USAReceived25June2003；receivedinrevisedform12January2004；accepted10February2004AbstractAcomputationalmodelofaplanetarygearsetisemployedtostudytheinuenceofsurfacewearonthedynamicbehaviorofatypicalplanetarygearset.Theoverallcomputationalschemecombinesawearmodelthatdenesgeometricdescriptionofcontactinggeartoothsurfaceshavingwearandadeformable-bodydynamicmodelofaplanetarygearset.Thewearmodelemploysaquasi-staticgearcontactmodeltocomputecontactpressuresandArchardswearmodeltodeterminetheweardepthdistributions.Thewornsurfacesareinputintothedynamicmodeltoquantifytheimpactofwearongeartoothandmeshdynamicforces.Theresultsonaplanetarygearsethavingaxedplanetcarrierindicatesthatthedynamicbehaviorisnonlinearduetotoothseparationsinitsresonanceregions.Theresultsforworngearsurfacesindicatethatsurfacewearhasasignicantinuenceino-resonancespeedrangeswhileitsinuencediminishesnearresonancepeaksprimarilyduetotoothseparations.Ó2004ElsevierLtd.Allrightsreserved.Keywords:Planetarygearsets；Geardynamics；Gearwear1.Introduction2Planetarygearsets,alsoknownasEpicyclicgeardrives,arecommonlyusedinalargenumberofautomotive,aerospaceandindustrialapplications.Theypossesnumerousadvantagesoverparallel-axisgeartrainsincludingcompactnessofdesign,availabilityofmultiplespeedreductionratios,andlessdemandingbearingrequirements.Mostcommonexamplesofplanetarygearsetscanbefoundinautomatictransmissions,gasturbines,jetengines,andhelicopterdrivetrains.Atypicalsimpleplanetarygearsetconsistsofasungear,aringgearandanumberofidenticalplanetgears(typically36)meshingbothwiththesunandringgears.Acommoncarrierholdstheplanetsinplace.Dynamicanalysisofplanetarygearsisessentialforeliminatingnoiseandvibrationproblemsoftheproductstheyareusedin.Thedynamicforcesatthesun-planetandring-planetmeshesarethemainsourcesofsuchproblems.Althoughplanetarygearsetshavegenerallymorefavorablenoiseandvibrationcharacteristicscomparedtoparallel-axisgearsystems,planetarygearsetnoisestillremainstobeamajorproblem.Thedynamicgearmeshloadsthataremuchlargerthanthestaticloadsaretransmittedtothesupportingstructures,inmostcases,increasinggearnoise.Largerdynamicloadsalsoshortenthefatiguelifeofthecomponentsoftheplanetarygearsetincludinggearsandbearings.Surfacewearisconsideredoneofthemajorfailuremodesingearsystems.Incaseofplanetarygearsets,experimentaldatahasshownthatespeciallythesungearmeshesmightexperiencesignificantsurfacewearwhenrunundertypicaloperatingconditions1.Whilewearisafunctionofalargenumberofparameters,slidingdistanceandcontactpressurewereshowntobemostsignificantparametersinfluencinggearwear1.Wearoftoothprofilesresultsinauniquesurfacegeometrythataltersthegearmeshexcitationsintheformofkinematicmotionerrors,enhancingthedynamiceffects.Modelingofplanetarygearsetdynamicsreceivedsignificantattentionforthelast30years.Anumberofstudiesproposedlumped-parametermodelstopredictfreeandforcedvibrationcharacteristicsofplanetarygearsets29.Thesemodelsassumedrigidgear3wheels,connectedtoeachotherbyspringsrepresentingtheflexibilityofthemeshingteeth.Inthesestudies(except6),nonlineareffectsduetogearbacklashandtime-varyingparametersduetogearmeshstiffnessfluctuationswereneglected.ThecorrespondingEigenvaluesolutionofthelinearequationsofmotionresultedinnaturalmodes.Modalsummationtechniquewastypicallyusedtofindtheforcedresponseduetoexternalgearmeshdisplacementexcitationsdefinedtorepresentmotiontransmissionerrors.Theselumped-parametermodelsvaryindegreesoffreedomincluded,frompurelytorsionalmodels24,9totwo5,6,8orthree-dimensionaltransverse-torsionalmodels7.Whilethesemodelsservedwellindescribingthedynamicbehaviorofplanetarygearsetsqualitatively,theylackedcertaincriticalfeatures.First,thegearmeshmodelswerequitesimplisticwithacriticalassumptionthatcomplexgearmeshcontactinteractioncanberepresentedbyasimplemodelformedbyalinearspringandadamper.Thesemodelsdemandthatthevaluesofthegearmeshstiffnessanddamping,aswellasthekinematicmotiontransmissionerrorexcitation,mustbeknowninadvance.Itisalsoassumedthattheseparametervaluesdeterminedquasi-staticallyremainunchangedunderdynamicconditions.Inaddition,gearrimdeflectionsandHertziancontactdeformationsarealsoneglected.Anothergroupofrecentmodels10,11usedmoresophisticatedfiniteelement-basedgearcontactmechanicsmodels.Thesecomputationalmodelsaddressalloftheshortcomingsofthelumped-parametermodelssincethegearmeshconditionsaremodeledasindividualnonlinearcontactproblems.Theneedforexternallydefinedgearmeshparametersiseliminatedwiththesemodels.Inaddition,rimdeflectionandsplinesupportconditionsaremodeledaccurately12.Thesemodelsarealsocapableofincludingtheinfluenceofthetoothprofilevariationsintheformofintentionalprofilemodifications,manufacturingerrorsorwearonthedynamicbehaviorofthesystem.Thestudyofwearofgearcontactisbecomingoneoftheemergingareasingeartechnology.Anumberofrecentgearwearmodelingefforts1,1316formasolidfoundationformoreaccurate,largersystemanalyses.AllofthesemodelsuseArchardswearmodel17inconjunctionwithagearcontactmodelandrelativeslidingcalculations.Thesestudies4focusedonpredictionofwearofeitherspur13,14orhelical1,15,16gearpairsinaparallel-axisconfiguration.ThetoothcontactpressureswerecomputedinthesemodelsusingeithersimplifiedHertziancontact1416orboundaryelement1formulationsunderquasi-staticconditions.SlidingdistancecalculationswerecarriedoutkinematicallybyusingtheinvolutegeometryandArchardswearmodelwasusedwithanempiricalwearcoefficienttocomputethesurfaceweardepthdistribution.Anumberofstudiesinvestigatedtheinfluenceofwearongeardynamicsresponse1820.Amongthem,KuangandLin18simulatedthetoothprofilewearprocessbythemodelproposedbyRef.14,andpredictedthevariationsofthedynamicloadsandthecorrespondingfrequencyspectraasafunctionofwearforasinglespurgearpair.WojnarowskiandOnishchenko20performedanalyticalandexperimentalinvestigationsoftheinfluenceofthetoothdeformationandwearonspurgeardynamics.Theystatedthatthechangeintheprofilesoftheteethduetowearmustbetakenintoaccountwhendealingwiththedurabilityofthegeartransmissionsaswell.Thesepreviousmodelsconsideredsurfaceweareffectsforonlyasinglespurgearpair,avoidingmulti-meshgearsystemssuchastheplanetarygearsets.Theyfocusedononlyexternalgearsandusedlumped-parameterdynamicmodelsexcludingnonlinearandtime-varyingeffects.1.1.ObjectivesandscopeAsnoneofthepreviousstudiesonplanetarygearsetdynamicstookintoaccounttheeffectofwear,thisstudyisintendedtodescribetotheinfluenceofgeartoothsurfacewearondynamicbehaviorofplanetarygears.Adeformable-bodydynamicmodelsimilartotheoneproposedearlier11willbeusedtoinvestigatetheinfluenceoftoothsurfacewearonthedynamicbehaviorofplanetarygearsets.Themainobjectivehereistoquantifytheinfluenceofsurfacewearondynamicbehaviorofplanetarygearsets.Aplanetarygearsetformedbyspurgearswillbeconsidered.Awearpredictionmodelwillbeproposedtopredictthegearsurfaceweardistributionunderquasi-staticconditions.Differentamountsofweardepthswillthenbeintroducedinthedynamicmodeltoquantifythedifferencesindynamicbehaviorfromthebaselinebehaviorrepresentingagearsethavingnowear.Severalcomplexdynamic