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外文翻译--关于渐开线齿轮润滑因素的研究.doc

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外文翻译--关于渐开线齿轮润滑因素的研究.doc

STUDYONTHELUBRICATIONFACTOROFINVOLUTESPURGEARSAbstractBasedonalotofnumericalsolutionstotheproblemsofthethermalnonNewtonianelastohydrodynamiclubricationandsomefatiguetestswithrollers,thelubricationfactorofinvolutespurgearscalledgearforshortisinvestigated.TheresultssuggestthatgearlubricationeffectsbearcloserelationstoadimensionlessparameterDwhichissyntheticallydeterminedbygearingrotationalspeed,load,material,dimensionandlubricantviscosity.WhenD≤8,thegearfatiguelifeincreasesasthelubricantviscosityisincreasedWhenD>8,however,thelifedecreaseswiththeviscosityaddition,whichisinmarkedcontrasttothelubricationfactorZLrecommendedbytheInternationalStandardforComputingCylindricalGearStrength.Attheend,asetofformulaeforcalculatinggearlubricationfactorssuitablefordifferentworkingconditionsareadvanced.KeywordsInvolutespurgearElastohydrodynamiclubricationEHLNonNewtonianfluidLubricationfactorFatiguetestsNOTATIONSA,BPressuredensitycoefficientsbHertzhalfwidthc1,c2SpecificheatofpinionandgearefSpecificheatoflubricantD0TemperaturedensitycoefficientEEquivalentYoungmodulusEl,E2YoungmoduliofpinionandgearFFrictionalforceperunitwidthuCoefficientoffrictionδLubricantfilmthicknessδ0FilmthicknessconstantkfThermalconductivityoflubricantk1,k2ThermalconductivitiesofpinionandgearpPressurepHMaximumHertzianpressureP0Appliedloadperunittoothlength.REquivalentradius,1/R1/R11/R2R1,R2RadiiofcurvatureofpinionandgearS0TemperatureviscosityindexTTemperatureT0InletlubricanttemperatureT1,T2TemperaturesofpinionandgearuXcomponentoflubricantvelocityul,u2PinionandgearteethsurfacevelocitiesurContactrollingvelocity,uru1u2/2UDimensionlessvelocityparameterUη0ur/ERWDimensionlessloadparameterWP0/ERxCoordinatedirectionalongsurfacemotionyCoordinatedirectionacrosslubricantzViscosityindexofRoelandsmodelη0AmbientviscosityoflubricantηEquivalentviscosityηeCrossfilmeffectiveviscosityoflubricantρ0AmbientdensityoflubricantρeCrossfilmeffectivedensityoflubricantρ1,ρ2DensitiesofpinionandgearτShearstresswithinlubricantfilmτ0Eyringstressτxy,Shearstressonpinionsubsurfaceσx,σyNormalstressesonpinionsubsurfaceσeffContactstressontoothsurfaceν1,ν2Possionratioesofpinionandgear0INTRODUCTIONThecurrentstandardforcomputingcontactfatiguestrengthofgearisbasedonHertziantheorywhichisonlysuitablefordrycontact.Inordertotakeintoaccountthelubricationeffect,lubricationfactorZLisraisedbytheInternationalStandardforComputingCylindricalGearStrengthISO/423E.Also,variousfactorsrelatedtogearlubricationaregiveninsomeotherGearStandards,suchasD.B,AGMA,JAMA,ThomasandDIN3990andsoon.Althoughthewaystodefinethelubricationfactorarevariousindifferentgearstandards,theprincipleisidenticalthatthehighertheviscosity,thegreaterthevalueofthelubricationfactorandthelongerthegearfatiguelife.Sofarastheauthorsknow,however,itisinconsistentwithsomepracticalconditionsoccurredintheindustrialgeardrives.Therefore,itisessentialtodofurtherresearches.Theproblemsofgearlubricationhavebeeninvestigatedbyquiteafewpeople.Forexample,R.ErrichellomadeacomprehensiveEHLanalysisofgeartransmissionsandgavearecommendationforselectinglubricanttype,viscosityandacasehistorywhichdemonstratedmanyoftheprinciplesofgearlubrication.L.ThibaultandJ.Kalonkostudiedtheeffectofappropriateselectionoflubricantongeardrivelife.Someguidelinesweregivenonhowtoselecttheproperlubricantintheirpaper.R.Rakiclhlinvestigatedtheinfluenceoftribologicalpropertiesoflubricantonthereliabilityofgearandfoundthatreliabilityofgearwasgreatlyaffectedbyboththetypeoflubricantoilandtheviscositygrade.Morerecently,alotofexperimentalresearchesweredonebyO.JarvioandA.Lehtovaara.Basedontheirexperimentalresults,theinfluenceoflubricanttypeanditsadditivesonmeancoefficientoffrictioningearcontactwasevaluated.Inthepresentanalysis,morethanfiftynumericalcalculationsofthermalnonNewtonianEHLarecompleted.Sixsetsofsimulatedfatiguetestswithrollersaredone.Threeformulaeforcomputinggearlubricationfactorsarepresented.1BASICEQUATIONS1.1Reynoldsequationerphuxxx1AnequivalentviscosityηhasbeenintroducedinEq.1todescribethenonNewtonianlubricantproperties.IftheEyringsfluidmodelisadoptedandassumingthevariationsofboththeviscosityanddensityacrossthefilmthicknessalongtheydirectioncanbeignored,whichisacceptableaccordingtoL.Chang,theeffectiveviscosityηcouldbecalculatedasfollows0011sinhe2ThepressureboundaryconditionsofEq.1aregivenbyix0pandeexxpx|0xpwheretheinletlocation,xi,ischosenaccordingto|xi|»4bandtheoutletlocation,xe,isdeterminedinthesolutionprocess.1.2Filmthicknessequation2202xsx0ln2seixxxpdsRE31.3Energyequation22ffTTTppuuckuxyTTy4Theboundaryconditionsofaboveequationcanbeexpressedasf001111kTx,0|kxyTdsTycuxsf02222kTx,|kxyTdsTycuxs51.4ViscositypressuretemperaturerelationThecrossfilmeffectiveviscosityoflubricantasafunctionofpressureandtemperaturecanbecalculatedusingtheRoelandsrelation0900138expln9.6715.1101138szeTpT61.5DensitypressuretemperaturerelationThecrossfilmeffectivedensitycanbedeterminedbytheDowsonHigginsonrelation00011eAPDTTBP7Theaveragecrossfilmtemperatureisusedinthecalculationsofboththeηeandρe.1.6Loadequation0eixxppsds81.7FrictionalforceequationAsismentionedabovethattheEyringsnonNewtonianfluidmodelisusedinthisanalysis.Forthismodel,theconstitutiveequationforthestressstrainrelationis00sinhuyor00sinhuaryThus,thefrictionalforceonthesurfaceofthepiniontoothisobtainedas00sinheixxyouFdxardxy9then,thecoefficientoffrictionwillthusbeμF/p0.1.8StressequationsWhenpressureandsurfaceshearstressareknownitispossibletocomputethesubsurfacestresscomponentsatanypointmx,yaccordingtothefollowingexpressions232222eixxxyxxpdxy222222eixxyxyxyxpdxy10Inthepresentanalysisthemaximumshearstressischosenasstresslevelmeasure.2COMPUTATIONSCHEMETheproblemissolvedindimensionlessformevenifallequationsaregivenindimensionhere.TosolvethethermalnonNewtonianlubricantproblem,theaboveEqs.18aresolvedsimultaneouslytoobtainthepressure,filmthicknessandtemperaturedistributionswithinthelubricantfilm.Theinverseiterationprocedureusedinthepreviouspaperbythecurrentauthorsisextendedtoallowsolutionsforthenonlinearviscousfluidrheologymodel.3COMPUTATIONALRESULTSANDREGRESSIONANALYSISListedinTable1aretheparametersofageartransmissionusedinacoalmine.PressureandstressdistributionsatpitchpointobtainedfromnumericalcalculationbasedonthedatalistedinTable1isshowninFig.1.LotsofrealdatasimilartoonesinTable1beingchosenasinputvalues,fiftyandtwosetsofEHLnumericalcalculationsarecompleted.SomeofthecomputationalresultsaretabulatedinTable2inwhichτmaxisthedimensionlessmaximumprincipalshearstressat322222eixyxyyxpdxy

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