外文资料--EXPERIMENTAL VALIDATION OF A COMPUTERIZED TOOL FOR FACE HOBBED GEAR CONTACT AND TENSILE STRESS ANALYSIS.pdf

Spitrantrucprocesses:facknGleasoemprodecadecocutter:successlotManystudiesabouttootFMOnthecmotheopProceedingsoftheASME2007InternationalDesignEngineeringTechnicalConferences&ComputersandInformationinEngineeringConferenceIDETC/CIE2007September4-7,2007,LasVegas,Nevada,USA1Copyright©2007byASMEIONralbevelandhypoidgeardrivesarewidelyappliedinthesmissionofmanyapplications,suchashelicopters,cars,ks,etc.Theyaremanufacturedusingmainlytwocuttingemillingorfacehobbingmethod.Aswellown,facemillingprocess,traditionallyadoptedbythenWorks®,utilizesacircularfacemilltypecutterandploysanintermittentindex.Onthecontrary,duringFHcess,traditionallyadoptedbyOerlikon®andinthelastsbytheGleasonWorks®aswell,theworkhasntinuousrotationandrotatesinatimedrelationshipwiththesivecutterbladegroupsengagessuccessivetoothsasthegearisbeingcut1.hsurfacerepresentationanddesignofspiralbevelandhypoidgearshavebeencarriedout2-5.ontrary,aboutFHprocess,thatistheconsiderablyrecomplex,onlyasmallnumberofworksareavailableinenliterature6-7.PinionGearModulemm4.94Offsetmm0ShaftAngle°90TeethNumber1236MeanSpiralAngle°35.000HandLHRHFaceWidthmm25.4MeanConeDistancemm81.05NominalPressureAngle°22.5Themodelvalidationrequiresthefollowingsteps.StartingfromtheinformationstoredinTable1,bymeansofacommercialgeardesignsoftware,thegeometricparameters,thebasicmachinesettingsandthecuttingbladedatawillbefirstlycomputed；afterthat,bymeansoftheproposedmodel,EXPERIMENTALVALIDATIONOFACOMPUTCONTACTANDTENSILESTRESSANALAndreaPiazzaandrea.piazzacrf.itPowertrainResearchandTechnoloStradaTorino50-10043OABSTRACTWhilefacemilledgearshavebeenwidelyanalyzed,aboutfacehobbedonesonlyveryfewstudieshavebeendevelopedandpresented.Goalofthispaperistoproposethevalidationofanaccuratetool,whichwaspresentedbytheauthorsinpreviousworks,aimedtothecomputerizeddesignoffacehobbedgears.Firstly,themathematicalmodelabletocomputedetailedgeartoothsurfacerepresentationonbothspiralandhypoidgearswillbebrieflyrecalled；then,thesoobtained3Dtoothgeometryisemployedasinputforanadvancedcontactsolverthat,usingahybridmethodcombiningfiniteelementtechniquewithsemianalyticalsolutions,isabletoefficientlycarryoutbothcontactanalysisunderlightorheavyloadsandstresstensilecalculation.Thevalidationanalyseswillbecarriedonpublishedaerospacefacehobbedspiralbevelgeardatacomparingmeasurementsofrootandfilletstresses.Goodagreementwithexperimentalresultsbothinthetimescaleandinmagnitudewillberevealed.1INTRODUCTERIZEDTOOLFORFACEHOBBEDGEARYSISMartinoVimercatigyCentroRicercheFIATrbassano(TO),ITALYTheauthorsofthispaperhaveworkedextensivelyonthattopicproposingamathematicalmodelaimedtothecomputationofthefacehobbedgeartoothsurfaces8；moreovertheyhandledtheoutputofthismodelinordertocarryoutacomputerizeddesignofthesegears9.Goalofthispaperistoprovidethevalidationofthattool.Tothisend,acomparisonwithexperimentaldatawillbeproposed；inparticulartheresultscollectedbyHandschuhetal.10willbeconsidered.Inthatreferenceanexperimentalevaluationoftheperformanceofanaerospacespiralbevelface-hobbedgeardrive,inthefollowingnamedTEST,isshown.Indetail,resultsintermsofloadedtoothcontactanalysis,stresscalculationandvibration/noisemeasurementarewidelydiscussed.ThebasiccharacteristicsoftheTESTgeardrivearesummarizedinTable1.Table1.BasiccharacteristicsoftheTESTgeardrive.DETC2007-35911thegeometryofthetoothcanbecalculatedandthegeardriveperformanceunderloadcanbeevaluated.Themaineffortisdevotedjusttovalidatethemodelbycomparingthestressesexperimentallymeasuredintherootandinthefilletareawiththeonenumericallycalculated；aqualitativecomparisonoftheloadedtoothcontactpatternwillbealsoprovided.2MODELDESCRIPTIONANDMETHODOFTHETable2.ToothgeometrydataoftheTESTgeardrive.PinionGearModulemm4.941Offsetmm0ShaftAngle°90TeethNumber1236ANALYSISThefirststepinordertobuildareliablenumericalmodelistogetafinegeometricalrepresentationofgeartoothsurfaces.Thisisespeciallytruewhenoneisdealingwithcomplextoothgeometrysuchasthefacehobbingone.Tothisaim,aseriesofalgorithmsabletocomputetoothsurfacesofFHgearsstartingfromcuttingprocesshasbeenimplementedbytheauthors8.ThegeometryofrealFHheadcutter(GleasonTri-Ac®)isconsidered；manykindsofbladeconfiguration(straightandcurveblades,withorwithoutToprem®)aretakenintoaccount.Then,accordingtothetheoryofgearing11,FHcuttingprocess(withandwithoutgenerationmotion)issimulatedandgeartoothsurfacesequationscanbecomputed.Theproposedmathematicalmodelisabletoprovideanaccuratedescriptionofthewholetooth,includingfilletregion；italsoconsidersundercuttingoccurrence,whichisverycommoninFHgearsduetouniformdepthtooth.Theobtainedtoothsurfacesareusedasfundamentalinputforapowerfulcontactsolverwhichisbasedonasemianalyticalfiniteelementformulation12-13.Thegeardrivecanbestudyunderlightloadbymonitoring,fordriveandcoastside,thecontactpatternandtransmissionerror(i.e.itcanbeperformedthecommonlycalledToothContactAnalysisTCA14).Moreover,withtheaimtofindoutgeardriveperformanceintherealserviceconditions,asetoftorquevaluescanbeappliedandtheinfluenceoftheloadoncontactpattern,ontransmissionerrorandonloadsharingcanbeaccuratelyanalyzed(LoadedToothContactAnalysisLTCA15).Contactpressureandstressdistributioncanbealsoeasilyevaluated.2.GEOMETRICANDMANUFACTORINGOFTHETESTGEARDRIVEUsingthedatacollectedinTable1aspreliminaryinputforacommercialsoftwareforgeardesign(GleasonT2000®),acalculationaimedtoreproducetheTESTgeardrivehasbeenattempted.Table2describestheobtainedtoothgeometry；Table3and4showthedetailsregardingthemachinesettingandthecuttingblades:thepinionisgeneratedandthegearisFormate®；boththemembersarecutbymeansofcurvedbladesusingaheadcutterwithnominalradiusequalto76mmand13bladegroups.2Copyright©2007byASMEMeanSpiralAngle°35.00035.000HandLHRHFaceWidthmm25.425.4OuterConeDistancemm93.74393.743PitchAngle°18.43571.565Addendummm4.9302.067Dedendummm2.9425.805Table3.BasicmachinesettingsfortheTESTgeardrive.PinionGearConcaveConvexConcaveConvexGeneratedFormateRadialSettingmm91.45191.45192.36492.364TiltAngle°20.09920.099-SwivelAngle°-25.371-25.371-BlankOffsetmm0.0000.000-MachineRootAngle°0.1540.15471.56571.565MachineCentertoBackmm-0.0722-0.0722-1.509-1.509SlidingBasemm13.86513.865-CradleAngle°53.69749.81751.40551.405RatioofRollmm2.9992.999-Table4.CuttingbladesdatafortheTESTgeardrive.PinionGearOBIBOBIBBladeTypeCurvedCurvedCurvedCurvedBladeRadiusmm75.49975.75876.20675.749BladeEccentric°17.83217.63317.73817.846BladeHeightmm4.3634.3634.3744.374BladeAngle°25.32318.12222.23121.681BladeGroupsNumber13131313NominalRakeAngle°12.00012.00012.00012.000HookAngle°4.4204.4204.4204.420CutterEdgeRadiusmm0.7000.7001.0001.000BladeRadiusofCurvaturemm762.000762.000762.000762.000TopremAngle°-TopremLengthmm-3.TOOTHGEOMETRYOFTHETESTGEARDRIVEFigure1illustratesthetoothgeometryrepresentationobtainedDuetothefactthatthereferencedoesnotprovideanytopologicaldata,justaqualitativecomparisonbetweentherealtoothgeometryandtheonecalculatedbymeansofthenumericalmodelisfeasible(Figure3).bymeansoftheproposedmodelfortheTESTgeardrive.Figure1.TESTgeartoothgeometryrepresentation.Figure2describesthefilletareabymeansofthetrendalongthefacewidthoftheNominalRootLineNRL,oftheRealRootLineRRLandoftheUnderCut/FilletUC/FLline.Accordingtothatpictureitispossibletonotethetoothdoesnotshowundercut.Figure2.Detailsofthefilletarea.3Copyright©2007byASMEFigure3.Qualitativecomparisonbetweentherealpiniontoothgeometryandthecalculatedone.3.1EvaluationofactualTESTgearfilletradiusStartingfromthepictureoftherealpiniontooth(Figure3above),aroughmeasurementoftheradiusofthefillethasbeenalsoattempted.Doingthisway,referringtothetoeoftheconcaveside,avalueaboutequalto0.94mmisobtained.Whenthesamezoneofthenumericallycomputedtoothisconsidered,avalueequalto1.26mmincorrespondenceofthemaximumcurvaturepointbetweenthemiddleofinnersurfaceandthecontactsurfaceisevaluated.Thedifferencemaybequitelarge(+34%)and,asitwillbeshownlater,thisevidencewillhaveasignificantinfluenceonthefilletstateofstress.Asknownthefilletradiusisstrictlyrelatedtotheedgeradiusofthecuttingblade.Thevalueusedtocuttherealtoothisunknownwhileinthenumericalmodelitisassumedtobeequalto0.7mm.Inordertoachieveafinercorrespondence,modelsconsideringotheredgeradiusvalueshavebeenbuilt.Namely,0.5mmand0.3mmhavebeentriedobtainingtheresultssummarizedinTable5andFigure4(thepointsusedfortheradiuscalculationarehighlighted).Itcanbenotedthatusinganedgeradiusequalto0.3mmthebestcorrespondencecanbeachieved.Table5.Comparisonbetweenthephotomeasuredandthenumericalfilletradiusbyvaryingedgeradius.schematizationitispossibletoaffirmthattheheelpositioncorrespondstot=+0.5,themidonetot=0andthetoeonetot=-0.5；therootareaislocatedintherange0s2whiletheCutterEdgeRadiusmmPinionFilletRadiusmmPhoto-measuredPinionFilletRadiusmmDifference%0.701.260.9434.040.501.100.9417.020.300.980.944.26Figure4.Comparisonbetweenthenumericalpinionconcavesideprofileandthephoto-measuredone(notethatthereferencesystemsaredifferent).4.STRESSCALCULATIONReferringtotheexperimentalinvestigation,thestressesareevaluatedbymeansofstraingagesinthefilletarea.Indetail,referringtothesketchdepictedinFigure5,onestraingageattheheelpositioninthefilletandthreestraingages(atheel,midandtoepositions)intheroot(i.e.ontherootcone).Ontheotherhand,withtheaimtonumericallycomputethestresses,itisnecessarytodefineasetofcoordinateswhichareabletostraightforwardlyprovidethestressmeasuringpointonthetooth.Here,thecurvilinearcoordinatetwhichrunsalongthefacewidth(-1t+1inFigure6.a)andthecurvilinearcoordinateswhichrunsalongthetoothprofile(0s48inFigure6.b)havebeendefined.Accordingtothis4Copyright©2007byASMEfilletoneintherange5s7.Figure5.SketchusedintheTESTreferenceforlocationofthestraingages.Figure6.a.Schematizationfordefiningthestressmeasuringsectionalongthefacewidthofthemodel.Figure6.b.Schematizationfordefiningthestressmeasuringpointonagenericsectionofthemodel.