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

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

SpitrantrucprocessesfacknGleasoemprodecadecocuttersuccesslotManystudiesabouttootFMOnthecmotheopProceedingsoftheASME2007InternationalDesignEngineeringTechnicalConferencesComputersandInformationinEngineeringConferenceIDETC/CIE2007September47,2007,LasVegas,Nevada,USA1Copyright©2007byASMEIONralbevelandhypoidgeardrivesarewidelyappliedinthesmissionofmanyapplications,suchashelicopters,cars,ks,etc.Theyaremanufacturedusingmainlytwocuttingemillingorfacehobbingmethod.Aswellown,facemillingprocess,traditionallyadoptedbythenWorks®,utilizesacircularfacemilltypecutterandploysanintermittentindex.Onthecontrary,duringFHcess,traditionallyadoptedbyOerlikon®andinthelastsbytheGleasonWorks®aswell,theworkhasntinuousrotationandrotatesinatimedrelationshipwiththesivecutterbladegroupsengagessuccessivetoothsasthegearisbeingcut1.hsurfacerepresentationanddesignofspiralbevelandhypoidgearshavebeencarriedout25.ontrary,aboutFHprocess,thatistheconsiderablyrecomplex,onlyasmallnumberofworksareavailableinenliterature67.PinionGearModulemm4.94Offsetmm0ShaftAngle°90TeethNumber1236MeanSpiralAngle°35.000HandLHRHFaceWidthmm25.4MeanConeDistancemm81.05NominalPressureAngle°22.5Themodelvalidationrequiresthefollowingsteps.StartingfromtheinformationstoredinTable1,bymeansofacommercialgeardesignsoftware,thegeometricparameters,thebasicmachinesettingsandthecuttingbladedatawillbefirstlycomputedafterthat,bymeansoftheproposedmodel,EXPERIMENTALVALIDATIONOFACOMPUTCONTACTANDTENSILESTRESSANALAndreaPiazzaandrea.piazzacrf.itPowertrainResearchandTechnoloStradaTorino5010043OABSTRACTWhilefacemilledgearshavebeenwidelyanalyzed,aboutfacehobbedonesonlyveryfewstudieshavebeendevelopedandpresented.Goalofthispaperistoproposethevalidationofanaccuratetool,whichwaspresentedbytheauthorsinpreviousworks,aimedtothecomputerizeddesignoffacehobbedgears.Firstly,themathematicalmodelabletocomputedetailedgeartoothsurfacerepresentationonbothspiralandhypoidgearswillbebrieflyrecalledthen,thesoobtained3Dtoothgeometryisemployedasinputforanadvancedcontactsolverthat,usingahybridmethodcombiningfiniteelementtechniquewithsemianalyticalsolutions,isabletoefficientlycarryoutbothcontactanalysisunderlightorheavyloadsandstresstensilecalculation.Thevalidationanalyseswillbecarriedonpublishedaerospacefacehobbedspiralbevelgeardatacomparingmeasurementsofrootandfilletstresses.Goodagreementwithexperimentalresultsbothinthetimescaleandinmagnitudewillberevealed.1INTRODUCTERIZEDTOOLFORFACEHOBBEDGEARYSISMartinoVimercatigy–CentroRicercheFIATrbassanoTO,ITALYTheauthorsofthispaperhaveworkedextensivelyonthattopicproposingamathematicalmodelaimedtothecomputationofthefacehobbedgeartoothsurfaces8moreovertheyhandledtheoutputofthismodelinordertocarryoutacomputerizeddesignofthesegears9.Goalofthispaperistoprovidethevalidationofthattool.Tothisend,acomparisonwithexperimentaldatawillbeproposedinparticulartheresultscollectedbyHandschuhetal.10willbeconsidered.Inthatreferenceanexperimentalevaluationoftheperformanceofanaerospacespiralbevelfacehobbedgeardrive,inthefollowingnamedTEST,isshown.Indetail,resultsintermsofloadedtoothcontactanalysis,stresscalculationandvibration/noisemeasurementarewidelydiscussed.ThebasiccharacteristicsoftheTESTgeardrivearesummarizedinTable1.Table1.BasiccharacteristicsoftheTESTgeardrive.DETC200735911thegeometryofthetoothcanbecalculatedandthegeardriveperformanceunderloadcanbeevaluated.Themaineffortisdevotedjusttovalidatethemodelbycomparingthestressesexperimentallymeasuredintherootandinthefilletareawiththeonenumericallycalculatedaqualitativecomparisonoftheloadedtoothcontactpatternwillbealsoprovided.2MODELDESCRIPTIONANDMETHODOFTHETable2.ToothgeometrydataoftheTESTgeardrive.PinionGearModulemm4.941Offsetmm0ShaftAngle°90TeethNumber1236ANALYSISThefirststepinordertobuildareliablenumericalmodelistogetafinegeometricalrepresentationofgeartoothsurfaces.Thisisespeciallytruewhenoneisdealingwithcomplextoothgeometrysuchasthefacehobbingone.Tothisaim,aseriesofalgorithmsabletocomputetoothsurfacesofFHgearsstartingfromcuttingprocesshasbeenimplementedbytheauthors8.ThegeometryofrealFHheadcutterGleasonTriAc®isconsideredmanykindsofbladeconfigurationstraightandcurveblades,withorwithoutToprem®aretakenintoaccount.Then,accordingtothetheoryofgearing11,FHcuttingprocesswithandwithoutgenerationmotionissimulatedandgeartoothsurfacesequationscanbecomputed.Theproposedmathematicalmodelisabletoprovideanaccuratedescriptionofthewholetooth,includingfilletregionitalsoconsidersundercuttingoccurrence,whichisverycommoninFHgearsduetouniformdepthtooth.Theobtainedtoothsurfacesareusedasfundamentalinputforapowerfulcontactsolverwhichisbasedonasemianalyticalfiniteelementformulation1213.Thegeardrivecanbestudyunderlightloadbymonitoring,fordriveandcoastside,thecontactpatternandtransmissionerrori.e.itcanbeperformedthecommonlycalledToothContactAnalysis–TCA14.Moreover,withtheaimtofindoutgeardriveperformanceintherealserviceconditions,asetoftorquevaluescanbeappliedandtheinfluenceoftheloadoncontactpattern,ontransmissionerrorandonloadsharingcanbeaccuratelyanalyzedLoadedToothContactAnalysis–LTCA15.Contactpressureandstressdistributioncanbealsoeasilyevaluated.2.GEOMETRICANDMANUFACTORINGOFTHETESTGEARDRIVEUsingthedatacollectedinTable1aspreliminaryinputforacommercialsoftwareforgeardesignGleasonT2000®,acalculationaimedtoreproducetheTESTgeardrivehasbeenattempted.Table2describestheobtainedtoothgeometryTable3and4showthedetailsregardingthemachinesettingandthecuttingbladesthepinionisgeneratedandthegearisFormate®boththemembersarecutbymeansofcurvedbladesusingaheadcutterwithnominalradiusequalto76mmand13bladegroups.2Copyright©2007byASMEMeanSpiralAngle°35.00035.000HandLHRHFaceWidthmm25.425.4OuterConeDistancemm93.74393.743PitchAngle°18.43571.565Addendummm4.9302.067Dedendummm2.9425.805Table3.BasicmachinesettingsfortheTESTgeardrive.PinionGearConcaveConvexConcaveConvexGeneratedFormateRadialSettingmm91.45191.45192.36492.364TiltAngle°20.09920.099SwivelAngle°25.37125.371BlankOffsetmm0.0000.000MachineRootAngle°0.1540.15471.56571.565MachineCentertoBackmm0.07220.07221.5091.509SlidingBasemm13.86513.865CradleAngle°53.69749.81751.40551.405RatioofRollmm2.9992.999Table4.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°TopremLengthmm3.TOOTHGEOMETRYOFTHETESTGEARDRIVEFigure1illustratesthetoothgeometryrepresentationobtainedDuetothefactthatthereferencedoesnotprovideanytopologicaldata,justaqualitativecomparisonbetweentherealtoothgeometryandtheonecalculatedbymeansofthenumericalmodelisfeasibleFigure3.bymeansoftheproposedmodelfortheTESTgeardrive.Figure1.TESTgeartoothgeometryrepresentation.Figure2describesthefilletareabymeansofthetrendalongthefacewidthoftheNominalRootLineNRL,oftheRealRootLineRRLandoftheUnderCut/FilletUC/FLline.Accordingtothatpictureitispossibletonotethetoothdoesnotshowundercut.Figure2.Detailsofthefilletarea.3Copyright©2007byASMEFigure3.Qualitativecomparisonbetweentherealpiniontoothgeometryandthecalculatedone.3.1EvaluationofactualTESTgearfilletradiusStartingfromthepictureoftherealpiniontoothFigure3–above,aroughmeasurementoftheradiusofthefillethasbeenalsoattempted.Doingthisway,referringtothetoeoftheconcaveside,avalueaboutequalto0.94mmisobtained.Whenthesamezoneofthenumericallycomputedtoothisconsidered,avalueequalto1.26mmincorrespondenceofthemaximumcurvaturepointbetweenthemiddleofinnersurfaceandthecontactsurfaceisevaluated.Thedifferencemaybequitelarge34and,asitwillbeshownlater,thisevidencewillhaveasignificantinfluenceonthefilletstateofstress.Asknownthefilletradiusisstrictlyrelatedtotheedgeradiusofthecuttingblade.Thevalueusedtocuttherealtoothisunknownwhileinthenumericalmodelitisassumedtobeequalto0.7mm.Inordertoachieveafinercorrespondence,modelsconsideringotheredgeradiusvalueshavebeenbuilt.Namely,0.5mmand0.3mmhavebeentriedobtainingtheresultssummarizedinTable5andFigure4thepointsusedfortheradiuscalculationarehighlighted.Itcanbenotedthatusinganedgeradiusequalto0.3mmthebestcorrespondencecanbeachieved.Table5.Comparisonbetweenthephotomeasuredandthenumericalfilletradiusbyvaryingedgeradius.schematizationitispossibletoaffirmthattheheelpositioncorrespondstot0.5,themidonetot0andthetoeonetot0.5therootareaislocatedintherange0≤s≤2whiletheCutterEdgeRadiusmmPinionFilletRadiusmmPhotomeasuredPinionFilletRadiusmmDifference0.701.260.9434.040.501.100.9417.020.300.980.944.26Figure4.Comparisonbetweenthenumericalpinionconcavesideprofileandthephotomeasuredonenotethatthereferencesystemsaredifferent.4.STRESSCALCULATIONReferringtotheexperimentalinvestigation,thestressesareevaluatedbymeansofstraingagesinthefilletarea.Indetail,referringtothesketchdepictedinFigure5,onestraingageattheheelpositioninthefilletandthreestraingagesatheel,midandtoepositionsintherooti.e.ontherootcone.Ontheotherhand,withtheaimtonumericallycomputethestresses,itisnecessarytodefineasetofcoordinateswhichareabletostraightforwardlyprovidethestressmeasuringpointonthetooth.Here,thecurvilinearcoordinatetwhichrunsalongthefacewidth1≤t≤1inFigure6.aandthecurvilinearcoordinateswhichrunsalongthetoothprofile0≤s≤48inFigure6.bhavebeendefined.Accordingtothis4Copyright©2007byASMEfilletoneintherange5≤s≤7.Figure5.SketchusedintheTESTreferenceforlocationofthestraingages.Figure6.a.Schematizationfordefiningthestressmeasuringsectionalongthefacewidthofthemodel.Figure6.b.Schematizationfordefiningthestressmeasuringpointonagenericsectionofthemodel.

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