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

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SpitrantrucprocessesfacknGleasoemprodecadecocuttersuccesslotManystudiesabouttootFMOnthecmotheopProceedingsoftheASME2007InternationalDesignEngineeringTechnicalConferencesComputersandInformationinEngineeringConferenceIDETC/CIE2007September4-7,2007,LasVegas,Nevada,USA1Copyright2007byASMEIONralbevelandhypoidgeardrivesarewidelyappliedinthesmissionofmanyapplications,suchashelicopters,cars,ks,etc.Theyaremanufacturedusingmainlytwocuttingemillingorfacehobbingmethod.Aswellown,facemillingprocess,traditionallyadoptedbythenWorks,utilizesacircularfacemilltypecutterandploysanintermittentindex.Onthecontrary,duringFHcess,traditionallyadoptedbyOerlikonandinthelastsbytheGleasonWorksaswell,theworkhasntinuousrotationandrotatesinatimedrelationshipwiththesivecutterbladegroupsengagessuccessivetoothsasthegearisbeingcut[1].hsurfacerepresentationanddesignofspiralbevelandhypoidgearshavebeencarriedout[2-5].ontrary,aboutFHprocess,thatistheconsiderablyrecomplex,onlyasmallnumberofworksareavailableinenliterature[6-7].PinionGearModule[mm]4.94Offset[mm]0ShaftAngle[]90TeethNumber1236MeanSpiralAngle[]35.000HandLHRHFaceWidth[mm]25.4MeanConeDistance[mm]81.05NominalPressureAngle[]22.5Themodelvalidationrequiresthefollowingsteps.StartingfromtheinformationstoredinTable1,bymeansofacommercialgeardesignsoftware,thegeometricparameters,thebasicmachinesettingsandthecuttingbladedatawillbefirstlycomputed;afterthat,bymeansoftheproposedmodel,EXPERIMENTALVALIDATIONOFACOMPUTCONTACTANDTENSILESTRESSANALAndreaPiazzaandrea.piazzacrf.itPowertrainResearchandTechnoloStradaTorino50-10043OABSTRACTWhilefacemilledgearshavebeenwidelyanalyzed,aboutfacehobbedonesonlyveryfewstudieshavebeendevelopedandpresented.Goalofthispaperistoproposethevalidationofanaccuratetool,whichwaspresentedbytheauthorsinpreviousworks,aimedtothecomputerizeddesignoffacehobbedgears.Firstly,themathematicalmodelabletocomputedetailedgeartoothsurfacerepresentationonbothspiralandhypoidgearswillbebrieflyrecalled;then,thesoobtained3Dtoothgeometryisemployedasinputforanadvancedcontactsolverthat,usingahybridmethodcombiningfiniteelementtechniquewithsemianalyticalsolutions,isabletoefficientlycarryoutbothcontactanalysisunderlightorheavyloadsandstresstensilecalculation.Thevalidationanalyseswillbecarriedonpublishedaerospacefacehobbedspiralbevelgeardatacomparingmeasurementsofrootandfilletstresses.Goodagreementwithexperimentalresultsbothinthetimescaleandinmagnitudewillberevealed.1INTRODUCTERIZEDTOOLFORFACEHOBBEDGEARYSISMartinoVimercatigy–CentroRicercheFIATrbassanoTO,ITALYTheauthorsofthispaperhaveworkedextensivelyonthattopicproposingamathematicalmodelaimedtothecomputationofthefacehobbedgeartoothsurfaces[8];moreovertheyhandledtheoutputofthismodelinordertocarryoutacomputerizeddesignofthesegears[9].Goalofthispaperistoprovidethevalidationofthattool.Tothisend,acomparisonwithexperimentaldatawillbeproposed;inparticulartheresultscollectedbyHandschuhetal.[10]willbeconsidered.Inthatreferenceanexperimentalevaluationoftheperformanceofanaerospacespiralbevelface-hobbedgeardrive,inthefollowingnamedTEST,isshown.Indetail,resultsintermsofloadedtoothcontactanalysis,stresscalculationandvibration/noisemeasurementarewidelydiscussed.ThebasiccharacteristicsoftheTESTgeardrivearesummarizedinTable1.Table1.BasiccharacteristicsoftheTESTgeardrive.DETC2007-35911thegeometryofthetoothcanbecalculatedandthegeardriveperformanceunderloadcanbeevaluated.Themaineffortisdevotedjusttovalidatethemodelbycomparingthestressesexperimentallymeasuredintherootandinthefilletareawiththeonenumericallycalculated;aqualitativecomparisonoftheloadedtoothcontactpatternwillbealsoprovided.2MODELDESCRIPTIONANDMETHODOFTHETable2.ToothgeometrydataoftheTESTgeardrive.PinionGearModule[mm]4.941Offset[mm]0ShaftAngle[]90TeethNumber1236ANALYSISThefirststepinordertobuildareliablenumericalmodelistogetafinegeometricalrepresentationofgeartoothsurfaces.Thisisespeciallytruewhenoneisdealingwithcomplextoothgeometrysuchasthefacehobbingone.Tothisaim,aseriesofalgorithmsabletocomputetoothsurfacesofFHgearsstartingfromcuttingprocesshasbeenimplementedbytheauthors[8].ThegeometryofrealFHheadcutterGleasonTri-Acisconsidered;manykindsofbladeconfigurationstraightandcurveblades,withorwithoutTopremaretakenintoaccount.Then,accordingtothetheoryofgearing[11],FHcuttingprocesswithandwithoutgenerationmotionissimulatedandgeartoothsurfacesequationscanbecomputed.Theproposedmathematicalmodelisabletoprovideanaccuratedescriptionofthewholetooth,includingfilletregion;italsoconsidersundercuttingoccurrence,whichisverycommoninFHgearsduetouniformdepthtooth.Theobtainedtoothsurfacesareusedasfundamentalinputforapowerfulcontactsolverwhichisbasedonasemianalyticalfiniteelementformulation[12-13].Thegeardrivecanbestudyunderlightloadbymonitoring,fordriveandcoastside,thecontactpatternandtransmissionerrori.e.itcanbeperformedthecommonlycalledToothContactAnalysis–TCA[14].Moreover,withtheaimtofindoutgeardriveperformanceintherealserviceconditions,asetoftorquevaluescanbeappliedandtheinfluenceoftheloadoncontactpattern,ontransmissionerrorandonloadsharingcanbeaccuratelyanalyzedLoadedToothContactAnalysis–LTCA[15].Contactpressureandstressdistributioncanbealsoeasilyevaluated.2.GEOMETRICANDMANUFACTORINGOFTHETESTGEARDRIVEUsingthedatacollectedinTable1aspreliminaryinputforacommercialsoftwareforgeardesignGleasonT2000,acalculationaimedtoreproducetheTESTgeardrivehasbeenattempted.Table2describestheobtainedtoothgeometry;Table3and4showthedetailsregardingthemachinesettingandthecuttingbladesthepinionisgeneratedandthegearisFormate;boththemembersarecutbymeansofcurvedbladesusingaheadcutterwithnominalradiusequalto76mmand13bladegroups.2Copyright2007byASMEMeanSpiralAngle[]35.00035.000HandLHRHFaceWidth[mm]25.425.4OuterConeDistance[mm]93.74393.743PitchAngle[]18.43571.565Addendum[mm]4.9302.067Dedendum[mm]2.9425.805Table3.BasicmachinesettingsfortheTESTgeardrive.PinionGearConcaveConvexConcaveConvexGeneratedFormateRadialSetting[mm]91.45191.45192.36492.364TiltAngle[]20.09920.099--SwivelAngle[]-25.371-25.371--BlankOffset[mm]0.0000.000--MachineRootAngle[]0.1540.15471.56571.565MachineCentertoBack[mm]-0.0722-0.0722-1.509-1.509SlidingBase[mm]13.86513.865--CradleAngle[]53.69749.81751.40551.405RatioofRoll[mm]2.9992.999--Table4.CuttingbladesdatafortheTESTgeardrive.PinionGearOBIBOBIBBladeTypeCurvedCurvedCurvedCurvedBladeRadius[mm]75.49975.75876.20675.749BladeEccentric[]17.83217.63317.73817.846BladeHeight[mm]4.3634.3634.3744.374BladeAngle[]25.32318.12222.23121.681BladeGroupsNumber13131313NominalRakeAngle[]12.00012.00012.00012.000HookAngle[]4.4204.4204.4204.420CutterEdgeRadius[mm]0.7000.7001.0001.000BladeRadiusofCurvature[mm]762.000762.000762.000762.000TopremAngle[]----TopremLength[mm]----3.TOOTHGEOMETRYOFTHETESTGEARDRIVEFigure1illustratesthetoothgeometryrepresentationobtainedDuetothefactthatthereferencedoesnotprovideanytopologicaldata,justaqualitativecomparisonbetweentherealtoothgeometryandtheonecalculatedbymeansofthenumericalmodelisfeasibleFigure3.bymeansoftheproposedmodelfortheTESTgeardrive.Figure1.TESTgeartoothgeometryrepresentation.Figure2describesthefilletareabymeansofthetrendalongthefacewidthoftheNominalRootLineNRL,oftheRealRootLineRRLandoftheUnderCut/FilletUC/FLline.Accordingtothatpictureitispossibletonotethetoothdoesnotshowundercut.Figure2.Detailsofthefilletarea.3Copyright2007byASMEFigure3.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,themidonetot0andthetoeonetot-0.5;therootareaislocatedintherange0≤s≤2whiletheCutterEdgeRadius[mm]PinionFilletRadius[mm]Photo-measuredPinionFilletRadius[mm]Difference[]0.701.260.9434.040.501.100.9417.020.300.980.944.26Figure4.Comparisonbetweenthenumericalpinionconcavesideprofileandthephoto-measuredonenotethatthereferencesystemsaredifferent.4.STRESSCALCULATIONReferringtotheexperimentalinvestigation,thestressesareevaluatedbymeansofstraingagesinthefilletarea.Indetail,referringtothesketchdepictedinFigure5,onestraingageattheheelpositioninthefilletandthreestraingagesatheel,midandtoepositionsintherooti.e.ontherootcone.Ontheotherhand,withtheaimtonumericallycomputethestresses,itisnecessarytodefineasetofcoordinateswhichareabletostraightforwardlyprovidethestressmeasuringpointonthetooth.Here,thecurvilinearcoordinatetwhichrunsalongthefacewidth-1≤t≤1inFigure6.aandthecurvilinearcoordinateswhichrunsalongthetoothprofile0≤s≤48inFigure6.bhavebeendefined.Accordingtothis4Copyright2007byASMEfilletoneintherange5≤s≤7.Figure5.SketchusedintheTESTreferenceforlocationofthestraingages.Figure6.a.Schematizationfordefiningthestressmeasuringsectionalongthefacewidthofthemodel.Figure6.b.Schematizationfordefiningthestressmeasuringpointonagenericsectionofthemodel.
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