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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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,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,EXPERIMENTALVALIDATI[email protected]crf.itPowertrainResearchandTechnoloStradaTorino50-10043OABSTRACTWhilefacemilledgearshavebeenwidelyanalyzed,aboutfacehobbedonesonlyveryfewstudieshavebeendevelopedandpresented.Goalofthispaperistoproposethevalidationofanaccuratetool,whichwaspresentedbytheauthorsinpreviousworks,aimedtothecomputerizeddesignoffacehobbedgears.Firstly,themathematicalmodelabletocomputedetailedgeartoothsurfacerepresentationonbothspiralandhypoidgearswillbebrieflyrecalled;then,thesoobtained3Dtoothgeometryisemployedasinputforanadvancedcontactsolverthat,usingahybridmethodcombiningfiniteelementtechniquewithsemianalyticalsolutions,isabletoefficientlycarryoutbothcontactanalysisunderlightorheavyloadsandstresstensilecalculation.Thevalidationanalyseswillbecarriedonpublishedaerospacefacehobbedspiralbevelgeardatacomparingmeasurementsofrootandfilletstresses.Goodagreementwithexperimentalresultsbothinthetimescaleandinmagnitudewillberevealed.1INTRODUCTERIZEDTOOLFORFACEHOBBEDGEARYSISMartinoVimercatigy–CentroRicercheFIATrbassano(TO),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].ThegeometryofrealFHheadcutter(GleasonTri-Ac®)isconsidered;manykindsofbladeconfiguration(straightandcurveblades,withorwithoutToprem®)aretakenintoaccount.Then,accordingtothetheoryofgearing[11],FHcuttingprocess(withandwithoutgenerationmotion)issimulatedandgeartoothsurfacesequationscanbecomputed.Theproposedmathematicalmodelisabletoprovideanaccuratedescriptionofthewholetooth,includingfilletregion;italsoconsidersundercuttingoccurrence,whichisverycommoninFHgearsduetouniformdepthtooth.Theobtainedtoothsurfacesareusedasfundamentalinputforapowerfulcontactsolverwhichisbasedonasemianalyticalfiniteelementformulation[12-13].Thegeardrivecanbestudyunderlightloadbymonitoring,fordriveandcoastside,thecontactpatternandtransmissionerror(i.e.itcanbeperformedthecommonlycalledToothContactAnalysis–TCA[14]).Moreover,withtheaimtofindoutgeardriveperformanceintherealserviceconditions,asetoftorquevaluescanbeappliedandtheinfluenceoftheloadoncontactpattern,ontransmissionerrorandonloadsharingcanbeaccuratelyanalyzed(LoadedToothContactAnalysis–LTCA[15]).Contactpressureandstressdistributioncanbealsoeasilyevaluated.2.GEOMETRICANDMANUFACTORINGOFTHETESTGEARDRIVEUsingthedatacollectedinTable1aspreliminaryinputforacommercialsoftwareforgeardesign(GleasonT2000®),acalculationaimedtoreproducetheTESTgeardrivehasbeenattempted.Table2describestheobtainedtoothgeometry;Table3and4showthedetailsregardingthemachinesettingandthecuttingblades:thepinionisgeneratedandthegearisFormate®;boththemembersarecutbymeansofcurvedbladesusingaheadcutterwithnominalradiusequalto76mmand13bladegroups.2Copyright©2007byASMEMeanSpiralAngle[°]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,justaqualitativecomparisonbetweentherealtoothgeometryandtheonecalculatedbymeansofthenumericalmodelisfeasible(Figure3).bymeansoftheproposedmodelfortheTESTgeardrive.Figure1.TESTgeartoothgeometryrepresentation.Figure2describesthefilletareabymeansofthetrendalongthefacewidthoftheNominalRootLineNRL,oftheRealRootLineRRLandoftheUnderCut/FilletUC/FLline.Accordingtothatpictureitispossibletonotethetoothdoesnotshowundercut.Figure2.Detailsofthefilletarea.3Copyright©2007byASMEFigure3.Qualitativecomparisonbetweentherealpiniontoothgeometryandthecalculatedone.3.1EvaluationofactualTESTgearfilletradiusStartingfromthepictureoftherealpiniontooth(Figure3–above),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;therootareaislocatedintherange0≤s≤2whiletheCutterEdgeRadius[mm]PinionFilletRadius[mm]Photo-measuredPinionFilletRadius[mm]Difference[%]0.701.26~0.9434.040.501.10~0.9417.020.300.98~0.944.26Figure4.Comparisonbetweenthenumericalpinionconcavesideprofileandthephoto-measuredone(notethatthereferencesystemsaredifferent).4.STRESSCALCULATIONReferringtotheexperimentalinvestigation,thestressesareevaluatedbymeansofstraingagesinthefilletarea.Indetail,referringtothesketchdepictedinFigure5,onestraingageattheheelpositioninthefilletandthreestraingages(atheel,midandtoepositions)intheroot(i.e.ontherootcone).Ontheotherhand,withtheaimtonumericallycomputethestresses,itisnecessarytodefineasetofcoordinateswhichareabletostraightforwardlyprovidethestressmeasuringpointonthetooth.Here,thecurvilinearcoordinatetwhichrunsalongthefacewidth(-1≤t≤+1inFigure6.a)andthecurvilinearcoordinateswhichrunsalongthetoothprofile(0≤s≤48inFigure6.b)havebeendefined.Accordingtothis4Copyright©2007byASMEfilletoneintherange5≤s≤7.Figure5.SketchusedintheTESTreferenceforlocationofthestraingages.Figure6.a.Schematizationfordefiningthestressmeasuringsectionalongthefacewidthofthemodel.Figure6.b.Schematizationfordefiningthestressmeasuringpointonagenericsectionofthemodel.
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