搜索
ComputeraidedstressanddeflectionanalysisofFellow’sgear-shapingcutter,fordifferentcuttingprocessparametersPPDatta1*,RNBanerjee2andTKChattopadhyay21SchoolofManagement,CranfieldUniversity,Cranfield,UK2MechanicalEngineeringDepartment,JadavpurUniversity,Calcutta,IndiaAbstract:Achievingmaximumefficiency(intermsofquantityofproductsproducedinastipulatedtime)withimprovedaccuracyandsurfacefinishthroughachatter-freehigh-speedcuttingprocessareproblemsofthemoderngearcuttingindustry.ModerntechniquesemployageneratingtypeofcuttersuchasFellow’sgear-shapingcutterfortheproductionofhigh-speednoiselessandaccurategears.Theliteraturereviewindicatesthatexperimentalandtheoreticalmethodshadbeenpredominantlyinuseinthedesignofgearcuttingtoolsascomparedtothecomputeraidedmethods.Inthisresearchthegear-shapingcutterismodelledusingthree-dimensionalten-nodetetrahedralfiniteelements.Theresearchiscarriedoutattheinstantwhenthegear-shapingcutterplungesontheworkpieceandthecuttingforcesduringthegenerationprocessbecomemaximum.Themaximumthree-dimensionaldisplacementsandstressvaluesaregeneratedunderdifferentcuttingconditions.Theeffectsofdifferentcuttingprocessparameters(speed,feedanddepthofcut)onthemaximumstressanddeflectionarestudiedindetail.Keywords:gear-shapingcutter,vibration,stressanalysisNOTATION½Bmatrixrelatingstrainsanddisplacements½cdampingmatrixforanelement½Cdampingmatrixforthestructure½DelasticitymatrixfegdisplacementvectorfFgbodyforceshgpdepthofcut(mm)½Kstiffnessmatrixmmoduleofthegear-shapingcutter(mm)½mmassmatrixforanelement½Mmassmatrixforastructure½NshapefunctionfpgiconcentratedloadsthatactontheelementPz,maxmaximumaxialcuttingforceofthegear-shapingcutterPy,maxmaximumradialcuttingforceinthegear-shapingcutterfRgloadvectorfRintginternalloadvectorfRextgexternalloadvectorSeelementalsurfaceSkprotaryfeedofthecutter(mm)/doublestrokeSy,Sznormalstressesinthegear-shapingcutterintheYandZdirectionsfUgGlobaldisplacementvectorUx,Uy,UzdisplacementofthefiniteelementmodelinthreedimensionsVcuttingspeed(m/min)VeelementalvolumeZcnumberofteethofthegear-shapingcutterZwnumberofteethofthegearblanktobecuttopclearanceanglerakeanglestrain,,localcoordinatesstressfgsurfacetractionforce1755B22903#IMechE2004Proc.InstnMech.EngrsVol.218PartB:J.EngineeringManufactureTheMSwasreceivedon25November2003andwasacceptedafterrevisionforpublicationon19July2004.*Correspondingauthor:SchoolofManagement,CranfieldUniversity,Cranfield,BedfordshireMK430AL,UK.E-mail:parthapriya_datta@yahoo.com1INTRODUCTIONAdvancesinmoderngearcuttingtechnologyofhighrateproductionhaveputseveredemandsontherequirementsofgearsforsmoothandvibration-freeoperation.Suchrequirementsnotonlydemandcorrectprocedureofgeardesignbutalsonecessitateimprovedmethodsoftheirmanufacturing,guaranteeingtheaccuracyofthegearprofiles.Achievingmaximumefficiencyoroptimizingeconomycoupledwithimprovedaccuracyandsurfacefinishthroughachatter-freehigh-speedgearcuttingprocessaretheproblemsofmodernindustrybecauseofwideusageoftheseelementsinalmostallmachinery.Becauseoftheever-increasingdemandforhigherproductivity,accuracyandreliabilityofgearcuttingmachinetools,thedesignofgearcuttingtoolsisreceivingmoreattentionthansingularattentionontheoperatingprocessparameters.Thisdemandsaknowledgeofthestressanddeflectionpatternsinducedintothecut-tingtoolsunderdifferentprocessparameters.Thiswouldgiveaninsightintoanunderstandingoftheprocessparametersresponsibleforwearofthecuttercontributingtochatter[1,2]andhencetheinaccuraciesofgearmachin-ing,sofarnotavailableinthebodyofliteraturereviewed.Theinfluenceandinteractionofcuttingparametersmustbeknownindetailinordertooptimizethekinematicsper-formanceofthegearsproduced[3].Theproductionofgearsbytheshapingmethodrepro-ducesthemeshingofapairofgears,whereonecompo-nentofthepairisthegearblankwhiletheotheristhecuttingtool.TheFellowgear-shapingcutterisshapedlikeagear,i.e.apartwhichcouldmeshwiththegearbeingcut,orthecutterismadesothatitscuttingedgesdescribeinspacethesurfacesofthetoothprofilesofacertainimaginarygearorrack,knownasthegeneratinggearorrack.Inthismeshingactionoftheworkpieceandtool,towhichanadditionalcuttingmotionisimparted,thecuttingedgesofthetool,graduallyremovingmaterialfromthetoothspaces,shapethegearteethtoprofilesthatareenvelopesoftheconsecutivepositionsofthecuttingedgesofthetool(Fig.1).Aliteraturereviewindicatesthatmainlyexperimentalandtheoreticalmodellinghasbeenusedforstabilityinvestigationofgearcuttingtoolsascomparedtocomputeraidedmethods.Thedynamicsofthegearcuttingoperationhasnotbeenexploredindetail,evennow.Thereforedesignersarenotfindingsufficientdatatoenablethemtodesignbettergearcuttingmachinetoolstructuresforchatter-freeandcost-effectivemachin-ingandproductionofgearswithabettersurfacefinish.BanerjeeandMedvodiskov[4]carriedoutextensiveinvestigationsongeartoothmillingcuttersinordertodeterminethetoollifeandmagnitudesofcuttingforcesactingonthecutter.LeeandXiao[5]presentedamethodforthedesignofformingcuttersformachiningmodifiedinvolutehelicalgearsusingthecontactcurveprincipleforthedesignofformingcutters,therebymakingacontribut