外文翻译--长梯形花键的冷挤压及其成形分析 英文版.pdf

ORIGINALARTICLEColdextrusionofalongtrapeziumsplineanditsforminganalysisYuanAnfuReceived:21August2007/Accepted:10March2008/Publishedonline:15April2008#Springer-VerlagLondonLimited2008AbstractThemachiningofalongtrapeziumsplineisdifficultduetoitsstiffness.Inthispaper,aspecialcoldextrusiontechniquehasbeenadoptedonthebasisofanalyzingitsthree-dimensionalvelocityfieldandsimula-tionusingthesoftwareprogrammeDeform-3D5.0tomakeaqualifiedtrapeziumsplineof12×840with16teeth.KeywordsColdextrusion.Trapeziumspline.Forminglimit.Deform1IntroductionTherectanglesplineismainlyusedtoholdheavyloadsduetoitsthickroot.Thereforeitiswidelyusedtotransmitpowerintheautoindustry.Thispapersmainlyfocusesontheformingofalongtrapeziumspline,whichisadifficultproblemtosolveinthemachiningindustry.Traditionalmachiningmethods,suchasmilling,hobbling,etc.,arenotcapableofformingsuchsplineinbatchesduetotheirlowefficiencyandquality；thereforespecialmanufacturingmethodssuchastwisting,extruding,etc.havebecomemoreandmorewidelyused.Still,forlongtrapeziumspline,asshowninFig.1,bothofthemhavesomedifficultiestoformaqualifiedpart17.2DetailsofparttobeformedThedrawingofatrapeziumsplinetobeformedreferstoFig.1.Itsdetailsareasfollows:Teeth:16ThickofTooth:1:3Material:20CrGBðÞElasticModule:205GpaPossionRatio:0:29Density:7850KgC14m3YieldStrength:685MpaTopdia:oftooth:Dt¼12:8mmRootdia:oftooth:10:86mm3StepstosolveTherearetwoproblemswhichneedtobesolvedinordertoformaqualifiedproduct:3.1StructureofthediecavityThestructureofthediecavitydirectlyinfluencesdeforma-tionoftheworkpieceandstressandstraindistributionduringextrusion.ThereforeitisnecessarytodesignareasonablediestructureaccordingtotheactualformingIntJAdvManufTechnol(2009)41:461467DOI10.1007/s00170-008-1480-yY.Anfu(*)InformationandControlCollege,NanjingUniversityofInformationScience&Technology,No.114PanchengNewStreetPukouDistrict,Nanjing,JiangsuProvince210044,Chinae-mail:charles-yuan163.comconditionstoobtainaminimumformingforce.Inthispaper,basedontheanalysistothethree-dimensionalvelocityfieldinmetalextrusionaccordingtoassumptionofisoextrusionratioflow,areasonablediestructurecanbedesigned.AndthenformingofextrusionunderthesameconditionswithactualextrusionissimulatedwithDeform.Finallytheextrusiondieismachinedaccordingtotheabovetworesults.3.2StiffnessofparttobeformedAstothethinlongtheworkpiecetobeformedinthispaper,howtokeepenoughstiffnessoftheworkpieceduringcoldextrusionbecomesanoverwhelmingproblem.Soinactualextrusion,traditionalpushforceischangedtoapullforceand,atthesametime,supportedbyspecialmechanism.Thesetechniquesaboveareprovedtobeeffective.4AnalysisofextrusionInthispaper,allanalysisismadeonthebasisofopendieextrusion.4.1ShapefunctionofsplineshaftDuetothesymmetryofthetrapeziumspline,onlyhalfthestructureofitsshapeisdrawninFig.2.Accordingtotheworkingprincipleoftrapeziumspline,itsshapefunctionofsurfacecanbeobtainedasfollows:fr；ZðÞ¼gðÞC0Rb½C138Z=LþRbð1ÞwhereLValidlengthofworkingzoneofdiecavity；RbRadiusofbasecircle,i.e.,radiusofrawbar；g()isdefinedasfollows:gðÞ¼Rt0<C2081SRðÞ81<C2082Rr81<C20828<:ð2ÞwhereRtRadiusoftopcircleofsplineRrRadiusofrootcircleofsplineSR()Equationoftrapeziumsplinewhichisdescribedasfollows:SRðÞ:Rrrsin81C0ðÞþRtrsinC082ðÞ¼RtRrsin81C082ðÞð3ÞwhereakPressureangleofthesplinetPolaranglewhentopcircleofsplineispolarradiusFig.2ShapefunctionoftrapeziumsplineanditscoordinationsystemFig.3DeformingzoneoftrapeziumsplineFig.1Partdrawingtobeformed462IntJAdvManufTechnol(2009)41:4614674.2ActualanglesAccordingtoactualdimensionsoftrapeziumspline,Eqs.(1,2and3)canbetransferredasfollows:81¼5:830；82¼6:88082¼12:30ZoneI:fr；ZðÞ¼RtC0RbðÞZ=LþRbð4ÞZoneII:fr；ZðÞ:r¼RtRrsin81C082ðÞRrsin81C0ðÞþRtsinC082ðÞ¼Z¼Z:8<:ð5ÞZoneIII:fr；ZðÞ¼RrC0RbðÞZ=LþRbð6Þ4.3Establishmentofthree-dimensionalvelocityfieldBeforeestablishingitsthree-dimensionalvelocityfield,itissupposedasfollows:ThematerialoftheworkpiecetobeformedisanisotropymaterialandconstrainedbyVonMiseprinciple.Volumeoftheworkpieceiskeptthesameduringextrusion.Aplasticboundaryisenclosedbytheshearsurfaceattheentranceandexit.Thematerialattheentrancefanzoneandexitfanzoneiskeptthesameontotalextrusionratio.Sinceeveryplasticmetalmustexperienceplasticdeformationduringextrusion,aplasticdeformingcell(ref.toFig.3)isconsidered.Itisenclosedwithshapefunctionandtwoplainsatentranceandexit,whichareperpendicularwiththeZ-axis.Now,selectonepointP(Z,r,)randomlywhosevelocitycanbeexpressedas:VP¼VZ；r；qðÞ¼VVz；Vr；VqðÞð7ÞAccordingtoEqs.(1)and(2),thefollowingequationcanbeobtained:1rrVrðÞrþ1rVqðÞqþVzðÞz¼0ð8ÞwhereVr,VqandVzareradial,circumferentialandaxialvelocities,respectively,andallofthemarefunctionsof(Z,r,),whicharestatedasfollows:1)ExpressionofVzItisassumedthat,duringextrusion,axialvelocityV0zisthesamewithintheperiodofO1O2(ref.toFig.4),But,intheperiodofOO1,axialvelocityVziscomposedwithV0zandanadditionalaxialvelocityV00z,whichisasfollows:Vz¼V0zþV00zð9ÞItissupposedthatthevelocityofPUSHBARatentrance(z=0)isV0anditsareaisA0；therefore,areaatpointz(Z=z)isAz.Inaddition,halfguideangleofextrusiondieisassumedtobe,thefollowingexpressioncanbeobtained:ZSVzdA¼VoA0ð10ÞwhereA0¼Z2p012f2r；q；0ðÞdq；Az¼Z2p012f2r；q；zðÞdqoFig.4ExtrusionzoneofatrapeziumsplineIntJAdvManufTechnol(2009)41:461467463RegardingV00z,itmeetsfollowingconditions:V00zz¼0¼V0；V00zC12C12C12C12z¼lr¼VLandZSV00zdz¼0ð11ÞFrom(11)andtheshapefunction,wefindthatV00zcanbewrittenasfollows:V00z¼az2þbzð12Þwherea¼VLC0V0l2rC014tg4aC2r2zC03DrtgaC2rzþ2DrtgaC2lrC012tg2aC2l2rVLC0V0ðÞ14tg4aC2r2zC03DrtgaC2rzþ13tg2aC2l2rrzC0C1ð13Þb¼14tg4aC2lrr2zC03DrtgaC2lrrzþ2DrtgaC2l2rC012tg2aC2l3rVLC0V0ðÞ14tg4aC2r2zC03DrtgaC2rzþ13tg2aC2l2rrzC0C1ð14Þwhererz¼Dr2þlrC0zðÞtga,allothersymbolspls.ref.toFig.4.Fromallaboveexpressions,VzcanbeobtainedfromEq.(9).2)RadialvelocityVrandcircumferentialvelocityVqSincetheinnersurfaceoftheextrusiondieisincontactwiththesurfaceoftheworkpiece,thefollowingexpressioncanbeobtained:Vrr¼fr；zðÞC01fr；zðÞC2fr；zðÞC12C12C12C12Vr¼fr；zðÞC0fr；zðÞzVzC12C12C12C12C12C12C12C12r¼fr；zðÞ¼0ð15ÞFromEq.(8),itcanbeintegratedasfollows:rVrþZrz0VqðÞqdrþZrz0rVzzdr¼0ð16ÞBysolvingEqs.(15and16)andputtingthemintoexpressionsofVz,rzandshapefunctionoff(r,z),onecanobtainthethree-dimensionalvelocityfieldasfollows:Vz¼V0zþV00zVr¼C0r2V0zC0rþ1C2G；zðÞC01rZrz0rV00zdrV¼1þðÞr2fr；zðÞ½C138pZizfr；zðÞ2V00zhid8>>><>>>>:ð17Þ4.4PowercalculationbyupperboundanalysisDuringextrusion,therearethreepowersofdeformationpowerinsidetheworkpiece,frictionpowerandshearpower,thatis:PT¼PdþPtþPfð18ÞwherePd,Pt,Pfarepowersofdeformationpowerinsidetheworkpiece,shearpowerandfrictionpoweronthecontactingsurfaceofthesplinerespectively.Theyareasfollows:Pd¼ZVsedvð19Þwheree¼23qe2rrþe2þe2zzþ2e2rzC2C31=2Pt¼ss3pZvjjdSð20ÞwhereistheinterruptingsurfaceofvelocityPf¼mss3pZvjjDAð21ÞFig.5SimulationobjectFig.6Simulationmodel464IntJAdvManufTechnol(2009)41:461467