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JournalofMaterialsProcessingTechnology114(2001)185±188Solutiontothebulgingproblemintheopen-diecoldextrusionofasplineshaftandrelevantphotoplastictheoreticalstudyZhaohuiHuanga,*,PeifuFubaForgingDivision,BeijingInstituteofAeronauticalMaterials,Beijing100095,PRChinabDepartmentofMaterialsScienceandEngineering,JilinUniversityofTechnology,Changchun130025,PRChinaReceived21June1999AbstractComparedwithotherformingmethods,thecoldextrusionofasplineshafthasmanyadvantages.However,theproblemofbulgingatthedieentrance,whichisnotyetsolved,resiststhewideapplicationofthisnet(ornearnet)shapetechnology.Tosolvethebulgingproblem,themethodofaddingaguidinglengthuponthedieentranceinthediedesigningisputforwardinthispaper.Onthebasisofphotoplasticexperiments,atheoreticalanalysismodelofthesolutionisfound,andthecalculatingmethodfortheguidinglengthisalsosubmitted.Theappropriateprocessingparametersarechosenbasedonthecalculatedresults,andasatisfactoryeffecthasbeenobtainedintheactualprocessing.#2001ElsevierScienceB.V.Allrightsreserved.Keywords:Splineshaft;Coldextrusion;Bulging;Photoplasticity1.IntroductionInrecentyears,netornearnetshapetechnologieswiththeirpossibilitiesofproducingpartswithready-to-built-infunctionalsurfaceshavebecomemoreandmoreinteresting,evenfortheproductionofcomplexparts.Thecoldextrusionofasplineshafthasagreaterpotentialthancutting,¯at-diethreadrollingandrolling,becauseofitsmanyoutstandingadvantagessuchasthesavingofrawmaterials,highpro-ductivity,superiorproductqualityandlowcost.However,thediedesignandthechoiceoftheprocessparametersrelyonempiricalfactorsduetothelackofsystematicanalysisandsothebilletusuallybulgesatthedieentrance,whichleadstothefailureofextrusionintheactualprocess.Recently,thisbulgingproblemhasbeenmainlysolvedbyexpensivetrial-and-errorinmajorplants,whichlimitsgreatlytheapplicationofthisadvancedprocess.Thecalcu-lationoftheformingforceandtheparametersofformingprocessofthecoldextrusionofasplineshafthavebeenstudiedbysomeresearchers1±5,butstudyonthebulgingproblemhasnotbeenreported.Thispaperputsemphasisonthesolutionofthebulgingproblem,andrelevantexperi-mentalandtheoreticalanalysis.*Correspondingauthor.E-mailaddress:huaping.xiongbiam.ac.cn(Z.Huang).2.Theformationofbulginganditssolution2.1.HowtoavoidbulgingDuringtheprocessingoftheopen-dieextrusionofasplineshaft,thatpartofthebilletwhichhasnotyetenteredtheplasticzoneofthedieandcannotberestrainedbythedie,shouldnotbedeformed.Thustheformingconditionofopen-dieextrusionispsswherepistheunitformingforceonthecross-sectionofthebillet,andssistheyieldlimitoftheextrudedmaterial.Ifp>ss,thenpartofthebilletinfrontoftheentranceoftheconicaldiewillbedeformedfirstandsubsequentlybulged.Finally,themetalflowisrestrictedandtheopen-dieextru-sionfails.Whichparameteristhemajorfactorfordiedesigningandhowtojudgethesuccessorfailureoftheopen-dieextrusionisaproblem.Somestudiesaboutthisproblemweredonewiththeupper-boundmethod6,7.Whentheotherparametersarefixed,therearetwocriticalvaluesofsemi-coneangleacr1andacr2acr1<acr2.Whenacr1aacr2,theformingconditionpssissatisfied,andthebulgingproblemcanbeavoided.Furthermore,thecriticalvaluesvarywiththechangeoftheotherprocessparametersinwhichaandssaretwoimportantvariables.Fig.1showsthevariationofthecriticaldieanglewith0924-0136/01/$±seefrontmatter#2001ElsevierScienceB.V.Allrightsreserved.PII:S0924-0136(01)00737-3186Z.Huang,P.Fu/JournalofMaterialsProcessingTechnology114(2001)185±188Fig.2.Thestateofsplineformingwithdifferentguidinglengths:(a)L02:8mm;(b)L02:5mm.theextrudedspline.InthecaseofL02:5mm,thebulgingphenomenonbecomesworse,thereareseriousdefectssuchFig.1.Variationofthecriticaldieanglewithdifferenthardnessofthebillet.differenthardnessofthebillet.Ifaiswithintherangeoftwocrosspoints,theformingprocesscanbecompletedsuccess-fully.Thesmallerthebillethardness,thenarroweristherangeofa.2.2.SolutiontobulgingIngeneral,thelengthofasplineconsistsofthelengthwithanentiretooth,andthelengthwithapartialtooth,wherethelattermeanstheaxiallengthofthedieangle.Inengineeringdesigning,thelengthwithapartialtoothisalwaysshortduetothelimitofthewholelengthoftheshaft,whichwillleadtoalargedieangle,frequentlyoutsidethecriticalrange,i.e.a>acr2,consequently,bulgingcannotbeavoided.Onthebasisofexperiments,afeasiblemethodofsolvingthebulgingproblemissubmittedasfollows:addingaguidinglengthL0atthedieentrancetorestraintheexpansionofthebulgingsothattheotherpartsofthebilletareextrudedcontinuously.Correspondingexperimentshavebeendone,beginningwithL04:0mm,andthendecreas-ingL0progressivelyiftheextrusionissuccessfuluntiltheextrusionfails.Otherparametersareasfollows:R1radiusoftoothroof10:1mm;R2radiusoftoothroot7:9mm;btoothwidth3:95mm;ztoothnumber6;RA30:59%.Thematerialusedis20CrMosteellubri-catedbyphosphatecoating.TheresultsarelistedinTable1.WhenL03:1mm,theidealsplineshaftcanbeobtained.ForL02:8mm,itsconditionisunstableasshowninFig.2(a),alittlebulgingappearsatthedieentrance,andtherearesome®necracksonthesurfaceofTable1EffectofdifferentguidinglengthonformingabilityGuidinglengthL0(mm)43.73.43.12.82.5FormingabilityOKOKOKOKUnsteadyPoorastearsandburnsonthesurfaceoftheextrudedsplineandonlyashortlengthofsplinedshaftiscompleted.Withtheincreaseofbulging,normalextrusionfails(asFig.2(b).ItisconcludedfromabovethatasuitableguidinglengthL0canrestrainbulging,andenableextrusiontobecarriedoutsuccessfully,evenifaisoutsidetheformabilityrangea>acr2.3.TheoreticalanalysismodelandcalculationmethodfortheguidinglengthL03.1.PhotoplasticexperimentsIto8stated®rstlythatpolycarbonate(PC)canreplacecelluloidasaphotoplasticmodelmaterial,andPCalsocansimulatecoldforming.Inthispaper,theauthorsselectaphysicalsimulationmethod9tostudytheabovesolutiontothebulgingproblem,theaimbeingtoobtainatheoreticalanalysismodelbytheobjectivesimulatedmethod.ThesimulatedmaterialisPC,andtwodieangles,a30anda45,arechosen.Fig.3(a)and(b)presentstheisochromaticpatternsforalongitudinalslicewithoutbul-ginga30andtheisochromaticpatternsforalong-itudinalslicewithbulginga45.Itisfoundthatwhena<acr2(withoutbulging)themetal¯owsnormallyalongthedieinterface,andthereisazoneofzerodegreefringes,whichmeansthatthereisnoplasticdeformationupontheentranceofthedieangle.Whena>acr2a45,thebilletbecomesbulgeduponenteringthedieangle,andthefringesinthiszoneareveryclose,signifyingthatacon-centrationofstrainoccurs.However,uponthebulging,thereisalsothezoneofzerodegreefringes.Asliceofcross-sectionatthebulgingisillustratedinFig.3(c).Therearesixsymmetricalzonesoffringes,whilsttheothersarezonesofzerodegreefringes,wherenoplasticdeformationoccurred.Thediameterofthesixfringedzonesislargerthanthatoftheotherzones,becauseinthesezones,theextrudedbilletisdeformedintheradialdirection,andexpandedtotheguid-inglengthinterface,leadingtobulging.Z.Huang,P.Fu/JournalofMaterialsProcessingTechnology114(2001)185±188Fig.4.Thetheoreticalanalysismodeloftheguidinglength.187Fig.3.Thefringesofphotoplasticexperiments:(a)theisochromaticpatternsforalongitudinalslicewithoutbulginga30;(b)theisochromaticpatternsforalongitudinalslicewithbulginga45;(c)theisochromaticpatternsforatransversesliceatthebulging.3.2.TheoreticalanalysismodelThetheoreticalanalysismodelofthesolutiontobulgingisthuspresentedonthebasisoftheabovephotoplasticexperiments(inFig.4).Whena>acr2,themetaldistortionissoseriousthatp>ss,resultinginbulging.WhenaguidinglengthL0isaddedatthedieentrancetorestraintheexpansionofthebulging,thebulgedmetalformsadeadzone.Theotherpartshearsthroughtheeasiest¯owingchannel(alsonamedthedead-zoneanglea1),whichwillminimizethetotalpowerrequiredwhenadeadzoneforms.Inthiswaythenormalopen-dieextrusioncanbeaccom-plishedsmoothlyevenifa>acr2.Duetoa1<a,thereisadistancebetweena1andaintheaxialdirection,andthisdistanceisjustthelimitinglengthoftheguidinglengthL0,namedL0lim.Obviously,onlywhenL0L0limcantheguidinglengthrestrainthebulgingandmakethemetal¯owcontinuously.Thisapproachproducesrestraintofthebilletbeforeenteringthedieangle,butashortL0limisexpectedfordiedesigning.3.3.CalculatingmethodoftheguidinglengthL0limItisknownfromtheabovediscussionthatdeadzonesappearwhena>acr2.Themetalinthedeadzoneadherestothedieandcannotmovesothatashearingsurfaceisgeneratedatthecone-anglea1,andthedeadzoneactsasthediesurfacethroughwhichthemetalis¯owing.Atthesurfacea1,thefrictionbetweenthedeadmetalandthe¯owingmetalisnothigherthantheshearingstrengthofthemetalusedts0=310,11.Then,whena>acr2,aismadeastheoptimalparameter,andtheoriginalfrictionconditionisreplacedusingm1.SubstitutingthesefactorsintotheUBM5,6,thevalueofa1canbeobtainedwhenminimizingthepvalue,andtherefore,thevalueofL0limisdeterminedbycalculatingthedistanceofa1andaintheaxialdirection.4.ExperimentsandanalysisInthissection,thetheoreticalanalysismodelandcalcula-tionmethodforL0limareveri®edbyexperiment.Threedifferentsizesofsplineareused,andthreeexperimentalmaterialsareapplied:polycabonate,20CrMosteeland20CrMnTisteel.Theirstress±straincurvesareobtained188Table2Z.Huang,P.Fu/JournalofMaterialsProcessingTechnology114(2001)185±188andthatthetheoreticalanalysisandcalculationmethodareComparisonofexperimentalvalueswithcalculatedvaluesExperimentalmaterialPolycarbonate20CrMosteel20CrMnTisteelExperimentalvalue5.602.863.42ofL0lim(mm)Calculatedvalueof7.203.524.52L0lim(mm)Error(%)28.6231.3032.25Fig.5.Splineshafts:(a)withoutand(b)withadeadzone.bytensiletesting.TherangeofcriticalangleisgainedbytheUBM6,7,thenanexperimentaldieanglelargerthanthecriticalangleischosenandthecoldextrusionofasplineiscarriedout.TheexperimentalvaluesandcalculatedresultsarecomparedinTable2.Thecalculatedresultsagreewellwiththeexperimentalresults,theerroroftheUBMbeing30%orso.ConsideringthatthevaluescalculatedbytheUBMarealwaysgreaterthan(orequalto)theactualvalues,theauthorsbelievethatitissafetochoosethesevaluesintheengineeringdesign.Finally,theactualformingprocessofthecoldextrusionofthesplineshaftofamotorcycletransmissionisdoneonthebasisoftheaboveresults.Here20CrMnTisteelisused,andtheparametersofthestraight-sidesplinewith6teethareasfollows:R110:125mm,R28:32mm,b4:825mm.Themaximumcriticalsemi-angleisacr226:68(valueobtainedfromtheUBM7).Intheexperiments,twodieangles,a30anda45,arechosen.Whena45,theguidinglengthisL0lim4:81mm7.Intheexperiments,theguidinglengthL0,4.9mm,isaddedinsuchacondition.Twogroupsofbilletsareannealedforsoftening,andlubricatedbyphosphatecoating,andthencoldextruded.TheresultsareshowninFig.5.Fig.5(a)givesthecriticalstatea30,wherenobulgingappears.Alloftheaboveaccordswellwiththecalculatedresults.InFig.5(b),thedieangleisa45(largerthanacr2),andthereisadeadmetalzoneuponthedieangleentrance,exhibitingawhitezoneontheextrudedshaftbecausethelocallubricantsaretornaway.Withenoughguidinglength,thecoldextrusionofasplineshaftcanbeaccomplishedsmoothly.Aboveexperimentsalsoverifythatthesolutionmethodofbulgingisfeasible,reasonable.5.Conclusions1.Themethodofsolvingthebulgingproblemisputforwardasfollows:addingaguidinglengthatthedieentrancetorestraintheexpansionofthebulgingsothattheextrusioncanbeaccomplishedsuccessfully.2.Thetheoreticalanalysismodelofthesolutiontothebulgingproblemisfound.Whena>acr2,theguidinglengthrestrainsbulgingsothatthebulgedmetalformsadeadzone,whiletheotherpartshearsthroughtheeasiestflowingchannel,andthensoundmetalflowcontinues.3.ThecalculationmethodforL0limisalsopresented.Whena>acr2,m1isselectedandaisusedasoptimalparameter.AllofthesefactorsaresubstitutedintotheUBM,whenminimizingthepvalue,theoptimalangleisjusta1,andL0limisdeterminedbycalculatingthedistancebetweena1andaintheaxialdirection.4.Thegoodagreementofthecalculatedresultswiththetheoreticalvaluesshowsthatnotonlyisthesolutionmethodofthebulgingproblemfeasible,butalsotherelevanttheoreticalanalysisandcalculationarereliable.References1S.Fujikawa,H.Yoshioka,S.Shimamura,Coldandwarm-forgingapplicationsintheautomotiveindustry,J.Mater.Process.Technol.35(1992)317±341.2H.Hirschrogel,V.Donmelen,Someapplicationsofcoldandwarmforging,J.Mater.Process.Technol.35(1992)343±356.3Z.C.Zhang,J.Li,Experimentalstudyonopen-diecoldextrusionformingtechniqueforinvolatesplineshaft,ChineseJ.Mech.Eng.9(1996)6±12(inChinese).4L.L.Jia,Anupperboundanalysisforextrusionofspline,in:AdvancedTechnologyofPlasticity,ProceedingoftheFourthInternationalConferenceonTechnologyofPlasticity,Beijing,China,1993,pp.582±586.5D.Y.Yang,C.H.Han,M.U.Kim,Ageneralizedmethodforanalysisofthree-dimensionalextrusionofarbitrarilyshapedsections,Int.J.Mech.Sci.28(1986)517±534.6P.F.Fu,Z.H.Huang,Studyontheformingconditionofopen-diecoldextrusionforsplineshaft,J.Agric.Mech.28(1997)129±133(inChinese).7Z.H.Huang,Ph.D.Thesis,JilinUniversityofTechnology,China,1998(inChinese).8K.Ito,Newmodelmaterialsforphotoelasticityandphotoplasticity,Agric.Mech.2(1962)373±376.9Z.H.Huang,P.F.Fu,Three-dimensionalphotoelasticstudyonthedeformationofasplineshaftincoldextrusion,J.Exp.Mech.14(1999)35±40(inChinese).10B.Avitzur,MetalForming:ProcessandAnalysis,LehighUniversity,NewYork,1979,pp.50±20011B.Avitzur,HandbookofMetal-formingProcess,LehighUniversity,NewYork,1983,pp.61±130