JournalofMaterialsProcessingTechnology114(2001)185188Solutiontothebulgingproblemintheopen-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-lationoftheformingforceandtheparametersofformingprocessofthecoldextrusionofasplineshafthavebeenstudiedbysomeresearchers15,butstudyonthebulgingproblemhasnotbeenreported.Thispaperputsemphasisonthesolutionofthebulgingproblem,andrelevantexperi-mentalandtheoreticalanalysis.*Correspondingauthor.E-mailaddress:(Z.Huang).2.Theformationofbulginganditssolution2.1.HowtoavoidbulgingDuringtheprocessingoftheopen-dieextrusionofasplineshaft,thatpartofthebilletwhichhasnotyetenteredtheplasticzoneofthedieandcannotberestrainedbythedie,shouldnotbedeformed.Thustheformingconditionofopen-dieextrusionispsswherepistheunitformingforceonthecross-sectionofthebillet,andssistheyieldlimitoftheextrudedmaterial.Ifpss,thenpartofthebilletinfrontoftheentranceoftheconicaldiewillbedeformedfirstandsubsequentlybulged.Finally,themetalflowisrestrictedandtheopen-dieextru-sionfails.Whichparameteristhemajorfactorfordiedesigningandhowtojudgethesuccessorfailureoftheopen-dieextrusionisaproblem.Somestudiesaboutthisproblemweredonewiththeupper-boundmethod6,7.Whentheotherparametersarefixed,therearetwocriticalvaluesofsemi-coneangleacr1andacr2acr1acr2,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,andtherearesomenecracksonthesurfaceofTable1EffectofdifferentguidinglengthonformingabilityGuidinglengthL0(mm)2.82.5FormingabilityOKOKOKOKUnsteadyPoorastearsandburnsonthesurfaceoftheextrudedsplineandonlyashortlengthofsplinedshaftiscompleted.Withtheincreaseofbulging,normalextrusionfails(asFig.2(b).ItisconcludedfromabovethatasuitableguidinglengthL0canrestrainbulging,andenableextrusiontobecarriedoutsuccessfully,evenifaisoutsidetheformabilityrangeaacr2.3.TheoreticalanalysismodelandcalculationmethodfortheguidinglengthL03.1.PhotoplasticexperimentsIto8statedrstlythatpolycarbonate(PC)canreplacecelluloidasaphotoplasticmodelmaterial,andPCalsocansimulatecoldforming.Inthispaper,theauthorsselectaphysicalsimulationmethod9tostudytheabovesolutiontothebulgingproblem,theaimbeingtoobtainatheoreticalanalysismodelbytheobjectivesimulatedmethod.ThesimulatedmaterialisPC,andtwodieangles,a30anda45,arechosen.Fig.3(a)and(b)presentstheisochromaticpatternsforalongitudinalslicewithoutbul-ginga30andtheisochromaticpatternsforalong-itudinalslicewithbulginga45.Itisfoundthatwhenaacr2a45,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)185188Fig.4.Thetheoreticalanalysismodeloftheguidinglength.187Fig.3.Thefringesofphotoplasticexperiments:(a)theisochromaticpatternsforalongitudinalslicewithoutbulginga30；(b)theisochromaticpatternsforalongitudinalslicewithbulginga45；(c)theisochromaticpatternsforatransversesliceatthebulging.3.2.TheoreticalanalysismodelThetheoreticalanalysismodelofthesolutiontobulgingisthuspresentedonthebasisoftheabovephotoplasticexperiments(inFig.4).Whenaacr2,themetaldistortionissoseriousthatpss,resultinginbulging.WhenaguidinglengthL0isaddedatthedieentrancetorestraintheexpansionofthebulging,thebulgedmetalformsadeadzone.Theotherpartshearsthroughtheeasiestowingchannel(alsonamedthedead-zoneanglea1),whichwillminimizethetotalpowerrequiredwhenadeadzoneforms.Inthiswaythenormalopen-dieextrusioncanbeaccom-plishedsmoothlyevenifaacr2.Duetoa1acr2.Themetalinthedeadzoneadherestothedieandcannotmovesothatashearingsurfaceisgeneratedatthecone-anglea1,andthedeadzoneactsasthediesurfacethroughwhichthemetalisowing.Atthesurfacea1,thefrictionbetweenthedeadmetalandtheowingmetalisnothigherthantheshearingstrengthofthemetalusedts0=310,11.Then,whenaacr2,aismadeastheoptimalparameter,andtheoriginalfrictionconditionisreplacedusingm1.SubstitutingthesefactorsintotheUBM5,6,thevalueofa1canbeobtainedwhenminimizingthepvalue,andtherefore,thevalueofL0limisdeterminedbycalculatingthedistanceofa1andaintheaxialdirection.4.ExperimentsandanalysisInthissection,thetheoreticalanalysismodelandcalcula-tionmethodforL0limareveriedbyexperiment.Threedifferentsizesofsplineareused,andthreeexperimentalmaterialsareapplied:polycabonate,20CrMosteeland20CrMnTisteel.Theirstressstraincurvesareobtained188Table2Z.Huang,P.Fu/JournalofMaterialsProcessingTechnology114(2001)185188andthatthetheoreticalanalysisandcalculationmethodareComparisonofexperimentalvalueswithcalculatedvaluesExperimentalmaterialPolycarbonate20CrMosteel20CrMnTisteelExperimentalvalue5.602.863.42ofL0lim(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.Whenaacr2,theguidinglengthrestrainsbulgingsothatthebulgedmetalformsadeadzone,whiletheotherpartshearsthroughtheeasiestflowingchannel,andthensoundmetalflowcontinues.3.ThecalculationmethodforL0limisalsopresented.Whenaacr2,m1isselectedandaisusedasoptimalparameter.AllofthesefactorsaresubstitutedintotheUBM,whenminimizingthepvalue,theoptimalangleisjusta1,andL0limisdeterminedbycalculatingthedistancebetweena1andaintheaxialdirection.4.Thegoodagreementofthecalculatedresultswiththetheoreticalvaluesshowsthatnotonlyisthesolutionmethodofthebulgingproblemfeasible,butalsotherelevanttheoreticalanalysisandcalculationarereliable.References1S.Fujikawa,H.Yoshioka,S.Shimamura,Coldandwarm-forgingapplicationsintheautomotiveindustry,J.Mater.Process.Technol.35(1992)317341.2H.Hirschrogel,V.Donmelen,Someap