1、JournalofMaterialsProcessingTechnology114(2001)185188Solutiontothebulgingproblemintheopen-diecoldextrusionofasplineshaftandrelevantphotoplastictheoreticalstudyZhaohuiHuanga/*/PeifuFubaForgingDivision/BeijingInstituteofAeronauticalMaterials/Beijing100095/PRChinabDepartmentofMaterialsScienceandEnginee
2、ring/JilinUniversityofTechnology/Changchun130025/PRChinaReceived21June1999AbstractComparedwithotherformingmethods/thecoldextrusionofasplineshafthasmanyadvantages/However/theproblemofbulgingatthedieentrance/whichisnotyetsolved/resiststhewideapplicationofthisnet(ornearnet)shapetechnology/Tosolvethebul
3、gingproblem/themethodofaddingaguidinglengthuponthedieentranceinthediedesigningisputforwardinthispaper/Onthebasisofphotoplasticexperiments/atheoreticalanalysismodelofthesolutionisfound/andthecalculatingmethodfortheguidinglengthisalsosubmitted/Theappropriateprocessingparametersarechosenbasedonthecalcu
4、latedresults/andasatisfactoryeffecthasbeenobtainedintheactualprocessing/#2001ElsevierScienceB/V/Allrightsreserved/Keywords/Splineshaft；Coldextrusion；Bulging；Photoplasticity1/IntroductionInrecentyears/netornearnetshapetechnologieswiththeirpossibilitiesofproducingpartswithready-to-built-infunctionalsu
5、rfaceshavebecomemoreandmoreinteresting/evenfortheproductionofcomplexparts/Thecoldextrusionofasplineshafthasagreaterpotentialthancutting/at-diethreadrollingandrolling/becauseofitsmanyoutstandingadvantagessuchasthesavingofrawmaterials/highpro-ductivity/superiorproductqualityandlowcost/However/thediede
6、signandthechoiceoftheprocessparametersrelyonempiricalfactorsduetothelackofsystematicanalysisandsothebilletusuallybulgesatthedieentrance/whichleadstothefailureofextrusionintheactualprocess/Recently/thisbulgingproblemhasbeenmainlysolvedbyexpensivetrial-and-errorinmajorplants/whichlimitsgreatlytheappli
7、cationofthisadvancedprocess/Thecalcu-lationoftheformingforceandtheparametersofformingprocessofthecoldextrusionofasplineshafthavebeenstudiedbysomeresearchers15/butstudyonthebulgingproblemhasnotbeenreported/Thispaperputsemphasisonthesolutionofthebulgingproblem/andrelevantexperi-mentalandtheoreticalana
8、lysis/*Correspondingauthor/E-mailaddress/(Z/Huang)/2/Theformationofbulginganditssolution2/1/HowtoavoidbulgingDuringtheprocessingoftheopen-dieextrusionofasplineshaft/thatpartofthebilletwhichhasnotyetenteredtheplasticzoneofthedieandcannotberestrainedbythedie/shouldnotbedeformed/Thustheformingcondition
9、ofopen-dieextrusionispsswherepistheunitformingforceonthecross-sectionofthebillet/andssistheyieldlimitoftheextrudedmaterial/Ifpss/thenpartofthebilletinfrontoftheentranceoftheconicaldiewillbedeformedfirstandsubsequentlybulged/Finally/themetalflowisrestrictedandtheopen-dieextru-sionfails/Whichparameter
10、isthemajorfactorfordiedesigningandhowtojudgethesuccessorfailureoftheopen-dieextrusionisaproblem/Somestudiesaboutthisproblemweredonewiththeupper-boundmethod6/7/Whentheotherparametersarefixed/therearetwocriticalvaluesofsemi-coneangleacr1andacr2acr1acr2/consequently/bulgingcannotbeavoided/Onthebasisofe
11、xperiments/afeasiblemethodofsolvingthebulgingproblemissubmittedasfollows/addingaguidinglengthL0atthedieentrancetorestraintheexpansionofthebulgingsothattheotherpartsofthebilletareextrudedcontinuously/Correspondingexperimentshavebeendone/beginningwithL04/0mm/andthendecreas-ingL0progressivelyiftheextru
12、sionissuccessfuluntiltheextrusionfails/Otherparametersareasfollows/R1radiusoftoothroof10/1mm；R2radiusoftoothroot7/9mm；btoothwidth3/95mm；ztoothnumber6；RA30/59%/Thematerialusedis20CrMosteellubri-catedbyphosphatecoating/TheresultsarelistedinTable1/WhenL03/1mm/theidealsplineshaftcanbeobtained/ForL02/8mm
13、/itsconditionisunstableasshowninFig/2(a)/alittlebulgingappearsatthedieentrance/andtherearesomenecracksonthesurfaceofTable1EffectofdifferentguidinglengthonformingabilityGuidinglengthL0(mm)43/73/43/12/82/5FormingabilityOKOKOKOKUnsteadyPoorastearsandburnsonthesurfaceoftheextrudedsplineandonlyashortleng
14、thofsplinedshaftiscompleted/Withtheincreaseofbulging/normalextrusionfails(asFig/2(b)/ItisconcludedfromabovethatasuitableguidinglengthL0canrestrainbulging/andenableextrusiontobecarriedoutsuccessfully/evenifaisoutsidetheformabilityrangeaacr2/3/Theoreticalanalysismodelandcalculationmethodfortheguidingl
15、engthL03/1/PhotoplasticexperimentsIto8statedrstlythatpolycarbonate(PC)canreplacecelluloidasaphotoplasticmodelmaterial/andPCalsocansimulatecoldforming/Inthispaper/theauthorsselectaphysicalsimulationmethod9tostudytheabovesolutiontothebulgingproblem/theaimbeingtoobtainatheoreticalanalysismodelbytheobje
16、ctivesimulatedmethod/ThesimulatedmaterialisPC/andtwodieangles/a30anda45/arechosen/Fig/3(a)and(b)presentstheisochromaticpatternsforalongitudinalslicewithoutbul-ginga30andtheisochromaticpatternsforalong-itudinalslicewithbulginga45/Itisfoundthatwhenaacr2a45/thebilletbecomesbulgeduponenteringthedieangle
17、/andthefringesinthiszoneareveryclose/signifyingthatacon-centrationofstrainoccurs/However/uponthebulging/thereisalsothezoneofzerodegreefringes/Asliceofcross-sectionatthebulgingisillustratedinFig/3(c)/Therearesixsymmetricalzonesoffringes/whilsttheothersarezonesofzerodegreefringes/wherenoplasticdeforma
18、tionoccurred/Thediameterofthesixfringedzonesislargerthanthatoftheotherzones/becauseinthesezones/theextrudedbilletisdeformedintheradialdirection/andexpandedtotheguid-inglengthinterface/leadingtobulging/Z/Huang/P/Fu/JournalofMaterialsProcessingTechnology114(2001)185188Fig/4/Thetheoreticalanalysismodel
19、oftheguidinglength/187Fig/3/Thefringesofphotoplasticexperiments/(a)theisochromaticpatternsforalongitudinalslicewithoutbulginga30；(b)theisochromaticpatternsforalongitudinalslicewithbulginga45；(c)theisochromaticpatternsforatransversesliceatthebulging/3/2/TheoreticalanalysismodelThetheoreticalanalysism
20、odelofthesolutiontobulgingisthuspresentedonthebasisoftheabovephotoplasticexperiments(inFig/4)/Whenaacr2/themetaldistortionissoseriousthatpss/resultinginbulging/WhenaguidinglengthL0isaddedatthedieentrancetorestraintheexpansionofthebulging/thebulgedmetalformsadeadzone/Theotherpartshearsthroughtheeasie
21、stowingchannel(alsonamedthedead-zoneanglea1)/whichwillminimizethetotalpowerrequiredwhenadeadzoneforms/Inthiswaythenormalopen-dieextrusioncanbeaccom-plishedsmoothlyevenifaacr2/Duetoa1acr2/Themetalinthedeadzoneadherestothedieandcannotmovesothatashearingsurfaceisgeneratedatthecone-anglea1/andthedeadzon
22、eactsasthediesurfacethroughwhichthemetalisowing/Atthesurfacea1/thefrictionbetweenthedeadmetalandtheowingmetalisnothigherthantheshearingstrengthofthemetalusedts0=310/11/Then/whenaacr2/aismadeastheoptimalparameter/andtheoriginalfrictionconditionisreplacedusingm1/SubstitutingthesefactorsintotheUBM5/6/t
23、hevalueofa1canbeobtainedwhenminimizingthepvalue/andtherefore/thevalueofL0limisdeterminedbycalculatingthedistanceofa1andaintheaxialdirection/4/ExperimentsandanalysisInthissection/thetheoreticalanalysismodelandcalcula-tionmethodforL0limareveriedbyexperiment/Threedifferentsizesofsplineareused/andthreee
24、xperimentalmaterialsareapplied/polycabonate/20CrMosteeland20CrMnTisteel/Theirstressstraincurvesareobtained188Table2Z/Huang/P/Fu/JournalofMaterialsProcessingTechnology114(2001)185188andthatthetheoreticalanalysisandcalculationmethodareComparisonofexperimentalvalueswithcalculatedvaluesExperimentalmater
25、ialPolycarbonate20CrMosteel20CrMnTisteelExperimentalvalue5/602/863/42ofL0lim(mm)Calculatedvalueof7/203/524/52L0lim(mm)Error(%)28/6231/3032/25Fig/5/Splineshafts/(a)withoutand(b)withadeadzone/bytensiletesting/TherangeofcriticalangleisgainedbytheUBM6/7/thenanexperimentaldieanglelargerthanthecriticalang
26、leischosenandthecoldextrusionofasplineiscarriedout/TheexperimentalvaluesandcalculatedresultsarecomparedinTable2/Thecalculatedresultsagreewellwiththeexperimentalresults/theerroroftheUBMbeing30%orso/ConsideringthatthevaluescalculatedbytheUBMarealwaysgreaterthan(orequalto)theactualvalues/theauthorsbeli
27、evethatitissafetochoosethesevaluesintheengineeringdesign/Finally/theactualformingprocessofthecoldextrusionofthesplineshaftofamotorcycletransmissionisdoneonthebasisoftheaboveresults/Here20CrMnTisteelisused/andtheparametersofthestraight-sidesplinewith6teethareasfollows/R110/125mm/R28/32mm/b4/825mm/The
28、maximumcriticalsemi-angleisacr226/68(valueobtainedfromtheUBM7)/Intheexperiments/twodieangles/a30anda45/arechosen/Whena45/theguidinglengthisL0lim4/81mm7/Intheexperiments/theguidinglengthL0/4/9mm/isaddedinsuchacondition/Twogroupsofbilletsareannealedforsoftening/andlubricatedbyphosphatecoating/andthenc
29、oldextruded/TheresultsareshowninFig/5/Fig/5(a)givesthecriticalstatea30/wherenobulgingappears/Alloftheaboveaccordswellwiththecalculatedresults/InFig/5(b)/thedieangleisa45(largerthanacr2)/andthereisadeadmetalzoneuponthedieangleentrance/exhibitingawhitezoneontheextrudedshaftbecausethelocallubricantsare
30、tornaway/Withenoughguidinglength/thecoldextrusionofasplineshaftcanbeaccomplishedsmoothly/Aboveexperimentsalsoverifythatthesolutionmethodofbulgingisfeasible/reasonable/5/Conclusions1/Themethodofsolvingthebulgingproblemisputforwardasfollows/addingaguidinglengthatthedieentrancetorestraintheexpansionoft
31、hebulgingsothattheextrusioncanbeaccomplishedsuccessfully/2/Thetheoreticalanalysismodelofthesolutiontothebulgingproblemisfound/Whenaacr2/theguidinglengthrestrainsbulgingsothatthebulgedmetalformsadeadzone/whiletheotherpartshearsthroughtheeasiestflowingchannel/andthensoundmetalflowcontinues/3/Thecalcul
32、ationmethodforL0limisalsopresented/Whenaacr2/m1isselectedandaisusedasoptimalparameter/AllofthesefactorsaresubstitutedintotheUBM/whenminimizingthepvalue/theoptimalangleisjusta1/andL0limisdeterminedbycalculatingthedistancebetweena1andaintheaxialdirection/4/Thegoodagreementofthecalculatedresultswiththe
33、theoreticalvaluesshowsthatnotonlyisthesolutionmethodofthebulgingproblemfeasible/butalsotherelevanttheoreticalanalysisandcalculationarereliable/References1S/Fujikawa/H/Yoshioka/S/Shimamura/Coldandwarm-forgingapplicationsintheautomotiveindustry/J/Mater/Process/Technol/35(1992)317341/2H/Hirschrogel/V/D
34、onmelen/Someapplicationsofcoldandwarmforging/J/Mater/Process/Technol/35(1992)343356/3Z/C/Zhang/J/Li/Experimentalstudyonopen-diecoldextrusionformingtechniqueforinvolatesplineshaft/ChineseJ/Mech/Eng/9(1996)612(inChinese)/4L/L/Jia/Anupperboundanalysisforextrusionofspline/in/AdvancedTechnologyofPlastici
35、ty/ProceedingoftheFourthInternationalConferenceonTechnologyofPlasticity/Beijing/China/1993/pp/582586/5D/Y/Yang/C/H/Han/M/U/Kim/Ageneralizedmethodforanalysisofthree-dimensionalextrusionofarbitrarilyshapedsections/Int/J/Mech/Sci/28(1986)517534/6P/F/Fu/Z/H/Huang/Studyontheformingconditionofopen-diecold
36、extrusionforsplineshaft/J/Agric/Mech/28(1997)129133(inChinese)/7Z/H/Huang/Ph/D/Thesis/JilinUniversityofTechnology/China/1998(inChinese)/8K/Ito/Newmodelmaterialsforphotoelasticityandphotoplasticity/Agric/Mech/2(1962)373376/9Z/H/Huang/P/F/Fu/Three-dimensionalphotoelasticstudyonthedeformationofasplineshaftincoldextrusion/J/Exp/Mech/14(1999)3540(inChinese)/10B/Avitzur/MetalForming/ProcessandAnalysis/LehighUniversity/NewYork/1979/pp/5020011B/Avitzur/HandbookofMetal-formingProcess/LehighUniversity/NewYork/1983/pp/61130
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