IntJAdvManufTechnol(2002)19:2532592002Springer-VerlagLondonLimitedAnAnalysisofDraw-WallWrinklinginaStampingDieDesignF.-K.ChenandY.-C.LiaoDepartmentofMechanicalEngineering,NationalTaiwanUniversity,Taipei,TaiwanWrinklingthatoccursinthestampingoftaperedsquarecupsandsteppedrectangularcupsisinvestigated.Acommoncharacteristicofthesetwotypesofwrinklingisthatthewrinklesarefoundatthedrawwallthatisrelativelyunsup-ported.Inthestampingofataperedsquarecup,theeffectofprocessparameters,suchasthediegapandblank-holderforce,ontheoccurrenceofwrinklingisexaminedusingfinite-elementsimulations.Thesimulationresultsshowthatthelargerthediegap,themoresevereisthewrinkling,andsuchwrinklingcannotbesuppressedbyincreasingtheblank-holderforce.Intheanalysisofwrinklingthatoccurredinthestampingofasteppedrectangularcup,anactualproductionpartthathasasimilartypeofgeometrywasexamined.Thewrinklesfoundatthedrawwallareattributedtotheunbalancedstretchingofthesheetmetalbetweenthepunchheadandthestepedge.Anoptimumdiedesignforthepurposeofeliminatingthewrinklesisdeterminedusingfinite-elementanalysis.Thegoodagreementbetweenthesimulationresultsandthoseobservedinthewrinkle-freeproductionpartvalidatestheaccuracyofthefinite-elementanalysis,anddemonstratestheadvantageofusingfinite-elementanalysisforstampingdiedesign.Keywords:Draw-wallwrinkle；Stampingdie；Steppedrec-tangularcup；Taperedsquarecups1.IntroductionWrinklingisoneofthemajordefectsthatoccurinthesheetmetalformingprocess.Forbothfunctionalandvisualreasons,wrinklesareusuallynotacceptableinafinishedpart.Therearethreetypesofwrinklewhichfrequentlyoccurinthesheetmetalformingprocess:flangewrinkling,wallwrinkling,andelasticbucklingoftheundeformedareaowingtoresidualelasticcompressivestresses.Intheformingoperationofstamp-ingacomplexshape,draw-wallwrinklingmeanstheoccurrenceCorrespondenceandoffprintrequeststo:ProfessorF.-K.Chen,Depart-mentofMechanicalEngineering,NationalTaiwanUniversity,No.1RooseveltRoad,Sec.4,Taipei,Taiwan10617.E-mail:fkchenL50560.twofwrinklesinthediecavity.Sincethesheetmetalinthewallareaisrelativelyunsupportedbythetool,theeliminationofwallwrinklesismoredifficultthanthesuppressionofflangewrinkles.Itiswellknownthatadditionalstretchingofthematerialintheunsupportedwallareamaypreventwrinkling,andthiscanbeachievedinpracticebyincreasingtheblank-holderforce；buttheapplicationofexcessivetensilestressesleadstofailurebytearing.Hence,theblank-holderforcemustliewithinanarrowrange,abovethatnecessarytosuppresswrinklesontheonehand,andbelowthatwhichproducesfractureontheother.Thisnarrowrangeofblank-holderforceisdifficulttodetermine.Forwrinklesoccurringinthecentralareaofastampedpartwithacomplexshape,aworkablerangeofblank-holderforcedoesnotevenexist.Inordertoexaminethemechanicsoftheformationofwrinkles,Yoshidaetal.1developedatestinwhichathinplatewasnon-uniformlystretchedalongoneofitsdiagonals.Theyalsoproposedanapproximatetheoreticalmodelinwhichtheonsetofwrinklingisduetoelasticbucklingresultingfromthecompressivelateralstressesdevelopedinthenon-uniformstressfield.Yuetal.2,3investigatedthewrinklingproblembothexperimentallyandanalytically.Theyfoundthatwrinklingcouldoccurhavingtwocircumferentialwavesaccordingtotheirtheoreticalanalysis,whereastheexperimentalresultsindi-catedfourtosixwrinkles.NarayanasamyandSowerby4examinedthewrinklingofsheetmetalwhendrawingitthroughaconicaldieusingflat-bottomedandhemispherical-endedpunches.Theyalsoattemptedtorankthepropertiesthatappearedtosuppresswrinkling.Theseeffortsarefocusedonthewrinklingproblemsassocia-tedwiththeformingoperationsofsimpleshapesonly,suchasacircularcup.Intheearly1990s,thesuccessfulapplicationofthe3Ddynamic/explicitfinite-elementmethodtothesheet-metalformingprocessmadeitpossibletoanalysethewrinklingprobleminvolvedinstampingcomplexshapes.Inthepresentstudy,the3Dfinite-elementmethodwasemployedtoanalysetheeffectsoftheprocessparametersonthemetalflowcausingwrinklesatthedrawwallinthestampingofataperedsquarecup,andofasteppedrectangularpart.Ataperedsquarecup,asshowninFig.1(a),hasaninclineddrawwalloneachsideofthecup,similartothatexistinginaconicalcup.Duringthestampingprocess,thesheetmetalonthedrawwallisrelativelyunsupported,andistherefore254F.-K.ChenandY.-C.LiaoFig.1.Sketchesof(a)ataperedsquarecupand(b)netowrinkling.Inthepresentstudy,theeffectofvariousprocessparametersonthewrinklingwasinvestigated.Inthecaseofasteppedrectangularpart,asshowninFig.1(b),anothertypeofwrinklingisobserved.Inordertoestimatetheeffectivenessoftheanalysis,anactualproductionpartwithsteppedgeometrywasexaminedinthepresentstudy.Thecauseofthewrinklingwasdeterminedusingfinite-elementanalysis,andanoptimumdiedesignwasproposedtoeliminatethewrinkles.Thediedesignobtainedfromfinite-elementanaly-siswasvalidatedbyobservationsonanactualproductionpart.2.Finite-ElementModelThetoolinggeometry,includingthepunch,dieandblank-holder,weredesignedusingtheCADprogramPRO/ENGINEER.Boththe3-nodeand4-nodeshellelementswereadoptedtogeneratethemeshsystemsfortheabovetoolingusingthesameCADprogram.Forthefinite-elementsimul-ation,thetoolingisconsideredtoberigid,andthecorrespond-ingmeshesareusedonlytodefinethetoolinggeometryandFig.2.Finite-elementmesh.arenotforstressanalysis.ThesameCADprogramusing4-nodeshellelementswasemployedtoconstructthemeshsystemforthesheetblank.Figure2showsthemeshsystemforthecompletesetoftoolingandthesheet-blankusedinthestampingofataperedsquarecup.Owingtothesymmetricconditions,onlyaquarterofthesquarecupisanalysed.Inthesimulation,thesheetblankisputontheblank-holderandthedieismoveddowntoclampthesheetblankagainsttheblank-holder.Thepunchisthenmoveduptodrawthesheetmetalintothediecavity.Inordertoperformanaccuratefinite-elementanalysis,theactualstressstrainrelationshipofthesheetmetalisrequiredaspartoftheinputdata.Inthepresentstudy,sheetmetalwithdeep-drawingqualityisusedinthesimulations.Atensiletesthasbeenconductedforthespecimenscutalongplanescoincidingwiththerollingdirection(0)andatanglesof45and90totherollingdirection.TheaverageflowstressH9268,calculatedfromtheequationH9268H11005(H92680H110012H926845H11001H926890)/4,foreachmeasuredtruestrain,asshowninFig.3,isusedforthesimulationsforthestampingsofthetaperedsquarecupandalsoforthesteppedrectangularcup.AllthesimulationsperformedinthepresentstudywererunonanSGIIndigo2workstationusingthefinite-elementpro-gramPAMFSTAMP.TocompletethesetofinputdatarequiredFig.3.Thestressstrainrelationshipforthesheetmetal.Draw-WallWrinklinginaStampingDieDesign255forthesimulations,thepunchspeedissetto10msH110021andacoefficientofCoulombfrictionequalto0.1isassumed.3.WrinklinginaTaperedSquareCupAsketchindicatingsomerelevantdimensionsofthetaperedsquarecupisshowninFig.1(a).AsseeninFig.1(a),thelengthofeachsideofthesquarepunchhead(2Wp),thediecavityopening(2Wd),andthedrawingheight(H)arecon-sideredasthecrucialdimensionsthataffectthewrinkling.Halfofthedifferencebetweenthedimensionsofthediecavityopeningandthepunchheadistermedthediegap(G)inthepresentstudy,i.e.GH11005WdH11002Wp.Theextentoftherelativelyunsupportedsheetmetalatthedrawwallispresumablyduetothediegap,andthewrinklesaresupposedtobesuppressedbyincreasingtheblank-holderforce.Theeffectsofboththediegapandtheblank-holderforceinrelationtotheoccurrenceofwrinklinginthestampingofataperedsquarecupareinvestigatedinthefollowingsections.3.1EffectofDieGapInordertoexaminetheeffectofdiegaponthewrinkling,thestampingofataperedsquarecupwiththreedifferentdiegapsof20mm,30mm,and50mmwassimulated.Ineachsimulation,thediecavityopeningisfixedat200mm,andthecupisdrawntothesameheightof100mm.Thesheetmetalusedinallthreesimulationsisa380mmH11003380mmsquaresheetwiththicknessof0.7mm,thestressstraincurveforthematerialisshowninFig.3.Thesimulationresultsshowthatwrinklingoccurredinallthreetaperedsquarecups,andthesimulatedshapeofthedrawncupforadiegapof50mmisshowninFig.4.ItisseeninFig.4thatthewrinklingisdistributedonthedrawwallandisparticularlyobviousatthecornerbetweenadjacentwalls.Itissuggestedthatthewrinklingisduetothelargeunsupportedareaatthedrawwallduringthestampingprocess,also,thesidelengthofthepunchheadandthediecavityFig.4.Wrinklinginataperedsquarecup(GH1100550mm).openingaredifferentowingtothediegap.Thesheetmetalstretchedbetweenthepunchheadandthediecavityshoulderbecomesunstableowingtothepresenceofcompressivetrans-versestresses.Theunconstrainedstretchingofthesheetmetalundercompressionseemstobethemaincauseforthewrink-lingatthedrawwall.Inordertocomparetheresultsforthethreedifferentdiegaps,theratioH9252ofthetwoprincipalstrainsisintroduced,H9252beingH9280min/H9280max,whereH9280maxandH9280minarethemajorandtheminorprincipalstrains,respectively.HosfordandCaddell5haveshownthatiftheabsolutevalueofH9252isgreaterthanacriticalvalue,wrinklingissupposedtooccur,andthelargertheabsolutevalueofH9252,thegreateristhepossibilityofwrinkling.TheH9252valuesalongthecross-sectionMNatthesamedrawingheightforthethreesimulatedshapeswithdifferentdiegaps,asmarkedinFig.4,areplottedinFig.5.ItisnotedfromFig.5thatseverewrinklesarelocatedclosetothecornerandfewerwrinklesoccurinthemiddleofthedrawwallforallthreedifferentdiegaps.Itisalsonotedthatthebiggerthediegap,thelargeristheabsolutevalueofH9252.Consequently,increasingthediegapwillincreasethepossibilityofwrinklingoccurringatthedrawwallofthetaperedsquarecup.3.2EffectoftheBlank-HolderForceItiswellknownthatincreasingtheblank-holderforcecanhelptoeliminatewrinklinginthestampingprocess.Inordertostudytheeffectivenessofincreasedblank-holderforce,thestampingofataperedsquarecupwithdiegapof50mm,whichisassociatedwithseverewrinklingasstatedabove,wassimulatedwithdifferentvaluesofblank-holderforce.Theblank-holderforcewasincreasedfrom100kNto600kN,whichyieldedablank-holderpressureof0.33MPaand1.98MPa,respectively.Theremainingsimulationconditionsaremaintainedthesameasthosespecifiedintheprevioussection.Anintermediateblank-holderforceof300kNwasalsousedinthesimulation.Thesimulationresultsshowthatanincreaseintheblank-holderforcedoesnothelptoeliminatethewrinklingthatoccursatthedrawwall.TheH9252valuesalongthecross-sectionFig.5.H9252-valuealongthecross-sectionMNfordifferentdiegaps.256F.-K.ChenandY.-C.LiaoMN,asmarkedinFig.4,arecomparedwithoneanotherforthestampingprocesseswithblank-holderforceof100kNand600kN.ThesimulationresultsindicatethattheH9252valuesalongthecross-sectionMNarealmostidenticalinbothcases.Inordertoexaminethedifferenceofthewrinkleshapeforthetwodifferentblank-holderforces,fivecross-sectionsofthedrawwallatdifferentheightsfromthebottomtothelineMN,asmarkedinFig.4,areplottedinFig.6forbothcases.ItisnotedfromFig.6thatthewavinessofthecross-sectionsforbothcasesissimilar.Thisindicatesthattheblank-holderforcedoesnotaffecttheoccurrenceofwrinklinginthestamp-ingofataperedsquarecup,becausetheformationofwrinklesismainlyduetothelargeunsupportedareaatthedrawwallwherelargecompressivetransversestressesexist.Theblank-holderforcehasnoinfluenceontheinstabilitymodeofthematerialbetweenthepunchheadandthediecavityshoulder.4.SteppedRectangularCupInthestampingofasteppedrectangularcup,wrinklingoccursatthedrawwalleventhoughthediegapsarenotsosignificant.Figure1(b)showsasketchofapunchshapeusedforstampingasteppedrectangularcupinwhichthedrawwallCisfollowedbyastepDE.Anactualproductionpartthathasthistypeofgeometrywasexaminedinthepresentstudy.Thematerialusedforthisproductionpartwas0.7mmthick,andthestressstrainrelationobtainedfromtensiletestsisshowninFig.3.Theprocedureinthepressshopfortheproductionofthisstampingpartconsistsofdeepdrawingfollowedbytrimming.Inthedeepdrawingprocess,nodrawbeadisemployedonthediesurfacetofacilitatethemetalflow.However,owingtothesmallpunchcornerradiusandcomplexgeometry,asplitoccurredatthetopedgeofthepunchandwrinkleswerefoundtooccuratthedrawwalloftheactualproductionpart,asshowninFig.7.ItisseenfromFig.7thatwrinklesaredistributedonthedrawwall,butaremoresevereatthecorneredgesofthestep,asmarkedbyADandBEinFig.1(b).Themetalistornapartalongthewholetopedgeofthepunch,asshowninFig.7,toformasplit.Inordertoprovideafurtherunderstandingofthedefor-mationofthesheet-blankduringthestampingprocess,afinite-elementanalysiswasconducted.Thefinite-elementsimulationwasfirstperformedfortheoriginaldesign.ThesimulatedshapeofthepartisshownfromFig.8.ItisnotedfromFig.8thatthemeshatthetopedgeofthepartisstretchedFig.6.Cross-sectionlinesatdifferentheightsofthedrawwallfordifferentblank-holderforces.(a)100kN.(b)600kN.Fig.7.Splitandwrinklesintheproductionpart.Fig.8.Simulatedshapefortheproductionpa