Determination of optimal shapes for the stampings of arbitrary shapes

JournalofMaterialsProcessingTechnology121(2002)116±122

Determinationofoptimalshapesforthestampingsofarbitraryshapes

HyunboShim

DepartmentofMechanicalEngineering,YeungnamUniversity,214-1Daedong,Gyongsan712749,SouthKorea

Received29February2000;receivedinrevisedform15November2001;accepted15November2001

Abstract

Thesensitivitymethodhasbeenusedinthisstudyinorderto®ndinitialblankshapeswhichwillresultinthedesiredshapesafterdeformation.Byassumingthe®nalshapetobethedrawncupwithuniformtrimmingwidthatthe¯ange,thecorrespondinginitialblankwhichgivesthe®nalshapeafterdeformationhasbeenfound.Withtheaidofawell-knowndynamicexplicitanalysiscodePam-Stamp1,shapesensitivityhasbeenobtained.Toobtaintheshapesensitivitynumerically,acoupleofdeformationprocesseshavetobeanalyzedateachdesignstage.Drawingoftrapezoidalcup,oilpan,andAUDIfrontdoorpanel,thebenchmarktestproblemofNumisheet'99havebeenchosenastheexample.Ateverycasetheoptimalblankshapehasbeenobtainedafteronlyafewstepsofmodi®cationwithoutanyassumeddeformationpath.Withthepredictedoptimalblank,bothcomputersimulationandexperimentareperformed.Excellentagreementsareobtainedbetweensimulationandexperimentineverycase.Throughthepresentinvestigation,thesensitivitymethodisfoundtobeveryeffectiveinthedesignofarbitraryshapeddrawingprocesses.#2002ElsevierScienceB.V.Allrightsreserved.

Keywords:Optimalblankdesign;Sensitivityanalysis;Arbitraryshapedcup

1.Introduction

Traditionallytheoptimalblankisreferredtoaninitialblankshapetoproduceanetshape.Inthestrictsenseoftheword,thenetshapemeansthatthetrimmingprocessiseliminatedcompletelyinformingprocess.Howeverformingwithouttrimmingisverydif®cultandriskyalthoughnotimpossiblesinceevensmallvariationofprocessparameterscanresultindefects.Assumingthattheoptimalblankisreferredtoaninitialblankshapetoproduceadesiredshapewhichincludestrimmingallowance,theprocessdesignofdeepdrawingbecomeseasytohandle.

Ingeneral,sheetmetalformingprocessesinthemodernindustriesdealwithcomplicatedshapesandtheformingprocessconsistsofseveralsuccessiveoperationsuntilthe®nalshapeisformed.Becauseofthecomplexity,3DCADsystemisanecessarytoolinthesheetmetalproductdesign.Withthe3DCADdataoftheproduct,diesurfacetoproducetheproductcanbemachinedbytheCAMandthedeforma-tionprocesscanbeanalyzedbyaCAEtechnique.

Optimalblankhasmanyevidentadvantages.Theoptimalblanknotonlyimprovesformabilityandproductqualitybutalsoreducesmaterialcost,numberoftrialsinthetry-outstageandtheconsequentproductdevelopmenttime.How-ever,itisnoteasyto®ndtheoptimalblankbecauseofthecomplexityofdeformationbehavior,especiallyintheactualstampingdiesdescribedwith3DCADsystem.

Sincetheoptimalblankdesignisanattractivesubjecttothesheetmetalengineersandtheultimategoalofprocessdesign,severalmethodshavebeendevisedandlotsofdifferentapproachesarecurrentlyused.Amongthemeth-ods,slipline®eldmethod[1±5],geometricmappingmethod[6,7],trial-and-errormethodbasedonFEmethod[8±10],inversemethod[11±13],idealforming[14],backwardtra-cing[15],volumeaddition/subtractionmethod[16],analogymethod[17,18],constrainedoptimizationmethod[19],anddeformationpathiterationmethod[20]areworthwhile.Recently,asensitivitymethod[21]hasbeenproposedbytheauthorsandsuccessfullyappliedtothedrawingofsquarecup,clovercupandL-shapedcup.

Inthisstudy,asystematicmethodbasedonthesensitivitymethodhasbeenappliedto®ndoptimalblankfordeepdrawingofarbitraryshapecupsdescribedbya3DCADsystem.Themethodhasbeenvalidatedbycarryingoutexperimentwiththeoptimalshapepredictedwithsensitivitymethod.

2.Theoreticalprinciples

Fig.1showsthemovementofanodeontheoutline.Thenodewillmovealonganonlinearpathduringdeformation.Consequently,the®nalmovingdirectionwillbedifferentfromtheinitialdirection.Asmallvariationofthe

initial

0924-0136/02/$±seefrontmatter#2002ElsevierScienceB.V.Allrightsreserved.PII:S0924-0136(01)01222-5

H.Shim/JournalofMaterialsProcessingTechnology121(2002)116±122117

Fig.1.Movement

ofanoutermostnode.

positionthenodedesiredoftheshapenodeafterresultsinadifferent®nalposition.Thattion.initialInonordertheoutlinetomakeisformingonthetargetisobtainedcontourmeansafterthatdeforma-everytheamountpositionofshapeofthethenodenodesshouldliebeonrepositionedthetargetcontour,basedtheonlocatedLetrepresenttheerror.

positionvectorofamaterialpointanddeformation.

representattheoutlinethepositionofaninitialvectorblankofthebeforematerialdeformationafter®nalanalyzedWiththeinitialblankde®nedbydeformationprocessisFig.bythePam-Stamp1.Fig.2describesdetailsofdeformedIf1todoesexplainnotthelieconceptonthetargetoferrorcontourcorrection.

,hencethepositionbeofshapethecannotresultinthedesiredshape,thewithmovedshapethetargetinordermaterialcontourtomakepointbeforedeformationshouldthedeformedcontourcoincide.changed.sensitivity,byconsideringTheshapethetwosensitivityshapeByofblanks,originalhasinitialintroducingtheconceptofbeenblank,i.e.canbeblankderivedandoffsetnumericallyblank.resultTheofoffsetFEanalysisblankshapewiththehasinitialbeenblankdeterminedde®nedfrombythe d(1)

wherethedrepresentstheunitoutlineamountvectorofinthepositionvectorofanodelocatedattheoffsetmovingblankbeforedeformation.isthemationofoffset.Withthedirectionoffsetblankatthede®ned®rststep.bydisthe,defor-materialprocesshasbeenanalyzedagaintoobtaindtheasThesensitivitypointpositionfortheafterdeformationdeformationateachforthenodeoffsetisde®nedblank.S

(2)

Ifdeformation,,thepositioncoincidesofnodewithatoutlineoftheblankafterTwhichliesonthetarget

Fig.(b)final2.Conceptstate.

ofsensitivityandcontourerrorcorrection:(a)initialstate;contour,ofthereisnoneedtomovetheinitialUnlessinitialblank.

correspondingnodepositionliesonshouldthetargetbemovedcontour,bythenthecorresponding i iÀ1 e(3)

wheredistanceeisthedirectionbetweenshapeSuperscripterrorofeachnode,de®nedastheTand(i)measuredmeansthealongnumberthe®nalofiterations.movinganalyzedAfterblankoutermostagainshapeuntilemodi®cation,reachesaspeci®eddeformationtoleranceprocessatisoptimalblanknode.designFig.3method.

shows¯owthechartofthepresenteveryshapeTheerrorisconvergencedependentonofthetheamountpresentofmethodoffsettodandgettheanoptimalcontourthesizeallowance,oftheblank.whichshouldbedeterminedaccordingto3.Examples

drawingsUsingthesensitivitymethod,optimalblanksforthedeeppanel,beentheofbenchmarkatrapezoidaltestcup,problemoilpan,ofandAUDIfrontdoortionWithfound.

Numisheet'99,havefrontandtheoptimaldoorexperimentpredictedpanelforming.wereoptimalblank,bothcomputersimula-Incarriedorderouttocarryexceptoutforexperiment,theAUDITheness.sheetblanksTablemetalare1showsusedpreparedtheiscold-rolledbyawirecuttingforeachcase.material

propertiessteelof0.76ofthemmblank.

thick-

118H.Shim/JournalofMaterialsProcessingTechnology121(2002)116±122

Fig.3.Optimalblankdesignprocedure.

3.1.Trapezoidalcupdeepdrawing

inDieshapeFig.geometryof4.thef130blankcircularfortrapezoidalcupdeepdrawingisshownto®ndblankoptimalhasbeenshapechosenforthisastheprocess.

initialFig.4.Diegeometryfortrapezoidalcupdeep

drawing.

TableMaterial1

propertyoftheblankYoung'sPoisson'smodulusE 2Â105RrationStress±strain-value

R MPas 0:3Coulomb'srelationoffriction

coefficientm 1 514:38

0:24 0punch:001 =sheete 0:2 MPa

;m 0:12 die=sheet

shapeThe¯ange.withtargetshapeafterdeformationisdeterminedastheerrorTheuniformoffsetdistrimmingtakenaswidth1.0mmof1.75mmattheblank,allowancepunchdeformationistakenas0.5mm.WithandthegiventhecontourinitialcedureFig.displacementprocesshasbeenanalyzeduntilthe5reaches20mmwithPam-Stamp1.targetbyshowscomparingtheevolutionthedeformedofoptimal¯angeblankcontourdesignandpro-analysis.shape.withFig.The5(a)deformedshowstheshape¯angeisobtainedfromthetheFEcupf130circularblank.The¯angecontourcontourofofdrawnthedrawncupandexhibitsstages,(c)showssomethedeviation¯angecontoursfromtargetof2ndcontour.andFig.5(b)sensitivityrespectively,tionmethod.Aswhichtheshapeisdeterminederrorbythe3rdpresentdesign0.5mmofblankateveryreachedoutermostwithinnode,thecontoureaftertheblankerror2ndshapeallowancemodi®ca-has

been

ofFig.design5.(Blankf130);shapes(b)2ndanddesign;deformed(c)3rdflangedesignatthe(optimaldesignblank).

stages:(a)initial

H.Shim/JournalofMaterialsProcessingTechnology121(2002)116±122119

Fig.flange6.contour;Experimental(b)beforeresultsdrawing;forthe(c)optimalafter

drawing.

blank(trapezoidalcup):(a)determinedcupastheoptimalblankofthecuttingWithdrawingbeenmethod,thedeterminedatthepunchdisplacementpresentof20mm.

trapezoidalthetrapezoidaloptimalcupblank,drawingpreparedexperimentbyawireblankFig.carriedhas6showsout.

theexperimentalresultsfortheoptimal¯angeatthepunchdepthof20mm.Fig.6(a)showsthe¯angecontourscontourcontourspecimenalmostbeforeexactly.afterwithdeformationthecomparisonandafterFig.drawing6(b)andcoincidesoftargetshape.Theexperiment,(c)showswiththetherespectively.photostargetof3.2.Oilpandeepdrawing

oilInplicatedpanorderformingtotesthastheperformanceofthesensitivitymethod,formingshape.Thebeenmainchosencharacteristicsastheexampleofofcom-depthisthattheprocesscontainsrapidchangetheofdrawingoilpanprogressiveandhencegeometrycontactrisingbetweenwallwrinklepunchandisaptblank,tooccureffectdueoftoatThetargettransition.

theshapehascontourthe¯ange.errorallowanceTheoffsetuniformisdtakenistakentrimmingwidthof1.75mmas0.5asmm.1.0mmwhiletheFig.7.Diegeometryforoilpandeepdrawing.

Fig.Theprocedure7.dieFig.geometry8showstheforoilevolutionpandeepofdrawingisshownintheFEcupanalysis.targetshape.bycomparingthedeformedoptimal¯angeblankcontourdesignandFig.The8(a)deformedshowstheshape¯angeiscontourobtainedfromthedrawnwithf130circularblank.The¯angecontourofadrawnoftheFig.design8(b)cupandexhibits(c)showssomedeviationfromthetargetcontour.presentstages,respectively,the¯angewhichcontoursisdeterminedof2ndandby3rdmodi®cationsensitivityallowanceofblankmethod.reachedAstheshapeerroreafter2ndtheshapeof0.5mmateveryoutermostwithinthenode,contourtheblankerrorpresenthasoilbeenpandrawing.

determinedastheoptimalblankofthecuttingWithcarriedmethod,thedeterminedtheoiloptimalpandrawingblank,experimentpreparedbyhasabeenwireblank.Fig.9out.

showstheexperimentalresultswiththeoptimalcomparisonFig.9(a)afteroftargetshowsshape.the¯angecontourtogetherwiththethepantargetdeformationnearly,thoughThenotdeformedexactly,¯angecoincidescontourwithtobedrawingshape.verypromising.iscollected,HoweverFig.theifthe9(b)experimentdeformationbehaviorofoiland(c)showscanbetheconsideredphotos

of

120H.Shim/JournalofMaterialsProcessingTechnology121(2002)116±122

Fig.(a)initial8.Blankdesignshapes(f130);and(b)deformed2nddesign;flange(c)at3rdthedesigndesign(optimal

stages(oilblank).

pan):specimenexperiment,beforerespectively.

deformationandafterdrawingusedinthe3.3.AUDIfrontdoorpaneldrawing

panelAsthethesurfacewhere®naldatatheexample,dieisimportedsurfacetheisdrawingofanAUDIfrontdoortopreparedthePam-StampbyaCAD1systemandformatshownhavebeenanalyzed.DiegeometryforthisinprocessanIGESisthecedurecommitteeinFig.10.ofStartingNumisheet'99,fromtheoptimalblankshapepreparedbylyzedblanktoisthecarriedout.Deformationprocessblankhasdesignbeenpro-ana-shapeiswidtherrorapproximatelyfullstrokeofallowanceare900thistakenmm,diesetup.Sincethelengthofasboth5mmtheandoffsetdandtherespectively.

whichdeterminetargetshapeissetthebytrimming20mm,theFig.deformedchange11(a)±(c)oftheshows¯angethecontoursevolutionofofundeformeddesignstageswithcontourinitialstagedesignexhibitsshapestage.someandtargetAsdeviationshape.theshapefromTheshape,errortargetdeformed¯angeeatthecontour3rddesignintheeveryreachedoptimaloutermostwithinblankofnode,thethepresenttheshapeblankerrorallowanceof5mmatfrontshapedoorhaspanelbeendrawing.

chosenastheFig.contour;9.Experimental(b)beforedrawing;results(c)forafter

theoptimaldrawing.

blank(oilpan):(a)flangeFig.10.DiegeometryforAUDIfrontdoorpaneldrawing.

frontFig.12(a)and(b)showsthedeformedshapeblank,panelwiththegiveninitialblankshapeandtheofoptimalAUDImethodThroughrespectively.

theinvestigationtheinthedesignofoptimalofdeep

blankdrawing.

designisfoundproposedtobeverysystematiceffective

H.Shim/JournalofMaterialsProcessingTechnology121(2002)116±122121

Fig.11.Evolutionofoptimalblankdesignstages:(a)initialshape(Numisheet'99);(b)2nddesign;(c)3rddesign(optimal

blank).

Acknowledgements

ThisworkwassupportedbytheBrainKorea21Project.References

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Asystematicmethodofoptimalblankdesignbasedonthesensitivityanalysishasbeenappliedtothedrawingsofarbitraryshape.Fromtheresultofdeformationprocessanalysis,shapesensitivityhasbeenobtainednumerically.Withtheshapesensitivity,initialblankhasbeenmodi®edinordertoobtainthedesiredshape.Thenumericalandexperi-mentalresultsdemonstratethatthepresentmethodprovidesexcellentpredictionofblankshapeandtheblankshapegivesthetargetshapealmostexactly.Throughtheinvestigationtheproposedsystematicmethodofoptimalblankdesignisfoundtobeveryeffective.

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