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