Determination of optimal shapes for the stampings of arbitra(2)

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-