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JournalofZhejiangUniversitySCIENCEAISSN1673565XPrintISSN18621775Onlinewwwzjueducn/jzuswwwspringerlink.comEmailjzuszjueducaLfefal/JZhejiangUnivSciA20078710771083SinglegateoptimizationforplasticinjectionmoldLIJiquan十,LIDequn,GUOZhiying,LVHaiyuanDepartmentofPlasticityTechnology,ShanghaiJiaoTongUniversity,Shanghai200030,ChinaEmailhutli163.cornReceivedNov.22,2006revisionacceptedMar.19,20071077AbstractThispaperdealswithamethodologyforsinglegatelocationoptimizationforplasticinjectionmold.Theobjectiveofthegateoptimizationistominimizethewarpageofinjectionmoldedparts,becausewarpageisacrucialqualityissueformostinjectionmoldedpartswhileitisinfluencedgreatlybythegatelocation.Featurewarpageisdefinedastheratioofmaximumdisplacementonthefeaturesurfacetotheprojectedlengthofthefeaturesurfacetodescribepartwarpage.Theoptimizationiscombinedwiththenumericalsimulationtechnologytofindtheoptimalgatelocation,inwhichthesimulatedannealingalgorithmisusedtosearchfortheoptimum.Finally,anexampleisdiscussedinthepaperanditcanbeconcludedthattheproposedmethodiseffectiveKeywordsInjectionmold,Gatelocation,Optimization,Featurewarpagedoi10.1631/jzus.2007.A1077DocumentcodeACLCnumberTQ320.66INTRODUCTIONPlasticinjectionmoldingisawidelyused.complexbuthighlyefficienttechniqueforproducingalargevarietyofplasticproducts,particularlythosewithhighproductionrequirement,tighttolerance,andcomplexshapes.Thequalityofinjectionmoldedpartsisafunctionofplasticmaterial,partgeometry,moldstructureandprocessconditions.Themostimportantpartofaninjectionmoldbasicallyisthefollowingthreesetsofcomponentscavities,gatesandrunners,andcoolingsystem.LamandSeow2000andJinandLain2002achievedcavitybalancingbyvaryingthewallthicknessofthepart.Abalancefillingprocesswithinthecavitygivesanevenlydistributedpressureandtemperaturewhichcandrasticallyreducethewarpageofthepart.Butthecavitybalancingisonlyoneoftheimportantinfluencingfactorsofpartqualities.Especially。theparthasitsfunctionalrequirements.anditsthicknessesshouldnotbevariedusually.ProjectNo.50675080supportedbytheNationalNaturalScienceFoundationofChinaFromthepointviewoftheinjectionmolddesign,agateischaracterizedbyitssizeandlocation.andtherunnersystembythesizeandlayout.ThegatesizeandruIlllerlayoutareusuallydeterminedasconstants.Relatively,gatelocationsandrunnersizesaremoreflexiblewhichcanbevariedtoinfluencethequalityofthepart.Asaresult,theyareoftenthedesignparametersforoptimization.LeeandKimrl996aoptimizedthesizesofrunnersandgatestobalancerunnersystemformultipleinjectioncavities.Therunnerbalancingwasdescribedasthedifferencesofentrancepressuresforamulticavitymoldwithidenticalcavities.andasdifferencesofpressuresattheendofthemeltflowpathineachcavityforafamilymoldwimdifferentcavityvolumesandgeometries.Themethodologyhasshownuniformpressuredistributionsamongthecavitiesduringtheentiremoldingcycleofmultiplecavitiesmold.Zhaieta1.2005a1presentedthetwogatelocationoptimizationofonemoldingcavitybyanef前一cientsearchmethodbasedonpressuregradientPGSS,andsubsequentlypositionedweldlinestothedesiredlocationsbyvaryingrunnersizesfor维普资讯http//www.cqvip.com1078L,ea1./dZhejiangUnivSciA20078710771083multigatepartsZhaieta1.,2006.Aslargevolumepart,multiplegatesareneededtoshortenthemaxi.mumflowpath,withacorrespondingdecreaseininjectionpressure.Themethodispromisingforde.signofgatesandrunnersforasinglecavitywichmultiplegates.Manyofinjectionmoldedpartsareproducedwithonegate.whetherinsinglecavitymoldorinmultiplecavitiesmold.Therefore.thegatelocationofasinglegateisthemostcommondesignparameterforoptimization.AshapeanalysisapproachwaspresentedbyCOHrbebaisseandGarcia2002,bywhichthebestgatelocationofiniectionmoldingwasesti.mated.Subsequently,theydevelopedthismethodo1.ogyfurtherandappliedittosinglegatelocationoptimizationofanLshapeexampleCourbebaisse,2005.Itiseasytouseandnottime.consuming.whileitonlyservestheturningofsimpleflatpartswichuniforii1thickness.PandelidisandZour1990presentedtheopti.mizationofgatelocation.byindirectqualitymeasuresrelevanttowarpageandmaterialdegradation.whichisrepresentedasweightedsumofatemperaturedifferentialterm.anover.packterm.andafrictionaloverheatingterm.Warpageisinfluencedbytheabovefactors.buttherelationshipbetweenthemisnotclear.Therefore,theoptimizationeffectisrestrictedbythedeterminationoftheweightingfactors.LeeandKimrl996bdevelopedanautomatedselectionmethodofgatelocation,inwhichasetofinitialgatelocationswereproposedbyadesignerandthentheoptimalgatewaslocatedbytheaacentnodeevaluationmethod.Theconclusiontoagreatextentdependsmuchonthehumandesignersintuition.becausethefirststepofthemethodisbasedonthedesignersproposition.Sotheresultistoalargeex.tentlimitedtothedesignersexperience.LamandJin200l、developedagatelocationoptimizationmethodbasedontheminimizationoftheStandardDeviationofFlowPathLengthSDLandStandardDeviationofFillingTimeSDTduringthemoldingfillingprocess.Subsequently,Shenet口,.004a2004boptimizedthegatelocationdesignbyminimizingtheweightedsumoffillingpressure,fillingtimedifferencebetweendifferentflowpaths,temperaturedifference,andoverpackpercentage.Zhaieta1.2005binvestigatedoptimalgatelocationwithevaluationcriteriaofiniectionpressureattheendoffilling.Theseresearcherspresentedtheobiec.tivefunctionsasperformancesofiniectionmoldingfillingoperation,whicharecorrelatedwithproductqualities.Butthecorrelationbetweentheperforii1.ancesandqualitiesisverycomplicatedandnoclearrelationshiphasbeenobservedbetweenthemyet.Itisalsodifficulttoselectappropriateweightingfactorsforeachterm.Anewobjectivefunctionispresentedheretoevaluatethewarpageofinjectionmoldedpartstooptimizegatelocation.Tomeasurepartqualitydirectly,thisinvestigationdefinesfeaturewarpagetoevaluatepartwarpage,whichisevaluatedfromtheflowpluswarpagesimulationoutputsofMoldflowPlasticsInsightMPIsoftware.Theobjectivefunctionisminimizedtoachieveminimumdeformationingatelocationoptimization.Simulatedannealingalgorithmisemployedtosearchfortheoptimalgatelocation.Anexampleisgiventoillustratetheeffectivityoftheproposedoptimizationprocedure.QUALITYMEASURESFEATUREWARPGEDefinitionoffeaturewarpageToapplyoptimizationtheorytothegatedesign,qualitymeasuresofthepartmustbespecifiedinthefirstinstance.Thetermqualitymaybereferredtomanyproductproperties,suchasmechanical,thermal,electrical,optical,ergonomicalorgeometricalproperties.Therearetwotypesofpartqualitymeasuresdirectandindirect.Amodelthatpredictstheproper.tiesfromnumericalsimulationresultswouldbecharacterizedasadirectqualitymeasure.Incontrast.anindirectmeasureofpartqualityiscorrelatedwithtargetquality,butitcannotprovideadirectestimateOfchatquality.Forwarpage,theindirectqualitymeasuresinrelatedworksareoneofperformancesofiniectionmoldingflowingbehaviororweightedsumofthose.Theperformancesarepresentedasfillingtimedifferentialalongdifferentflowpaths.temperaturedifferential,overpackpercentage,andsoon.Itisobviousthatwarpageisinfluencedbytheseperforii1.ances,buttherelationshipbetweenwarpageandtheseperformancesisnotclearandthedeterminationoftheseweightingfactorsisratherdifficult.Therefore.theoptimizationwiththeaboveObiectivefunction维普资讯http//www.cqvip.comLfefal/JZhejiangUnivSciA2007810771083probablywillnotminimizepartwarpageevenwithperfectoptimizationtechnique.Sometimes,improperweightingfactorswillresultinabsolutelywrongresults.Somestatisticalquantitiescalculatedfromthenodaldisplacementswerecharacterizedasdirectqualitymeasurestoachieveminimumdeformationinrelatedoptimizationstudies.Thestatisticalquantitiesareusuallyamaximumnodaldisplacement,anaverageoftop10percentilenodaldisplacements,andanoverallaveragenodaldisplacementLeeandKim,l995I996b.ThesenodaIdisplacementsareeasytoobtainfromthesimulationresults,thestatisticalvalues,tosomeextents,representingthedeformation.Butthestatisticaldisplacementcannoteffectivelydescribethedeformationofthein_iectionmoldedparts.Inindustry.designersandmanufacturersusuallypaymoreattentiontothedegreeofpartwarpageonsomespecificfeaturesthanthewholedeformationofthein.,_iectionmoldedpartsInthisstudyfeaturewarpageisdefinedtodescribethedeformationoftheinjectionparts.ThefeaturewarpageistheratioofthemaximumdisplacementofthefeaturesurfacetotheprojectedlengthofthefeaturesurfaceFig.1_h100%,Lwhereyisthefeaturewarpage,histhemaximumdisplacementonthefeaturesurfacedeviatingfromthereferenceplatform,andListheprojectedlengthofthefeaturesurfaceonareferencedirectionparallelingthereferenceplatform.SurfaceceplaneFig.1ThedefinitionoffeaturewarpageForcomplicatedfeaturesonlyplanefeaturediscussedhere,thefeaturewarpageisusuallyseparatedintotwoconstituentsonthereferenceplane,whicharerepresentedona2Dcoordinatesystemhl0l00o/o,1079where,yyaretheconstituentfeaturewarpagesintheXYdirectionandLx,LaretheprojectedlengthsofthefeaturesurfaceonYcomponent.EvaluationoffeaturewarpageAtierthedeterminationoftargetfeaturecombinedwithcorrespondingreferenceplaneandproiectiondirection,thevalueofLcanbecalculatedimmediatelyfromthepartwiththecalculatingmethodofanalyticgeometryFig.2.Lisaconstantforanypartonthespecifiedfeaturesurfaceandproiecteddirection.ButtheevaluationofhismorecomplicatedthanthatofL.yFeatureFig.2TheprojectedlengthevaluationSimulationofiniectionmoldingprocessisacommontechniquetoforecastthequalityofpartdesign,molddesignandprocesssettings.TheresultsofwarpagesimulationareexpressedasthenodaldeflectionsonZcomponent,,,andthenodaldisplacementWisthevectorlengthofvectorsumof,,andWzk,where,,karetheunitvectorsonZcomponent.Thehisthemaximumdisplacementofthenodesonthefeaturesurface,whichiscorrelatedwiththenormalorientationofthereferenceplane,andcanbederivedfromtheresultsofwarpagesimulation.Tocalculateh.thedeflectionoffthnodeisevaluatedfirstlyasfollowsCOSOcosflW,zcosy一%%,3whereisthedeflectioninthenormaldirectionofthereferenceplaneofithnodeW,WI1、,WizarethedeflectionsonX,Y,Zcomponentofithnode伐,B,aretheanglesofnormalvectorofthereferenceAandBaretheterminalnodesofthefeaturetoproiectingdirectionFig.2andarethedeflectionsofnodesAand维普资讯http//www.cqvip.com1080Lfefal/dZhefiangUnivSciA20078.10771083fCOSacosflcosy,lCOSacosflGzcosy,whereWA,WAy,arethedeflectionsonZcomponentofnodeWsx,andWezarethedeflectionsonX,Y,ZcomponentofnodeCOiAand∞lBaretheweightingfactorsoftheterminalnodedeflectionscalculatedasfollows2iA1一LiA/L,co1一JiA,whereLiAistheprojectordistancebetweenfthnodeandnodeA.Ultimately,histhemaximumoftheabsolutevalueofhmax{lI,I.,1}}Inindustry,theinspectionofthewarpageiscarriedoutwiththehelpofafeelergauge,whilethemeasuredpartshouldbeplacedonareferenceplatform.Thevalueofhisthemaximumnumericalreadingofthespacebetweenthemeasuredpartsurfaceandthereferenceplatform.GATEL0CAT10N0PTIMIZAT10NPR0BLEMFORMATIONThequalitytermwarpagemeansthepermanentdeformationofthepart,whichisnotcausedbyanappliedload.Itiscausedbydifferentialshrinkagethroughoutthepart,duetotheimbalanceofpolymerflow,packing,cooling,andcrystallization.Theplacementofagateinaniniectionmoldisoneofthemostimportantvariablesofthetotalmolddesign.Thequalityofthemoldedpartisgreatlyaffectedbythegatelocation.becauseitinfluencesthemannerthattheplasticf1owsintothemoldcavity.Therefore,differentgatelocationsintroduceinhomogeneityinorientation,density,pressure,andtemperaturedistribution,accordinglyintroducingdifferentvalueanddistributionofwarpage.Therefore.gatelocationisavaluabledesignvariabletominimizetheinjectionmoldedpartwarpage.Becausethecorrelationbetweengatelocationandwarpagedistributionistoalargeextentindependentofthemeltandmoldtemperatureitisassumedthatthemoldingconditionsarekeptconstantinthisinvestigation.Theinjectionmoldedpartwarpageisquantifiedbythefeaturewarpagewhichwasdiscussedintheprevioussection.Thesinglegatelocationoptimizationcanthusbeformulatedasfo11owsMinimizeminiX,SubjecttogXP/Po一10,X∈X,i1,2,,N,where,isthefeaturewarpagePistheinjectionpressureatthegatepositionP0istheallowableiniectionpressureofinjectionmoldingmachineortheallowableinjectionpressurespecifiedbythedesignerormanufacturerXisthecoordinatevectorofthecandidategatelocationsisthenodeonthefiniteelementmeshmodelofthepartforinjectionmoldingprocesssimulationNisthetotalnumberofnodes.Inthefiniteelementmeshmodelofthepart,everynodeisapossiblecandidateforagate.Therefore,thetotalnumberofthepossiblegatelocationⅣnisafunctionofthetotalnumberofnodesNandthetotalnumberofgatelocationstobeoptimizedNN一1Ⅳ一一1Inthisstudy,onlythesinglegatelocationproblemisinvestigated.SIMULATEDANNEALINGALG0RITHMThesimulatedannealingalgorithmisoneofthemostpowerfulandpopularmetaheuristicstosolveoptimizationproblemsbecauseoftheprovisionofgoodglobalsolutionstorealworldproblems.ThealgorithmisbaseduponthatofMetropoliseta1.1953,whichwasoriginallyproposedasameanstofindanequilibriumconfigurationofacollectionofatomsatagiventemperature.TheconnectionbetweenthisalgorithmandmathematicalminimizationwasfirstnotedbyPincusr1970.butitwasKirkpatricketa1.1983whoproposedthatitformedthebasisofanoptimizationtechniqueforcombinationalandotherproblems.Toapplythesimulatedannealingmethodtoop维普资讯http//www.cqvip.com
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