SinglegateoptimizationforplasticinjectionmoldAbstract:Abstract:Thispaperdealswithamethodologyforsinglegatelocationoptimizationforplasticinjectionmold.Theobjectiveofthegateoptimizationistominimizethewarpageofinjectionmoldedparts,becausewarpageisacrucialqualityissueformostinjectionmoldedpartswhileitisinfluencedgreatlybythegatelocation.Featurewarpageisdefinedastheratioofmaximumdisplacementonthefeaturesurfacetotheprojectedlengthofthefeaturesurfacetodescribepartwarpage.Theoptimizationiscombinedwiththenumericalsimulationtechnologytofindtheoptimalgatelocation,inwhichthesimulatedannealingalgorithmisusedtosearchfortheoptimum.Finally,anexampleisdiscussedinthepaperanditcanbeconcludedthattheproposedmethodiseffective.Keywords:Injectionmold,Gatelocation,Optimization,Featurewarpage.INTRODUCTIONPlasticinjectionmoldingisawidelyused,com-plexbuthighlyefficienttechniqueforproducingalargevarietyofplasticproducts,particularlythosewithhighproductionrequirement,tighttolerance,andcomplexshapes.Thequalityofinjectionmoldedpartsisafunctionofplasticmaterial,partgeometry,moldstructureandprocessconditions.Themostimportantpartofaninjectionmoldbasicallyisthefollowingthreesetsofcomponents:cavities,gatesandrunners,andcoolingsystem.LamandSeow(2000)andJinandLam(2002)achievedcavitybalancingbyvaryingthewallthick-nessofthepart.Abalancefillingprocesswithinthecavitygivesanevenlydistributedpressureandtem-peraturewhichcandrasticallyreducethewarpageofthepart.Butthecavitybalancingisonlyoneoftheimportantinfluencingfactorsofpartqualities.Espe-cially,theparthasitsfunctionalrequirements,anditsthicknessesshouldnotbevariedusually.Fromthepointviewoftheinjectionmolddesign,agateischaracterizedbyitssizeandlocation,andtherunnersystembythesizeandlayout.Thegatesizeandrunnerlayoutareusuallydeterminedasconstants.Relatively,gatelocationsandrunnersizesaremoreflexible,whichcanbevariedtoinfluencethequalityofthepart.Asaresult,theyareoftenthedesignpa-rametersforoptimization.LeeandKim(1996a)optimizedthesizesofrunnersandgatestobalancerunnersystemformul-tipleinjectioncavities.Therunnerbalancingwasdescribedasthedifferencesofentrancepressuresforamulti-cavitymoldwithidenticalcavities,andasdifferencesofpressuresatthe1endofthemeltflowpathineachcavityforafamilymoldwithdifferentcavityvolumesandgeometries.Themethodologyhasshownuniformpressuredistributionsamongthecavitiesduringtheentiremoldingcycleofmultiplecavitiesmold.Zhaietal.(2005a)presentedthetwogateloca-tionoptimizationofonemoldingcavitybyaneffi-cientsearchmethodbasedonpressuregradient(PGSS),andsubsequentlypositionedweldlinestothedesiredlocationsbyvaryingrunnersizesformulti-gateparts(Zhaietal.,2006).Aslarge-volumepart,multiplegatesareneededtoshortenthemaxi-mumflowpath,withacorrespondingdecreaseininjectionpressure.Themethodispromisingforde-signofgatesandrunnersforasinglecavitywithmultiplegates.Manyofinjectionmoldedpartsareproducedwithonegate,whetherinsinglecavitymoldorinmultiplecavitiesmold.Therefore,thegatelocationofasinglegateisthemostcommondesignparameterforoptimization.Ashapeanalysisapproachwaspre-sentedbyCourbebaisseandGarcia(2002),bywhichthebestgatelocationofinjectionmoldingwasesti-mated.Subsequently,theydevelopedthismethodol-ogyfurtherandappliedittosinglegatelocationop-timizationofanLshapeexample(Courbebaisse,2005).Itiseasytouseandnottime-consuming,whileitonlyservestheturningofsimpleflatpartswithuniformthickness.PandelidisandZou(1990)presentedtheopti-mizationofgatelocation,byindirectqualitymeasuresrelevanttowarpageandmaterialdegradation,whichisrepresentedasweightedsumofatemperaturedif-ferentialterm,anover-packterm,andafrictionaloverheatingterm.Warpageisinfluencedbytheabovefactors,buttherelationshipbetweenthemisnotclear.Therefore,theoptimizationeffectisrestrictedbythedeterminationoftheweightingfactors.LeeandKim(1996b)developedanautomatedselectionmethodofgatelocation,inwhichasetofinitialgatelocationswereproposedbyadesignerandthentheoptimalgatewaslocatedbytheadjacentnodeevaluationmethod.Theconclusiontoagreatextentdependsmuchonthehumandesignersintuition,becausethefirststepofthemethodisbasedonthedesignersproposition.Sotheresultistoalargeex-tentlimitedtothedesignersexperience.LamandJin(2001)developedagatelocationoptimizationmethodbasedontheminimizationoftheStandardDeviationofFlowPathLength(SDL)andStandardDeviationofFillingTime(SDT)duringthemoldingfillingprocess.Subsequently,Shenetal.(2004a；2004b)optimizedthegatelocationdesignbyminimizingtheweightedsumoffillingpressure,fillingtimedifferencebetweendifferentflowpaths,temperaturedifference,andover-packpercentage.Zhaietal.(2005b)investigatedoptimalgatelocationwithevaluationcriteriaofinjectionpressureattheendoffilling.Theseresearcherspresentedtheobjec-tivefunctionsas2performancesofinjectionmoldingfillingoperation,whicharecorrelatedwithproductqualities.Butthecorrelationbetweentheperform-ancesandqualitiesisverycomplicatedandnoclearrelationshiphasbeenobservedbetweenthemyet.Itisalsodifficulttoselectappropriateweightingfactorsforeachterm.Anewobjectivefunctionispresentedheretoevaluatethewarpageofinjectionmoldedpartstooptimizegatelocation.Tomeasurepartqualitydi-rectly,thisinvestigationdefinesfeaturewarpagetoevaluatepartwarpage,whichisevaluatedfromthe“flowpluswarpage”simulationoutputsofMoldflowPlasticsInsight(MPI)software.Theobjectivefunc-tionisminimizedtoachieveminimumdeformationingatelocationoptimization.Simulatedannealingal-gorithmisemployedtosearchfortheoptimalgatelocation.Anexampleisgiventoillustratetheeffec-tivityoftheproposedoptimizationprocedure.QUALITYMEASURES:FEATUREWARPGEDefinitionoffeaturewarpageToapplyoptimizationtheorytothegatedesign,qualitymeasuresofthepartmustbespecifiedinthefirstinstance.Theterm“quality”maybereferredtomanyproductproperties,suchasmechanical,thermal,electrical,optical,ergonomicalorgeometricalprop-erties.Therearetwotypesofpartqualitymeasures:directandindirect.Amodelthatpredictstheproper-tiesfromnumericalsimulationresultswouldbecharacterizedasadirectqualitymeasure.Incontrast,anindirectmeasureofpartqualityiscorrelatedwithtargetquality,butitcannotprovideadirectestimateofthatquality.Forwarpage,theindirectqualitymeasuresinrelatedworksareoneofperformancesofinjectionmoldingflowingbehaviororweightedsumofthose.Theperformancesarepresentedasfillingtimedif-ferentialalongdifferentflowpaths,temperaturedif-ferential,over-packpercentage,andsoon.Itisob-viousthatwarpageisinfluencedbytheseperform-ances,buttherelationshipbetweenwarpageandtheseperformancesisnotclearandthedeterminationoftheseweightingfactorsisratherdifficult.Therefore,theoptimizationwiththeaboveobjectivefunctionprobablywillnotminimizepartwarpageevenwithperfectoptimizationtechnique.Sometimes,improperweightingfactorswillresultinabsolutelywrongre-sults.Somestatisticalquantitiescalculatedfromthenodaldisplacementswerecharacterizedasdirectqualitymeasurestoachieveminimumdeformationinrelatedoptimizationstudies.Thestatisticalquantitiesareusuallyamaximumnodaldisplacement,anav-erageoftop10percentilenodaldisplacements,andanoverallaveragenodaldisplacement(LeeandKim,31995；1996b).Thesenodaldisplacementsareeasytoobtainfromthesimulationresults,thestatisticalval-ues,tosomeextents,representingthedeformation.Butthestatisticaldisplacementcannoteffectivelydescribethedeformationoftheinjectionmoldedparts.Inindustry,designersandmanufacturersusuallypaymoreattentiontothedegreeofpartwarpageonsomespecificfeaturesthanthewholedeformationoftheinjectionmoldedparts.Inthisstudy,featurewarpageisdefinedtodescribethedeformationoftheinjectionparts.Thefeaturewarpageistheratioofthemaximumdisplacementofthefeaturesurfacetotheprojectedlengthofthefeaturesurface(Fig.1