SinglegateoptimizationforplasticinjectionmoldLIJi-quan,LIDe-qun,GUOZhi-ying,LVHai-yuan(DepartmentofPlasticityTechnology,ShanghaiJiaoTongUniversity,Shanghai200030,China)E-mail:ReceivedNov.22,2006；revisionacceptedMar.19,2007Abstract:Thispaperdealswithamethodologyforsinglegatelocationoptimizationforplasticinjectionmold.Theobjectiveofthegateoptimizationistominimizethewarpageofinjectionmoldedparts,becausewarpageisacrucialqualityissueformostinjectionmoldedpartswhileitisinfluencedgreatlybythegatelocation.Featurewarpageisdefinedastheratioofmaximumdisplacementonthefeaturesurfacetotheprojectedlengthofthefeaturesurfacetodescribepartwarpage.Theoptimizationiscombinedwiththenumericalsimulationtechnologytofindtheoptimalgatelocation,inwhichthesimulatedannealingalgorithmisusedtosearchfortheoptimum.Finally,anexampleisdiscussedinthepaperanditcanbeconcludedthattheproposedmethodiseffective.Keywords:Injectionmold,Gatelocation,Optimization,Featurewarpagedoi:10.1631/jzus.2007.A1077Documentcode:ACLCnumber:TQ320.66INTRODUCTIONPlasticinjectionmoldingisawidelyused,complexbuthighlyefficienttechniqueforproducingalargevarietyofplasticproducts,particularlythosewithhighproductionrequirement,tighttolerance,andcomplexshapes.Thequalityofinjectionmoldedpartsisafunctionofplasticmaterial,partgeometry,moldstructureandprocessconditions.Themostimportantpartofaninjectionmoldbasicallyisthefollowingthreesetsofcomponents:cavities,gatesandrunners,andcoolingsystem.LamandSeow(2000)andJinandLam(2002)achievedcavitybalancingbyvaryingthewallthicknessofthepart.Abalancefillingprocesswithinthecavitygivesanevenlydistributedpressureandtemperaturewhichcandrasticallyreducethewarpageofthepart.Butthecavitybalancingisonlyoneoftheimportantinfluencingfactorsofpartqualities.Especially,theparthasitsfunctionalrequirements,anditsthicknessesshouldnotbevariedusually.Fromthepointviewoftheinjectionmolddesign,agateischaracterizedbyitssizeandlocation,andtherunnersystembythesizeandlayout.Thegatesizeandrunnerlayoutareusuallydeterminedasconstants.Relatively,gatelocationsandrunnersizesaremoreflexible,whichcanbevariedtoinfluencethequalityofthepart.Asaresult,theyareoftenthedesignparametersforoptimization.LeeandKim(1996a)optimizedthesizesofrunnersandgatestobalancerunnersystemformultipleinjectioncavities.Therunnerbalancingwasdescribedasthedifferencesofentrancepressuresforamulti-cavitymoldwithidenticalcavities,andasdifferencesofpressuresattheendofthemeltflowpathineachcavityforafamilymoldwithdifferentcavityvolumesandgeometries.Themethodologyhasshownuniformpressuredistributionsamongthecavitiesduringtheentiremoldingcycleofmultiplecavitiesmold.Zhaietal.(2005a)presentedthetwogatelocationoptimizationofonemoldingcavitybyanefficientsearchmethodbasedonpressuregradient(PGSS),andsubsequentlypositionedweldlinestothedesiredlocationsbyvaryingrunnersizesformulti-gateparts(Zhaietal.,2006).Aslarge-volumepart,multiplegatesareneededtoshortenthemaxi-mumflowpath,withacorrespondingdecreaseininjectionpressure.Themethodispromisingforde-signofgatesandrunnersforasinglecavitywithmultiplegates.Manyofinjectionmoldedpartsareproducedwithonegate,whetherinsinglecavitymoldorinmultiplecavitiesmold.Therefore,thegatelocationofasinglegateisthemostcommondesignparameterforoptimization.AshapeanalysisapproachwaspresentedbyCourbebaisseandGarcia(2002),bywhichthebestgatelocationofinjectionmoldingwasestimated.Subsequently,theydevelopedthismethodologyfurtherandappliedittosinglegatelocationoptimizationofanLshapeexample(Courbebaisse,2005).Itiseasytouseandnottime-consuming,whileitonlyservestheturningofsimpleflatpartswithuniformthickness.PandelidisandZou(1990)presentedtheoptimizationofgatelocation,byindirectqualitymeasuresrelevanttowarpageandmaterialdegradation,whichisrepresentedasweightedsumofatemperaturedifferentialterm,anover-packterm,andafrictionaloverheatingterm.Warpageisinfluencedbytheabovefactors,buttherelationshipbetweenthemisnotclear.Therefore,theoptimizationeffectisrestrictedbythedeterminationoftheweightingfactors.LeeandKim(1996b)developedanautomatedelectionmethodofgatelocation,inwhichasetofinitialgatelocationswereproposedbyadesignerandhentheoptimalgatewaslocatedbytheadjacentnodeevaluationmethod.Theconclusiontoagreatextentdependsmuchonthehumandesignersintuition,becausethefirststepofthemethodisbasedonthedesignersproposition.Sotheresultistoalargeextentlimitedtothedesignersexperience.DefinitionoffeaturewarpageToapplyoptimizationtheorytothegatedesign,qualitymeasuresofthepartmustbespecifiedinthefirstinstance.Theterm“quality”maybereferredtomanyproductproperties,suchasmechanical,thermal,electrical,optical,ergonomicalorgeometricalproperties.Therearetwotypesofpartqualitymeasures:directandindirect.Amodelthatpredictstheproper-tiesfromnumericalsimulationresultswouldbecharacterizedasadirectqualitymeasure.Incontrast,anindirectmeasureofpartqualityiscorrelatedwithtargetquality,butitcannotprovideadirectestimateofthatquality.Forwarpage,theindirectqualitymeasuresinrelatedworksareoneofperformancesofinjectionmoldingflowingbehaviororweightedsumofthose.Theperformancesarepresentedasfillingtimedifferentialalongdifferentflowpaths,temperaturedifferential,over-packpercentage,andsoon.Itisobviousthatwarpageisinfluencedbytheseperformances,buttherelationshipbetweenwarpageandtheseperformancesisnotclearandthedeterminationoftheseweightingfactorsisratherdifficult.Therefore,theoptimizationwiththeaboveobjectivefunctionprobablywillnotminimizepartwarpageevenwithperfectoptimizationtechnique.Sometimes,improperweightingfactorswillresultinabsolutelywrongresults.Inindustry,designersandmanufacturersusuallypaymoreattentiontothedegreeofpartwarpageonsomespecificfeaturesthanthewholedeformationoftheinjectionmoldedparts.Inthisstudy,featurewarpageisdefinedtodescribethedeformationoftheinjectionparts.Thefeaturewarpageistheratioofthemaximumdisplacementofthefeaturesurfacetotheprojectedlengthofthefeaturesurface(Fig.1):=Lh100%(1)whereisthefeaturewarpage,histhemaximumdisplacementonthefeaturesurfacedeviatingfromthereferenceplatform,andListheprojectedlengthofthefeaturesurfaceonareferencedirectionparallelingthereferenceplatform.EvaluationoffeaturewarpageAfterthedeterminationoftargetfeaturecombinedwithcorrespondingreferenceplaneandprojectiondirection,thevalueofLcanbecalculatedimmediatelyfromthepartwiththecalculatingmethodofanalyticgeometry(Fig.2).Lisaconstantforanypartonthespecifiedfeaturesurfaceandprojecteddirection.ButtheevaluationofhismorecomplicatedthanthatofL.Simulationofinjectionmoldingprocessisacommontechniquetoforecastthequalityofpartdesign,molddesignandprocesssettings.TheresultsofwarpagesimulationareexpressedasthenodaldeflectionsonX,Y,Zcomponent(Wx,Wy,Wz),andthenodaldisplacementW.WisthevectorlengthofvectorsumofWxi,Wyj,andWzk,wherei,j,karetheunitvectorsonX,Y,Zcomponent.Thehisthemaximumdisplacementofthenodesonthefeaturesurface,whichiscorrelatedwiththenormalorientationofthereferenceplane,andcanbederivedfromtheresultsofwarpagesimulation.Tocalculateh,thedeflectionofIthnodeisevaluatedfirstlyasfollows:whereWiisthedeflectioninthenormaldirectionofthereferenceplaneofithnode；Wix,Wiy,WizarethedeflectionsonX,Y,Zcomponentofithnode；,aretheanglesofnormalvectorofthereference；AandBaretheterminalnodesofthefeaturetoprojectingdirection(Fig.2)；WAandWBarethedeflectionsofnodesAandB.APPLICATIONANDDISCUSSIONTheapplicationtoacomplexindustrialpartispresentedinthissectiontoillustratetheproposedqualitymeasureandoptimizationmethodology.Thepartisprovidedbyamanufacturer,asshowninFig4.Inthispart,theflatnessofbasalsurfaceisthemostimportantprofileprecisionrequirement.Therefore,thefeaturewarpageisdiscussedonbasalsurface,inwhichreferenceplatformisspecifiedasahorizontalplaneattachedtothebasalsurface,andthelongitudinaldirectionisspecifiedasprojectedreferencedirection.Theparameterhisthemaximumbasalsurfacedeflectiononthenormaldirection,namelytheverticaldirection,andtheparameterL