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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