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INTJADVMANUFTECHNOL2001172973042001SPRINGERVERLAGLONDONLIMITEDOPTIMUMGATEDESIGNOFFREEFORMINJECTIONMOULDUSINGTHEABDUCTIVENETWORKJCLINDEPARTMENTOFMECHANICALDESIGNENGINEERING,NATIONALHUWEIINSTITUTEOFTECHNOLOGY,YUNLIN,TAIWANTHISSTUDYUSESTHEINJECTIONPOSITIONANDSIZEOFTHEGATEASTHEMAJORCONTROLPARAMETERSFORASIMULATEDINJECTIONMOULDONCETHEINJECTIONPARAMETERSGATESIZEANDGATEPOSITIONAREGIVEN,THEPRODUCTPERFORMANCEDEFORMATIONCANBEACCURATELYPREDICTEDBYTHEABDUCTIVENETWORKDEVELOPEDTOAVOIDTHENUMEROUSINFLUENCINGFACTORS,FIRSTTHEPARTLINEOFTHEPARAMETEREQUATIONISCREATEDBYANABDUCTIVENETWORKTOLIMITTHERANGEOFTHEGATETHEOPTIMALINJECTIONPARAMETERSCANBESEARCHEDFORBYASIMULATIONANNEALINGSAOPTIMISATIONALGORITHM,WITHAPERFORMANCEINDEX,TOOBTAINAPERFECTPARTTHEMAJORPURPOSEISSEARCHINGFORTHEOPTIMALGATELOCATIONONTHEPARTSURFACE,ANDMINIMISINGTHEAIRTRAPANDDEFORMATIONAFTERPARTFORMATIONTHISSTUDYALSOUSESAPRACTICALEXAMPLEWHICHHASBEENANDPROVEDBYEXPERIMENTTOACHIEVEASATISFACTORYRESULTKEYWORDSABDUCTIVENETWORKINJECTIONMOULDSIMULATIONANNEALINGSA1INTRODUCTIONOWINGTOTHERAPIDDEVELOPMENTOFINDUSTRYANDCOMMERCEINRECENTYEARS,THEREISANEEDFORRAPIDANDHIGHVOLUMEPRODUCTIONOFGOODSTHEPRODUCTSAREMANUFACTUREDUSINGMOULDSINORDERTOSAVETHETIMEANDCOSTPLASTICPRODUCTSARETHEMAJORITYOWINGTOTHESEPRODUCTSNOTREQUIRINGCOMPLICATEDPROCESSESITISPOSSIBLETOCOPEWITHMARKETDEMANDSPEEDILYANDCONVENIENTLYINTRADITIONALPLASTICPRODUCTION,THEDESIGNSOFTHEPORTIONSOFTHEMOULDAREDETERMINEDBYHUMANSHOWEVER,BECAUSEOFTHEINCREASEDPERFORMANCEREQUIREMENTS,THECOMPLEXITYOFPLASTICPRODUCTSHASINCREASEDFIRST,THEGEOMETRICSHAPESOFTHEPLASTICPRODUCTSAREDIFFICULTTODRAW,ANDTHEINTERNALSHAPEISOFTENCOMPLEXWHICHALSOAFFECTSTHEPRODUCTIONOFTHEPRODUCTINJECTIONPROCESSINGCANBEDIVIDEDINTOTHREESTAGESCORRESPONDENCEANDOFFPRINTREQUESTSTODRJCLIN,DEPARTMENTOFMECHANICALDESIGNENGINEERING,NATIONALHUWEIINSTITUTEOFTECHNOLOGY,YUNLIN632,TAIWANEMAILLINRCKSUNWSNHITEDUTW1HEATTHEPLASTICMATERIALTOAMOLTENSTATETHEN,BYHIGHPRESSURE,FORCETHEMATERIALTOTHERUNNER,ANDTHENINTOTHEMOULDCAVITY2WHENTHEFILLINGOFTHEMOULDCAVITYISCOMPLETED,MOREMOLTENPLASTICSHOULDBEDELIVEREDINTOTHECAVITYATHIGHPRESSURETOCOMPENSATEFORTHESHRINKAGEOFTHEPLASTICTHISENSURESCOMPLETEFILLINGOFTHEMOULDCAVITY3TAKEOUTTHEPRODUCTAFTERCOOLINGTHOUGHTHEFILLINGPROCESSISONLYASMALLPROPORTIONOFTHECOMPLETEFORMATIONCYCLE,ITISVERYIMPORTANTIFFILLINGININCOMPLETE,THEREISNOPRESSUREHOLDINGANDCOOLINGISREQUIREDTHUS,THEFLOWOFTHEPLASTICFLUIDSHOULDBECONTROLLEDTHOROUGHLYTOENSURETHEQUALITYOFTHEPRODUCTTHEISOTHERMALFILLINGMODELOFANEWTONIANFLUIDISTHESIMPLESTINJECTIONMOULDFLOWFILLINGMODELRICHARDSON1PRODUCEDACOMPLETEANDDETAILEDCONCEPTTHEMAJORCONCEPTISBASEDONTHEAPPLICATIONOFLUBRICATIONTHEORY,ANDHESIMPLIFIEDTHECOMPLEX3DFLOWTHEORYTO2DHELESHAWFLOWTHEHELESHAWFLOWWASUSEDTOSIMULATETHEPOTENTIALFLOWANDWASFURTHERMOREUSEDINTHEPLASTICITYFLOWOFTHEPLASTICHEASSUMEDTHEPLASTICITYFLOWONANEXTREMELYTHINPLATEANDFULLYDEVELOPEDTHEFLOWBYIGNORINGTHESPEEDCHANGETHROUGHTHETHICKNESSKAMALETALUSEDSIMILARMETHODSTOOBTAINTHEFILLINGCONDITIONFORARECTANGULARMOULDCAVITY,ANDTHEANALYTICALRESULTOBTAINEDWASALMOSTIDENTICALTOTHEEXPERIMENTALRESULTPLASTICMATERIALFOLLOWSTHENEWTONIANFLUIDMODELFORFLOWINAMOULDCAVITY,ANDBIRDETAL24DERIVEDMOULDFLOWTHEORYBASEDONTHISWHENTHESHAPEOFAMOULDISCOMPLICATEDANDTHEREISVARIATIONINTHICKNESS,THENTHEEQUILIBRIUMEQUATIONSCHANGESTONONLINEARANDHASNOANALYTICALSOLUTIONTHUS,ITCANBESOLVEDONLYBYFINITEDIFFERENCEORNUMERICALSOLUTIONS2,5OFCOURSE,ASTHEPOLYMERISAVISCOELASTICFLUID,ITISBESTTOSOLVETHEFLOWPROBLEMBYUSINGVISCOELASTICITYEQUATIONSIN1998,GOYALETALUSEDTHEWHITEMETZNERVISCOELASTICITYMODELTOSIMULATETHEDISKMOULDFLOWMODELFORCENTRALPOURINGMETZNER,USINGAFINITEDIFFERENCEMETHODTOSOLVETHEGOVERNINGEQUATION,FOULDTHEVISCOELASTICITYEFFECTWOULDNOTCHANGETHEDISTRIBUTIONOFSPEEDANDTEMPERATUREHOWEVER,ITAFFECTSTHESTRESSFIELDVERYMUCHIFITISAPUREVISCOELASTIC298JCLINFLOWMODEL,THEPOPULARGNFMODELISGENERALLYUSEDTOPERFORMNUMERICALSIMULATIONCURRENTLY,FINITEELEMENTMETHODSAREMOSTLYUSEDFORTHESOLUTIONOFMOULDFLOWPROBLEMSOTHERMETHODSAREPUREVISCOELASTICMODELS,SUCHASCFOLWANDMOLDFLOWSOFTWAREWEUSEDTHISMETHODASWELLSOMESOFTWAREEMPLOYSTHEVISCOELASTICWHITEMETZNERMODEL,BUTITISLIMITEDTO2DMOULDFLOWANALYSISSIMPLEMOULDFLOWANALYSISISLIMITEDBYCPUTIMEFORTHECOMPLICATEDMOULDSHAPES,PAPTHANASIONETALUSEDUCMFLUIDFORFILLINGANALYSIS,USINGAFINITEDIFFERENCEMETHODANDBFCCCOORDINATIONSYSTEMAPPLICATIONFORTHESOLUTIONOFTHEMORECOMPLICATEDMOULDSHAPEANDFILLINGPROBLEM,BUTITWASNOTCOMMERCIALISED6MANYFACTORSAFFECTPLASTICMATERIALINJECTIONTHEFILLINGSPEED,INJECTIONPRESSUREANDMOLTENTEMPERATURE,HOLDINGPRESSURE712,COOLINGTUBE13,14ANDINJECTIONGATEAFFECTTHEACCURACYOFTHEPLASTICPRODUCT,BECAUSE,WHENTHEINJECTIONPROCESSINGISCOMPLETED,THEFLOWOFMATERIALINTHEMOULDCAVITYRESULTSINUNEVENTEMPERATUREANDPRESSURE,ANDINDUCESRESIDUALSTRESSANDDEFORMATIONOFTHEWORKPIECEAFTERCOOLINGITISDIFFICULTTODECIDEONTHEMOULDPARTSURFACEANDGATEPOSITIONSGENERALLY,THEMOULDPARTSURFACEISLOCATEDATTHEWIDESTPLANEOFTHEMOULDSEARCHINGFORTHEOPTIMALGATEPOSITIONDEPENDSONEXPERIENCEMINIMALMODIFICATIONTOTHEMOULDISREQUIREDIFYOUARELUCKYHOWEVER,THETIMEANDCOSTREQUIREDFORTHEMODIFICATIONOFMOSTINJE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HISSTUDYUSESANACTUALINDUSTRIALPRODUCTASASAMPLE,FIG1THEMOULDPARTSURFACEISLOCATEDATTHEMAXIMUMPROJECTIONAREAASSHOWNINFIG1,THEBOTTOMISTHEWIDESTPLANEANDISCHOSENASTHEMOULDPARTSURFACEHOWEVER,MOSTIMPORTANTISTHESEARCHINGOFGATEPOSITIONONTHEPARTSURFACETHISSTUDYESTABLISHESTHEPARAMETEREQUATIONBYUSINGANABDUCTIVENEURONNETWORK,INORDERTOESTABLISHTHESIMULATEDANNEALINGMETHODSATOFINDTHEOPTIMALGATEPATHPOSITIONTHEPARAMETEREQUATIONOFAPARTSURFACEISEXPRESSEDBYFYXFIRST,USEACMMSYSTEMTOMEASURETHEXYZCOORDINATEVALUESINTHISSTUDYZ0OF22POINTSONTHEMOULDPARTLINEONTHEMOULDPARTSURFACEASILLUSTRATEDINTABLE1,ANDTHEGATEPOSITIONISCOMPLETELYONTHECURVEINTHISSPACEPRIORTODEVELOPINGASPACECURVEMODEL,ADATABASEHASTOBETRAINED,ANDAGOODRELATIONSHIPMSUTEXISTBETWEENTHECONTROLPOINTANDABDUCTIVENETWORKSYSTEMACORRECTANDFIG1INJECTIONMOULDPRODUCT300JCLINTABLE1X,YCOORDINATESETNUMBERXCOORDINATEYCOORDINATE1002462163433332835452920457310566934097113323581298394913855571014127341113699671212961191310002103149332316158642528167982739177872831187802929197833034207603130217073215226113249PRECISECURVEEQISHELPFULFORFINDINGTHEOPTIMALGATELOCATIONTOBUILDACOMPLETEABDUCTIVENETWORK,THEFIRSTREQUIREMENTISTOTRAINTHEDATABASETHEINFORMATIONGIVENBYTHEINPUTANDOUTPUTPARAMETERSMUSTBESUFFICIENTAPREDICTEDSQUAREERRORPSECRITERIONISTHENUSEDTODETERMINEAUTOMATICALLYANOPTIMALSTRUCTURE23THEPSECRITERIONISUSEDTOSELECTTHELEASTCOMPLEXBUTSTILLACCURATENETWORKTHEPSEISCOMPOSEDOFTWOTERMSPSEFSEKP16WHEREFSEISTHEAVERAGESQUAREERROROFTHENETWORKFORFITTINGTHETRAININGDATAANDKPISTHECOMPLEXPENALTYOFTHENETWORK,SHOWNBYTHEFOLLOWINGEQUATIONKPCPM2S2PKN17WHERECPMISTHECOMPLEXPENALTYMULTIPLIER,KPISACOEFFICIENTOFTHENETWORKNISTHENUMBEROFTRAININGDATATOBEUSEDANDS2PISAPRIORESTIMATEOFTHEMODELERRORVARIANCEBASEDONTHEDEVELOPMENTOFTHEDATABASEANDTHEPREDICTIONOFTHEACCURACYOFTHEPARTSURFACE,ATHREELAYERABDUCTIVENETWORK,WHICHCOMPRISEDDESIGNFACTORSINPUTVARIOUSYCOORDINATEANDOUTPUTFACTORSXCOORDINATEISSYNTHESISEDAUTOMATICALLYITISCAPABLEOFPREDICTINGACCURATELYTHESPACECURVEATANYPOINTUNDERVARIOUSCONTROLPARAMETERSALLPOLYNOMIALEQUATIONSUSEDINTHISNETWORKARELISTEDINAPPENDIXAPSE58103TABLE2COMPARESTHEERRORPREDICTEDBYTHEABDUCTIVEMODELANDCMMMEASUREMENTDATATHEMEASUREMENTDAAISEXCLUDEDFROMTHE22SETSOFCMMMEASUREMENTDATAFORESTABLISHINGTHEMODELTHISSETOFDATAISUSEDTOTESTTHEAPPROPRIATENESSOFTHEMODELESTABLISHEDABOVEWECANSEEFROMTABLE2THATTHEERRORISAPPROXIMATELY213,WHICHSHOWSTHATTHEMODELISSUITABLEFORTHISSPACECURVETABLE2CMMSCOORDINATEANDNEURALNETWORKPREDICTCOMPAREDITISNOTINCLUDEDINANYORIGINAL22SETSDATABASEITEMSCMMSNEURALNETWORKERRORVALUESCOORDINATEPREDICTCMMSPREDICT/COORDINATECMMSCOORDINATE1125,1601101,1602135CREATETHEINJECTIONMOULDMODELSIMILARLY,THERELATIONSHIPISESTABLISHEDBETWEENINPUTPARAMETERSGATELOCATIONANDGATESIZEANDTHEOUTPUTPARAMETERDEFORMATIONDURINGTHEINJECTIONPROCESSTOBUILDACOMPLETEABDUCTIVENETWORK,THEFIRSTREQUIREMENTISTOTRAINTHEDATABASETHEINFORMATIONGIVENBYTHEINPUTANDTHEOUTPUTDATAMUSTBESUFFICIENTTHUS,THETRAININGFACTORGATELOCATIONFORABDUCTIVENETWORKTRAININGSHOULDBESATISFACTORYFORMAKINGDEFECTFREEPRODUCTSFIGURE2SHOWSTHESIMULATIONOFFEMMOULDFLOWTABLE3SHOWSTHEPOSITIONOFTHEGATEANDTHEMAXIMUMDEFORMATIONOFTHEPRODUCTOBTAINEDFROMMOULDFLOWANALYSISBASEDONTHEDEVELOPMENTOFTHEINJECTIONMOULDMODEL,THREELAYERABDUCTIVENETWORKS,WHICHARECOMPRISEDOFINJECTIONMOULDCONDITIONSANDTHEINJECTIONRESULTSDEFORMATION,ARESYNTHESISEDAUTOMATICALLYTHEYARECAPABLEOFPREDICTINGACCURATELYTHEPRODUCTSTRAINTHERESULTOFINJECTIONMOULDEDPRODUCTUNDERVARIOUSCONTROLPARAMETERSALLPOLYNOMIALEQUATIONSUSEDINTHISNETWORKARELISTEDINAPPENDIXBPSE23105TABLE4COMPARESTHEERRORPREDICTEDBYTHEABDUCTIVEMODELANDTHESIMULATIONCASETHESIMULATIONCASEISEXCLUDEDFROMTHE22SETSOFSIMULATIONCASESFORESTABLISHINGTHEMODELTHISSETOFDATAISUSEDTOTESTTHEAPPROPRIATENESSOFTHEMODELESTABLISHEDABOVEWECANSEEFROMTABLE4THATTHEERRORISFIG2THEDEFORMATIONOFFEMMOULDFLOWOPTIMUMGATEDESIGNOFFREEFORMINJECTIONMOULD301TABLE3GATELOCATIONANDTHEMAXIMUMSTRAINRELATIONSHIPSETNUMBERXCOORDINATEYCOORDINATEGATEWIDTHGATELENGTHPRODUCEMAXSTRAIN100246052511475034821634330715303153332835087519125027104529204105229502858573105605251147503017693409071530526711332350875191250236981298394105229502517913855570525114750278810141273407153027731113699670875191250298812129611910522950299713100021030525114750257614933231607153026241586425280875191250254216798273910522950249517787283105251147502503187802929071530245619783303408751912502596207603130105229502457217073215052511475024992261132490715302511TABLE4MOULDFLOWSIMULATEDANDNEURALNETWORKPREDICTCOMPAREDITISNOTINCLUDEDINANYORIGINAL22SETDATABASEITEMSFEMMOULDFLOWNEURALNETWORKSIMULATIONPREDICTXCOORDINATE11011101YCOORDINATE160160GATEWIDTH1818GATEHEIGHT0909PRODUCEMAXDEFORMATION0317803325ERRORVALUES462FEMPREDICT/FEMAPPROXIMATELY462,WHICHSHOWSTHATTHEMODELISSUITABLEFORTHISMODELREQUIREMENT6SIMULATIONANNEALINGTHEORYIN1983,ATHEORYTHATWASCAPABLEOFSOLVINGTHEGLOBALOPTIMISATIONPROBLEMWASDEVELOPEDFORTHEOPTIMISEDPROBLEMTHECONCEPTWASAPOWERFULOPTIMISATIONALGORITHMBASEDONTHEANNEALINGOFASOLIDWHICHSOLVEDTHECOMBINATORIALOPTIMISATIONPROBLEMOFMULTIPLEVARIABLESWHENTHETEMPERATUREISTANDENERGYE,THETHERMALEQUILIBRIUMOFTHESYSTEMISABOLTZMANDISTRIBUTIONPR1ZTEXPSEKBTD18ZTNORMALISATIONFACTORKBBOLTZMANCONSTANTEXPE/KBTBOLTZMANFACTORMETROPOLIS24PROPOSEDACRITERIONFORSIMULATINGTHECOOLINGOFASOLIDTOANEWSTATEOFENERGYBALANCETHEBASICCRITERIONUSEDBYMETROPOLISISANOPTIMISATIONALGORITHMCALLED“SIMULATEDANNEALING”THEALGORITHMWASDEVELOPEDBYKIRKPATRICKETAL20INTHISPAPER,THESIMULATIONANNEALINGALGORITHMISUSEDTOSEARCHFORTHEOPTIMALCONTROLPARAMETERSFORGATELOCATIONFIGURE3SHOWSTHEFLOWCHARTOFTHESIMULATEDANNEALINGSEARCHFIRST,THEALGORITHMISGIVENANINITIALTEMPERATURETSANDAFINALTEMPERATURETE,ANDASETOFINITIALPROCESSVECTORSOXTHEOBJECTIVEFUNCTIONOBJISDEFINED,BASEDONTHEINJECTIONPARAMETERPERFORMANCEINDEXTHEOBJECTIVEFUNCTIONCANBERECALCULATEDFORALLTHEDIFFERENTPERTURBEDCOMPENSATIONPARAMETERSIFTHENEWOBJECTIVEFUNCTIONBECOMESSMALLER,THEPETURBEDPROCESSPARAMETERSAREACCEPTEDASTHENEWPROCESSPARAMETERSANDTHETEMPERATUREDROPSALITTLEINSCALETHATISTI1TICT19WHEREIISTHEINDEXFORTHETEMPERATUREDECREMENTANDTHECTISTHEDECAYRATIOFORTHETEMPERATURECT,1HOWEVER,IFTHEOBJECTIVEFUNCTIONBECOMESLARGER,THEPROBABILITYOFACCEPTANCEOFTHEPERTURBEDPROCESSPARAMETERSISGIVENASPROBJEXPFDOBJKBTG20WHEREKBISTHEBOLTZMANCONSTANTANDDOBJISTHEDIFFERENTINTHEOBJECTIVEFUNCTIONTHEPROCEDUREISREPEATEDUNTILTHETEMPERATURETIAPPROACHESZEROITSHOWSTHEENERGYDROPPINGTOTHELOWESTSTATEONCETHEMODELOFTHERELATIONSHIPAMONGTHEFUNCTIONSOFTHEGATELOCATION,THEINPUTPARAMETERSANDOUTPUTPARAMETERSAREESTABLISHED,THISMODELCANBEUSEDTOFINDTHEOPTIMALPARAMETERFORTHEGATELOCATIONTHEOPTIMALPARAMETERFORTHEPROCESSCANBEOBTAINEDBYUSINGTHEOBJECTIVEFUNCTIONTOSERVE302JCLINFIG3FLOWCHARTOFTHESIMULATEDANNEALINGSEARCHINGASASTARTINGPOINTTHEOBJECTIVEFUNCTIONOBJISFORMULATEDASFOLLOWSOBJW1XCOORDINATEW2YCOORDINATE21W3GATEWIDESIZEW3GATEHEIGHTSIZEWHEREW1,W2,ANDW3ARETHEWEIGHTFUNCTIONSTHECONTROLPARAMETRICOFTHEX,YLOCATIONSHOULDCOMPLYWITHTHEPARTSURFACEPARAMETEREQUATIONTHATMEANSTHEBASICCONDITIONOFOPTIMISATIONSHOULDFALLWITHINACERTAINRANGE1THEXCOORDINATEVALUEOBTAINEDFROMOPTIMISATIONSHOULDBELARGERTHANTHEMINIMUMXCOORDINATEVALUE,ANDSMALLERTHANTHEMAXIMUMXCOORDINATEVALUE2THEYCOORDINATEVALUEOBTAINEDFROMOPTIMISATIONSHOULDBELARGERTHANTHEMINIMUMYCOORDINATEVALUE,ANDSMALLERTHANTHEMAXIMUMXCOORDINATEVALUETHEX,YCOORDINATEDEPENDSONTHEAPPENDIXANEURALNETWORKEQUATION3THEGATEWIDESIZEOBTAINEDFROMOPTIMISATIONSHOULDBELARGERTHANTHEMINIMUMSIZEOFGATEWIDTH,ANDSMALLERTHANTHEMAXIMUMGATEWIDTHSIZE4THEGATEHEIGHTSIZEOBTAINEDFROMOPTIMISATIONSHOULDBELARGERTHANTHEMINIMUMSIZEOFGATEHEIGHT,ANDSMALLERTHANTHEMAXIMUMGATEHEIGHTSIZETHEINEQUALITIESAREGIVENASFOLLOWSTHESMALLESTXCOORDINATEVALUE,XCOORDINATEVALUE,THELARGESTXCOORDINATEVALUE22THESMALLESTYCOORDINATEVALUE,YCOORDINATEVALUE,THELARGESTYCOORDINATEVALUE23THESMALLESTGATEWIDTHSIZE,GATEWIDTHSIZE,THELARGESTWIDTHGATESIZE24THESMALLESTGATEHEIGHTSIZE,GATEHEIGHTSIZE,THELARGESTHEIGHTGATESIZE25THEUPPERBOUNDCONDITIONSSHOULDBEKEPTTOANACCEPTABLELEVELSOASTOFINDTHEOPTIMALACCCURATEGATECOORDINATE7RESULTSANDDISCUSSIONANEXAMPLEOFTHESIMUL