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temperaturePujos,Cedex,greatmoldingnumercoolingistoeffectandqualityfastestlarindustrieincreasewellknowneconomicallymermeltsufficientlysothatthepartcanbeejectedwithoutanysignificantdeformation2.Anefficientcoolingsystemdesignofthecoolingchannelsaimingatreducingcycletimemustminimizesuchundesireddefectsassinkmarks,differentialshrinkage,thermalresidualstressbuiltupandpartwarpage.Duringthepostfillingandcoolingstagesofinjectionmolding,hotmoltenpolymertouchesthecoldmoldwall,andasolidlayerformsonthewall.tiontothecoolantmovingthroughthecoolingchannelsandbynaturalconvectiontotheairaroundtheexteriormoldsurface.Thecoolantisflowingthroughthechannelsatagivenflowrateandagiventemperaturewhichisconsideredconstantthroughoutthelengthofthechannel.Inthiswork,timedependenttwodimensionalmodelisconsideredwhichconsistsofanentirecomputationaldomainofthecavity,moldandcoolingchannelsurfaces.ThecyclictransienttemperaturedistributionofthemoldandpolymerTshapecanbeobtainedbysolvingthetransientenergyequation.Correspondingauthor.Tel.330540006348fax330540002731.AppliedThermalEngineering2920091786–1791ContentslistsavailableEmailaddresshassanenscpb.frH.Hassan.cesswherepolymerisinjectedintoamouldcavity,andsolidifiestoformaplasticpart.Therearethreesignificantstagesineachcycle.Thefirststageisfillingthecavitywithmelthotpolymerataninjectiontemperaturefillingandpostfillingstage.Itisfollowedbytakingawaytheheatofthepolymertothecoolingchannelscoolingstage,finallythesolidifiedpartisejectedejectionstage.Thecoolingstageisofthegreatestimportancebecauseitsignificantlyaffectstheproductivityandthequalityofthefinalproduct.Itiswellknownthatmorethanseventypercentofthecycletimeintheinjectionmoldingprocessisspentincoolingthehotpolydistributionofthemoldandpolymer,therefore,theireffectonthesolidificationdegreeofthatpolymer.AfullytransientmoldcoolinganalysisisperformedusingthefinitevolumemethodforaTshapeplasticmoldwithsimilardimensionsto5,asshowninFig.1.Differentcoolingchannelspositionsandformsarestudied.2.MathematicalmodelTheheatofthemoltenpolymeristakenawaybyforcedconvec1.IntroductionPlasticindustryisoneoftheworldsrankedasoneofthefewbilliondolinjectionmoldedpartscontinuestoplasticinjectionmoldingprocessiscientmanufacturingtechniquesforprecisionplasticpartswithvariousshapesatlowcost1.Theplasticinjectionmolding13594311/seefrontmatterC2112008ElsevierLtd.Alldoi10.1016/j.applthermaleng.2008.08.011growingindustries,s.DemandforeveryyearbecauseasthemosteffiproducingofandcomplexgeometryprocessisacyclicproAsthematerialcoolsdown,thesolidskinbeginstogrowwithincreasingtimeasthecoolingcontinuesuntiltheentirematerialsolidifies.Overtheyears,manystudiesontheproblemoftheoptimizationofthecoolingsystemlayoutininjectionmoldingandphasechangeofmoldingprocesshavebeenmadebyvariousresearchersandoneswhichfocusedintensityonthesetopicsandwillusedinoursystemdesignandvalidationsare3–6.ThemainpurposeofthispaperistostudytheeffectofthecoolingchannelspositionanditscrosssectionshapeonthetemperatureCoolingsystemleadstominimumcoolingtimeisnotachievinguniformcoolingthroughoutthemould.C2112008ElsevierLtd.Allrightsreserved.EffectofcoolingsystemonthepolymerduringinjectionmoldingHamdyHassan,NicolasRegnier,CedricLebot,CyrilLaboratoireTREFLEBordeaux1UMR8508,SiteENSCPB,16Av.PeyBerland,33607PessacarticleinfoArticlehistoryReceived15November2007Accepted19August2008Availableonline30August2008KeywordsPolymerSolidificationInjectionmoldingabstractCoolingsystemdesignisofiscrucialnotonlytoreduceityofthefinalproduct.Aperformed.Acyclictransientofthemoldcoolingstudycoolingsystemdesign.Theturedistributionofthemoldtivityoftheprocess,thecoolingshouldbenecessaryfortheAppliedThermaljournalhomepagewww.elsevirightsreserved.GuyDefayeFranceimportanceforplasticproductsindustrybyinjectionmoldingbecauseitcycletimebutalsoitsignificantlyaffectstheproductivityandqualicalmodelingforaTmoldplasticparthavingfourcoolingchannelsisanalysisusingafinitevolumeapproachiscarriedout.Theobjectivedeterminethetemperatureprofilealongthecavitywalltoimprovetheofcoolingchannelsformandtheeffecttheirlocationonthetemperathesolidificationdegreeofpolymerarestudied.Toimprovetheproductimeshouldbeminimizedandatthesametimeahomogeneouscoolingoftheproduct.TheresultsindicatethatthecoolingsystemwhichandsolidificationatScienceDirectEngineeringer.com/locate/apthermengdissipationoftheheatthroughphasechangeprocess.Thistechplicit/implicittechniquealreadyvalidatedinpreviousstudiesbyVincent8,andLeBot9thatisbasedonthetechniqueNewSourceofVoller10.Thismethodproposestomaintainthenodeswherephasechangeoccurstothemeltingtemperature.Thissolutionisrepeateduntiltheconvergenceofthetemperaturewiththesourcetermequalstothelatentheat.ThesourcetermisdiscretizedbySc¼qLfofsot¼qLffnþ1sC0fnsDtð5ÞThesolidfractionwhichisfunctionofthetemperatureislinearizedasNomenclatureCPJ/kgKspecificheatatconstantpressurefssolidfractionhW/m2KheattransfercoefficientKnumberoftheinternaliterationsLlatentheatoffusion,J/kgnnumberoftheexternaliterationsNnormaldirectionScsourcetermTKtemperaturetstimeH.Hassanetal./AppliedThermalEngineeringniqueisappliedonfixednodesandtheenergyequationinthiscaseisrepresentedasfollowqCPoTot¼rðkrTÞþScð2ÞAndthesourcetermScisrepresentedbySc¼qLfofsotð3ÞwherefsT0.0atTC31Tf,fullliquidregion0C30fsC301,atTTfisothermalphasechangeregionand,fsT1atTC30Tffullsolidregion.Onthewholedomain,thefollowingboundaryconditionsareappliedC0koToN¼hcðTC0TcÞ2C1andC0koToN¼haðTC0TaÞ2C2ð4Þ3.NumericalsolutionThenumericalsolutionofthemathematicalmodelgoverningthebehaviorofthephysicalsystemiscomputedbyfinitevolumemethod.TheequationsaresolvedbyanimplicittreatmentforqCPoTot¼rðkrTÞð1ÞInordertotakeintoaccountthesolidification,asourcetermisaddedtotheenergyequationcorrespondingtoheatabsorptionorheatrelease7,whichtakesinconsiderationtheabsorptionorthethedifferenttermsoftheequationssystem.Whenwetakeinconsiderationthesolidificationeffect,theenergyequationissolvedwithafixedpointalgorithmforthesolidfraction.Foreach,iterationofthatfixedpoint,weusediscretizationwithtimehybridex0.20.40.20.0040.030.004P2P3P4P1P6P7P5Exteriorair,freeconvection,haCoolingchannels,forcedconvection,hfFig.1.MoldstructurewithaTshapeproductandfourcoolingchannelsDim.Inm.GreeksymbolskW/mKthermalconductivityqkg/m3densityC1interiorsurfaceofthecoolingchannelsC2exteriorsurfaceofthemoldSubscriptsaambientairccoolingfluidfphasechange0.010.010.010.010.010.02A1A2A3A4A5A7B1B2B3B4B5B7C1C2C3C4C5D1D2D3D4D50.040.020.010.015PolymerFig.2.DifferentcoolingchannelspositionsDim.Inm.2920091786–17911787fnþkþ1Ks¼fnþkKsþdFsdTC18C19nþkKðTnþkþ1KC0TnþkKÞð6ÞThen,weforcethetemperaturetotendtothemeltingtemperaturewherethesourcetermisnotnullbyupdatingthesourcetermSkþ1c¼SkcþqCpðTC0TfÞDtð7ÞTheenergyequationisdiscretizedasfollowqCPDtC0qLfDtdFdTC18C19nþkKTnþkþ1KC0rðkrTÞnþkþ1K¼qLfDtðfnþkþ1KsC0fnsÞC0qLfDtdFdTC18C19nþkKTfþqCPDtTnð8ÞWithdFdTC01if0C30fnþkKsC301anddFdT¼0iffnþkKs¼0or1ð9ÞThisprocessallowsdifferentiatingthetemperaturefieldandsolidfractioncalculatedatthesameinstantandthelinearsystemissolvedbycentraldiscretizationmethod11.Foreachinternaliteration,theresolutionofthatequationprovidesfnþkþ1KsandTnþkþ1K.Theconvergenceisachievedwhenthecriteriaofthesolidfractionandtemperatureareverifiedbyfnþkþ1KsC0fnþkKsC13C13C13C13C13C13C302fandTnþkþ1KC0TnþkKC13C13C13C13C13C13C302Tð10ÞFurtherdetailsonthenumericalmodelanditsvalidationarepresentedin9.thehorizontaldirectionbetweenpositionsB2andB5orpositionsA2andA5whichhavethemaximumsolidificationpercent.WhenwecomparethesolidificationpercentfordifferentlocationsoftheupperpositionsCandD,wefindthatasthechannelapproachestotheproductinthehorizontaldirectionthesolidificationpercentincreases,andthecoolingrateincreaserapidlycomparedwiththeeffectoflowerposition.Wenoticethat,theeffectofthecoolingchannelpositiononthetemperaturedistributionandsolidificationdecreasesasthecoolingtimeaugmentstohighervalueanditsef1788H.Hassanetal./AppliedThermalEngineering4.ResultsanddiscussionAfulltwodimensionaltimedependentmoldcoolinganalysisininjectionmoldingiscarriedoutforaplatemouldmodelwithTshapeplasticmoldandfourcoolingchannelsasindicatedinFig.1.Duetothesymmetry,halfofthemoldismodeledandanalyzed.Allthecoolingchannelshavethesamesizeandtheyhavediameterof10mmeachincaseofcircularchannels.ThecoolingoperatingparametersandthematerialpropertiesarelistedinTables1and2,respectively,andtheyareconsideredconstantduringallnumericalresults5,7.Eachnumericalcycleconsistsoftwostages,coolingstagewherethecavityisfilledwithhotpolymerinitiallyatpolymerinjectedtemperature,theejectionstagewherethecavityisfilledwithairinitiallyatambienttemperature.Figs.3and4showthecyclictransientvariationsofthemouldtemperaturewithtimefor16smoldcoolingtimeatlocationsP1,P2,P3,P4besidethemouldwallsandP5toP7insidethemouldwalls,respectivelyFig.1andthatincaseofappliedthesolidificationandwithoutappliedsolidification.Theyaresimulatedforthefirst30cyclesincaseofcircularcoolingchannelspositionA5,D3asshowninFig.2.Wefindthat,thesimulatedresultsareingoodagreementwiththetransientcharacteristicofthecyclicmoldtemperaturevariationsdescribedin5.Itisfoundthatthereisaslightlydifferenceintemperaturesvaluesbetweenthetworesults,thusduetothedifferenceinnumericalmethodusedandtheaccuracyinthenumericalcalculations.Thefiguresshowthat,therelativelytemperaturefluctuationislargestnearthecavitysurfaceanddiminishesawayfromthecavitysurface.Wefindthatthemaximumamplitudeoftemperaturefluctuationduringthesteadycyclecanreach10C176Cwithoutapplyingsolidificationand15C176Cincaseofapplyingthesolidification.4.1.EffectofcoolingchannelsformAnefficientcoolingsystemdesignprovidinguniformtemperaturedistributionthroughouttheentirepartduringthecoolingprocessshouldensureproductqualitybypreventingdifferentialshrinkage,internalstresses,andmouldreleaseproblems.ItalsoshouldreducetimeofcoolingandacceleratethesolidificationprocessoftheproducttoaugmenttheproductivityofthemoldingTable1CoolingoperatingparametersCoolingoperatingparameterCoolingoperatingparameterCoolantfluidtemperature30C176CAmbientairtemperature30C176CPolymerinjectedtemperature220C176CHeattransfercoefficientofambientair77W/m2KTemperatureoffusionofpolymer110C176CHeattransfercoefficientinsidecoolingchannel3650W/m2KLatentheat115kJ/Moldopeningtime4skgprocess.Todemonstratetheinfluenceofthecoolingchannelsformonthetemperaturedistributionthroughoutthemouldandsolidificationprocessoftheproduct,weproposedthreedifferentcrosssectionalformsofthecoolingchannels,circular,square,rectangular1withlongtowidthratioof0.5andrectangular2withwidthtolongratioof0.25.Twocasesarestudiedfirstcase,allthecoolingchannelshavethesamecrosssectionalarea,andthesecondcase,theyhavethesameperimeter.ThecomparisoniscarriedoutforthesamecoolingchannelspositionA5,D3.Fig.5showsthesolidificationpercentcalculatednumericallyasthesummationofthesolidfractionofeachelementmultipliedbytheareaofthatelementtototalareaoftheproductfordifferentformswithdifferentcoolingtime.Thefigureindicatesthattheeffectofcoolingchannelsformonthecoolingratedecreaseswithincreasingthecoolingtime.Italsoshowsthatthecoolingchannelformrectangle2hasthemaximumsolidificationpercentforcase1,andincase2thechangingofthecoolingchannelsformhasnotasensibleeffectonthesolidificationpercent.Thesameresultscanbeobtainedwhenwecomparedthesolidificationintheproductandthetemperaturedistributionthoughthemouldfordifferentformswiththesamecrosssectionalareaattheendofthecoolingstageforcoolingtime24sforcoolingcycle25,asshowninFigs.6and7,respectively.Theresultsindicatethatthecoolingprocessisimprovedasthecoolingchannelstendtotaketheformoftheproduct.4.2.EffectofcoolingchannelspositionToinvestigatetheeffectofthecoolingchannelsposition,wedividedtheproposedpositionsintofourgroups,groupsAandBfordifferentpositionsofthebottomcoolingchannel,withafixedpositionofthetopcoolingchannel,andwithviceversaforgroupsCandDforthesamecoolingchannelformcircularasillustratedinFig.2.Fig.8representstheeffectofdifferentcoolingchannelpositionsontheofsolidificationpercentattheendof25thcoolingcycleforgroupsAandBlowercoolingchanneleffect,CandDuppercoolingchanneleffectwithcoolingtime.Itindicatesthatforlowercoolingchannelpositioneffect,thecoolingrateincreasesandhencethesolidificationpercentofthepolymerincreasesasthecoolingchannelapproachesthepolymerintheverticaldirectionpositionBhassolidificationpercentgreaterthanpositionA,andwiththesamepositionsCandD.Thefigureshowsalsothemostefficientcoolingrateisobtainedasthecoolingchanneltakesthepositionbetween20and50throughtheproductlengthforTable2MaterialpropertiesMaterialDensitykg/m3SpecificheatJ/kgKConductivityW/mKMould767042636.5Polymer93818000.25Air1.1710060.02632920091786–1791fectonthecoolingrateoftheproductisnotthesamefordifferentpositions.Engineering6065abH.Hassanetal./AppliedThermalThesolidificationdegreedistributionthroughtheproductattheendofcoolingstageattheendofcoolingtime24sand25thcoolingcyclefordifferentlocationsofcoolingchannelisshowninFig.9,andthetemperaturedistributionthroughoutthemouldandthepolymeratthesameinstantfordifferentcoolingchannelsTemperature,oCTime,s0200400600303540455055P1P2P3P4Fig.3.Temperaturehistoryofthefirst30cyclesatlocationsTime,s3035404550556065P5P6P7abTemperature,oC0200400600Fig.4.Temperaturehistoryofthefirst30cyclesatlocationsSolidificationpercentCoolingperiodconstantperimeterCoolinvgperiodconstantarea1616182022242628300.680.720.760.80.840.880.920.96CircleRectangle1Rectangle2SquareCircleRectangle1Rectangle2Square30282624222018Fig.5.Changingthesolidificationpercentofthepolymerpartwithcoolingtimefordifferentcoolingchannelforms.70752920091786–17911789positionisshowninFig.10.Whenweexaminethesolidificationdegreeoftheproductandthetemperaturedistributionthroughoutthemoldfordifferentpositions,wefindthatasthecoolingchannelpositionmovestowardtheproducts,thehomogeneityofthetemperaturedistributionthroughoutthepolymerandthemoldduringTemperature,oCTime,s03035404550556065P1P2P3P4600500400300200100P1toP4awithoutsolidificationbwithsolidification.Time,s30354045505560657075P5P6P7Temperature,oC0200400600P5toP7awithoutsolidificationbwithsolidification.Fig.6.Solidificationpercentdistributionthroughtheproductfordifferentcoolingchannelsformsarectangular2andbcircularhavingthesamecrosssectionalarea.
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