3Effect of cooling system.docx
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3Effectofcoolingsystem
AppliedThermalEngineering29(2009)1786–1791
ContentslistsavailableatScienceDirect
AppliedThermalEngineering
journalhomepage:
www.elsevi
Effectofcoolingsystemonthepolymertemperatureandsolidification
duringinjectionmolding
HamdyHassan
*
NicolasRegnier,CedricLebot,CyrilPujos,GuyDefaye
LaboratoireTREFLE-Bordeaux1-UMR8508,SiteENSCPB,16Av.PeyBerland,33607PessacCedex,France
articleinfo
Articlehistory:
Received15November2007
Accepted19August2008
Availableonline30August2008
Keywords:
Polymer
Solidification
Injectionmolding
Coolingsystem
Abstract
Coolingsystemdesignisofgreatimportanceforplasticproductsindustrybyinjectionmoldingbecauseit
iscrucialnotonlytoreducemoldingcycletimebutalsoitsignificantlyaffectstheproductivityandqual-
ityofthefinalproduct.AnumericalmodelingforaT-moldplasticparthavingfourcoolingchannelsis
performed.Acyclictransientcoolinganalysisusingafinitevolumeapproachiscarriedout.Theobjective
ofthemoldcoolingstudyistodeterminethetemperatureprofilealongthecavitywalltoimprovethe
coolingsystemdesign.Theeffectofcoolingchannelsformandtheeffecttheirlocationonthetempera-
turedistributionofthemoldandthesolidificationdegreeofpolymerarestudied.Toimprovetheproduc-
tivityoftheprocess,thecoolingtimeshouldbeminimizedandatthesametimeahomogeneouscooling
shouldbenecessaryforthequalityoftheproduct.Theresultsindicatethatthecoolingsystemwhich
leadstominimumcoolingtimeisnotachievinguniformcoolingthroughoutthemould.
_2008ElsevierLtd.Allrightsreserved.
1.Introduction
Plasticindustryisoneoftheworld’sfastestgrowingindustries,
rankedasoneofthefewbillion-dollarindustries.Demandfor
injectionmoldedpartscontinuestoincreaseeveryyearbecause
plasticinjectionmoldingprocessiswellknownasthemosteffi-
cientmanufacturingtechniquesforeconomicallyproducingof
precisionplasticpartswithvariousshapesandcomplexgeometry
atlowcost[1].Theplasticinjectionmoldingprocessisacyclicpro-
cesswherepolymerisinjectedintoamouldcavity,andsolidifies
toformaplasticpart.Therearethreesignificantstagesineachcy-
cle.Thefirststageisfillingthecavitywithmelthotpolymeratan
injectiontemperature(fillingandpost-fillingstage).Itisfollowed
bytakingawaytheheatofthepolymertothecoolingchannels
(coolingstage),finallythesolidifiedpartisejected(ejectionstage).
Thecoolingstageisofthegreatestimportancebecauseitsignifi-
cantlyaffectstheproductivityandthequalityofthefinalproduct.
Itiswellknownthatmorethanseventypercentofthecycletime
intheinjectionmoldingprocessisspentincoolingthehotpoly-
mermeltsufficientlysothatthepartcanbeejectedwithoutany
significantdeformation[2].Anefficientcoolingsystemdesignof
thecoolingchannelsaimingatreducingcycletimemustminimize
suchundesireddefectsassinkmarks,differentialshrinkage,ther-
malresidualstressbuilt-upandpartwarpage.Duringthepost-fill-
ingandcoolingstagesofinjectionmolding,hotmoltenpolymer
touchesthecoldmoldwall,andasolidlayerformsonthewall.
Asthematerialcoolsdown,thesolidskinbeginstogrowwith
increasingtimeasthecoolingcontinuesuntiltheentirematerial
solidifies.Overtheyears,manystudiesontheproblemoftheopti-
mizationofthecoolingsystemlayoutininjectionmoldingand
phasechangeofmoldingprocesshavebeenmadebyvarious
researchersandoneswhichfocusedintensityonthesetopics
andwillusedinoursystemdesignandvalidationsare[3–6].
Themainpurposeofthispaperistostudytheeffectofthecooling
channelspositionanditscrosssectionshapeonthetemperature
distributionofthemoldandpolymer,therefore,theireffecton
thesolidificationdegreeofthatpolymer.Afullytransientmold
coolinganalysisisperformedusingthefinitevolumemethodfor
aT-shapeplasticmoldwithsimilardimensionsto[5],asshown
inFig.1.Differentcoolingchannelspositionsandformsare
studied.
1359-4311/$-seefrontmatter_2008ElsevierLtd.Allrightsreserved.
doi:
10.1016/j.applthermaleng.2008.08.011
*Correspondingauthor.Tel.:
+330540006348;fax:
+330540002731.
E-mailaddress:
hassan@enscpb.fr(H.Hassan).
2.Mathematicalmodel
Theheatofthemoltenpolymeristakenawaybyforcedconvec-
tiontothecoolantmovingthroughthecoolingchannelsandby
naturalconvectiontotheairaroundtheexteriormoldsurface.
Thecoolantisflowingthroughthechannelsatagivenflowrate
andagiventemperaturewhichisconsideredconstantthroughout
thelengthofthechannel.Inthiswork,time-dependent
two-dimensionalmodelisconsideredwhichconsistsofanentire
computationaldomainofthecavity,moldandcoolingchannel
surfaces.Thecyclictransienttemperaturedistributionofthemold
andpolymerT-shapecanbeobtainedbysolvingthetransient
energyequation.
H.Hassanetal./AppliedThermalEngineering29(2009)1786–17911787
Nomenclature
C
P
(J/kgK)specificheatatconstantpressure
f
s
solidfraction
h(W/m
2
K)heattransfercoefficient
Knumberoftheinternaliterations
Llatentheatoffusion,J/kg
nnumberoftheexternaliterations
Nnormaldirection
S
csourceterm
T(K)temperature
t(s)time
Greeksymbols
k(W/mK)thermalconductivity
q(kg/m
3
)density
C1
interiorsurfaceofthecoolingchannels
C2
exteriorsurfaceofthemold
Subscripts
aambientair
ccoolingfluid
fphasechange
Inordertotakeintoaccountthesolidification,asourcetermis
addedtotheenergyequationcorrespondingtoheatabsorptionor
heatrelease[7],whichtakesinconsiderationtheabsorptionorthe
dissipationoftheheatthroughphasechangeprocess.Thistech-niqueisappliedonfixednodesandtheenergyequationinthis
caseisrepresentedasfollow:
AndthesourcetermScisrepresentedby:
wherefs(T)=0.0atT>Tf,(fullliquidregion)0 3.Numericalsolution Thenumericalsolutionofthemathematicalmodelgoverning thebehaviorofthephysicalsystemiscomputedbyfinitevolume method.Theequationsaresolvedbyanimplicittreatmentfor thedifferenttermsoftheequationssystem.Whenwetakeincon- siderationthesolidificationeffect,theenergyequationissolved withafixedpointalgorithmforthesolidfraction.Foreach,itera- tionofthatfixedpoint,weusediscretizationwithtimehybridex- Fig.1.MoldstructurewithaT-shapeproductandfourcoolingchannels(Dim.Inm). Fig.2.Differentcoolingchannelspositions(Dim.Inm). plicit/implicittechniquealreadyvalidatedinpreviousstudiesby Vincent[8],andLeBot[9]thatisbasedonthetechnique‘‘New Source”ofVoller[10].Thismethodproposestomaintainthenodes wherephasechangeoccurstothemeltingtemperature.Thissolu- tionisrepeateduntiltheconvergenceofthetemperaturewiththe sourcetermequalstothelatentheat.Thesourcetermisdiscret- izedby: Thesolidfractionwhichisfunctionofthetemperatureisline- arizedas: Then,weforcethetemperaturetotendtothemeltingtemper-aturewherethesourcetermisnotnullbyupdatingthesourceterm: Theenergyequationisdiscretizedasfollow: Thisprocessallowsdifferentiatingthetemperaturefieldandso-lidfractioncalculatedatthesameinstantandthelinearsystemis solvedbycentraldiscretizationmethod[11].Foreachinternaliter-ation,theresolutionofthatequationprovidesf nþ kþ1 K s andT nþ kþ1 K .The convergenceisachievedwhenthecriteriaofthesolidfractionand temperatureareverifiedby: Furtherdetailsonthenumericalmodelanditsvalidationare presentedin[9]. 4.Resultsanddiscussion Afulltwo-dimensionaltime-dependentmoldcoolinganalysis ininjectionmoldingiscarriedoutforaplatemouldmodelwith T-shapeplasticmoldandfourcoolingchannelsasindicatedin Fig.1.Duetothesymmetry,halfofthemoldismodeledandana-lyzed.Allthecoolingchannelshavethesamesizeandtheyhave diameterof10-mmeachincaseofcircularchannels.Thecooling operatingparametersandthematerialpropertiesarelistedinTa-bles1and2,respectively,andtheyareconsideredconstantduring allnumericalresults[5,7].Eachnumericalcycleconsistsoftwo stages,coolingstagewherethecavityisfilledwithhotpolymer initiallyatpolymerinjectedtemperature,theejectionstagewhere thecavityisfilledwithairinitiallyatambienttemperature.Figs.3 and4showthecyclictransientvariationsofthemouldtempera-turewithtimefor16smoldcoolingtimeatlocations; (P1,P2,P3,P4)besidethemouldwallsandP5toP7insidethemould walls,respectively(Fig.1)andthatincaseofappliedthesolidifica-tionandwithoutappliedsolidification.Theyaresimulatedforthe first30cyclesincaseofcircularcoolingchannelsposition(A5,D3) asshowninFig.2.Wefindthat,thesimulatedresultsareingood agreementwiththetransientcharacteristicofthecyclicmoldtem-peraturevariationsdescribedin[5].Itisfoundthatthereisa slightlydifferenceintemperaturesvaluesbetweenthetworesults, thusduetothedifferenceinnumericalmethodusedandtheaccu-racyinthenumericalcalculations.Thefiguresshowthat,therela-tivelytemperaturefluctuationislargestnearthecavitysurfaceand diminishesawayfromthecavitysurfa
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