REVISTA MEXICANA DE FÍSICA -tS SU'LE.\IE:STO 1, 1-)

Injection moulding proccss modelling anel optimization

A. García-Rcjon. J.-E Hétll, D.M. Gao, ami L. PecoraIndustrial IvlafC'rials /lIstitltfC', Nmiollal Research Cmmcil Callada

75 De MortaRllc, BOllcherl'illc, Québec J.JB 6 Y'¡ C(llIada

Recibido el 2ú de febrero de ItJ9X:aceptado el 15 de Illar/o de It)t)X

JUNIO 1999

The rapid gro\\'lh in Ihe use 01' advanccd matcrinls in a large numhl'r of highly demanding aulolllolive, ~porlS &.. leisure. elcclronics. tram-pmlation ami packaging applications has promotcd the dcvclopment uf ne\\' and more nllnple;<; Illaterial forming proccsses. The polymcrprocc~siJlg lidd has gained imponance due to Ihe optimi/ation 01'nisling processes and lo the de"l'lupl1lerlt 01' ne\\' proccssing techniquesernploying novel cOllceplS. Injection moulding techniques such as gas-assislcd injection moulding have cxpamlt:L1Iheir range 01'application~.The complcxily of Ihese new moulding: lechniques amllhe need lo comply lo slricter tolerances ami demanding scrvice condilions calJs for;)J1l11chhet1er underslanding of Ihe material hchaviour during lhe hasic stagcs 01'lhe process and ils relalion lo the propcrties and performance01'lhe linal pan. Thesc characteristics are dirc(.'lly dependent upon fllould dcsigns and on lhe opcrating conditions during melting:. injecti(lnand cooting in lhe l11oulds. In Ihis papcr \"'Cwill uemonslrate ho\\' lhe nUl11cricalsirnulation (2.5 ami JD models) of the individual sleps 01'lhe injel"tioll alltl gas assislcd injection moulding processes can he used to optimize the process alltl prodll(,:t performance 01'industrinl pans.

}\('.l"\l'Imls: Injl'clioll mOlllding; gas assisted injeclion ll1outding: compuler simlllalion; oplimizalion

El r¡ípido allmenlo en el liSOde materiales avanzados en un gran mJmero dc automotores altamente dl'millldados. deportes y enseres. etec-trúnica. transporte y empaques. ha fomentado el desarrollo de Iluevos y m:ís complejos procesos de formación de maleriales. El rampo tkpn)(.'esillllicnto dc polímeros ha ganado importancia dehido a la oplimi/aci6n de !os pr(lcesos e;<;isll'ntes y al desarrollo de nuevas técnicasdc proceso l'mpkillldo cOI1l:eptos novedosos. Las técniGls dl' moldeo por inyecci6n como el Illoldeo por inyección asistido por gas, hnnC'xtl'nuidil su l'iunpo de aplicaciones. La complejidad tIe estas nuevas técnicas de moluco y la nl'(.'csidad dc cumplir con las loleranciasestrii..'las y conLli(:iones dl' servicio demandados, requieren de un mejor entendimiento del Ctllllpt1rtamil'nto de los malerinles durante lasetapas h:ísicas JcJ proceso y su relación con las propicJades y funcionamiento de la parte final. Estas caral"terísticas dependen directamentl'lIl' los diseilos dcJ molde y de las condiciones de oper.¡ci6n duranll' la fundición. inyen:it'in y enfriamiento en los moldes. En este artículodellloslraremos rómo la simulación numérica (moldes 2.5 y JD) de los intervalos individuales de los pnx"csos tIl' moldeo por inyección y deinyecci(lll asistida por gas pueden usarse para optimizar el proreso y funcionamiento del producto de partes induslriales.

1h'.\{Til'tOH'.\: ~loldl..'o por inyeccidn: moldeo por inyc(.'rión asi~tiuo: simulación por computadora: optimi/:ll'ión

I'"es: 1'1.20.-n

1. Injection llIoulding process [1 J

Injection lIlo1l1ding (Pig. 1) can he dividcd into four basi(.;SI¡¡g~S: plastifkalion; injc(.;tion; packing and (.;ooling and ~jec-lion. In Ihe plastilkation slagc the raw malerial in solid forlllis lransforllled inlo mollen material through lhe comhincd¡¡((ioll 01" the friction providcd hy a rotating sue\\' ami lhehe al provided hy exlernal heating elcrnents. Thc screw re-lrarls durillg rotation in orde!" to accolllodale the Illollen lT1a-lcriallhal ;ll"l'Ulllulales in front of the screw. Onl"C a suflicient<llIllTlounl of material is availahlc. lhe scrcw 1110VCSforward,(.;tlusing lhe molten rnalerial to nll the cavity. Upolll'olllple-¡ion 01' lil1ing, additional material is packcd inlo the cavily inonlcr lo compensale for lhe shrinkage occurring during lhei..'ooling slagc. Once solitlilicd. the J110ulded artide is ejectedand the scqllence 01' evenls is rcpcalcJ in a cyclic manllcr.Due lo lhe pOOl' thermal (';(lIldllctivity of polymcric material s,lhe cooling lime gencrally constitules the dominanl portion(JI' ¡he 1l1Oulding l'ycle.

Gas assisled inje<..'lion moulding (Fig. 2) has rapiJlygained a(,l'eplanee dlle to its \'crsatilily in lhe prodllclioll nI"

rH,URE l. Injcclioll Illoulding rroccss.

complex hollo\\' parts. Duc to lhe gas/polymcr interactiotlduring the gas interaclion during the gas injection phase,the pressure reqllircl11cnts as wcll as lhe shrinkage/warpageof the part can he grcatly reduecd. The typical gas-assistedinjection moulding process comprises lhe fol1O\\'ing stcps:a) polymcr f1l1ing; h) gas injcclion; and e) packing slagc.During polymer lilling the cavily is partly fillcd (up lo 80%).Shortly after the cnd 01' the polymcr injcction, the gas is in-jected to hollo\\'-ollt lhe gas channels until the cavity is com-pletely t1l1ed. The rclativc Illclt/gas llowrate \ViII determine

2 A GARCíA-REJON. J.-F. IIÉTU. IlM GAO. ANO L I'ECORA

Fr(iU\{E") Gas AssislcLl injectíon llloulJing.

Frozsn layerGas pene!ra1iOnregion• PoIymeifIIedrBQIOl'1 IE~ f't9on

Calculaban cIomain

2.1. :"'umcri<.'all11ndcl

In Ihis sludy, the plllymc]" lIlelt is i..'ollsit.lered as a GCllcralilet.lNe\\'lonian Fluid (Carrcall- \VLf). Thc 11m\' is assllllled lo heqU:lsi.slcat.!y slale and Ihe inertia tenns are ncglccted tluelo Ihe low Reynolds nUlllbers encountered in moltcn poI)'.IIlcr Ilo\\". Since lllosl parls prodUl'cd hy gas-assislcd injectionIlloulding haye a shl'lIlikc g.colllelry, ¡.c. Ihe part thickness ismuch smallcr (ove]" Ol1l' order of magnilude) Ihan olher partdilllensions, Ihe lul1rication approximation (Helc-Shav.'llow)can he used rOl" 1Il0delling lhe glohal 11m\' hehavior in IhelIlould cavity. \Vilh thesc assumplions Ihe t1l1ing of a molocavit)' hecoll1cs a 2D llo\\' pmhlclll for the gapwisc avcragedvclocily which is relaled 10 Ihe pressure gradient Ihrougha qllanlily called "Iluidily" rcprcscnling Ihe slIm of Ihe cf-rcet 01"changing Il'lllpl'ralure ano rheology ¡¡cross the gap.Thcse Illodels are cOllll1lonly knowll as 2.5D IlHH.kls 1'2,31.The Hele-Shaw approx.illlalion can oc written as

Empty

3

FI(;UkE~. Schcmatil.:of now noss s('('lion during gaspenelf;llioll 'V, S'V r = O, ( 1 )

\\-'herc S represents Ihe flllidily delineo hy

and P is lhe in-plane presslln.' and :.; represel1ls any locailonacross the thickness nI" lhe parto

1I should he noted Iha,l dLle lo Ihe Helc-Shaw appmxima-tion, lhe full IHH.lip condilioll does nOI hold at Ihe mould\\'all.

The cncrgy equalion can he wrillen as

Ihe <11ll0Ullt(O he 1101l0wcd. In practicc. due 10 lhe gcolllclricalcomplcxitiy 01' parls, Illultiple. disconncctcd gas channcls areoftL'n lIscd lo transmil lhe prcssurc as unifonnly as possihlcOvef lhe clltirc parto

The optilllization 01' Ihe injcctioll Illoulding proccss im.plics Ilnding lhe approprialc rclalions hClwccn allll1e rroccssparamCll:rs as \\'ell as ils n:lalionship with lhe Illould gcolll-l'lry and the final pan propcrtics. Silllulalion models can beUSL't11Osyslcmatically sludy ¡hese relalions wilhotll having tolkpcnd 011time-consuming ami expensive Illoulding lrials. In[his paper we will Jemonstrale ho\V Ihe l1umcrical simulalionof lhe individual sleps 01"Ihe process can be used lo optilllilelile gas assisled injeclion Illolllding oran experimental par! aswe]] as Ihe 3D Iilling nI' a cal" door handle.

/

,11 (Z')S = - do. [) '1

'{UT (U,7') (iJT)} D [ (UF)]1'( -+ i/ - + /' - =- k -/' DI iJ,,, j)y uo Do

(2)

+ <1', (.1)

In Eq. (3),.1' amI y denole Ihe coordinales of lhe middle planc,.:-is Ihe gapv •.'ise dircclion. T is Ihe lemperalure, {I is lhe dcn-sily, e" is Ihe specilic hcal, k is Ihe Ihennal t.."onduclivily ami<J. rcprcscnls lhe visc{)us dissipalion. A dimensional analy-sis 01' lhe energy equallon sho\\!s that Ihe heal COndUl'lion inIh~ now direclion can he lleglecteJ since lhe lhil'kncss 01' Ihecavil)" is Illuch smaller Ihan lhe other IWO dilllcnsiotls. Thcl'onvcclion in Ihe gapwise dirccli(ln is also ncgkeled. Thc 1"01-lowing houndary conditions have to be applicd:

2. (;as assisted injccti()n lII()ulding

¡\ schelllatic "ie\\' of lhe Ilow eross seclion Jurin!! Ihe gasinjection is SIHl\Iin in Fig. 3. During lhe gas injec[ion slage.Ihree dislinel flow regions can hl' idenlified: 1) gas pCIll'lra-lion I"egion. 2) polymer 1ll1'It region, and 3) elllply 01"unlilledregion. Rcgion I is inilialty fil!ed hy Ihe polymer. The gasIk'nelrales illlO IIH.~poIYllll'l"mell and creales a gas ((lI"e. Dur-ing lile gas penclratioll, the gas is transmitling Ihe pressuu:requirl'd 10 advance Ihe JIlclt fronl. Thc polYlllcr skin layerht:lween lhe gas and lhe IlHHlld walls is slagnant. Il is assllllledIhallhl' skin layer COllsiSls 01"a ...•olidified la)'er amI an adhl'n:dIayer. The solidilied layn is formeJ by Ihe polymer frcoingUPOll contacl willl Ihe cold ll1ullld. The adherenee hCI\\'ú'll[he polYlllcr !low ami lhc solidilicd layer creates lhe adhen:dbyer. Rq!iolls 2 alld 3 ¡¡re idclIlical to Ihose elll'Olllllercd inCOllVeJ1liollal injcclion mUllid filling excepllhat tW(l lIlovinghoundarics for Ihe polymcr ml'll regioll are prescnt.

PnlYllll'f Iilling phase

Atthe POIYIIlCf gate ..••i2 = i2(1) or [' = 1'(1)r = J~,,,,lt

Al lhe l10w frollt

J> = OT = 7~"",.(FOlllltaíll

Ilow l'ffl'cl)

T(t = O) = TI1l011ld.

Ga\ lilling: ph~scAllhe gas injl'ction locatioll"1'=1'(1)r = l~mlll~1lt lO •. ga ..•COf'~

(4)

H{,\ ....\11'\. ¡:¡"\ -13SI (199tJj 1-)

INJECTION MOULDING PROCESSMODELI.I:'\G ANI) (Wn~lIZAT/().\I

r:1(iURE 4. PolYl1lcr. Front lor.:alion al Ihe eno of potimcr injeclion.

l.~,= 1 (.I(,lllE'll! l'Olllllll'tl'iy fil1cd wilil polYlllcr.

0< F, < () ('J<'lIlt.'lll isaskinlayer(gaSIH't1ctratioIl).

3. Illjectioll lIlouldillg 01'a car door halldle

.•

.,_.•.,.-.•., .•.•. -.1...•.•..

...•..•,.•.

(h)

(a)

Fl(jUR[; (¡ TcmpnalUrl" di"lrihulioll al lhe cml uf polymcr injcc-(ion.

J." Eqllatioll."; in Iht, t"avily

F[(;U1n: 5. Gas pl'lIelralioll al the end of lllouloing: (a) llulllericalprcdiction: (h) cxpl'rirnelllal

Tlle Slokes equalions (creeping I1mv, U(' .......,O) are solvcd on¡he fil1ed porlion nI" lhe cOlllpulalional domain as well as onlhe emply region l'losc lo lhe now front. 11is asslllllcd Ihal (heair can exit Ihe cavity withouI reslrÍ<.:tions and that ils \"cloci-

(5 )F, = O ('lIlJlt~'I'IPIllPllt.

The Helc-Shaw equatioll is solved using a (Jalcrkin Iype [i-nile elclllellllllelhod l;jl.

Figure 4 shows the IOC:llion nf the polymer front al Iheend of (he polYllIcr injcctioll (72l'A, lill). To assurc a halanceJ1¡I!jng, two injcetioll gales were lIsed.

figure:) shmvs lile final gas pelletralion al lhe eno nI'Il1Iing. Sinee Ihe gas channel designed for this part containsIhree hranching palhs. Ihe gas injeclion point is lo<:ateu at theinlcr ...•eclion 01' Ih(: branch(:s. The gas p(:nclralion (darl..: arcas)in Ihe gas channels is wcll predicted hy the numericallllodelas delllonslrated in an actual JI1(lulded part (fig. 5h).

At Ihe eml uf polymer injeclion (fig. 6), a hroad tcmper-allln; dislrihution is present in Ihe part, specially arollnd Ihegales arca. The injeclion of the gas generales a more uniforlll11'Illpcralure licld (Fig. 7). This will result in a more uniforlllshrinkage and tess warpage compared lo convcntional injcc-lion lllolllJing.

Several situalions (ll"l"urring during Illold f1l1ing cannol how-L'\'cr he accur¡¡lely pn:dicled lIsing lhe Hcle-Shaw approxi-maliofl. Alllong 111(:most important \Ve can cile lhe Huid he-haviour al the free surfacc (!low front); the fluid hehaviuor!lear and al Ihe solid \\'alls: the phenomenon occurring at theIllerging nf {wo or more tluid streallls (\\'eldlines): lhe kine-1Il:llics in arcas where shear ami cXlensional dcformationsconlrihu(c signiti\.':llllly lo lIJ\."stress licld (gates, rihs, sud-den Ihickness changes, etc); and Ihe now hchaviour in thicl..:.walled parts. Thcrcfore, a fuI! 3D Illodel has lo he used topredict lhe filling 01"a cavity IGI.

A control \'olulllc approal'h has hecn cmployed lo traeklhe !low front advaIlCClllcnll.l, ,JI. A scalar parameler, F, of-len ealled "lilling faclor". is llseo lo represent the state 01' lill-ing for each elelllenl inside Ihe c¡¡vily. A polymer skin Ihick-!le...•...•fraelioll. F, i...•dclillcd as

J<e\~Me.\'. Fis. -l5SI ([t)t)t)) 1-5

A, GARCíA-REJON. J.-F IIÉTLJ. J),~1 GAO, ANI> L I'En mA

.('" .-, (1 ••• = I,,,,[T - T",I Oll r('oolillK lill"s'~,.(111 = 1,,,[1'- 1'0] on ramhi"lllo ( 1 1 )

,...'~"•...-~....•.04_'"

FI(illl<1: 7. Telllpcr:ltllrc dislrihlltioll al lhe cnd 01' gas injcction.

ty is small ¡,:olllparcd lo lIJe spccd 01' sound. Thc fluid is :lS-Sllllll'd lo bl' incompn:ssible ami gravily lcrllls are I1cglcctcd.The cqll:ltiollS govcrning Ihe laminar llow 01' lhe polymermdt are (hen exprcsscd as

wllcre "11" Tu'o and "a, T.¡ represent tlle heat lransfer coeffi-cient and lile tempcralurc al lhe l110uld wal! and al amhicl11cont!ilions respectively.

-'.J. Ca\'ity~mnllld interface

¡\ lhl'rlllal L'Olllacl n: ...•i"lance is lIscd al tlle Illould/cavily sur-face 10 model Ihe heat lr;¡nsfcr modilied hy lhe presente 01'luhricants (noll-ideal contacl)o elL'. The heal Ilux al lhe inter-face can he \\Tillcll as

v [' - v. [2'/h, F)¡(ú)] = O, (ha) -'•..•• Fl'OlIt tr~Il'kill~

( 1,1)[')l' ]_'_o +1l.\"FiJI

The tracking 01' lhe /low front in the moulJ cadty is Illodelcdusin~ lhe PSl'Udo-collcenlralion ~1Clhod [GI. The Pselldo-cOIKl'ntration l'qualion can he writtcll as

(7)

(6,)

(6h)v . fI = O OH nc;wítyo

-0'f(1 \')"')'I-I/"'/ = ,/O t'xl' + "'-,- -.

whl'rC

-,(/1) = ~ [VII + (V/I)T].

The matcrials rheological hchaviuor is Illodelled hy llsingtlll' Carreau-Arrhcllius conslillltive eqllation

Tlll' COllSl'f\':llioll 01' encrgy in lhe c:lvily is cxprcsscd as

[iJl! ]/' ¡¡¡+ /l' vI! = V. (kvT), (X)

This mollel delines a distanel' fllllclion F(.I', t)o \vhich repre-sents 11lL'filkd portioll of lhe CI\'ily whell F is grealcr lhan acrilicd value, ¡:;.. Thc critical G~is an isosurfacc rerrcsenl-ing tlll' lllL'lt-air inlerface. Thc prohlelll slalclllenl 01' Eq. (S)is l'Oll1plclL'd willi llll~ following definition 01' lhc fllllClioll F:

¡f(./"1) rcpresl'l1ts lhe dis!ance fmm lhe interlal'c. F'(.r, t) ISrl'inilialilcd afler caeh time qCP lo guaranlL'L' mass con ....l.rV;I-Iion.

Tlll' incornpre ...."ible 0.'~I\in-SI{)kc ....and lOlllillllil~ Eqs.(6) illlhc c<lvily are ....ofvL'd hy llslng: a mi.\ed \'t:locity-prcssurclinitL' c1CIllCllllllCthod [-;-.~I.AII lhc eqll~l1ion" are ....ol\cd lIS-in~ a sll'camline 1I11\\'illd PClnl\'~(lalerkin tSUPG) slahililedformulalion. Tlll' supe, rormulalion i'i ¡tl...o lI'ied to ....oln: thefmllt Irad;,in~ l'qU:llioll. Thi'i cquation is disLTCli/ed lI"illg lin-l':tr cklllCllls.

h,gllrl' :-; sho\Vs thl' ....olid lllodL'l {JI" the cal' door handll:ílnd llIould :lS....l'1I1hly. Thl' lillilc c1Clllcnt mesh ha" 1(,9 633letr<d1l'drall'lclllcllls~52 I(JI in lhe (avily ami 117532 in111l'I¡¡(luld. t\ liul 1'L1llncrwilll :1 CL'IlICr"rrue i....used to fecdtlll' 1I1alnial illlo lhl' L,;tvily.

\\'hl're 11 dCllolcs t!Jl: fluidOs enlhalpy,Thc following hOllndary conditions apply:

/1=0 011 r (Dirichlot) ,

(2,/', .//)-['//=0 on rlfflcliono

/1 = O for (F 2 F,),

(1'n=O for (F:S. Fe) onrwall' (<) I

TIlL' hOllnd;¡r~ COllditioll on rwall i" imposcd only on lhl' lil]-ing malcrial.

-'020 Equatiolls in tl1(' mOllld

Tlll' 111\luld i ..• l'tlll"iden:d unl)' ror l1eal tramfer purpose ....Tlll'refore. Illl' enl'r~y cqllalioll is ,givcn as

¡)I'/lIl/('/)III[7i/]=\"'(I,'//lVT) OH OIll()llld, (lO)

wilh htHllldary l'tllldili(lnS

{

j.;. + "(." i)q,l, /) = j.;.

1;-"(.1,/)

,1' il1 I he filk,( 1n 'gi(lll

.1 al dI" (1-1)

.1' in tIH'I'JrIpt.\' n'!l,i()H

Un . .\-/n. ¡:Ú 45 SI (]t)l)(j) 1-)

I~JECTION MOULDlNG PROCESSMODELLING AND OPTI~lIZATION 5

(b)

(d)

(f)(e)

(a)

(e)

FIGURE 9. Flow front aJvanccmcnl at Jiffercnl tilling stages.(a) 0025 scc, (b) 0.05 sce, (e) 0.10 see. (d) 0.30 scc, (e) 0.40 sce,(f) 0.50 see.

4. Conclusions

FIGURE 8. SaliJ moJel of the C,lr Joor hanJle anJ moulJ a~scmbly,

T\vo l¡nile elclllent mollels (2,5 and 3D) have heen tlevelopcd((l simulate thc lilling slagc for gas assistcd injeclioll Illould-ing and Ihe injeclion mllUlding of a thick-walletl parl. The ha-sic phenomcna 01"!low front advanccmcnt antl prcssure andlemperaturc tlistrihulions can he accuralely prediclcd hy themodcls.

Figure 9 shows Ihe advancclIlcnt 01"Ihe !low fronl al dif-ferent slages 01"lhe filling rhasc. Jt can he scen that Ihc ma-Icrial cn(ers lhc cavity, hits thc oppositc waIl and thcn ad-\'anccs towards Ihe mctal inscrt locatcd at both ends of theparto The malerial 110ws around Ihc inserl and \vill form awcldlinc \vhich might he a possihlc weak spot in the finalparl.

1. D, Rosalo anJ D. Rosato. ¡"jection ",oldi,,~ IIwulhook. (VanNostranJ. Ncw York 1989).

2. C.A. lIicbcr. 1. NOII-New(ollia" Fluid Mec!ulIlics 7 (1980) 1.

3 p, KcnncJy. Flo\\' Allalysis oIllIj('clion Motllds. (Hanscr. NcwYork. 1995) .

.1. c.w. Hirtand B.D. Nichols.J. Comp. Physio39(1981)201,

:i J.M. Floryan. and 11, Rasmusscn. Al'pl. Mech. Rt'I'. 42 (1989)323.

G. J.-E Hétu. O_M.Gao. A. García-Rcjon. and G. Salloum. PolYIn.FII!:. Sei . .'X (1998) l.

7, F. Ilinca. J.~F Hétu. and D. PcJ1cticr. ProCt't'dill[!.so/ tire 13thAlAA Con/en'flcl" AIAA97-1863. Snowmass. ca (June 1997).

8. J.-F. Hétu and F. 1Iinca, Proeeedings o/ ¡he 10th I"tema-tim/(/l Cm,{t'rt'llce m¡ Numaical Ml'tJlOds /or Thermal Probolel1/J. Swansca U.K. (July 1997),

Rl'I'. A/c.\". Fú. 45 S1 (1999) 1-5