A LOW COST COMPUTATION FOR APPROXIMATE PREDICITON OF GAS CORE CROSS SECTIONS IN GAS ASSISTED INJECTION MOLDING.

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1 A LOW COST COMPUTATION FOR APPROXIMATE PREDICITON OF GAS CORE CROSS SECTIONS IN GAS ASSISTED INJECTION MOLDING. A. Polynkin, J. F. T. Pittman, and J. Sinz Cntr for Polymr Procssing Simulation and Dsign, C 2 EC, School of Enginring, Swansa Univrsity, SA2 8PP, UK j.f.t.pittman@swansa.ac.uk A low cost mthod for th approximat prdiction of gas cor gomtry in gas assistd injction molding is dscribd. This uss a stady, singl phas flow solution for th mlt. For straight prismatic channls, a two-dimnsional solution is rquird. For channls of varying cross sction, or with bnds, a stady thr dimnsional solution is usd. Th location of th gas/mlt intrfac is prdictd by idntifying an appropriat isovl of th flow solution on th channl cross sction. Whn a gas dlay is usd, th influnc of cooling of mlt to th channl walls is takn into account by carrying out th transint conduction solution, followd by a flow solution using th tmpratur fild at th nd of cooling. Prdictions ar compard with molding trials, and usful agrmnt is obtaind, including th variation of rsidual layr thicknss around th circumfrnc of non-circular channls, th asymmtric location of th gas channl in bnds, and th incrasd rsidual layr thicknss rsulting from cooling during a gas dlay. Th computational costs of th mthod ar substantially lowr than th 3D transint, two-phas simulations that would othrwis b ndd. Introduction Gas assistd injction molding (GAIM) is an important variant of th traditional tchnology for injction molding of thrmoplastics. Aftr th mold cavity is filld or partially filld with polymr mlt, prssurizd gas is injctd to cor out thickr parts of th molding. This is usful for manufacturing two main typs of part: thin wall structurs with hollow rinforcing ribs, such as TV cabints, and fully thr dimnsional hollow articls such as handls. Th procss has svral advantags, including th us of a rducd packing prssur which is applid uniformly, rsulting in rduction of moldd-in strsss and incrasd dimnsional stability. Rducd wall thicknss also rducs th liklihood of sink marks, and rducs cooling tim. As for othr typs of molding, th availability of simulation softwar is important for tooling and procss dsign. Widly usd commrcial packags,.g. (1), rduc computational dmands by simplifying th gomtry, rprsnting th parts cord out by th gas as quivalnt circular sction channls. Information on th wall layr dpositd whn gas displacs liquid from cylindrical tubs is thn usd to stimat gas cor out. Th rsult is a figur for th prcntag of th channl cross sction occupid by th gas cor. It follows that no information is providd on variations of th plastic wall thicknss around th circumfrnc of th channl, or on variations of wall thicknss in bnds tc. Additionally, th dfinition of an quivalnt circular sction channl can bcom difficult whn th part gomtry is mor complx. To addrss ths limitations thr-dimnsional simulations of GAIM hav bn dvlopd,.g. (2, 3). Dtails of our work in this ara ar givn in (4, 5). Ths calculations ar computationally intnsiv, and a quickr, chapr mthod for stimating gas cor cross sction and location in channls of arbitrary sction would b usful. In th prsnt not w dscrib such a mthod. For straight, prismatic or slowly varying channls this rquirs only th two-dimnsional solution of th stady dvlopd mlt vlocity profil on th channl cross sction. For channls that ar curvd or of varying cross sction a solution of th stady thr-dimnsional flow fild is rquird. If mlt cooling is significant, as whn a dlay is usd bfor gas injction, a prliminary solution of th transint conduction problm is also ncssary. Th computational dmands of ths calculations ar on or two ordrs of magnitud lowr than rquird for th full thr-dimnsional transint simulation of th two phas gas injction procss, such as is usd in (2-5). Whil this lattr approach will still b ncssary for complx parts, th prsnt approximat mthod will b hlpful in many othr cass. In rcnt work w studid th displacmnt of shar thinning liquids by a gas in prismatic channls of various cross sctions (6). W wr abl to rlat th thicknss of th rsidual layr lft aftr gas has cord out th channl to th shar rat at th wall. This is rflctd in th pattrn of isovls on th cross sction, and this forms th basis of th prsnt approach. Th Polymr Procssing Socity 23rd Annual Mting

2 Computation Th mthod uss a finit lmnt solution for th stady, singl phas flow of th polymr mlt passing through th channl of intrst. For a straight prismatic channl, with z th axial dirction, a solution for th dvlopd flow v z (x, y) is rquird. For channls that ar curvd or of mor sharply varying cross sction a solution of th stady thrdimnsional flow is rquird. Th location of th gas-mlt intrfac rsulting from gas injction is thn approximatd by th isovl of an appropriatly dfind man vlocity on a plan prpndicular to th principal flow dirction. This man vlocity is computd by intgrating th vlocity componnt normal to th cross sction and dividing by th cross sctional ara. From numrical xprimnts it has bn found, howvr, that bttr rsults ar obtaind if rgions of low flow vlocity ar dltd from th calculation of ara. Thus th adjustd man vlocity is thus computd as v da' n v = da whr v a' n a, A a a = a if v v =, λ, λ 0.1 n n a = if v < v = 0 λ, λ 0.1 n (1) (2) Hr A ' is th adjustd cross sctional ara, obtaind by summation of th aras of th finit lmnts, a, within which th man normal vlocity is gratr than or qual th spcifid fraction of th imum valu on th cross sction. Th fraction λ = 0.1 is chosn mpirically. This adjustmnt is particularly important in accounting for th ffcts of cooling, whn incrasd viscosity nar th walls rsults in rgions of low flow vlocity. In this cas A ' can b significantly lss than th actual cross sction. Sinc vlocity componnts lying in th plan of th cross sction ar gnrally small, th magnitud of th vlocity vctor v can convnintly b usd in plac of th normal componnt. In th flow simulations th polymr mlt rhology is rprsntd by a tmpratur dpndnt, truncatd powr law modl, which avoids unboundd viscosity at zro shar rat. n 1 (3) µ = K γ γ > γmin µ = µ γ γ min K = K xp[ b( T T )] rf In th non-isothrmal cas, mlt solidification is rprsntd by a rapid incras in viscosity at th no-flow tmpratur. Dnsity and thrmal proprtis ar tmpratur dpndnt. Comparison with molding trials Th approximat mthod is hr compard with rsults from molding trials rportd arlir (4, 5). Tubular handl rf Th gomtry of th part and injction gat location ar shown in Fig. 1. Matrial usd is th polystyrn STYRON 634. Gas injction prssur is 110 bar, and gas dlay (aftr compltion of th plastic short shot) 1.2s is usd. A dtaild account of molding conditions can b found in (4). Computd rsults using th approximat mthod ar compard with moldd parts sctiond on th plans as shown in Fig. 1, and also with th rsults of a full transint 3D simulation. Th Polymr Procssing Socity 23rd Annual Mting

3 Fig. 1. Comparison of prdictions by th approximat mthod, dottd lins, with rsults of molding trials, and with prdictions by a full, transint, two-phas 3D analysis, full lins Th simulation givs good approximations of wall thicknss variation on a longitudinal sction of th handl (.g. in th upstram part) and on a cross sction in th middl part of th handl. In this xampl, polymr and gas injction is sufficintly rapid for ngligibl cooling to tak plac, and th procss can b considrd to tak plac undr isothrmal conditions. In th following xampl, whr a gas dlay is usd, this is not th cas. Glass window mold tool Th xampl is from a spcial tst tool producing a part with typical faturs of gas assistd injction application, having a hollow rib attachd to a thin plat. Th cavity is cut into on half of th tool mad of stl. Th othr half consists of a thick, flat glass plat, allowing vido rcording of th progrss of th molding. Polymr injctd is BP matrial PS HF888. A full dscription of th application xampl including molding conditions is givn in (5). In th prsnt study two procssing conditions hav bn chosn for comparison. Gas dlays 4s and 8s wr usd with injction prssur 50 bar. To tak into account th ffcts of th gas dlay, th transint conduction simulation for cooling of static mlt to th cavity walls is first carrid out. Th flow problm is thn solvd using th tmpratur fild at th nd of th cooling priod. It should b notd that th short cut mthod has bn dvlopd to captur th cor formation by primary pntration of th gas, and it dos not modl th scondary pntration rsulting from polymr shrinkag during cooling. Thus th cutting sctions on th moldd part shown hr wr mad in locations whr th gas channl is influncd only slightly by scondary gas pntration. Th rgion adjacnt to th thin plat whr fingring du to scondary pntration occurs has not bn includd. Cross-sctions of th gas channl at positions 1 and 2 ar shown in Fig. 2 and 3. Th prdictions of th short cut mthod agr closly with xprimntal rsults. Th thickr wall rsulting from a longr gas dlay is capturd wll, as is th unvn thicknss distribution in bnds. Th Polymr Procssing Socity 23rd Annual Mting

4 Fig. 2. Comparison of prdictions by th approximat mthod with rsults from molding trials. 4s gas dlay. Conclusion Fig. 2. Comparison of prdictions by th approximat mthod with rsults from molding trials. 8s gas dlay. A simplifid approach to stimat th form and location of th gas cor and th rsidual plastic wall thicknss in gas assistd injction molding has bn dscribd. Th approach is basd on stady-stat flow analysis for a singl fluid (polymr mlt) and th idntification of an appropriatly chosn isovl of th flow. Th mthod is inxpnsiv sinc it dos not involv transint two-phas flow solutions, and for prismatic or slowly varying channls only a twodimnsional dvlopd flow solution is rquird. Th rsults prsntd hav shown how rasonably accurat prdictions ar obtaind for th position of th gas bubbl intrfac in channls of various cross sctions for both isothrmal and non-isothrmal cass whr cooling occurs during a gas dlay. In contrast to othr approximat mthods currntly in Th Polymr Procssing Socity 23rd Annual Mting

5 us, variation in plastic wall thicknss around th circumfrnc of non-circular channls is capturd, as is th asymmtric cor location on bnds. Studis aimd at adapting th valu of λ to matrial proprtis or procssing conditions may also provid mor prcis prdictions in gnral. In furthr softwar dvlopmnts, rsults of th analysis may b usd to prdict th lngth of gas pntration by intgrating th gas cor cross sction along th flow dirction. In short shot procssing, whn th plastic initially fills only part of th cavity, th gas pntration distanc is obtaind whn th gas cor volum quals th initially unfilld cavity volum. By also intgrating th volum of th rsidual plastic layr, th occurrnc of blow-out (th gas cor catchs up and blows through th mlt front) can b dtctd. In full shot procssing, whn gas displacs polymr into an ovrflow chambr, pntration continus until th gas cor volum is qual to th ovrflow volum. Th rsulting information on th gas cor gomtry may b usd to construct a 3-D CAD modl of th gas cor, and thnc of th hollow molding, for subsqunt strss analysis, part wight dtrmination tc. Whil th dscribd mthod provids good approximations at low cost, full thr-dimnsional analysis will still b ncssary for complx parts and whr high accuracy is rquird. Rfrncs 1. MPI/Gas 2. G. A. V. Haagh, G.W.M. Ptrs, F.N. Van D Voss, H.E.H. Mijr, Polym. Eng. Sci., 41, 449 (2001). 3. F. Ilinca, J.-F. Htu, Int. J. Numr. Mth. Eng., 53, 2003 (2002). 4. A. Polynkin, J. F. T. Pittman, J. Sinz, Polym. Eng. Sci., 2005, 45, A. Polynkin, J. F. T. Pittman, J. Sinz, Int. Polym. Procss, 2005, 20, A. Polynkin, J. F. T. Pittman, J. Sinz, Chmical Enginring Scinc, 2005, 60, Th Polymr Procssing Socity 23rd Annual Mting