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Effect of cooling system on the polymer temperature and solidificationduring injection moldingHamdy Hassan*, Nicolas Regnier, Cedric Lebot, Cyril Pujos, Guy DefayeLaboratoire TREFLE-Bordeaux1-UMR 8508, Site ENSCPB, 16 Av. Pey Berland, 33607 Pessac Cedex, Francea r t i c l ei n f oArticle history:Received 15 November 2007Accepted 19 August 2008Available online 30 August 2008Keywords:PolymerSolidificationInjection moldingCooling systema b s t r a c tCooling system design is of great importance for plastic products industry by injection molding because itis crucial not only to reduce molding cycle time but also it significantly affects the productivity and qual-ity of the final product. A numerical modeling for a T-mold plastic part having four cooling channels isperformed. A cyclic transient cooling analysis using a finite volume approach is carried out. The objectiveof the mold cooling study is to determine the temperature profile along the cavity wall to improve thecooling system design. The effect of cooling channels form and the effect their location on the tempera-ture distribution of the mold and the solidification degree of polymer are studied. To improve the produc-tivity of the process, the cooling time should be minimized and at the same time a homogeneous coolingshould be necessary for the quality of the product. The results indicate that the cooling system whichleads to minimum cooling time is not achieving uniform cooling throughout the mould.? 2008 Elsevier Ltd. All rights reserved.1. IntroductionPlastic industry is one of the worlds fastest growing industries,ranked as one of the few billion-dollar industries. Demand forinjection molded parts continues to increase every year becauseplastic injection molding process is well known as the most effi-cient manufacturing techniques for economically producing ofprecision plastic parts with various shapes and complex geometryat low cost 1.The plastic injection molding process is a cyclic pro-cess where polymer is injected into a mould cavity, and solidifiesto form a plastic part. There are three significant stages in each cy-cle. The first stage is filling the cavity with melt hot polymer at aninjection temperature (filling and post-filling stage). It is followedby taking away the heat of the polymer to the cooling channels(cooling stage), finally the solidified part is ejected (ejection stage).The cooling stage is of the greatest importance because it signifi-cantly affects the productivity and the quality of the final product.It is well known that more than seventy percent of the cycle timein the injection molding process is spent in cooling the hot poly-mer melt sufficiently so that the part can be ejected without anysignificant deformation 2. An efficient cooling system design ofthe cooling channels aiming at reducing cycle time must minimizesuch undesired defects as sink marks, differential shrinkage, ther-mal residual stress built-up and part warpage. During the post-fill-ing and cooling stages of injection molding, hot molten polymertouches the cold mold wall, and a solid layer forms on the wall.As the material cools down, the solid skin begins to grow withincreasing time as the cooling continues until the entire materialsolidifies. Over the years, many studies on the problem of the opti-mization of the cooling system layout in injection molding andphase change of molding process have been made by variousresearchers and ones which focused intensity on these topicsand will used in our system design and validations are 36.The main purpose of this paper is to study the effect of the coolingchannels position and its cross section shape on the temperaturedistribution of the mold and polymer, therefore, their effect onthe solidification degree of that polymer. A fully transient moldcooling analysis is performed using the finite volume method fora T-shape plastic mold with similar dimensions to 5, as shownin Fig. 1. Different cooling channels positions and forms arestudied.2. Mathematical modelThe heat of the molten polymer is taken away by forced convec-tion to the coolant moving through the cooling channels and bynatural convection to the air around the exterior mold surface.The coolant is flowing through the channels at a given flow rateand a given temperature which is considered constant throughoutthelengthofthechannel.Inthiswork,time-dependenttwo-dimensional model is considered which consists of an entirecomputational domain of the cavity, mold and cooling channelsurfaces. The cyclic transient temperature distribution of the moldand polymer T-shape can be obtained by solving the transientenergy equation.1359-4311/$ - see front matter ? 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.applthermaleng.2008.08.011* Corresponding author. Tel.: +330540006348; fax: +330540002731.E-mail address: hassanenscpb.fr (H. Hassan).Applied Thermal Engineering 29 (2009) 17861791Contents lists available at ScienceDirectApplied Thermal Engineeringjournal homepage: /locate/apthermengqCPoTotr:krT1In order to take into account the solidification, a source term isadded to the energy equation corresponding to heat absorption orheat release 7, which takes in consideration the absorption or thedissipation of the heat through phase change process. This tech-nique is applied on fixed nodes and the energy equation in thiscase is represented as follow:qCPoTotr:krT Sc2And the source term Scis represented by:ScqLfofsot3where fs(T) = 0.0 at T ? Tf,(full liquid region) 0 ? fs? 1, at T = Tf(iso-thermal phase change region) and, fs(T) = 1 at T ? Tf(full solidregion).On the whole domain, the following boundary conditions areapplied?koToN hcT ? Tc2C1; and ? koToN haT ? Ta2C2:43. Numerical solutionThe numerical solution of the mathematical model governingthe behavior of the physical system is computed by finite volumemethod. The equations are solved by an implicit treatment forthe different terms of the equations system. When we take in con-sideration the solidification effect, the energy equation is solvedwith a fixed point algorithm for the solid fraction. For each, itera-tion of that fixed point, we use discretization with time hybrid ex-plicit/implicit technique already validated in previous studies byVincent 8, and Le Bot 9 that is based on the technique NewSource” of Voller 10. This method proposes to maintain the nodeswhere phase change occurs to the melting temperature. This solu-tion is repeated until the convergence of the temperature with thesource term equals to the latent heat. The source term is discret-ized by:ScqLfofsotqLffn1s? fnsDt5The solid fraction which is function of the temperature is line-arized as:fnk1Ks fnkKsdFsdT?nkKTnk1K? TnkK6Then, we force the temperature to tend to the melting temper-ature where the source term is not null by updating the sourceterm:Sk1c SkcqCpT ? TfDt7The energy equation is discretized as follow:qCPDt?qLfDtdFdT?nkK !Tnk1K?r:krTnk1KqLfDtfnk1Ks? fns ?qLfDtdFdT?nkKTfqCPDtTn8With:dFdT! ?1if 0 ? fnkKs? 1anddFdT 0if fnkKs 0 or 19NomenclatureCP(J/kg K) specific heat at constant pressurefssolid fractionh (W/m2K) heat transfer coefficientKnumber of the internal iterationsLlatent heat of fusion, J/kgnnumber of the external iterationsNnormal directionScsource termT (K)temperaturet (s)timeGreek symbolsk (W/m K) thermal conductivityq(kg/m3) densityC1interior surface of the cooling channelsC2exterior surface of the moldSubscriptsaambient airccooling fluidfphase change0.20.4 0 .2 0.004 0.03 0.004 P2 P3 P4 P1 P6P7 P5 Exterior air, free convection, ha Cooling channels, forced convection, hfFig. 1. Mold structure with a T-shape product and four cooling channels (Dim. In m).0.01 0.01 0.01 0.01 0.010.02A1 A2 A3 A4A5A7B1 B2B3 B4B5B7C1 C2C3C4 C5D1D2 D3D4D50.04 0.02 0.01 0.015 Polymer Fig. 2. Different cooling channels positions (Dim. In m).H. Hassan et al./Applied Thermal Engineering 29 (2009) 178617911787This process allows differentiating the temperature field and so-lid fraction calculated at the same instant and the linear system issolved by central discretization method 11. For each internal iter-ation, the resolution of that equation provides fnk1Ksand Tnk1K. Theconvergence is achieved when the criteria of the solid fraction andtemperature are verified by:fnk1Ks? fnkKs? ? 2fand;Tnk1K? TnkK? ? 2T10Further details on the numerical model and its validation arepresented in 9.4. Results and discussionA full two-dimensional time-dependent mold cooling analysisin injection molding is carried out for a plate mould model withT-shape plastic mold and four cooling channels as indicated inFig. 1. Due to the symmetry, half of the mold is modeled and ana-lyzed. All the cooling channels have the same size and they havediameter of 10-mm each in case of circular channels. The coolingoperating parameters and the material properties are listed in Ta-bles 1 and 2, respectively, and they are considered constant duringall numerical results 5,7. Each numerical cycle consists of twostages, cooling stage where the cavity is filled with hot polymerinitially at polymer injected temperature, the ejection stage wherethe cavity is filled with air initially at ambient temperature. Figs. 3and 4 show the cyclic transient variations of the mould tempera-turewithtimefor16 smoldcoolingtimeatlocations;(P1,P2,P3,P4) beside the mould walls and P5 to P7 inside the mouldwalls, respectively (Fig. 1) and that in case of applied the solidifica-tion and without applied solidification. They are simulated for thefirst 30 cycles in case of circular cooling channels position (A5, D3)as shown in Fig. 2. We find that, the simulated results are in goodagreement with the transient characteristic of the cyclic mold tem-perature variations described in 5. It is found that there is aslightly difference in temperatures values between the two results,thus due to the difference in numerical method used and the accu-racy in the numerical calculations. The figures show that, the rela-tively temperature fluctuation is largest near the cavity surface anddiminishes away from the cavity surface. We find that the maxi-mum amplitude of temperature fluctuation during the steady cyclecan reach 10 ?C without applying solidification and 15 ?C in case ofapplying the solidification.4.1. Effect of cooling channels formAn efficient cooling system design providing uniform tempera-ture distribution throughout the entire part during the cooling pro-cess should ensure product quality by preventing differentialshrinkage, internal stresses, and mould release problems. It alsoshould reduce time of cooling and accelerate the solidification pro-cess of the product to augment the productivity of the moldingprocess. To demonstrate the influence of the cooling channels formon the temperature distribution throughout the mould and solidi-fication process of the product, we proposed three different crosssectional forms of the cooling channels, circular, square, rectangu-lar1 with long to width ratio of 0.5 and rectangular 2 with width tolong ratio of 0.25. Two cases are studied; first case, all the coolingchannels have the same cross sectional area, and the second case,they have the same perimeter. The comparison is carried out forthe same cooling channels position (A5, D3).Fig. 5 shows the solidification percent (calculated numericallyas the summation of the solid fraction of each element multipliedby the area of that element to total area of the product) for differ-ent forms with different cooling time. The figure indicates that theeffect of cooling channels form on the cooling rate decreases withincreasing the cooling time. It also shows that the cooling channelform rectangle 2 has the maximum solidification percent for case1, and in case 2 the changing of the cooling channels form hasnot a sensible effect on the solidification percent. The same resultscan be obtained when we compared the solidification in the prod-uct and the temperature distribution though the mould for differ-ent forms with the same cross sectional area at the end of thecooling stage for cooling time 24 s for cooling cycle 25, as shownin Figs. 6 and 7, respectively. The results indicate that the coolingprocess is improved as the cooling channels tend to take the formof the product.4.2. Effect of cooling channels positionTo investigate the effect of the cooling channels position, we di-vided the proposed positions into four groups, groups A and B fordifferent positions of the bottom cooling channel, with a fixed po-sition of the top cooling channel, and with vice versa for groups Cand D for the same cooling channel form (circular) as illustrated inFig. 2.Fig. 8 represents the effect of different cooling channel positionson the of solidification percent at the end of 25th cooling cycle forgroups A and B (lower cooling channel effect), C and D (upper cool-ing channel effect) with cooling time. It indicates that for lowercooling channel position effect, the cooling rate increases andhence the solidification percent of the polymer increases as thecooling channel approaches the polymer in the vertical direction(position B has solidification percent greater than position A, andwith the same positions C and D). The figure shows also the mostefficient cooling rate is obtained as the cooling channel takes theposition between 20% and 50% through the product length forthe horizontal direction (between positions B2 and B5 or positionsA2 and A5 which have the maximum solidification percent). Whenwe compare the solidification percent for different locations of theupper positions C and D, we find that as the channel approaches tothe product in the horizontal direction the solidification percentincreases, and the cooling rate increase rapidly compared withthe effect of lower position. We notice that, the effect of the coolingchannel position on the temperature distribution and solidificationdecreases as the cooling time augments to higher value and its ef-fect on the cooling rate of the product is not the same for differentpositions.Table 1Cooling operating parametersCooling operatingparameterCooling operating parameterCoolant fluidtemperature30 ?CAmbient air temperature30 ?CPolymer injectedtemperature220 ?CHeat transfer coefficient ofambient air77 W/m2KTemperature of fusionof polymer110 ?CHeat transfer coefficient insidecooling channel3650 W/m2KLatent heat115 kJ/kgMold opening time4 sTable 2Material propertiesMaterialDensity (kg/m3)Specific heat (J/kg K)Conductivity (W/m K)Mould767042636.5Polymer93818000.25Air1.1710060.02631788H. Hassan et al./Applied Thermal Engineering 29 (2009) 17861791The solidification degree distribution through the product at theend of cooling stage at the end of cooling time 24 s and 25th cool-ing cycle for different locations of cooling channel is shown inFig. 9, and the temperature distribution throughout the mouldand the polymer at the same instant for different cooling channelsposition is shown in Fig. 10. When we examine the solidificationdegree of the product and the temperature distribution throughoutthe mold for different positions, we find that as the cooling channelposition moves toward the products, the homogeneity of the tem-perature distribution throughout the polymer and the mold duringTemperature, oC Temperature, oC Time, s 02004006003035404550556065P1P2P3P4Time, s 030354045505560657075P1P2P3P4ab600500400300200100Fig. 3. Temperature history of the first 30 cycles at locations P1 to P4 (a) without solidification (b) with solidification.Time,sTime,s3035404550556065P5P6P730354045505560657075P5P6P7abTemperature, oC Temperature, oC 02004006000200400600Fig. 4. Temperature history of the first 30 cycles at locations P5 to P7 (a) without solidification (b) with solidification.Solidification percent Coolingperiod (constant perimeter )Coolinvgperiod (constant area )+1616182022242628300.680.720.760.80.840.880.920.96CircleRectangle1Rectangle2SquareCircleRectangle1Rectangle2Square+30282624222018Fig. 5. Changing the solidification percent of the polymer part with cooling time fordifferent cooling channel forms.Fig. 6. Solidification percent distribution through the product for different coolingchannels forms (a) rectangular 2 and (b) circular having the same cross sectionalarea.H. Hassan et al./Applied Thermal Engineering 29 (2009) 1786179117893840404042424545454545505050555560606565707080809090XY00.000.035353737383838404040404242424242545454545505055556060656570708090XY00.000.0abFig. 7. Temperature distribution through the mould for different cooling channels forms (a) circular and (b) rectangular 2 having the same cross sectional area.Time, s Solidification percent +200.820.840.860.880.90.920.940.960.981B1,D3B2,D3B3,D3B5,D3B7,D3A1,D3A2,D3A3,D3A5,D3A7,D3+Solidification percent 0.820.840.860.880.90.920.940.960.981B2,C1B2,C2B2,C3B2,C5B2,D1B2,D2B2,D3B2,D53028262422Time, s 203028262422abFig. 8. Changing the solidification percent of the polymer part with cooling time for different cooling channel positions (a) lower cooling channel positions A and B and(b) upper cooling channel positions C and D.Fig. 9. Solidification percent distribution through the product for different cooling channels positions for cooling time 24 s and 25th cooling period (a) B7, D3 (b) B2, D3,(c) B2, C5, and (d) B2, C3.1790H. Hassan et al./Applied Thermal Engineering 29 (2009) 17861791the solidification process decrease for example positions (B2, D3)and (B2, C3). The figure indicates that as the channel approachesthe product in the horizontal direction and vertical direction, thetemperature distribution throughout the polymer divided intotwo regions during the cooling process (B7, D3), (B2, D3), (C5,B2), (C3, B2) and thus has the same effect on the solidification pro-cess. These two areas of the temperature distribution and that dif-ferent cooling rate through the cooling process lead to differentsevere warpage and thermal residual stress in the final productwhich affect on the final product quality.5. ConclusionThe variation of the temperature of the mould through a num-ber of molding cycles is carried out. The simulated results are ingood agreement with the transient characteristic of the cyclicmold temperature variations described in 5 and It is found thatthere is a slightly difference in temperatures values between thesimulated results and those described in 5. The effect of coolingchannels form and the effect of its position on the temperaturesdistribution throughout the polymer and the solidification ofthe product are studied. The results indicate that as the coolingchannels take the form of the product, the cooling rate is im-proved. The position of cooling channels has a great effect onthe cooling process and temperature distribution through themould and the polymer. The results show that the cooling systemlayout which performs minimum cooling time not necessaryachieves