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temperaturePujos,Cedex,greatmoldingnumercoolingis toeffectandqualityfastestlar industrieincreasewell knowneconomicallymer 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.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 throughoutthe length of the channel. In this work, 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.* Corresponding author. Tel.: +330540006348; fax: +330540002731.Applied Thermal Engineering 29 (2009) 17861791Contents lists availableE-mail address: hassanenscpb.fr (H. Hassan).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-distribution 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-1. IntroductionPlastic industry is one of the worldsranked as one of the few billion-dolinjection molded parts continues toplastic injection molding process iscient manufacturing techniques forprecision plastic parts with various shapesat low cost 1.The plastic injection molding1359-4311/$ - see front matter C211 2008 Elsevier Ltd. Alldoi:10.1016/j.applthermaleng.2008.08.011growing industries,s. Demand forevery year becauseas the most effi-producing ofand complex geometryprocess is a cyclic pro-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 temperatureCooling systemleads to minimum cooling time is not achieving uniform cooling throughout the mould.C211 2008 Elsevier Ltd. All rights reserved.Effect of cooling system on the polymerduring injection moldingHamdy Hassan*, Nicolas Regnier, Cedric Lebot, CyrilLaboratoire TREFLE-Bordeaux1-UMR 8508, Site ENSCPB, 16 Av. Pey Berland, 33607 Pessacarticle infoArticle history:Received 15 November 2007Accepted 19 August 2008Available online 30 August 2008Keywords:PolymerSolidificationInjection moldingabstractCooling system design is ofis crucial not only to reduceity of the final product. Aperformed. A cyclic transientof the mold cooling studycooling system design. Theture distribution of the moldtivity of the process, the coolingshould be necessary for theApplied Thermaljournal homepage: www.elsevirights reserved.Guy DefayeFranceimportance for plastic products industry by injection molding because itcycle time but also it significantly affects the productivity and qual-ical modeling for a T-mold plastic part having four cooling channels isanalysis using a finite volume approach is carried out. The objectivedetermine the temperature profile along the cavity wall to improve theof cooling channels form and the effect their location on the tempera-the solidification degree of polymer are studied. To improve the produc-time should be minimized and at the same time a homogeneous coolingof the product. The results indicate that the cooling system whichand solidificationat ScienceDirectE/locate/apthermengntsdissipation of the heat through phase change process. This tech-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:ScqLfofsotqLffn1sC0fnsDt5The solid fraction which is function of the temperature is line-arized as:NomenclatureCP(J/kg K) specific heat at constant pressurefssolid fractionh (W/m2K) heat transfer coefficientK number of the internal iterationsL latent heat of fusion, J/kgn number of the external iterationsN normal directionScsource termT (K) temperaturet (s) timeH. Hassan et al./Applied Thermal Engineeringnique is applied on fixed nodes and the energy equation in thiscase is represented as follow:qCPoTotr:krTSc2And the source term Scis represented by:ScqLfofsot3where fs(T) = 0.0 at TC31Tf,(full liquid region) 0C30 fsC301, at T = Tf(iso-thermal phase change region) and, fs(T)=1 at TC30Tf(full solidregion).On the whole domain, the following boundary conditions areappliedC0koToN hcT C0Tc2C1; and C0koToN haT C0Ta2C2: 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 forqCPoTotr: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 thethe 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-0.20.4 0 .2 0.004 0.03 0.004 P2 P3 P4 P1 P6P7 P5 Exterior air, free convection, haCooling channels, forced convection, hfFig. 1. MoldstructurewithaT-shapeproductandfourcoolingchannels(Dim.Inm).Greek symbolsk (W/m K) thermal conductivityq (kg/m3) densityC1interior surface of the cooling channelsC2exterior surface of the moldSubscriptsa ambient airc cooling fluidf phase change0.01 0.01 0.01 0.01 0.010.02A1 A2 A3 A4A5 A7B1 B2 B3 B4B5B7C1 C2C3C4 C5D1D2 D3 D4D50.04 0.02 0.01 0.015 Polymer Fig. 2. Different cooling channels positions (Dim. In m).29 (2009) 17861791 1787fnk1Ks fnkKsdFsdTC18C19nkKTnk1KC0TnkK6Then, we force the temperature to tend to the melting temper-ature where the source term is not null by updating the sourceterm:Sk1c SkcqCpT C0TfDt7The energy equation is discretized as follow:qCPDtC0qLfDtdFdTC18C19nkK!Tnk1KC0r:krTnk1KqLfDtfnk1KsC0fnsC0qLfDtdFdTC18C19nkKTfqCPDtTn8With:dFdT!C01 if 0 C30 fnkKsC30 1 anddFdT 0iffnkKs 0or1 9ntsThis 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:fnk1KsC0fnkKsC13C13C13C13C13C13C302fand; Tnk1KC0TnkKC13C13C13C13C13C13C302T10Further details on the numerical model and its validation arepresented in 9.the 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-1788 H. Hassan et al./Applied Thermal Engineering4. 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-ture with time for 16 s mold cooling time at locations;(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 C176C without applying solidification and 15 C176C 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 moldingTable 1Cooling operating parametersCooling operatingparameterCooling operating parameterCoolant fluidtemperature30 C176C Ambient air temperature 30 C176CPolymer injectedtemperature220 C176C Heat transfer coefficient ofambient air77 W/m2KTemperature of fusionof polymer110 C176C Heat transfer coefficient insidecooling channel3650 W/m2KLatent heat 115 kJ/ Mold opening time 4 skgprocess. 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 forTable 2Material propertiesMaterial Density (kg/m3) Specific heat (J/kg K) Conductivity (W/m K)Mould 7670 426 36.5Polymer 938 1800 0.25Air 1.17 1006 0.026329 (2009) 17861791fect on the cooling rate of the product is not the same for differentpositions.ntsEngineering6065abH. Hassan et al./Applied ThermalThe 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 channelsTemperature, oC Time, s 0 200 400 600303540455055P1P2P3P4Fig. 3. Temperature history of the first 30 cycles at locationsTime,s3035404550556065P5P6P7abTemperature, oC 0 200 400 600Fig. 4. Temperature history of the first 30 cycles at locationsSolidification 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.707529 (2009) 17861791 1789position 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 Time, s 03035404550556065P1P2P3P4600500400300200100P1 to P4 (a) without solidification (b) with solidification.Time,s30354045505560657075P5P6P7Temperature, oC 0 200 400 600P5 to P7 (a) without solidification (b) with solidification.Fig. 6. Solidification percent distribution through the product for different coolingchannels forms (a) rectangular 2 and (b) circular having the same cross sectionalarea.nts38404040424245454545455050505555606056570708080990XY0 0.05 0.1 0.15 0.200.03535373738383840404040424242424254545454550505555606065657070809XY0 0.05 0.1 0.15 0.200.0abFig. 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 20 3028262422abFig. 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, C3.1790 H. Hassan et al./Applied Thermal Engineering 29 (2009) 17861791nts37383838404040424224245454545455050505060607708809090100100110110Y0.0353737383838404040424245454550505055555606065655707075780809Y0.0abpositionsH. Hassan et al./Applied Thermal Engineering 29 (2009) 17861791 1791the solidification process decrease for example positions (B2, D3)and (B2, C
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