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temperature Pujos, Cedex, great molding numer cooling is to effect and quality fastest lar industrie increase well known economically mer melt sufficiently so that the part can be ejected without any significant deformation 2. An efficient cooling system design of the cooling channels aiming at reducing cycle time must minimize such 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 polymer touches the cold mold wall, and a solid layer forms on the wall. tion to the coolant moving through the cooling channels and by natural convection to the air around the exterior mold surface. The coolant is flowing through the channels at a given flow rate and a given temperature which is considered constant throughout the length of the channel. In this work, time-dependent two-dimensional model is considered which consists of an entire computational domain of the cavity, mold and cooling channel surfaces. The cyclic transient temperature distribution of the mold and polymer T-shape can be obtained by solving the transient energy equation. * Corresponding author. Tel.: +330540006348; fax: +330540002731. Applied Thermal Engineering 29 (2009) 17861791 Contents lists available E-mail address: hassanenscpb.fr (H. Hassan). cess where polymer is injected into a mould cavity, and solidifies to 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 an injection temperature (filling and post-filling stage). It is followed by 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 time in the injection molding process is spent in cooling the hot poly- distribution of the mold and polymer, therefore, their effect on the solidification degree of that polymer. A fully transient mold cooling analysis is performed using the finite volume method for a T-shape plastic mold with similar dimensions to 5, as shown in Fig. 1. Different cooling channels positions and forms are studied. 2. Mathematical model The heat of the molten polymer is taken away by forced convec- 1. Introduction Plastic industry is one of the worlds ranked as one of the few billion-dol injection molded parts continues to plastic injection molding process is cient manufacturing techniques for precision plastic parts with various shapes at low cost 1.The plastic injection molding 1359-4311/$ - see front matter C211 2008 Elsevier Ltd. All doi:10.1016/j.applthermaleng.2008.08.011 growing industries, s. Demand for every year because as the most effi- producing of and complex geometry process is a cyclic pro- As the material cools down, the solid skin begins to grow with increasing time as the cooling continues until the entire material solidifies. Over the years, many studies on the problem of the opti- mization of the cooling system layout in injection molding and phase change of molding process have been made by various researchers and ones which focused intensity on these topics and will used in our system design and validations are 36. The main purpose of this paper is to study the effect of the cooling channels position and its cross section shape on the temperature Cooling system leads 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 polymer during injection molding Hamdy Hassan * , Nicolas Regnier, Cedric Lebot, Cyril Laboratoire TREFLE-Bordeaux1-UMR 8508, Site ENSCPB, 16 Av. Pey Berland, 33607 Pessac article info Article history: Received 15 November 2007 Accepted 19 August 2008 Available online 30 August 2008 Keywords: Polymer Solidification Injection molding abstract Cooling system design is of is crucial not only to reduce ity of the final product. A performed. A cyclic transient of the mold cooling study cooling system design. The ture distribution of the mold tivity of the process, the cooling should be necessary for the Applied Thermal journal homepage: www.elsevi rights reserved. Guy Defaye France importance for plastic products industry by injection molding because it cycle time but also it significantly affects the productivity and qual- ical modeling for a T-mold plastic part having four cooling channels is analysis using a finite volume approach is carried out. The objective determine the temperature profile along the cavity wall to improve the of 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 cooling of the product. The results indicate that the cooling system which and solidification at ScienceDirect Engineering dissipation of the heat through phase change process. This tech- plicit/implicit technique already validated in previous studies by Vincent 8, and Le Bot 9 that is based on the technique New Source” of Voller 10. This method proposes to maintain the nodes where phase change occurs to the melting temperature. This solu- tion is repeated until the convergence of the temperature with the source term equals to the latent heat. The source term is discret- ized by: S c qL f of s ot qL f f n1 s C0f n s Dt 5 The solid fraction which is function of the temperature is line- arized as: Nomenclature C P (J/kg K) specific heat at constant pressure f s solid fraction h (W/m 2 K) heat transfer coefficient K number of the internal iterations L latent heat of fusion, J/kg n number of the external iterations N normal direction S c source term T (K) temperature t (s) time H. Hassan et al./Applied Thermal Engineering nique is applied on fixed nodes and the energy equation in this case is represented as follow: qC P oT ot r:krTS c 2 And the source term S c is represented by: S c qL f of s ot 3 where f s (T) = 0.0 at TC31T f ,(full liquid region) 0C30 f s C301, at T = T f (iso- thermal phase change region) and, f s (T)=1 at TC30T f (full solid region). On the whole domain, the following boundary conditions are applied C0k oT oN h c T C0T c 2C 1 ; and C0k oT oN h a T C0T a 2C 2 : 4 3. Numerical solution The numerical solution of the mathematical model governing the behavior of the physical system is computed by finite volume method. The equations are solved by an implicit treatment for qC P oT ot r:krT1 In order to take into account the solidification, a source term is added to the energy equation corresponding to heat absorption or heat release 7, which takes in consideration the absorption or the the different terms of the equations system. When we take in con- sideration the solidification effect, the energy equation is solved with a fixed point algorithm for the solid fraction. For each, itera- tion of that fixed point, we use discretization with time hybrid ex- 0.2 0.4 0 .2 0.004 0.03 0.004 P2 P3 P4 P1 P6 P7 P5 Exterior air, free convection, h a Cooling channels, forced convection, h f Fig. 1. MoldstructurewithaT-shapeproductandfourcoolingchannels(Dim.Inm). Greek symbols k (W/m K) thermal conductivity q (kg/m 3 ) density C 1 interior surface of the cooling channels C 2 exterior surface of the mold Subscripts a ambient air c cooling fluid f phase change 0.01 0.01 0.01 0.01 0.01 0.02 A1 A2 A3 A4 A5 A7 B1 B2 B3 B4 B5 B7 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 0.04 0.02 0.01 0.015 Polymer Fig. 2. Different cooling channels positions (Dim. In m). 29 (2009) 17861791 1787 f n k1 K s f n k K s dF s dT C18C19 n k K T n k1 K C0T n k K 6 Then, we force the temperature to tend to the melting temper- ature where the source term is not null by updating the source term: S k1 c S k c qC p T C0T f Dt 7 The energy equation is discretized as follow: qC P Dt C0 qL f Dt dF dT C18C19 n k K ! T n k1 K C0r:krT n k1 K qL f Dt f n k1 K s C0f n s C0 qL f Dt dF dT C18C19 n k K T f qC P Dt T n 8 With: dF dT !C01 if 0 C30 f n k K s C30 1 and dF dT 0iff n k K s 0or1 9 This process allows differentiating the temperature field and so- lid fraction calculated at the same instant and the linear system is solved by central discretization method 11. For each internal iter- ation, the resolution of that equation provides f n k1 K s and T n k1 K . The convergence is achieved when the criteria of the solid fraction and temperature are verified by: f n k1 K s C0f n k K s C13 C13 C13 C13 C13 C13C302 f and; T n k1 K C0T n k K C13 C13 C13 C13 C13 C13C302 T 10 Further details on the numerical model and its validation are presented in 9. the horizontal direction (between positions B2 and B5 or positions A2 and A5 which have the maximum solidification percent). When we compare the solidification percent for different locations of the upper positions C and D, we find that as the channel approaches to the product in the horizontal direction the solidification percent increases, and the cooling rate increase rapidly compared with the effect of lower position. We notice that, the effect of the cooling channel position on the temperature distribution and solidification decreases as the cooling time augments to higher value and its ef- 1788 H. Hassan et al./Applied Thermal Engineering 4. Results and discussion A full two-dimensional time-dependent mold cooling analysis in injection molding is carried out for a plate mould model with T-shape plastic mold and four cooling channels as indicated in Fig. 1. Due to the symmetry, half of the mold is modeled and ana- lyzed. All the cooling channels have the same size and they have diameter of 10-mm each in case of circular channels. The cooling operating parameters and the material properties are listed in Ta- bles 1 and 2, respectively, and they are considered constant during all numerical results 5,7. Each numerical cycle consists of two stages, cooling stage where the cavity is filled with hot polymer initially at polymer injected temperature, the ejection stage where the cavity is filled with air initially at ambient temperature. Figs. 3 and 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 mould walls, respectively (Fig. 1) and that in case of applied the solidifica- tion and without applied solidification. They are simulated for the first 30 cycles in case of circular cooling channels position (A5, D3) as shown in Fig. 2. We find that, the simulated results are in good agreement with the transient characteristic of the cyclic mold tem- perature variations described in 5. It is found that there is a slightly 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 and diminishes away from the cavity surface. We find that the maxi- mum amplitude of temperature fluctuation during the steady cycle can reach 10 C176C without applying solidification and 15 C176C in case of applying the solidification. 4.1. Effect of cooling channels form An efficient cooling system design providing uniform tempera- ture distribution throughout the entire part during the cooling pro- cess should ensure product quality by preventing differential shrinkage, internal stresses, and mould release problems. It also should reduce time of cooling and accelerate the solidification pro- cess of the product to augment the productivity of the molding Table 1 Cooling operating parameters Cooling operating parameter Cooling operating parameter Coolant fluid temperature 30 C176C Ambient air temperature 30 C176C Polymer injected temperature 220 C176C Heat transfer coefficient of ambient air 77 W/ m 2 K Temperature of fusion of polymer 110 C176C Heat transfer coefficient inside cooling channel 3650 W/ m 2 K Latent heat 115 kJ/ Mold opening time 4 s kg process. To demonstrate the influence of the cooling channels form on the temperature distribution throughout the mould and solidi- fication process of the product, we proposed three different cross sectional forms of the cooling channels, circular, square, rectangu- lar1 with long to width ratio of 0.5 and rectangular 2 with width to long ratio of 0.25. Two cases are studied; first case, all the cooling channels have the same cross sectional area, and the second case, they have the same perimeter. The comparison is carried out for the same cooling channels position (A5, D3). Fig. 5 shows the solidification percent (calculated numerically as the summation of the solid fraction of each element multiplied by the area of that element to total area of the product) for differ- ent forms with different cooling time. The figure indicates that the effect of cooling channels form on the cooling rate decreases with increasing the cooling time. It also shows that the cooling channel form rectangle 2 has the maximum solidification percent for case 1, and in case 2 the changing of the cooling channels form has not a sensible effect on the solidification percent. The same results can 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 the cooling stage for cooling time 24 s for cooling cycle 25, as shown in Figs. 6 and 7, respectively. The results indicate that the cooling process is improved as the cooling channels tend to take the form of the product. 4.2. Effect of cooling channels position To investigate the effect of the cooling channels position, we di- vided the proposed positions into four groups, groups A and B for different positions of the bottom cooling channel, with a fixed po- sition of the top cooling channel, and with vice versa for groups C and D for the same cooling channel form (circular) as illustrated in Fig. 2. Fig. 8 represents the effect of different cooling channel positions on the of solidification percent at the end of 25th cooling cycle for groups A and B (lower cooling channel effect), C and D (upper cool- ing channel effect) with cooling time. It indicates that for lower cooling channel position effect, the cooling rate increases and hence the solidification percent of the polymer increases as the cooling channel approaches the polymer in the vertical direction (position B has solidification percent greater than position A, and with the same positions C and D). The figure shows also the most efficient cooling rate is obtained as the cooling channel takes the position between 20% and 50% through the product length for Table 2 Material properties Material Density (kg/m 3 ) Specific heat (J/kg K) Conductivity (W/m K) Mould 7670 426 36.5 Polymer 938 1800 0.25 Air 1.17 1006 0.0263 29 (2009) 17861791 fect on the cooling rate of the product is not the same for different positions. Engineering 60 65 ab H. Hassan et al./Applied Thermal The solidification degree distribution through the product at the end of cooling stage at the end of cooling time 24 s and 25th cool- ing cycle for different locations of cooling channel is shown in Fig. 9, and the temperature distribution throughout the mould and the polymer at the same instant for different cooling channels Temperature, o C Time, s 0 200 400 600 30 35 40 45 50 55 P1 P2 P3 P4 Fig. 3. Temperature history of the first 30 cycles at locations Time,s 30 35 40 45 50 55 60 65 P5 P6 P7 ab Temperature, o C 0 200 400 600 Fig. 4. Temperature history of the first 30 cycles at locations Solidification percent Coolingperiod (constant perimeter -) Coolinvgperiod (constant area ) + + + + + + + + + + + + + + + 16 1618202224262830 0.68 0.72 0.76 0.8 0.84 0.88 0.92 0.96 Circle Rectangle1 Rectangle2 Square Circle Rectangle1 Rectangle2 Square + + 30282624222018 Fig. 5. Changing the solidification percent of the polymer part with cooling time for different cooling channel forms. 70 75 29 (2009) 17861791 1789 position is shown in Fig. 10. When we examine the solidification degree of the product and the temperature distribution throughout the mold for different positions, we find that as the cooling channel position moves toward the products, the homogeneity of the tem- perature distribution throughout the polymer and the mold during Temperature, o C Time, s 0 30 35 40 45 50 55 60 65 P1 P2 P3 P4 600500400300200100 P1 to P4 (a) without solidification (b) with solidification. Time,s 30 35 40 45 50 55 60 65 70 75 P5 P6 P7 Temperature, o C 0 200 400 600 P5 to P7 (a) without solidification (b) with solidification. Fig. 6. Solidification percent distribution through the product for different cooling channels forms (a) rectangular 2 and (b) circular having the same cross sectional area. 3 8 4 0 4 0 4 0 4 2 4 2 4 5 45 4 5 4 5 4 5 5 0 5 0 5 0 5 5 55 60 6 0 5 65 70 70 80 80 9 90 X Y 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 35 35 3 7 37 3 8 3 8 38 4 0 4 0 4 0 40 4 2 42 4 2 4 2 4 2 5 45 4 5 4 5 45 5 0 5 0 55 55 60 60 65 65 70 70 809 X Y 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 ab Fig. 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 + + + + + + + + + + 20 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 B1,D3 B2,D3 B3,D3 B5,D3 B7,D3 A1,D3 A2,D3 A3,D3 A5,D3 A7,D3 + + Solidification percent 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 B2,C1 B2,C2 B2,C3 B2,C5 B2,D1 B2,D2 B2,D3 B2,D5 3028262422 Time, s 20 3028262422 ab Fig. 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) 17861791 37 3 8 3 8 38 4 0 4 0 4 0 4 2 4 2 2 4 2 45 45 4 5 4 5 4 5 5 0 5 0 5 0 50 60 60 7 70 8 80 90 90 100 100 110110Y 0.05 0.1 0.15 0.2 3 5 3 7 37 3 8 3 8 38 4 0 4 0 4 0 4 2 4 2 4 5 4 5 4 5 5 0 50 5 0 5 55 5 5 60 6 0 65 65 5 70 70 75 7 80 80 9Y 0.05 0.1 0.15 0.2 a b positions H. Hassan et al./Applied Thermal Engineering 29 (2009) 17861791 1791 the solidification process decrease for example positions (B2, D3) and (B2, C3). The figure indicates that as the channel approaches the product in the horizontal direction and vertical direction, the temperature distribution throughout the polymer divided into two 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 different severe warpage and thermal residual stress in the final product which affect on the final product quality. 5. Conclusion The variation of the temperature of the mould through a num- ber of molding cycles is carried out. The simulated results are in good agreement with the transient characteristic of the cyclic mold temperature variations described in 5 and It is found that there is a slightly difference in temperatures values between the simulated results and those described in 5. The effect of cooling channels form and the effect of its position on the temperatures distribution throughout the polymer and the solidification of 7 4 2 X 0 0 0.20.150.10.05 Fig. 10. Temperature distribution through the mould for different cooling channels the product are studied. The results indicate that as