Effect of cooling channels position on the shrinkage of plastic material during injection molding

Effect of cooling channels position on the shrinkage of plastic material during injection molding Hamdy HASSAN, Nicolas REGNIER, Eric ARQUIS, Guy DEFAYE Laboratoire TREFLE-Bordeaux1-UMR 8508, site ENSCPB, 16 av Pey Berland, 33607, Pessac Cedex, France Abstract A mold for plastic part (Polystyrene) of T shape and having four cooling channels are assumed is the study. Different positions of the cooling channels are studied. A compressible fluid model for the physical system is presented. The compressible behavior of Polystyrene material according to the equation of state (P-v-T equation) is represented by Tait equation. A Cross type rheological model is assumed for the plastic material. The results show that the cyclic variation of the mold temperature reaches steady state after 15 cycles. They also show that the cooling channels position has a great effect on the shrinkage rate distribution through the product. Keywords: Cooling channels; Shrinkage; Plastic; Injection molding Nomenclatures viscous shear stress tensor Pa B Polymer material constant Pa.s dynamic viscosity Pa.s C Tait equation universal interior surface of the cooling 1 constant channels CP specific heat J.kg -1.K -1 2 exterior surface of the mold fs solid fraction density Kg.m -3 g gravity acceleration m.s -2 thermal conductivity W.m -1.K -1 h heat transfer coefficient W.m -2.K -1. equivalent shear rate s -1 N normal condition to heat loss zero shear rate s -1 o n power law index shear rate viscosity s -1 p pressure Pa ß isobaric dilatation coefficient K -1 q movement quantity Kg.m -2.s -1 T isothermal compressibility Pa -1 coefficient T temperature K dynamic viscosity Pa.s t time s Subscripts Tb polymer material constant a ambient air V velocity m.s -1 c cooling fluid v specific volume m 3.kg -1 l liquid Greek Symbols s solid critical stress level Pa t transition 1. Introduction Plastic injection molding process is well known as the most efficient manufacturing techniques for economically producing of precision plastic parts with various shapes and complex geometry at low cost [1]. The plastic injection molding process is a cyclic process, which consists of three stages. These stages are filling and packing stage, cooling stage and ejection stage. The cooling stage is of the greatest importance because it significantly affects the productivity and the quality of the final product. More than seventy percent of the cycle time in the injection molding process is spent in cooling sufficiently the hot polymer melt so that the product can be ejected without any significant deformation [1]. An efficient cooling system, aiming at reducing cycle time, reducing operation cost, must minimize such undesired defects as sink marks, differential shrinkage, thermal residual stress built-up, and product warpage, and achieves uniform

0.004 Y1 0.2 0.03 Y2 19 ème Congrès Français de Mécanique Marseille, 24-28 août 2009 temperature distribution through the product [2]. Extensive researches and commercial codes have been conducted into the analysis of cooling systems and to carry out these goals. Most of all earlier studies on the cooling system design considered the polymer as an incompressible fluid, and didn t consider the effect of compressibility on other product properties like shrinkage. Shrinkage is one of many important factors determining the quality of injection molded products. Shrinkage behavior can be affected by many factors, including material properties, processing parameters, and mold designs [3]. In this study, the effect of the cooling channels position on the shrinkage of a compressible polymer material (polystyrene) is carried out during the cooling stage of injection molding process. A transient mold cooling analysis is performed using the finite volume method for a T-shaped plastic mold as shown in FIG. 1. The cooling process is carried out by four cooling channels. The effect of the positions of different cooling channels is studied. The Tait equation is used to define the density of the polymer material and its change with respect to temperature and pressure. The modified Cross model is used to express the viscosity of the polymer material. Exterior air, free convection, h a 0.004 Y X2 Cooling channels forced convection, h f 1 2 3 X1 4 FIG. 1 Mold structure with a T-shape product and four cooling channels (Dimension, m). 2. Compressible fluid Model 0.2 0.4 The solution of the physical model in case of compressible polymer is governed by the solution of the conservation equations of continuity, momentum, and energy with the law of state. The constant value of density with time in the case of non compressible fluid permits to solve the Navier Stokes equation in terms of velocity, but in case of compressible fluid, the conservation of mass flow is performed in terms of movement quantity. Hence, we note q the vector of the movement quantity, produced by multiplying the density with the velocity vector V as follows. q V (1) Then, the system of equations used for describing the movement of compressible fluid is [4]: The continuity equation.. q 0 (2) t The momentum equation. q q T q 2 q. qv p g.. (3) t 3 The energy equation. c p T T 2 V. T. T T. V. V V V.. V V t x (4) T 3 The equation of state. f p,, T 0 (5) The compressibility and dilatation coefficients are defined as. X

v xt 1 v and, 1 (6) v P T v T P The Tait equation is used to express the density variation with the temperature and pressure [6] and is applied throughout the analysis including liquid and solid states. P vt, P v T 1 C ln1 (7) o B( T) Where C = 0.0894 is a constant seen as a universal constant [5], v o (T) and B(T) are represented differently for each state as follows. b2s 2l T b b 5 b1 s T b if T Tt vo T (8) b1 l b b5 if T Tt b3 s exp 4s T b5 if T Tt BT (9) b3 l exp 4l T b5 if T Tt Where b 1 (m 3.kg -1 ), b 2 (m 3.kg -1. o C -1 ), b3 (Pa), b 4 ( o C -1 ) are material constants, l stands for liquid state and s for solid state. The transition temperature T t is assumed to be a linear function of the pressure. b b p T t 5 6 The rheological behavior of the polymer is described by a Cross type equation. [5]. o( T, p) (10). 1n 1 o( T, p) The zero shear rate viscosity o is presented by [5]., exp A1 T T o T p D1 A2 T T (11) D D p and p A 2 D p (12) T 2 3 ~ A2 3 Where, D 1 (Pa.s), D 2 (K), D3 ( o C/Pa), A 1 and A 2 ( o C ) are material constants. On the whole domain, the following boundary conditions are applied. T T hc ( T Tc ) and, 1 ha ( T Ta ) (13) 2 N N 3. Numerical solution The numerical solution of the mathematical model reproducing the behaviour of the physical system is computed by finite volume method. The equations are solved by an implicit treatment for the different terms of the equations system. The solution of the diescreitized equations are solved by an iterative algorithm of Augmented Lagrangien. Further details on the numerical model and the numerical algorithm are available in [4]. 4. Results and discussions A full two dimensional time dependent analysis of mold cooling during injection molding is carried out. The model studied consists of a plate mold with T-shape polymer material and four cooling channels as shown in FIG. 1. Due to the symmetry, half of the mold is modeled and analyzed. All the cooling channels have the same size and they are 10 mm diameter. The polymer material is a polystyrene and it follows the Tait state equation. The material rheological constants and Tait law constants are shown in table 1. The cooling operating parameters and the other materials properties are shown in tables 2 and 3 respectively and they are considered constant during all numerical simulations [6, 7]. Each numerical cycle consists of two stages : cooling stage where the cavity is filled with hot polymer initially at injection temperature and ~

injection pressure, and the ejection stage for which the cavity is filled with air initially at ambient temperature. Table 1: Specific volume model constants based on Tait equation, Viscosity Cross model constants and material properties constant Unit value constant Unit value b 1l b 2l b 31 b 4l b 1s b 2s b 3s b 4s b 5 b 6 m3/kg m3/kg o C Pa oc -1 m3/kg m3/kg o C Pa o C -1 K o C/Pa 1.0064X10-03 6.2748X 10-07 1.3957X 10 08 4.0564X 10-03 1.0049X 10-03 2.3766X 10-07 1.9856X 10 08 2.1512X 10-03 3.6407X 10 02 3.0068X 10-07 C P n D 1 D 2 D 3 A 1 ~ Table 2: Cooling operating parameters A 2 W.m -1.K -1 J.kg -1.K -1 Pa Pas K o C.Pa -1 o C 0.18 2300 2.740X 10-01 2.484X 10 04 1.812X 10 13 3.731X 10 02 0 3.062X 10 01 5.160X 10 01 Cooling operating parameter value Cooling operating parameter value Coolant fluid temperature 30 o C Ambient air temperature 30 o C Polymer injection temperature 220 o C Mold opening time 4 s Heat transfer coefficient to ambient air 77 W.m -2.K -1 Heat transfer coefficient inside cooling channel 3650 W.m -2.K -1 Initial pressure (injection pressure) 50 MPa Cooling time 50 s Table 3: Material properties Material Density, kg.m -3 Specific heat, J.kg -1.K -1 Conductivity, W.m -1.K -1 Mold 7670 426 36.5 Air 1.17 1006 0.0263 The mold temperature is an important factor in injection molding of thermoplastics and has a significant influence on the injection molding cycle and the quality of molded parts. Figure 2 shows the cyclic transient variations of the mold temperature with time at locations 1 to 4 for cooling channels position (X1= 0.02, Y1= 0.01, X2 = 0.02, and Y2 = 0.01) as shown in FIG. 1. Figure 2 shows that the simulated results are in good agreement with the transient characteristic of the cyclic mold temperature variations described in [7]. It shows that the cyclic variation of the temperature of the mold reaches steady state after about 15 cycles and the maximum cyclic variation of temperature is about 30 o C. It shows that the temperature of the upper surface near the position 1 arrives to the greatest value of the mold temperature. The results show that the temperature of lower position 4 is greater than the temperatures of upper positions 1 and 3. This means that the upper surface of the product needs more cooling beneath to position 1 and the lower surface needs more cooling beneath position 4. 4.1 Effect of lower cooling channel position To study the effect of the lower cooling channels position, different positions are proposed for the lower cooling channel (X1, Y1) with a fixed position of the upper cooling channel at ( X2 = 0.01 m, and Y2 = 0.01m) as shown in FIG.1. The value of X1 changes from 0.01 to 0.06 and the value of Y1 changes from 0.01 to 0.03. One measure of the variation of the specific volume of the polymer is the shrinkage rate, which illustrates the ability of the material to shrink. The shrinkage rate is calculated as the difference of the specific volume at the present conditions to the specific volume at room conditions (Temperature = 20 o C, and atmospheric pressure) with respect to specific volume at room conditions as follows [6]:

Température, o C 19 ème Congrès Français de Mécanique Marseille, 24-28 août 2009 p, T Shrinkagerate 1 (24) p atm, T amb Due to the great effect of the cooling channels position on the horizontal part of the product and his greater length, the shrinkage rate distribution is shown on this part and is omitted for the vertical part. The shrinkage rate distributions through the horizontal part of the product at the end of the cooling stage for the 35 th cycle and for the following positions of the lower cooling channel (X1 = 0.01 m, Y1= 0.01m); (X1 = 0.06 m, Y1= 0.01m); and (X1 = 0.01 m, Y1= 0.03m) are shown in FIG. 3, 4 and 5 respectively. The figures represent the extreme positions studied for the lower cooling channel in X and Y directions, which show the maximum effect. Figures 3 and 4 produce that when the position of the lower cooling channel X1 increases, the shrinkage rate distributions take the form of the product (i.e the homogeneity of the shrinkage rate distribution increases). Contrarily, when the cooling channel position moves opposite to X direction (decreasing X1), a separated region of the shrinkage rate distribution throughout the polymer appears during the cooling process (FIG. 3). This separated region of the shrinkage rate distribution leads to different severe warpage and thermal residual stress in the final product, which affect on the final product quality. When we compare the results of figures 3, 4 and 5, it is found that the effect of vertical position of the lower cooling channel on the shrinkage rate distribution is less effective than the effect of the horizontal position. 60 55 50 T1 T2 T3 T4 45 40 35 30 0 200 400 600 800 1000 Temps, s FIG. 2 Temperature history of the first 28 cycles at locations P1 and P2. FIG. 3 The shrinkage rate distribution through the horizontal part of the product at lower cooling channel X1=0.01 m, and Y1=0.01m, at the end of the cooling stage for 35 th cycle. FIG. 4 The shrinkage rate distribution through the horizontal part of the product at lower cooling channel X1=0.06 m, and Y1=0.01m at the end of the cooling stage for 35 th cycle.. FIG. 5 The shrinkage rate distribution through the horizontal part of the product at lower cooling channel X1=0.01 m, and Y1=0.03 m, at the end of the cooling stage for 35 th cycle. 4.2 Effect of upper cooling channel position To study the effect of the upper cooling channels position, different positions are assumed with a fixed position of the lower cooling channel at (X1= 0.01 m and Y1 = 0.01m) as shown in FIG. 1. The effect

of upper cooling channel positions (X2 = 0.06 m, Y2 = 0.01) and (X2 = 0.01 m, Y2 = 0.02) on the shrinkage rate distribution through the product at the end of the cooling stage for the 35 th cycle is shown in FIG. 6, and 7 respectively. The figures show that, when the distance X2 increases (horizontal position of upper cooling channel) the homogeneity of the shrinkage rate distribution increases (FIG. 3 and FIG. 6). When we compare the results of FIG. 3, 6 and 7, it is found that, when the upper channel approaches to the product in Y and X directions, shrinkage rate distribution throughout the polymer divided itself into two separated regions during the cooling process. These two regions of the shrinkage rate distributions will affect negatively on the final product quality. The results show that when the cooling channel (upper or lower ) departures from the product in Y direction, the effect of the cooling channel position on the shrinkage rate distribution will be almost the same (FIG. 2,5 and 7). From the results of the mold temperature and shrinkage rate distribution, it is fount that for uniform shrinkage rate distribution, the position of X1 increases, and position Y1, X2, and Y2 decreases. FIG. 6 The shrinkage rate distribution through the horizontal part of the product at bottom cooling channel X2=0.06 m, and Y2=0.01 m the end of the cooling stage for 35 th cycle. 5. Conclusion FIG. 7 The shrinkage rate distribution through the horizontal part of the product at bottom cooling channel X2=0.01 m, and Y2=0.02 m the end of the cooling stage for 35 th cycle. The effect of cooling system on the shrinkage thought the polymer during the cooling stage of the injection molding is studied. A finite volume method is used to solve the general two dimensional physical model. The cooling of a T shaped plastic part inside a mold by four cooling channel is carried out. The results show that the position of the cooling channels has a great effect on the shrinkage rate distribution. They also show that when the cooling channels move in X direction, the shrinkage rate distribution tends to take the form of the product. For optimum positioning of the cooling channels, the position X1 increases and positions Y1, X2 and Y2 decrease. References [1]S.H. Tang, Y.M. Kong, and S.M. Sapuan,, Design and Thermal Analysis of Plastic Injection Mold, J. of Materials Processing Technology, vol. 171, P. 259-267, 2006. [2] Li Q. Tang, Constantin Chassapis, Souran Manoochehri, Optimal cooling system design for multi-cavity injection Molding, Finite Elements in Analysis and Design 26 P.229-251,1997. [3] C.G. Li, C.L. Li, Plastic injection mold cooling system design by the configuration space method, Computer-Aided Design 40, 334 349, 2008. [4] J. Figué, Modélisation des écoulements compressibles en milieu poreux application à la détente de Joule- Thomson. Ph.D. thesis, Bordeaux 1 University, 1996. [5]. H.H. Chiang, N. Hieber, and K.K. Wang, A unified simulation of the filling and postfilling stages in injection molding. Part I: Formulation, Polymer Engineering Science,31, P. 116-124,1991. [6] Rocha Da Silva, Viscoelastic Compressible Flow and Application in 3D injection molding Simulation, Ph.D. thesis, L école Nationale Superieure de Mines de Paris, 2004. [7] H. Qiao, Transient Mold Cooling Analysis Using the BEM with the Time- Dependent Fundamental Solution, Int. Com. in Heat and Mass Transfer, vol. 32, P. 315-322,2005.