Applied Mechanics and Materials Online: 2012-12-13 IN: 1662-7482, ols. 249-250, pp 472-476 doi:10.4028/www.scientific.net/amm.249-250.472 2013 Trans Tech Publications, witzerland A Numerical tudy of an Injection-Compression Molding Process by using a Moving Grid Bambang Arip Dwiyantoro Department of Mechanical Engineering, Institute of Technology epuluh Nopember, urabaya, Indonesia bambangads@me.its.ac.id Keywords: Numerical tudy, Injection-Compression Molding Process, Moving Grid Abstract. A numerical study for the simulation of melt in an injection-compression molding process by using moving grid is proposed in this paper. The fully three-dimensional Navier-tokes equations are solved together with the front transport equation using a front capturing approach. Different from previous studies, the proposed model can take the movement of cavity through a moving grid approach. The melt filling of a disk is conducted to illustrate the applications of the proposed numerical model with several computations under different processing conditions. The numerically predicted results show the influence of compression time or compression speed in determining the molding pressure and the melt temperature. Introduction Injection molding is one of the most important polymer processing operations. The injection-compression molding (ICM) process combines conventional injection molding process and compression molding process. ome related researches in the injection-compression molding can be found from Refs. [1,2]. Compared with injection molding, the injection-compression molding techniques have the following advantages including the decreasing molding pressure through cavity wall movement, reducing uneven shrinkage and birefringence, reducing density variation, and higher dimension accuracy. Kim et al. [3]studied a physical model and the numerical analysis of the injection compression molding process based on finite-difference method (FDM) for center-gated disk. They investigated the effect of the compression stage, flow rate, mold temperature, melt temperature, velocity of the mold on the density distribution and the birefringence of the injection-molded products. Chen et al. [4] studied the filling stage simulation of injection-compression molding (ICM) process by using Hele-haw fluid flow model and finite element method (FEM), and also compared with the conventional injection molding assuming the same entrance flow rate. They developed a numerical algorithm with an additional source term inserted in the continuity equation to account for the volumetric decrease of cavity of the injection-compression processes. In the present study, a numerical algorithm using a finite volume formation and grid movement is proposed to simulate the injection-compression molding process of disk with different processing conditions. Figure 1. Geometry of the disk part All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 130.203.136.75, Pennsylvania tate University, University Park, UA-17/05/16,18:55:42)
Applied Mechanics and Materials ols. 249-250 473 Mathematical Model and Numerical Method The governing equations describing the melt flow inside cavities during an injection molding process, i.e. the conservations of mass, momentum, energy and species, are expressed in the differential form as follows: ρ + ( ρu) ( ρh) ( ρu) = 0 + + ( ρuu) = T+ ρg ( ρu h) = ( k T) + 2ηD : D (1) (2) (3) c + u. c=0 (4) where ρ, t, h, k, T, η, u, T, g, D and c denote the density, time, enthalpy, thermal conductivity, temperature, viscosity, velocity vector, stress tensor, gravitational acceleration, rate of strain tensor and volume fraction, respectively. The melt front is determined by solving the transport equation for volume fraction c. The value of volume fraction c complies with the following convection, c=1 for cells fully filled by air, c=0 for cells are fully filled by melt, and 0<c<1 for cells filled by both fluids. The stress tensor T and rate of strain tensor D are then given as follows: 2 T= 2 ηd η( u) I pi (5) 3 1 T D= u+ u (6) 2 ( ) where I and p denote the unit vector and pressure. To describe the rheological properties of polymer melt, the modified-cross model is adopted in the numerical scheme: η η0( T), = (7) 1 1+ ( T γ) * ( η γ/ τ ) n 0 Tb η 0( T) = Bexp (8) T where γ denotes the shear rate, η 0 the viscosity of zero shear rate, n, τ *, B, T b are parameters of material properties. To simulate the injection-compression molding process with more flexibility, a moving grid approach [5] is adopted in the study, where the computational domain will deform with time. In the filling process, there is no grid movement involved and therefore the grid face velocity is insignificant here. The deformation of melt cavity during the compression process will be exactly reflected by the grid movement at different time instances in the numerical simulations. Therefore, the velocity must be redefined as follows: u = u 0 u f (9) where u 0 represents the absolute flow velocity and u f represents the grid velocity defined at the face center of face f bounding a control volume. The differential form of governing equations can be expressed in the integral form over a control volume as follows: d + ρ( u 0 uf) d = ρ 0 (10)
474 Applied Mechanics and Mechanical Engineering III ρuu ( uf) d = ( T n) d+ ρud + 0 ρgd (11) hd + ρh( u 0 uf) d = k( T n) d+ 2η( D: D) ρ d (12) cd + c( 0 uf) d = u 0 (13) The numerical scheme used to solve these coupled governing equations is based on finite volume method [6]. Using the Picard iteration method, the generalized convective flux term C f at cell face f is approximated by equation: C ( n) = ρφ v d φf (14) f m f where m f the mass flux across the cell face f, φ f represents the generalized field variable at the cell face f. The diffusion terms is approximated by the central difference scheme with second-order accuracy [7].The generalized diffusive flux D f at cell face f is expressed as follows: D f = Γ n (15) ( φ ) d Γf φff where Γ f and f denote the generic diffusion coefficient and the area of cell face f. Finally, IMPLE algorithm [8] is adopted to calculate the velocity and pressure coupling. The melt filling of a disk part is chosen to illustrate the applications of proposed numerical model to fully three-dimensional injection-compression molding simulations. The geometry of the simulated disk part is given in Fig. 1, where diameter of disk part is 70 mm and thickness of disk part is 1.0 mm. Melt temperatures for Polystyrene resin is 240 C and mold temperature is 40 C. Table 1 summarizes the constants of employed Modifield-Cross model and related material properties for the injected melt. Filling times for full injection molding is 0.2 s. The melt was first injected for a specified period then the compression started. Used compression speeds are 10 mm/s. The melt filling of disk is simulated under several processing conditions, while a conventional injection molding case is also conducted for the purpose of comparison. Table 2 summarizes the employed processing parameters of all simulated case. Case A represents the conventional injection modeling case, while case B, C, D and E denote the simulated cases using injection-compression molding techniques. In the injection-compression molding cases, the melt is injected into the cavity with a constant opening in the depth direction during the injection phase. Then in the compression phase, the mold is closed within the given compression time. For all simulations, a multi-block structured grid system with approximately 25350 cells is used to discretize the cavity in the filling simulation. Table 1. Modified-cross model and material properties for Polystyrene ρ (kg/m3) 940 c p (J/kg.K) 2100 k (W/m.K) 0.18 n 0.2838 τ * (Pa) 1.791 10 4 B (Pa-s) 2.591 10-7 T b (K) 11680
Applied Mechanics and Materials ols. 249-250 475 Case Name Table 2. Parameters for simulated cases Injection Time (sec) Compression Time (sec) Results and discussions CIM 0.2 0.0 ICM 1 0.2 0.1 ICM-2 0.2 0.05 ICM-3 0.2 0.025 ICM-4 0.2 0.01 Figure 2 shows the evolution of the melt front at different time instances in the injection molding process for the CIM case. In this case, the melt is injected into the cavity simultaneously with the closing of cavity wall. However, the melt still fails to purge the rest of air out of the cavity through the mold gap located at the mold outer boundary before the melt encloses all mold outer boundaries. Figure 3 depicts the locations of melt front at different melt filling percentages in the injection and compression phase for case ICM-2. In the compression phase, the movement of cavity wall clearly accelerates the melt. It leads to more uniform melt front velocity, and no trapped air in melt is expected. Figure 2. Melt front evolution of case CIM (a) Figure 3. Melt front evolution of case ICM-2 (a) in the injection phase. (b) in the compression phase (b)
476 Applied Mechanics and Mechanical Engineering III (a) Figure 4. (a) Predicted pressure profiles along injection and compression time. (b) Predicted temperature profile at different distance from inlet Figure 4(a) shows the pressure distribution at the end of the filling stage with different compression times. It was found that under higher compression time the process resulted in lower pressure distribution. The influence of compression time or compression speed in determining the molding pressure is important. Figure 4(b) shows the melt-temperature distribution within the cavity at different distances from the inlet. For the injection-compression molding, the compression time decreases with the increase of averaged melt temperature. Conclusion In this study, a numerical model using a finite volume formulation for three-dimensional simulations of melt filling in injection-compression molding processes by using a moving grid is proposed. At the fully three-dimensional methods, the full Navier-tokes equations are solved together with the front transport equation using a front capturing approach. In the compression phase, the movement of cavity wall clearly through a grid moving approach. Compression speed or compression time is one of factor that affects the molding pressure and the temperature of the melt. References [1]. C. Chen, Y. C. Chen, H.. Peng, imulation of injection-compression-molding process. II. Influence of process characteristics on part shrinkage, J. Applied Polymer ci. 75 (2000) 1640-1654. [2] R. Y. Chang, W. Y. Chang, W. H. Yang, Three-dimensional simulation of injection-compression molding of a compact disc, ANTEC Conference Proceedings (2001), 1-5. [3] I. H. Kim,. J. Park,. T. Chung, T. H. Kwon, Numerical modeling of injection/compression molding for center-gated disk: Park II. Effect of compression stage, Polymer Engineering and cience 39 (1999) 1943-1951. [4]. C. Chen, Y. C. Chen, N. T. Cheng, M.. Huang, imulation of injection-compression mold-filling process, Int. Comm. Heat Mass Transfer 25 (1998) 907-917. [5]. W. Chau, Y. D. Lin, Three-dimensional simulation of injection-compression molding process, ANTEC Conference Proceedings (2007) 2504-2508. [6]. W. Chau, Numerical investigation of free-stream rudder characteristics using a multi-block finite volume method, PhD Thesis, Universit at Hamburg, Hamburg, 1997. [7] M. Peri c, J. H. Ferziger, Computational Methods for Fluid Dynamics, pringer, Berlin, 1996. [8].. Pantankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980. (b)
Applied Mechanics and Mechanical Engineering III 10.4028/www.scientific.net/AMM.249-250 A Numerical tudy of an Injection-Compression Molding Process by Using a Moving Grid 10.4028/www.scientific.net/AMM.249-250.472 DOI References [1]. C. Chen, Y. C. Chen, H.. Peng, imulation of injection-compression-molding process. II. Influence of process characteristics on part shrinkage, J. Applied Polymer ci. 75 (2000) 1640-1654. 10.1002/(ICI)1097-4628(20000328)75:13<1640::AID-APP10>3.0.CO;2-L [4]. C. Chen, Y. C. Chen, N. T. Cheng, M.. Huang, imulation of injection-compression mold-filling process, Int. Comm. Heat Mass Transfer 25 (1998) 907-917. 10.1016/0735-1933(98)00082-7