THREE-DIMENSIONAL COMPUTER-AIDED MOLD COOLING DESIGN FOR INJECTION MOLDING

Rong-Yeu Chang*

National Tsing-Hua University, HsinChu, Taiwan 30043, ROC

Wen-Hsien Yang, David C.Hsu and Venny Yang CoreTech System Co.,Ltd., HsinChu, Taiwan, ROC

Abstract

Mold cooling system design in injection molding is of great importance because it is crucial not only to reduce molding cycle time but also to improve part quality. Traditional mold cooling analysis is based on the hybrid finite-difference/ boundary element (FD/BEM) approach. This approach was developed to accommodate the conventional 2.5D Hele-Shaw flow-based shell element model. In this paper, a true three-dimensional mold cooling analysis approach is developed. A fully tree-dimensional numerical analysis faithfully simulates the effects of part geometry, cooling system design, and ambient temperature on the solidification of the part. Finite volume method (FVM) is adopted as the numerical engine of the new approach. This developed approach is proved from numerical experiments to be a cost-effective method for true 3D simulation in injection mold cooling analysis.

Introduction

Mold cooling process of an injection molding cycle is critical from the viewpoint of productivity and quality of molded part. Efficient cooling systems cut down cooling time required and improve molding productivity by shortening the cycle time. On the other hand, undesired defects such as sink marks, differential shrinkage, thermal residual stress built-up, as well as part warpage are attributed to poor cooling system design. These defects can be relieved or even be eliminated through a proper arrangement of cooling channels and the best combination of process conditions. CAE (Computer-Aided Engineering) has been proved to be an efficient engineering tool for part designers and mold engineers to optimize molding cooling system design parameters and verify the design on the computer before mold is build.

However, most current available mold-cooling CAE

systems adopt the hybrid boundary element method (BEM)-finite difference method (FDM) as the numerical engine. The actual three-dimensional, cyclic, transient heat conduction problem is decoupled into a one-dimensional transient heat conduction problem within the thin part and

a cycle-averaged steady-state three-dimensional heat conduction problem of the mold base [1-8]. The configuration of part, cooling channel, and mold base assembly usually leads to poorly conditioned full matrix regarding the boundary element cooling solver, therefore intensive calculations and iterative procedure are required to obtain a converged mold temperature distribution. In comparison with mold filling calculation, mold cooling analysis takes too much time and storage memory requirement, several hours to day CPU time is required for the cooling analysis of a typical geometry model composed of thousands elements in a high-end workstation. This hinders mold cooling CAE software from being a practical tool for mold design application. Chang et.al [9-10] proposed a so-called Fast Finite Element (FFE) mold cooling analysis framework and was implemented in a commercial mold cooling package [11]. This new calculation method significantly reduce the effort for mold cooling analysis. However, the method is developed based on 2.5D shell model to match the 2.5D generalized Hele-Shaw flow model based filling result. Geometry transformation and mapping technique is developed in the method to generate pseudo-3D mesh for 3D cooling analysis.

In this paper, a new computational framework

of true 3D mold cooling analysis is proposed. This new approach is based on three-dimensional solid model and mold-filling results. Finite volume method (FVM) is adopted as the numerical engine of the new approach. This method is proved from numerical experiments to be a cost-effective method for true 3D simulation in injection mold cooling analysis.

Governing Equations

Energy Conservation. During the molding cooling process, a three-dimensional, cyclic, transient heat conduction problem with convective boundary conditions on the cooling channel and mold base surfaces is involved. The overall heat transfer phenomena is governed by a three-dimensional Poisson equation

rfor

zT

yT

xTk

tTCP

v2

2

2

2

2

2 (1)

where T is the temperature, t is the time, x, y, and z are the Cartesian coordinates, is the density, PC is the specific heat, k is the thermal conductivity. Equation (1) holds for both mold base and plastic part with modification on thermal properties:

Because mold temperature is fluctuated periodically with time, what we cared is not the actual mold temperature but the effect of the mold temperature on heat transfer of molded part. We can assume there is a cycle-averaged mold temperature that is invariant with time. This cycle-average principle (CAP) [1-8] is a key concept in the traditional mold-cooling analysis. To reduce the iteration time of the fully transient process, we also introduce the CAP in the calculation of mold temperature. That is, a cycle-averaged temperature distribution of mold base is obtained by solving the following steady-state Laplace equation:

mm rforzT

yT

xTk

v02

2

2

2

2

2 (2)

where T is the cycle-averaged mold temperature. Initial Condition: the mold temperature is initially assumed to be equal to the coolant temperature. The initial part temperature distribution is obtained from the analysis results at the end of filling and packing stages.

pp

mc

rforrTrforT

rT vv

vv

,,

,0 (3)

Boundary Conditions: Heat of the molten plastic part is removed by the coolant flowing through the cooling channel as well as the ambient air surrounding the exterior surfaces of the mold base via a heat convection mechanism. In this work, the effect of thermal radiation is ignored. The conditions defined over the boundary surfaces and interfaces of the mold are specified as,

om TThnTktfor ,0 (4)

Where n is the normal direction of mold boundary. On the exterior surfaces of the mold base

m:

mairair rforTThh v0, (5a)

On the cooling channel surfaces c:

ccc rforTThh v0, (5b)

The heat transfer coefficients ch and airh are obtained from the empirical equations cited in the standard text of

transport phenomena [12].

Numerical Method

Numerical Discretization Method : In this work, a numerical solver based on Finite Volume Method (FVM) is developed to solve the governing equations. The solver has been successfully applied in injection molding filling simulation [13-14]. Numerical experiments confirm the reliability and efficiency of the solver. In addition to this, our solver is based on edge face data structure of the mesh, therefore it has greater flexibility in the element type. Currently the proposed solver can handle tetra, hexa, prism, pyramid, and mixing elements. Prism layer element [15] can also be used for analysis to improve thermal boundary resolution while without extensive refining of mesh. This is valuable in mold cooling analysis that may involve millions of elements.

Integrated Analysis Procedure: the proposed computation framework is schematically shown in Figure 1 [16]. The software package first reads the input data (including mesh data, material data, and process condition data), performs 3D filling analysis (based on specified uniform mold temperature or mold temperature distribution obtained from previous mold temperature iteration). 3D Cooling analysis is then conducted to obtain part temperature distribution at the end of cooling stage. Cycle-average mold temperature obtained from the cooling analysis fed back to filling modules for improving calculation or serves as an input boundary condition for warpage analysis. The iteration of mold temperature is continued until the mold temperature variation between iterations is small. This integrated analysis ensures a coupling between mold filling and mold cooling results and is of practical value to improve the accuracy of analysis.

Results and Discussion

A geometry model composed of T-shaped part with four cooling channels and mold base are simulated by the proposed cooling solver. The configure is shown in Figure 2. In this case, tetra elements are generated for simulation. There are 3,689/24,075/283,464 elements for part/cooling channels/moldbase, respectively. On Pentium III/933 PC the calculation time of molding filling and cooling analysis is about 60 sec and 5 minutes. The required RAM is about 300Mbyte for cooling analysis.

Figure 3(a) shows the filling analysis result. Melt front at 80% filling and iso-surfaces at different filling time is displayed. Figure 3(b) shows part temperature distribution at the end of cooling. Local hot spots due to arrange of cooling channels and geometry effect should be noticed. Figure 3(c) shows the cycle-averaged mold

temperature distribution of cooling channel and exterior surface of moldbase. Figure 3(d) shows the cycle-averaged heat flux distribution of cooling channels and exterior surface of moldbase. From the heat flux the heat load and hence cooling efficiency of each cooling channel can be evaluated for design purpose. Figure 3(e) shows the slicing of part temperature. In the end of cooling the temperature of the hot core of the part has been reduced to below 90oC(in this case, injection melt temperature is 230oC, coolant temperature is 30oC, cooling time is 50 sec).Figure 3(f) shows the temperature slicing across the moldbase. Note most portion of the moldbase remains a temperature about 30oC, there is a thermal boundary layer near the part. Mesh should be refined to capture the sharp temperature gradient change for reliable solution. Figure 4(a)-(f) shows the 3D-Cool analysis results of some industrial cases.

Conclusions

In this paper, a new true 3D mold cooling analysis framework is proposed. This method is based on extended finite volume method and is proved from numerical experiments to be a cost-effective method for true 3D simulation in injection mold cooling analysis.

Reference

[1]. M. Razayet and T. E. Burton, Int. J. Numer. Methods Engrg., 29,263-273 (1990).

[2]. M. Razayet, Int. J. Numer. Methods Engrg.,33, 1109-1118 (1992).

[3]. M. Razayet, Int. J. Numer. Methods Engrg.,36, 1563-1572 (1993).

[4]. K. Himasekhar, C. A. Hieber and K. K. Wang, SPE ANTEC Tech. Paper, 352-355 (1992).

[5]. R. K. Shah (ed.), Numerical Heat Transfer with Personal Computers and Supercomputing, HTD-Vol. 110, ASME, (1989).

[6]. L. S. Turng and K. K. Wang, J. Eng. Ind., 112, 261-267 (1990).

[7]. K. Himasekhar, J. Lottey and K. K. Wang, J. Eng. Ind., 114, 213-221 (1992).

[8]. S. C. Chen and S. Y. Hu, Int. Comm. Heat Mass Transfer, 18, 823-832 (1991).

[9]. R.Y.Chang and David C.Hsu, Molding 98 conference (1998)

[10]. R.Y.Chang, S.H.Huang, W.L.Yang, L.Y.Chen, and C.C.Lai, SPE ANTEC Tech. Paper, paper 513 (2000)

[11]. CoreTech System, Moldex-Cool Theory, Moldex Training Material, CoreTech System, HsinChu, Taiwan (2000)

[12]. J. R. Welty, C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, 3rd ed., John Wiley and Sons (1984).

[13]. R.Y.Chang and W.H.Yang, Int. J. Numer. Methods Fluids, 37, 125-148 (2001).

[14]. R.Y.Chang and W.H.Yang, SPE ANTEC Tech. Paper, paper 740,(2001)

[15]. R.Y.Chang, L.Louis, W.H.Yang,V.Yand, David Hsu, SPE

[16]. CoreTech System, Moldex-3DCool Theory, Moldex Training Material, CoreTech System, HsinChu, Taiwan (2001)

Key Words: Three-Dimensional CAE, Mold Cooling Analysis, Injection Molding Cooling

Figure 1.Computational framework of true 3D molding cooling analysis proposed in this work.

Figure 2: Configuration of the testing case.

(a): Melt front advancement and iso-filling time surfaces of the testing case.

(b) : Part temperature distribution of the testing case.

(c) : Mold temperature distribution of the testing case.

(d) : Heat flux distribution of the testing case.

(e): Part temperature slicing of the testing case.

(f): Mold temperature slicing of the testing case.

Figure 3: Analysis results of T-Mold testing case

(a): Part, moldbase geometry and Coolant layout. (d): Temperature at end of cooling.

(b): Cooling time distribution in the cutting plane (e): Temperature distribution on the exterior surface

(c): Surface temperature distribution inside moldbase (f): Temperature in the cutting plane of mold base

Figure 4: Analysis results of a real industrial case