A computer-aided optimal design system was developed to improve the performance of a cooling system for injection molding. This was done by minimizing a weighted combination of the uniformity of the part temperature and the cooling time. The C O " algorithm was adopted to obtain the optimal design using the special boundary integral formulation and a corresponding design sensitivity analysis formulation. Design variables related to the processing conditions (i.e., inlet coolant temperature and volumetric flow rate of each cooling channel) and mold cooling system design (radius and location of each cooling channel) were considered. Three different optimization strategies are suggested, and three Sample problems were solved to demonstrate the efficiency and the usefulness of this optimization procedure.

DSA will ultimately play an important role in the design optimization process. Part 2 of this paper presents an efficient and accurate methodology for the DSA of the cooling stage of the injection molding process. The DSA program developed in the present study utilizes the implicit differentiation of the boundary integral equations and the B.C.s presented in Part I with respect to all DVs to yield the sensitivity equations. In this DSA, we have considered various DVs as follows: (i) (DVs related to processing conditions) inlet coolant bulk temperature and inlet coolant volumetric flow rate of each cooling channel inlet, and (ii) (DVs related to mold cooling system design) radius and location of each cooling channel. Two sample problems are solved to demonstrate the accuracy and efficiency of the present DSA formulation and to discuss the characteristics of each DV.

In recent years, increased attention has been paid to the design of cooling systems in injection molding, as it becomes clear that the cooling system affects significantly both productivity and part quality. In designing the cooling system of a mold efficiently in terms of rapid and uniform cooling, it would be desirable for mold designers to have an optimal CAD system. For this optimal design, one needs capabilities of both a thermal analysis (to be discussed in Part 1) and a corresponding DSA (to be presented in Part II) for the 3-d mold heat transfer during the cooling stage of an injection molding process. It was found that seemingly negligible inaccuracy in the thermal analysis result sometimes leads to meaningless DSA result. With a successful DSA being an intermediate goal towards optimum design, we have improved the thermal analysis system based on the modified BEM in terms of accuracy and developed rigorous treatments of B.C.s appropriate for DSA by considering the following issues: (i) numerical convergency, (ii) the series solution in part thermal analysis, iii) treatment of tip surface of line elements, (iv) treatment of coolant, and (v) treatment of mold exterior surface. Using two examples, this paper amply demonstrates the importance of these issues.

In the accompanying paper, Part I, we have presented a physical modeling and the associated numerical analysis of the injection molding process with a compressible viscoelastic fluid model. In Part II, effects of the compression stage in the injection/compression molding process are presented. Numerical results showed that the injection/compression molding process reduced birefringence as compared with the injection molding process. In this respect, the injection/compression molding process seems to be more suitable for manufacturing precise optical products of good optical quality than the injection molding process. Effects of the packing stage on the birefringence distribution in the injection/compression molding process were found to be similar to those in the injection molding process. Our numerical results show that the birefringence becomes smaller as the melt temperature gets higher and the closing velocity of the mold gets smaller with the flow rate and the mold temperature affecting the birefringence insignificantly. As far as the density distribution is concerned, the flow rate, melt temperature, and mold closing velocity have insignificant effects on the density distribution in comparison with the mold temperature.

The present study attempted to numerically simulate the process in detail by developing an appropriate physical modeling and the corresponding numerical analysis for injection molding and injection/compression molding processes of centergated disks. In Part I, a physical modeling and associated numerical analysis of injection molding with a compressible viscoelastic fluid model are presented. In the distribution of birefringence, the packing procedure results in the inner peaks in addition to the outer peaks near the mold surface, and values of the inner peaks increase with the packing time. Also, values of the density in the core region increase with the packing time. From the numerical results, we also found that birefringence becomes smaller as the melt temperature gets higher and that it is insignificantly affected by the flow rate and the mold temperature. As far as the density distribution is concerned, mold temperature affects the distribution of density especially near the wall. But it was not significantly affected by flow rate and melt temperature. Numerical results of birefringence coincided with experimental data qualitatively, but not quantitatively.