Modeling of heat flow in sand castings: Part II. Applications of the boundary curvature method
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I.
INTRODUCTION
INrecent years, much attention has been given to the use of simulations to improve manufacturing processes. In the area of foundry casting, a number of programs have been developed for this purpose (of. References 1 through 5). The programs require significant computation time to achieve accurate results. For this reason, attempts have been made to reduce the amount of computation necessary in the programs. Thomas, et al. 6 examined the effects on computation time and accuracy obtained by using different simulation methods (finite difference vs finite element), different time stepping techniques, and various methods for handling latent heat evolution. Wei, et al. 4 and Hong, et al. s developed methods for reducing the size of the simulation by eliminating the requirement for solving the heat flow problem in the mold surrounding a metal casting. The latter approach is especially attractive because it should be capable of reducing the problem size by an order of magnitude. In Part I of this paper, a new method was presented for eliminating the solution of the heat flow problem in the mold. The method consists of determining the effective curvature (for heat flow) at each element on the surface of a finite element model of the casting. A boundary condition is then applied at that location to give the local heat flux from the casting, based on a library of solutions for surfaces having equivalent curvatures. In Part I, a systematic means for determining the effective curvature was given, and the library of solutions was generated. The purpose of this paper is to provide validation of the method. Example problems are solved using both conventional simulation methods (with the sand mold enmeshed) and the new boundary curvature method. The results of the simulations are compared to each other, and to experimental results. The differences in computer time using the two methods of simulation are also discussed.
II.
METHODS
(1) Enmesh the pattern for the casting. (2a) Enmesh the mold surrounding the pattern or, (2b) Using one of the boundary methods described in Part I of this paper, assign boundary properties to each element on the surface of the part. (3) Assign material properties for the casting. (4) Set the initial conditions for the simulation, and solve for the temperature as a function of time at all of the nodes over the time period of the simulation. The mesh generation of Steps (1) and (2a) can be done by hand, by using various geometric modelers, or a preprocessor of the FEM program. In any case, mesh generation is a time-consuming process for complex shapes. Reducing this time by decreasing the size of the FEM model is an important part of the savings derived from adopting the proposed method. Step (2a) is eliminated in favor of Step (2b). In this paper, the procedure described in Part I was used to assign boundary properties. The systematic method for determining the appropriate surface curvatures is straightforward and readily adapted to automation. The FEM model of the pattern is all that
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