Optimal riser design for metal castings

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systematically modified to minimize the gate and riser volume, while simultaneously ensuring that no porosity appears in the product. In this approach, we combine finite-element analysis of the solidification heat-transfer process with design sensitivity analysis and numerical optimization to systematically improve the casting design. Methods are presented for performing the sensitivity analysis, including the sensitivity of important solidification parameters such as freezing time, temperature gradient, and cooling rate. We also present methods for performing Newton-Raphson iteration for solidification models that use the boundary-curvature method to represent the sand mold. Finally, the methods are applied to design risers for an L-shaped steel plate to control microporosity and for a steel hammer to control macroporosity. It is demonstrated that the size of a conventionally designed riser can be reduced by a significant amount while retaining the quality of the cast product.

I.

INTRODUCTION

CASTING simulation has seen widespread application in industry as a means to understand and improve product quality. The introduction of relatively lowpriced powerful workstations, the development of robust numerical methods embodied in commercially available codes, and the growing need for shortened productdevelopment cycles have also contributed to its growing popularity. Ul A number of researchers have begun to use these analyses' capabilities to design castings, as opposed to simply analyzing them. Upadhya et al. t2] and Bradley et al. t31 described knowledge-based expert system approaches to casting design, which relate feeding distances to rigging designs. Zabaras et al. t41 and Zabaras and Kang, t51 in a series of articles that is closely related to our work, have applied optimization techniques to define boundary conditions to produce a desired liquidsolid interface motion or minimize residual stresses in the solidified casting. Overfelt t6~ used a finite-difference sensitivity method to study the effect of various material properties on the solidification time in a casting. Tortorelli et al. t7'81 have introduced methods for optimizing solidification processes through both shape and processing parameter modifications. In this article, we formalize the design process for castings by integrating solidification process modeling, explicit design-sensitivity analysis, and numerical optimization into a single framework. Knowing that the process analysis can be computationally intensive, we focus our efforts on using efficient techniques. In this section, we describe the formal approach to design, and in the T.E. MORTHLAND, Graduate Student, Department of Mechanical and Industrial Engineering, D.A. TORTORELLI, Assistant Professor, Departments of Mechanical and Industrial Engineering and Theoretical and Applied Mechanics, and J.A. DANTZIG, Associate Professor, Department of Mechanical and Industrial Engineering, are with the University of Illinois, UrbanaChampaign, IL 61801. P.E. BYRNE, formerly Graduate Student, Departme