Optimum Process Design for Sheet Forming Using the Finite-Element Method and Mathematical Programing. 2nd Report. Proposal of Sweeping Simplex method.

Abstract

Recently, the development of an optimum forming process design system based on computer-aided technology has been required to reduce both time consumption and cost. The authors have developed an optimum forming process design system based on a concept which integrates the FEA and the numerical optimization method. In this design, an objective function has several local optimum points, and it is necessary to find the global optimum point. Therefore, in this paper, the sweeping simplex method is proposed, which finds the global optimum point efficiently. The proposed method was applied to a drawing process design. In order to obtain products with uniform thickness, two-stage drawing was employed. Two values of punch heights which characterize the first-stage punch shape were chosen as the design variables, and deviation of thickness from the average thickness was chosen as an objective function. It was demonstrated that the system could find the optimum condition efficiently. Furthermore, the optimum condition evaluated by the proposed system was verified to be in good agreement with the experimental results.