Design optimization for three-dimensional forming processes by an approximation scheme based on state variable linearization

Abstract

Among the methodologies to improve processes, product quality and productivity, the optimization approach is a powerful method to effectively achieve design objectives. Optimization can be applied to obtain desired designs in various large-scale problems due to the recent development of numerical simulation tools and computer features. In extrusion or forging processes, optimization is generally carried out by comprehensively using the results of finite element analyses. In cases where the material has large-scale non-linear behavior and the tool shape is very complex, the computation time for the finite element analysis is increased sharply. In addition, the optimization process is also very complicated and requires enormous computation time. Owing to the complexity and time-consuming process of the optimization, most studies have opted to deal with two-dimensional problems or simplified three-dimensional problems. A new optimization scheme is proposed to reduce computation time effectively and applied to various extrusion and forging processes. Through the approximation of the objective function by state variable linearization, the convergence is improved and the number of iterations is reduced efficiently, even for an optimization problem under unconstrained conditions. The proposed scheme is applied to the extrusion processes of ‘l’, ’H’ and ‘L’ sections. From the results of optimization using the proposed scheme, the optimal design has been found with only a few finite element analyses. Moreover, even if the number of design variables increases linearly, the increase of the number of iterations is slight. After shape optimization of the flow guide, the processes result in the balanced material flow at the exit section. The optimization of material properties is introduced and applied to the practical three-dimensional extrusion processes. The deviation of effective strain is regarded as a measure of material quality of the product and defined as the de...