In order to produce various structural frames of complex cross-sectional geometry, more complicated profiles requiring better quality are manufactured, thus demanding a systematic approach to quality assurance of the extruded products. From detailed information such as forming load, flow characteristics, temperature, and state of stress and strain, which can be obtained through numerical analyses, the necessary design specifications and data are obtained to optimize the design of dies. Although various approaches have been tried to find the optimized die shape in extrusion processes, they still have difficulties in representing complicated die shapes and suffer from enormous computation time. To effectively reduce the computation time and to widen the application of optimization to various extrusion processes, a new optimization scheme is proposed. Through the approximation of the objective function by state variable linearization, the convergence of the objective function can be improved and the number of iterations can be efficiently reduced, even for an optimization under unconstrained conditions. In this study, an optimization technique is presented and applied to various extrusion examples with an H-section, L-section, and triply-connected rectangular tubular section in order to yield a balanced flow on the outlet section. Also, the distribution of the effective strain, which is regarded as a material quality, and the wear rate of the die land are optimized in the extrusion processes.
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