PREFORM DIE SHAPE DESIGN IN METAL-FORMING USING AN OPTIMIZATION METHOD

An optimization algorithm for preform die shape design in metal-formin g processes is developed in this paper. The preform die shapes are rep resented by cubic B-spline curves. The control points of the B-spline are used as the design variables. The optimization objective is to red uce the difference between the realized and desired final forging shap es. The sensitivities of the objective function with respect to the de sign variables are developed in detail. The numerical examples show th at the optimization method and the sensitivity analysis developed in t his paper are very useful and the design results are satisfactory. Imp ortantly, the preform die shapes designed by this method are easily ma nufacturable and can be implemented in practical metal-forming operati ons. This optimization method and the sensitivity analysis can also be applied in the preform design of complex industrial metal-forming pro blems. (C) 1997 by John Wiley & Sons, Ltd.