Preform die shape design for uniformity of deformation in forging based on preform sensitivity analysis

A finite element based sensitivity analysis method for preform die shape design in metal forging by controlling the deformation uniformity is developed in this paper. The optimization problem is to minimize the effective strain variation within the final forging through optimizing the preform die shape, so that a more uniform deformation within the final forging can be obtained. The preform die shapes are presented by cubic B-spline curves. The control points of the B-spline curves are used as the design variables. The objective function expressed by the effective strain variation is constructed. For two-dimensional forging problems, the sensitivity equations of the objective function, elemental volume, elemental effective strain-rate and the elemental strain-rate with respect to the design variables are developed. The optimization procedures of the method are given. The preform die shapes of two H-shaped forging processes in axisymmetric and plane-strain deformation are designed using the method.