Sensitivity analysis based preform die shape design for net-shape forging

A sensitivity analysis method for preform die shape design in net-shape forging processes is developed in this paper using the rigid viscoplastic finite element method. The preform die shapes are represented by cubic B-spline curves. The control points or coefficients of B-spline are used as the design variables. The optimization problem is to minimize the zone where the realized and desired final forging shapes do not coincide. The sensitivities of the objective function, nodal coordinates and nodal velocities with respect to the design variables are developed in detail. A procedure for computing the sensitivities of history-dependent functions is presented. The remeshing procedure and the interpolation/transfer of the history-dependent parameters, such as effective strain, are stated. The procedures of sensitivity analysis based preform die design are also described. In addition, a method for the adjustment of the volume loss resulting from the finite element analysis is given in order to make the workpiece volume consistent in each optimization iteration. The method developed in this paper is used to design the preform die shape of H-shaped forging processes, including plane strain and axisymmetric deformations. The results show that a flashless forging with a complete die fill is realized using the optimized preform die shape.