SENSITIVITY ANALYSIS BASED PREFORM DIE SHAPE DESIGN USING THE FINITE-ELEMENT METHOD

This paper uses a finite element-based sensitivity analysis method to design the preform die shape for metal forming processes. The sensitiv ity analysis was developed using the rigid visco-plastic finite elemen t method. The preform die shapes are represented by cubic B-spline cur ves. The control points or coefficients of the B-spline are used as th e design variables. The optimization problem is to minimize the differ ence between the realized and the desired final forging shapes. The se nsitivity analysis includes the sensitivities of the objective functio n, nodal coordinates, and nodal velocities with respect to the design variables. The remeshing procedure and the interpolation/transfer of t he history/dependent parameters are considered. An adjustment of the v olume loss resulting from the finite element analysis is used to make the workpiece volume consistent in each optimization iteration and imp rove the optimization convergence. In addition, a technique for dealin g with fold-over defects during the forming simulation is employed in order to continue the optimization procedures of the preform die shape design. The method developed in this paper is used to design the pref orm die shape for both plane strain and axisymmetric deformations with shaped cavities. The analysis shows that satisfactory final forging s hapes are obtained using the optimized preform die shapes.