Response surface methodology for design of sheet forming parameters to control springback effects

This paper deals with the optimization of tools geometry in sheet metal forming in order to reduce the springback effects after forming. A response surface method (RSM) based on diffuse approximation is used; this technique has been proved more efficient than classical gradient based methods since it requires fewer iterations and convergence is guaranteed especially for nonlinear problems. A new improved Inverse Approach for the stamping simulation based on DKTRF shell element is presented. In the new version, the strains and stresses due to bending and unbending effects are calculated analytically from the final workpiece, especially on the die entrance radii for curvature changes. The bending/unbending moments and the final shape are used to calculate springback using a second incremental Approach based on the Updated Lagrangian Formulation. The benchmark on the “U” bending problem of NUMISHEET’93 has been used to validate the method, good results on the elimination of springback have been obtained. The final results are validated using STAMPACK^® and ABAQUS^® commercial codes.