SENSITIVITY ANALYSIS BASED PREFORM DIE SHAPE DESIGN FOR NET-SHAPE FORGING

A sensitivity analysis method for preform die shape design in net-shap e forging processes is developed in this paper using the rigid viscopl astic 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 mini mize the zone where the realized and desired final forging shapes do n ot coincide. The sensitivities of the objective function, nodal coordi nates and nodal velocities with respect to the design variables are de veloped in detail. A procedure for computing the sensitivities of hist ory-dependent functions is presented. The remeshing procedure and the interpolation/transfer of the history-dependent parameters, such as ef fective strain, are stated. The procedures of sensitivity analysis bas ed preform die design are also described. In addition, a method for th e adjustment of the volume loss resulting from the finite element anal ysis 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 f lashless forging with a complete die fill is realized using the optimi zed preform die shape. (C) 1997 Elsevier Science Ltd. All rights reser ved.