Tool design optimization in extrusion processes

Tool design optimization in steady-state extrusion processes, based on the finite element discretization and non-linear mathematical programming techniques, is considered in this paper. In order to perform the optimization the die geometry is adequately parameterized, according to the polynomial representation. By imposing real technological and geometry constraints the optimal tool design is effected by extremizing the actual optimization objectives. In particular, the minimization of the forming energy consumption and the maximization of the possible area reduction are considered. The results, obtained numerically by assuming the Lagrange incremental elastic–plastic finite element formulation in modelling the material flow and the considered optimization approach, are compared to the known theoretical solutions, in cases where such solutions are available. It is demonstrated that the discussed approach is quite effective.