Reliability Based Economical Optimization of Sheet Metal Forming Processes

In metal forming, optimization under uncertainty, e.g. by Reliability Based Design Optimization (RBDO), in combination with the results of FEM simulations has been recently opened. In RBDO, optimal process solutions should be robust with respect to uncontrollable or unpredictable variations of working conditions. Many try to solve the problem of optimizing some sort of objective function, under a reliability constraint. However, to the author’s knowledge, all the objective functions previously presented are expressed in terms of part quality (e.g. thickness uniformity) or process robustness with respect to failures (wrinkles, tears, etc.). In this paper a new approach is proposed for design optimization, under uncertainty, based on the minimisations of direct variable industrial costs (namely the material costs and the failure costs) rather than quality or reliability. It is called Reliability Based Economical Design Optimization (RBEO), and is demonstrated using the #1 benchmark case of Numisheet 1993. A simple cost model is used in order to build an economical objective function, which directly correlates the traditional technological design variables of the stamping process (e.g. the blank holder force) to the manufacturing costs.