Computational optimisation of robust sheet forming processes

Mathematical optimisation consists of the modelling and solving of optimisation problems. Although both the modelling and the solving are essential for successfully optimising metal forming problems, much of the research published until now has focussed on the solving part, i.e. the development of a specific optimisation algorithm and its application to a specific optimisation problem for a specific metal forming process. We propose a generally applicable optimisation strategy which makes use of FEM simulations of metal forming processes. It consists of a methodology for modelling optimisation problems related to metal forming. Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design variables. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. However, the above strategy is deterministic, which implies that the robustness of the optimum solution is not taken into account. Robustness is a major item in the metal forming industry, hence the deterministic strategy is extended in order to include noise variables (e.g. material variation) in optimisation. This yields a robust optimisation strategy that enables to optimise to a robust solution of the problem, which contributes significantly to the industrial demand to design robust metal forming processes. Just as the deterministic optimisation strategy, it consists of a modelling, screening and solving stage. The deterministic and robust optimisation strategies are compared to each other by application to an analytical test function.