Solving optimisation problems in metal forming using FEM: A metamodel based optimisation algorithm

During the last decades, Finite Element (FEM) simulations of metal forming processes have become important tools for designing feasible production processes. In more recent years, several authors recognised the potential of coupling FEM simulations to mathematical opti- misation algorithms to design optimal metal forming processes instead of only feasible ones. This report describes the selection, development and implementation of an optimisa- tion algorithm for solving optimisation problems for metal forming processes using time consuming FEM simulations. A Sequential Approximate Optimisation algorithm is pro- posed, which incorporates metamodelling techniques and sequential improvement strate- gies for enhancing the e±ciency of the algorithm. The algorithm has been implemented in MATLABr and can be used in combination with any Finite Element code for simulating metal forming processes. The good applicability of the proposed optimisation algorithm within the ¯eld of metal forming has been demonstrated by applying it to optimise the internal pressure and ax- ial feeding load paths for manufacturing a simple hydroformed product. Resulting was a constantly distributed wall thickness throughout the ¯nal product. Subsequently, the algorithm was compared to other optimisation algorithms for optimising metal forming by applying it to two more complicated forging examples. In both cases, the geometry of the preform was optimised. For one forging application, the algorithm managed to solve a folding defect. For the other application both the folding susceptibility and the energy consumption required for forging the part were reduced by 10% w.r.t. the forging process proposed by the forging company. The algorithm proposed in this report yielded better results than the optimisation algorithms it was compared to.