Multi-objective optimization based on meta-models of an aeronautical hub including the ductile damage constraint

In forging process, geometric design of initial billet and tools is very important. Traditionally, engineers use their knowledge and experience to design and optimize the geometric model of forging process by using trial-and-error methods. Such methods are time consuming and cost expensive. It is therefore interesting to design an automatic tools builder based on optimization methodology coupled with virtual finite element simulations, thus helping engineers to improve products and reduce cost. In this article we describe a meta-model based multi-objective optimization methodology for forging process designed to build the theoric Pareto optimal front of the mechanical problem. We go through a four-step process: building parametric computer-aided design geometry model, simulating the forging process according to the DOE, fitting meta-models, and optimizing the process by using an advanced algorithm. Two different meta-models, including polynomial and kriging methods, are constructed, based on the simulation values for different responses. Then optimization algorithms NBI-NLPQLP and NSGA-II are applied to find the optimum solutions based on each different meta-model. In order to drive this procedure automatically we use ModeFRONTIER (R) software. Using this environment, several macro commands are used to connect the geometry modelling (made with CATIA V5) and numerical simulation process. As an industrial example, a two-step forging of an aeronautic component shows the efficiency of the proposed methodology. That shows contributions of research in dealing with optimization design of die geometry taking into account technological interactions related to the process and the ductile damage inside the deformed part. A set of solutions selected in particular points of the optimal Pareto front are also presented and analysed.