GA-based optimization to control the thickness distribution in components manufactured via superplastic forming

Superplastic forming (SPF) is a net-thinning sheet metal forming process that allows to achieve very complex geometries; nevertheless, due to its deformation mechanics, it is difficult to achieve a uniform thickness distri-bution in the final component since the most stretched regions of the blank are contemporarily characterized by the most severe thinning. With the aim of proposing a robust approach, a new methodology able to optimize the thickness distribution in components produced by SPF is proposed. Although two different titanium-based (Ti-6Al-4 V ELI) axisymmetric components - i.e., a hemisphere and a frustum of cone - were chosen as case studies, the methodology can be extended to any material and to any geometry, even considering more than one objective function. The superplastic forming was numerically simulated, and the Finite Element (FE) model was embedded into an automatic procedure managed by the multi-objective genetic algorithm MOGA-II. The blank's initial thickness distribution was modelled using a second-order polynomial function and its coefficients were determined to get, at the end of the SPF process, a uniform thickness in the formed part irrespective of the specific geometry. Titanium blanks were machined on a 5-axis milling machine to obtain the calculated optimal initial thickness distribution; subsequently, such blanks were superplastically formed and inspected in order to measure the thickness distribution. Tests showed a very good fitting with the numerical prediction thus con-firming the robustness and the effectiveness of the proposed methodology.