Multi-objective optimization of blank shape for deep drawing with variable blank holder force via sequential approximate optimization

Optimal blank shape minimizing earing in deep drawing has a direct influence on material saving as well as product quality. A number of methods for blank shape optimization have been previously proposed, most of which adopt a closed-loop type algorithm that requires a large number of simulation runs. Numerical simulation in sheet metal forming is so numerically intensive that it is preferable to find an optimal blank shape with a small number of simulation runs. This paper proposes a method for determining the optimal blank shape design in square cup deep drawing using sequential approximate optimization (SAO) with a radial basis function (RBF) network. Sheet metal forming is multi-objective in nature, and thus the blank shape design problem is formulated as a multi-objective design optimization. The aim is therefore to identify the pareto-frontier with a small number of simulation runs. The earing is minimized under tearing and wrinkling constraints with a variable blank holder force (VBHF), which varies through the punch stroke. Numerical results show that the disconnected pareto-frontier is well identified with a small number of simulation runs. The earing of the optimal blank shape with the VBHF is also drastically reduced, when compared to a reference blank shape. Based on the numerical results, the experiments using a servo press are carried out. Consequently, the validity of the proposed approach is confirmed through the numerical and experimental results.