Robust springback optimization of a dual phase steel seven-flange die assembly

Abstract

This paper investigates robust springback optimization of a DP600 dual phase steel seven-flange die assembly composed of different flange designs. The optimum values of the die radius and the punch radius are sought to minimize the mean and the standard deviation of springback using surrogate based optimization. Springback values at the training points of surrogate models are evaluated using the finite element analysis code LS-DYNA. In this work, four different surrogate modeling types are considered: polynomial response surfaces (PRS) approximations, stepwise regression (SWR), radial basis functions (RBF) and Kriging (KR). Two sets of surrogate models are constructed in this study. The first set is constructed to relate the springback to the design variables as well as the random variables. It is found for the first set of surrogate models that KR provides more accurate springback predictions than PRS, SWR and RBF. The mean and the standard deviation of springback are calculated using Monte Carlo simulations, where the first set of surrogate models is utilized. The second set of surrogate models is generated to relate the mean and the standard deviation of springback to the design variables. It is found for the second set of surrogate models that PRS provides more accurate springback predictions than SWR, RBF and KR. It is also found that introducing beads increases the mean performance and the robustness. The robust optimization is performed and significant springback reductions are obtained for all flanges ranging between 7% and 85% compared to the nominal design. It is also found that a design change that decreases the mean springback also reduces the springback variation. It is observed that the optimization results heavily dependent on the bounds of the die and punch radii. In addition, optimization with multiple surrogates is investigated. Finding multiple candidates of optimum with multiple surrogates and selecting the one with the best actual performance is found to be a better strategy than optimizing using the most accurate surrogate model.