Comparing metamodeling techniques for variability analysis in sheet metal forming processes

Abstract

This study presents a systematic comparison on the performance of different metamodeling techniques in the analysis of variability in sheet metal forming processes. For this purpose, three steel grades (DC06, DP600 and HSLA340) are selected as reference materials and two sheet metal forming processes are considered: the U-Channel and the Square Cup forming processes. The sources of variability selected for this study are the Young's modulus, the isotropic hardening law parameters, the anisotropy coefficients and the initial thickness of the sheet metal; the variability is described for all of them by a probabilistic normal distribution. The process outputs selected for analysis are the springback and maximum thinning, in case of the U-Channel forming process, and the maximum equivalent plastic strain and maximum thinning, in case of the Square Cup deep-drawing. Firstly, a number of random simulations is performed for each material and forming process. Then, metamodeling techniques based on 2nd degree polynomial RSM and three Kriging methods (Simple, Ordinary and Universal Kriging) are established, and their performance is evaluated. The results show that the performance of Kriging metamodels is generally better than RSM; also, the performance of RSM metamodels is strongly dependent on the number of design (training) points, which is not the case for Kriging metamodels.