Pocketing Design of Stamped Metal Sheet Using Reduced Order Modelling

Abstract

This article is dedicated to the numerical design of aluminum sheets forming using a Hot Forming (HF)-Super Plastic Forming (SPF) hybrid process by the means of reduced order modelling. The HF step consists in a stamping. At the end of that first step, the punch and the die are sealed thanks to the metallic sheet and a peculiar geometric design. Then, follows the SPF step. Given the airtightness, the sheet is therefore shaped using controlled pressure through the injection of a gaz. Unlike during the HF step, the thickness varies noticeably during this second stage. A requirement is that the final thickness should be closed to uniform over the part or at least not drop below a critical target. Since, mass is a critical aspect in several industrial domains, the sheet has to be as thin as possible. Thus, performing pockets on the flat sheet before the forming seems very convenient. Finite element simulations may help designer to solve the corresponding optimization problem. Nevertheless, this type of simulation may be touchy (convergence issues due to contact interactions, exotic material behavior), and very costly which make them not suitable for optimization. To tackle this problem, dedicated optimization processes that are rather frugal in simulation calls might be developed. Alternatively, the simulation time was speed up here by means of reduced order modelling via the ReCUR method. ReCUR comes from: Regression model lying on the use of the CUR low rank tensor approximation. The latter is parametric with respect to the thickness and allows estimation of a new technical configuration within a few seconds (regarding hours for the finite element simulation) using no external solver. It only requires existing simulation results to be computed. First results are promising since a 30% mass gain has been achieved with only three finite element computations.