Design of sheet stamping operations to control springback and thinning: A multi-objective stochastic optimization approach

The aim of this paper is to develop a design tool for stamping processes, which is able to deal with the scattering of the final part quality due to the inner variability of such operations. Such variability is one of the main drawbacks for a robust process design. It results in a scattering of the most significant process results and depends on several parameters. The so called noise factors greatly influence final result variability, which often means rejecting parts and anyway achieving final properties different from the specified ones.The process investigated in the paper is an S-shaped U-channel stamping operation carried out on a lightweight aluminum alloy of automotive interest. The main topic of the paper is the prevention of excessive part thinning and the control of springback phenomena; thus, thinning and springback are the objective functions taken into account. The blank holder force (BHF) value was considered as process design variable while two noise factors were considered: lubricating conditions (represented by the friction coefficient μ) and strain-hardening index of the material (exponent n in material flow rule). The approach proposed in this paper is a multi-objective optimization problem consisting of an integration among finite element (FEM) numerical simulation, Response Surface Methodology (RSM) and Monte Carlo Simulation (MCS) method. The developed tool starts from a Pareto optimal solutions search technique and takes into account noise factors. The design procedure is able to foresee the potential direction along which a Pareto solution may move due to the effects of the noise factors. In this way, the proposed design tool is fully able to take into account process variability effects and to provide a precise overview of the possible perturbations the analyzed objective functions may undergo.