Mathematical Optimization for the Virtual Design of Process Chains with Electromagnetic Forming

Abstract

In this work, a framework for virtual process design for coupled processes including electromagnetic impulse forming is presented. Virtual process design is here understood as the computer based identification of suitable geometry and process parameters to reach a predefined forming result via physically feasible process paths. Implementation of this concept relies on three pillars: a physical process model, its implementation within a numerical simulation, and a mathematical optimization algorithm. This methodology is particularly applied to a combination of deep drawing and subsequent electromagnetic forming (EMF). In this case, the model is given by an anisotropic elasto-viscoplastic material model augmented by damage evolution and coupled with the magneto-quasistatic approximation to Maxwell's equations. For constrained mathematical optimization, an inner point algorithm is applied. With this method for virtual process design at hand, several technological problems are addressed including tool coil design and the identification of ideal electrical parameters of the tool coil circuit. Employing this framework requires the identification of the material model described above. It turns out that a high precision identification of material parameters can be achieved with basically the same mathematical algorithm as derived for process identification.