Insight into analytical modeling of electromagnetic forming

Due to its simplicity and clear physical meaning, the analytical method is attractive for analyzing the multiphysics of electromagnetic forming; however, the reliability of the analytical method is of great concern due to numerous simplifications. Targeting on an efficient and reliable analytical model of electromagnetic forming, this paper focuses on two objectives. Firstly, we developed a multiphysics-coupled analytical model for a commonly used electromagnetic actuator—uniform pressure coil. This model considers the interaction between the electromagnetic and mechanical fields and takes the influences of the geometry and material parameters into account, thus enhancing the accuracy of the analysis. After that, we proposed a criterion to assess the applicability of a fundamental assumption made about the analytical model, that is, the magnetic field induced by the electromagnetic coil could be completely confined by the workpiece. The applicability of this assumption is of fundamental importance, as it determines the reliability of the analytical model. The proposed criterion enables the quantitative evaluation of the applicability of the assumption in terms of process parameters. We validated the proposed model by a combination of experimental, analytical, and numerical investigations. Then, we identified the effectiveness and universality of the proposed criterion by comparing it with a widely accepted one; the underlying physical foundation of the proposed criterion was also discussed. The presented study could contribute to a fundamental understanding on the analytical model of electromagnetic forming, which provides a critical guidance for an efficient and reliable analytical work.