Simplified mathematical modeling for an electromagnetic forming system with flat spiral coil as actuator

Abstract

This study presents mathematical modeling and calculation procedure for problems of electromagnetic forming of thin circular metal sheets using a flat spiral coil as actuator. The method based on the Biot-Savart Law focuses specifically on the calculation of the electromagnetic field generated by the flat coil and analysis of the circuit that models the electromagnetic forming system to the initial time, before the plastic deformation of the sheet. The solution of magnetic induction integral equations is performed by numerical methods specifically with the use of Matlab® software, providing important information that serves as feedback for system design. Free bulging experiments were performed to demonstrate a good relationship with the mathematical model predictions for electrical discharge current in the coil and induced currents in the metal sheet, behavior of the transient electromagnetic force between coil and workpiece, and distribution of magnetic field, electromagnetic density force along the coil.