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 methodbased 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.

Electromagnetic forming (EMF) is a high-speed forming process that uses energy density of a pulsed magnetic field to deform metallic workpieces. This paper presents a method to calculate the electromagnetic force in thin flat plates using a flat spiral coil as an actuator. The method is based on the Biot-Savart law, and the solution of magnetic induction integral equations is performed inside Matlab^® by a numerical method based on discretizing the EMF system in a system of ordinary differential equations that couple the electric and magnetic phenomena. Free bulging experiments and a comparison with Ansoft Maxwell^® software are presented demonstrating a good correlation with the proposed implementation.