Mathematical Modeling of an Electromagnetic Forming System with Flat Spiral Coils as Actuator

Abstract

This study presents mathematical modeling and calculation procedure for problems of electromagnetic forming of thin circular metal sheets using flat spiral coil as actuator. The method 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. The flat coil is approximated by concentric circles carrying the current discharge from the capacitors. The calculation of electromagnetic force and magnetic couplings between the coil and metal sheet are made to the initial time, before the plastic deformation of the sheet. The method is based on the Biot-Savart law, and the solution of magnetic induction integral equations is performed by numerical methods specifically with the use of Matlab commercial software. A routine calculation, which models the problem as a set of differential equations was implemented in the Matlab, this provides 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 and electromagnetic density force along the coil. Also, achieved results showed that there is a strong dependence of the back electromagnetic force with respect to plate thickness for the system analyzed. The difference phase between the current induced in the coil and workpiece with higher negative peaks generate the back electromagnetic force.