Numerical Simulation of Pulsed Electromagnetic Stamping Processes

In earlier published papers simulation of electromagnetic forming (EMF) was often conducted assuming that pulsed electromagnetic load can be replaced by the pulse of mechanical force calculating its parameters similar to R-L-C electric circuit. However, in many practical cases, parameters of this circuit are variable during the process because of the displacement of the blank and from one operation to another due to the accumulation of heat in the coil. The distribution of electromagnetic forces is also non-uniform and may affect the quality of the part being stamped. In our opinion, the accuracy of the simulation of EMF can be significantly improved if the formulation of the problem includes Maxwell equations of the electromagnetic field propagation, equations of dynamic elastic-plastic deformation, and heat transfer equations all coupled together. In addition, this approach may provide knowledge of electromagnetic coil deformation, which was investigated earlier with significant simplifications. The complexity of the problem is defined by mutual dependence of all three physical processes (electromagnetic field propagation, dynamic elastic-plastic deformation, and heat transfer) and variable boundary conditions. The propagation of the electromagnetic field is defined by quasi-stationary Maxwell equations transformed in Lagrangian form. The dynamics of elastic-plastic deformation is modeled using the solid mechanics equation of motion, the modified theory of elastic plastic flow, and the Von Mises yield criterion. The energy conservation law is employed for the simulation of heat transfer, which is important to define the appropriate stamping rate without overheating the coil. The developed methodology is illustrated by 2D examples of cone formation from sheet using a flat coil and the conical die and 2D plane strain sheet formation by direct propagation of the electric current through the metal bar, serving as a coil, and through the deformed sheet