Analytical optimization on geometry of uniform pressure coil in electromagnetic forming and welding

This paper reported an analytical formulation for the optimum geometry of a uniform pressure coil used in electromagnetic forming and welding. To characterize the energy efficiency of the coil, we defined the objective function as the ratio between the produced magnetic pressure and the required magnetic energy. We then deduced an analytical formulation of the objective function in terms of the geometry and electromagnetic parameters. Based on the analytical formulation, we finally deduced the optimum configuration of the coil geometry in analytical form. To validate the proposed analytical formulation, we analytically and numerically analyzed a uniform pressure coil fabricated in our laboratory, showing that the proposed analytical formulation can well reproduce the numerical results over a broad range of geometric parameters. In addition, it was found that the uniform pressure coil exhibits an optimum channel height, which can be analytically expressed in terms of the coil geometry. In summary, the present study provides an efficient method for designing a uniform pressure coil.