Evaluation of global force and interaction body force density in permanent magnet employing virtual air-gap concept

The global force and interaction body force density were evaluated in permanent magnets by using the virtual air-gap scheme incorporating the finite-element method. Until now, the virtual air-gap concept has been successfully applied to calculate a contact force and a body force density in soft magnetic materials. These force calculating methods have been called as generalized methods such as the generalized magnetic charge force density method, the generalized magnetizing current force density method, and the generalized Kelvin force density method. For permanent magnets, however, there have been few research works on a contact force and a force density field. Unlike the conventional force calculating methods resulting in surface force densities, the generalized methods are novel methods of evaluating body force density. These generalized methods yield the actual total force, but their distributions have an irregularity, which seems to be random distributions of body force density. Inside permanent magnets, however, a smooth pattern was obtained in the interaction body force density, which represents the interacting force field among magnetic materials. To evaluate the interaction body force density, the intrinsic force density should be withdrawn from the total force density. Several analysis models with permanent magnets were tested to verify the proposed methods evaluating the interaction body force density and the contact force, in which the permanent magnet contacts with a soft magnetic material.