Evaluation of magnetic force distribution and torque due to smooth interaction body force density in permanent-magnet materials

A smooth interaction body force density and torque were evaluated in permanent-magnet (PM) systems by using the virtual air-gap scheme coupled with the finite-element method. The virtual air-gap method has been successfully applied to soft magnetic materials for evaluating the force density, global contact force, and optimal shape design. These force-calculating methods employing the virtual air-gap scheme have been called generalized methods. Unlike the soft magnetic materials, there have been few research works related to force density and global force in PMs. We evaluated the interaction body force density, which represents the smooth and pure interacting force field between PMs and other magnetic components, by withdrawing the self-body force density from the total body force density. From this result, the smooth interaction body force density can explicitly show the trend of resulting mechanical torque. The torque by the self-body force density, of course, was zero and the torque, here, was evaluated by using the total body force density. From the previous results, the torque by total body force density shows some numerical instability, and we used edge-force components in each element for removing the numerical instability. Finally, the global quantities, such as global force from the smooth interaction body force density and torque from the total body force density, were successfully evaluated and verified by the conventional force calculating methods, such as the Maxwell stress tensor method and the virtual work principle method.