Computer-aided design of electromagnetic actuators using finite difference techniques

A numerical method is described, which is used for static and dynamic calculations of electromagnetic actuators. The mathematical model consists of three systems representing the electric, magnetic, and mechanical components, which are governed by coupled differential equations for coil current, magnetic vector potential, and armature displacement. As yet, only magnets with rotational symmetry have been considered and eddy currents have been neglected. The non-linear partial differential equation for the magnetic vector potential is solved by finite difference techniques using the line iteration method with overrelaxation of the vector potential and underrelaxation of the reluctivity. Acceleration of convergence is achieved by the multiplicative method based on Ampere´s law. For the solution of the electric and mechanical differential equations, inductances and forces are calculated from the magnetic field distribution. A computer program based on these techniques is outlined. It automatically adapts the finite difference grid to the time-varying geometry and chooses the surface of integration for the evaluation of the magnetic force. Some calculations are discussed, which were performed to assist the design of print needle actuators.