Machine and actuator design: Modeling 3-D fields and forces using the analytical surface charge expressions

Many modern advanced electromagnetic devices, e.g. motors and actuators, use permanent magnets as a source of magnetic fields. The strong and reliable magnetic fields of today's rare-earth permanent magnets increase their force density. Most of them are based on the interaction between the magnetic field of permanent magnets and current-carrying coils. However, magnetic couplings or electromagnetic vibration isolation systems rely on the strong and position-dependent passive force between permanent magnets instead of an active force resulting from a current. An accurate, noise-free computational description of these interactions is therefore essential for future developments of these high-performance devices. The considered configurations are free-space unbounded problems and do not exhibit structural periodicity. As a three-dimensional magnetic field solution is required, the analytical surface charge method is the model of choice. The expressions for the interaction force between PMs with an (anti-)parallel, perpendicular, and rotated magnetization are derived considering a configuration with two PMs. These could be extended to include various other electromagnetic device structures. Further, the developments in the analytical surface charge expressions of the interaction forces between cuboidal permanent magnets are addressed. Finally, extensions to the surface charge method are proposed, aiming to create a fully 6-DoF permanent magnet interaction model, which can serve as a fast, analytical replacement to the finite element method.