3D Analytical Calculation of Interactions Between Perpendicularly Magnetized Magnets—Application to Any Magnetization Direction

Study of Magnetic Gravity Compensator Topologies Using an Abstraction in the Analytical Interaction Equations

“…The analytical surface charge model is an elegant way to evaluate electromechanical properties of magnet structures [2,3,[5][6][7][8].…”

“…It is based on a scalar potential formulation of Maxwell's equations. The most important assumption of this static model assumes are that the relative permeability of the permanent magnets µ r = 1, which has a small but well-predictable influence on the force as is experimentally shown in [3,5,7,8] …”

“…If the superposition principle is employed, it is possible to model the field of multiple magnets and to model cuboidal magnets with an arbitrary magnetization vector [3,7,8,10].…”

“…The analytical equations that describe the interaction force between these permanent magnets, based on the surface charge model, have been successfully derived and validated with experiments and FEA in [3,[5][6][7][8]. The force between two permanent magnets may be obtained with Virtual work [5,8] or by the Lorentz force method [3,6,7].…”

“…1(b). The analytical form of this vector has been derived and validated in [5,6] (parallel magnetization) and in [3,7,8] (perpendicular magnetization). As (6) shows, the integrand in the Lorentz force equation (6) concerns a multiplication of the flux density B 1 over the second magnet's surfaces which have a magnetic charge density σ m .…”