Semi-analytical calculation of the force between two magnets with rhombus-shaped cross-sections

Analytical calculations of interaction forces between permanent magnets are essential for the fast and accurate modeling of magnetic springs and bearings. Whereas extensive research has been conducted on interaction forces between cuboidal magnets, there is a lack of research on force calculations between other prismatic magnets in existing literature. This paper newly develops a semi-analytical method for force calculation between two magnets with rhombus-shaped cross-sections. The method is based on interaction force between two rectangular magnetically charged surfaces which are inclined toward each other. Under a Cartesian coordinate system, two components of the force between inclined rectangular magnetically charged surfaces are presented with fully analytical expressions, whereas the other component is expressed with one numerical integral. By applying these expressions repeatedly, the force between two magnets with rhombus-shaped cross-sections is derived. Moreover, a test rig is constructed to validate this semi-analytical method. Furthermore, the method can be extended to force calculations between prismatic magnets with arbitrary-shaped cross-sections, which allows a simple and fast modeling of many magnetic applications.