Equivalent Formulas for Global Magnetic Force Calculation From Finite Element Solution

The paper presents the Lorentz force and Maxwell stress formulas that give the same result of global force calculation for FE method. Edge element method (EEM) using vector potential A and nodal element method (NEM) using scalar potential Ω are considered. The formulas have been obtained from virtual work principle that has been adapted to the FE model. The FE network must be regular of homogenous element to obtain the equivalent formulas for EEM and equivalent formulas for NEM. The results of force calculation using the proposed methods have been compared with the analytical results. The systems with three cuboidal magnets and an induction motor with solid rotor described in TEAM Workshops Problem No. 30 were analyzed. Moreover, repulsive forces in the systems presented by TEAM Workshops Problem No. 7 and in the system with two ring-shaped magnets have been investigated.