Energy calculation of a permanent magnet system by surface and flux integrals (the flux-mmf method)

Formulas are derived for the total magnetic energy of a system with no currents, linear soft magnetic materials, and linear permanent magnets that satisfy a zero curl condition involving their magnetization vector (zero equivalent volume current density). This class of magnets includes common parallel and radially magnetized NdFeB and ferrite magnets above the knee in their demagnetization curves. The formulas express the energy as a constant plus either an integral over the magnet surface of the magnetic vector potential or an integral through the magnet of the magnetic flux. The formulas provide theoretical foundation for the flux-magnetomotive force (mmf) method for calculating cogging torque of permanent magnet motors