Analytical derivation of emf waveforms in PM machines based on permanent magnet volume integration

An analytical expression is developed for predicting EMF waveforms resulting from permanent magnets (PM) in electrical machines. The expressions derived in the paper for the flux linkage are based on a volume integral over the PM volume, rather than the usual surface integral over the coil. The proposed method consists in applying a virtual current in the coil of the machine and calculating the magnetic field generated inside the PM volume. The EMF waveform is obtained by derivating the flux linkage with respect to time. Analytical expressions of the emf are given for various PM shapes and Halbach magnetization patterns. Experimental verifications of the waveforms obtained are presented in the paper, demonstrating the validity of the expressions obtained theoretically.