An investigation on influence of magnet arc shaping upon back electromotive force waveforms for design of permanent-magnet brushless motors

This paper presents the magnet arc shaping technique to effectively produce the required sinusoidal back electromotive force (EMF) waveforms for design of permanent-magnet brushless motors. The magnet shapes to produce sinusoidal air gap flux distributions are first obtained using the Laplace\´s equation. A modified magnetic circuit model with "variable reluctance" is proposed for calculating the air gap flux distributions. Finite-element analysis is then employed to verify the calculated flux distributions and to generate the corresponding back EMF waveforms. The simulation results present a close approximation to sinusoidal back EMF waveforms for the motors investigated and, thus, verify the effectiveness of the developed method.