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

This paper presents the technique to effectively obtain required back EMF waveforms, e.g., sinusoidal, for permanent-magnet (PM) brushless motors by magnet arc shaping rather than the common stator arc shaping method. Motor back EMF waveforms partly depend on the air-gap flux distribution produced by magnets. Therefore, in this paper, the relationship between the flux distribution of a magnet and its shape is derived using the Laplace´s equation so that the magnet shape can be determined in accordance with the back EMF waveform required. Having determined the magnet shape, finite element analysis is employed to verify the effectiveness of the technique developed by comparing the back EMF waveforms of the unmodified arc-shape magnet, the shaped breadloaf and the idea sinusoids. The simulation results show that, by properly shaping the magnets, a back EMF waveform with close approximation to the ideal sinusoid can be obtained, differing from the quasi trapezoidal waveform generated by the original arc shape magnet. Moreover, the results also show that the cogging torque is significantly improved by the magnet shaping. The major advantage of using the developed method is that the required back EMF waveform can be easily obtained at the preliminary design stage so that the entire design efficiency can be improved.