Analysis of cogging torque in brushless machines having non-uniformly distributed stator slots and stepped rotor magnets

In this paper, a simple analytical method is proposed to synthesize the cogging torque waveform, which results in a permanent magnet brushless machine from the cogging torque waveform, which is associated with a single stator slot. It is then used to analyse the cogging torque waveforms which result in 12-slot, 10-pole motor machines having both uniformly and non-uniformly distributed stator slots, and to demonstrate the utility of incorporating skew simply by circumferentially displacing the two magnet segments of each pole. It is shown that (i) the resultant cogging torque waveforms can be synthesized to a high accuracy, as confirmed by both finite element analysis and measurements; (ii) not all the harmonics which exist in the cogging torque waveform due to a single slot are present in the resultant cogging torque, and that the most significant components can be identified analytically; (iii) although the method is generally applicable to any design of permanent magnet brushless machine, it is particularly useful for investigating the influence of the number of stator slots when a fractional number of slots per pole is employed, or when the machine has non-uniformly distributed stator slots; (iv) the method can easily be used to analyse the cogging torque waveform which results in machines having stepped magnets and to determine the optimal step angle.