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The torque ripple of a permanent magnet (PM) machine is mainly due to the cogging torque and distortions of the back-emf waveforms, winding inductances and current waveforms. Both the cogging torque and back-emf are normally calculated at open-circuit conditions. However, they are affected by the electric loading and magnetic saturation. This paper investigates the influence of the load conditions on the cogging torque and back-emf waveform by employing a frozen permeability finite element technique. Furthermore, the effectiveness of the rotor skew on the minimization of the cogging torque, thus torque ripple, is also highlighted. It is found that the cogging torque magnitude is significantly increased under load conditions due to more flux leakage through tooth tips. However, the more important issue is that the cogging torque periodicity also changes, thus the rotor skew technique becomes less effective. In addition, the back-emf waveform under load conditions contains more harmonics, which leads to more electromagnetic torque ripple. It is also proven that the cogging torque, back-emf harmonics and consequently the output torque ripple are effectively diminished if the machine is skewed by one actual cogging torque period, i.e., when the electrical loading influence is considered. The analysis results are supported by experimental measurements.
Azar et al. (Thu,) studied this question.