Theoretically, the layout of fractional pitch permanent magnet motors should ensure the cancellation of most cogging torque harmonics. In reality, manufacturing errors lead to incomplete cancellation and higher than expected cogging torque. One potential manufacturing error is the variation in angle between neighboring magnets. This paper uses the superposition technique to analytically determine the expected magnitude of each cogging torque harmonic based on a Gaussian distribution of angular magnet placement variation. A simple expression is presented for the expected value of each harmonic's magnitude based upon the harmonic number, the number of magnets, and the standard deviation of the Gaussian placement distribution. The derived expression is validated using Monte Carlo simulations and experimental implementation.
Heins, G., Brown, T., & Thiele, M. (2011). Statistical analysis of the effect of magnet placement on cogging torque in fractional pitch permanent magnet motors. IEEE Transactions on Magnetics, 47(8), 2142-2148. https://doi.org/10.1109/TMAG.2011.2125795