Distortion of Back-EMF and Torque of PM Brushless Machines Due to Eccentricity

The paper investigates the influence of slot/pole number combination and winding configuration on the electromagnetic performance, such as flux density, back-EMF and electromagnetic torque, of permanent magnet machines having static or rotating rotor eccentricities. It shows that the eccentricity does not affect the back-EMF and electromagnetic torque of rotational symmetrical machines whose configuration repeats every certain amount of angle. However, it significantly distorts the back-EMF and torque waveforms of rotational asymmetric machines. Further, the static eccentricity does not change the harmonic contents of back-EMF, but results in unbalanced three phase back-EMF. Hence, the temporal order of the main torque ripple due to the static eccentricity is equal to the pole number. On the other hand, the rotating eccentricity results in more back-EMF harmonics of orders equal to the PM magnetisation order plus/minus one. Therefore, the temporal order of the main torque ripple due to the rotating eccentricity is equal to the triplen number closest to the pole number. The prediction is validated by the experiment.