Influence of slot and pole number combinations on unbalanced magnetic force in permanent magnet machines

Unbalanced magnetic forces (UMF) exist in permanent magnet machines having pole and slot numbers differed by one and two, even when there is no rotor eccentricity. In machines having pole and slot numbers differed by two, the on-load UMF results only when the single layer winding is employed and the number of coils is odd. This paper investigates the influence of slot and pole number combinations on the UMF. UMF may be divided into two components due to the radial and tangential traveling force waves. It is found that they are additive for machines having a pole pair number p=3k+1, e.g. 8-pole/9-slot and 8-pole/6-slot, but cancelling for machines having p=3k-1, e.g. 16-pole/15-slot and 16-pole/18-slot. Further, due to the additive and cancelling effects, for the same slot number, the machine having a smaller pole number exhibits larger UMF when the slot/pole numbers differ by one, while the machine having a larger pole number exhibits larger UMF when the slot/pole numbers differ by two and the slot number is higher than 6. For the same pole number, machines having slot/pole numbers differed by two exhibit smaller UMF than machines having slot/pole numbers differed by one. It is also found that if p=3k-1, the UMF gradually diminishes to 0 with the increase of pole number. On the other hand, when p=3k+1, it reduces to a certain value with the increase of pole number. The experimental results verify the predictions.