Influence of Slot and Pole Number Combinations on Unbalanced Magnetic Force in PM Machines With Diametrically Asymmetric Windings

Unbalanced magnetic forces (UMFs) exist in permanent magnet machines with diametrically asymmetric windings, e.g., 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 by using an analytical method based on the finite-element predicted airgap flux densities. A UMF may be divided into two components due to the radial and circumferential traveling stresses. It is found that they are additive for machines having pole number 2p = 3k - 1, e.g., 8-pole/9-slot and 8-pole/6-slot, but partially canceling for machines having 2p = 3k + 1, e.g., 16-pole/15-slot and 16-pole/18-slot. Furthermore, due to the additive and canceling effects, for the same slot number, the machine having a smaller pole number exhibits a larger UMF when the slot/pole numbers differ by one, whereas the machine having a larger pole number exhibits a 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 a smaller UMF than machines having slot/pole numbers differed by one. It is also found that, if 2p = 3k + 1, the UMF gradually diminishes to 0 with the increase in pole number. On the other hand, when 2p = 3k - 1 , it reduces to a certain value with the increase in pole number. The experimental results are provided to verify the analysis.