Characterization and reduction of zeroth spatial-order radial force in permanent magnet synchronous machines

When the lowest non-zero spatial order of the electromagnetic force is high enough in permanent magnet synchronous machines (PMSMs), the contribution of zeroth spatialorder (ZSO) radial force to the acoustic noise becomes evident. On account of this, this paper specially focuses its attention on the ZSO radial force. Finite element simulations and theoretical analyses are put to illustrate the physical essence of the force. It is found the frequency characteristics of ZSO radial force are totally the same as those of torque ripple (including cogging torque). Meanwhile, simulations show the ZSO radial force and cogging torque arrive at their local minimums simultaneously along with their low-order components under no load condition, while it is not the case under the load condition. The reason is analyzed in detail in the paper. However, when numerous flux density harmonics have been mitigated by shaping the PM arc in surface-mounted PMSMs, or the critical slot harmonics are cut down in PM-assisted synchronous reluctance machines, the relevant components of ZSO radial and torque ripple under load condition can be simultaneously largely reduced. The latter is successfully realized in an electric drive machine by the proposed method to improve the noise performance.