Influence of Magnet Field Harmonics on Radial Force of Fractional-Slot PM Machines Considering Slot/Pole Combinations

The permanent magnet (PM) machines are commonly shaped with specific harmonics to maximize the average torque and minimize the torque ripple. However, this might increase the radial force, which is deemed as the main source of noise and vibration. Therefore, this article will investigate its effect on the radial force of fractional-slot PM machines considering slot/pole combinations. The relationship of phase angle and order between magnetic field and radial force is established. It is found that the phase and order of the radial force generated by magnet field harmonics are closely related to the modulation effect of stator teeth on the magnetic field. For the machine with close slot and pole numbers, such as
$Z=2p\,\,\pm $
2 and
$Z= 3p$
, the magnetic field harmonics can generate components with the same order and out of phase as the dominant one by tooth modulation, thereby reduction the dominant radial force. However, for the machines with overlapping winding such as
$Z= 2$
(
$2p \pm $
2) and
$Z=2$
(
$2p \pm $
1), the difference in armature harmonic magnetic field phase leads to the superposition of radial force components and increases the radial force. In addition, the electromagnetic vibration is also analyzed by finite-element method. Finally, the fractional-slot PM machines with specific harmonics are prototyped and experimental results are given to verify the analysis.