Influence of slot and pole number combination on radial force and vibration modes in fractional slot PM brushless machines having single- and double-layer windings

This paper systematically investigates the radial force and vibration modes in fractional slot surface-mounted permanent magnet (PM) brushless machines having different slot and pole numbers, viz. 2p = N
_s
plusmn 2 , 2p = N
_s
plusmn1, q = 0.5, respectively, with either single- or double-layer winding. The dominant vibration mode can be determined from the lowest order of radial force harmonic. It shows that for integer slot PM machines, q = 1, the dominant radial force is mainly caused by the fundamental magnet field itself, and the dominant vibration mode order is equal to pole number which is usually high. However, in all fractional slot PM machines, the dominant radial force is mainly produced by the interaction between the harmonic in magnet field and the harmonic in armature reaction field, while the noise and vibration can be significantly higher since the dominant vibration mode order can be as low as 1 or 2, which strongly depends on the slot and pole number combinations, as well as the winding topologies, as confirmed by both developed analytical model and finite element (FE) analyses.