Difference in unbalanced magnetic force of fractional-slot PM machines between interna and external rotor topologies

This paper presents a comparative investigation into unbalanced magnetic force (UMF) of asymmetric permanent magnet machines without rotor eccentricities, particularly focusing on the difference between internal- and external-rotor topologies. The asymmetric field distribution results in radial and tangential asymmetric force waves. Although the radial and tangential stresses are in different direction, the UMF components they produce are nearly aligned. The UMF from asymmetric radial force wave can be additive or subtractive to that from asymmetric tangential force wave. Investigation shows that for the same pole slot number combination, if the UMFs due to radial and tangential force waves are additive in internal rotor machine, they are subtractive in the external rotor counterpart, and vice versa. Investigation reveals a general rule determining whether additive or cancelling: for a UMF produced by any two field harmonics, they are additive if the higher order is produced by the outer part outside the airgap, but cancelling if the higher order is produced by the inner part. Therefore, for a machine with pole number 2p=3k+1, they are additive if it is an external-rotor machine, but otherwise subtractive. On the other hand, for a machine with pole number 2p=3k−1, they are subtractive if it is an external-rotor machine, but otherwise additive. For the UMF due to armature reaction only, they are subtractive for external-rotor machines, but otherwise additive. The investigation is carried out by an analytical model and validated by finite element analysis.