Analytical modelling and finite element computation of radial vibration force in fractional-slot permanent magnet brushless machines

Analytical models have been developed for analysing the radial vibration force in fractional-slot permanent magnet machines and validated extensively by finite element analyses. They are used to investigate the influence of (a) stator slotting, (b) tangential field component, (c) radius in the airgap for computation, and (d) load condition etc. on the radial vibration force calculation. The major findings can be summarised as follows. (1) Even on open-circuit, the low harmonic component (e.g. 2
^nd
for 10-pole/12-slot machine, and 1
^st
for 8-pole/9-slot machine) of radial force exists due to slotting effect although the amplitude is relatively low, while the slotless analytical model cannot predict this phenomenon; (2) However, on load, slotless analytical model is accurate enough in the radial force analysis, since in this case, the low order harmonic component of radial force is mainly due to the interaction between the magnet field and the armature reaction field, and is largely determined by the combination of pole and slot numbers; (3) It is much more reliable to calculate the radial force in the middle of airgap, rather than close to the stator bore, while the harmonic contents of radial force are almost independent of radius in the airgap; (4) The simple formula accounts only for the radial field component in the middle of airgap is accurate enough for radial force calculation.