Contribution of winding space harmonics to average torque in fractional-slot concentrated permanent magnet machines with equal/unequal teeth

This study investigates the modulation effects in any m-phase permanent magnet machines with fractional-slot concentrated windings and separates the average torque contributed by the winding space harmonics, with particular emphasis on unequal stator teeth. First, winding space harmonics of m-phase machines with double/single layer windings are analysed and modulation effects of equal/unequal teeth are studied. It is found that, apart from the conventional torque contributed by main harmonic (v = p) and modulated torque by v = p +/- N-s harmonics (N-s is slot number and p is pole pair number), additional modulated torque owing to v = p +/- N-s/2 harmonic appears in the unequal teeth machines. Then, 12-slot/10-pole (12S10P) three-phase and 10S8P five-phase machines are employed to verify the analysis through finite element method. It is demonstrated that, for unequal teeth machine, v = p - N-s and v = p - N-s/2 harmonics have positive average torque contribution, around 6.5 and 6% to the total torque. The v = p + N-s and v = p + N-s/2 order harmonics produce negative average torque but with much smaller values. Finally, experiments are carried out on the 10S8P unequal teeth prototype.