Effect of Slot and Pole Number Combinations on No-Load Airgap Vibration Forces of PMSM

The effect of slot and pole number combination on the airgap vibration forces of permanent magnet synchronous machines at no-load condition is studied in this paper. This analysis is carried out using finite element method for three external-rotor topologies, i.e. integer-slot, fractional-slot, and fractional-slot with modular stator. Firstly, a comparison between different vibration force calculation methods is made to select the most suitable one. Then, using the selected method, the study shows the period of the rotor vibration forces is equal to a slot-pitch and their harmonic orders depend on the slot and pole number combination. Analogously, the period of the stator vibration forces is equal to a pole-pitch and their harmonic orders are multiples of two regardless of the slot and pole number combination. Finally, an analytical expression, which depends on the slot and pole number combination, is proposed to obtain the periodicity of the stator and rotor vibration forces.