Comparative Study of Electromagnetic Forces in External Rotor SPMSMs with Different Slot/Pole Combinations Considering Force Modulation Effect

This study comprehensively investigates and compares the electromagnetic force characteristics in external-rotor surface-mounted permanent magnet machines, considering the modulation effect. Four representative slot/pole number combinations, i.e., 10p9s, 8p9s, 10p12s, and 14p12s, are studied. The discrete radial force couple model, commonly used for stator analysis, is extended into a continuous formulation to capture the relationship between tangential force and its resultant radial vibration. Furthermore, the study highlights how phase relationships, both between radial and tangential forces and between low- and high-order harmonics, can lead to either amplification or suppression of vibrations. Additionally, the influence of geometric parameters, including pole arc ratio and stator tooth-tip arc ratio, on force amplitude and phase is thoroughly explored. The results reveal that, with a fixed slot number, a higher pole count tends to induce stronger vibration due to the reinforcement between the radial force modulated from radial force harmonics and the equivalent radial force from tangential force harmonics. Moreover, a contrasting pattern is observed that high-order forces intensify low-order components in 9-slot machines but suppress them in 12-slot machines.