Analytical calculation of magnetic field in surface-mounted permanent-magnet vernier motors

This paper proposes an analytical method to calculate the on-load magnetic field, Back electromotive force (BEMF) and torque of the surface-mounted permanent-magnet vernier machine (SMPMVM) accounting for slots, tooth-tips, flux modulation pole slots (FMPS) and the shape of magnet. The on-load magnetic field is predicted according to the surface-current method of permanent magnet, subdomain model and the superposition principle. BEMF and torque are calculated based on the magnetic field. The results show that THD of open-circuit and on-load radial flux density in the SMPMVM with concentric magnet poles is smaller than that in the conventional SMPMVM with eccentric magnet poles. 30th and 50th harmonic orders are obvious between two motors. Moreover, the peak cogging torque of the motor with concentric magnet poles is almost six times of the peak cogging torque of motor with eccentric magnet poles. The finite-element and experimental results confirm that the developed analytical method has high accuracy for predicting the magnetic field, BEMF, cogging torque and on-load electro-magnetic torque of SMPMVM with different shape of magnet.