Analytical Calculation of the Airgap Flux in PM Vernier Machine Considering Pole Transition Over Slots Effect

Based on the flux modulation theory, PM vernier machine has features including high torque density, low cogging torque, which makes it preferable for low-speed-high-torque fields such as marine propulsion system and wind generator. Accurate calculation of the airgap flux densities is significant for the analysis and optimization of electromagnetic performances in PM vernier machines. Based on conventional MMF-permeance model, the radial airgap flux density can be calculated instantly but with relatively low accuracy, while it cannot calculate tangential flux. Based on finite element analysis or subdomain model, the radial and tangential airgap flux can be calculated precisely. However, these methods need longer time to solve matrix equations. In this paper, through mirror magnetic circuit and leakage flux circuit analysis, the calculation error brought by pole-transition-over-slot effect in vernier machines is corrected. Then, through modified complex MMF-permeance model, the airgap radial and tangential flux densities are calculated precisely and instantly. On this basis, the no-load back EMF of PM vernier machine is calculated, and the calculation result is proved to be corrected combining FEA method.