Analytical Solution of a Fractional-Slot Double-Layer-Winding Open-Slot Vernier Permanent Magnet Machine with Tooth Tips

An analytical solution (ANA) for a fractional-slot double-layer-winding open-slot vernier permanent magnet (VPM) machine with tooth tips is presented. Magnetic vector potential equations are analytically solved using the technique of variable separation in four subdomains in a two-dimensional polar coordinate system. Based on the solved magnetic vector potential, the flux density distribution, torque, flux linkage, inductance, electromotive force (EMF) and power factor are analytically developed. An 18-slot/32-rotor-pole prototype is analyzed, and the results match well with the finite element analysis (FEA), which validates that the ANA consumes less time than FEA. Therefore, the tooth tips are optimized using the ANA to improve the average torque. Moreover, the ANA can be used to evaluate the demagnetization withstand capabilities of permanent magnets. The material utilization, slot-filling factor, EMF, and torque are compared between the models with three and four subdomains. Finally, an experimental prototype is constructed and tested, and the results validate the ANA.