Comparison of Two Analytical Methods for Calculating Cogging Torque Based on Homopolar Inductor Machines

Cogging torque can cause the torque ripple and noise of machines and reduce the machine control accuracy. The analytical calculation method of cogging torque has always been a hot research topic in the field of machine. Conventional energy method is usually adopted to compute the cogging torque. Recently, a novel energy method is proposed. To reveal the fundamental difference and respective merits of these two energy methods, this article first derives the analytical models of cogging torque in homopolar inductor machines (HIMs) considering the leakage fluxes of the stator slots by the two energy methods. Based on the derived analytical models, the cogging torque production mechanisms expressed by the two energy methods are analyzed and compared from the viewpoint of air-gap field modulation principle. The cogging torque computed by the two energy methods is all produced by the interactions of the air-gap magnetic fields modulated by the harmonics of the air-gap magnetomotive force (MMF) and air-gap permeance. However, due to the difference in the approaches of solving the air-gap magnetic field energy density, the novel energy method considers more harmonics of the air-gap MMF and air-gap permeance. Furthermore, the computational accuracy and complexity of the two energy methods are analyzed and compared based on the analytical calculations and 3-D finite-element analysis (FEA) for the cogging torque in a 48-slot/4-pole (48S4P) permanent magnet (PM) HIM and a 45-slot/6-pole (45S6P) field winding HIM. Compared with the conventional energy method, the novel energy method has higher accuracy but is more complex. Finally, a prototype of the 48S4P PM HIM is manufactured. The results of analytical calculation, 3-D FEA, and comparison are verified by experiments.