Design Trade-off Between Torque Density and Power Factor in Surface-Mounted PM Vernier Machines Through Closed-Form Per-Unit Equations

Benefited from flux modulation effects, surface-mounted permanent magnet vernier machines (SPMVMs) present the high-torque low-speed properties, which can become the potential candidates for direct-drive applications. However, their power factor is inferior to conventional PM machines due to the large inductance caused by parasitic no-working harmonics. This paper is devoted to propose some design considerations of SPMVMs to make a good compromise between torque density and power factor. Via constructing closed-from per-unit equations, the cross-coupling influences of slot/pole combinations and normalized geometric variables on machine performances are revealed. It is found that there is a tradeoff between torque density and power factor. The high magnet thickness to air-gap length ratio is beneficial to decrease inductance, while the flux modulation effect under the large equivalent air-gap length would be impaired. Moreover, the pole-pair ratio, i.e., the PM pole-pair to armature winding pole-pair, should be carefully selected, where the SPMVMs with high pole-pair ratio have the relatively high magnetic loading owing to the strong flux modulation effects, whereas they suffer from the low power factor due to serious harmonic leakage inductance. In particular, taking the end-winding length into consideration, the high torque advantages of high pole-pair ratio SPMVMs under the same copper losses can be well performed with high length-radius ratio. Combined with the analysis, the preferable selections of critical parameters to satisfy various technical indexes are determined. Then, the general design approach is proposed, and two design examples are built and compared. Meanwhile, finite element analysis (FEA) and prototype experiments are carried out to verify the feasibility