A Quantitative Air-Gap Construction Method to Maximize Torque of Vernier PM Machines

The vernier permanent magnet machines (VPMMs) have attracted extensive research interest due to inherent high torque density, which is brought by the "magnetic gearing effect" based on slot-toothed air gap. Regularly, the air-gap topology of VPMM is initially determined and produces the certain composition of magnetic field harmonics, which decides the torque capability. Output torque is improved in a limited way via repeatedly optimizing the air-gap structure parameters. Herein, a quantitative air-gap construction method is proposed to construct the air-gap topology that could produce the magnetic field harmonics of which the total torque generation is maximum. With air-gap permeance as the bridge between torque and magnetic field harmonics, the proposed method quantitatively designs the optimal amplitude of individual radial air-gap permeance unit. Then, the length of the corresponding air-gap unit is obtained, which are assembled to form the final air-gap topology. The proposed method is applied on a surface-mounted VPMM (SVPMM) to illustrate. In theory, the torque density of the proposed machine could achieve 32 Nm/L under natural cooling when electric loading is 250 A/cm. Compared to the open-slot counterpart under the same conditions, the rated torque of the proposed machine is theoretically 68% larger, and is still 32% larger despite the saturation in steel. Finally, a prototype is fabricated, and the test results verify the feasibility of the proposed method.