Performance analysis and optimization of secondary U-shaped double-sided toroidal winding linear permanent magnet vernier machine

Aiming at the issues of low thrust density, significant thrust ripple, the lengthy end and the large axial attraction force in conventional single-sided distributed winding linear permanent magnet vernier machine (LPMVM), this paper presents an enhanced U-shaped double-sided toroidal winding linear permanent magnet vernier machine (US-DTWLPMVM). Firstly, the topology of US-DTWLPMVM is introduced and the flux concentration effect of the U-shaped permanent magnet structure is analyzed using the equivalent magnetic circuit method. The operation principle of US-DTWLPMVM is analyzed based on the principle of magnetic field modulation. Subsequently, the US-DTWLPMVM multi-objective optimization is performed using the Taguchi-RSM-Egret Swarm Optimization Algorithm (ESOA). Then, combined with the surface-mounted and Halbach PM structure double-sided toroidal winding linear permanent magnet vernier machine (DTWLPMVM), the impact of the U-shaped permanent magnet structure on the magnetic field and the resulting differences in thrust performance of the DTWLPMVM are investigated. Finally, the related experimental tests of US-DTWLPMVM are carried out to verify the reliability of the theoretical analysis and finite element simulation results. The results show that, the proposed USDTWLPMVM confers several advantages. These include the improvement of winding ends, an increase in the thrust density of the motor, and a reduction in thrust ripple and balance of the attractive forces of the mover.