Analysis of Bidirectional Magnetic Field Modulation on Concentrated Winding Spoke-Type PM Machines

Spoke-type permanent magnet (STPM) machine shows a typical flux concentrated effect to improve torque density. In this article, the bidirectional magnetic field modulation effect on STPM machines with fractional slot concentrated winding (FSCW) is investigated by the torque quantification analysis to illustrate their torque production mechanism. First, the equivalent permanent magnet (PM) magnetomotive force (MMF) permeance model is built considering the stator and rotor slotting, and the fundamental and harmonic electromagnetic torque are calculated and demonstrated based on the Maxwell stress tensor (MST) method. In addition, the electromagnetic torque contributions of main-order working field harmonics are obtained and quantified by the proposed analytical method and verified by the finite-element method (FEM). It reveals the fact that the FSCW STPM machines have multiworking harmonics for torque generation under different operating conditions. To improve the torque density, the rotor parameters are evaluated and optimized for FSCW STPM machine considering the field modulation harmonics. Finally, a 40-kW, 9000-r/min STPM machine prototype with semi-closed rotor slot is manufactured and tested to confirm the effectiveness of the theoretical analysis.