Influence of Sinusoidal Magnetic Field Injection on Torque Characteristics of Flux-Switching PM Machines

Flux-switching permanent magnet (FSPM) machines have emerged as promising candidates for high-torque-density applications owing to their stator-mounted magnets and mechanically robust rotor. However, severe torque ripple arising from the interaction between permanent magnet magnetomotive force (MMF) and permeance modulation remains a critical challenge. This paper proposes a sinusoidal magnetic field injection method based on sinusoidal shaping of spoke-type permanent magnets to suppress torque ripple at the magnetic-field source. By introducing a sinusoidal profile on both sides of the spoke-type magnets, the circumferential PM MMF is intentionally reshaped and equivalently injected into the air gap through the split-tooth structure, inherently accounting for slotting and permeance distribution effects. A FE model with parameterized slot area and constant magnet volume is established to ensure consistent electrical loading during parametric analysis. The influence of the injected sinusoidal MMF amplitude and phase on air-gap flux density harmonics and torque characteristics is systematically investigated, revealing a clear trade-off between average torque and torque ripple. A weighted multi-objective criterion is employed to identify the optimal design, and its parameter sensitivity is examined to ensure the robustness of the selected solution. FE results demonstrate that, compared with the baseline design, the proposed method reduces torque ripple from 16.0% to 4.5% (72% reduction) while maintaining nearly unchanged average torque with less than 1% degradation.