Effects of Harmonics Into Magnet Shape and Current of Dual Three-Phase Permanent Magnet Machine on Output Torque Capability

The harmonics can be utilized in the outer frame of a permanent magnet and phase current waveform in a multiphase machine to improve the output torque capability. The relationship between the output torque and harmonics in both the shape of the permanent magnet and phase current waveform is mathematically established in this paper. Consequently, the optimum harmonics are quantitatively identified and verified by the finite-element (FE) method. It is found that the incremental output torque decreases with the order of the harmonics. However, the output torque does not increase when the harmonic order is higher than seventh. It is also shown that the harmonics in the shape of the permanent magnet and phase current waveform influenced each other. The optimum of the interacted harmonics is dependent on the fundamental and harmonic winding factors. For the dual three-phase surface-mounted permanent magnet (SPM) machines with tile rotors, sinusoidal field rotor, and sinusoidal with third harmonic field rotor, their airgap flux density, back electromotive forces, and torque characteristics are compared. It is demonstrated that the average torque with the optimal harmonics into both the shape of the permanent magnet and phase current waveforms can be enhanced while the torque ripple remains similar to that of the one with the sinusoidal field rotor. Finally, the prototype machine is built and measured to verify the analytical and FE analysis.