Torque Optimization of Six-Phase Arcuate Sine + Third Harmonic Shaping Surface Permanent Magnet Synchronous Motor

To increase the torque density of direct-drive surface permanent-magnet synchronous motors (SPSMs), the model of arcuate sine + third harmonic (3rd) shaping SPSM with parallel magnetization and the optimal $\text{3rd}$ current when the machine loaded with $\text{Sine}+3\text{rd}$ current are derived. The finite-element (FE) models of six-phase arcuate $\text{Sine}+3\text{rd}$ shaping and sine shaping SPSMs are established based on the principle of the same maximum permanent-magnet (PM) thickness, and their air-gap flux densities under no-load are compared. The $\text{Sine}+3\text{rd}$ current and sine current are applied to the $\text{Sine}+3\text{rd}$ shaping and sine shaping motors, respectively, based on the principle of equal current amplitude. The results show that the amplitude of air-gap flux density fundamental wave under no load condition of the Sine shaping SPSM is significantly lower than that of the $\text{Sine}+3\text{rd}$ shaping SPSM, and the amplitude of other higher harmonics is unchanged except for the third harmonic. When a rated load is applied, the average torque of the $\text{Sine}+3\text{rd}$ shaping SPSM loaded with $\text{Sine}+3\text{rd}$ current is increased by 17.5^% compared with the $\text{Sine}+3\text{rd}$ shaping SPSM which is only loaded with the sine current mentioned above, and is increased by 26.5% compared with the sine shaping motor. The result is consistent with the theoretical calculation and provides theoretical guidance for torque optimization of direct-drive SPSMs.