In this article, the air-gap field modulation effects (AFMEs) in spoke-type permanent magnet (STPM) machines with concentrated winding are investigated and revealed by quantifying the torque contributions of the various air-gap flux density harmonics. Due to the relatively stronger flux concentrated effect, the STPM structure exhibits greater resulting air-gap field harmonics for torque generation. In order to provide an in-depth understanding of their torque generation mechanism, the contributed torque components of the various air-gap field working harmonics are quantified by employing the Maxwell stress tensor (MST) approach. It identifies a fact that the abundant air-gap flux density harmonics have participated in torque production in the STPM machine. As a consequence, the field-modulated harmonics contributed a nonnegligible torque component, and hence, a pronounced AFME can be obtained in the STPM machine. Besides, the influences of the key dimension parameters, including split ratio, stator slot opening ratio, rotor PM thickness, and length, on AFEM for torque performance of the STPM machines are evaluated by the finite-element (FE) method. Finally, the reliability and effectiveness of theoretical analysis and FE simulation are verified by experiments on an STPM machine prototype.

中文翻译：

---

辐条式永磁电机中气隙场调制效应的研究


在本文中，通过量化各种气隙磁通密度谐波的扭矩贡献，研究并揭示了具有集中绕组的辐条型永磁体 (STPM) 电机中的气隙场调制效应 (AFME)。由于相对较强的磁通集中效应，STPM 结构表现出更大的气隙场谐波以产生扭矩。为了深入了解其扭矩产生机制，采用麦克斯韦应力张量 (MST) 方法对各种气隙场工作谐波的贡献扭矩分量进行量化。它确定了一个事实，即大量的气隙磁通密度谐波参与了 STPM 电机中的扭矩产生。因此，场调制谐波贡献了不可忽略的扭矩分量，因此，可以在 STPM 机器中获得明显的 AFME。此外，通过有限元（FE）方法评估了关键尺寸参数（包括分流比、定子槽开口比、转子PM厚度和长度）对STPM电机扭矩性能的AFEM的影响。最后，通过STPM样机上的实验验证了理论分析和有限元仿真的可靠性和有效性。