Fractional-slot permanent magnet (PM) machines with an odd number of stator slots are attractive candidates for industrial applications due to their high torque density and low torque ripple. However, the unbalanced magnetic force is detrimental to the bearing and yields noise and vibration. This paper determines the existence criterion of UMF on both open-circuit and on-load conditions by analysis of air gap field and magnetic force waves. Only when the machine periodicity is one, will the open-circuit UMF be generated due to the mutual interaction between the modulated PM harmonics and the original PM harmonics. In addition, the existence of on-load UMF in machines with a periodicity of one is confirmed even when the slotting effect is ignored. Furthermore, among the five investigated machines with a given odd slot number of 9 but different pole numbers, the UMF in a machine with two poles is the smallest since the magnitude of the 2nd harmonic in the armature reaction is the smallest compared with other contributing harmonics. Meanwhile, the UMF in a machine with pole number 2p = Ns-1 is the largest due to the relatively larger magnitude of the (p + 1)th armature reaction harmonic and the additive effect between the first order radial and tangential stresses.

中文翻译：

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定子槽数为奇数的分数槽永磁电机不平衡磁力研究


具有奇数个定子槽的分数槽永磁 (PM) 电机由于其高扭矩密度和低扭矩脉动而成为工业应用的有吸引力的候选者。然而，不平衡的磁力对轴承有害，并产生噪音和振动。本文通过气隙场和磁力波的分析，确定了开路和带载条件下UMF的存在判据。只有当机器周期为1时，调制后的PM谐波与原始PM谐波之间的相互作用才会产生开路UMF。此外，即使忽略开槽效应，也能确认周期性为 1 的机器中存在负载 UMF。此外，在给定奇数槽数为 9 但极数不同的五台研究机器中，具有两极的机器中的 UMF 最小，因为电枢反应中的二次谐波的幅度与其他贡献谐波相比最小。 。同时，由于第(p+1)次电枢反应谐波的幅度相对较大以及一阶径向应力和切向应力之间的相加效应，极数2p=Ns-1的电机中的UMF最大。