Unbalance Magnetic Force Suppression in Fractional Slot Concentrated Winding PMSM Based on Phase Regulation of Air-Gap Flux Density Harmonics
Yang Gongde1, Chen Zongxiao1, Lin Mingyao2
1. School of Electrical Engineering and Automation Fuzhou University Fuzhou 350108 China; 2. School of Electrical Engineering Southeast University Nanjing 210018 China
Abstract：The fractional slot concentrated winding (FSCW) permanent magnet synchronous motor (PMSM) with a slot pole combination satisfying Ns=2pr±1 has a high fundamental coefficient of winding and low end resistance, which has attracted attention in motor design. However, the FSCW PMSM has a significant unbalanced magnetic force (UMF) in its rotor, resulting in motor vibration and noise. Currently, most literature employs multi-objective optimization algorithms and modal analysis to optimize motor “modulators” for suppressing UMF. However, there is a lack of theoretical research on minimizing electromagnetic torque output reduction while achieving UMF suppression. Based on the theory of magnetic field modulation, this paper optimizes the slot pole combination. By adjusting the harmonic phase of the air gap magnetic density, the cancellation effect between the first-order radial electromagnetic force waves is enhanced, while suppressing the motor UMF and maintaining the motor electromagnetic torque output. Firstly, the influence of air gap magnetic permeability on the time coefficient and spatial coefficient of the first-order electromagnetic force wave in PMSM is analyzed, and the main harmonic orders of air gap magnetic density that generate UMF and electromagnetic torque are determined. Secondly, the UMF and electromagnetic torque of the motor are quantitatively decomposed, and the cancellation relationship between first-order electromagnetic waves is analyzed. Then, the structural parameters of the stator slot and auxiliary slot are optimized, the harmonic phase of the air gap magnetic density is adjusted, and the cancellation effect between the first-order electromagnetic waves is enhanced. Finally, simulation analysis and prototype experiments were conducted on an 8-pole 9-slot FSCW PMSM. The results show that the electromagnetic torque generated by the 4th air gap magnetic density harmonic is 2.48 N·m, accounting for 97.2% of the total electromagnetic torque (2.55 N·m). In comparison, other air gap magnetic density harmonics only contribute 2.8% of the electromagnetic torque. The phase cancellation relationship between the first-order radial electromagnetic force waves can be enhanced by adjusting the phase between the main air gap magnetic density harmonics. After optimization, the phase difference between the 8-pole 9-slot FSCW PMSM’s f4&5 and f12&13 is 178°, and the phase difference between f3&4 and f4&5 has significantly increased after optimization, resulting in an increased cancellation effect. At rated state, the electromagnetic torque decreases from 2.55 N·m to 2.5 N·m, representing a 1.9% decrease. The total UMF decreased from 134 N to 118 N, representing a 12% decrease. The error between the measurement and the simulation is small. The UMF change rate measured by the pressure sensor in the UMF measurement experiment is approximately equal to the UMF change rate in the finite element simulation. The following conclusions can be drawn. (1) The main air gap magnetic density harmonic order for generating electromagnetic torque in an 8-pole 9-slot FSCW PMSM is 4th, and the main air gap magnetic density harmonic orders for generating UMF are 3rd, 4th, 5th, 12th, and 13th. To maintain the electromagnetic torque output of the motor, the amplitude of the 4th air gap magnetic resonance wave cannot be weakened. However, to effectively suppress the UMF of the motor, the phase cancellation relationship between the first-order radial electromagnetic force waves can be enhanced by adjusting the main air gap magnetic density harmonic phase. (2) Auxiliary slots with smaller stator slot opening width, moderate area, and uniform distribution should be used in the motor manufacturing process to suppress the UMF of FSCW PMSM with a slot pole combination that satisfies Ns=2pr±1 and maintain electromagnetic torque output.
杨公德, 陈宗孝, 林明耀. 基于气隙磁通密度谐波相位调节的分数槽集中绕组PMSM不平衡磁拉力抑制[J]. 电工技术学报, 2025, 40(22): 7179-7192.
Yang Gongde, Chen Zongxiao, Lin Mingyao. Unbalance Magnetic Force Suppression in Fractional Slot Concentrated Winding PMSM Based on Phase Regulation of Air-Gap Flux Density Harmonics. Transactions of China Electrotechnical Society, 2025, 40(22): 7179-7192.
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2025, Vol. 40 
