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| Mechanism and Performances Analysis of Functional-Rotor Flux-Switching Machines with Low Cogging Torque |
| Zhang Tianxiang1, Zhang Zhiheng1, Hua Wei1, Wang Peixin2, Wu Zhongze1 |
1. School of Electrical Engineering Southeast University Nanjing 210096 China;
2. School of Electrical and Information Engineering Zhengzhou University Zhengzhou 450001 China |
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Abstract Stator permanent magnet flux-switching (SPM-FS) machines are promising in electric vehicles and rail transit due to the advantages of simple rotor structure, high reliability, and easy cooling of permanent magnets. However, this type of machine typically exhibits an ample cogging torque because of its special doubly-salient structure. Therefore, this paper proposes two kinds of functional rotors for the SPM-FS machines: the outer profiles of rotor tips that match the y=k|x| function and the y=ax2 function distribution, respectively. Compared to the SPM-FS machine with the original rotor, the magnetic field modulation mechanism and performance of SPM-FS machines with functional rotors are studied.
Firstly, the structures of the proposed y=k|x| and y=ax2 function-rotor SPM-FS machines are introduced. Taking the y=k|x| machine as an example, variations in key parameters (cogging torque, torque ripple, and torque ripple reduction coefficient) with coefficient k are analyzed. The influence of tooth width on machine performance in relation to k is also studied. A selection method for the coefficients k and a is provided.
Secondly, the machines’ air-gap magnetic field modulation mechanism, along with the generation and suppression mechanisms of cogging torque and torque ripple, is analyzed. The cogging torque and ripple are mainly influenced by harmonic components of the air-gap flux density resulting from the rotor modulation function. The relationships between air-gap flux density harmonics and cogging torque/average torque are analyzed. Both proposed machines improve the waveform of rotor modulation function, effectively suppressing high-order harmonics in the air-gap flux density, thereby reducing cogging torque and torque ripple.
Finally, based on the finite element method (FEM), the back electromotive force (back-EMF), cogging torque, torque characteristics, and losses for the original, y=k|x|, and y=ax2 machines are presented. Compared to the original machine, the proposed y=k|x| and y=ax2 machines reduce cogging torque by 88.15% and 98.31%, respectively, while their rated average torque decreases by merely 5.52% and 4.75%. Furthermore, the rated torque ripple of the y=k|x| and y=ax2 machines is reduced from 25.79% to 4.73% and 1.42%, respectively. Prototypes of both proposed machines are manufactured and tested, which further validates the correctness of the theoretical and simulation analysis.
In summary, this paper conducted magnetic field modulation analysis and performance comparisons for the original, y=k|x|, and y=ax2 SPM-FS machines. (1) The average torque of SPM-FS machines is primarily contributed by low-order harmonics modulated via a combination of i=1, 3, and j=1 (|iPpm±jPr|), while cogging torque and torque ripple are mainly generated by high-order air-gap flux density harmonics. (2) The suppression mechanisms for cogging torque and torque ripple are revealed. Specifically, while the y=k|x| machine effectively suppresses other cogging torque harmonics, its prominent 54th and 66th harmonics mutually cancel. The y=ax2 machine directly suppresses high-order harmonic components in the cogging torque. (3) The y=ax2 machine exhibits the smallest no-load back-EMF total harmonic distortion (THD), cogging torque, and torque ripple, with minimal reduction in rated no-load back-EMF fundamental amplitude and average torque. The y=k|x| machine yields the lowest losses.
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Received: 07 March 2025
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2026, Vol. 41 
