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| Modified Sinusoidal Pole Shaping Model of Arcuate Pole Permanent Magnet Motors |
| Zhao Haoran, Wang Dong, Hu Pengfei, Wei Yingsan, Yi Xinqiang |
| National Key Laboratory of Science and Technology on Vessel Integrated Power System Naval University of Engineering Wuhan 430033 |
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Abstract Electric machines are gradually taking the place of traditional machines powered by fossil fuels in many industries for environmental issues, such as automobile industry and aviation industry. PMSM is usually the prime choice among all motor types because of its merits of high torque density, high power density, and high efficiency. Suppressing the noise and vibration of PMSM has become a key issue in recent years and the technology of pole shaping is one of the effective solutions. Eccentric magnet pole and sinusoidal magnet pole are most commonly used in pole shaping. When designing the eccentric magnet poles, much calculation and parameter sweeping are needed for optimization. The process is rather time-consuming, and the physical mechanism of eccentric pole shaping in making the air gap magnetic flux density sinusoidal needs to be clearer. Simplified sinusoidal pole shaping is to make the shape of magnet poles conform to sine function to make the air gap magnetic flux density sinusoidal. The mechanism is clear, and the designing process is time-saving. However, the influence of stator slot, pole-to-pole leakage, edge effect, and magnetic circuit saturation is not considered in simplified sinusoidal pole shaping. The air gap magnetic flux density needs to be more sinusoidal. Therefore, this paper proposes a modified sinusoidal pole shaping model, which optimizes the motor's electromagnetic performance in a time-saving way and has a clear theoretical basis. The research object is an arcuate pole permanent magnet motor. Compared with a magnet pole with an arc bottom, an arcuate magnet pole can provide greater power density when the diameter of the rotor and the thickness of the magnet pole are the same. Besides, the model of the arcuate pole is more complex, and the derivation process is applicable to the model of the magnet pole with an arc bottom.
The functions of the air gap length and the thickness of the magnet are deduced. In the functions, the Carter coefficient formula is used to consider the influence of stator slots. Pole-to-pole leakage and edge effect are considered using the proposed leakage coefficient formula. Besides, the distributed magnetic circuit method is used to consider the saturation of the magnetic circuit. Compared with the model built by finite element analysis (FEA), the analytical model is accurate. Also, the fundamental component amplitude of the air gap magnetic flux density and the average torque of the modified sinusoidal pole shaping motor are higher than those of the simplified sinusoidal pole shaping motor and close to those of the eccentric pole shaping motor. Moreover, the total harmonic distortion (THD) of the air gap magnetic flux density of the modified sinusoidal pole shaping is 41.3 % and 23.4 % lower than that of the simplified sinusoidal pole shaping motor and the eccentric pole shaping motor, respectively. The THD of the radial electromagnetic force density of the modified sinusoidal pole shaping is 29.82 % and 19.24 % lower than that of the simplified sinusoidal motor and the eccentric motor, respectively. As a result, the torque ripple of the motor is reduced.
Therefore, the modified sinusoidal pole shaping model can save much time in the designing process and provide better performance in reducing vibration than the eccentric pole shaping model and simplified pole shaping model.
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Received: 30 September 2022
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2023, Vol. 38 
