Abstract：The load form of the bearingless permanent magnet slice motor (BPMSM) is complex and changeable. For example, during the operation of the magnetic suspension pump, the imbalance of the force acting on the surface of the impeller by the liquid flow causes the rotor to produce displacement or torsion in the axial direction. According to the principle of minimum reluctance, axial force and axial torque are generated between the stator and the rotor. However, the axial passive levitation structure has weak axial force stiffness, and its stability is insufficient. Therefore, this paper establishes a mathematical model of the axial force and analyzes its dynamic and static characteristics. A stiffness adjustment scheme is proposed to control the axial motion of the rotor. Finally, the effectiveness of the proposed axial force stiffness control strategy is verified by simulation and experiment. (1) The magnetic circuit equivalent model of BPMSM is established, including the stator magnetic circuit, the air gap magnetic circuit, and the rotor magnetic circuit. Considering the influence of winding current, the expression for the rotor axial passive levitation force is derived using the virtual work method. (2) The influencing factors of axial force are analyzed through the mathematical model and finite element simulation. In a specific range, the axial force of BPMSM is inversely proportional to the length of the air gap, and the axial force is proportional to the rotor radius and the magnetization length of the permanent magnet. The axial force direction of BPMSM is opposite to the axial displacement direction, and the amplitude increases with the increase of axial displacement. With the rise in displacement, the increment in the axial force amplitude gradually decreases. When the current of the direct axis armature is greater than zero, the axial force increases, and vice versa. When the current is small, the change in the axial force amplitude is proportional to the absolute value of the current. The accuracy of the mathematical model of axial force established in this paper is verified by finite element simulation and experiment. Under the full working conditions of displacement and current, the error between the established model and simulation is less than 9.39%, and the error between the established model and experiment is less than 7.5%. (3) According to the characteristic relationship between axial force and d-axis armature current, an axial force stiffness regulation strategy is proposed to enhance axial suspension stability and disturbance immunity. Firstly, according to the simplified axial force model, a new axial force stiffness expression is obtained. Then, by adjusting the relationship between the armature current and the rotor vibration velocity, the damping force is generated to restrain the rotor axial vibration. Its implementation does not require additional structure or control winding. The simulation and experiment of BPMSM show that the axial control scheme based on stiffness regulation can effectively suppress axial vibration caused by disturbances or load changes and shorten the adjustment time for vibration attenuation.
李正龙, 王晓琳, 鲍旭聪, 范臻雪, 石滕瑞. 永磁型无轴承薄片电机轴向力建模及控制策略[J]. 电工技术学报, 2026, 41(4): 1236-1247.
Li Zhenglong, Wang Xiaolin, Bao Xucong, Fan Zhenxue, Shi Tengrui. Bearingless Permanent Magnet Slice Motor Axial Force Modeling and Control Strategy. Transactions of China Electrotechnical Society, 2026, 41(4): 1236-1247.
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2026, Vol. 41 
