Abstract：For bearing-less permanent magnet synchronous motors (BLPMSM) in high-precision applications, cogging torque is an inherent characteristic of the motor. Due to the motor's uneven air gap magnetic permeability caused by the stator core's slotting, the rotor is subjected to varying tangential forces at different circumferential positions, namely the cogging torque. The existence of cogging torque can cause speed pulsation. The pulsation amplitude of the cogging torque is smaller than the load torque under high speed and heavy load conditions, so the torque pulsation caused can be ignored. However, under low speed and light load conditions, the torque pulsation is too large, which may even destroy the stability of the motor operation. Most existing cogging torque analysis methods do not consider the unique rotor eccentricity in bearing-less motors, making them unsuitable for bearing-less motors. Compared with traditional permanent magnet synchronous motors with bearings, BLPMSM does not have the friction resistance of mechanical bearings. It results in less damping for the motor, and the speed pulsation caused by the cogging torque is particularly severe at low speeds. The compensation method for a permanent magnet synchronous motor's cogging torque usually includes motor topology structure optimization and control strategy. Regarding topology design, BLPMSM needs to consider the torque and suspension force performance simultaneously. Compared with traditional bearing motors, BLPMSM requires two sets of windings for torque and suspension, and sensors for measuring rotor displacement need to be installed. There are many limitations in spatial structure design, and the machining process of the motor is more complex than general motors. Therefore, from the perspective of motor body design, only limited suppression of cogging torque can be achieved. In the control algorithm, the accurate analytical expression of the cogging torque must be obtained to compensate for the cogging torque. In the actual operation of BLPMSM, although the radial displacement of the rotor can be controlled within a minimal range, the rotor still has small displacement fluctuations at the geometric origin. It is in a dynamic equilibrium state, a unique situation in bearing-less motors. Such small displacement causes a change in the length of the air gap, and the magnetic permeability of the air gap around the permanent magnet rotor also changes with the displacement. Directly applying the analytical formula for cogging torque in the original bearing permanent magnet synchronous motor to the BLPMSM is impossible. To solve the cogging torque compensation problem of BLPMSM when the rotor is eccentric, this paper proposes an analytical method for the cogging torque of BLPMSM. This method reconstructs the distorted magnetic field inside the eccentric motor, dividing the magnetic field into the inherent magnetic field of the PMSM and the unique magnetic field caused by rotor eccentricity in the bearingless motor. Therefore, when analyzing the cogging torque, the internal magnetic field and cogging torque of a BLPMSM can be equivalent to the superposition of a bearing permanent magnet synchronous motor and a ‘variable magnetic flux’ PMSM. After proposing an analytical formula for cogging torque considering rotor eccentricity, cogging torque feedforward is introduced into the motor control algorithm based on the analytical formula. Finally, simulations and experiments verify the correctness and effectiveness of the proposed analytical formula.
卢志远, 王宇, 王锁. 基于磁导等效分离的无轴承永磁同步电机齿槽转矩解析[J]. 电工技术学报, 2025, 40(18): 5818-5831.
Lu Zhiyuan, Wang Yu, Wang Suo. Analysis of Cogging Torque in a Bearing-Less Permanent Magnet Synchronous Motor Based on Magnetic Permeability Equivalent Saparation. Transactions of China Electrotechnical Society, 2025, 40(18): 5818-5831.
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