基于频域拟合的无轴承永磁薄片电机径向悬浮力建模分析

doi:10.19595/j.cnki.1000-6753.tces.220547

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Abstract In bearingless permanent magnet slice motor system, it is a necessary condition for the realization of precise and stable radial suspension control of slice rotor to construct an accurate mathematical model of radial suspension force. However, structural characteristics of large air gap makes the rotor have a large eccentricity space range without bearing support, which brings nonlinear errors of controllable radial suspension force and eccentric magnetic force. To address this issue, this paper proposes a reconstruction method of radial suspension force model based on frequency domain fitting. It improves model accuracy by transforming the nonlinear components into functions of eccentricity coefficient and compensating them.
Firstly, the general radial suspension force model is derived by Maxwell stress tensor method. Factors causing model errors in the process of derivation are summarized as follows: approximation error of permeability function, radial suspension force ellipsis error and difference between equivalent air gap and absolute air gap. The following conclusions can be drawn from the systematic analysis: ① The error of radial suspension force caused by the approximation of permeability function is positively correlated with the eccentricity coefficient. ② Radial suspension force ellipsis has little effect on model accuracy. ③ The modification of equivalent air gap length is a necessary condition for establishing accurate radial suspension force model.
Secondly, the model reconstruction method based on frequency domain fitting is designed in detail. On the basis of correction of eccentricity coefficient and related physical quantity, the difference function is constructed and its frequency domain function is expanded by Fourier transform. The sum of the constant term to the fifth harmonic term in the frequency domain expansion is selected as the fitting function, and compensated to the calculation formula to solve the reconstructed model. By mathematical proof, the analytical model is equivalent to the radial suspension force model under the actual permeability function, which is divided into two parts: controllable radial suspension force and uncontrollable radial suspension force. The nonlinear component of the model is expressed mathematically by the eccentricity coefficient.
Finally, the two-dimensional finite element simulation model is constructed to verify the accuracy of the reconstructed model. The following conclusions can be put forward from the simulation analysis: ① The difference between the analytical model results and the finite element simulation results is small, and the curves of them are consistent with each other and have the same variation rule. ② The nonlinear component of the controllable radial suspension force occupies a small proportion and can be ignored approximately compared with the whole. ③ The nonlinear error of the uncontrollable radial suspension force is positively correlated with the eccentricity coefficient and the range of eccentricity of the rotor must be limited when designing the motor structure.

Key words： Bearingless permanent magnet slice motors radial suspension force Maxwell stress tensor method frequency domain fitting finite element simulation

Received: 11 April 2022

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TM351

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	Wang Xiaolin
	Shi Tengrui
	Bao Xucong

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Wang Xiaolin,Shi Tengrui,Bao Xucong. Accurate Mathematical Modeling of Radial Suspension Force on Bearingless Permanent Magnet Slice Motors Based on Frequency Domain Fitting[J]. Transactions of China Electrotechnical Society, 2023, 38(2): 317-329.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.220547 OR https://dgjsxb.ces-transaction.com/EN/Y2023/V38/I2/317

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