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  

Accurate Mathematical Modeling of Radial Suspension Force on Bearingless Permanent Magnet Slice Motors Based on Frequency Domain Fitting

作　　者：王晓琳[1] 石滕瑞 鲍旭聪 Wang Xiaolin;Shi Tengrui;Bao Xucong(Key Laboratory of More Electric Aircraft and Electrical System Nanjing University of Aeronautics and Astronautics,Nanjing 211106 China)

机构地区：[1]南京航空航天大学多电飞机与电气系统重点实验室,南京211106

出　　处：《电工技术学报》2023年第2期317-329,共13页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金(52177048);江苏省自然科学基金(BK20201297)资助项目。

摘　　要：在无轴承永磁薄片电机系统中,永磁转子因失去轴承支承容易发生偏心位移,为控制转子在几何中心稳定悬浮,径向悬浮力精确建模是无轴承系统高性能可靠运行的关键基础。针对大气隙无轴承永磁薄片电机因转子偏心程度大而引起的径向悬浮力模型非线性误差问题,该文提出一种基于频域拟合的径向悬浮力精确建模方法,将非线性分量转化为相应函数补偿至径向悬浮力模型中,从而提高了模型精确度。首先,对推导一般径向悬浮力模型过程中出现的多个误差因素及其影响进行系统分析;在此基础上,提出频域拟合方法重构径向悬浮力模型,并分析其非线性特性;最后,将解析模型与有限元仿真所得到的可控径向悬浮力、偏心磁拉力进行深入对比分析,验证了该解析模型的正确性与精确性。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:①The error of radial suspension force caused by the approximation of permeability function is positively correlated with the eccentricity coefficient.②Radial suspension force ellipsis has little effect on model accuracy.③The 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 fo

关 键 词：无轴承永磁薄片电机 径向悬浮力 麦克斯韦应力张量法 频域拟合 有限元仿真 

分 类 号：TM351[电气工程—电机]