基于双曲余切变换的Halbach阵列表贴式永磁电机转子偏心气隙磁场解析模型  

Analytical Model for Air-Gap Magnetic Field in Halbach Arrays Surface-Mounted Permanent Magnet Motor with Rotor Eccentricity Based on Hyperbolic Cotangent Transformation

作　　者：刘蓉晖 刘锦坤 章君达 孙改平 Liu Ronghui;Liu Jinkun;Zhang Junda;Sun Gaiping(School of Electrical Engineering,Shanghai University of Electric Power,200090,China;School of Mechatronic Engineering and Automation,Shanghai University,200072,China)

机构地区：[1]上海电力大学电气工程学院,上海200090 [2]上海大学机电工程与自动化学院,上海200072

出　　处：《电工技术学报》2023年第6期1433-1446,共14页Transactions of China Electrotechnical Society

摘　　要：精确计算气隙磁场是设计和分析永磁电机的关键。Halbach阵列永磁电机具有良好的转矩输出特性。转子偏心会对永磁电机产生不良影响,准确获得其偏心气隙磁场分布具有重要意义。采用双曲余切变换解析计算Halbach阵列表贴式永磁电机转子偏心气隙磁场。该文建立了Halbach阵列定子开槽、转子偏心永磁电机二维模型。将同心解析模型分为三类子区域,利用各区域边界条件求解拉普拉斯方程和泊松方程,通过矢量磁位求得同心气隙磁场,利用相对磁导函数对其进行修正,从而获得偏心空载气隙磁场,对其进行研究,并利用回归评价指标进行评估。不同偏心率下气隙磁通密度、不平衡磁拉力、齿槽转矩的解析结果同有限元结果吻合,验证了该文解析模型的有效性和正确性。Accurate calculation of air-gap magnetic field is the key to design and analyse the permanent magnet(PM)motors.The Halbach arrays PM motor has outstanding torque output performance.Rotor eccentricity will cause the noise,rotor loss and torque ripple,which will have adverse effects on the PM motors.Therefore,it is of great significance to solve and analyse the air-gap magnetic field of the Halbach arrays surface-mounted(HASM)PM motor with rotor eccentricity.This paper combines the hyperbolic cotangent transformation and the relative permeance function,the air-gap magnetic field of the HASM PM motor with rotor eccentricity is analytically calculated.A two-dimensional model of the HASM PM motor with rotor eccentricity is established.As shown in Fig.A1,two groups of orthogonal circles representing the equipotential and magnetic force lines in the w plane are obtained by using the above transformation for the rotor eccentricity region in the z plane.The hyperbolic cotangent transformation can be expressed as follows:z=λe^(w)+1/e^(w)-1λcoth w/2(1)whereλis a constant related to the rotor radius,the stator radius and the relative deviation distance between the stator and the rotor center.The radial magnetic flux density of the eccentric magnetic field when the magnetic potential difference is 1 is calculated in the w plane,and the radial air-gap relative permeance function can be obtained.The radial air-gap relative permeance function fr can be expressed as f_(r)=B'_(r_ecc)/B'_(r_noecc)where B'_(r_ecc)is the radial magnetic flux density when the rotor is eccentric,and B'_(r_noecc)is the radial magnetic flux density when the stator and the rotor are concentric.The concentric analytical model is divided into three sub-regions:Halbach PMs,air-gap and slots.The Laplace equations and the Poisson equations are solved by using the boundary conditions of each region,and the air-gap magnetic field when the stator and the rotor are concentric is obtained by the vector magnetic potential.By modifying the concentric air-gap magne

关 键 词：Halbach阵列永磁电机 双曲余切变换 转子偏心 矢量磁位 空载气隙磁场 

分 类 号：TM351[电气工程—电机]