﻿ 表贴式永磁电机外围环境磁场分布规律研究
 舰船科学技术  2022, Vol. 44 Issue (1): 119-124    DOI: 10.3404/j.issn.1672-7649.2022.01.023 PDF

Research on the distribution law of external ambient magnetic field of surface-mounted permanent magnet motor
RAO Fan, WU Xu-sheng, GAO Wei
College of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: Explore the distribution law and influencing factors of the peripheral magnetic field of the permanent magnet motor, using Comsol simulation software to establish static and no-load simulation models, and compare different parameters (permanent magnet magnetization method, pole pair number, stator core thickness, non-conductive The influence of the magnetic thickness, the relative permeability of the stator core, the polar arc coefficient, and the air gap length on the environmental magnetic field shows that the circumferential and radial components of the environmental magnetic field are sinusoidally distributed on the far motor surface, and the magnetic flux density mode is attenuated The number of times is equal to the number of motor pole pairs plus 1. Provide ideas for anti-electromagnetic interference and magnetic field compensation of permanent magnet motors.
Key words: surface-mounted permanent magnet motor     external ambient magnetic field     Comsol
0 引　言

1 磁场模型 1.1 模型建立

 图 1 电机等效模型 Fig. 1 Motor′s equivalent model

 ${{{M}}} = {M_r}{{r}} + {M_\theta }{\mathbf{\theta }} ，$ (1)
 $\left\{ \begin{gathered} {M_r} = \left| {{{ M}}} \right|\cos \theta ，\hfill \\ {M_\theta } = - \left| {{{ M}}} \right|\sin \theta 。\hfill \\ \end{gathered} \right.$ (2)

 $\left\{ \begin{gathered} {\nabla ^2}{A_{Sz}} = 0 ，\hfill \\ {\nabla ^2}{A_{Rz}} = 0 ，\hfill \\ {\nabla ^2}{A_{Pz}} = - \nabla \times ({\mu _0}{{M}}) = 0，\hfill \\ {\nabla ^2}{A_{Az}} = 0，\hfill \\ {\nabla ^2}{A_{Iz}} = 0 ，\hfill \\ {\nabla ^2}{A_{Cz}} = 0 。\hfill \\ \end{gathered} \right.$ (3)
1.2 模型求解

 $\left\{ \begin{gathered} {B_r}(r,\theta ) = {B_r}(r,-\theta )\qquad (a)，\hfill \\ {B_r}(r,\theta ) = -{B_r}(r,\pi -\theta )\quad (b)，\hfill \\ \end{gathered} \right.$ (4)
 $\left\{ \begin{gathered} {B_\theta }(r,\theta ) = -{B_\theta }(r,-\theta )\quad(a) ，\hfill \\ {B_\theta }(r,\theta ) = {B_\theta }(r,\pi -\theta )\quad(b) 。\hfill \\ \end{gathered} \right.$ (5)

 $\begin{gathered} SR:\left\{ \begin{gathered} {B_{rS}}(r,\theta ) = {B_{rP}}(r,\theta ){|_{r = {R_S}}}，\hfill \\ {H_{\theta S}}(r,\theta ) = {H_{\theta R}}(r,\theta ){|_{r = {R_S}}}，\hfill \\ \end{gathered} \right.{\text{ }} \hfill \\ RP:\left\{ \begin{gathered} {B_{rR}}(r,\theta ) = {B_{rP}}(r,\theta ){|_{r = {R_R}}} ，\hfill \\ {H_{\theta R}}(r,\theta ) = {H_{\theta P}}(r,\theta ){|_{r = {R_R}}}，\hfill \\ \end{gathered} \right.{\text{ }} \hfill \\ PA:\left\{ \begin{gathered} {B_{rP}}(r,\theta ) = {B_{rA}}(r,\theta ){|_{r = {R_P}}} ，\hfill \\ {H_{\theta P}}(r,\theta ) = {H_{\theta A}}(r,\theta ){|_{r = {R_P}}}，\hfill \\ \end{gathered} \right.{\text{ }} \hfill \\ AI:\left\{ \begin{gathered} {B_{rA}}(r,\theta ) = {B_{rI}}(r,\theta ){|_{r = {R_A}}}，\hfill \\ {H_{\theta A}}(r,\theta ) = 0{|_{r = {R_A}}} ，\hfill \\ \end{gathered} \right.{\text{ }} \hfill \\ IC:\left\{ \begin{gathered} {B_{rI}}(r,\theta ) = {B_{rC}}(r,\theta ){|_{r = {R_I}}}，\hfill \\ {H_{\theta I}}(r,\theta ) = {H_{\theta C}}(r,\theta ){|_{r = {R_I}}}。\hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$ (6)

$r \to 0$ 时，矢量磁位Az为定值。在无穷远处，即 $r \to \infty$ ，磁感应强度为0，即

 $\left\{ \begin{gathered} {B_{rC}}(r,\theta ) = 0{|_{r \to \infty }}，\hfill \\ {H_{\theta C}}(r,\theta ) = 0{|_{r \to \infty }}。\hfill \\ \end{gathered} \right.$ (7)

 $\begin{split} {A_z} =& R(r)\varPhi (\theta ) =\sum\limits_{m = 1}^n ({C_{1m}}{r^m} +\\ & {C_{2m}}{r^{ - m}})({B_{1m}}\cos (m\theta ) + {B_{2m}}\sin (m\theta )) ，\end{split}$ (8)

 $\left\{ \begin{gathered} {B_r}(r,\theta ) = \frac{1}{r}\frac{{\partial {A_z}}}{{\partial \theta }}{\text{ = }}\sum\limits_{m = 1}^{2n{\text{ - }}1} {{D_{2m}}{r^{ - m - 1}}\cos (m\theta )}，\hfill \\ {B_\theta }(r,\theta ) = - \frac{{\partial {A_z}}}{{\partial r}} = \sum\limits_{m = 1}^{2n{\text{ - }}1} {{D_{2m}}{r^{ - m - 1}}\sin (m\theta )} 。\hfill \\ \end{gathered} \right.$ (9)

 $|B| = \sqrt {|{B_r}{|^2} + |{B_\theta }{|^2}} {\text{ = }}{D_{C2}}{r^{ - 2}}{\text{ = }}{D_{C2}}{(d{\text{ + }}{R_I})^{ - 2}}。$ (10)

2 仿真研究

2.1 静态仿真

 图 2 静态仿真磁力线分布 Fig. 2 Distribution of magnetic field lines under static state

 图 3 环境中周向与径向磁场分布 Fig. 3 Circumferential and radial flux density distribution in the environment

 图 4 环境中距电机表面不同距离dq轴磁通密度模值 Fig. 4 The modulus of d & q axis flux density at different distances from the motor surface in the environment

 图 5 环境磁通密度模等值线 Fig. 5 Contours of ambient magnetic flux density modulus

2.2 空载仿真

 图 6 不同时间周向与径向磁场分布 Fig. 6 Distributions of the circumferential and radial flux density at different times

 $\left\{ \begin{gathered} {B_r}(r,\theta ) = \frac{1}{r}\frac{{\partial {A_z}}}{{\partial \theta }}{\text{ = }}{D_2}{r^{ - 2}}\cos (\omega t{\text{ + }}\theta ) ，\hfill \\ {B_\theta }(r,\theta ) = - \frac{{\partial {A_z}}}{{\partial r}} = {D_2}{r^{ - 2}}\sin (\omega t{\text{ + }}\theta )。\hfill \\ \end{gathered} \right.$ (11)

 图 7 空载不同时间固定方向（x轴）磁通密度模 Fig. 7 Flux density mode of the no-load motor at different times (x axis)

2.3 电机参数影响

2.3.1 充磁方式

 图 8 不同充磁方式仿真图 Fig. 8 Different magnetizing methods

2.3.2 极数

 图 9 不同极数仿真图 Fig. 9 Different number of poles

2.3.3 定子铁芯厚度

 图 10 不同定子铁芯厚度仿真图 Fig. 10 Different stator core thickness

2.3.4 不导磁轴半径

 图 11 不同不导磁轴半径仿真图 Fig. 11 Different non-magnetic shaft radius

2.3.5 不同铁芯磁导率

 图 12 不同定子铁芯磁导率仿真图 Fig. 12 Magnetic permeability of different stator cores

2.3.6 气隙长度

 图 13 不同气隙长度仿真图 Fig. 13 Different air gap lengths

2.3.7 极弧系数

 图 14 不同极弧系数仿真图 Fig. 14 Different pole arc coefficients

3 结　语

1）电机环境磁场周向分量与径向分量均近似呈现正弦分布，相位上两者相差1/4周期。

2）在近电机面（d≤约半个电机半径）径向分量类似于平顶波，周向分量类似于尖顶波，在远电机面（d>半个电机半径），两者更接近于正弦波形，在越远的地方越接近。

3）电机旋转时，环境磁场各分量也随着旋转，转速和转向与电机同步速一致，但等圆周线上磁通密度模不会发生变化（无论静态与旋转），与距离呈平方反比衰减。

4）定子铁芯厚度、铁芯磁导率对环境磁场大小有很大影响；永磁体的充磁方式、气隙长度、极弧系数对环境磁场大小有一定影响；不导磁轴半径对环境磁场无影响；但这些均不影响磁场的正弦规律和平方衰减规律。

5）电机极对数影响环境磁场的周期性、衰减性，极数越多，环境磁场周期各分量周期数越多，衰减越快，衰减次数等于电机极对数加1。

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