Study on high frequency radial electromagnetic wave of motor driven by frequency conversion
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摘要: 采用场路耦合法对永磁同步电机高频径向电磁力特征频率产生原因和主要组成成分进行研究。通过解析法分析谐波电流的产生机理及谐波特性，并利用数值仿真对其进行验证；结合磁动势−磁导法和麦克斯韦张量法分析出高频径向电磁力特征频率的分布；对有限元计算得到的气隙磁场进行时空分解，采用麦克斯韦张量法计算磁场相互作用产生的高频径向电磁力。结果表明，变频驱动下永磁同步电机的高频径向电磁力主要是由变频器谐波电流引入的谐波磁场和定子基波磁场的相互作用产生，这对永磁同步电机的研究提供了一定的指导意义。Abstract: By using the field-route coupling method, the causes and main components of the high frequency radial electromagnetic force characteristic frequency of permanent magnet synchronous motor were studied. The generation mechanism and harmonic characteristics of harmonic current were analyzed by analytical method, and verified by numerical simulation. The characteristic frequency distribution of high frequency radial electromagnetic force was analyzed by means of the magnetomotive force permeability method and Maxwell tensor method. The air gap magnetic field obtained by finite element calculation was decomposed in time and space, and the high frequency radial electromagnetic force generated by magnetic field interaction was calculated by Maxwell tensor method. The results show that the high frequency radial electromagnetic force of PMSM driven by frequency conversion is mainly generated by the interaction between the harmonic magnetic field and the stator fundamental magnetic field introduced by the harmonic current of the frequency converter, which has certain guiding significance for the research of PMSM.
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图 7 调制比对变频器谐波电流幅值的影响
Figure 7. Influence of modulation ratio on harmonic current amplitude of frequency converter
图 9 变频器供电时气隙磁场的二维傅里叶分解
Figure 9. Two-dimensional Fourier decomposition of air gap magnetic field when inverter is powered
图 10 径向电磁力二维傅里叶分解图
Figure 10. Two-dimensional Fourier decomposition diagram of radial electromagnetic force
表 1 内置式永磁同步电机的参数
Table 1. Parameters of built-in permanent magnet synchronous motors
参数 数据 极对数P 4 定子电阻R/Ω 0.6271 d轴电感${L}_{d}$/mH 4.06 q轴电感$ {L}_{q} $/mH 8.17 永磁体磁链$ {\psi }_{f} $/$ \mathrm{W}\mathrm{b} $ 0.1998 转动惯量J/(kg·m2) 0.0168 阻尼系数B/($\rm{N}·(\rm{m}·\rm{s^{-1})^{-1}}$) 0.0114 直流电压源Ed/V 550 开关频率$ {f}_{\rm{s}} $/Hz 9000 采样周期${T}_{\mathrm{s} }$/$ \mathrm{\mu }\mathrm{s} $ 10 
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表 2 0阶和8阶PWM谐波径向电磁力的主要频率分布
Table 2. Main frequency distribution of radial electromagnetic force of order 0 and order 8 PWM harmonics
变频器电流
谐波频率/Hz电磁力波
空间阶次PWM谐波径向
电磁力频率/Hz$ {f_{\rm{s}}} \pm 2{f_0} $ 0,8 $ {f_{\rm{s}}} \pm {f_0} $
$ {f_{\rm{s}}} \pm 3{f_0} $$ {f_{\rm{s}}} \pm 4{f_0} $ 0,8 $ {f_{\rm{s}}} \pm 3{f_0} $
$ {f_{\rm{s}}} \pm 5{f_0} $$ 2{f_{\rm{s}}} \pm {f_0} $ 0,8 $ 2{f_{\rm{s}}} $
$ 2{f_{\rm{s}}} \pm 2{f_0} $$ 2{f_{\rm{s}}} \pm 5{f_0} $ 0,8 $ 2{f_{\rm{s}}} + 4{f_0} $
$ 2{f_{\rm{s}}} \pm 6{f_0} $$ 2{f_{\rm{s}}} \pm 7{f_0} $ 0,8 $ 2{f_{\rm{s}}} + 6{f_0} $
$ 2{f_{\rm{s}}} \pm 8{f_0} $
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表 3 PWM谐波径向电磁力主要成分验证
Table 3. Verification of main components of PWM harmonic radial electromagnetic force
频率/Hz PWM谐波与定子基波作用
产生电磁力幅值/Pa有限元计算
幅值/Pa百分比/
%8000 1027.05 1106.89 92.8 8400 90.26 103.03 87.6 8600 1117.31 1181.82 94.5 9200 980.37 1040.33 94.2 9600 99.59 113.00 88.1 10000 880.77 939.61 93.7
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表 4 噪声频率计算值与径向电磁力频率值的比较
Table 4. Comparison of calculated noise frequency with radial electromagnetic force frequency
PWM谐波径向电磁力的
频率/Hz有限元计算电机噪声
频率/Hz误差/% 8000 7940 0.75 8400 8320 0.95 8800 8860 0.68 9200 9340 1.30 9600 9720 1.25 10000 10180 1.80
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