CN109039215A - Inverter harmonic is to automobile permanent magnet synchronous motor vibration noise impact analysis method - Google Patents
Inverter harmonic is to automobile permanent magnet synchronous motor vibration noise impact analysis method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
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Abstract
本发明涉及一种逆变器谐波对车用永磁同步电机振动噪声影响分析方法，对逆变器谐波对车用永磁同步电机振动噪声进行分析。首先建立多物理场永磁同步电机PMSM振动噪声分析模型，理论分析了PMSM电磁力波特征参数和各阶力波的谐波来源，特征参数包括力波阶数r，力波频率fr和力波幅值Peak‑r/fr，建立了PMSM多物理场耦合振动分析有限元模型，计算恒转矩调速和弱磁调速工况下样机的电流和电磁力频谱，分析不同电流源供电时振动噪声频谱特性；最后实验与理论和仿真进行验证。本发明分析方法可以推广到一般整数槽多极对数电动汽车PMSM，为电动汽车低振动噪声PMSM的设计提供理论基础。
The invention relates to a method for analyzing the influence of inverter harmonics on the vibration and noise of a permanent magnet synchronous motor for vehicles, which analyzes the vibration and noise of the inverter harmonics on the permanent magnet synchronous motor for vehicles. First, a multi-physics field permanent magnet synchronous motor PMSM vibration and noise analysis model is established, and the PMSM electromagnetic force wave characteristic parameters and the harmonic sources of each order force wave are theoretically analyzed. The characteristic parameters include force wave order r, force wave frequency f r and force Wave amplitude P eak ‑r/f r , established a PMSM multi-physics field coupled vibration analysis finite element model, calculated the current and electromagnetic force spectrum of the prototype under the constant torque speed regulation and field weakening speed regulation conditions, and analyzed different current sources Spectrum characteristics of vibration and noise during power supply; the final experiment is verified with theory and simulation. The analysis method of the invention can be extended to the general integer slot multi-pole logarithm electric vehicle PMSM, and provides a theoretical basis for the design of the electric vehicle PMSM with low vibration and noise.
Description
技术领域technical field
本发明涉及一种永磁同步电机振动噪声分析技术，特别涉及一种逆变器谐波对车用永磁同步电机振动噪声影响分析方法。The invention relates to a vibration and noise analysis technology of a permanent magnet synchronous motor, in particular to a method for analyzing the influence of inverter harmonics on the vibration and noise of a permanent magnet synchronous motor for vehicles.
背景技术Background technique
整数槽PMSM(永磁同步电机Permanent Magnet Synchronous Motor)由于其高功率密度、宽调速范围、高效率等良好性能广泛应用于电动汽车。然而逆变器谐波引起的电磁振动噪声会降低电动汽车乘坐舒适性和运行可靠性。因此分析逆变器谐波对车用永磁同步电机振动噪声的影响，并指导电机电磁或者结构的优化设计，对提高电动汽车的舒适可靠性和运行稳定性具有重要意义。Integer slot PMSM (Permanent Magnet Synchronous Motor) is widely used in electric vehicles due to its high power density, wide speed range, and high efficiency. However, the electromagnetic vibration noise caused by inverter harmonics will reduce the ride comfort and operational reliability of electric vehicles. Therefore, it is of great significance to analyze the influence of inverter harmonics on the vibration and noise of permanent magnet synchronous motors for vehicles, and to guide the optimization design of motor electromagnetic or structure, which is of great significance to improve the comfort, reliability and operation stability of electric vehicles.
发明内容Contents of the invention
本发明是针对逆变器谐波恶化永磁同步电机振动噪音的问题，提出了一种逆变器谐波对车用永磁同步电机振动噪声影响分析方法，分析逆变器谐波对车用永磁同步电机振动噪声的影响，为永磁同步电机设计提供理论基础。The present invention aims at the problem that inverter harmonics deteriorate the vibration and noise of permanent magnet synchronous motors, and proposes an analysis method for the influence of inverter harmonics on the vibration and noise of permanent magnet synchronous motors for vehicles, and analyzes the influence of inverter harmonics on the vibration and noise of permanent magnet synchronous motors for vehicles. The influence of vibration and noise of permanent magnet synchronous motor provides a theoretical basis for the design of permanent magnet synchronous motor.
本发明的技术方案为：一种逆变器谐波对车用永磁同步电机振动噪声影响分析方法，具体包括如下步骤：The technical solution of the present invention is: a method for analyzing the influence of inverter harmonics on the vibration and noise of permanent magnet synchronous motors for vehicles, which specifically includes the following steps:
1)理论分析了永磁同步电机电磁力波特征参数和各阶力波的谐波来源，特征参数包括力波阶数r，力波频率fr和力波幅值 1) Theoretical analysis of the characteristic parameters of the electromagnetic force wave of the permanent magnet synchronous motor and the harmonic sources of the force waves of each order, the characteristic parameters include the force wave order r, the force wave frequency f r and the force wave amplitude
2)建立永磁同步电机电磁场和结构场强耦合模型，计算加载不同电流源情况下永磁同步电机的电流和电磁力频谱，并仿真其振动噪声频谱；2) Establish a permanent magnet synchronous motor electromagnetic field and structural field strength coupling model, calculate the current and electromagnetic force spectrum of the permanent magnet synchronous motor under different current sources, and simulate its vibration and noise spectrum;
3)针对所研究永磁同步电机对象，分析步骤2)得到的不同电流供电时电流、电磁力和振动噪声频谱特性，研究逆变器电流谐波对永磁同步电机宽调速范围内振动噪声的影响；3) For the permanent magnet synchronous motor object under study, analyze the current, electromagnetic force and vibration noise spectrum characteristics obtained in step 2) when supplying different currents, and study the influence of inverter current harmonics on the vibration noise of the permanent magnet synchronous motor within a wide speed regulation range Impact;
4)对所研究永磁同步电机对象进行实验测试，得到实验数据，利用实验数据对比步骤2)仿真数据，验证步骤2)利用所建立的永磁同步电机电磁场和结构场强耦合模型进行振动噪声仿真方法的准确性。4) Perform experimental tests on the researched permanent magnet synchronous motor object to obtain experimental data, use the experimental data to compare step 2) simulation data, and verify step 2) Use the established permanent magnet synchronous motor electromagnetic field and structural field strength coupling model to conduct vibration noise analysis The accuracy of the simulation method.
所述步骤1)具体步骤如下：Described step 1) concrete steps are as follows:
1.1)推导永磁同步电机气隙磁场，不考虑铁芯磁阻和饱和的影响，正弦电流供电时气隙磁密的表达式为：1.1) Deduce the air gap magnetic field of permanent magnet synchronous motor, without considering the influence of iron core reluctance and saturation, the expression of air gap magnetic density when the sinusoidal current is powered is:
其中，fμ(θ,t)＝Fμcos(μpθ-μωt)为μ次转子永磁体谐波磁动势，μ＝1,3,5…，p为电机极对数，ω为基波磁势角频率，Fμ为转子永磁体μ次谐波磁动势幅值，θ为电机机械角度；Among them, f μ (θ,t)=F μ cos(μpθ-μωt) is the harmonic magnetomotive force of the rotor permanent magnet of the μ order, μ=1,3,5..., p is the number of pole pairs of the motor, and ω is the fundamental wave The angular frequency of the magnetomotive force, F μ is the amplitude of the μ-order harmonic magnetomotive force of the rotor permanent magnet, and θ is the mechanical angle of the motor;
fν(θ,t)＝Fνcos(νpθ-lωt-φν)为定子v次谐波磁动势，v＝1,5,7，Fv为转子永磁体μ次谐波磁动势幅值，l为定子电流谐波次数，φv为v次定子电枢谐波初相位；f ν (θ,t)=F ν cos(νpθ-lωt-φ ν ) is the v-order harmonic magnetomotive force of the stator, v=1,5,7, F v is the μ-order harmonic magnetomotive force of the rotor permanent magnet Amplitude, l is the harmonic order of the stator current, φ v is the initial phase of the stator armature harmonic of the v order;
为相对磁导函数；式中Λ0为气隙磁导函数的恒定分量，Λk为气隙磁导谐波分量的幅值，k＝1,2,3…为气隙磁导谐波次数，z为定子槽数； is the relative permeance function; where Λ0 is the constant component of the air gap permeance function, Λ k is the amplitude of the air gap permeance harmonic component, and k =1,2,3... is the air gap permeance harmonic order , z is the number of stator slots;
为平均磁导调制产生的转子磁场在气隙中的磁密，为开槽磁导调制产生的转子磁场在气隙中的磁密；为平均磁导调制产生的定子磁场在气隙中的磁密，为开槽磁导调制产生的定子磁场在气隙中的磁密；Bpm为平均磁导调制产生的转子磁场在气隙中的磁密与开槽磁导调制产生的转子磁场在气隙中的磁密之和，Bsl为平均磁导调制产生的定子磁场在气隙中的磁密与开槽磁导调制产生的定子磁场在气隙中的磁密之和； is the flux density of the rotor field in the air gap generated by the average permeance modulation, The flux density of the rotor magnetic field in the air gap generated for slot permeance modulation; is the flux density of the stator field in the air gap generated by the average permeance modulation, Bpm is the magnetic density of the stator magnetic field in the air gap generated by the slotted permeance modulation; B pm is the magnetic density of the rotor magnetic field generated by the average permeance modulation in the air gap and the rotor magnetic field generated by the slotted permeance modulation in the air gap B sl is the sum of the magnetic density of the stator magnetic field in the air gap generated by the average permeance modulation and the magnetic density of the stator magnetic field generated by the slot permeance modulation in the air gap;
1.2)按照麦克斯韦应力张量法并忽略切向磁通密度，单位面积上径向电磁力波的瞬时值表达式为：1.2) According to Maxwell's stress tensor method and ignoring the tangential magnetic flux density, the expression of the instantaneous value of the radial electromagnetic force wave per unit area is:
pr(θ,t)是定子内表面单位面积上的径向电磁力密度，单位为N/m2，b(θ,t)为气隙磁密，μ0＝4π×10-7H/m为真空磁导率。ppm为转子磁场相互作用产生的电磁力密度，psl为定子磁场相互作用产生的电磁力密度，ppm-sl为定转子磁场互相作用产生的电磁力密度；p r (θ,t) is the radial electromagnetic force density per unit area of the inner surface of the stator, in N/m 2 , b(θ,t) is the air gap flux density, μ 0 =4π×10 -7 H/ m is the vacuum magnetic permeability. p pm is the electromagnetic force density generated by the rotor magnetic field interaction, p sl is the electromagnetic force density generated by the stator magnetic field interaction, and ppm-sl is the electromagnetic force density generated by the stator and rotor magnetic field interaction;
1.3)推导转子磁场相互作用产生电磁力密度特征参数，1.3) Deduce the characteristic parameters of the electromagnetic force density generated by the rotor magnetic field interaction,
转子磁场相互作用产生的电磁力密度ppm为：平均磁导调制的转子磁场相互作用产生的电磁力波平均磁导调制的转子磁场和定子开槽磁导调制的转子磁场相互作用产生的电磁力波定子开槽磁导调制的转子磁场相互作用产生的电磁力波之和；The electromagnetic force density p pm generated by the interaction of the rotor magnetic field is: the electromagnetic force wave generated by the interaction of the rotor magnetic field modulated by the average permeance The electromagnetic force wave generated by the interaction between the rotor magnetic field modulated by the average permeance and the rotor magnetic field modulated by the slotted permeance of the stator Electromagnetic force waves generated by interaction of rotor magnetic field modulated by stator slot permeance Sum;
整理电磁力特征参数如表1所示转子磁场相互作用产生的径向力波特征参数表，表1The characteristic parameters of the electromagnetic force are sorted out as shown in Table 1. The radial force wave characteristic parameter table generated by the interaction of the rotor magnetic field is shown in Table 1.
其中n为电机的转速，p为电机的极对数，为平均磁导调制的转子磁场气隙磁密；为开槽磁导调制的转子磁场气隙磁密；μ1和μ2分别代表相互作用的两个相互作用转子磁场的谐波次数，与μ同含义；当μ1和μ2相等时，用μ代替；in n is the speed of the motor, p is the number of pole pairs of the motor, is the air-gap flux density of the rotor magnetic field modulated by the average permeance; is the air-gap flux density of the rotor magnetic field modulated by slot permeance; μ 1 and μ 2 respectively represent the harmonic orders of the two interacting rotor magnetic fields, which have the same meaning as μ; when μ 1 and μ 2 are equal, use μ replaces;
1.4)推导定转子磁场相互作用产生电磁力波特征参数,1.4) Deduce the characteristic parameters of the electromagnetic force wave generated by the interaction between the stator and rotor magnetic fields,
定转子磁场互相作用产生的电磁力密度ppm-sl为：平均磁导调制的定转子磁场相互作用引起的电磁力波平均磁导调制的转子磁场和定子开槽磁场调制的定子磁场相互作用产生的电磁力波定子开槽调制产生的转子磁场和平均磁导调制定子磁场相互作用产生的电磁力波定子开槽磁导调制产生的定转子磁场相互作用产生的电磁力波之和；The electromagnetic force density p pm-sl generated by the interaction of the stator and rotor magnetic fields is: the electromagnetic force wave caused by the interaction of the stator and rotor magnetic fields modulated by the average permeance Electromagnetic force waves generated by the interaction of the rotor magnetic field modulated by the average permeance and the stator magnetic field modulated by the stator slotted magnetic field The electromagnetic force wave generated by the interaction of the rotor magnetic field generated by stator slot modulation and the average permeability modulation stator magnetic field Electromagnetic force waves generated by stator-rotor magnetic field interaction generated by stator slot permeance modulation Sum;
整理电磁力波特征参数如表2所示定转子磁场相互作用产生径向力波的特征参数表，The characteristic parameters of the electromagnetic force wave are sorted out as shown in Table 2. The characteristic parameter table of the radial force wave generated by the interaction of the stator and rotor magnetic fields
表2Table 2
其中为平均磁导调制的定子磁场气隙磁密，为开槽磁导调制的定子磁场气隙磁密；v1和v2分别代表相互作用的两个相互作用定子电枢磁场的谐波次数，与v同含义；当v1和v2相等时，用v代替；in is the air-gap flux density of the stator magnetic field modulated by the average permeance, It is the air-gap flux density of the stator magnetic field modulated by slot permeance; v 1 and v 2 respectively represent the harmonic orders of the two interacting stator armature magnetic fields, which have the same meaning as v; when v 1 and v 2 are equal , replace with v;
1.5)推导定子磁场相互作用产生电磁力波特征参数，1.5) Deduce the characteristic parameters of the electromagnetic force wave generated by the interaction of the stator magnetic field,
定子磁场相互作用产生的电磁力密度psl为：平均磁导调制的定子磁场相互作用产生的电磁力波平均磁导调试的定子磁场和定子开槽磁导调制的定子磁场相互作用产生的电磁力波定子开槽磁导调制的定子磁场相互作用产生的电磁力波之和；The electromagnetic force density p sl generated by the interaction of the stator magnetic field is: the electromagnetic force wave generated by the interaction of the stator magnetic field modulated by the average permeance The electromagnetic force wave generated by the interaction of the stator magnetic field adjusted by the average permeance and the stator magnetic field modulated by the slotted permeance Electromagnetic force waves generated by stator magnetic field interaction modulated by stator slot permeance Sum;
整理电磁力波特征参数如表3所示定子磁场相互作用产生径向力波的特征参数表，The characteristic parameters of the electromagnetic force wave are sorted out, as shown in Table 3, the characteristic parameter table of the radial force wave generated by the interaction of the stator magnetic field,
表3table 3
所述步骤2)具体步骤如下：Described step 2) concrete steps are as follows:
2.1)在Simplorer中建立永磁同步电机三相电源供电电路，将实测三相电流数据设置为电机电流源，导出为“.sph”文件；2.1) Establish a permanent magnet synchronous motor three-phase power supply circuit in Simplorer, set the measured three-phase current data as the motor current source, and export it as a ".sph" file;
2.2)在Maxwell有限元仿真软件中以永磁同步电机具体结构参数建立永磁同步电机2D电磁有限元模型，设置电源为上一步保存的“.sph”文件，即将实际引入逆变器谐波的三相电流设置为永磁同步电机2D电磁有限元模型的电流源，计算电流谐波作用下的电磁力；2.2) Establish the 2D electromagnetic finite element model of the permanent magnet synchronous motor with the specific structural parameters of the permanent magnet synchronous motor in the Maxwell finite element simulation software, and set the power supply to the ".sph" file saved in the previous step, which will actually introduce the harmonics of the inverter The three-phase current is set as the current source of the 2D electromagnetic finite element model of the permanent magnet synchronous motor, and the electromagnetic force under the action of the current harmonic is calculated;
2.3)在SolidWorks设计软件中以永磁同步电机具体结构参数建立永磁同步电机3D定子结构模型；2.3) Establish the 3D stator structure model of the permanent magnet synchronous motor with the specific structural parameters of the permanent magnet synchronous motor in the SolidWorks design software;
2.4)在Workbench有限元仿真软件中设置永磁同步电机材料参数，对永磁同步电机进行模态分析，得到永磁同步电机各阶模态频率和振型；2.4) Set the material parameters of the permanent magnet synchronous motor in the Workbench finite element simulation software, perform modal analysis on the permanent magnet synchronous motor, and obtain the modal frequencies and vibration shapes of each order of the permanent magnet synchronous motor;
2.5)在Workbench有限元仿真软件中设置永磁同步电机材料参数，建立永磁同步电机电磁场和结构场强耦合模型，进行电磁场与结构场耦合仿真分析，计算恒转矩调速和弱磁调速工况下振动噪声频谱特性。2.5) Set the material parameters of the permanent magnet synchronous motor in the Workbench finite element simulation software, establish the strong coupling model of the electromagnetic field and the structural field of the permanent magnet synchronous motor, conduct the coupling simulation analysis of the electromagnetic field and the structural field, and calculate the constant torque speed regulation and the weak field speed regulation Spectrum characteristics of vibration and noise under working conditions.
本发明的有益效果在于：本发明逆变器谐波对车用永磁同步电机振动噪声影响分析方法，实现对逆变器谐波对车用永磁同步电机振动噪声影响进行有效的分析。此方法可广泛应用于一般整数槽多极对数电动汽车永磁同步电机PMSM振动噪声的分析。The beneficial effect of the present invention is that: the method for analyzing the influence of the inverter harmonics on the vibration and noise of the permanent magnet synchronous motor for vehicles in the present invention realizes the effective analysis of the influence of the inverter harmonics on the vibration and noise of the permanent magnet synchronous motor for vehicles. This method can be widely used in the analysis of vibration and noise of permanent magnet synchronous motor PMSM of general integer slot multi-pole logarithm electric vehicle.
附图说明Description of drawings
图1为本发明电逆变器谐波对车用永磁同步电机振动噪声影响分析方法流程示意图；Fig. 1 is a schematic flow chart of the method for analyzing the impact of electric inverter harmonics on the vibration and noise of a permanent magnet synchronous motor for vehicles;
图2为本发明永磁同步电机三相电流源供电电路仿真图；Fig. 2 is the simulation diagram of the power supply circuit of the permanent magnet synchronous motor three-phase current source of the present invention;
图3a为本发明永磁同步电机3000rpm下2种电流源A相电流波形图；Fig. 3 a is 2 kinds of current source A-phase current waveform diagrams under permanent magnet synchronous motor 3000rpm of the present invention;
图3b为本发明永磁同步电机8000rpm下2种电流源A相电流波形图；Fig. 3 b is the A-phase current waveform diagram of two kinds of current sources under the permanent magnet synchronous motor 8000rpm of the present invention;
图4为本发明永磁同步电机2D电磁有限元模型图；Fig. 4 is a 2D electromagnetic finite element model diagram of a permanent magnet synchronous motor of the present invention;
图5为本发明永磁同步电机3000rpm和8000rpm电流各次谐波占比图；Fig. 5 is the proportion diagram of each harmonic of the current of permanent magnet synchronous motor 3000rpm and 8000rpm;
图6a为本发明永磁同步电机3000rpm时r＝0阶电磁力波频谱图；Fig. 6 a is r=0 order electromagnetic force wave spectrogram when permanent magnet synchronous motor 3000rpm of the present invention;
图6b为本发明永磁同步电机8000rpm时r＝0阶电磁力波频谱图；Fig. 6b is r=0 order electromagnetic force wave spectrum diagram when permanent magnet synchronous motor 8000rpm of the present invention;
图7a为本发明永磁同步电机3000rpm时r＝8阶电磁力波频谱图；Figure 7a is r=8th order electromagnetic force wave spectrum diagram when the permanent magnet synchronous motor of the present invention is 3000rpm;
图7b为本发明永磁同步电机3000rpm时r＝8阶电磁力波频谱图；Fig. 7 b is r=8th order electromagnetic force wave spectrum diagram when permanent magnet synchronous motor 3000rpm of the present invention;
图8为本发明永磁同步电机3D定子结构模型图；Fig. 8 is a structural model diagram of a 3D stator of a permanent magnet synchronous motor of the present invention;
图9为本发明永磁同步电机3D定子结构模态图；Fig. 9 is a structural modal diagram of a 3D stator of a permanent magnet synchronous motor according to the present invention;
图10为本发明永磁同步电机电磁场-结构场耦合图；Fig. 10 is the electromagnetic field-structural field coupling diagram of the permanent magnet synchronous motor of the present invention;
图11a为本发明永磁同步电机3000rpm电磁振动计算结果图；Fig. 11a is a calculation result diagram of 3000rpm electromagnetic vibration of the permanent magnet synchronous motor of the present invention;
图11b为本发明永磁同步电机8000rpm电磁振动计算结果图；Fig. 11b is a calculation result diagram of 8000rpm electromagnetic vibration of the permanent magnet synchronous motor of the present invention;
图12a为本发明永磁同步电机3000rpm电磁噪声计算结果图；Fig. 12a is a calculation result diagram of 3000rpm electromagnetic noise of the permanent magnet synchronous motor of the present invention;
图12b为本发明永磁同步电机8000rpm电磁噪声计算结果图；Fig. 12b is a diagram of calculation results of 8000rpm electromagnetic noise of a permanent magnet synchronous motor according to the present invention;
图13a为本发明永磁同步电机3000rpm电磁振动实验仿真对比图；Fig. 13a is a simulation comparison diagram of a permanent magnet synchronous motor 3000rpm electromagnetic vibration experiment of the present invention;
图13b为本发明永磁同步电机8000rpm电磁振动实验仿真对比图。Fig. 13b is a comparison diagram of the electromagnetic vibration experiment simulation of the permanent magnet synchronous motor at 8000rpm according to the present invention.
具体实施方式Detailed ways
如图1所示电动汽车永磁同步电机宽范围调速振动噪声源分析方法流程示意图，具体包括如下步骤：As shown in Figure 1, the flow diagram of the method for analyzing the vibration and noise source of the permanent magnet synchronous motor with wide range speed regulation, specifically includes the following steps:
步骤1、理论分析了永磁同步电机PMSM电磁力波特征参数(力波阶数r，力波频率fr,力波幅值)和各阶力波的谐波来源。Step 1. Theoretical analysis of the permanent magnet synchronous motor PMSM electromagnetic force wave characteristic parameters (force wave order r, force wave frequency f r , force wave amplitude ) and the harmonic sources of force waves of each order.
1.1推导永磁同步电机气隙磁场，不考虑铁芯磁阻和饱和的影响，正弦电流供电时气隙磁密的表达式为：1.1 Deduce the air gap magnetic field of permanent magnet synchronous motor, without considering the influence of iron core reluctance and saturation, the expression of air gap magnetic density when the sinusoidal current is powered is:
其中，fμ(θ,t)＝Fμcos(μpθ-μωt)为μ次转子永磁体谐波磁动势，μ＝1,3,5…，p为电机极对数，ω为基波磁势角频率，Fμ为转子永磁体μ次谐波磁动势幅值，θ为电机机械角度。Among them, f μ (θ,t)=F μ cos(μpθ-μωt) is the harmonic magnetomotive force of the rotor permanent magnet of the μ order, μ=1,3,5..., p is the number of pole pairs of the motor, and ω is the fundamental wave The angular frequency of the magnetomotive force, F μ is the amplitude of the μ order harmonic magnetomotive force of the rotor permanent magnet, and θ is the mechanical angle of the motor.
fν(θ,t)＝Fνcos(νpθ-lωt-φν)为定子v次谐波磁动势，v＝1,5,7，Fv为转子永磁体μ次谐波磁动势幅值，l为定子电流谐波次数，φv为v次定子电枢谐波初相位。f ν (θ,t)=F ν cos(νpθ-lωt-φ ν ) is the v-order harmonic magnetomotive force of the stator, v=1,5,7, F v is the μ-order harmonic magnetomotive force of the rotor permanent magnet Amplitude, l is the harmonic order of the stator current, φv is the initial phase of the stator armature harmonic of the vth order.
为相对磁导函数；式中Λ0为气隙磁导函数的恒定分量，Λk为气隙磁导谐波分量的幅值，k＝1,2,3…为气隙磁导谐波次数，z为定子槽数； is the relative permeance function; where Λ0 is the constant component of the air gap permeance function, Λ k is the amplitude of the air gap permeance harmonic component, and k =1,2,3... is the air gap permeance harmonic order , z is the number of stator slots;
为平均磁导调制产生的转子磁场在气隙中的磁密，为开槽磁导调制产生的转子磁场在气隙中的磁密；为平均磁导调制产生的定子磁场在气隙中的磁密，为开槽磁导调制产生的定子磁场在气隙中的磁密；Bpm为平均磁导调制产生的转子磁场在气隙中的磁密与开槽磁导调制产生的转子磁场在气隙中的磁密之和，Bsl为平均磁导调制产生的定子磁场在气隙中的磁密与开槽磁导调制产生的定子磁场在气隙中的磁密之和。 is the flux density of the rotor field in the air gap generated by the average permeance modulation, The flux density of the rotor magnetic field in the air gap generated for slot permeance modulation; is the flux density of the stator field in the air gap generated by the average permeance modulation, Bpm is the magnetic density of the stator magnetic field in the air gap generated by the slotted permeance modulation; B pm is the magnetic density of the rotor magnetic field generated by the average permeance modulation in the air gap and the rotor magnetic field generated by the slotted permeance modulation in the air gap B sl is the sum of the magnetic density of the stator magnetic field in the air gap generated by the average permeance modulation and the magnetic density of the stator magnetic field generated by the slot permeance modulation in the air gap.
1.2按照麦克斯韦应力张量法并忽略切向磁通密度，单位面积上径向电磁力波的瞬时值表达式为：1.2 According to Maxwell's stress tensor method and ignoring the tangential magnetic flux density, the expression of the instantaneous value of the radial electromagnetic force wave per unit area is:
pr(θ,t)是定子内表面单位面积上的径向电磁力密度，单位为N/m2，b(θ,t)为气隙磁密，μ0＝4π×10-7H／m为真空磁导率。ppm为转子磁场相互作用产生的电磁力密度，psl为定子磁场相互作用产生的电磁力密度，ppm-sl为定转子磁场互相作用产生的电磁力密度。p r (θ,t) is the radial electromagnetic force density per unit area of the inner surface of the stator, in N/m 2 , b(θ,t) is the air gap flux density, μ 0 =4π×10 -7 H/ m is the vacuum magnetic permeability. ppm is the electromagnetic force density generated by the rotor magnetic field interaction, p sl is the electromagnetic force density generated by the stator magnetic field interaction, and ppm-sl is the electromagnetic force density generated by the stator and rotor magnetic field interaction.
1.3推导转子磁场相互作用产生电磁力密度特征参数(力波阶数r，力波频率fr,力波幅值)，来源为下式和表1转子磁场相互作用产生的径向力波特征参数表。1.3 Deduce the characteristic parameters of the electromagnetic force density generated by the rotor magnetic field interaction (force wave order r, force wave frequency f r , force wave amplitude ), the source is the following formula and the table of characteristic parameters of the radial force wave generated by the interaction of the rotor magnetic field in Table 1.
平均磁导调制的转子磁场相互作用产生的电磁力波为：The electromagnetic force wave generated by the interaction of the rotor magnetic field modulated by the average permeance is:
平均磁导调制的转子磁场和定子开槽磁导调制的转子磁场相互作用产生的电磁力波为：The electromagnetic force wave generated by the interaction between the rotor magnetic field modulated by the average permeance and the rotor magnetic field modulated by the stator slot permeance is:
定子开槽磁导调制的转子磁场相互作用产生的电磁力波为：The electromagnetic force wave generated by the interaction of the rotor magnetic field modulated by the slotted permeance of the stator is:
其中为平均磁导调制的转子磁场气隙磁密；为开槽磁导调制的转子磁场气隙磁密；μ1和μ2分别代表相互作用的两个相互作用转子磁场的谐波次数，与μ同含义；当μ1和μ2相等时，用μ代替；下同。in is the air-gap flux density of the rotor magnetic field modulated by the average permeance; is the air-gap flux density of the rotor magnetic field modulated by slot permeance; μ 1 and μ 2 respectively represent the harmonic orders of the two interacting rotor magnetic fields, which have the same meaning as μ; when μ 1 and μ 2 are equal, use μ instead; the same below.
整理电磁力特征参数如表1所示，表1为转子磁场相互作用产生的径向力波特征参数表。The characteristic parameters of the electromagnetic force are shown in Table 1, and Table 1 is the characteristic parameter table of the radial force wave generated by the interaction of the rotor magnetic field.
表1Table 1
其中n为电机的转速，p为电机的极对数。in n is the rotational speed of the motor, and p is the number of pole pairs of the motor.
1.4推导定转子磁场相互作用产生电磁力波特征参数,来源为下式和表2定转子磁场相互作用产生径向力波的特征参数表。1.4 Deduce the characteristic parameters of the electromagnetic force wave generated by the interaction between the stator and rotor magnetic fields. The source is the following formula and Table 2.
平均磁导调制的定转子磁场相互作用引起的电磁力波：The electromagnetic force wave caused by the stator-rotor magnetic field interaction modulated by the average permeance:
平均磁导调制的转子磁场和定子开槽磁场调制的定子磁场相互作用产生的电磁力波：The electromagnetic force wave generated by the interaction between the rotor magnetic field modulated by the average permeance and the stator magnetic field modulated by the stator slotted magnetic field:
定子开槽调制产生的转子磁场和平均磁导调制定子磁场相互作用产生的电磁力波：The electromagnetic force wave generated by the interaction of the rotor magnetic field generated by stator slot modulation and the average permeance modulation stator magnetic field:
定子开槽磁导调制产生的定转子磁场相互作用产生的电磁力波：The electromagnetic force wave generated by the stator-rotor magnetic field interaction generated by the slotted permeance modulation of the stator:
其中为平均磁导调制的定子磁场气隙磁密，为开槽磁导调制的定子磁场气隙磁密；v1和v2分别代表相互作用的两个相互作用定子电枢磁场的谐波次数，与v同含义；当v1和v2相等时，用v代替。in is the air-gap flux density of the stator magnetic field modulated by the average permeance, It is the air-gap flux density of the stator magnetic field modulated by slot permeance; v 1 and v 2 respectively represent the harmonic orders of the two interacting stator armature magnetic fields, which have the same meaning as v; when v 1 and v 2 are equal , replaced by v.
整理电磁力波特征参数如表2所示，表2为定转子磁场相互作用产生径向力波的特征参数表.The characteristic parameters of the electromagnetic force wave are shown in Table 2, and Table 2 is the characteristic parameter table of the radial force wave generated by the interaction of the stator and rotor magnetic fields.
表2Table 2
1.5推导定子磁场相互作用产生电磁力波特征参数,来源为下式和表3定子磁场相互作用产生径向力波的主要频率分量及其谐波来源表。1.5 Deduce the characteristic parameters of the electromagnetic force wave generated by the interaction of the stator magnetic field. The source is the following formula and Table 3. The main frequency components and harmonic sources of the radial force wave generated by the interaction of the stator magnetic field.
平均磁导调制的定子磁场相互作用产生的电磁力波：The electromagnetic force wave generated by the interaction of the stator magnetic field modulated by the mean permeance:
平均磁导调试的定子磁场和定子开槽磁导调制的定子磁场相互作用产生的电磁力波：The electromagnetic force wave generated by the interaction between the stator magnetic field adjusted by the average permeance and the stator magnetic field modulated by the slotted permeance:
定子开槽磁导调制的定子磁场相互作用产生的电磁力波：The electromagnetic force wave generated by the interaction of the stator magnetic field modulated by the permeance of the stator slot:
整理电磁力波特征参数如表3所示，表3为定子磁场相互作用产生径向力波的特征参数表The characteristic parameters of the electromagnetic force wave are shown in Table 3, and Table 3 is the characteristic parameter table of the radial force wave generated by the stator magnetic field interaction
表3table 3
其中n为电机的转速，p为电机的极对数。in n is the rotational speed of the motor, and p is the number of pole pairs of the motor.
步骤2、建立PMSM多物理场耦合振动分析有限元模型并计算恒转矩调速和弱磁调速时永磁体电机振动噪声频谱特性。Step 2. Establish a PMSM multi-physics field coupled vibration analysis finite element model and calculate the vibration and noise spectrum characteristics of the permanent magnet motor during constant torque speed regulation and field weakening speed regulation.
2.1在Simplorer仿真软件中建立永磁同步电机三相电源供电电路，如图2所示,样机为一个48槽8极内置式永磁同步电机，在4000rpm以下采用最大转矩电流比控制，4000rpm以上采用弱磁控制，分别将以下4种电流数据设置为电流源，并导出为“.sph”文件，其A相电流波形如图3a、3b所示。2.1 Establish a permanent magnet synchronous motor three-phase power supply circuit in the Simplorer simulation software, as shown in Figure 2, the prototype is a 48-slot 8-pole built-in permanent magnet synchronous motor, which adopts the maximum torque-current ratio control below 4000rpm, and above 4000rpm Using field weakening control, set the following four kinds of current data as current sources, and export them as ".sph" files. The A-phase current waveforms are shown in Figures 3a and 3b.
1)Ih3000为电机在恒转矩调速区运行，转速3000rpm额定功率运行时实测谐波电流。1) I h3000 is the measured harmonic current when the motor is running in the constant torque speed regulation area, the speed is 3000rpm, and the rated power is running.
2)Is3000＝194A，即幅值为194A的正弦电流，为3000rpm额定功率时的基波电流。2) I s3000 =194A, that is, a sinusoidal current with an amplitude of 194A, which is the fundamental wave current at the rated power of 3000rpm.
3)Ih8000为电机在弱磁调速区运行，转速8000rpm额定功率运行时实测谐波电流。3) I h8000 is the actual measured harmonic current when the motor is running in the field-weakening speed regulation area with a speed of 8000rpm and rated power.
4)Is8000＝145A，即幅值为145A的正弦电流，为8000rpm额定功率时的基波电流。4) I s8000 =145A, that is, a sinusoidal current with an amplitude of 145A, which is the fundamental wave current at the rated power of 8000rpm.
2.2在Maxwell有限元仿真软件中以永磁同步电机具体结构参数建立永磁同步电机2D电磁有限元模型，如图4所示，设置电源为上一步保存的“.sph”文件，计算不同电流供电情况下的电流和电磁力频谱，如图5、6a、6b、7a、7b所示。2.2 Establish the 2D electromagnetic finite element model of the permanent magnet synchronous motor with the specific structural parameters of the permanent magnet synchronous motor in the Maxwell finite element simulation software, as shown in Figure 4, set the power supply to the ".sph" file saved in the previous step, and calculate the power supply of different currents The current and electromagnetic force spectra in the case are shown in Figures 5, 6a, 6b, 7a, and 7b.
2.3在SolidWorks设计软件中以永磁同步电机具体结构参数建立永磁同步电机3D定子结构模型，如图8所示。2.3 Establish the 3D stator structure model of the permanent magnet synchronous motor with the specific structural parameters of the permanent magnet synchronous motor in the SolidWorks design software, as shown in Figure 8.
2.4在Workbench有限元仿真软件中设置永磁同步电机材料参数，对永磁同步电机进行模态分析(见图9)，模态分析得到电机定子结构的固有频率和振型，其中对本文样机来说，0阶和8阶固有频率是有效模态，当电机径向力波的阶数和频率和固有频率一致时，电机可能会发生共振，引起比较大的振动噪声。2.4 Set the material parameters of the permanent magnet synchronous motor in the Workbench finite element simulation software, and perform a modal analysis on the permanent magnet synchronous motor (see Figure 9). The modal analysis obtains the natural frequency and mode shape of the motor stator structure. That is to say, the 0-order and 8-order natural frequencies are effective modes. When the order and frequency of the radial force wave of the motor are consistent with the natural frequency, the motor may resonate, causing relatively large vibration and noise.
2.5在Workbench有限元仿真软件中设置永磁同步电机材料参数，建立如图10所示的永磁同步电机电磁场和结构场强耦合模型，进行电磁场与结构场耦合仿真分析，计算4种电流供电下振动噪声频谱特性，计算结果如图11a、11b和12a、12b所示，开关频率附近的0阶和8阶固有频率处产生最大的振动噪声。2.5 Set the material parameters of the permanent magnet synchronous motor in the Workbench finite element simulation software, establish the strong coupling model of the electromagnetic field and the structural field of the permanent magnet synchronous motor as shown in Figure 10, carry out the coupling simulation analysis of the electromagnetic field and the structural field, and calculate the Spectrum characteristics of vibration and noise, the calculation results are shown in Figures 11a, 11b and 12a, 12b. The 0th order and 8th order natural frequencies near the switching frequency produce the largest vibration noise.
步骤3、分析逆变器谐波对样机的振动噪声的影响。Step 3. Analyze the influence of inverter harmonics on the vibration and noise of the prototype.
3.1分析逆变器谐波对样机的振动噪声的影响3.1 Analysis of the influence of inverter harmonics on the vibration and noise of the prototype
分析步骤2)得到的电流、径向电磁力和振动噪声频谱，由图5可以看出，逆变器电流主要谐波频率为k1fc±k2f(k1、k2为奇偶相异的正整数)，整个频段范围内8000rpm电流谐波占比高于3000rpm；由图6a、6b和7a、7b可以看出，与正弦电流供电时相比，逆变器谐波电流供电时r＝0阶电磁力波的6f、12f频谱分量、逆变器开关频率k1fc±k2f(k1、k2为奇偶相同的正整数)处力波幅值均大幅增加；与正弦电流供电时相比，逆变器谐波电流供电时r＝8阶电磁力波的频谱分量的4f、8f、16f处幅值增加较大，开关频率k1fc±k2f(k1、k2为奇偶相同的正整数)处r＝8阶电磁力波有增加，没有r＝0阶电磁力波增加明显；由图11a、11b和12a、12b可以看出，与正弦电流相比，逆变器谐波电流供电时，振动噪声在开关频率附近的0阶和8阶固有频率幅值增加；与恒转矩调速相比，弱磁调速时振动噪声整体都增加，在开关频率附近的0阶和8阶固有频率处增幅较明显。Analyzing the current, radial electromagnetic force and vibration noise spectrum obtained in step 2), it can be seen from Figure 5 that the main harmonic frequency of the inverter current is k 1 f c ±k 2 f (k 1 and k 2 are odd and even phases Different positive integers), the proportion of current harmonics at 8000rpm in the entire frequency range is higher than 3000rpm; it can be seen from Figures 6a, 6b and 7a, 7b that compared with sinusoidal current power supply, the inverter harmonic current power supply r = The 6f and 12f frequency spectrum components of the 0th-order electromagnetic force wave, and the force wave amplitude at the inverter switching frequency k 1 f c ± k 2 f (k 1 and k 2 are positive integers with the same parity) all increase significantly; Compared with current power supply, when the inverter is powered by harmonic current, the amplitudes at 4f, 8f, and 16f of the spectral components of the r=8th order electromagnetic force wave increase greatly, and the switching frequency k 1 f c ±k 2 f(k 1 , k2 is the same positive integer of parity) place r=8th order electromagnetic force wave has increase, there is no r= 0 order electromagnetic force wave to increase obviously; As can be seen from Fig. 11a, 11b and 12a, 12b, compared with sinusoidal current , when the inverter is powered by harmonic current, the vibration noise increases at the 0th order and 8th order natural frequency amplitude near the switching frequency; compared with the constant torque speed regulation, the overall vibration noise increases during the field weakening speed regulation. The increase is more obvious at the 0th and 8th natural frequencies near the frequency.
步骤4、实验与理论和仿真进行验证。Step 4, experiment and theory and simulation for verification.
4.1利用振动传感器对所研究永磁同步电机进行振动实验，实验和仿真振动加速度对比频谱图如图13a、13b所示，实验和仿真振动加速度结果基本相符，可以说明本发明仿真方法的准确性。4.1 Vibration experiments are carried out on the researched permanent magnet synchronous motor by means of vibration sensors. The comparison spectrum diagrams of the experimental and simulated vibration accelerations are shown in Figures 13a and 13b. The experimental and simulated vibration acceleration results are basically consistent, which can illustrate the accuracy of the simulation method of the present invention.
4.2利用实验数据对比仿真数据，进行验证。对比分析实验和仿真结果，对于本文样机，逆变器谐波供电时会引入新的r＝0阶和r＝8阶电磁力波的时域频谱分量，r＝0阶力波的12f频谱分量、逆变器开关频率k1fc±k2f(k1、k2为奇偶相同的正整数)；r＝8阶电磁力波的4f、8f、16f频谱分量，k1fc±k2f(k1、k2为奇偶相同的正整数)处r＝0阶电磁力波开关频率处增加更加明显；恒转矩调速和弱磁调速时，逆变器谐波电流的引入都会加剧永磁同步电机的振动噪声，相比较之下，逆变器谐波对8000rpm弱磁调速的影响大于对3000rpm恒转矩调速的影响；引入逆变器谐波电流会加剧0阶和8阶固有频率处共振，严重降低电动汽车乘坐舒适性和运行可靠性。4.2 Use experimental data to compare simulation data for verification. Comparing and analyzing the experimental and simulation results, for the prototype in this paper, the new r=0th order and r=8th order electromagnetic force wave time-domain spectrum components will be introduced when the inverter is powered by harmonics, and the 12f frequency spectrum component of r=0th order force wave , Inverter switching frequency k 1 f c ±k 2 f (k 1 and k 2 are positive integers with the same parity); r=4f, 8f, 16f spectral components of the 8th order electromagnetic force wave, k 1 f c ±k 2 f (k 1 , k 2 are positive integers with the same parity) increases more obviously at the r=0th order electromagnetic force wave switching frequency; during constant torque speed regulation and field-weakening speed regulation, the introduction of inverter harmonic current Both will aggravate the vibration and noise of the permanent magnet synchronous motor. In comparison, the influence of inverter harmonics on 8000rpm field-weakening speed regulation is greater than that on 3000rpm constant torque speed regulation; the introduction of inverter harmonic current will aggravate the zero-order It resonates with the 8th order natural frequency, seriously reducing the ride comfort and operating reliability of electric vehicles.
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