Analytical Modeling of Radial Electromagnetic Force of IPMSM Considering Asymmetric Saturation

doi:10.3969/j.issn.1009-086x.2024.04.005

Abstract

Abstract:

Due to the magnetic saturation characteristic of the interior permanent magnet synchronous motor （IPMSM）， there is no effective method to analyze the radial electromagnetic force on the stator of PMSM. It is also disadvantageous to suppress the electromagnetic vibration and noise of the motor in the early stage of design and development. An analytical calculation model of electromagnetic force is presented to solve the problem of rotor unsymmetrical magnetic saturation of IPMSMs. By combining the winding function method with the equivalent magnetic circuit method， the magnetic dynamic potential of the motor considering the electromagnetic saturation is derived. The equivalent air gap permeability of the motor is calculated by using Carter factor. The air gap magnetic field model is established by the method of magnetic potential multiply permeability， and the analytical model of the radial electromagnetic force of the motor is finally established by the Maxwell stress equation. Finally， the accuracy of the model is verified by finite element method. The model can reflect the relationship between the electromagnetic force and the structure parameters of the motor， and is helpful to improve the structure of the motor quickly in the design stage to suppress the electromagnetic vibration and noise.

Key words: permanent magnet synchronous motor （PMSM）, analytical model, saturation effect, radial electromagnetic force, winding function method, equivalent magnetic circuit method, magnetic potential times permeability method

摘要：

由于内置式永磁同步电机磁饱和特性的存在，使得解析分析电机运行过程中定子所受的径向电磁力缺乏系统有效的方法，不利于在前期设计开发阶段进行电机电磁振动和噪声的抑制。针对内置式永磁同步电机转子不对称磁饱和的问题提出了一种电磁力的解析计算模型。通过将绕组函数法与等效磁路法相结合，推导了考虑电磁饱和情况下的电机磁动势。利用卡特系数计算了电机的等效气隙磁导。通过磁势乘磁导法建立气隙磁场模型，并结合Maxwell应力方程最终建立了电机径向电磁力的解析模型。最终通过有限元法验证了该模型的准确性。该模型能够反应电磁力与电机各结构参数的关系，有利于在设计阶段快速改进电机结构来抑制电机电磁振动和噪声。

关键词: 永磁同步电机, 解析模型, 饱和, 径向电磁力, 绕组函数法, 等效磁路法, 磁势乘磁导法

CLC Number:

TM351

Xuelei ZHANG, Shu WANG, Zhengyu LIU, Chenghao KOU, Zuxu GUO. Analytical Modeling of Radial Electromagnetic Force of IPMSM Considering Asymmetric Saturation[J]. Modern Defense Technology, 2024, 52(4): 45-57.

张学磊, 王姝, 刘正宇, 寇成浩, 郭祖旭. 考虑不对称饱和的电机径向电磁力解析建模[J]. 现代防御技术, 2024, 52(4): 45-57.

Figures/Tables 22

Fig. 1 Model of a 48-slot/8-pole IPM motor

Table 1 Main parameters of PMSM

参数	数值
额定转速/（r·min^-1）	3 000
额定电压/V	220
额定功率/kW	20
额定转矩/（N·m）	64
槽数	48
极对数	4
定子外径/mm	210
定子内径/mm	130
转子外径/mm	128
转子内径/mm	48
电机轴向长度/mm	140

Fig. 2 Magnetic field line distribution at slot

Fig. 3 Schematic diagram of rotor structure

Fig. 4 Magnet MMF drop developed diagram

Fig. 5 Equivalent magnetic circuit of rotor

Fig. 6 Magnetic field lines of motor

Fig. 7 Magnetic leakage of the flux barriers of rotor

Fig. 8 Improved magnet MMF drop developed diagram

Fig. 9 Distribution of tangential flux in the pole shoe of rotor

Fig. 10 Fall of MMF in the pole shoe of rotor

Fig. 11 Magnetic flux density and magnetic field intensity

Fig. 12 No-load radial electromagnetic force by analytical and FE method

Fig. 13 Radial electromagnetic force at I=20 A，φ=90°

Fig. 14 Radial electromagnetic force at I=50 A， φ=0°

Fig. 15 Radial electromagnetic force at I=50 A， φ=36°

Fig. 16 Radial electromagnetic force at I=80 A， φ=54°

Fig. 17 Radial electromagnetic force at I=110 A， φ=0°

Fig. 18 Radial electromagnetic force at I=140 A， φ=72°

Fig. 19 Radial electromagnetic force at I=140 A， φ=90°

Fig. 20 Radial electromagnetic force at I=170A， φ=18°

Table 2 Comparison of the error of the radial electromagnetic force

电流有效值/A	电流相角/（°）	电磁力时间阶次		电磁力空间阶次
电流有效值/A	电流相角/（°）	平均误差/%	最大误差/%	平均误差/%	最大误差/%
20	90	1.23	3.45	0.74	1.76
50	0	0.65	2.07	1.96	2.78
50	36	2.63	4.12	0.89	1.84
80	54	3.71	5.25	2.87	3.22
110	0	4.33	7.24	3.12	4.66
140	72	5.15	6.13	4.47	4.87
140	90	6.11	7.82	5.28	5.37
170	18	5.87	7.54	5.36	5.16

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