Abstract：Modal analysis is an important part of motor vibration and noise analysis. To accurately obtain the results of motor modal analysis, it is necessary to assign corresponding elastic modulus parameters to the stator, armature winding, casing, end cover, and other structures. When the structural material is determined, its elastic modulus is also determined. Analytical and finite element calculations are based on ideal conditions, and there is often a significant error between the calculated and actual results based on the determined elastic modulus. The structure of the entire machine model, such as the casing and end cover, greatly affects the stator modal. For a finite element model, adjusting anisotropic parameters like the stator core and winding is necessary. At this stage, the determination of the elastic modulus of the motor structure is mainly done through modal experiments to adjust the parameters of the simulation results. Their errors converge to a reasonable error range. Although this method can obtain stator modal analysis results with high accuracy, the influence of parameter adjustment on each order of natural frequencies is not linear. Suppose its directionality cannot be clearly pointed out, it is difficult to adjust the parameters of the stator assembly and the entire machine. As a result, adjusting the errors of each order is difficult. Therefore, a double-stator electric-excitation field-modulated machine is taken as the research object. First, the initial values of the material parameters of each structure are determined, and the elastic modulus that affects its modal analysis is studied using finite element software. The relative influence rate of the elastic modulus changes in the outer stator, armature winding, casing, and end cover on each order of natural frequency is observed. According to the value relationship between elastic modulus, distinct adjustment methods were identified: three for the outer stator, four for the armature winding, and singular for the casing and end cover, thereby clarifying the directionality of elastic modulus adjustment for each structure. After that, the hammer method was used to conduct modal experiments on the outer stator, the outer stator assembly, and the entire machine. The error magnitude between modal experimental results and simulation results was obtained. Finally, the elastic modulus of the outer stator, armature winding, casing, and end cap was adjusted based on the error magnitude and the directionality for elastic modulus adjustments. Due to the complexity of the entire machine’s structure, it is necessary to appropriately equate the motor structure before adjusting the elastic modulus. It is found that modifying the elastic modulus of the outer stator, casing, and equivalent end cover has a similar effect on the natural frequencies across various orders of the entire machine. The effects on the 2nd and 3rd orders are significantly greater than the 4th order, and the armature winding has an opposite effect. Therefore, according to the error between the finite element modal analysis and experimental results obtained with the initial elastic modulus, the elastic modulus adjustment values for the outer stator and armature windings, determined through modal experiments, are selected. The elastic modulus of the casing and end cover is directly adjusted to minimize errors. The error of the finite element modal analysis results for the entire machine is within 4%. It proves that the proposed elastic modulus adjustment method can obtain more accurate modal analysis results for the entire machine, thereby facilitating the electromagnetic noise prediction and analysis of the motor.
宋春同, 王玉彬. 基于模态分析的双定子电励磁场调制电机弹性模量调整方法[J]. 电工技术学报, 2024, 39(6): 1713-1724.
Song Chuntong, Wang Yubin. The Elastic Modulus Adjustment Method of Double-Stator Electric-Excitation Field-Modulated Machine Based on Modal Analysis. Transactions of China Electrotechnical Society, 2024, 39(6): 1713-1724.
[1] Cheng Ming, Han Peng, Hua Wei.General airgap field modulation theory for electrical machines[J]. IEEE Transactions on Industrial Electronics, 2017, 64(8): 6063-6074. [2] 黄海林, 李大伟, 曲荣海, 等. 磁齿轮复合永磁电机拓扑及应用综述[J]. 电工技术学报, 2022, 37(6): 1381-1397. Huang Hailin, Li Dawei, Qu Ronghai, et al.A review of magnetic geared machines: topologies and appli- cations[J]. Transactions of China Electrotechnical Society, 2022, 37(6): 1381-1397. [3] Zhu Z Q, Liu Yue.Analysis of air-gap field modulation and magnetic gearing effect in fractional- slot concentrated-winding permanent-magnet syn- chronous machines[J]. IEEE Transactions on Indu- strial Electronics, 2017, 65(5): 3688-3698. [4] 王于涛, 隋义, 刘国鹏, 等. 横向错位磁场调制型无刷双转子电机的工作机理与性能分析[J]. 电工技术学报, 2022, 37(22): 5677-5686. Wang Yutao, Sui Yi, Liu Guopeng, et al.Operating principle and performance analysis of transverse- dislocated magnetic-field modulated brushless double- rotor machine[J]. Transactions of China Electro- technical Society, 2022, 37(22): 5677-5686. [5] 鲍晓华, 朱然, 刘佶炜, 等. 基于相位分析的双定子低速大转矩永磁同步电动机转矩脉动研究[J]. 电工技术学报, 2022, 37(22): 5660-5669. Bao Xiaohua, Zhu Ran, Liu Jiwei, et al.Torque ripple analysis of dual-stator surface mounted low-speed high-torque permanent magnet synchronous motors based on phase analysis[J]. Transactions of China Electrotechnical Society, 2022, 37(22): 5660-5669. [6] 李祥林, 李金阳, 杨光勇, 等. 电励磁双定子场调制电机的多目标优化设计分析[J]. 电工技术学报, 2020, 35(5): 972-982. Li Xianglin, Li Jinyang, Yang Guangyong, et al.Multi-objective optimization analysis of electric- excitation double-stator field-modulated machine[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 972-982. [7] Wang Yubin, Zhao Chenchen, Li Xianglin.Vibration and noise analysis of flux-modulation double stator electrical-excitation synchronous machine[J]. IEEE Transactions on Energy Conversion, 2021, 36(4): 3395-3404. [8] 肖阳, 宋金元, 屈仁浩, 等. 变频谐波对电机振动噪声特性的影响规律[J]. 电工技术学报, 2021, 36(12): 2607-2615. Xiao Yang, Song Jinyuan, Qu Renhao, et al.The effect of harmonics on electromagnetic vibration and noise characteristic in inverter-duty motor[J]. Transa- ctions of China Electrotechnical Society, 2021, 36(12): 2607-2615. [9] 罗玉涛, 卢若皓. 基于结构参数分级优化的电机电磁噪声抑制[J]. 电工技术学报, 2021, 36(14): 2957-2970. Luo Yutao, Lu Ruohao.Hierarchical optimization of structural parameters for motor electromagnetic noise suppression[J]. Transactions of China Electrotech- nical Society, 2021, 36(14): 2957-2970. [10] 诸自强, 陈永校. 电机定子固有频率及其模态的有限元法分析[J]. 电工技术学报, 1987, 2(4): 39-46. Zhu Ziqiang, Chen Yongxiao.The analysis of natural freqencies and modes of electrical machine stators by finite element method[J]. Transactions of China Electrotechnical Society, 1987, 2(4): 39-46. [11] Xing Zezhi, Wang Xiuhe, Zhao Wenliang, et al.Calculation method for natural frequencies of stator of permanent magnet synchronous motors based on three-dimensional elastic theory[J]. IEEE Transa- ctions on Energy Conversion, 2021, 36(2): 755-766. [12] 王天煜, 王凤翔. 大型异步电动机定子振动与模态分析[J]. 中国电机工程学报, 2007, 27(12): 41-45. Wang Tianyu, Wang Fengxiang.Vibration and modal analysis of stator of large induction motors[J]. Proceedings of the CSEE, 2007, 27(12): 41-45. [13] 李晓华, 黄苏融, 张琪. 电动汽车用永磁同步电机定子结构固有频率分析[J]. 中国电机工程学报, 2017, 37(8): 2383-2391. Li Xiaohua, Huang Surong, Zhang Qi.Analysis of natural frequencies of stator structure of permanent magnet synchronous motors for electric vehicles[J]. Proceedings of the CSEE, 2017, 37(8): 2383-2391. [14] Chai Feng, Li Yi, Pei Yulong, et al.Accurate modelling and modal analysis of stator system in permanent magnet synchronous motor with con- centrated winding for vibration prediction[J]. IET Electric Power Applications, 2018, 12(8): 1225-1232. [15] 代颖, 崔淑梅, 宋立伟. 车用电机的有限元模态分析[J]. 中国电机工程学报, 2011, 31(9): 100-104. Dai Ying, Cui Shumei, Song Liwei.Finite element method modal analysis of driving motor for electric vehicle[J]. Proceedings of the CSEE, 2011, 31(9): 100-104. [16] 谢颖, 王严, 吕森, 等. 小型异步电机模态计算与试验分析[J]. 电工技术学报, 2015, 30(16): 1-9. Xie Ying, Wang Yan, Lü Sen, et al.Modal calculation and test of small asynchronous motor[J]. Transactions of China Electrotechnical Society, 2015, 30(16): 1-9. [17] Wang Shanming, Hong Jianfeng, Sun Yuguang, et al.Analysis of zeroth-mode slot frequency vibration of integer slot permanent-magnet synchronous motors[J]. IEEE Transactions on Industrial Electronics, 2020, 67(4): 2954-2964. [18] Lin Fu, Zuo Shuguang, Deng Wenzhe, et al.Modeling and analysis of electromagnetic force, vibration, and noise in permanent-magnet synchronous motor con- sidering current harmonics[J]. IEEE Transactions on Industrial Electronics, 2016, 63(12): 7455-7466. [19] 吴建华. 基于物理模型开关磁阻电机定子模态和固有频率的研究[J]. 中国电机工程学报, 2004, 24(8): 109-114. Wu Jianhua.Study on the stator mode shapes and natural frequencies of switched reluctance motor based on real structual model[J]. Proceedings of the CSEE, 2004, 24(8): 109-114. [20] 左曙光, 张耀丹, 阎礁, 等. 考虑定子各向异性的永磁同步电机振动噪声优化[J]. 西安交通大学学报, 2017, 51(5): 60-68. Zuo Shuguang, Zhang Yaodan, Yan Jiao, et al.Optimization of vibration and noise in permanent magnet synchronous motor considering stator anisotropy[J]. Journal of Xi’an Jiaotong University, 2017, 51(5): 60-68. [21] 邓文哲, 左曙光, 孙罕, 等. 考虑定子铁芯和绕组各向异性的爪极发电机模态分析[J]. 振动与冲击, 2017, 36(12): 43-49. Deng Wenzhe, Zuo Shuguang, Sun Han, et al.Modal analysis of a claw-pole alternator considering orthotropy of the stator core and windings[J]. Journal of Vibration and Shock, 2017, 36(12): 43-49. [22] Yin Hongbin, Ma Fangwu, Zhang Xueyi, et al.Research on equivalent material properties and modal analysis method of stator system of permanent magnet motor with concentrated winding[J]. IEEE Access, 2019, 7: 64592-64602. [23] Yu Yinquan, Bi Chao, Jiang Quan, et al.Prediction of vibration in PM synchronous motor based on calculation of stator natural frequency[J]. Micro- system Technologies, 2015, 21(12): 2803-2810. [24] Liu Feng, Wang Xiuhe, Xing Zezhi, et al.Reduction of cogging torque and electromagnetic vibration based on different combination of pole arc coefficient for interior permanent magnet synchronous machine[J]. CES Transactions on Electrical Machines and Systems, 2021, 5(4): 291-300.
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