在世界邁向人工智能及全自動化的時代下，電機作為所有設備的驅動元件，已逐漸彰顯了它的重要性，其中又以感應電機的高可靠性、易於控制等優勢，成為電機產業大宗。隨著電機廣泛應用於工業設備、農業機械、家庭器具等各項領域，人們開始發現電機噪音及振動對於整體系統的運動特性影響深遠，且直接關乎系統的使用壽命。電磁噪音已然成為評價電機性能的重點指標之一。本文以三相感應電機為例進行電機結構的動力學分析，並將結構動力學影響因子區分為電磁振動及結構振動展開研究。
　　在感應電機的電磁激振力分析中，採用Maxwell 2D/3D®軟件進行電機電磁特性分析，給出電機氣隙的時空間場徑向及切向磁通密度，利用半解析方法及快速傅利葉方法分別計算氣隙及定子齒部在時域及頻域下的電磁力波，並且與電磁力波解析算法進行頻率階次對比，其對比結果具有準確性。
　　在轉子系統動力學特性分析中，討論陀螺效應對於轉子動力學的影響。針對電機的轉子系統進行動特性及動力學響應分析，並且考慮轉子支承剛度及不平衡激振力產生位置對於系統的影響，確定轉子系統在工作轉速區間內可以穩定運行。
　　在感應電機的外殼振動研究中，採用ANSYS®結構力學軟件進行電機外殼的結構振動研究。首先分析電機整體的各階固有頻率及模態振型，給出激振頻率與結構頻率特性曲線。接著，分別探討由轉子不平衡力及電磁激振力作用下所造成的電機外殼振動響應，確定各階次激振頻率下的結構振動加速度響應幅值皆符合工業電動機械相關規範。最後，針對三相感應電機進行振動水平量測，觀測空載幾個轉速下的重要測點振動響應特性。

In the era of artificial intelligence and automation in the world, motor, as the driving component of all equipment, has gradually shown its importance. Among them, induction motor has become a major part of the motor industry because of its high reliability and easy control. With the wide application of motors in industrial equipment, agricultural machinery, household appliances and other fields, people find that motor noise and vibration have a profound impact on the overall system's motion characteristics, and directly related to the system's service life. Electromagnetic noise has become one of the key indicators for evaluating motor performance. Taking three-phase induction motor as an example, the dynamic analysis of the motor structure is carried out by dividing the structural dynamic influencing factors into electromagnetic vibration and structural vibration.
In the electromagnetic force analysis of induction motor, Ansys Maxwell software is used to analyze the electromagnetic characteristics of the motor. The radial and tangential flux densities of the air gap in time and space are given. Moreover, the electromagnetic force waves of air gap and stator tooth in time and frequency domain are calculated by Semi-Analytical Method and Fast Fourier Transform Method respectively. The frequency order of the electromagnetic force wave analysis is compared to that of the electromagnetic force wave analysis algorithm. The comparison results are accurate.
In the analysis of dynamic characteristics of rotor system, the influence of gyroscopic effect on rotor dynamics is discussed. The dynamic characteristics and dynamic response of the rotor system are analyzed. Considering the influence of the support stiffness of the rotor and the position of the unbalanced exciting force on the system, it is determined that the rotor system can operate stably in the working speed range.
In the research of the shell vibration of induction motor, ANSYS software is used to study the structural vibration response of the motor shell. First, the natural frequencies and mode shapes of the whole motor are analyzed, and the curves of excitation frequency and structural frequency characteristics are given. Next, the vibration response of the motor shell caused by the unbalanced force of the rotor and the electromagnetic excitation force are discussed respectively. It is determined that the amplitude of the structural vibration acceleration response under each order of excitation frequency conforms to the relevant specifications of industrial electromechanical systems. Finally, the vibration level of the three-phase induction motor is measured, and the vibration response characteristics of the important measuring points under no-load for several rotating speeds are observed.

中鋼公司. 電磁鋼捲/產品手冊. 高雄: 中鋼股份有限公司出版, 2016.
王天熤. 高速永磁電機轉子綜合設計方法及動力學特性的研究[博士學位論文]. 瀋陽: 瀋陽工業大學, 2010.
王玎, 祝長生, 符嘉靖. 基於有限元的異部電機電磁震動分析[J]. 振動與沖擊, 2012, 31(2):140-154.
王合斌. 轉子斜槽對感應電機振動影響的分析[碩士學位論文]. 瀋陽: 瀋陽工業大學, 2018.
王正. 轉動機械的轉子動力學設計. 北京: 清華大學出版社, 2015.
代穎, 張千帆, 宋立偉等. 抑制車用異步電機電磁噪音的槽配合[J]. 中國電機工程學報, 2010, 30(27):32-35.
代穎, 崔淑梅, 宋立偉, 車用電機的有限元模態分析[J]. 中國電機工程學報, 2011, 31(9):100-104.
田啟楊. 不同槽參數對異部電積電磁振動的影響[碩士學位論文]. 瀋陽: 瀋陽工業大學, 2014.
左曙光, 高麗華, 吳旭東, 馬琮淦, 沈健. 電動車用永磁同步電機轉子偏心對電磁力影響分析[J]. 佳木斯大學學報(自然科學版), 2014,32(02):166-171.
朱福先, 周金宇, 孫奎洲, 韓文欽. 基於有限元的深溝球軸承應力和剛度研究. 機床與液壓,2014, 42(17):42-44.
李里. 轉子系統的動力學建模與分析[碩士學位論文]. 北京: 華北電力大學, 2017.
李岩, 劉佳男, 夏加寬. 三相異部電機電磁振動有限元計算分析[J]. 電器工程學報, 2015, 10(9):30-34.
何芝仙, 劉喆. 滾動軸承支承剛度計算. 機械設計,2016, 33(9):46-50.
胡絢. 反向旋轉雙轉子系統動力學特性研究[D]. 南京: 南京航空航天大學, 2007.
祝長生, 陳永校. 變頻器供電的三相異步電機的噪音特性[J]. 中小型電機, 1997(5):539-544.
祝長生, 陳永校, 徐國卿. 小型三相異步電機定子結構的試驗模態分析[J], 中小型電機, 1995, 22(4):3-5.
唐慶華, 張林. 採用斜槽降低三相異步電動機電磁噪音[J]. 防爆電機. 2015,50(1):14-16.
徐愛杰. 高速電機轉子系統動力學特性分析[碩士學位論文]. 哈爾濱: 哈爾濱工業大學, 2012.
孫利民, 趙軍. 振動測試技術. 北京: 中國建築工業出版社, 2017
袁惠群. 轉子動力學基礎. 北京: 冶金工業出版社, 2014.
陸秋海, 李德葆. 工程振動試驗分析. 北京: 清華大學出版社, 2015.
郭洪民, 楊湘杰. 流變壓鑄YL112鋁合金的熱處理與力學性能. 中國有色金屬學報,2008, 18(3):394-399.
黃國治, 傅豐禮. 中小旋轉電機設計手冊: 中國電力出版社, 2014.
黃濤. 變頻供電感應電機電磁振動研究[博士學位論文]. 武漢:武漢大學, 2014.
黃志堅. 機械設備振動故障監測與診斷. 北京: 化學工業出版社, 2018.
張宇, 謝里陽, 錢文學, 張曉瑾. 深溝球軸承的載荷分布與剛度特徵研究. 機械設計,2012, 29(3):45-49.
陳永校, 諸自強. 電機震動分析中的機電類比[J]. 電機技術, 1985(3):31-34.
陳永校, 諸自強, 應善成. 電機噪音的分析與控制[M]. 杭州:浙江大學出版社, 1987.
崔江. 雙轉子-滾動軸承系統的動力學特性研究[碩士學位論文]. 哈爾濱: 哈爾濱工業大學, 2017.
舒波夫. 電機的噪音和振動[M]. 北京: 機械工業出版社, 1980.
葉海燕, 周馳, 范子杰. 軸向預緊力對深溝球軸承剛度影響的有限元方法. 汽車安全與節能學報,2016, 7(2):188-195.
楊浩東. 永磁同步電機電磁振動分析[博士學位論文]. 浙江:浙江大學, 2011.

劉佳男. 變頻供電下異步電機電磁振動的特性分析[碩士學位論文]. 瀋陽: 瀋陽工業大學, 2013.
劉昌奇. 基於有限元的鼠籠電機電磁振動噪音研究[碩士專業學位論文]. 上海: 上海電機學院, 2016.
謝穎, 王嚴, 呂森. 小型異步電機模態計算與試驗分析[J]. 電工技術學報, 2015, 30(16):1-9.
鍾一諤, 何衍宗, 王正, 李方澤. 轉子動力學. 北京: 清華大學出版社, 1987.
GB/T 9239.1-2006 機械振動　恆態(剛性)轉子平衡品質要求　第1部分 規範與平衡允差的檢驗.
GB/T 9329.2-2006 機械振動　恆態(剛性)轉子平衡品質要求　第2部分 平衡誤差.
Alger P L, Hesse M H. Induction machines: their behavior and uses[M]. New York: Gordon and Breach, 1970.
Belahcen A. Magnetoelastic coupling in rotating electrical machines[J]. IEEE Transactions on Magnetics, 2005:1624-1627.
Bert R J, Yung C S. dynamics of Machine Tool Spindle/Bearing Systems under Thermal Growth[J]. Journal of Tribology, 1997,119(10):876-882.
Chiang H W D, Hsu C N, Jeng W, et al. Turbomachinery Dual Rotor-Bearing System Analysis[C]. ASME Turbo Expo 2002:803-810.
Chouksey M, Dutt J, Modak S. Modal analysis of rotor-shaft system under the influence of rotor-shaft material damping and fluid film forces[J]. Mechanism and Machine Theory, 2011, 48(1):81-93.
Ciprian G N, et al. Numerical modeling of magnetic noise for three phase asynchronous notors through the software flux 2D[C]. 2012 ICATE Proceedings, 2012:1-4.
D. H. Im, et al. Analysis of radial force as a source of vibration in an induction motor with skewed slots. IEEE Transactions On Magnetics. 1997, 33(2):1650-1653.
Ellison A J, Yang S J. Natural frequencies of stators of small electric machines[J]. Proceedings of the Institution of Electrical Engineers, 1971:90-185.
Frauman P, Burakov A, Arkkio A. Effects of the slot harmonics on the unbalanced magnetic pull in an induction motor with an eccentric rotor[J]. IEEE Transactions on Magnetics, 2007, 43(8):3441-3444.
Henneberger G, Sattler P k, Hadrys W, et al. Procedure for the numerical computation of mechanical vibrations in electrical machines[J]. IEEE Transactions on Magnetics, 1992, 28(2):1351-1354.
Huang S, Aydin M, Lipo T A. Electromagnetic vibration and noise assessment for surface mounted PM machines[C]. Power Engineering Society Summer Meeting, IEEE, 2001:1417-1426.
Hwang S M, et al. Cogging torque and acoustic noise reduction in permanent magnet motors by teeth pairing[J]. IEEE Transactions on Magnetics, 2000, 36(5):3144-3146.
Ishibashi F, Kamimoto K, Hayashi T, et al. Natural frequency of stator core of small induction motor[J]. IEE Proceedings-Electric Power Applications, 2003, 150(2):210-214.
Jeffcott H H. The Lateral Vibration of Loaded Shafts in the Neignbourhood of a Whirling Speed. -The Effect of Want of Balance[J]. Philosophical Magazine 6, 37(1919):304-314.
Ko H S, Kim K J. Characterization of noise and vibration sources in interior permanent-magnet brushless DC motors[J]. IEEE Transactions on Magnetics, 2004,40(6):L3482-3489.
Kobayashi T, Tajima F, Ito M. Effects of Slot Combination on Acoustic Noise from Induction Motors[J]. IEEE Transactions on Magnetics, 1997, 33(2):2101-2104.
Kyung-Tae Kim, Kwang-Suk Kim, Sang-Moon Hwang, Yoong-Ho Jung. Comparison of Magnetic Forces for IPM and SPM Motor with Rotor Eccentricity[J]. IEEE Transactions on Magnetics. 2001,37(5):3448-3451.
Le Besnerais J. Reduction of magnetic noise in PWM-supplied induction machines-low-noise design rules and multi-objective optimization[D]. Ecole Centrale de Lille, 2008.
Lee J H, Lee Y H, Kim D H, et al. Dynamics vibration analysis of switched reluctance motor using magnetic charge force desity and mechanical analysis. IEEE Transactions on Applied Superconductivity, Geneva, Switzerland, 2002:1511-1514.
Li W L, Qiu J J, Yang Z A. The double resonances of magnetism amd solid coupling of hydroelectric-generator stator system. Applied Mathematics and Mechanic[J], 2000, 21(10):1069-1076.
Liwschitz M M. Field harmonics in induction motors[J]. American Institute of Electrical Engineers, Transactions of the Volume, 1942(62):797-803.
Long S A, Zhu Z Q, Howe D. Vibration behavior of stators of switched reluctance motors[C]. IEE Proceedings-Electric Power Applications, IET, 2001:257-264.
Maliti K C. Modeling and analysis of magnetic noise in squirre-cage induction motors[D]. KTH Royal Institute of Technology, 2000.
Mori D, Ishihawa T. Force and Vibration analysis of induction motors[J]. IEEE Transactions on Magnetics, 2005,41(5):1948-1951.
Nelson H D. A Finite Rotating Shaft Element Using Timoshenko Beam Theory[J]. J. Mech. Des, 1980, 102(4):793-803.
Qing G H, Qiu J J, Viu Y H. Hamiltonian parametric element and semi-analytical solution for smart laminated plates[J]. Applied Mathematics and Mechanics, 2007,28(1):51-58.
Sekhar A S, Prabhu B S. Effects of Coupling Misalightment on Bibrations of Rotating Machinery[J]. Journal of Sound and Vibration, 1995, 184(4):655-671.
Singhal S, Singh K V. Hyder A. Effect of laminated core on rotor mode shape of large high speed induction motor[C]. IEEE International ElectricMachines and Drives Congerence, 2001:1557-1562.
Tang Z, Pillay P, Omekanda A M, et al. Young’s modulus for laminated machine structures with particular reference to switched reluctance motor vibrations[J]. IEEE Transactions on Industry Application, 2004, 40(3):748-754.
Tenhunen A, Benedetti T, Holopainen T P, et al. Electromagnetic forces in cage induction motors with rotor eccentricity[J]. IEEE Transactions on Machines and Drives, 2003, 29(3):1616-1622.
Wantanabe S, Kenjo S, Ide K, et al. Natural frequencies and vibration behavior of motor stators[J]. IEEE Power Engineering Review, 2010, PER-3(4):36-36.
Werner U. A mathematical model for lateral rotor dynamic analysis of soft mounted asynchronous machines[J]. Springer, 2008, 88(11):910-926.
Yim K H, Jang J W, Jang G H, et al. Forced vibration analysis of an IPM motor for Electrical Vehicles due to magnetic force. IEEE Transactions on Magnetics, 2012, 48(11):2981-2984.
Yu S. Tang R. Electromagnetic and mechanical characterizations of noise and vibration in permanent magnet synchronous machines[J]. IEEE Transactions on Magnetics, 2006:1335-1338.