Abstract：An eccentric rotor does not only occur with dynamic loads, but also has vibrations with static loads. A unified formula is given for the air-gap length for an eccentric rotor considering both the dynamic and static eccentricities. The unbalanced magnetic pull (UMP) of the rotor is calculated numerically. Differential motion equations are given for the rotor system for the effect of UMP, static load (gravity), and unbalanced mass excitation. The rotor shaft orbit and displacement spectra are analyzed for a dynamic eccentricity and a mixed eccentricity with a static load. The direction and magnitude of the static eccentricity are related to the vibration characteristics of the rotor system. The results show that the static eccentricity angle affects the rotor shaft orbit and makes the displacement frequency component amplitudes vary periodically. A harmonic appears at four times the rotating speed with increasing static eccentricity. The effects of a static load on the rotor system can be regarded as a static eccentricity in the direction of the load.
徐学平, 韩勤锴, 褚福磊. 静载荷作用下偏心转子电磁振动特性[J]. 清华大学学报（自然科学版）, 2016, 56(2): 176-184.
XU Xueping, HAN Qinkai, CHU Fulei. Electromagnetic vibration characteristics of an eccentric rotor with a static load. Journal of Tsinghua University(Science and Technology), 2016, 56(2): 176-184.
[1] 徐进友, 刘建平, 宋轶民, 等. 考虑电磁激励的水轮发电机组扭转振动分析 [J]. 天津大学学报, 2008, 41(12): 1411-1416. XU Jinyou, LIU Jianping, SONG Yimin, et al. Torsional vibration analysis of hydrogenerators considering electromagnetic excitation [J]. Journal of Tianjin University, 2008, 41(12): 1411-1416. (in Chinese)
[2] Gustavsson R K, Aidanpaa J. The influence of nonlinear magnetic pull on hydropower generator rotors [J]. Journal of Sound and Vibration, 2006, 297(3): 551-562.
[3] 张雷克, 马震岳. 不平衡磁拉力作用下水轮发电机组转子系统碰摩动力学分析 [J]. 振动与冲击, 2013, 33(8): 48-54.ZHANG Leike, MA Zhenyue. Dynamic analysis for rotor system with rub-impact of a hydraulic generating set under unbalanced magnetic pull [J]. Journal of Vibration and Shock, 2013, 33(8): 48-54. (in Chinese)
[4] Wang L, Cheung R W, Ma Z Y, et al. Finite-element analysis of unbalanced magnetic pull in a large hydro-generator under practice operations [J]. IEEE Transactions on Magnetics, 2008, 44(6): 1558-1561.
[5] Lundin U, Wolfbrandt A. Method for modeling time- dependent no uniform rotor/stator configurations in electrical machines [J]. IEEE Transactions on Magnetics, 2009, 45(7): 2976-2980.
[6] Guo D, Chu F, Chen D. The unbalanced magnetic pull and its effects on vibration on a three-phase generator with eccentric rotor [J]. Journal of Sound and Vibration, 2002, 254(2): 297-312.
[7] Perers R, Lundin U, Leijon M. Saturation effects on unbalanced magnetic pull in a hydroelectric generator with an eccentric rotor [J]. IEEE Transactions on Magnetics, 2007, 43(10): 3884-3890.
[8] 万书亭, 李和明, 李永刚. 气隙偏心对汽轮发电机定转子振动特性的影响 [J]. 振动与冲击, 2005, 24(6): 21-23.WAN Shuting, LI Heming, LI Yonggang. Analysis on vibration characteristics of generator with the fault of eccentric air-gap [J]. Journal of Vibration and Shock, 2005, 24(6): 21-23. (in Chinese)
[9] 陈小安, 张朋, 陆永亚, 等. 计电磁不平衡磁拉力的高速电主轴转子偏心特性研究[J]. 振动与冲击, 2014, 33(2): 37-40.CHEN Xiaoan, ZHANG Peng, LU Yongya, et al. Dynamic characteristics of high-speed motorized spindles affected by rotor's eccentric mass [J]. Journal of Vibration and Shock, 2014, 33(2): 37-40. (in Chinese)
[10] 王天煜, 王凤翔, 方程. 高速永磁电机机组轴系振动研究 [J]. 振动与冲击, 2011, 30(9): 111-115.WANG Tianyu, WANG Fengxiang, FANG Cheng. Vibration analysis of shafting of high speed permanent magnetic machinery [J]. Journal of Vibration and Shock, 2011, 30(9): 111-115. (in Chinese)
[11] 徐进友, 刘建平, 宋轶民, 等. 水轮发电机转子非线性电磁振动的幅频特性[J]. 中国机械工程, 2012, 21(3): 348-350. XU Jinyou, LIU Jianping, SONG Yimin, et al. Amplitude- frequency characteristics of nonlinear electromagnetic vibration in a hydro-generator rotor [J]. China Mechanical Engineering, 2012, 21(3): 348-350. (in Chinese)
[12] 岳二团, 甘春标, 杨世锡. 气隙偏心下永磁电机转子系统的振动特性分析 [J]. 振动与冲击, 2014, 33(8): 29-34.YUE Ertuan, GAN Chunbiao, YANG Shixi. Vibration characteristics analysis of a rotor for a permanent magnet motor with air-gap eccentricity [J]. Journal of Vibration and Shock, 2014, 33(8): 29-34. (in Chinese)
[13] 李志和, 李正光, 孙维鹏. 不平衡磁拉力作用下偏心转子的非线性振动 [J]. 吉林大学学报: 理学版, 2011, 49(3): 459-461. LI Zhihe, LI Zhengguang, SUN Weipeng. Nonlinear vibration of an eccentric rotor subjected to unbalanced magnetic pull [J]. Journal of Jilin University: Science Edition, 2011, 49(3): 459-461. (in Chinese)
[14] Wu B, Sun W, Li Z. Circular whirling and stability due to unbalanced magnetic pull and eccentric force [J]. Journal of Sound and Vibration, 2011, 330(21): 4949-4954.
[15] Dorrell D G. Sources and characteristics of unbalanced magnetic pull in three-phase cage induction motors with axial-varying rotor eccentricity [J]. IEEE Transactions on Industry Applications, 2011, 47(1): 12-24.
[16] Dorrell D G, Shek J K, Mueller H. Damper windings in induction machines for reduction of unbalanced magnetic pull and bearing wear [J]. IEEE Transactions on Industry Applications, 2013, 49(5): 2206-2216.
2016, Vol. 56 
