以磁悬浮轴承支承的航空发动机高压模拟转子为对象,研究了在压气机叶尖气流激振力和磁悬浮轴承电磁力共同作用下的转子系统动力学特性。采用Timoshenko梁理论建立了模拟转子的有限元模型,在模型中引入由PID方法控制的差动磁悬浮轴承电磁力以及由Alford力表示的压气机叶尖气流激振力,利用Newmark-β法求解了转子系统的动力学响应。计算结果表明,在非线性Alford力和磁轴承电磁力共同作用下,转子系统表现出了较复杂的动力学特征;磁悬浮轴承的控制参数对转子系统特性有较大影响,不同取值可能导致转子出现单周期、多周期拟周期甚至失稳等不同动力学行为;因此,对由磁悬浮轴承支承并含轴流压气机的转子,需考虑叶尖气流激振力与电磁轴承力的相互影响进而确定轴承控制参数。
Abstract
The dynamic characteristics of a rotor system incorporating flow induced Alford forces and electromagnetic forces of active magnetic bearings (AMBs) were studied, based on a simplified model high-pressure rotor of an aero engine supported by AMBs.The Timoshenko beam theory and a finite element method were utilized to model the rotor.Electromagnetic forces of the AMBs controlled by differential PID methods and flow induced Alford forces at the tip of the compressor vanes were introduced, before the dynamic responses of the rotor system were calculated through the Newmark-β method.The results reveal complex dynamic behaviors of the rotor system simultaneously excited by the nonlinear Alford forces and bearing electromagnetic forces.Control parameters of the AMBs show remarkable influences on the rotor system dynamics, by changing it into period 1, multi-period and quasi-period motions with different values.Therefore, for rotors supported by AMBs and with axial compressors, effects of the flow induced Alford forces and electromagnetic forces need to be considered before determining control parameters.
关键词
磁悬浮轴承 /
Alford力 /
非线性 /
转子动力学
{{custom_keyword}} /
Key words
active magnetic bearing /
Alford force /
nonlinear /
rotor dynamics
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] SCHWEITZER G, MASLEN E H. Magnetic Bearings: Theory, Design, and Application to Rotating Machinery [M]. Springer, 2012.
[2] ALFORD J S. Protecting turbomachinery from self-excited rotor whirl [J]. Journal of Engineering for Power, 1965, October: 333-344.
[3] 柴山, 张耀明, 曲庆文等. 汽轮机扭叶片级间隙气流激振力分析 [J]. 中国电机工程学报, 2001, 21(5): 68-72.
CHAI Shan, ZHANG Yao-ming, QU Qing-wen, et al. An analysis on the air exciting vibration force of twist blade of steam turbine [J]. Engineering Science, 2001, 3(4): 68-72.
[4] JUNG DaeYi, DESMIDT H. A.. Limit-Cycle Analysis of Planar Rotor/Autobalancer System Influenced by Alford’s Force [J]. 2016, 138(2): 021018.
[5] STORACE A F, WISLER D C, SHIN H W, et al. Unsteady Flow and Whirl-Inducing Forces in Axial-Flow Compressors. Part I - Experiment [M]. Proceedings of ASME Turbo EXPO 2000: International Gas Turbine & Aeroengine Congress & Exhibition. Munich, Germany. 2000: 2000-GT-0565.
[6] 辛晓辉, 曹树谦, 丁千. 汽轮机转子在气流力和油膜力作用下的非线性动力学特性 [J]. 非线性动力学学报, 2005, 12: 45-52.
XIN Xiao-hui, CAO Shu-qian, DING Qian. Nonlinear dynamic characteristics of steam turbine rotor under flow forces and oil film forces [J], Journal of nonlinear dynamics, 2005, 12: 45-52.
[7] 黄来, 黄丕维, 刘永辉等. 气流力、油膜力和质量偏心共同作用下的转子非线性动力学研究 [J]. 汽轮机技术, 2007, 49(6): 428-438.
HUANG Lai, HUANG Wei-pi, LIU Yong-hui, et al. Study of Nonlinear Dynamic Characteristics of Turbine Rotor System under Oil-film Force Alford Force and Quality Eccentricity [J]. Turbine Technology, 2007, 49(6): 428-438.
[8] 白长青, 许庆余, 李跃明. Alford 力和滚动轴承对轴流压缩机转子系统动力特性和稳定性的影响 [J]. 航空学报, 2009, 30(10): 5.
BAI Chang-qing, XU Qing-yu, LI Yue-ming. Effect of Alford Forces and Ball Bearings on Dynamic Characteristics and Stability of Axial Flow Compressor Rotor System [J]. Acta Aeronutica et Astronautica Sinica, 30(10): 1901-1905, 2009..
[9] 成玫, 孟光, 吴秉瑜. Alford力和滚动轴承对转子系统动力特性的影响 [J]. 振动与冲击, 2011, 30(12): 6.
CHENG Mei, MENG Guang, WU Bing-yu. Effect of Alford force and ball bearing on dynamic characteristics of a rotor system [J]. Journal of Vibration and Shock, 2011, 30(12): 164-168.
[10] JI J C, YU L, LEUNG A Y T. Bifurcation behavior of a rotor supported by active magnetic bearings [J]. Journal of Sound and Vibration, 2000, 235(1): 133-151.
[11] JI J C, HANSEN C H. Non-linear oscillations of a rotor in active magnetic bearings [J]. Journal of Sound and Vibration, 2001, 240(4): 599-612.
[12] KATO Junya, INOUE Tsuyoshi, TAKAGI Kentaro et al. Nonlinear Analysis for Influence of Parametric Uncertainty on the Stability of Rotor System With Active Magnetic Bearing Using Feedback Linearization [J]. J. Comput. Nonlinear Dynam, 2018, 13(7): 071004.
[13] ENEMARK Soren, SANTOS Ilmar F. Nonlinear dynamic behavior of a rotor-foundation system coupled through passive magnetic bearings with magnetic anisotropy – Theory and experiment [J]. Journal of Sound and Vibration, 2016, 363:407-427.
[14] SHAFAI B., BEALE S., LAROCCA P. et al. Magnetic bearing control systems and adaptive force balancing [J]. IEEE Control Systems Magazine, 1994, 14(2): 4-13.
[15] NOSHADI Amin, SHI Juan, LEE Wee Sit, et al. Optimal PID-type fuzzy logic controller for a multi-input multi-output active magnetic bearing system [J]. 2016, 27: 2031.
[16] LIJESH K.P., HIRANI Harish. Optimization of Eight Pole Radial Active Magnetic Bearing [J]. Journal of Tribology, 2015, 137(2): 024502.
[17] 王金堂. 电磁轴承数字控制系统的设计与研究 [D]; 浙江大学, 2005.
WANG Jing-tang. Design and research of the digital control system of an active magnetic bearing [D]. Zhejiang University, 2005.
[18] JIANG K, ZHU C, CHEN L, et al. Multi-DOF rotor model-based measurement of stiffness and damping for active magnetic bearing using multi-frequency excitation [J]. Mechanical Systems and Signal Processing, 2015, 60-61(358-74.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}