汽流激振下转子—轴承系统的稳定性
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摘要
作为一种基础工业设施,大型旋转机械已经成为国家工业的关键设备之一。旋转机械向着高速化、高效化的方向发展,因此,对于旋转机械的动力特性、可靠性及稳定性,人们也提出了更高的要求,这些现实要求促进了转子动力学的发展。随着现代非线性动力学理论的发展,非线性动力学理论与转子动力学越来越紧密的结合在一起,这使得转子动力学的研究也呈现出了一个新的面貌。
目前转子动力学的国内外研究热门是:通过研究旋转机械动、静部件之间的微小间隙约束对轴系的非线性激励的影响,来深入分析研究大型旋转机械的非线性动力学行为。在对转子系统的研究中,人们关注更多的是对系统中多种自激振动源(不对称轴承刚度、迷宫密封中的非轴对称间隙等)的分析、识别和研究,但对于涡轮机和压缩机中由于非轴对称间隙而导致的转子动态力,人们却很少关注。
本文首先建立了一个两端简支的Jeffcott转子模型(短直叶片转子),圆盘偏心时受到不均匀间隙汽流激振力的作用。基于流体动力学,通过对叶片流道内的流体模型应用动量定理,得到此汽流激振力模型,并采用四阶龙格库塔法,得出了单盘弹性转子系统的周期响应规律,然后根据系统的相轨迹及Poincare映射图,分析了系统在特定转速及特定的转子系统参数下的运动特征。
其次,建立了一个用来模拟简单汽轮机轴系(只含有短直叶片)的两端用滑动轴承支撑的Jeffcott转子模型,并用Newmark方法求得了系统的周期响应,根据系统的周期响应、Poincare映射图、频谱图、分岔图等,分析了系统在特定转速及特定的转子系统参数下的运动特征。
最后,考虑到汽轮机轴系中含有的叶片种类的不同,建立了一个较复杂的两端用滑动轴承支撑的双盘Jeffcott转子模型,其中一圆盘为短直叶片圆盘,另一圆盘为长扭叶片圆盘,并应用Newmark方法求得了系统的周期响应,根据系统的周期响应、Poincare映射图、频谱图、分岔图等,分析了系统在特定转速及特定的转子系统参数下的运动特征。
本文所采用的方法可用于分析同类转子系统的稳定性。
Large-scale rotating machinery, as a kind of industrial infrastructure, has become one of key equipments in national foundation establishment and industry. With the increment of the speed and efficiency, higher requirements for dynamic characteristic, reliability and stability to large-sized rotating machinery has been made along. These realistic demands have promoted the development of rotor dynamics. With the development of the theory of modern nonlinear dynamics, nonlinear dynamics connects with rotor dynamics more tightly, which makes the research on rotor dynamics present a new outlook.
Recently, it is the focus of domestic and international research to study the nonlinear forces acting on shaft, which generated by the small gap restraint between the motional and immobile parts, and to analyze and study the nonlinear dynamics actions of large-scale rotating machinery. In the study of rotor system, sources of self-exciter vibration (e.g., asymmetric bearing stiffness and non-asymmetic clearance in labyrinth seals) have been identified and extensively analyzed by investigators. However, the rotor dynamic forces due to clearance in turbines and compressors have received little attention.
A Jeffcott rotor which is simple supported at its two ends is established first in this article. The disc comes under the effect of the air exciting-vibration force due to the eccentricity. Based on the hydrodynamic, by using momentum theory to the liquid in the flow channel, the computational formula of the air exciting-vibration force is acquired. By using four-step Runge-Kutta method, the periodic response results of the elastic rotor system with one single-disc are gained. Then the dynamic characteristics of the rotor system at the certain rotate speed and the certain physic parameter of system are analyzed by using the phase spaces and Poincare maps of this system.
Second, a Jeffcott rotor model supported by two seals bearings in its two ends is established to simulate the shafting of simple turbines (only short-and-straight-blades are included in the shafting). And periodical response of the system is obtained by using the Newmark method. Then, the dynamic characteristics of rotor system at the certain rotate speed and the certain physic
目前转子动力学的国内外研究热门是:通过研究旋转机械动、静部件之间的微小间隙约束对轴系的非线性激励的影响,来深入分析研究大型旋转机械的非线性动力学行为。在对转子系统的研究中,人们关注更多的是对系统中多种自激振动源(不对称轴承刚度、迷宫密封中的非轴对称间隙等)的分析、识别和研究,但对于涡轮机和压缩机中由于非轴对称间隙而导致的转子动态力,人们却很少关注。
本文首先建立了一个两端简支的Jeffcott转子模型(短直叶片转子),圆盘偏心时受到不均匀间隙汽流激振力的作用。基于流体动力学,通过对叶片流道内的流体模型应用动量定理,得到此汽流激振力模型,并采用四阶龙格库塔法,得出了单盘弹性转子系统的周期响应规律,然后根据系统的相轨迹及Poincare映射图,分析了系统在特定转速及特定的转子系统参数下的运动特征。
其次,建立了一个用来模拟简单汽轮机轴系(只含有短直叶片)的两端用滑动轴承支撑的Jeffcott转子模型,并用Newmark方法求得了系统的周期响应,根据系统的周期响应、Poincare映射图、频谱图、分岔图等,分析了系统在特定转速及特定的转子系统参数下的运动特征。
最后,考虑到汽轮机轴系中含有的叶片种类的不同,建立了一个较复杂的两端用滑动轴承支撑的双盘Jeffcott转子模型,其中一圆盘为短直叶片圆盘,另一圆盘为长扭叶片圆盘,并应用Newmark方法求得了系统的周期响应,根据系统的周期响应、Poincare映射图、频谱图、分岔图等,分析了系统在特定转速及特定的转子系统参数下的运动特征。
本文所采用的方法可用于分析同类转子系统的稳定性。
Large-scale rotating machinery, as a kind of industrial infrastructure, has become one of key equipments in national foundation establishment and industry. With the increment of the speed and efficiency, higher requirements for dynamic characteristic, reliability and stability to large-sized rotating machinery has been made along. These realistic demands have promoted the development of rotor dynamics. With the development of the theory of modern nonlinear dynamics, nonlinear dynamics connects with rotor dynamics more tightly, which makes the research on rotor dynamics present a new outlook.
Recently, it is the focus of domestic and international research to study the nonlinear forces acting on shaft, which generated by the small gap restraint between the motional and immobile parts, and to analyze and study the nonlinear dynamics actions of large-scale rotating machinery. In the study of rotor system, sources of self-exciter vibration (e.g., asymmetric bearing stiffness and non-asymmetic clearance in labyrinth seals) have been identified and extensively analyzed by investigators. However, the rotor dynamic forces due to clearance in turbines and compressors have received little attention.
A Jeffcott rotor which is simple supported at its two ends is established first in this article. The disc comes under the effect of the air exciting-vibration force due to the eccentricity. Based on the hydrodynamic, by using momentum theory to the liquid in the flow channel, the computational formula of the air exciting-vibration force is acquired. By using four-step Runge-Kutta method, the periodic response results of the elastic rotor system with one single-disc are gained. Then the dynamic characteristics of the rotor system at the certain rotate speed and the certain physic parameter of system are analyzed by using the phase spaces and Poincare maps of this system.
Second, a Jeffcott rotor model supported by two seals bearings in its two ends is established to simulate the shafting of simple turbines (only short-and-straight-blades are included in the shafting). And periodical response of the system is obtained by using the Newmark method. Then, the dynamic characteristics of rotor system at the certain rotate speed and the certain physic
引文
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8 Glienicke J. Feder-und Dampfungskonstanten Von Gleitlagern for Turbomas-chinen Und Deren Einfluss Auf Das Schwingungsverhalten Eincs Einfachen Rotors. Diss TH Karisruhe. 1966, 22～36
9 Ehrich F. F. Subharmonic Vibration of Rotors in Bearing Clearance. American Society of Mechanical Engineers. 1966: 66-MD-1
10 Bently D. E. Forced Subrotative Speed Dynamic Action of Rotating Machinery. American Society of Mechanical Engineers. 1974: 74-Pet-16
11 Childs D W. Fractional Frequency Rotor Motion Due to Nonsymmetric Clearan-ce Effects. ASME Journal of Engineering for Power. 1982, 104(3): 533～541
12 Choi Y S, Noah S T. Nonlinear Steady-state Response of a Rotor-support System. ASME Journal of Vibration, Acoustics, Stress and Reliability in Design. 1987, 109(3): 255～261
13 Homes A G, Ettles C M, Mayes I W. Periodic Behavior of a Rigid Shaft in Short Journal Bearing. International Journal of Numerical Method in Engineering. 1978, 12: 695～702
14 Ehrich F. F. Some Observations of Chaotic Vibration Phenomena in High-speed Rotordynamics. ASME Journal of Vibration and Acoustics. 1991, 113(1): 50～57
15 Brown R D, Addison P, Chan A H C. Chaos in the Unbalance Response of Journal Bearings. Nonlinear Dynamics. 1994, 5: 421～432
16 孟光,薛中擎. 带挤压油膜阻尼器的柔性转子非线性响应的 Duffing 特性分析. 航空动力学报,1989,4(2): 173～178
17 Ishida Y. Nonlinear Vibrations and Chaos in Rotordynamics. JSME International Journal, Series C, Dynamics, Control, Robotics, Design and Manufacturing. 1994, 37(2): 237～245
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23 陈予恕,丁千,孟泉. 非线性转子的低频振动失稳机理分析. 应用力学学报. 1998, 15(1): 113～117
24 孟泉,陈予恕. 非线性转子—轴承系统 1/2 亚谐共振全局分岔研究. 非线性动力学学报. 1996, 3(2): 189～197
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26 Sundararajan P, Noah S T. Dynamics of Forced Nonlinear Systems Using Shooting/arc-length Continuation Method-application to Rotor Systems. ASME Journal of Vibration and Acoustics. 1997, 119(1): 9～20
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29 Myers C. J. Bifurcation Theory Applied to Oil Whirl in Plain Cylindrical Journal Bearings. ASME Journal of Mechanics. 1984, 51(2): 244～250
30 Hollis P, Taylor D L. Hopf Bifurcation to Limit Cycles in Fluid Film Bearings. ASME Journal of Tribology. 1986, 108(2): 184～189
31 Brindley J, Savage M D, Taylor C M. The Nonlinear Dynamics of Journal Bearing. Phil. Trans. R. Coc. Lond. A. 1990, 332: 107～119
32 Kim Y B, Noah S T. Stability and Bifurcation Analysis of Oscillators with Piecewise Linear Characteristics: a General Approach. ASME Journal of Applied Mechanics. 1991, 58: 545～553
33 Glasgow D A, Nelsom H D. Stability Analysis of Rotor-bearing Systems Using Component Mode Synthesis. ASME Journal of Mechanical Design. 1980, 102: 352～358
34 Nelson H D, Meacham W L. Transient Response of Rotor-bearing Systems Using Component Mode Synthesis. American Society of Mechanical Engineers. 1981: 81–GT-110
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2 邹经湘. 结构动力学. 黑龙江: 哈尔滨工业大学出版社. 1996
3 闻邦椿,王正等. 高等转子动力学. 北京:机械工业出版社. 1999
4 张文. 转子动力学理论基础. 北京: 科学出版社. 1990
5 周纪卿,朱因远. 非线性振动. 陕西: 西安交通大学出版社. 1998
6 陈予恕. 非线性振动. 北京: 高等教育出版社, 2002
7 Lund J. W. The Stability of an Elastic Rotor in Journal Bearing with Flexible Damped Supports. ASME Journal of Applied Mechanics. 1965, 32: 911～920
8 Glienicke J. Feder-und Dampfungskonstanten Von Gleitlagern for Turbomas-chinen Und Deren Einfluss Auf Das Schwingungsverhalten Eincs Einfachen Rotors. Diss TH Karisruhe. 1966, 22～36
9 Ehrich F. F. Subharmonic Vibration of Rotors in Bearing Clearance. American Society of Mechanical Engineers. 1966: 66-MD-1
10 Bently D. E. Forced Subrotative Speed Dynamic Action of Rotating Machinery. American Society of Mechanical Engineers. 1974: 74-Pet-16
11 Childs D W. Fractional Frequency Rotor Motion Due to Nonsymmetric Clearan-ce Effects. ASME Journal of Engineering for Power. 1982, 104(3): 533～541
12 Choi Y S, Noah S T. Nonlinear Steady-state Response of a Rotor-support System. ASME Journal of Vibration, Acoustics, Stress and Reliability in Design. 1987, 109(3): 255～261
13 Homes A G, Ettles C M, Mayes I W. Periodic Behavior of a Rigid Shaft in Short Journal Bearing. International Journal of Numerical Method in Engineering. 1978, 12: 695～702
14 Ehrich F. F. Some Observations of Chaotic Vibration Phenomena in High-speed Rotordynamics. ASME Journal of Vibration and Acoustics. 1991, 113(1): 50～57
15 Brown R D, Addison P, Chan A H C. Chaos in the Unbalance Response of Journal Bearings. Nonlinear Dynamics. 1994, 5: 421～432
16 孟光,薛中擎. 带挤压油膜阻尼器的柔性转子非线性响应的 Duffing 特性分析. 航空动力学报,1989,4(2): 173～178
17 Ishida Y. Nonlinear Vibrations and Chaos in Rotordynamics. JSME International Journal, Series C, Dynamics, Control, Robotics, Design and Manufacturing. 1994, 37(2): 237～245
18 Zhen J B, Meng G. Bifurcation and Chaos Response of Nonlinear Crack Rotor. International Journal of Bifurcation & Chaos. 1998, 8(3): 597～607
19 Adiletta G, Guido A R, Rossi C. Chaotic Motion of a Rigid Rotor in Short Journal Bearings. Nonlinear Dynamics. 1996, 10: 251～269
20 Yan H-T, Chen C-L. Chaos and Bifurcation Analysis of a Flexible Rotor Supported by Short Journal Bearings with Non-linear Suspension. Proceedings of the I MECH E, Part C, Journal of Mechanical Engineering Science. 2000, 214(7): 931～947
21 袁小阳. 轴系的稳定裕度、非线性振动和动力性能优化研究. 西安交通大学博士学位论文. 1994, 27～39
22 陈予恕,孟泉. 非线性转子—轴承系统的分岔. 振动工程学报. 1996, 9(3): 266～275.
23 陈予恕,丁千,孟泉. 非线性转子的低频振动失稳机理分析. 应用力学学报. 1998, 15(1): 113～117
24 孟泉,陈予恕. 非线性转子—轴承系统 1/2 亚谐共振全局分岔研究. 非线性动力学学报. 1996, 3(2): 189～197
25 郑惠萍. 滑动轴承不平衡转子系统非线性动力学稳定性及其稳定性裕度的研究. 天津大学博士学位论文. 2000, 48～66
26 Sundararajan P, Noah S T. Dynamics of Forced Nonlinear Systems Using Shooting/arc-length Continuation Method-application to Rotor Systems. ASME Journal of Vibration and Acoustics. 1997, 119(1): 9～20
27 刘恒. 转子轴承系统稳定性分岔问题的研究. 西安交通大学博士学位论文, 1997, 15～75
28 Newkirk B L, Taylor H D. Shaft Whipping Due to Oil Action in Journal Bearings. General Electric Review. 1925, 28: 559～568
29 Myers C. J. Bifurcation Theory Applied to Oil Whirl in Plain Cylindrical Journal Bearings. ASME Journal of Mechanics. 1984, 51(2): 244～250
30 Hollis P, Taylor D L. Hopf Bifurcation to Limit Cycles in Fluid Film Bearings. ASME Journal of Tribology. 1986, 108(2): 184～189
31 Brindley J, Savage M D, Taylor C M. The Nonlinear Dynamics of Journal Bearing. Phil. Trans. R. Coc. Lond. A. 1990, 332: 107～119
32 Kim Y B, Noah S T. Stability and Bifurcation Analysis of Oscillators with Piecewise Linear Characteristics: a General Approach. ASME Journal of Applied Mechanics. 1991, 58: 545～553
33 Glasgow D A, Nelsom H D. Stability Analysis of Rotor-bearing Systems Using Component Mode Synthesis. ASME Journal of Mechanical Design. 1980, 102: 352～358
34 Nelson H D, Meacham W L. Transient Response of Rotor-bearing Systems Using Component Mode Synthesis. American Society of Mechanical Engineers. 1981: 81–GT-110
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