交角不对中转子-轴承系统非线性动力学行为研究
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摘要
考虑转子交角不对中和质量不平衡等因素,研究了在滑动轴承支承下柔性转子-轴承耦合系统的非线性动力学行为。首先,基于转子间交角不对中的约束关系,利用第二类Lagrange方程推导了具有交角不对中故障的柔性多转子系统运动微分方程。采用数值方法,分析系统的非线性振动特性,例如,系统的轴心轨迹、响应频谱和最大Lyapunov指数等。结果表明:在较低转速时,系统主要呈现出与转速同步的周期运动特性。随着转速的提高,稳态响应在某些参数下出现分叉、跳跃以及混沌等非线性现象。最后讨论了交角不对中量以及质量不平衡对系统动力学特性的影响。
The non-linear dynamical behaviors caused by the faults of angular misalignment and mass unbalance of the journal bearing supported flexible rotor-bearing system are investigated in this paper.Firstly,the motion equation of the rotor system is derived by the second class Lagrange method with the effects of the motion relation between the two rotors,in which a rheonomic holonomic constraint characterized by the angular misalignment is embedded.Then its nonlinear vibration features,such as the frequency spectra,rotor orbit and Poincarésection,and the largest Lyapunov exponent under different conditions are primarily analyzed based on numerical techniques.The results reveal that the vibration of the rotor system are synchronous at low speed,while as the rotating speed increase,some non-linear characteristics such as jumping,period-doubling and chaotic motions will occur.Furthermore,the parameter analysis for the effects of angular misalignment and mass unbalance is also discussed.
The non-linear dynamical behaviors caused by the faults of angular misalignment and mass unbalance of the journal bearing supported flexible rotor-bearing system are investigated in this paper.Firstly,the motion equation of the rotor system is derived by the second class Lagrange method with the effects of the motion relation between the two rotors,in which a rheonomic holonomic constraint characterized by the angular misalignment is embedded.Then its nonlinear vibration features,such as the frequency spectra,rotor orbit and Poincarésection,and the largest Lyapunov exponent under different conditions are primarily analyzed based on numerical techniques.The results reveal that the vibration of the rotor system are synchronous at low speed,while as the rotating speed increase,some non-linear characteristics such as jumping,period-doubling and chaotic motions will occur.Furthermore,the parameter analysis for the effects of angular misalignment and mass unbalance is also discussed.
引文
[1] Lu Siliang,He Qingbo,Wang Jun.A review of stochastic resonance in rotating machine fault detection[J].Mechanical Systems and Signal Processing,2019,116:230-260.
[2]郭玉杰,李克,石峰.某台汽轮发电机联轴器不对中振动故障的诊断处理[J].轴承,2013,8:56-58.Guo Yujie,Li Ke,Shi Feng.Diagnosis and treatment for vibration fault of coupling misalignment on a turbine generator[J].Bearing,2013,8:56-58.
[3] Li Zigang,Jiang Jun,Tian Zhui.Stochastic dynamics of a nonlinear misaligned rotor system subject to random fluid-induced forces[J].Journal of Computational and Nonlinear Dynamics,2017,12:011004.
[4]李自刚,李明.具有轴承不对中故障的柔性非圆截面多转子系统非线性动力学行为[J].振动工程学报,2012,25(1):68-73.Li Zigang,Li Ming.Nonlinear dynamics of flexible multi-rotor system with a misaligned journal bearing and non-circular cross section of shaft[J].Journal of Vibration Engineering,2012,25(1):68-73.
[5] Felipe Wenzel,Katia Lucchesi Cavalca,Vibration signatures of a rotor-coupling-bearing system under angular misalignment[J].Mechanism and Machine Theory,2019,133:559-583.
[6]陈予恕,李军.汽轮发电机组轴系弯扭耦合振动问题研究综述[J].汽轮机技术,2012,54(3):161-164.Chen Yushu,Li Jun.Research on bending-torsion coupling vibration of shaft system of turbine generator[J].Turbine Technology,2012,54(3):161-164.
[7] Slim Bouaziz,Molka Attia Hili,Mohamed Mataar,et al.Dynamic behaviour of hydrodynamic journal bearings in presence of rotor spatial angular misalignment[J].Mechanism and Machine Theory,2009,44:1548-1559.
[8] Redmond I.Study of a misaligned flexibly coupled shaft system having nonlinear bearings and cyclic coupling stiffness—Theoretical model and analysis[J].Journal of Sound and Vibration,2010,329:700-720.
[9] Al-Hussain K M.Dynamic stability of two rigid rotors connected by a flexible coupling with angular misalignment[J].Journal of Sound and Vibration,2003,266(2):217-234.
[10]Palolo Pennacchi,Andrea Vania,Steven Chatterton.Nonlinear effects caused by coupling misalignment in rotors equipped with journal bearings[J].Mechanical Systems and Signal Processing,2012,30:306-322.
[11]李明.转角不对中故障的转子系统非线性动力学特征[J].振动、测试与诊断,2011,31(5):552-556.Li Ming.Nonlinear dynamics characteristics of rotor system with angular misalignment[J].Journal of Vibration,Measurement&Diagnosis,2011,31(5):552-556.
[12]Li Ming.Nonlinear vibration of a multirotor system connected by a flexible coupling subjected to the holonomic constraint of dynamic angular misalignment[J].Mathematical Problems in Engineering,2012:243758.
[13]Wang Nanfei,Jiang Dongxiang.Vibration response characteristics of a dual-rotor with unbalance-misalignment coupling faults:theoretical analysis and experimental study[J].Mechanism and Machine Theory,2018,125:207-219.
[14]Li Zigang,Jiang Jun,Tian Zhui.Nonlinear vibration of an angular-misaligned rotor system with uncertain parameters[J].Journal of Vibration and Control,2016,22(1):129-144.
[15]朱拥勇,王德石.含万向铰偏斜旋转轴的组合共振及其稳定性分析[J].应用力学学报,2012,29(4):361-367.Zhu Yongyong,Wang Deshi.The stability analysis on combination resonance of misaligned rotary shafts driven through a universal joint[J].Chinese Journal of Applied Mechanics,2012,29(4):361-367.
[16]Farzad Hemmati,Mohammad Miraskari,Mohamed S Gadala.Dynamic analysis of short and long journal bearings in laminar and turbulent regimes,application in critical shaft stiffness determination[J].Applied Mathematical Modelling,2017,48:451-475.
[17]PawePietkiewicz,Sawomir Banaszek,GrzegorzZywica.The stability loss of the rotor-slide bearings system under random load variations[J].Journal of Vibroengineering,2017,19(7):4921-4935.
[18]王延博.大型汽轮发电机组轴系不对中振动的研究[J].动力工程,2004,24:768-774.Wang Yanbo.Shaft mis-alignment induced vibration in high capacity steam-turbine generator sets[J].Power Engineering,2004,24:768-774.
[2]郭玉杰,李克,石峰.某台汽轮发电机联轴器不对中振动故障的诊断处理[J].轴承,2013,8:56-58.Guo Yujie,Li Ke,Shi Feng.Diagnosis and treatment for vibration fault of coupling misalignment on a turbine generator[J].Bearing,2013,8:56-58.
[3] Li Zigang,Jiang Jun,Tian Zhui.Stochastic dynamics of a nonlinear misaligned rotor system subject to random fluid-induced forces[J].Journal of Computational and Nonlinear Dynamics,2017,12:011004.
[4]李自刚,李明.具有轴承不对中故障的柔性非圆截面多转子系统非线性动力学行为[J].振动工程学报,2012,25(1):68-73.Li Zigang,Li Ming.Nonlinear dynamics of flexible multi-rotor system with a misaligned journal bearing and non-circular cross section of shaft[J].Journal of Vibration Engineering,2012,25(1):68-73.
[5] Felipe Wenzel,Katia Lucchesi Cavalca,Vibration signatures of a rotor-coupling-bearing system under angular misalignment[J].Mechanism and Machine Theory,2019,133:559-583.
[6]陈予恕,李军.汽轮发电机组轴系弯扭耦合振动问题研究综述[J].汽轮机技术,2012,54(3):161-164.Chen Yushu,Li Jun.Research on bending-torsion coupling vibration of shaft system of turbine generator[J].Turbine Technology,2012,54(3):161-164.
[7] Slim Bouaziz,Molka Attia Hili,Mohamed Mataar,et al.Dynamic behaviour of hydrodynamic journal bearings in presence of rotor spatial angular misalignment[J].Mechanism and Machine Theory,2009,44:1548-1559.
[8] Redmond I.Study of a misaligned flexibly coupled shaft system having nonlinear bearings and cyclic coupling stiffness—Theoretical model and analysis[J].Journal of Sound and Vibration,2010,329:700-720.
[9] Al-Hussain K M.Dynamic stability of two rigid rotors connected by a flexible coupling with angular misalignment[J].Journal of Sound and Vibration,2003,266(2):217-234.
[10]Palolo Pennacchi,Andrea Vania,Steven Chatterton.Nonlinear effects caused by coupling misalignment in rotors equipped with journal bearings[J].Mechanical Systems and Signal Processing,2012,30:306-322.
[11]李明.转角不对中故障的转子系统非线性动力学特征[J].振动、测试与诊断,2011,31(5):552-556.Li Ming.Nonlinear dynamics characteristics of rotor system with angular misalignment[J].Journal of Vibration,Measurement&Diagnosis,2011,31(5):552-556.
[12]Li Ming.Nonlinear vibration of a multirotor system connected by a flexible coupling subjected to the holonomic constraint of dynamic angular misalignment[J].Mathematical Problems in Engineering,2012:243758.
[13]Wang Nanfei,Jiang Dongxiang.Vibration response characteristics of a dual-rotor with unbalance-misalignment coupling faults:theoretical analysis and experimental study[J].Mechanism and Machine Theory,2018,125:207-219.
[14]Li Zigang,Jiang Jun,Tian Zhui.Nonlinear vibration of an angular-misaligned rotor system with uncertain parameters[J].Journal of Vibration and Control,2016,22(1):129-144.
[15]朱拥勇,王德石.含万向铰偏斜旋转轴的组合共振及其稳定性分析[J].应用力学学报,2012,29(4):361-367.Zhu Yongyong,Wang Deshi.The stability analysis on combination resonance of misaligned rotary shafts driven through a universal joint[J].Chinese Journal of Applied Mechanics,2012,29(4):361-367.
[16]Farzad Hemmati,Mohammad Miraskari,Mohamed S Gadala.Dynamic analysis of short and long journal bearings in laminar and turbulent regimes,application in critical shaft stiffness determination[J].Applied Mathematical Modelling,2017,48:451-475.
[17]PawePietkiewicz,Sawomir Banaszek,GrzegorzZywica.The stability loss of the rotor-slide bearings system under random load variations[J].Journal of Vibroengineering,2017,19(7):4921-4935.
[18]王延博.大型汽轮发电机组轴系不对中振动的研究[J].动力工程,2004,24:768-774.Wang Yanbo.Shaft mis-alignment induced vibration in high capacity steam-turbine generator sets[J].Power Engineering,2004,24:768-774.