轴承-转子系统在基础运动作用时的非线性分析
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摘要
轴承-转子系统的非线性特性及其在基础运动作用时的响应,是离心机设备设计阶段必须考虑的。本文使用简化的多自由度转子模型进行模拟分析,运动方程考虑了非线性的油膜润滑轴承模型。应用自适应时间步长的Runge-Kutta-Felburg法求解微分运动方程组,将人造的正弦波加速度作为基础运动输入系统,使用Poincaré图、分岔图和瀑布图分别考察了垂直放置转子在有无基础运动作用时的动力学性质。快速傅里叶变换在频域内揭示了转动频率与基础振动频率之间的组合共振现象。计算的结果不仅给出了泵转子自身的非线性性质,也展示了泵转子在基础运动作用时的组合共振。
Nonlinear dynamics characteristics of bearing-rotor system are necessary to be investigated for centrifugal machines in design stage as well as nonlinear response of the system subjected to base movements.The simplified model with multi-freedom-degree is applied to perform the numerical simulation.The nonlinear model of oil film bearing is taken into account in motion equations.The adaptive step method of Runge-Kutta-Felburg is applied to solve the differential equations.The artificial sine wave acceleration is considered as base movement input to the system.The Poincaré maps,bifurcation diagrams and cascade maps are used to investigate the dynamics of vertical rotor system.Combination resonance behavior which due to both rotational speed and base movement is discovered by the Fast Fourier Transform.The results yield not only nonlinear characteristics of the pump rotor,but also combination resonance under base movements.
Nonlinear dynamics characteristics of bearing-rotor system are necessary to be investigated for centrifugal machines in design stage as well as nonlinear response of the system subjected to base movements.The simplified model with multi-freedom-degree is applied to perform the numerical simulation.The nonlinear model of oil film bearing is taken into account in motion equations.The adaptive step method of Runge-Kutta-Felburg is applied to solve the differential equations.The artificial sine wave acceleration is considered as base movement input to the system.The Poincaré maps,bifurcation diagrams and cascade maps are used to investigate the dynamics of vertical rotor system.Combination resonance behavior which due to both rotational speed and base movement is discovered by the Fast Fourier Transform.The results yield not only nonlinear characteristics of the pump rotor,but also combination resonance under base movements.
引文
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[3]Adiletta G,Guido A R,Rossi C.Nonlinear dynamics of a rigid unbalanced rotor in journal bearings.Part I:theoretical analysis[J].Nonlinear Dynamics,1997,14(1):57-87.
[4]Adiletta G,Guido A R,Rossi C.Nonlinear dynamics of a rigid unbalanced rotor in journal bearings.Part II:experimental analysis[J].Nonlinear Dynamics,1997,14(2):157-189.
[5]Muszynska A.Stability of whirl and whip in rotor/bearing systems[J].Journal of Sound and Vibration,1988,127(1):49-64.
[6]李德信,徐健学.非线性转子-轴承系统的周期解及近似解析表达式[J].计算力学学报,2004,21(5):557-563.(LI De-xin,XU Jian-xue.Periodic solution and its approximate analytic expressions of the nonlinear rotor-bearing system[J].Chinese Journal of Computational Mechanics,2004,21(5):557-563.(in Chinese))
[7]丁千,郎作贵,曹树谦.双跨柔性转子-轴承系统动力学理论与实验研究[J].工程力学,2005,22(2):162-167.(DING Qian,LANG Zuo-gui,CAO Shuqian.Theoretical and experimental investigations of flexible multi-bearing-rotor dynamics[J].Engineering Mechanics,2005,22(2):162-167.(in Chinese))
[8]Yu H,Chen Y S,Cao Q J.Bifurcation analysis for nonlinear multi-degree-of-freedom rotor system with liquid-film lubricated bearings[J].Applied Mathematics and Mechanics,2013,34(6):777-790.
[9]Samali B,Kim K B,Yang J N.Random vibration of rotating machines under earthquake excitations[J].Journal of Engineering Mechanics,1986,112(6):550-565.
[10]Duchemin M,Berlioz A,Ferraris G.Dynamic behavior and stability of a rotor under base excitation[J].Journal of Vibration and Acoustics,2006,128(5):576-585.
[11]Chen Y J,Zhu C S.Active vibration control based on linear matrix inequality for rotor system under seismic excitation[J].Journal of Sound and Vibration,2008,314(1):53-69.
[12]Ito T,Hatta M,Shintani A,et al.Study on the seismic response of high-speed rotational disk-shaft system[A].Proceedings of the ASME Pressure Vessels and Piping Conference[C].2012.
[13]李伟东,吴坤岳,胡平.周期激励下单搭接接头强度与振动特性研究[J].计算力学学报,2014,31(4):446-452.(LI Wei-dong,WU Kun-yue,HU Ping.Study on strength and fatigue behavior of single lap joint under periodic excitation[J].Chinese Journal of Computational Mechanics,2014,31(4):446-452.(in Chinese))
[14]闻邦椿,李以农,徐培民,等.工程非线性振动[M].北京:科学出版社,2007.(WEN Bang-chun,LI Yi-nong,XU Pei-min,et al.Nonlinear Vibration in Engineering[M].Beijing:Science Press,2007.(in Chinese))
[15]陈宏,李鹤,张晓伟,等.双盘悬臂裂纹转子-轴承系统的动力学分析[J].振动工程学报,2005,18(1):113-117.(CHEN Hong,LI He,ZHANG Xiao-wei,et al.Dynamics analysis of a dual disk over hung rotor-bearing system with crack[J].Journal of Vibration Engineering,JP22005,18(1):113-117.(in Chinese))
[16]张直明,张言羊,谢友柏,等.滑动轴承的流体动力润滑理论[M].北京:高等教育出版社,1986.(ZHANG Zhi-ming,ZHANG Yan-yang,XIE You-bai,et al.Hydrodynamic Lubrication Theory of Journal Bearing[M].Beijing:Higher Education Press,1986.(in Chinese))