有限长轴承支撑的转子系统非线性动力学分析

摘要/Abstract

摘要：

基于π油膜假设，运用变分约束原理和分离变量法求得了有限长动压轴承非线性油膜力的近似解析表达式。通过计算比较可知，该方法和有限元法的计算结果非常接近，而且可以节约大量计算时间。在此基础上，以转子的角速度、圆盘处的偏心量及转轴的刚度为控制参数，运用Newmark法分析了轴承-转子系统的非线性动力学行为。数值结果揭示系统具有周期运动、倍周期运动、准周期运动、六周期运动、十周期运动等复杂丰富的非线性动力学特征。

关键词: 非线性动力学, 轴承-转子系统, 有限长轴承, 稳定性, 分岔

Abstract:

Based on the assumption of π oil film, an approximation expression of nonlinear oil film force of finite hydrodynamic bearing was obtained by variational constraint principal and the separation of variables. The results calculated by the proposed method are in good agreement with the oil film forces by the finite element method, and the computing cost is reduced greatly. Based on the nonlinear oil film force, the speed of rotor, eccentricity of disk and stiffness of shaft were taken as control parameters, nonlinear dynamic behaviors of bearing-rotor system were analyzed by Newmark method. Numerical results reveal periodic, double-periodic, quasi-periodic, 6-periodic, 10-periodic of rich and complex nonlinear behaviors of the system.

Key words: nonlinear dynamics, bearing-rotor system, finite long bearing, stability, bifurcation

中图分类号:

TH133

黑棣, 吕延军, 张永芳. 有限长轴承支撑的转子系统非线性动力学分析[J]. 中国机械工程, 2015, 26(19): 2633-2640.

Hei Di, Lü Yanjun, Zhang Yongfang. Analysis of Nonlinear Dynamics of Rotor System Supported by Finite Long Bearing[J]. China Mechanical Engineering, 2015, 26(19): 2633-2640.

参考文献

[1]Wang Ligang，Cao Dengqin，Huang Wenhu. Nonlinear Coupled Dynamics of Flexible Blade-rotor-bearing Systems[J]. Tribology International，2010，43(4)：759-778.
[2]Castroa H F，Cavalca K L，Nordmann R. Whirl and Whip Instabilities in Rotor-bearing System Considering a Nnonlinear Force Model[J]. Journal of Sound and Vibration，2008，317(1/2)：273-293.
[3]Xie Wenhui, Tang Yougang, Chen Yushu. Analysis of Motion Stability of the Flexible Rotor-bearing System with Two Unbalanced Disks[J]. Journal of Sound and Vibration, 2008, 310(1/2): 381-393.
[4]Jing Jianping, Meng Guang, Sun Yi, et al. On the Non-linear Dynamic Behavior of a Rotor–bearing System[J]. Journal of Sound and Vibration, 2004, 274(3/5): 1031-1044.
[5]Wang Junguo, Zhou Jianzhong, Dong Dawei, et al. Nonlinear Dynamic Analysis of a Rub-impact Rotor Supported by Oil Film Bearings[J]. Archive of Applied Mechanics, 2013, 83(3): 413-430.
[6]Wang Jianke, Khonsari M M. Bifurcation Analysis of a Flexible Rotor Supported by Two Fluid-film Journal Bearings[J]. ASME Journal of Tribology, 2006, 128(3): 594-603.
[7]Li Dexin, Xu Jianxue. A Method to Determine the Periodic Solution of the Non-linear Dynamics System[J]. Journal of Sound and Vibration, 2004, 275(1/2): 1-16.
[8]Chang Jian，CaiWan. Non-linear Dynamic Analysis of Dual Flexible Rotors Supported by Long Journal Bearings[J]. Mechanism and Machine Theory, 2010, 45(6): 844-866.
[9]Wang Jianke, Khonsari M M. Effects of Oil Inlet Pressure and Inlet Position of Axially Grooved Infinitely Long Journal Bearings, Part I: Analytical Solutions and Static Performance[J]. Tribology International, 2008, 41(2): 119-131.
[10]Wang Jianke, Khonsari M M. Effects of Oil Inlet Pressure and Inlet Position of Axially Grooved Infinitely Long Journal Bearings, Part II: Nonlinear Instability Analysis[J]. Tribology International, 2008, 41(2): 132-140.
[11]Zheng Tiesheng, Yang Shuhua, Xiao Zhonghui, et al. A Ritz Model of Unsteady Oil-film Forces for Nonlinear Dynamic Rotor-bearing System[J]. ASME Journal of Applied Mechanics, 2004, 71(2): 219-224.
[12]Xiao Zhonghui, Wang Liping, Zheng Tiesheng. An Efficient Algorithm for Fluid Force and Its Jacobian Matrix in Journal Bearing[J]. ASME Journal of Triboogy, 2006, 128(2): 291-295.
[13]Vignolo G G, Barilá D O, Quinzani L M. Approximate Analytical Solution to Reynolds Equation for Finite Length Journal Bearings[J]. Tribology International, 2011, 44(10): 1089-1099.
[14]Hirani H, Athre K, Biswas S. Dynamically Loaded Finite Length Journal Bearings: Analytical Method of Solution[J]. ASME Journal of Tribology, 1999, 121(4): 844-852.
[15]Bastani Y, Queiroz M D. A New Analytic Approximation for the Hydrodynamic Forces in Finite-length Journal Bearings[J]. ASME Journal of Tribology, 2010, 132(1): 014502-1-9.
[16]Wang Yongliang, Liu Zhansheng, Kang Weijia, et al. Approximate Analytical Model for Fluid Film Force of Finite Length Plain Journal Bearing[J]. IMechE, Part C: Journal of Mechanical Engineering Science, 2012, 226(5): 1345-1355.