Complex nonlinear behaviors of a rotor dynamical system with non-analytical journal bearing supports  

作　　者：吕延军 虞烈 刘恒 张永芳 

机构地区：[1]Theory of Lubrication and Bearing Institute, Xi＇ an Jiaotong University, Xi＇ an 710049, P.R. China [2]School of Electronic and Information , Northwestern Polytechnical University, Xi＇an 710072, P.R. China

出　　处：《Journal of Shanghai University(English Edition)》2006年第3期247-255,共9页上海大学学报（英文版）

基　　金：Project supported by National Natural Science Foundation of China （Grant No. 50275116）, and National High-Technology Research and Development Program of China （ Nos. 2002AA414060, 2002AA503020）

摘　　要：Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available. This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy. Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor. A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system. Meanwhile the dynamic coefficients of bearing are obtained. The nonlinear unbalance periodic responses of the system are obtained by using Poincaré-Newton-Floquet method and a combination of predic- tor-corrector mechanism and Poincaré-Newton-Floquet method. The local stability and bifuration behaviors of periodic motions are analyzed by the Floquet theory. Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum. The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available. This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy. Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor. A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system. Meanwhile the dynamic coefficients of bearing are obtained. The nonlinear unbalance periodic responses of the system are obtained by using Poincaré-Newton-Floquet method and a combination of predic- tor-corrector mechanism and Poincaré-Newton-Floquet method. The local stability and bifuration behaviors of periodic motions are analyzed by the Floquet theory. Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum. The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.

关 键 词：nonlinear dynamics journal bearing-rotor system BIFURCATION CHAOS stability finite element method. 

分 类 号：TH113[机械工程—机械设计及理论]