Nonlinear Coupled Dynamic Characteristics and the Stability of Rotor-Bearing System under Rub-Impact and Oil-Film Forces

: The nonlinear coupled dynamic model of a rotor-bearing system with interaction between the rub-impact and oil-film forces is established by the Lagrangian’s equation and D'Alembert principle. The nonlinear coupled dynamic equation of rotor-bearing system with rub-impact and oil film force is investigated by the 4th-order Runge-Kutta method. Base on the dynamic model of rotor-bearing system, through Time domain response, shaft trajectory, phase plane and amplitude spectrum are proposed to illustrate the nonlinear coupled dynamic behaviors. then the largest Lyapunov exponent, Poincare map are identified to the stability of the obtained computational data. The excitation frequency, stator stiffness and mass eccentricity as the control parameters to study the influence of rotor-bearing system dynamics. Various nonlinear dynamic characteristics are discovered in the rotor-bearing system, such as periodic-1, multi-periodic, quasi-periodic and chaos motion are observed through the numerical simulation in this study. The numerical results indicated that coupled effects of rub-impact and nonlinear oil film force have a great influence on the vibration and instability of the rotor-bearing system as the varied excitation frequency. The nonlinear oil film force causes the oil whirl in the rotor-bearing system at the low excitation frequency. The rub-impact force mainly affects the dynamic characteristics of the high excitation frequency. The instability of rotor-bearing system occurs in the critical speed due to the instability of oil film. Larger stator stiffness can simplify the nonlinear dynamic response of system. As the stiffness of the stator increases, the system response gradually transforms from chaotic motion to period-1 motion. Under the effect of a large imbalance, jump phenomenon of system will be more obvious. and instability of system will occur in advance. The corresponding results obtained in this paper may promote to the further understanding of nonlinear dynamic behaviors of a rotor-bearing system and provide useful reference for suppressing the fault of rotating machinery.