Study On Nonlinear Dynamical Behavior Of A Rotor System With Rub-Impact And Chaos Control

The typical theory and algorithm of bifurcation and chaos in the nonlinear dynamical system are analyzed and summarized, which are used to perform some particular studies on the rub-impact rotor system, and the results show that these systems have rich dynamical behaviors. The results explain effectively the complex nonlinear phenomena of the rotor-bearing systems, which may provide theory references to fault diagnoses, vibration control and safety operating of the rotor system. Fixed point theorem is used to analyze their relations and several contraction-mapping are supplied to the system, variables, thus, the chaotic behavior of several systems are controlled successfully. This paper tries to find four effective methods for the chaos of a kind of non-smooth self-excited vibration system. It proposes a new method that can save great energy and that can keep high periodic and quasiperiodic motions at the same time to the chaos and hyperchaos of the general two dimensional quadratic map, which provides a new way for studying some discrete system model. Therefore it makes sense in theory and it is applicable.The main contributions of this paper are:(1) Establish a kind of nonlinear stiffness model of local rub-impact rotor system, and analyze the representative behaviors in nonlinear dynamical system through numerical method, study the nonlinear phenomena of the rub-impact model of linear stiffness. This paper adopts the single condition bifurcation analysis method and Poincare mapping method and shows the periodic motions, quasiperiodic motions, chaotic motions and the evolutive process of these motion's forms by analyzing unbalance, lateral-stiffness ration and damping ration.(2) Present nonlinear oil film force and rub-impact rotor model, the effect of nonbalance, the bearing radial gap, the friction coefficient of the rotor and stator, different lubricating oil and the block factor of the bearing to the rotor are analyzed by applying Poincare mapping diagram, bifurcation diagram and phase portrait, the abundant dynamical behaviors are found. The results provide further understanding of the rub-impact fault and enable early prediction of this fault in rotating machinery.(3) Based on the analysis to the chaos controlling method, metric spaces is constructed, which inner relationships are analyzed by fixed point theorem and several contractive mappings such as the nonlinear mapping on wavelet function and linear contraction-mapping are constructed, thus the chaotic behavior of several systems are controlled successfully. The analysis of the chaotic control of non-smooth self-excited system is given, the system is controlled effectively by applying the largest Lyapunov exponent diagram, global Poincare mapping diagram, parametric diagram after controlling, time series diagram and phase portrait in many ways and different methods. Proposes a method saving great energy and keeping high periodic and quasiperiodic motions to the chaos and hyperchaos of the the general two dimensional quadratic map, which provides a new way for studying some discrete system model.