| In allusion to the characteristics of a nonlinear bearing-rotor system, a system model was established based on rotor dynamics and nonlinear dynamics theory. The applicability and the stability of the numerical methods to the investigation of the system is investigated and the calculation shows that the four order variable step size Gill method is better than Runge-Kutta method in numerical stability. The nonlinear vibration of a horizontal rigid rotor supported by a deep groove ball bearing having radial internal clearance is studied by the Gill numerical integral method.The radial internal clearance of a deep groove ball bearing is taken as the main parameter, the effect of which on the dynamics response of the two kinds of rotor system(balanced or unbalanced) is studied. The results of a parametric study have resulted in the observation that the systems may undergo period doubling bifurcation, quasi-periodic and chaotic motions. In some typical parameter regions the periodic results, the bifurcation diagrams, the shaft centerline orbit, the phase portrait, the Poincare maps and the frequency spectrums of the systems are acquired by with numerical integral method. At the same time, a method to calculate the Laypunov exponents of a balanced rotor system is used to determine whether the system is in a state of chaos motion. The analytic results in this paper provide the theoretical reference for design this kind of bearing-rotor system.For the balanced rotor system, radial internal clearance is an important parameter for determining the dynamics response. It is seen that with increase in clearance the regions of unstable and chaotic response become wider. Increase damping results in lowered amplitude response and also reduced instability.For the unbalanced rotor system, the non-linearity is both due to Herzian contact and the radial internal clearance of bearing. The system is excited by the varying compliance frequency and the rotational frequency. The results have shown the appearance of instability and chaos in the dynamics response of the system as the speed of the bearing-rotor system is changed. Period doubling and intermittency have been observed as the route to chaos. |
