Analysis of Nonlinear Phenomena in High Speed Ball Bearings due to Radial Clearance and Unbalanced Rotor Effects

The dynamic behavior of a high speed unbalanced rotor supported on roller bearings with damping has been studied, focusing particular attention on its nonlinear aspects. The non-linearity in the rotor bearing system has been considered mainly due to Hertzian contact, unbalanced rotor effect and radial internal clearance. This is modeled as an oscillating spring-mass-damper system. Various techniques like Time Response curves, Poincare maps, Orbits plots, fast Fourier transformation, Hopf bifurcation and Phase Trajectory are used to study the nature of response. The motion of an unbalanced rotor is categorized with respect to the ratio of the Forcing/Natural frequency of the system as Harmonic, Sub-harmonic, Quasi periodic and Chaotic. The results show the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed. Period doubling and mechanism of intermittency have been observed that lead to chaos. The outcomes illustrate the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed. This work differs from the previous studies in the way that the complex model simulates nonlinear vibrations, considering that both the lubricated nonlinear contact stiffness and damping correspond to the conservative and dissipative energies, respectively. The comprehensive model developed in this investigation is a useful tool to predict the system behavior and for performance evaluation of a rotor bearing system.