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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, Poincaré 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.

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The dynamic response of bearing under load and speed often determine the performance limitations of the machines and it is necessary to be able to predict bearing dynamic performance as an integral part of machine design analysis. In this paper, a mathematical model has been developed to investigate a nonlinear dynamic behavior of a rotor-bearing system due to localized defects of inner race and outer race. In the mathematical formulation, the contacts between rolling elements and inner/outer race is considered as nonlinear springs whose stiffness is obtaining using Hertz contact stress theory. Here nonlinear damping is also taken into consideration for cylindrical roller bearing. The governing equations of motion are formulated by using energy approach. Contact force and contact stiffness having nonlinearity and is calculated by using Newton-Raphson method for n-unknown nonlinear simultaneous equation. The new mark implicit integration technique is coupled with the Newton-Raphson method to solve the differential equations. A computer program is developed to simulate the defect on inner race and outer race and all the results are represented in the time and frequency domain. Equations of motions are solved by using Newmark-b method for phase plot/Poincare map. The proposed mathematical model is also compared with experimental results having radial and axial load condition. From the results obtained from the predicted model for frequency spectrum and phase plot at various speeds, the mathematical modeling and experimental results are found quite similar.

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