Rolling Bearing Vibrations—The Effects of Surface Waviness and Radial Internal Clearance

Abstract

This paper presents the nonlinear dynamic analysis of a balanced rotor supported by roller bearings. The mathematical formulation accounted for tangential motions of rolling elements as well as inner and outer races with the sources of non-linearity such as Hertzian contact force and radial internal clearance resulting transition from no-contact to contact state between rolling elements and the races. In the formulation the contacts between the rolling elements and the races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark-β with Newton-Raphson method is used to solve the nonlinear differential equations iteratively. 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, which lead to chaos. The appearance of regions of periodic, subharmonic and chaotic behavior is seen to be strongly dependent on these imperfections. Poincarè maps, phase plots and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.