Nonlinear dynamic analysis of a high-speed rotor supported by rolling element bearings

The paper presents an analytical model for investigating structural vibrations of a high-speed rotor supported by rolling bearings. The mathematical formulation accounted for tangential motions of rolling elements as well as inner and outer races with the sources of nonlinearity such as Hertzian contact force, geometrical imperfections, i.e. surface waviness 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 as the routes to chaos. The appearance of regions of periodic, sub-harmonic and chaotic behavior is seen to be strongly dependent on rotor speed and these imperfections. Poincarè maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.