Non-linear dynamic response of a balanced rotor supported on rolling element bearings

Abstract

In this paper, the response of a balanced rigid rotor supported by rolling element bearings is studied. In the analytical formulation the contacts between the balls and races are considered as non-linear springs, whose stiffness are obtained by using Hertzian elastic contact deformation theory. The governing differential equations of motion are obtained by using Lagrange's equations. The implicit type numerical integration technique Newmark-β with Newton–Raphson method is used to solve the non-linear differential equations iteratively. The results of a parametric study done by taking radial internal clearance and rotor speed have resulted in the observation of a third region of instability, which has not been reported in the literature. The appearance of regions of periodic, subharmonic and chaotic behaviour is seen to be strongly dependent on the radial internal clearance and rotor speed. Poincarè maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behaviour.