Nonlinear dynamic response of a balanced rotor supported by rolling element bearings due to radial internal clearance effect

This paper presents a model for investigating structural vibrations in rolling element bearings due to radial internal clearance. The mathematical formulation accounted for tangential motions of rolling elements as well as inner and outer races with sources of nonlinearity such as Hertzian contact force and internal radial clearance resulting transition from no contact to contact state between rolling elements and races. The contacts between rollers and races are treated as nonlinear springs and the springs act only in compression to simulate contact deformation and resulting force. The nonlinear stiffness is obtained by application of equations for the Hertzian elastic contact deformation theory. The effect of radial internal clearance for rotor bearing system in which rolling element bearings show periodic, quasi-periodic and chaotic behavior are analyzed. Time response, rotor trajectories, Poincarè maps and power spectra are used to elucidate and to illustrate the diversity of system behavior.