On the dynamics of elastohydrodynamic mixed lubricated ball bearings. Part II: non-linear structural vibration

Equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange's equation considering the vibrational characteristics of the individual constituents such as inner race, outer race, cage, and balls, in order to investigate the structural vibration of the bearing. This article is the second part of the present study dealing with structural vibration, whereas in the first part, elastohydrodynamic mixed lubricated contact stiffness and damping coefficients are determined. Utilizing these stiffness and damping coefficients, a non-linear load-deflection contact model is developed. This is then used in the equations of motion. The equations of motion are solved using Runge-Kutta integration technique. This work differs from the previous studies in the sense that the model simulates the vibration, considering that both the lubricated contact stiffness and damping correspond to the conservative and dissipative energies, respectively. It is observed that under undamped conditions, all the elements of the bearing actively participate in energy sharing and oscillate periodically, containing more than one frequency. The system vibration, however, died down rapidly in the presence of damping.