Formulation of five degrees of freedom ball bearing model accounting for the nonlinear stiffness and damping of elastohydrodynamic point contacts

The knowledge of the dynamic behavior of rolling elements bearings and the contact properties have shown to be essential for model based fault diagnosis, lifetime estimation and reduction of noise in several industrial equipment application. This paper formulates the force and moments equilibrium of an angular contact ball bearing with five degrees of freedom accounting for the effects of the elastohydrodynamic (EHD) lubrication of its elements. A complete nonlinear model is derived and equivalent parameters for stiffness and damping of each contact were evaluated for different loading conditions. An iterative solution process was proposed to couple the bearing equilibrium and the EHD contact calculation, so as to generate the most suitable representation of the lubrication condition at the equilibrium point. The resulting reduced order model is promising to save computational costs and to make feasible the analysis of complex rotating systems supported by oil lubricated angular contact ball bearings.