Nonlinear tribodynamics of an elastic shaft with a flexible bearing outer race

In this paper, a mathematical model of a rotor-bearing system is presented. The model includes modal elastodynamics of a flexible rotor as well as the in-plane radial dynamics of the bearing with a flexible outer race. Elastodynamics of the flexible shaft utilises a solution based on Green's function to provide a computationally efficient approach. The flexible bearing outer race is modelled using Timoshenko beam theory. The system model also includes detailed lubricated contact mechanics of balls-to-races contacts with viscous friction. Therefore, the rotor-bearing analysis represents a detailed multi-physics tribodynamics and modal elastodynamic responses of the system which closely represents broad-band vibration response of such systems in practice, an approach not hitherto reported in the literature. It is also demonstrated that the outer race flexibility changes the location of the stability orbital centres, as well as the spread of limit cycle vibrations. Furthermore, it accentuates the occurrence of multiples of ball pass frequency. The importance of integrated system dynamics and lubricated contact mechanics is highlighted, showing that although the elastodynamic response of the rotor's flexible elements may not be clear in the acquired vibration signal, its effect on energy efficiency of the system can be quite important.