Vibration modeling of wind turbine shaft as rigid shaft supported by EHL contact ball bearings with overhung disc system

An investigation into the dynamic behavior of Elastohydrodynamic Lubricated (EHL) angular contact ball bearings employed in wind turbines is given in this paper considering non-linear contact characteristics due to combined dynamic loads, different rotation speeds, hydrodynamic effects and load-deformation relation. In order to investigate the dynamic behavior of shaft-bearing system, a rigid shaft with overhung disk which is supported by a couple of EHL angular contact ball bearings is modeled as a 5 DoF nonlinear system. The contact between the rolling element and running surfaces in the bearing is modeled as an equivalent spring and damper. Hertz contact theory and EHL theory are used to obtain EHL contact characteristics and contact forces. Simplified rolling contact theory is used and pure rolling is assumed in the kinematic analysis. The contact angle and mutual approach of rolling elements are obtained analytically. The contact forces and film thickness are calculated iteratively for the quasi-static case using the Newton-Raphson method. In order to express the dynamic behavior of the system, nonlinear equations of motion are solved by a numerical method using Runge Kutta algorithm. The results indicate that the stiffness in EHL contact increases with the increase in load, the damping decreases with the increase in speed, the vibration behavior of the system is more complicated than the dry contact as the natural frequencies are now dependent on system running speed. It has also been observed that there is a significant decrease in vibration amplitude of the system under lubricated contact conditions as well as the frequencies.