Analysis of a Rotor Supported by Angular Contact Ball Bearings Under EHD Lubrication

Abstract

Rotors are crucial components of machinery, widely used in different areas of industry, as compressors, automotive transmissions, wind turbines and others. The development of accurate computational models able to aid the project phase of rotating machines is essential to drop tests and prototypes costs and to reduce processing time consumption, with good performance in predicting the dynamic behaviors of rotor-bearing systems. The present work studies the Laval Rotor modeled with a five-degrees-of-freedom decentered disc subject to rotating unbalanced force and combining radial and thrust loads. The rotor is supported on two ball bearings with angular contact under elastohydrodynamic (EHD) lubrication. Although these bearings are identical, they are under different loads due to forces distribution, being, consequently, characterized separately. In order to obtain stiffness and damping equivalent parameters for each bearing, in axial and radial directions, an optimization is carried out, integrating the dynamic equilibrium of the bearings’ spheres with the transient multi-level algorithm solution of EHD equations. Further on, a lumped parameter model of the rotor is analyzed. The shaft inertia is assumed negligible, and its stiffness matrix is obtained using influence coefficients. The dissipative forces approach considers proportional structural damping. As consequence of the disc decentered position, a gyroscopic component is present in the system. The nonlinear bearings reaction forces are included in the model as external forces and the complete system of equations is solved in time domain, enabling the analysis of rotor and bearing responses. Finally, the fundamental frequencies of the complete system are obtained.