Finite element modeling of a rotor shaft rolling bearings system with consideration of bearing nonlinearities

Analytical procedures are developed for predicting the dynamic behavior of rotor shaft systems supported on radial rolling element bearings. In Section 3 of this article, a C-0 four-node isoparametric rotating-shaft finite element model is developed using the finite element displacement method, including the translational motions, rotary inertia, shear deformations, gyroscopic moments, and system proportional damping. Euler angles are employed to monitor the orientation of the deflected rotor in space. In Section 5, a nonlinear bearing model is proposed, taking into account the rolling elements speed of rotation, nonlinear stiffness, clearance(s) (with allowance for coupling between the radial clearance and deadband), and elastic interaction with the rotating shaft. The bearing nonlinear reaction forces and the gyroscopic loading vector are treated as external loads. With rigid disks included, Lagrange's equations are used to derive equations of motion that, in turn, are decoupled using modal analysis, expressed in the normal coordinates representation. The above analyses are implemented in the finite element program DAMRO 1. With results in both the time domain and frequency domain being discussed, a case study concludes that bearing clearance has a pronounced effect on the system chaos and the bearing loads. The presented analyses offer a more advanced modeling tool in the held of nonlinear rotor dynamics.