Bifurcation Analysis of a Non-Linear On-Board Rotor-Bearing System

The non-linear dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings and subject to rigid base excitations is investigated in this work. The proposed finite element rotor model takes into account the geometric asymmetry of shaft and/or rigid disk and considers six types of base deterministic motions (rotations and translations) and non-linear fluid film forces obtained from the Reynolds equation. The equations of motion contain time-varying parametric coefficients because of the geometric asymmetry of the rotor and the base rotations. In the case when sinusoidal excitations of the rotor base lead to periodic (harmonic and sub-harmonic) responses, an optimized shooting algorithm based on the non-linear Newmark time integration scheme is employed to solve the equations of motion. The non-linear phenomena observed in the on-board rotor-bearing system, such as period-doubling motion and chaos, are characterized by means of bifurcation diagrams, rotor orbits and Poincaré maps.