Nonlinear Vibration of Saturated Water Journal Bearing and Bifurcation Analysis

Abstract

We developed a turbo compressor that has water-lubricated bearings driven at 30,000 rpm in a saturation condition, where the ambient pressure is at the saturation point of the discharged lubricant water. The bearings are supported with nonlinear elastomeric O-rings. At rotational speed exceeding 15,000 rpm, the rotor showed many subharmonic vibrations that are nonlinear phenomena unpredictable from a linear equation of motion. Instead, a stability analysis with a bifurcation diagram is an effective method to tackle these problems. In this paper, we investigated these rotor vibrations by bifurcation diagrams of the vibrations measured in experiments of saturated water journal bearings. The angular velocity was used as a bifurcation parameter. The bifurcations among synchronous, subharmonic, and chaotic vibrations were shown. Next, the nonlinear dynamics of the rotating rigid shaft were analyzed numerically with the nonlinear stiffness obtained by a commercial code that utilizes the two-dimensional (2D) Reynolds equation. The dynamic properties of the supporting structure were modeled with a complex stiffness coefficient. As a result, a Hopf bifurcation was found and a subharmonic limit cycle appeared spontaneously as observed in the experiments. The parametric studies revealed the influences of the dynamic properties of the structural components, especially the sensitive effect of the damping of the bearing support on the onset frequency and the amplitude of these vibrations. Furthermore, linear eigenvalue analysis of the motion equations clarified the mechanism of the sensitive effects.