Nonlinear Vibration of a Saturated Water Journal Bearing and Bifurcation Analysis

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. Such a saturated water journal bearing is located at both end of the rotor, each of which has a conical part to produce thrust force without another thrust bearing or a thrust collar. The bearings are supported with nonlinear elastomeric O-rings. At rotational speed over 15,000 rpm, the rotor showed many sub-harmonic 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, sub-harmonic, 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 Reynolds equation. The dynamic properties of the supporting structure were modeled with a complex stiffness coefficient. The equation of motion of the rotating shaft was solved numerically in a time domain with these dynamic properties. MATLAB Simulink code was built to integrate the equations. As a result, a Hopf bifurcation was found and a sub-harmonic limit cycle appeared spontaneously. The rotational speed and such other properties as the unbalanced force and the damping of the supporting structures were parameterized to investigate the onset and the amplitude of these vibrations. These numerical results agreed well with the experimental results.