Investigation of Turbulence Effects on the Nonlinear Vibration of a Rigid Rotor Supported by Finite Length 2-Lobe and Circular Bearings

Abstract

AbstractThis study investigated the effect of turbulence on the nonlinear vibration of a symmetrical rigid rotor supported by two identical journal bearings. The bearings consisted of various length to diameter (L/D) ratio circular and 2-lobe bearings with differing pad preloads. Two turbulent (Ng–Pan–Elrod and Constantinescu model) and one laminar Reynolds equations were selected for comparison, and they were solved using a finite difference method to obtain nonlinear bearing forces. The nonlinear equations of motion for the rotor-bearing system were solved using a shooting method and arclength continuation to obtain limit cycles for each bearing configuration. Floquet multiplier analysis was then utilized to identify the stability of the obtained limit cycles. For the cases of the circular and 2-lobe bearing without pad preload, the turbulent Reynolds equations yielded a lower onset speed of instability and L/D ratio at which the bifurcation type changed from supercritical to subcritical than the laminar Reynolds equation. However, at higher pad preloads (preloads of 0.25 or 0.5), the turbulence effects increased the onset speed of instability, especially for L/D ratios > 0.7, and only supercritical bifurcation was observed. For all bearing configurations, the ratio of the limit cycle whirl frequency to shaft rotational speed for both turbulence bearing models was higher than that of the laminar bearing model, and the Ng–Pan–Elrod turbulence model always generated lower onset speed of instability than the Constantinescu model.