Stability Analysis Of Bearings Research Articles

Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings

The purpose of this paper is to analyze the influence of turbulent, inertia, and misaligned effects on the static and dynamic characteristics and stability of high-speed water-lubricated hydrodynamic journal bearings. Based on the Navier–Stokes equation, the mixing-length theory, and the essential assumption that the velocity profile is not strongly affected by inertia force, the fluid lubrication model with turbulent, inertia, and misaligned effects is established, and then the stability analysis of bearings is carried out based on the equation of motion with four degrees of freedom. The model is solved by the finite difference method and the numerical results are compared under different operating conditions. The results show that the turbulent effect greatly increases the load capacity, power consumption, stiffness and damping coefficients, and stability of bearings, and the inertia effect significantly increases the volume flow rate of bearings, and the misaligned effect increases the load capacity, stiffness and damping coefficients, and stability of bearings. In high rotary speed and moderate eccentricity ratios, the influence of the inertia effect on the load capacity, stiffness coefficients, and stability cannot be neglected.

Non-linear stability analysis of floating ring bearings using Hopf bifurcation theory

Floating ring bearings are used to support and guide rotors in several high-speed rotating machinery applications. They are usually credited for lower heat generation and higher vibration suppressing ability. Similar to conventional hydrodynamic bearings, floating ring bearings may exhibit unstable behaviour above a certain stability critical speed. Linear stability analysis is usually applied to predict the stability threshold speed. Non-linear stability analysis, however, is needed to predict the presence and the size of stable limit cycles above the stability threshold speed or unstable limit cycles below the stability critical speed. The prediction of limit cycles is an important step in bearing stability analysis. In this article, a non-linear dynamic model is derived and used to investigate the stability of a perfectly balanced symmetric rigid rotor supported by two identical floating ring bearings near the critical stability boundaries. The fluid film hydrodynamic reactions of the floating ring bearings are modelled by applying the short bearing theory and the half Sommerfeld solution. Hopf bifurcation theory is then utilized to determine the existence and the approximate size of stable and unstable limit cycles in the neighbourhood of the stability critical speed depending on the bearing design parameters. Numerical integration of the non-linear equations of motion is then carried out in order to compare the trajectories obtained by numerical integration to those obtained analytically using Hopf bifurcation analysis. Stability boundary curves for typical bearing design parameters have been decomposed into boundaries with supercritical stable limit cycles and boundaries with subcritical unstable limit cycles. The shape and size of the limit cycles for selected bearing parameters are presented using both analytical and numerical approaches. This article shows that floating ring stability boundaries may exhibit either stable supercritical limit cycles or unstable subcritical limit cycles predictable by Hopf bifurcation.