Numerical Continuation of Equilibrium Point and Limit Cycles of a Rigid Rotor Supported by Floating Ring Bearings

Abstract

Today, floating ring bearings are commonly used in rotors of high-speed turbochargers because of their low cost and their vibration suppressing capability. Nevertheless, and similar to conventional hydrodynamic bearings, floating ring bearings may exhibit self-excited vibrations and become unstable above the instability threshold speed. In this paper, a nonlinear dynamic model of a perfectly balanced rigid rotor supported by two identical floating ring bearings is used to determine the rotor vibration behavior. The hydrodynamic forces are modeled by applying the short bearing theory and the half Sommerfeld conditions for both fluid films. Numerical continuation is applied to determine stable or unstable limit cycles bifurcating from the equilibrium point at the Hopf bifurcation. This paper shows that the stable limit cycles undergo a single limit point bifurcation however no bifurcation is predicted for the unstable limit cycles.KeywordsFloating ring bearingNonlinear stability analysisbifurcations of limit cyclesNumerical continuation