Hopf Bifurcation to Limit Cycles in Fluid Film Bearings

Abstract

The nonlinear response of a cylindrical journal bearing operating close to the critical speed stability boundary is studied in this paper. Using linear stability theory, the value of the critical variable (usually speed) at the point of loss of stability is obtained and shown to agree with results of previous researchers. Using Hopf bifurcation analysis, parameters for determining the behavior close to this point are obtained. Analytically, these parameters prove that the system can exhibit stable limit cycles for speeds above the critical speed. Such supercritical limit cycles only exist for a narrow range of values of modified Sommerfeld number. In other cases, subcritical limit cycles are predicted. The results are supported by numerical simulation. The results show why it may be difficult to observe supercritical limit cycles in test rigs.