Hopf bifurcation to a short porous journal-bearing system using the Brinkman model: weakly nonlinear stability

On the basis of the Brinkman model, the weakly nonlinear stability characteristics of short porous journal-bearing systems are presented. By applying the Hopf bifurcation theory, the weakly nonlinear behaviors near the critical stability boundary are predicted. According to results, the onset of oil whirl for porous bearings is a bifurcation phenomenon; it can exhibit supercritical limit cycles or subcritical limit cycles for journal speeds in the vicinity of the bifurcation point. With a fixed permeability parameter, such supercritical limit cycles for journal speeds in excess of the threshold speed are confined to a specific region in the (ω, ϵs) plane; and outside this region subcritical limit cycles exist for journal speeds below the threshold speed. In addition, increasing the value of system parameter, Sp, may change supercritical bifurcation into the more complicated subcritical bifurcation.