Chaotic response of a short journal bearing

Abstract

The non-linear response of fluid-film bearings has been studied for nearly 40 years. Apart from a paper on aperiodic behaviour by Holmes et al. in 1978, much of the work has concentrated on limit cycle behaviour and the practical bounds of linear models. Brindley et al. in 1990 examined the free vibration of a rigid rotor supported by a short bearing oil film. Numerical integration of the equations of motion demonstrated the existence of both large and small limit cycles at operating conditions close to the stability boundary. Hopf bifurcations were shown to exist using a theoretical method. Brindley et al. clearly recognized that the inclusion of unbalance in the model would produce a wider range of behaviour but no results were presented. In recent years the chaotic response of many non-linear systems has received much attention. The main requirements for chaos in a dynamic system are sufficient non-linearity and a minimum of three first-order differential equations. These conditions are satisfied by a rigid journal supported on a hydrodynamic bearing film operating at a high eccentricity. At moderate levels of unbalance the bearing is stable and the behaviour is approximated by a linear treatment. Nevertheless, when the rotating unbalance force exceeds the static load, the bearing is intermittently unloaded and chaos can result. In this paper the region of interest is bounded by three parameters, the dynamic-static force ratio, the operating eccentricity and the non-dimensional frequency ω √ C/g, the latter an established measure of stability. For values of ω √ C/g above 2.5, and eccentricity ratios greater than 0.65 a region of chaos is established for a moderate range of dynamic-static force ratio values. If the unbalance is increased further, the response again becomes periodic, as might be expected. There is a possibility that turbomachinery with heavily loaded bearings may experience chaotic behaviour.