CHAOTIC MOTIONS OF A RIGID ROTOR IN SHORT JOURNAL BEARINGS

In the present paper the conditions that give rise to chaotic motions in a rigid rotor on short journal bearings are investigated and determ ined. A suitable symmetry was given to the rotor, to the supporting sy stem, to the acting system of forces and to the system of initial cond itions, in order to restrict the motions of the rotor to translatory w hirl. For an assigned distance between the supports, the ratio between the transverse and the polar mass moments of the rotor was selected c onveniently small, with the aim of avoiding conical instability. Since the theoretical analysis of a system's chaotic motions can only be ca rried out by means of numerical investigation, the procedure here adop ted by the authors consists of numerical integration of the rotor's eq uations of motion, with trial and error regarding the three parameters that characterise the theoretical model of the system: m, the half no n-dimensional mass of the rotor, sigma, the modified Sommerfeld number relating to the lubricated bearings, and rho, the dimensionless value of rotor unbalance. In the rotor's equations of motion, the forces du e to the lubricating him are written under the assumption of isotherma l and laminar flow in short bearings. The number of numerical trials n eeded to find the system's chaotic responses has been greatly reduced by recognition of the fact that chaotic motions become possible when t he value of the dimensionless static eccentricity epsilon(s) is greate r than 0.4. In these conditions, non-periodic motions can be obtained even when rotor unbalance values are not particularly high (rho = 0.05 ), whereas higher values (rho > 0.4) make the rotor motion periodic an d synchronous with the driving rotation. The present investigation has also identified the route that leads an assigned rotor to chaos when its angular speed is varied with prefixed values of the dimensionless unbalance rho. The theoretical results obtained have then been compare d with experimental data. Both the theoretical and the experimental da ta have pointed out that in the circumstances investigated chaotic mot ions deserve more attention, from a technical point of view, than is n ormally ascribed to behaviours of this sort. This is mainly because su ch behaviours are usually considered of scarce practical significance owing to the typically bounded nature of chaotic evolution. The presen t analysis has shown that when the rotor exhibits chaotic motions, the centres of the journals describe orbits that alternate between small and large in an unpredictable and disordered manner. In these conditio ns the thickness of the lubricating film can assume values that are ex tremely low and such as to compromise the efficiency of the bearings, whereas the rotor is affected by inertia forces that are so high as to determine severe vibrations of the supports.