In the present paper the conditions that give rise to chaotic motions in a rigid rotor on short journal bearings are investigated and determined. A suitable symmetry was given to the rotor, to the supporting system, to the acting system of forces and to the system of initial conditions, in order to restrict the motions of the rotor to translatory whirl. For an assigned distance between the supports, the ratio between the transverse and the polar mass moments of the rotor was selected conveniently small, with the aim of avoiding conical instability. Since the theoretical analysis of a system's chaotic motions can only be carried out by means of numerical investigation, the procedure here adopted by the authors consists of numerical integration of the rotor's equations of motion, with trial and error regarding the three parameters that characterise the theoretical model of the system: m, the half non-dimensional mass of the rotor, σ, the modified Sommerfeld number relating to the lubricated bearings, and ρ, the dimensionless value of rotor unbalance. In the rotor's equations of motion, the forces due to the lubricating film are written under the assumption of isothermal and laminar flow in short bearings. The number of numerical trials needed to find the system's chaotic responses has been greatly reduced by recognition of the fact that chaotic motions become possible when the value of the dimensionless static eccentricity εsis greater than 0.4. In these conditions, non-periodic motions can be obtained even when rotor unbalance values are not particularly high (ρ = 0.05), whereas higher values (ρ > 0.4) make the rotor motion periodic and 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 ρ. The theoretical results obtained have then been compared with experimental data. Both the theoretical and the experimental data have pointed out that in the circumstances investigated chaotic motions deserve more attention, from a technical point of view, than is normally ascribed to behaviours of this sort. This is mainly because such behaviours are usually considered of scarce practical significance owing to the typically bounded nature of chaotic evolution. The present 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 conditions the thickness of the lubricating film can assume values that are extremely 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

An experiment was carried out to investigate the distribution of oil pressure within a squeeze film damper. The damper was made so that its operation turned out to be as simple as possible, in order to highlight the main causes of practical deviation from theoretical prediction, with particular reference to cavitating mechanisms and regardless of inertia effects. The journal of the damper was given an eccentric orbital precession, with adoption of two distinct values of the offset. A groove placed laterally to the film secured the oil feeding. An outlet plenum at the opposite side of the film was operated with two different levels of exposure to the ambient air. Observation of the oil pressure was restricted to the film section midway between the inlet and outlet border, by means of three piezoelectric transducers plus a strain gage sensor. Theoretical prediction with a simple isoviscous short bearing uncavitated model was shown to be a significant reference for the experimental data. Analysis of the pressure levels and shape of the pressure waves made it possible to recognize operating conditions with the presence of tensile stresses and rupture of the film. The latter conditions were chiefly due to vapour cavitation. Spikes with tensile strength preceded in many circumstances the ruptured region. Air entrainment and its effects proved to be restricted at high frequency regimes with very low supply pressures and coexisted with vapour cavitation. The influence of moderate orbital distortion on pressure signals was highlighted. Significant differences in the pressure behaviour from one sensor location to the other, for the same operating conditions, were frequently observed

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The conditions that give rise to non-periodic motions of a Jeffcott rotor in the presence of non-linear elastic restoring forces are examined. It is well known that non-periodic behaviours that characterise the dynamics of a rotor are fundamentally a consequence of two aspects: the non-linearity of the hydrodynamic forces in the lubricated bearings of the supports and the non-linearity that affects the elastic restoring forces in the shaft of the rotor. In the present research the analysis was restricted to the influence of the non-linearity that characterises the elastic restoring forces in the shaft, adopting a system that was selected the simplest as possible. This system was represented by a Jeffcott rotor with a shaft of mass that was negligible respect to the one of the disk, and supported with ball bearings. In order to check in a straightforward manner the non-linearity of the system and to confirm the results obtained through theoretical analysis, an investigation was carried out using an experimental model consisting of a rotating disk fitted in the middle of a piano wire pulled taut at its ends but leaving the tension adjustable. The adopted length/diameter ratio was high enough to assume the wire itself was perfectly flexible while its mass was negligible compared to that of the disk. Under such hypotheses the motion of the disk centre can be expressed by means of two ordinary, non-linear and coupled differential equations. The conditions that make the above motion non-periodic or chaotic were found through numerical integration of the equations of motion. A number of numerical trials were carried out using a 4th order Runge-Kutta routine with adaptive stepsize control. This procedure made it possible to plot the trajectories of the disk centre and the phase diagrams of the component motions, taken along two orthogonal coordinate axes, with their projections of the Poincaré sections. On the basis of the theoretical results obtained, the conditions that give rise to non-periodic motions of the experimental rotor were identified