Stochastic analysis of flexible rotor supported on hydrodynamic bearings

Rotating shaft instability leading to high amplitude vibration is a key problem with a wide range of industrial applications. The purpose of this study is to identify the response statistics for a conceptual model of a flexible shaft supported on hydrodynamic bearings (HDBs) and propose design strategies to reduce the response. A conceptual model of a flexible shaft with three discs supported on the HDBs is developed. A linearised model of the system is developed using the short bearing assumption. A Campbell diagram is developed for the conceptual model to identify the critical speeds wherein a high response is produced. These high responses occur at the rotor speeds corresponding to the synchronous forward whirl and the oil whip. The identified rotor speeds are validated by carrying out a run-up analysis on the test rig. Since the manufacturing process and operating conditions induce uncertainty by varying the eccentricity and the relative phase of the unbalance mass, the influence of the whirling modes on the response is investigated. The nominal positions of the unbalance masses are such that the predominant mode excited is the first mode. Experimentally a scatter plot on the maximum response at the bearing location is identified using six different positions of the eccentric mass. Further, a stochastic analysis using reduced order nonlinear model of the system is carried out. The probability density obtained is compared with a Monte Carlo simulation and the bounds of the experimental results. A control strategy is designed by altering the relative position of the unbalance masses to reduce the excitation of the first mode. The robustness of the strategy is verified by using a stochastic analysis, which indicates a reduction in the response magnitude.