Stability Analysis of Rotor-Bearing Systems under the Influence of Misalignment and Parameter Uncertainty

Abstract

Stability is a well-known challenge for rotating systems supported by hydrodynamic bearings (HDBs), particularly for the condition where the misalignment effect and the parametric uncertainty are considered. This study investigates the impact of misalignment and inherent uncertainties in bearings on the stability of a rotor-bearing system. The misalignment effect is approximately described by introducing two misaligned angles. The characteristics of an HDB, such as pressure distribution and dynamic coefficients, are calculated by the finite difference method (FDM). The stability threshold is evaluated as the intersection of run-up curve and borderline. Viscosity and clearance are considered as uncertain parameters. The generalized polynomial chaos (gPC) expansion is adopted to quantify the uncertainty in parameters by evaluating unknown coefficients. The unknown gPC coefficients are obtained by using the collocation method. The results obtained by the gPC expansion are compared with those of the Monte Carlo (MC) simulation. The results show that the characteristics of the HDB and the stability threshold are affected by misalignment and parameter uncertainties. As the uncertainty analysis using the gPC expansion is performed on a relatively small number of predefined collocation points compared with the large number of MC samples, the method is very efficient in terms of computation time.

A state-of-the-art review on uncertainty analysis of rotor systems

“…Most importantly, nearly all commonly used bearings in rotor systems, e.g., journal/slider bearings, rolling element bearings and active magnetic bearings (AMB) are exposed to uncertainties and they have become the special focuses of many researchers. Journal bearings operate with lubricant fluid forces to support the rotating shaft, which is significantly dependent on the loads, rotating speed and lubricant viscosity [53][54][55]. The latter has a strong relationship with lubricant temperature and the temperature can be difficult to control.…”

“…To clarify key issues in the stochastic rotor systems, many works have been carried out based on the applications of the PCE [45,55,92,94,156,202]. Sarrouy et al [18] presented the stochastic Campbell diagram and the corresponding mode shape variability based on the PCE with 10 % dispersions in the density of a disc, as shown in Fig.…”

“…The dynamics of rotor systems under the fuzzy or random uncertainties associated with different kinds of bearings are the most heated research topics [53][54][55]60,103,104,108,111,117,195,[217][218][219][220][221][222][223], among which the journal bearings are major focuses of many researchers. For uncertainties in journal bearings, three main points were generally investigated, i.e., the rough surfaces, radial clearance and lubricant viscosity (caused by lubricant temperature variations).…”

“…Therefore, it is appropriate to introduce uncertainty representations for robust dynamic analysis. Sun et al [109] investigated the stability of an uncertain rotor supported on misaligned journal bearings and demonstrated that the stability threshold increases with misaligned angles. As shown in Fig.…”

Stochastic Analysis of Lubrication in Misaligned Journal Bearings

“…Ideally, the rotary shaft will be perfectly aligned with the bearing centerline and the oil film provides expected hydrodynamic lubrication [4,5]. However, it is recognized in practice that there is always a certain degree of misalignment between the journal and bush causing them to be unparallel [6,7]. The reasons for it vary from shaft deformation due to external load, inappropriate assembling, manufacturing error, and thermal effects.…”