Analysis of a rotor-bearing nonlinear system model considering fluid-induced instability and uncertainties in bearings

Abstract

In the analysis of rotating systems supported by hydrodynamic bearings, linear models and synchronous responses usually suffice. However, in some respects this type of approach fails to correctly describe these machine’s dynamic behaviour. Fluid-induced instabilities known as “oil whirl” and “oil whip,” in which unstable motion and residual unbalance cause a precessional vibration in the rotor system, are two conditions that point to the shortcomings of linear models. Furthermore, rotor-bearing systems possess inherent uncertainties, which a more reliable model must take into consideration. In this sense, a stochastic solution may be more adequate, and the traditional deterministic model should not be directly applied. Meanwhile, Monte Carlo simulation has a high computational cost, and deterministic problem solution for complex systems—such as rotating machinery modelling—requires a long period of evaluation. Thus, a method able to achieve better computational efficiency while remaining as convergent as Monte Carlo is necessary. Rotating machines under these conditions can be described by means of a nonlinear journal bearing model, and Monte Carlo can still be used to evaluate this stochastic solution, since it allows for the application of deterministic solvers. In this study, generalized polynomial chaos expansion was employed to analyse a rotor-bearing system’s stochastic response, and the stochastic collocation method was used to evaluate expansion coefficients. A convergence comparison between stochastic collocation and Monte Carlo simulations was performed, in order to validate the usage of polynomial approximation. Then, a sensitivity analysis was performed to determine which random parameter had the most effect over the system’s stochastic response. This analysis allowed for the identification of distinct rotational velocity regions of instability. Nonlinear characteristics presented themselves in the stochastic approach as well as in the deterministic models. Difficulties in analysing the sub-synchronous response by means of the proposed approach are discussed.