Use of nonlinear journal-bearing impedance descriptions to evaluate linear analysis of the steady-state imbalance response for a rigid symmetric rotor supported by two identical finite-length hydrodynamic journal bearings at high eccentricities

Abstract

This paper concerns the investigation of validity limits of linear models in predicting rotor trajectory inside the bearing clearance for a rigid symmetric rotor supported by two identical journal bearings operating at high eccentricities.The inherent nonlinearity of hydrodynamic journal bearings becomes strong for eccentricities grater than 60% of the bearing clearance where most existing linear models are not able to accurately predict the rotor trajectory.The usefulness of nonlinear journal-bearing impedance description method in this investigation is due to the analytical formulations of the linearised bearing coefficients, and the analytical nonlinear bearing models. These analytically derived bearing coefficients do not require any numerical differentiation (or integration) and are therefore more accurate for large eccentricities. The analytically derived nonlinear bearing models markedly decrease the simulation time while valid for all L/D (length to diameter ratios) and all eccentricities.The results contained in this paper show that linear models derived from the nonlinear impedance descriptions of the Moes-cavitated (π-film) finite-length bearing can predict the steady-state imbalance response of a symmetric rigid rotor supported by two identical journal bearings at high eccentricities. This is, however, only the case when operating conditions are below the threshold speed of instability and when the system has period-one solutions. The error will become larger closer to the resonance speed.

Stability Analysis of the Rotor-Journal Bearing System Considering Shear and Gaseous Cavitation

“…Liu et al [10] proposed a calculation method of 16 dynamic coefficients considering the deformation of the lining and analyzed the influence of structural parameters such as eccentricity on the dynamic characteristics of bearings. However, the linear oil film force is only valid under the condition of small oil film whirling motion and is unacceptable for the prediction of large unbalanced responses or oil film whirling motion [11][12][13]. By iteratively solving the fluid dynamic pressure lubrication equation and the rotor dynamics equation, nonlinear transient analysis methods offer a more comprehensive approach to analyzing rotor stability and predicting central trajectories.…”

Dynamic characteristics of water-lubricated journal bearings

“…However, a comparative linear and nonlinear dynamic analysis of cylindrical journal bearing has shown that a linear model is found to deliver acceptable results at a relatively small shaft unbalance [7]. Meanwhile, linear models can predict the imbalance response only when operating conditions are below the instability threshold speed at high eccentricities [8]. In addition, the difference of linear and nonlinear hydrodynamic forces is relative to bearing structures [9].…”

“…Up to now, there are two possible modeling approaches for numerical solution of hydrodynamic flow issue of waterlubricated journal bearings: on the one hand, as listed above, there are models based on classical Reynolds equation [3][4][5][6][7][8][9]. However, low viscosity of water compared to oil increases Reynolds number drastically and makes these bearings prone to significant fluid inertia effects.…”