Abstract
This work proposes a numerical model that incorporates the effect of lubricant inertia on the hydrodynamic pressure distribution, fluid film reaction forces, and the fluid velocity component profiles for finite-length open-ended squeeze film dampers (SFDs). Firstly, the thin film flow equations for the SFD in presence of fluid inertia effects are introduced. Furthermore, a small first-order perturbation by means of the expressions for the fluid film velocity components and the lubricant pressure distribution that are expanded in power series of the squeeze film Reynolds number is applied to the flow equations. Subsequently the developed lubricant flow equations are solved to develop expressions for the velocity component profiles and the hydrodynamic pressure distribution in SFDs. The pressure expression is numerically solved by using Gauss–Seidel method with finite difference discretization. Moreover, the fluid film reaction forces are determined by numerically integrating the hydrodynamic pressure expressions over the journal surface. Additionally, the proposed pressure distribution expression and the numerical SFD forces are incorporated into a simulation model and the simulation results are compared with the existing models in the literature under different operating conditions, including eccentricity ratios and inertia effects (i.e., Reynolds numbers). The simulation results demonstrate the significant influence of both convective and temporal (i.e., unsteady) lubricant inertia terms on the SFD hydrodynamic pressure distribution and the fluid film reaction forces. Furthermore, the proposed SFD model is incorporated into a multi-mass flexible rotordynamic model to evaluate the effect of SFD fluid inertia on the mass unbalance induced steady-state vibrations of the rotor and the nodal transient orbits by implementing finite element method and transient modal integration with predictor–corrector solver. The results of the analysis demonstrate the significant effect of fluid inertia on the resonance frequencies of the rotor and the steady-state vibration amplitudes and the transient orbits at the resonance zone.
Highlights
Unbalance induced vibrations are the main source of structural vibrations in high-speed turbomachinery
The results of the analysis demonstrate the significant effect of fluid inertia on the resonance frequencies of the rotor and the steady-state vibration amplitudes and the transient orbits at the resonance zone
In order to investigate the contribution of convective inertia on the SFD dynamics, the results of the simulations are compared against [24], where the effect fluid inertia is described for SFDs executing small-amplitude circular-centered orbits (CCOs)
Summary
Unbalance induced vibrations are the main source of structural vibrations in high-speed turbomachinery. The precedent studies assumed that the effect of lubricant inertia on the fluid film reaction forces in SFDs is negligible and either used the complete or the approximate (i.e., long bearing and short bearing approximations) Reynolds equation to represent the SFD dynamics. This work proposes a numerical model that represents the effect of lubricant inertia on the hydrodynamic pressure distribution, fluid film reaction forces, and the fluid velocity component profiles for finite-length open-ended squeeze film dampers (SFDs). The proposed models in this work are powerful tools that provide precise and accelerated evaluation of the SFD hydrodynamic pressure distribution, velocity profiles, and fluid film reaction forces, for application in rotordynamic models as well as the study of the effect of lubricant cavitation and lubricant temperature variation on the damping effectiveness of SFDs. The following sections describe the derivation of the analytical pressure and velocity expressions. The proposed SFD model is incorporated into a flexible multi-mass rotordynamics model, to determine the effect of SFD lubricant inertia on the transient orbits and the steady-state unbalance induced vibrations of rotor systems
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