A Study of Lubricant Inertia Effects for Squeeze Film Dampers Incorporated into High-Speed Turbomachinery

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.

Vibration analysis of rotor-bearing system using polynomial interpolation for squeeze film damper models

“…This result occurs due to the presence of fluid inertia in the oil film, whose effect is significant when the journal eccentricity ratio becomes high and it could possibly change the direction of radial force from positive to negative. The same result has been previously reported in the literature [34]. The interpolation method underestimates the radial force for 25% around the critical speed, which leads to a higher displacement prediction as shown in Fig.…”

Application of Squeeze Film Dampers

“…In this work, different cavitation models have been tested. Two are based on the LCP, [27] and [28], and one is based on the Elrod's cavitation algorithm, [29]. All the models tested are effective in calculating the pressure distribution when the standard Reynolds equation is considered.…”

Squeeze film dampers supporting high-speed rotors: Fluid inertia effects

“…Firstly, equations (59) and (60) are integrated in the radial direction and the integration constants are determined by applying the velocity boundary conditions in equation (61) and the pressure boundary conditions at the axial ends of the SFD and the solution for the inertialess SFD parameters are determined as follows 21 …”

“…They have developed a finite difference numerical procedure to determine the SFD fluid film reaction forces. Additionally, they have incorporated the firstorder perturbation technique to provide expressions for the pressure distribution for SFDs executing small amplitude CCOs in the presence of the lubricant inertia effects 20,21 and numerically determined the solution by using finite difference approximation. The bulk flow model [22][23][24] is a supplementary numerical method that is incorporated to solve the thin film equations for SFDs.…”