scholarly journals Squeeze Film Dampers Executing Small Amplitude Circular-Centered Orbits in High-Speed Turbomachinery

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Sina Hamzehlouia ◽  
Kamran Behdinan
Keyword(s):  
Pressure Distribution ◽  
Small Amplitude ◽  
High Speed ◽  
Fluid Film ◽  
Distribution Model ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Squeeze Film Dampers ◽  
Reaction Forces

This work represents a pressure distribution model for finite length squeeze film dampers (SFDs) executing small amplitude circular-centered orbits (CCOs) with application in high-speed turbomachinery design. The proposed pressure distribution model only accounts for unsteady (temporal) inertia terms, since based on order of magnitude analysis, for small amplitude motions of the journal center, the effect of convective inertia is negligible relative to unsteady (temporal) inertia. In this work, the continuity equation and the momentum transport equations for incompressible lubricants are reduced by assuming that the shapes of the fluid velocity profiles are not strongly influenced by the inertia forces, obtaining an extended form of Reynolds equation for the hydrodynamic pressure distribution that accounts for fluid inertia effects. Furthermore, a numerical procedure is represented to discretize the model equations by applying finite difference approximation (FDA) and to numerically determine the pressure distribution and fluid film reaction forces in SFDs with significant accuracy. Finally, the proposed model is incorporated into a simulation model and the results are compared against existing SFD models. Based on the simulation results, the pressure distribution and fluid film reaction forces are significantly influenced by fluid inertia effects even at small and moderate Reynolds numbers.

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

2019 ◽  
Vol 234 (1) ◽  
pp. 18-32 ◽  
Author(s):  
Sina Hamzehlouia ◽  
Kamran Behdinan
Keyword(s):  
Thin Film ◽  
Pressure Distribution ◽  
Closed Form ◽  
Hydrodynamic Pressure ◽  
Fluid Film ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Thin Film Equations ◽  
Squeeze Film Dampers ◽  
Reaction Forces

This work represents closed-form analytical expressions for the operating parameters for short-length open-ended squeeze film dampers, including the lubricant velocity profiles, hydrodynamic pressure distribution, and lubricant reaction forces. The proposed closed-form expressions provide an accelerated calculation of the squeeze film damper parameters, specifically for rotordynamics applications. In order to determine the analytical solutions for the squeeze film damper parameters, the thin film equations for lubricant are introduced in the presence of the influence of lubricant inertia. Subsequently, two different analytical techniques, namely the momentum approximation method, and the perturbation method are applied to the thin film equations. Moreover, the solution for the lubricant flow equations are analytically determined to represent closed-form expressions for the hydrodynamic pressure distribution and the velocity component profiles in squeeze film dampers. Additionally, the expressions for the hydrodynamic pressure distribution are integrated over the journal surface, either numerically or analytically by using Booker’s integrals, to develop expressions for the fluid film reaction forces. Lastly, the developed squeeze film damper models are incorporated into simulation models in Matlab and Simulink®, and the results are compared against a well-established force coefficient model to verify the accuracy of the calculations. The results of the simulations verify the effect of the lubricant inertia components, namely the convective and temporal (i.e., unsteady) inertia components on the squeeze film damper dynamics, including hydrodynamic pressure distribution and fluid film reaction forces. Additionally, the simulation results suggest a close agreement between the proposed models and the results in the literature.

Dynamic Characterization of an Integral Squeeze Film Bearing Support Damper for a Supercritical CO2 Expander

2017 ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado ◽  
Jeffrey Moore
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Mechanical Impedance ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Damping Behavior ◽  
Impedance Testing ◽  
Stiffness And Damping ◽  
Onset Of Cavitation

The present work advances experimental results and analytical predictions on the dynamic performance of an integral squeeze film damper (ISFD) for application in a high-speed super-critical CO2 (sCO2) expander. The test campaign focused on conducting controlled orbital motion mechanical impedance testing aimed at extracting stiffness and damping coefficients for varying end seal clearances, excitation frequencies, and vibration amplitudes. In addition to the measurement of stiffness and damping; the testing revealed the onset of cavitation for the ISFD. Results show damping behavior that is constant with vibratory velocity for each end seal clearance case until the onset of cavitation/air ingestion, while the direct stiffness measurement was shown to be linear. Measurable added inertia coefficients were also identified. The predictive model uses an isothermal finite element method to solve for dynamic pressures for an incompressible fluid using a modified Reynolds equation accounting for fluid inertia effects. The predictions revealed good correlation for experimentally measured direct damping, but resulted in grossly overpredicted inertia coefficients when compared to experiments.

Extended Finite Element Analysis of Journal Bearing Dynamic Forced Performance to Include Fluid Inertia Force Coefficients

2012 ◽  
Author(s):  
Luis San Andrés
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Small Amplitude ◽  
Forced Response ◽  
Inertia Force ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Force Coefficients ◽  
Reaction Forces ◽  
Bearing Stiffness

Reynolds equation governs the generation of hydrodynamic pressure in oil lubricated fluid film bearings. The static and dynamic forced response of a bearing is obtained from integration of the film pressure on the bearing surface. For small amplitude journal motions, a linear analysis represents the fluid film bearing reaction forces as proportional to the journal center displacements and velocity components through four stiffness and four damping coefficients. These force coefficients are integrated into rotor-bearing system structural analysis for prediction of the system stability and the synchronous response to imbalance. Fluid inertia force coefficients, those relating reaction forces to journal center accelerations, are routinely ignored because most oil lubricated bearings operate at relatively low Reynolds numbers, i.e., under slow flow conditions. Modern rotating machinery operates at ever increasing surface speeds to deliver more power in smaller size units. Under these operating conditions fluid inertia effects need to be accounted for in the forced response of oil lubricated bearings, as recent experimental test data also reveal. The paper presents a finite element formulation to predict added mass coefficients in oil lubricated bearings by extending a basic formulation that already calculates the bearing stiffness and damping force coefficients. That is, a small amplitude perturbation analysis of the lubrication flow equations keeps the temporal fluid inertia effects and develops a set of equations to obtain the bearing stiffness, damping and inertia force coefficients. The method does not impose on the cost of the original formulation which makes it very attractive for ready implementation in existing software. Predictions of the computational model are benchmarked against archival test data for an oil-lubricated pressure dam bearing supporting large compressors. The comparisons show fluid inertia effects cannot be ignored for operation at high rotor speeds and with small static loads.

scholarly journals Squeeze-Film Damper Technology: Part 1 — Prediction of Finite Length Damper Performance

1983 ◽  
Author(s):  
J. W. Lund ◽  
A. J. Smalley ◽  
J. A. Tecza ◽  
J. F. Walton
Keyword(s):  
Finite Length ◽  
Gas Turbines ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Strongly Coupled ◽  
Squeeze Film Damper ◽  
Rotor Systems ◽  
Squeeze Film Dampers ◽  
Calculation Results

Squeeze-film dampers are commonly used in gas turbine engines and have been applied successfully in a great many new designs, and also as retrofits to older engines. Of the mechanical components in gas turbines, squeeze-film dampers are the least understood. Their behavior is nonlinear and strongly coupled to the dynamics of the rotor systems on which they are installed. The design of these dampers is still largely empirical, although they have been the subject of a large number of past investigations. To describe recent analytical and experimental work in squeeze-film damper technology, two papers are planned. This abstract outlines the first paper, Part 1, which concerns itself with squeeze-film damper analysis. This paper will describe an analysis method and boundary conditions which have been developed recently for modelling dampers, and in particular, will cover the treatment of finite length, feed and drain holes and fluid inertia effects, the latter having been shown recently to be of great importance in predicting rotor system behavior. A computer program that solves the Reynolds equation for the above conditions will be described and sample calculation results presented.

First Order Perturbation Technique for Squeeze Film Dampers Executing Small Amplitude Circular Centered Orbits With Aero-Engine Application

2016 ◽  
Author(s):  
Sina Hamzehlouia ◽  
Kamran Behdinan
Keyword(s):  
Pressure Distribution ◽  
Small Amplitude ◽  
Slenderness Ratio ◽  
Order Perturbation ◽  
Squeeze Film ◽  
Zeroth Order ◽  
Flow Equations ◽  
First Order ◽  
Squeeze Film Dampers ◽  
First Order Perturbation

This work develops inertial expressions for the lubricant pressure distribution and fluid velocity components for squeeze film dampers (SFDs) executing small amplitude circular centered orbits (CCO), by applying a first order perturbation to the fluid equations. For small amplitude motions of the journal center, it is assumed that the fluid convective inertia terms are negligible relative to the unsteady (temporal) inertia terms. Firstly, a first order perturbation is applied to the pressure and velocity components in the flow equations. Subsequently, the flow equations are solved for the zeroth-order (i.e. non-inertial) velocities and the first-order (i.e. inertial) velocities. The velocity components are incorporated into the flow equations to develop separate expressions for the zeroth-order and the first order pressures. Furthermore, the pressure expressions are numerically solved by applying finite difference approximations to the equations. Finally, a simulation model is developed to determine the lubricant pressure distribution and fluid film reaction forces for different damper operating parameters, including Reynold’s number (i.e. inertia effect), journal eccentricity ratio, and bearing slenderness ratio.

scholarly journals Effects of Fluid Inertia and Turbulence on the Force Coefficients for Squeeze Film Dampers

1986 ◽  
Vol 108 (2) ◽  
pp. 332-339 ◽  
Author(s):  
L. San Andre´s ◽  
J. M. Vance
Keyword(s):  
Squeeze Film ◽  
Fluid Inertia ◽  
High Eccentricity ◽  
Small Eccentricity ◽  
Inertia Effects ◽  
Force Coefficients ◽  
Inertia Coefficient ◽  
Squeeze Film Dampers ◽  
Order Of Magnitude ◽  
Large Eccentricity

The effects of fluid inertia and turbulence on the force coefficients of squeeze film dampers are investigated analytically. Both the convective and the temporal terms are included in the analysis of inertia effects. The analysis of turbulence is based on friction coefficients currently found in the literature for Poiseuille flow. The effect of fluid inertia on the magnitude of the radial direct inertia coefficient (i.e., to produce an apparent “added mass” at small eccentricity ratios, due to the temporal terms) is found to be completely reversed at large eccentricity ratios. The reversal is due entirely to the inclusion of the convective inertia terms in the analysis. Turbulence is found to produce a large effect on the direct damping coefficient at high eccentricity ratios. For the long or sealed squeeze film damper at high eccentricity ratios, the damping prediction with turbulence included is an order of magnitude higher than the laminar solution.

Experimental Pressures and Film Forces in a Squeeze Film Damper

1993 ◽  
Vol 115 (1) ◽  
pp. 134-140 ◽  
Author(s):  
G. L. Arauz ◽  
L. A. San Andres
Keyword(s):  
Tangential Force ◽  
Radial Force ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Fluid Inertia ◽  
Damping Force ◽  
Inertia Effects ◽  
Squeeze Film Dampers ◽  
Tangential Forces ◽  
Lubricant Viscosity

The effect of whirl frequency and lubricant viscosity on the dynamic pressures and force response of an open end and a partially sealed squeeze film dampers (SFD) with a radial clearance of 0.38 mm is determined experimentally. The experiments are carried out in a damper test rig executing circular centered orbits and for whirl frequencies ranging from 33 to 83 Hz. The experimental results show that the sealed SFD configuration produces larger tangential forces than the open end SFD. The tangential (damping) force increases linearly with increasing whirl frequency. For this radial clearance fluid inertia effects in the damper are found to be negligible since the squeeze film Reynolds number is less than 1.20. Cavitation was observed in both damper configurations at high frequencies and high lubricant viscosities. This condition limited the rate of increment of the damping (tangential) force with increasing frequency and reduced the radial force when lubricant viscosity increased.

The Effect of Fluid Inertia in Squeeze Film Damper Bearings: A Heuristic and Physical Description

1983 ◽  
Author(s):  
John A. Tichy
Keyword(s):  
Hydrodynamic Lubrication ◽  
Turbulence Models ◽  
Squeeze Film ◽  
Squeezing Flow ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Practical Applications ◽  
Viscous Forces ◽  
Squeeze Film Dampers ◽  
Inertia Forces

Fluid inertia forces are comparable to viscous forces in squeeze film dampers in the range of many practical applications. This statement appears to contradict the commonly held view in hydrodynamic lubrication that inertia effects are small. Upon closer inspection, the latter is true for predominantly sliding (rather than squeezing) flow bearings. The basic equations of hydrodynamic lubrication flow are developed, including the inertia terms. The appropriate orders of magnitude of the viscous and inertia terms are evaluated and compared, for journal bearings and for squeeze film dampers. Exact equations for various limiting cases are presented: low eccentricity, high and low Reynolds number. The asymptotic behavior is surprisingly similar in all cases. Due to inertia, the damper force may shift 90° forward from its purely viscous location. Inertia forces are evaluated for typical damper conditions. The effect of turbulence in squeeze film dampers is also discussed. On physical grounds it is argued that the transition occurs at much higher Reynolds numbers than the usual lubrication turbulence models predict.

Theoretical and Experimental Comparisons for Damping Coefficients of a Short-Length Open-End Squeeze Film Damper

1996 ◽  
Vol 118 (4) ◽  
pp. 810-815 ◽  
Author(s):  
L. A. San Andres
Keyword(s):  
High Speed ◽  
Mechanical Energy ◽  
Short Length ◽  
Fluid Film ◽  
Squeeze Film ◽  
Absolute Pressure ◽  
Dynamic Force ◽  
Fluid Inertia ◽  
Squeeze Film Damper ◽  
Damping Coefficients

Squeeze film dampers (SFD) provide load isolation and attenuate rotor vibrations in high speed turbomachinery. Operating parameters such as whirl frequency, amplitude of journal motion, and value of external pressure supply determine the SFD dynamic force response and its dissipation of mechanical energy. Measurements of pressure fields and fluid film forces in a fully submerged open-end squeeze film damper are presented for tests with rotor speeds to 5000 cpm and low supply pressures. The damper has a clearance of 381 µm (0.015 in.) and the journal describes circular centered orbits of amplitudes ranging from 30 to 50 percent of the bearing clearance. Experimental film pressures depict a vapor cavitation (close to zero absolute pressure) zone increasing in extent as the whirl frequency increases. Estimated fluid film forces from the measured pressure profiles are found to be proportional to whirl speed and lubricant viscosity. Test cross-coupled damping coefficients (Crt) are smaller than predicted values based on the short-length bearing model with a π film cavitation assumption. The direct damping coefficients (Ctt) are larger than theoretical values, especially at low frequencies where the dynamic cavitation region has not grown to half the circumferential flow extent. The experiments demonstrate the viscous character of the fluid film forces in a SFD test apparatus where fluid inertia effects are minimal (squeeze film Reynolds number less than one). On the other hand, the extent of the cavitation zone appears to be dominant on the generation of fluid film forces.

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