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.

scholarly journals Measurements of Squeeze Film Bearing Forces to Demonstrate the Effect of Fluid Inertia

1984 ◽  
Author(s):  
John A. Tichy
Keyword(s):  
Dynamic Systems ◽  
High Speed ◽  
Hydrodynamic Lubrication ◽  
Reynolds Numbers ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Viscous Forces ◽  
Rotor Dynamic ◽  
Inertia Forces

Squeeze film dampers are commonly applied to high speed rotating machinery, such as aircraft engines, to reduce vibration problems. The theory of hydrodynamic lubrication has been used for the design and modeling of dampers in rotor dynamic systems despite typical modified Reynolds numbers in applications between ten and fifty. Lubrication theory is strictly valid for Reynolds numbers much less than one, which means that fluid viscous forces are much greater than inertia forces. Theoretical papers which account for fluid inertia in squeeze films have predicted large discrepancies from lubrication theory, but these results have not found wide acceptance by workers in the gas turbine industry. Recently, experimental results on the behavior of rotor dynamic systems have been reported which strongly support the existence of large fluid inertia forces. In the present paper direct measurements of damper forces are presented for the first time. Reynolds numbers up to ten are obtained at eccentricity ratios 0.2 and 0.5. Lubrication theory underpredicts the measured forces by up to a factor of two (100% error). Qualitative agreement is found with predictions of earlier improved theories which include fluid inertia forces.

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.

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.

A simple expression for fluid inertia force acting on micro-plates undergoing squeeze film damping

2010 ◽  
Vol 467 (2126) ◽  
pp. 522-536 ◽  
Author(s):  
Shujuan Huang ◽  
Diana-Andra Borca-Tasciuc ◽  
John A. Tichy
Keyword(s):  
Separation Distance ◽  
Simple Expression ◽  
Squeeze Film ◽  
Inertia Force ◽  
Viscous Damping ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Viscous Forces ◽  
Squeeze Film Damping ◽  
Micro Plates

Squeeze film damping in systems employing micro-plates parallel to a substrate and undergoing small normal vibrations is theoretically investigated. In high-density fluids, inertia forces may play a significant role affecting the dynamic response of such systems. Previous models of squeeze film damping taking inertia into account do not clearly isolate this effect from viscous damping. Therefore, currently, there is no simple way to distinguish between these two hydrodynamic effects. This paper presents a simple solution for the hydrodynamic force acting on a plate vibrating in an incompressible fluid, with distinctive terms describing inertia and viscous damping. Similar to the damping constant describing viscous losses, an inertia constant, given by ρL 3 W / h (where ρ is fluid density, L and W are plate length and width, respectively, and h is separation distance), may be used to accurately calculate fluid inertia for small oscillation Reynolds numbers. In contrast with viscous forces that suppress the amplitude of the oscillation, it is found that fluid inertia acts as an added mass, shifting the natural frequency of the system to a lower range while having little effect on the amplitude. Dimensionless parameters describing the relative importance of viscous and inertia effects also emerge from the analysis.

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.

Observations on the Nonlinear Fluid Forces in Short Cylindrical Squeeze Film Dampers

1993 ◽  
Vol 115 (4) ◽  
pp. 692-698 ◽  
Author(s):  
J. Zhang ◽  
J. Ellis ◽  
J. B. Roberts
Keyword(s):  
Theoretical Work ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equation ◽  
Fluid Forces ◽  
Recent Theoretical Work ◽  
Starting Point ◽  
Squeeze Film Dampers ◽  
Inertia Forces

Recent theoretical work by Tichy and Bou-Said (1991) and El-Shafei and Crandall (1991) has resulted in new theoretical expressions for the nonlinear inertia forces for both short and long cylindrical squeeze film dampers (SFDs). This paper provides alternative derivations for the short cylindrical SFD using as a starting point a simplified two-dimensional Navier-Stokes equation. The resulting expressions for the fluid inertia forces are similar to the Tichy and Bou-Said/El-Shafei and Crandall expressions except for differences in certain numerical constants which can be explained by the different averaging methods used within the squeeze-film thickness. The analyses give additional insight into the temporal and convective origins of the various coefficients. The theoretical results are compared with published theoretical and experimental work involving nonlinear cylindrical SFD behavior. The paper highlights the importance of convective inertia terms when cylindrical SFDs operate at large values of eccentricity ratio.

Unbalance Response of a Jeffcott Rotor Incorporating Short Squeeze Film Dampers

1989 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Fast Algorithm ◽  
Vibration Isolation ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Unbalance Response ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Second Mode ◽  
Parametric Studies ◽  
Inertia Forces

The steady state unbalance response of a Jeffcott rotor incorporating short squeeze film dampers executing circular centered whirl is obtained by a fast algorithm. Savings in execution time of the order of fifty times are gained over numerical integration. Fluid inertia forces are included in the model of the squeeze film dampers. The fast algorithm allows parametric studies to be performed. It is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor, decreases the possibility of jump resonance, and decreases the useful range of vibration isolation of the dampers. It is also shown that a squeeze film damper with no centering spring (or a very soft spring) may be advantageous with regards to the unbalance response and the vibration isolation capability of the dampers.

Unbalance Response of a Jeffcott Rotor Incorporating Short Squeeze Film Dampers

1990 ◽  
Vol 112 (4) ◽  
pp. 445-453 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Fast Algorithm ◽  
Vibration Isolation ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Unbalance Response ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Second Mode ◽  
Parametric Studies ◽  
Inertia Forces

The steady-state unbalance response of a Jeffcott rotor incorporating short squeeze film dampers executing circular centered whirl is obtained by a fast algorithm. Savings in execution time of the order of fifty times are gained over numerical integration. Fluid inertia forces are included in the model of the squeeze film dampers. The fast algorithm allows parametric studies to be performed. It is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor, decreases the possibility of jump resonance, and decreases the useful range of vibration isolation of the dampers. It is also shown that a squeeze film damper with no centering spring (or a very soft spring) may be advantageous with regards to the unbalance response and the vibration isolation capability of the dampers.

Unbalance Response of a Jeffcott Rotor Incorporating Long Squeeze Film Dampers

1991 ◽  
Vol 113 (1) ◽  
pp. 85-94 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Vibration Isolation ◽  
Fluid Velocity ◽  
Resonance Phenomenon ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Unbalance Response ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Second Mode ◽  
Inertia Forces

The steady state unbalance response of a Jeffcott rotor incorporating long squeeze film dampers executing circular centered precession is obtained. Fluid inertia forces are included in the model of the squeeze film dampers, using an energy approximation. The fluid velocity profiles are assumed not to change much due to fluid inertia, and the kinetic coenergy of the fluid is calculated. The fluid inertia forces are then obtained by Lagrange’s equations in conjunction with Reynolds transport theorem. The unbalance response of the rotor is obtained by assuming circular centered precession, and it is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor and decreases the useful range of vibration isolation of the dampers. It is also shown that the second mode can exhibit the jump resonance phenomenon.

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