Normal Instantaneous Squeeze Film Force for a Finite Length Cylinder

1994 ◽  
Vol 116 (3) ◽  
pp. 588-596 ◽  
Author(s):  
Yong Lu ◽  
Robert J. Rogers
Keyword(s):  
Theoretical Model ◽  
Finite Length ◽  
Wide Frequency Range ◽  
Squeeze Film ◽  
Viscous Term ◽  
Inertia Term ◽  
Corrected Equation ◽  
Instantaneous Position ◽  
Parabolic Flow ◽  
Weighting Coefficients

A theoretical model for the normal instantaneous squeeze film force for a finite length cylinder is developed in this paper. The model assumes large unidirectional cylinder motion along a sleeve diameter. Based on the assumption of a parabolic flow field, a normal squeeze film model for an infinitely long cylinder is first obtained. Combining the infinitely long model with side-leakage factors, a finite length model is then obtained. The model shows that the instantaneous squeeze film force consists of three position-dependent nonlinear terms: namely a viscous term, an unsteady inertia term and a convective inertia term. From experimental measurements using water and a clearance to radius ratio of 0.032, the viscous term of the theoretical model should be corrected by a factor involving the instantaneous squeeze film Reynolds number and the absolute value of instantaneous eccentricity. The synthesized squeeze force waveforms obtained using the corrected equation with averaged weighting coefficients agree very well with the experimental waveforms for eccentricity ratios up to 0.9 and a wide frequency range. The corrected equation is suitable for the calculation of the normal instantaneous squeeze film force given the instantaneous position, velocity, and acceleration of the cylinder center.

A Nonlinear Model for Short Length, Cylindrical Squeeze Films With Large Planar Motions

1992 ◽  
Vol 114 (1) ◽  
pp. 192-198 ◽  
Author(s):  
Yong Lu ◽  
R. J. Rogers
Keyword(s):  
Heat Exchanger ◽  
Short Length ◽  
Squeeze Film ◽  
Inertia Force ◽  
Flow Induced Vibration ◽  
Damping Force ◽  
Rotating Shaft ◽  
Viscous Term ◽  
Inertia Term ◽  
Planar Motions

A rotating shaft vibrating in a squeeze film bearing and a tube in a heat exchanger oscillating with fluid-filled cylindrical supports both involve cylindrical squeeze films. Many theoretical and experimental results show that the squeeze film force consists of both a damping force and an inertia force. For relatively large amplitude motions or when the initial eccentricity is large, the time waveform of the squeeze force is significantly nonlinear. In order to predict the transient response of a rotor with squeeze film bearings or a heat exchanger tube subject to flow induced vibration, the nonlinear instantaneous squeeze force must be calculated. This paper presents a model for the instantaneous cylindrical squeeze film force for planar motion. The squeeze film model for a two-dimensional plate shows that there are three nonlinear terms included in the squeeze force. Based on this model, an equation for the short length, cylindrical squeeze film force for moderately large eccentricities is developed. The equation includes the three nonlinear terms: the viscous term, the unsteady inertia term, and the convective inertia term. All three terms are functions of instantaneous eccentricity. The equation predicts the nonlinear multi-harmonic and unsymmetrical time waveforms of the instantaneous squeeze film force for planar motions with both in-line and out-of-line initial eccentricities. The results are compared with experimentally measured squeeze force waveforms obtained with a length to diameter ratio of 0.75 and instantaneous eccentricities less than 0.75. The squeeze force waveforms for this finite length geometry can be reasonably predicted if correction coefficients, which account for the circumferential flow, are applied to the three nonlinear force terms. These coefficients are themselves functions of frequency, initial eccentricity and amplitude.

scholarly journals The Damping Capacity of a Sealed Squeeze Film Bearing

1985 ◽  
Vol 107 (3) ◽  
pp. 411-418 ◽  
Author(s):  
M. M. Dede ◽  
M. Dogan ◽  
R. Holmes
Keyword(s):  
Theoretical Model ◽  
Gas Turbine ◽  
Squeeze Film ◽  
Damping Capacity ◽  
Test Rig ◽  
Squeeze Film Damper ◽  
Aero Engine

The purpose of this paper is to establish a theoretical model to represent a sealed squeeze-film damper bearing and to assess it against results from a test rig, simulating the essential features of a medium-sized gas turbine aero engine.

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.

Non-Darcian Boundary Layer Flow and Forced Convective Heat Transfer Over a Flat Plate in a Fluid-Saturated Porous Medium

1990 ◽  
Vol 112 (1) ◽  
pp. 157-162 ◽  
Author(s):  
A. Nakayama ◽  
T. Kokudai ◽  
H. Koyama
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Flat Plate ◽  
Similarity Solution ◽  
Temperature Fields ◽  
Solid Boundary ◽  
Local Similarity ◽  
Viscous Term ◽  
Inertia Term

The local similarity solution procedure was successfully adopted to investigate non-Darcian flow and heat transfer through a boundary layer developed over a horizontal flat plate in a highly porous medium. The full boundary layer equations, which consider the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables deduced from a scale analysis. The results from this local similarity solution are found to be in good agreement with those obtained from a finite difference method. The effects of the convective inertia term, boundary viscous term, and porous inertia term on the velocity and temperature fields were examined in detail. Furthermore, useful asymptotic expressions for the local Nusselt number were derived in consideration of possible physical limiting conditions.

A Theoretical Series Solution for the Dynamics of Finite-Length Bearings and Squeeze-Film Dampers

2003 ◽  
Author(s):  
Jose´ Antunes ◽  
Miguel Moreira ◽  
Philippe Piteau
Keyword(s):  
Fourier Series ◽  
Galerkin Method ◽  
Finite Length ◽  
Reynolds Equation ◽  
Double Fourier Series ◽  
Squeeze Film ◽  
Algebraic Equations ◽  
Squeeze Film Dampers ◽  
Galerkin Solution ◽  
The Galerkin Method

In this paper we develop a non-linear dynamical solution for finite length bearings and squeeze-film dampers based on a Spectral-Galerkin method. In this approach the gap-averaged pressure is approximated, in the lubrication Reynolds equation, by a truncated double Fourier series. The Galerkin method, applied over the residuals so obtained, generate a set of simultaneous algebraic equations for the time-dependent coefficients of the double Fourier series for the pressure. In order to assert the validity of our 2D–Spectral-Galerkin solution we present some preliminary comparative numerical simulations, which display satisfactory results up to eccentricities of about 0.9 of the reduced fluid gap H/R. The so-called long and short-bearing dynamical solutions of the Reynolds equation, reformulated in Cartesian coordinates, are also presented and compared with the corresponding classic solutions found on literature.

scholarly journals Experimental Evaluation of Squeeze Film Supported Flexible Rotors

1982 ◽  
Author(s):  
M. D. Rabinowitz ◽  
E. J. Hahn
Keyword(s):  
Theoretical Model ◽  
Experimental Evaluation ◽  
Measurement Errors ◽  
Vibration Amplitude ◽  
Squeeze Film ◽  
Experimental Investigations ◽  
Flexible Rotors ◽  
The Mean ◽  
Lubricant Viscosity ◽  
Theory And Experiment

This paper describes the experimental investigations which were conducted to verify existing theoretical vibration amplitude predictions for centrally preloaded, squeeze film supported flexible rotors. The influence of measurement errors and operating condition uncertainties are quantified. The agreement between theory and experiment was excellent, and it is shown that any discrepancy can be explained in terms of errors in determining the mean lubricant viscosity and the orbit magnitudes. Hence, for the range of parameters investigated, the theoretical model and predictions therefrom are validated.

scholarly journals Tangential motion mechanism and reverse hydrodynamic effects of acoustic platform with nonparallel squeeze film

2018 ◽  
Vol 233 (1) ◽  
pp. 194-204 ◽  
Author(s):  
Wei Bin ◽  
Ran Shaham ◽  
Izhak Bucher ◽  
Jianbin Luo
Keyword(s):  
Theoretical Model ◽  
Travelling Waves ◽  
Tangential Component ◽  
Squeeze Film ◽  
Hydrodynamic Effect ◽  
Driving Mechanism ◽  
Transient Pressure ◽  
Hydrodynamic Effects ◽  
Tangential Directions ◽  
Theoretical Results

In order to explain the reverse hydrodynamic effects on acoustic platform with nonparallel squeeze film, a theoretical model was proposed to evaluate the levitation and movement capacity in this paper. The mechanism of movement and levitation was revealed by the viscous fluid mechanics and dynamic lubrication theory. The transient pressure gradient and steady average velocity were calculated in different deflection angles of nonparallel squeeze film by means of numerical calculation of Reynolds equation. The theoretical results indicated that the platform of nonparallel squeeze film was provided with a bearing and pushing capacity in both normal and tangential directions and it was amazing that the reverse hydrodynamic effects made the levitated plate move into the opposite direction of gravitational tangential component. This proposed theoretical model for acoustic platform with nonparallel squeeze film was different with the original parallel one. Its driving mechanism was the reverse hydrodynamic effect instead of travelling waves. This reverse hydrodynamic effect was proved in the experiments, which could be used in levitation and transport field for precise component in future.

A Theoretical and Experimental Investigation of a Gas-Operated Bearing Damper for Turbomachinery: Part I—Theoretical Model and Predictions

1995 ◽  
Vol 117 (4) ◽  
pp. 742-749 ◽  
Author(s):  
P. Sundararajan ◽  
J. M. Vance
Keyword(s):  
Theoretical Model ◽  
Squeeze Film ◽  
Working Fluid ◽  
Previous Theory ◽  
Damping Characteristics ◽  
Squirrel Cage ◽  
Theoretical Predictions ◽  
Current Design ◽  
Gas Damper ◽  
Hardware Designs

This is the first (Part I) of two papers describing recent results of the research program directed at developing a vibration damper suitable for high-temperature turbomachinery applications. It is expected that such dampers will replace squeeze-film dampers, which use oil as the working fluid and have limitations at higher temperatures. A novel gas-operated bearing damper has been evaluated analytically and experimentally for its damping characteristics. A theory based on the isentropic assumptions predicts the damper performance characteristics reasonably well. A maximum damping level of 2311 N-m/s (13.2 lb-s/in.) at a frequency of 100 Hz was measured with a single actuator of the gas damper. Since many such actuators could be placed circumferentially around the squirrel cage, considerable damping levels can be realized. The study also shows that significantly higher damping levels can be achieved by modifying the current design. Part I describes the theoretical model that has been developed based on isentropic assumptions. This model is an improved version of the previous theory (Vance et al., 1991) and includes the supply groove effects, dynamic area changes of the inlet feeding holes, and the effects of flow choking on damper behavior. The governing equations are derived and theoretical predictions using these equations have been made for two hardware designs that were experimentally investigated (see Part II for experimental results).

Effects of Fluid Inertia on Finite-Length Squeeze-Film Dampers

1987 ◽  
Vol 30 (3) ◽  
pp. 384-393 ◽  
Author(s):  
L. A. San Andres ◽  
J. M. Vance
Keyword(s):  
Finite Length ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Squeeze Film Dampers
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