A Mass-Conserving Complementarity Formulation to Study Lubricant Films in the Presence of Cavitation

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Matteo Giacopini ◽  
Mark T. Fowell ◽  
Daniele Dini ◽  
Antonio Strozzi
Keyword(s):  
Liquid Film ◽  
Reynolds Equation ◽  
New Method ◽  
Squeeze Film ◽  
Current Formulation ◽  
Squeeze Film Dampers ◽  
Lubricant Films ◽  
Good Agreement

A new mass-conserving formulation of the Reynolds equation is developed using the concept of complementarity. This new method overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. Validation against a number of analytical and semi-analytical formulations, for a variety of problems including textured bearings and squeeze film dampers, is performed. The current formulation is shown to be in very good agreement with existing analytical and numerical mass-conserving solutions.

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.

Squeeze Film Dampers: Amplitude Effects at Low Squeeze Numbers

1975 ◽  
Vol 97 (4) ◽  
pp. 1366-1370 ◽  
Author(s):  
Martin H. Sadd ◽  
A. Kent Stiffler
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Squeeze Film ◽  
Periodic Disturbance ◽  
Squeeze Film Dampers ◽  
Parallel Surfaces ◽  
Load Characteristics ◽  
Squeeze Number ◽  
Stiffness And Damping ◽  
Film Stiffness

Gaseous squeeze film dampers are analyzed to determine the effect of periodic disturbance amplitude on the dynamic performance. Both circular and rectangular parallel surfaces are investigated. A solution of the nonlinear Reynolds equation is obtained by expanding the pressure in powers of the squeeze number σ, retaining up to and including terms 0(σ2). The time dependent load characteristics are found. The effect of disturbance amplitude on the film stiffness and damping is given.

Design of Nonlinear Squeeze-Film Dampers for Aircraft Engines

1977 ◽  
Vol 99 (1) ◽  
pp. 57-64 ◽  
Author(s):  
E. J. Gunter ◽  
L. E. Barrett ◽  
P. E. Allaire
Keyword(s):  
Reynolds Equation ◽  
Nonlinear Effects ◽  
Aircraft Engine ◽  
Squeeze Film ◽  
Aircraft Engines ◽  
Transient Method ◽  
Squeeze Film Damper ◽  
Wide Range ◽  
Squeeze Film Dampers ◽  
Bearing Stiffness

This paper examines the effect of squeeze-film damper bearings on the steady state and transient unbalance response of aircraft engine rotors. The nonlinear effects of the damper are examined, and the variance of the motion due to unbalance, static pressurization, retainer springs, and rotor preload is shown. The nonlinear analysis is performed using a time-transient method incorporating a solution of the Reynolds equation at each instant in time. The analysis shows that excessive stiffness in the damper results in large journal amplitudes and transmission of bearing forces to the engine casing which greatly exceed the unbalance forces. Reduction of the total effective bearing stiffness through static pressurization and rotor preload is considered. The reduction in stiffness allows the damping generated by the bearing to be more effective in attenuating rotor forces. It is observed that in an unpressurized damper, the dynamic transmissibility will exceed unity when the unbalance eccentricity exceeds approximately 50 percent of the damper clearance for the relatively wide range of conditions examined in this study.

Dynamics of Multilayer Microplates Considering Nonlinear Squeeze Film Damping

2006 ◽  
Author(s):  
M. T. Ahmadian ◽  
M. Moghimi Zand ◽  
H. Borhan
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Reynolds Equation ◽  
Finite Difference Methods ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Squeeze Film ◽  
First Order ◽  
Squeeze Film Damping ◽  
Good Agreement

This paper presents a model to analyze pull-in phenomenon and dynamics of multi layer microplates using coupled finite element and finite difference methods. First-order shear deformation theory is used to model dynamical system using finite element method, while Finite difference method is applied to solve the nonlinear Reynolds equation of squeeze film damping. Using this model, Pull-in analysis of single layer and multi layer microplates are studied. The results of pull-in analysis are in good agreement with literature. Validating our model by pull-in results, an algorithm is presented to study dynamics of microplates. These simulations have many applications in designing multi layer microplates.

Squeeze-Film Damper Predictions for Simulation of Aircraft Engine Rotordynamics

2004 ◽  
Author(s):  
Cyril Defaye ◽  
Franck Laurant ◽  
Philippe Carpentier ◽  
Mihai Arghir ◽  
Olivier Bonneau ◽  
...  
Keyword(s):  
Reynolds Equation ◽  
Aircraft Engine ◽  
Theoretical Work ◽  
Analytical Models ◽  
Squeeze Film ◽  
Design Parameters ◽  
Aircraft Engines ◽  
Predictive Tool ◽  
Squeeze Film Dampers ◽  
Inertia Forces

On aircraft engines, a common recurring problem is excessive vibration levels generated by unbalance. With rotors mounted on usual undamped ball bearings, an amount of damping is required to limit peak amplitudes at traversed critical speeds: a solution is to introduce external damping with squeeze-film dampers. Such dampers can be added with minor modifications of the rotor system design. This paper presents experimental and theoretical work in progress focused on the analysis of squeeze film dampers (SFD) based on serial aircraft engines design. Several squeeze-film geometries were tested to measure the influence of different design parameters as the fluid clearance and the groove feeding system. Next, a damper model based on the numerical solution of the Reynolds equation is correlated with the experimental data to obtain predictive global forces. It is shown that the theoretical model is a good predictive tool if it is correctly adjusted and if temporal inertia forces are negligible. The present damper model is further compared with analytical models taken from the literature which are obviously more appropriate to be used in whole engine rotordynamic analysis. The limits of the models are then underlined by comparisons with experimental results.

Calculated Rotordynamic Behaviour of a Twin Spool Engine and the Comparison With Test Results

1995 ◽  
Author(s):  
B. Domes ◽  
H. Hartmüller ◽  
G. Tokar ◽  
G. Wang
Keyword(s):  
Dynamic Behaviour ◽  
Complex Structure ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Test Results ◽  
Engine Model ◽  
Damping Characteristics ◽  
Resonance Frequencies ◽  
Squeeze Film Dampers ◽  
Good Agreement

Abstract The new BR 700 series of twin spool engines, of the thrust class of 15,000 to 20,000 pounds, is being developed for business jets. In this paper the rotordynamic vibration analysis is performed with a detailed whole engine model including both rotors, bearings with oil squeeze film dampers and squirrel cages, the engine structure, the mounts and the fuselage. The analytical method is described and some calculated results are presented. The effectiveness of the oil squeeze film dampers on all main bearings will be demonstrated. The comparison of the analytical and the measured results gives a good agreement in the resonance frequencies and in the damping characteristics. It also shows that a linear analysis can describe with sufficient accuracy the dynamic behaviour of such a complex structure like a twin spool engine under normal operating conditions.

Perturbation Solutions for Eccentric Operation of Squeeze Film Damper Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 619-623 ◽  
Author(s):  
Xuehai Li ◽  
D. L. Taylor
Keyword(s):  
Numerical Simulation ◽  
Experimental Results ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Synchronous Motion ◽  
Squeeze Film Dampers ◽  
Large Speed ◽  
Good Agreement ◽  
Perturbation Solutions

The study focuses on the effect of a small unidirectional load such as comes from imperfect balance between preloading on centering springs and gravitational load on squeeze film dampers. A rigid rotor-squeeze film damper system is considered, and a thorough study of the synchronous motion of the system is performed. Two perturbation solutions are developed: one for large speed and one for small speed. The perturbation solutions are shown to be in good agreement with numerical simulation and published experimental results.

A Dynamic Analysis of a Dual Clearance Squeeze Film Damper

2010 ◽  
Author(s):  
L. Moraru ◽  
T. G. Keith ◽  
F. Dimofte ◽  
S. Cioc ◽  
N. Ene ◽  
...  
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Rotating Machinery ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers ◽  
Abnormal Operating Conditions ◽  
Oil Films

Squeeze film dampers (SFD) are devices utilized to control the shafts of high-speed rotating machinery. A dual squeeze film damper (DSFD) consists of two squeeze film bearings that are separated by a sleeve, which is released when the rotor experiences abnormal operating conditions. In this part of our study of DSFD we analyze the case when both the inner and the outer oil films are active. We present computed and measured unbalance responses of a shaft supported in DSFD. The oil forces which are utilized in the calculation of the unbalance response are obtained from numerical solutions of the Reynolds equation. A finite-difference algorithm is utilized for solving the pressure equation within the calculation of the dynamic response of the shaft.

Time Transient Analysis of Horizontal Rigid Rotor Supported With O-Ring Sealed Squeeze Film Damper

2013 ◽  
Author(s):  
Saeid Dousti ◽  
Timothy W. Dimond ◽  
Paul E. Allaire ◽  
Houston E. Wood
Keyword(s):  
Transient Analysis ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Numerical Data ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers

This study addresses the nonlinear dynamic behavior of O-ring seals as the retaining spring in squeeze film dampers (SFDs). An analytical model is developed to predict the restoring and hysteresis forces of elastomer O-rings based on experimental and numerical data. This model takes into account the temperature softening and excitation frequency hardening effects in O-rings as well as the installation conditions in the form of radial and vertical preloads, σ and γ, respectively. Long bearing assumption is adopted for the solution of Reynolds equation. The equations of motion of horizontal unbalanced rigid rotor are derived, and a dimensional analysis is conducted on them. The numerical results substantiates the synchronizing effects of bearing parameter, B and vertical preload, γ, and the asynchronizing effects of O-ring parameter, O and radial preload, σ. It is shown that the variation of temperature and rotational speed as operating conditions influence the rotor response significantly.

Rotordynamic Performance of Finite Length Squeeze Film Dampers

2003 ◽  
Author(s):  
A. El-Shafei ◽  
A. S. El-Kabbany
Keyword(s):  
Finite Length ◽  
Reynolds Equation ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Damping Coefficients ◽  
At Resonance ◽  
R Ratio ◽  
Squeeze Film Dampers ◽  
Current Design ◽  
Analytical Formulae

A recently developed finite length model of squeeze film dampers is extended and used in predicting the behavior of a rigid rotor supported by squeeze film dampers (SFDs). The model is based on a perturbation solution of Reynolds’ equation. The finite length SFD damping coefficients are presented for various L/R ratios. The effect of damper finite length is studied. Simulations of the behavior of a rigid rotor with the finite length SFDs illustrate the response of the roto-rbearing system. The accuracy of the finite damper model is shown for cases comparable to short and long dampers models. The short damper and long damper models are generally accepted to be valid for L/D < 1/4, and for L/D > 4, respectively. The capability of the finite length damper model to capture the main essence of the L/R ratio on the rotor response at resonance is illustrated. Analytical formulae for damping estimates are provided for finite length dampers. It is shown that the finite length damper actually provides less damping than either the short or the long damper models, which means that current design practices actually overestimate the SFD damping capabilities.

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