Chebyshev Polynomials Fits for Efficient Analysis of Finite Length Squeeze Film Damped Rotors

2002 ◽  
Vol 125 (1) ◽  
pp. 175-183 ◽  
Author(s):  
F. A. Rodrigues ◽  
F. Thouverez ◽  
C. Gibert ◽  
L. Jezequel
Keyword(s):  
Steady State ◽  
Finite Length ◽  
Pressure Field ◽  
Fluid Pressure ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Squeeze Film ◽  
Approximate Methods ◽  
Squeeze Film Dampers ◽  
The Time Domain

The nonlinear behavior of the hydrodynamic forces generated by squeeze film dampers makes dynamical analyses of rotor-bearing systems incorporating such devices a complex and often long task. When steady-state orbits are to be sought, approximate methods (e.g., harmonic balance method, trigonometric collocation method) can be used in order to save computation cost. However, numerical integration in the time domain cannot be avoided if one wishes to calculate transient responses, or to carry out more meticulous analyses concerning the effects of the damper nonlinear nature on the motion of the system. For finite length squeeze film dampers, neither the short nor the long bearing approximations can be suitably applied, and the fluid pressure field has to be estimated numerically, thus rendering rotordynamics predictions even longer and, for engineering purposes computationally prohibitive. To surmount this problem, the present paper proposes a straightforward procedure to derive polynomial expressions for the squeeze film damper (SFD) forces, for given damper geometry and boundary conditions. This is achieved by applying Chebyshev orthogonal polynomial fits over force data generated by numerically solving the two-dimensional pressure field governing equation. For both transient and steady-state calculations, the use of the SFD forces polynomial expressions is seen to be very efficient and precise.

scholarly journals Stability Analysis of a Gear Pair System Supported by Squeeze-Film Dampers

2001 ◽  
Vol 7 (2) ◽  
pp. 143-151 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Harmonic Balance Method ◽  
Squeeze Film ◽  
Hybrid Technique ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Squeeze Film Dampers ◽  
The Stability

This paper examines the stability of the steady-state periodic response of a gear pair system supported by squeeze-film dampers. The steady-state response of the system is obtained by using the hybrid technique of Harmonic Balance Method and Time Collocation. The Fioquet-Liapunov theory is used to perform the stability analysis of the first variation equations with periodic coefficients, which is generated by the perturbation technique. The stability charts on gear mesh stiffness, spin ratio, disk unbalance, gravity, and squeeze-film damper are used to perform parameter studies. The numerical results show that the unstable region always occurs when the spin ratio is near the second coupled mode of the gear pair system. Furthermore, the mesh stiffness has a significant influence on the coupled critical speeds. Therefore, it plays an important role in determining the spin ratio stability range.

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.

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 Imbalance Response of a Test Rotor Supported on Squeeze Film Dampers

1998 ◽  
Vol 120 (2) ◽  
pp. 397-404 ◽  
Author(s):  
L. San Andre´s ◽  
D. Lubell
Keyword(s):  
Chaotic Behavior ◽  
Nonlinear Behavior ◽  
Theoretical Models ◽  
Forced Response ◽  
Analytical Models ◽  
Squeeze Film ◽  
Test Rig ◽  
Critical Speeds ◽  
Highly Nonlinear ◽  
Squeeze Film Dampers

Squeeze film dampers (SFDs) provide vibration attenuation and structural isolation to aircraft gas turbine engines which must be able to tolerate larger imbalances while operating above one or more critical speeds. Rotor-bearing-SFD systems are regarded in theory as highly nonlinear, showing jump phenomena and even chaotic behavior for sufficiently large levels of rotor imbalance. Yet, few experimental results of practical value have verified the analytical predictions. A test rig for measurement of the dynamic forced response of a three-disk rotor (45 kg) supported on two cylindrical SFDs is described. The major objective is to provide a reliable data base to validate and enhance SFD design practice and to allow a direct comparison with analytical models. The open-ends SFD are supported by four-bar centering structures, each with a stiffness of 3.5 MN/m. Measured synchronous responses to 9000 rpm due to various imbalances show the rotor-SFD system to be well damped with amplification factors between 1.6 and 2.1 while traversing cylindrical and conical modes critical speeds. The rotor amplitudes of motion are found to be proportional to the imbalances for the first mode of vibration, and the damping coefficients extracted compare reasonably well to predictions based on the full-film, open-ends SFD. Tight lip (elastomeric) seals contribute greatly to the overall damping of the test rig. Measured dynamic pressures at the squeeze film lands are well above ambient values with no indication of lubricant dynamic cavitation as simple theoretical models dictate. The measurements show absence of nonlinear behavior of the rotor-SFD apparatus for the range of imbalances tested.

Application of CFD Analysis for Rotating Machinery: Part 1 — Hydrodynamic, Hydrostatic Bearings and Squeeze Film Damper

2003 ◽  
Author(s):  
Zenglin Guo ◽  
Toshio Hirano ◽  
R. Gordon Kirk
Keyword(s):  
Traditional Method ◽  
Reasonable Agreement ◽  
Pressure Field ◽  
Squeeze Film ◽  
Cfd Analysis ◽  
Complex Flow ◽  
Static And Dynamic Characteristics ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers ◽  
Machinery Part

The traditional method for bearing and damper analysis usually involves a development of rather complicated numerical calculation programs that may just focus on a simplified and specific physical model. The application of the general CFD codes may make this analysis available and effective where complex flow geometries are involved or when more detailed solutions are needed. In this study, CFX-TASCflow is employed to simulate various fixed geometry fluid-film bearing and damper designs. Some of the capabilities in CFX-TASCflow are applied to simulate the pressure field and calculate the static and dynamic characteristics of hydrodynamic, hydrostatic and hybrid bearings as well as squeeze film dampers. The comparison between the CFD analysis and current computer programs used in industry has been made. The results show reasonable agreement in general. Some of possible reasons for the differences are discussed. It leaves room for further investigation and improvement on the methods of computation.

Application of CFD Analysis for Rotating Machinery—Part I: Hydrodynamic, Hydrostatic Bearings and Squeeze Film Damper

2005 ◽  
Vol 127 (2) ◽  
pp. 445-451 ◽  
Author(s):  
Zenglin Guo ◽  
Toshio Hirano ◽  
R. Gordon Kirk
Keyword(s):  
Traditional Method ◽  
Reasonable Agreement ◽  
Pressure Field ◽  
Squeeze Film ◽  
Cfd Analysis ◽  
Complex Flow ◽  
Static And Dynamic Characteristics ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers ◽  
Machinery Part

The traditional method for bearing and damper analysis usually involves a development of rather complicated numerical calculation programs that may just focus on a simplified and specific physical model. The application of the general CFD codes may make this analysis available and effective where complex flow geometries are involved or when more detailed solutions are needed. In this study, CFX-TASCflow is employed to simulate various fixed geometry fluid-film bearing and damper designs. Some of the capabilities in CFX-TASCflow are applied to simulate the pressure field and calculate the static and dynamic characteristics of hydrodynamic, hydrostatic, and hybrid bearings as well as squeeze film dampers. The comparison between the CFD analysis and current computer programs used in industry has been made. The results show reasonable agreement in general. Some of the possible reasons for the differences are discussed. It leaves room for further investigation and improvement on the methods of computation.

Squeeze film dampers supporting high-speed rotors: Rotordynamics

2020 ◽  
pp. 135065012092208
Author(s):  
Sina Hamzehlouia ◽  
Kamran Behdinan
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Gas Turbines ◽  
High Speed ◽  
Squeeze Film ◽  
Jet Engines ◽  
Transient Vibration ◽  
Element Analysis ◽  
Squeeze Film Damper ◽  
The Time Domain

This work develops a finite element based multi-mass flexible rotor model for theoretical investigation of the influence of the squeeze film damper lubricant inertia on the unbalance-induced steady-state and transient vibration amplitudes of high speed turbomachinery. The rotordynamic model is developed by applying the principles of finite element analysis to discretize the rotor components, including the rotor shaft and disk, into local elements with mass, stiffness, and gyroscopic matrices. Subsequently, the local matrices are assembled together to develop the global model of the rotordynamic system. The influence of squeeze film damper lubricant inertia is incorporated into the model by using short-length cavitated damper models with retaining springs executing circular-centered orbits. Additionally, the rotordynamic model incorporating the nonlinear squeeze film damper models is iteratively solved in the time domain by applying a predictor-corrector transient modal integration numerical method and the steady-state and transient motions of the rotor system are investigated under different rotor and squeeze film damper parameters. The results of the study verify the substantial influence of squeeze film damper lubricant inertia on attenuating the vibrations of high-speed turbomachinery. Furthermore, the developed rotordynamic model delivers an efficient and powerful platform for the analysis of high-speed turbomachinery, including jet engines and gas turbines.

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

Use of the Harmonic Balance Method for Flexible Aircraft Engine Rotors With Nonlinear Squeeze Film Dampers

2014 ◽  
Author(s):  
Feng He ◽  
Paul Allaire ◽  
Timothy Dimond
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Aircraft Engine ◽  
Balance Method ◽  
Squeeze Film ◽  
Spring Stiffness ◽  
Squeeze Film Damper ◽  
Flexible Rotors ◽  
Squeeze Film Dampers ◽  
Nonlinear Transient

Squeeze film dampers in flexible rotors such as those in compressors, steam turbines, aircraft engines and other rotating machines are often modeled as linear devices. This linearization is valid only for a specified orbit where appropriate equivalent stiffness and damping coefficients can be found. However, squeeze film dampers are inherently nonlinear devices which complicates the analysis. This paper develops the harmonic balance method with a direct force model of the SFDs. This model is used for flexible rotors with squeeze film dampers where the rotor is treated as linear and the squeeze film damper is treated as nonlinear. The predictor-corrector method is employed to obtain the system forced response in the frequency domain after separating the nonlinear components from the linear components of the equations of motion. This approach is much more efficient than conventional full nonlinear transient analysis. The application considered in this paper is the low pressure (LP) compressor of an aircraft engine. The LP compressor rotor has two roller bearings with squeeze film dampers and one ball bearing without a squeeze film damper. Orbits at the fan end dampers and the turbine end dampers for both the harmonic balance and nonlinear transient modeling are compared for accuracy and calculation time. The HB method is shown to be 5 to 12 times faster computationally for similar results. Fast Fourier transform results were obtained for various shaft operating speeds. Results were also obtained for the unbalance response at different locations with gravity loading. Finally, unbalance response of the rotor with varying centering spring stiffness values were obtained. The results show that the centering spring stiffness for the turbine end damper is less sensitive than the fan end damper.

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