Calculation of Stiffness and Damping Coefficients for Elastically Supported Gas Foil Bearings

1993 ◽  
Vol 115 (1) ◽  
pp. 20-27 ◽  
Author(s):  
J.-P. Peng ◽  
M. Carpino
Keyword(s):  
Reynolds Equation ◽  
Structural Model ◽  
Structural Equations ◽  
Perfect Gas ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Foil Bearing ◽  
Stiffness And Damping ◽  
Elastically Supported

The stiffness and damping coefficients of an elastically supported gas foil bearing are calculated. A perfect gas is used as the lubricant, and its behavior is described by the Reynolds equation. The structural model consists only of an elastic foundation. The fluid equations and the structural equations are coupled. A perturbation method is used to obtain the linearized dynamic coefficient equations. A finite difference formulation has been developed to solve for the four stiffness and the four damping coefficients. The effect of the bearing compliance on the dynamic coefficients is discussed in this paper.

Finite Element Approach to the Prediction of Foil Bearing Rotor Dynamic Coefficients

1997 ◽  
Vol 119 (1) ◽  
pp. 85-90 ◽  
Author(s):  
J.-P. Peng ◽  
M. Carpino
Keyword(s):  
Finite Element ◽  
Coulomb Friction ◽  
Structural Model ◽  
Perturbation Approach ◽  
Barotropic Fluid ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Foil Bearing ◽  
Bearing Stiffness ◽  
Stiffness And Damping

A finite element perturbation approach to the prediction of foil bearing stiffness and damping coefficients is presented. The fluid lubricant is modeled as a simple barotropic fluid which is described by the Reynolds equation. The structural model includes membrane, bending, and elastic foundation effects in a general geometry. The equivalent viscous damping of the Coulomb friction caused by the foil relative motion is included in the structural calculation. Bearing stiffness and damping coefficients are predicted for an air-lubricated foil bearing with a corrugated sub-foil. The effects of the bearing number, bearing compliance, sub-foil Coulomb friction, and foil membrane stiffness on the bearing dynamic coefficients are discussed.

Limiting Stiffness and Damping Coefficients of Foil Bearing

2005 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
T. V. V. L. N. Rao
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Necessary Conditions ◽  
Load Capacity ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Infinitesimal Perturbation ◽  
Stiffness And Damping ◽  
Limiting Values ◽  
Gas Journal Bearing

The limiting values of load capacity, stiffness and damping coefficients for a foil bearing are presented. The necessary conditions for high bearing numbers (journal operating at high speed) are obtained by simplifying the compressible Reynolds equation. Linearized stiffness and damping coefficients are obtained using infinitesimal perturbation method. Results of load capacity, stiffness and damping coefficients, for foil bearing are compared with those obtained for a rigid gas journal bearing. The limiting values of dynamic characteristics for a foil bearing are constant for all eccentricity ratios.

Effect of Circumferential Location of Radial Injection on Rotordynamic Performance of Hybrid Air Foil Bearings

2018 ◽  
Author(s):  
Behzad Zamanian Yazdi ◽  
Daejong Kim
Keyword(s):  
Time Domain ◽  
High Speed ◽  
Substantial Improvement ◽  
Reliable Operation ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Radial Injection ◽  
Parametric Studies ◽  
Stiffness And Damping

Air foil bearings (AFBs) are introduced as promising bearings for oil-free turbomachinery applications. AFBs provide reliable operation at high speed and high temperature with negligible power loss. Hybrid Air Foil Bearing (HAFB) technology utilizes the radial injection of externally pressurized air into the traditional hydrodynamic AFB’s film thickness through orifices attached to the top foil. Previous studies have reported enhancement in the rotordynamic stability of HAFBs compared to traditional hydrodynamic AFBs. HAFBs have several orifices distributed in the circumferential direction. In this study, the effect of the circumferential location of radial injection on the rotordynamic performance of the rotor-HAFB is studied. Analytical and experimental evaluations of the rotordynamic performance of a rotor supported by two single-pad HAFBs are presented. Parametric studies are conducted using three sets of single-pad HAFBs. The circumferential locations of orifices are different for each set. The presented simulation analyses consist of time-domain orbit simulation and frequency-domain modal analysis. Imbalance responses of rotor-HAFB were measured with various orifice locations and the results agree well with predictions. Comparison of the rotordynamic performance of HAFBs with different orifice configurations demonstrate substantial improvement in rotordynamic stability as well as enhancement in the stiffness and damping coefficients of HAFBs by choosing the best circumferential location for radial injection to control rotor eccentricity and attitude angle.

Effect of Circumferential Location of Radial Injection on Rotordynamic Performance of Hybrid Air Foil Bearings

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Behzad Zamanian Yazdi ◽  
Daejong Kim
Keyword(s):  
Time Domain ◽  
High Speed ◽  
Substantial Improvement ◽  
Reliable Operation ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Radial Injection ◽  
Parametric Studies ◽  
Stiffness And Damping

Air foil bearings (AFBs) are introduced as promising bearings for oil-free turbomachinery applications. AFBs provide reliable operation at high speed and high temperature with negligible power loss. Hybrid air foil bearing (HAFB) technology utilizes the radial injection of externally pressurized air into the traditional hydrodynamic AFB's film thickness through orifices attached to the top foil. Previous studies have reported enhancement in the rotordynamic stability of HAFBs compared to traditional hydrodynamic AFBs. HAFBs have several orifices distributed in the circumferential direction. In this study, the effect of the circumferential location of radial injection on the rotordynamic performance of the rotor-HAFB is studied. Analytical and experimental evaluations of the rotordynamic performance of a rotor supported by two single-pad HAFBs are presented. Parametric studies are conducted using three sets of single-pad HAFBs. The circumferential locations of orifices are different for each set. The presented simulation analyses consist of time-domain orbit simulation and frequency-domain modal analysis. Imbalance responses of rotor-HAFB were measured with various orifice locations and the results agree well with predictions. Comparison of the rotordynamic performance of HAFBs with different orifice configurations demonstrates substantial improvement in rotordynamic stability as well as enhancement in the stiffness and damping coefficients of HAFBs by choosing the best circumferential location for radial injection to control rotor eccentricity and attitude angle.

Influences of journal with 3D form errors on dynamic coefficients of hydrodynamic bearings yielded to JFO boundary conditions

2018 ◽  
Vol 233 (2) ◽  
pp. 289-302 ◽  
Author(s):  
Xun Ma ◽  
Wubin Xu ◽  
Xueping Zhang ◽  
Siyi Ding
Keyword(s):  
Boundary Conditions ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Form Error ◽  
Form Errors ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness And Damping

The dynamic characteristics of the journal with form error are analyzed, including normalized stiffness and damping coefficients. A new expression for journal surface with form error is presented, which is capable of formulating any types of form errors on the journal, and the dimensionless Reynolds equation is renewed and solved suffering from the Jakobsson, Floberg, and Olsson boundary conditions. The results show that form errors do have a significant influence on the dynamic performance of journal bearings and that the uncertainty attribute of form error could result in variations of dynamic properties so significantly that the system might operate in an entirely different way. Therefore, it is necessary to take more operating information into account, such as the elaborate state of the journal surface, in order to predict the bearing performance more accurately.

The Integration of Structural and Fluid Film Dynamic Elements in Foil Bearings: Part I — Past Approaches to the Problem

1999 ◽  
Author(s):  
Hooshang Heshmat
Keyword(s):  
Coulomb Friction ◽  
Dynamic Models ◽  
New Approach ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
The Past ◽  
Bearing Stiffness ◽  
Stiffness And Damping ◽  
Work Done

Abstract A review was conducted on work done in the past on the performance of foil bearings. The main aim of the survey was to see how the two-tiered construction of foil bearings, consisting as they do of two generically disparate elements, one hydrodynamic in nature and the other following the laws of elasticity, have been modeled in order to obtain integrated values of bearing stiffness and damping. A compilation was made of the parameters and processes inherent in the operation of foil bearings, including the kinematics of the bump foil and the accompanying Coulomb friction and damping. The main effort went into examining the results obtained from different dynamic models aimed at obtaining the values of the stiffness and damping coefficients. In Part II of this investigation it is shown that serious discrepancies exist between theory and experimental results and a new approach is offered for modeling the two-tiered domain of foil bearings to calculate the dynamic coefficients.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

Structural Stiffness and Damping Coefficients of a Multileaf Foil Bearing With Bump Foils Underneath

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
Ye Tian ◽  
Yanhua Sun ◽  
Lie Yu
Keyword(s):  
Excitation Frequency ◽  
Magnetic Bearing ◽  
Damping Capacity ◽  
Structural Stiffness ◽  
Test Rig ◽  
Domain Identification ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Applied Forces ◽  
Stiffness And Damping

This paper presents a multileaf foil bearing (MLFB), which consists of four resilient top foils and four stiff bump foils underneath; thus, a high supporting capacity and a high damping capacity can be achieved. A specially designed test rig is used to identify the structural stiffness and damping coefficients of the MLFB. The rotor of the test rig is supported by two journal MLFBs and a thrust active magnetic bearing (AMB) and the static and dynamic loads are applied by two radial AMBs. The tests on MLFBs were conducted under conditions of no shaft rotation at different angular positions and journal displacements with different excitation frequency. A frequency domain identification method is presented to determine the stiffness and damping coefficients. Static measurements show nonlinear deflections with applied forces, which varies with the orientation of the load angular position. The dynamic measurements show that the stiffness and equivalent viscous damping change with the excitation frequency. Furthermore, the stiffness and damping coefficients are related to the operating position where dynamic load tests were conducted. The investigation provides extensive measurements of the static and dynamic characteristics of the MLFB. These results can serve as a benchmark for the calibration of analytical tools under development.

Experimental Analyses of a First Generation Foil Bearing: Start-Up Torque and Dynamic Coefficients

2010 ◽  
Author(s):  
Laurent Rudloff ◽  
Mihai Arghir ◽  
Olivier Bonneau ◽  
Pierre Matta
Keyword(s):  
Dynamic Characteristics ◽  
Static Load ◽  
Excitation Frequency ◽  
Base Plate ◽  
Test Rig ◽  
Dynamic Coefficients ◽  
Foil Bearing ◽  
Start Up ◽  
Lift Off ◽  
Stiffness And Damping

The paper presents the results of the experimental analysis of static and dynamic characteristics of a generation 1 foil bearing of 38.1 mm diameter and L/D = 1. The test rig is of floating bearing type, the rigid shaft being mounted on ceramic ball bearings and driven up to 40 krpm. Two different casings are used for start-up and for measurement of dynamic coefficients. In its first configuration, the test rig is designed to measure the start-up torque. The foil bearing casing is made of two rings separated by a needle bearing for enabling an almost torque free rotation between the foil bearing and the static load. The basic results are the start up torque and the lift off speed. In its second configuration a different casing is used for measuring the impedances of the foil bearing. Misalignment is a problem that is minimized by using three flexible stingers connecting the foil bearing casing to the base plate of the test rig. The test rig enables the application of a static load and of the dynamic excitation on the journal bearing casing, and can measure displacements, forces and accelerations. Working conditions consisted of static loads comprised between 10 N and 50 N and rotation frequencies ranging from 260 Hz to 590 HZ. Excitation frequencies comprised between 100 Hz are 600 Hz are applied by two orthogonally mounted shakers for each working condition. Stiffness and damping coefficients are identified from the complex impedances and enable the calculation of natural frequencies. The experimental results show that the dynamic characteristics of the tested bearing have a weak dependence on the rotation speed but vary with the excitation frequency.

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