The Influence of the Slip Flow on Steady-State Load Capacity, Stiffness and Damping Coefficients of Elastically Supported Gas Foil Bearings

A theoretical analysis of the steady-state and dynamic characteristics of multi-recess hybrid oil journal bearings is presented. A perturbation theory for small vibrations is used to solve an incompressible, finite journal bearing with a time-dependent term. Load capacity, attitude angle, friction parameter, stiffness and damping coefficients are evaluated for a capillary-compensated bearing.

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A Comparison of the Steady-State and Dynamic Performance of First- and Second-Generation Foil Bearings

Volume 6: Structures and Dynamics, Parts A and B ◽

10.1115/gt2010-23683 ◽

2010 ◽

Cited By ~ 5

Author(s):

M. J. Conlon ◽

A. Dadouche ◽

W. M. Dmochowski ◽

R. Payette ◽

J.-P. Be´dard

Keyword(s):

Steady State ◽

Experimental Evaluation ◽

First Generation ◽

Second Generation ◽

Load Capacity ◽

Dynamic Stiffness ◽

Dynamic Performance ◽

Foil Bearings ◽

Foil Bearing ◽

Stiffness And Damping

Oil-free foil bearing technology has advanced intermittently over the years, driven by research efforts to improve both steady-state and dynamic performance characteristics, namely: load capacity, stiffness, and damping. Bearing designs are thus classified according to “generation”, with first-generation bearings being the most primitive. This paper presents an experimental evaluation of a first- and a second-generation foil bearing, and aims to provide the high-fidelity data necessary for proper validation of theoretical predictive models of foil bearing performance. The aforementioned test bearings were fabricated in-house, and are both 70mm in diameter with an aspect ratio of 1; bearing manufacturing details are provided. The work makes use of a facility dedicated to measuring both the steady-state and dynamic properties of foil bearings under a variety of controlled operating conditions. The bearing under test is placed at the midspan of a horizontal, simply-supported, stepped shaft which rotates at up to 60krpm. Static and dynamic loads of up to 3500N and 450N (respectively) can be applied by means of a pneumatic cylinder and two electrodynamic shakers. The bearings’ structural (static) stiffnesses are highly nonlinear, and this affects the accuracy of the dynamic coefficient determination. Both dynamic stiffness and damping are found to vary nonlinearly with excitation frequency, and are over-predicted by a structural experimental evaluation — the film plays an important role in bearing dynamics. The second-generation bearing is found to have a higher load capacity, dynamic stiffness, and damping than the first-generation bearing.

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Performance Analysis of Double-Bumped Air Foil Bearings

ASME/STLE 2007 International Joint Tribology Conference, Parts A and B ◽

10.1115/ijtc2007-44069 ◽

2007 ◽

Author(s):

Y. C. Kim ◽

D. H. Lee ◽

K. W. Kim

Keyword(s):

Theoretical Model ◽

Friction Coefficient ◽

Performance Analysis ◽

Active Region ◽

Load Capacity ◽

Equivalent Stiffness ◽

Vertical Deflection ◽

Foil Bearings ◽

Damping Coefficients ◽

Stiffness And Damping

This paper presents a theoretical model for the analysis of double-bumped Air Foil Bearings (AFBs). The stiffness and damping coefficients of the double bump vary depending on the external load and its friction coefficient. The double bump can be either in the single or double active region depending on vertical deflection. The equivalent stiffness and damping coefficients of the bump system are derived from the vertical and horizontal deflection of the bump, including the friction effect. The results of the performance analysis for a double bumped AFB are compared with those obtained for a single bumped AFB. This paper successfully proves that a double bumped AFB has higher load capacity, stiffness, and damping than a single bump AFB in a heavily loaded condition.

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Improvements to the Analysis of Gas Foil Bearings: Integration of Top Foil 1D and 2D Structural Models

Volume 5: Turbo Expo 2007 ◽

10.1115/gt2007-27249 ◽

2007 ◽

Cited By ~ 24

Author(s):

Luis San Andre´s ◽

Tae Ho Kim

Keyword(s):

Film Thickness ◽

Gas Turbines ◽

Load Capacity ◽

Structural Models ◽

Underlying Structure ◽

Fe Model ◽

Foil Bearings ◽

Damping Coefficients ◽

Minimum Film Thickness ◽

Stiffness And Damping

Gas foil bearings (GFBs) find widespread usage in oil-free turbo expanders, APUs and micro gas turbines for distributed power due to their low drag friction and ability to tolerate high level vibrations, including transient rubs and shaft misalignment, static and dynamic. The static load capacity and dynamic forced performance of GFBs depends largely on the material properties of the support elastic structure, i.e. a smooth foil on top of bump strips. Conventional models include only the bumps as an equivalent stiffness uniformly distributed around the bearing circumference. More complex models couple directly the elastic deformations of the top foil to the bump underlying structure as well as to the hydrodynamics of the gas film. This paper details two FE models for the top foil supported on bump strips, one considers a 2D shell anisotropic structure and the other a 1D beam-like structure. The Cholesky decomposition of the stiffness matrix representing the top foil and bump strips is performed off-line prior to computations coupling it to the gas film analysis governed by Reynolds equation. The procedure greatly enhances the computational efficiency of the numerical scheme. Predictions of journal attitude angle and minimum film thickness for increasing static loads and two journal speeds are obtained for a GFB tested decades ago. 2D FE model predictions overestimate the minimum film thickness at the bearing centerline, while underestimating it at the bearing edges. Predictions from the 1D FE model compare best to the limited tests data; reproducing closely the experimental circumferential wavy-like minimum film thickness profile. The 1D top foil model is recommended due to its low computational cost. Predicted stiffness and damping coefficients versus excitation frequency show that the two FE top foil structural models result in slightly lower direct stiffness and damping coefficients than those from the simple elastic foundation model.

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

Journal of Tribology ◽

10.1115/1.2920982 ◽

1993 ◽

Vol 115 (1) ◽

pp. 20-27 ◽

Cited By ~ 116

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.

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On the Dynamics of Elastohydrodynamic Mixed Lubricated Ball Bearings. Part I: Formulation of Stiffness and Damping Coefficients

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1243/135065005x34071 ◽

2005 ◽

Vol 219 (6) ◽

pp. 411-421 ◽

Cited By ~ 13

Author(s):

M Sarangi ◽

B. C. Majumdar ◽

A. S. Sekhar

Keyword(s):

Surface Roughness ◽

Steady State ◽

Pressure Distribution ◽

Reynolds Equation ◽

Load Capacity ◽

Design Parameters ◽

Asperity Contact ◽

Damping Coefficients ◽

Damping Characteristics ◽

Stiffness And Damping

The problems of stiffness and damping characteristics of isothermal elastohydrodynamic mixed lubricated point contact are evaluated numerically considering surface roughness effect including asperity contact load. A set of equations under steady-state and dynamic conditions is derived from the classical Reynolds equation, using linear perturbation method. The elasticity equation and steady-state Reynolds equation are solved simultaneously for finding the steady-state pressure distribution, using finite difference method. Then, the set of perturbed equations is solved for the dynamic pressure distribution in the contact. A Gaussian surface roughness is adopted to model both surface roughness and mixed lubrication. Total load capacity of the contact is calculated from the lubricant film pressure and contact pressure distribution. Results are compared with those of smooth isothermal cases. The stiffness and damping coefficients of the contact are determined using the dynamic pressures. The asperity contact stiffness is calculated separately. Effect of various design parameters on stiffness and damping characteristics of a ball bearing is investigated.

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Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2718233 ◽

2006 ◽

Vol 129 (3) ◽

pp. 850-857 ◽

Cited By ~ 36

Author(s):

Luis San Andrés ◽

Dario Rubio ◽

Tae Ho Kim

Keyword(s):

High Speed ◽

Critical Speed ◽

Load Capacity ◽

Test System ◽

Foil Bearings ◽

Rotor Imbalance ◽

Synchronous Motion ◽

Damping Characteristics ◽

Rotor Surface ◽

Stiffness And Damping

Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e., simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10mm. Coast down rotor responses from 25krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5krpm to 15krpm with a whirl frequency at ∼50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Posttest inspection reveal wear spots on the top foils and rotor surface.

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Helical-Grooved Journal Bearing Operated in Turbulent Regime

Journal of Lubrication Technology ◽

10.1115/1.3451407 ◽

1970 ◽

Vol 92 (2) ◽

pp. 346-357 ◽

Cited By ~ 11

Author(s):

C. Y. Chow ◽

J. H. Vohr

Keyword(s):

Steady State ◽

Journal Bearing ◽

Critical Mass ◽

Reynolds Numbers ◽

Turbulent Regime ◽

Damping Coefficients ◽

Radial Stiffness ◽

Performance Curves ◽

Stiffness And Damping ◽

Laminar And Turbulent Regimes

An analysis for helical bearings operated in turbulent regime, with negligible inertia in an incompressible fluid film, was performed [10, 11]. The analysis is based on the linearised lubrication theory developed by Ng and Pan [4]. The outlines for this analysis and, in particular, the bearing performance data for various helical groovings are given in this paper. The data presented include the bearing performance at the steady state, the stiffness and damping coefficients, and the critical mass of journal in both laminar and turbulent regimes. To facilitate designs, these data are computed for optimal geometries of helical grooved bearings to provide maximum radial stiffness at various Reynolds numbers. In addition, the effect of external pressurized supply of lubricant are shown in the performance curves.

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Rotordynamic Behavior of 225 kW (300 HP) Class PMS Motor–Generator System Supported by Gas Foil Bearings

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4029712 ◽

2015 ◽

Vol 137 (9) ◽

Cited By ~ 7

Author(s):

Bok Seong Choe ◽

Tae Ho Kim ◽

Chang Ho Kim ◽

Yong Bok Lee

Keyword(s):

Axial Length ◽

High Speed ◽

Load Capacity ◽

Stability Margin ◽

Generator System ◽

Thrust Bearings ◽

Foil Bearings ◽

Speed Up ◽

The Stability ◽

Stiffness And Damping

This paper presents the dynamic behavior of a 225 kW class (300 HP), 60,000 rpm, permanent magnet synchronous (PMS) motor–generator system supported on gas foil bearings (GFBs). The rotor of a 225 kW PMS motor is supported by two identical gas foil journal bearings (GFJBs) and one pair of gas foil thrust bearings (GFTBs). The total weight and axial length of the coupled rotors are 272 N and 1042 mm, respectively. During the speed-up test to 60,000 rpm, unexpected large subsynchronous rotor motions appear at around 120–130 Hz above 35,040 rpm. After disassembling the motor, an inspection of the top foils of the GFJBs reveals significant rotor rubbing. Thus, the GFJBs are redesigned to have a smaller load capacity by reducing their axial length to 45 mm. In addition, three 50 μm thick shims are installed in the GFJBs at 120 deg intervals for reducing the swirl speed of air and producing bearing preloads. The modification delays the onset speed of subsynchronous motions to 43,200 rpm and decreases the amplitude of the subsynchronous motions from 20 to 15 μm. These results indicate that the modification improves the stability margin of the high-speed rotor system with increasing stiffness and damping. In addition, the logarithmic decrement trends are in good agreement with the test results.

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Multi-Objective Optimisation of an Aerostatic Pad: Design of Position, Number and Diameter of the Supply Holes

Journal of Mechanics ◽

10.1017/jmech.2019.41 ◽

2020 ◽

Vol 36 (3) ◽

pp. 347-360

Author(s):

F. Colombo ◽

F. Della Santa ◽

S. Pieraccini

Keyword(s):

Genetic Algorithm ◽

Load Capacity ◽

Design Parameters ◽

Objective Functions ◽

Aerostatic Bearing ◽

Multiobjective Optimisation ◽

Damping Coefficients ◽

Supply Pressure ◽

Design Variables ◽

Stiffness And Damping

ABSTRACTIn this paper, a rectangular aerostatic bearing with multiple supply holes is optimised with a multiobjective optimisation approach. The design variables taken into account are the supply holes position, their number and diameter, the supply pressure, while the objective functions are the load capacity, the air consumption and the stiffness and damping coefficients. A genetic algorithm is applied in order to find the Pareto set of solutions. The novelty with respect to other optimisations which can be found in literature is that number and location of the supply holes is completely free and not associated to a pre-defined scheme. A vector x associated with the supply holes location is introduced in the design parameters and given in input to the optimizer.

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