Compliant Foil Bearing Structural Stiffness Analysis: Part I—Theoretical Model Including Strip and Variable Bump Foil Geometry

1992 ◽  
Vol 114 (2) ◽  
pp. 394-400 ◽  
Author(s):  
C.-P. Roger Ku ◽  
H. Heshmat
Keyword(s):  
Theoretical Model ◽  
Variable Load ◽  
Distribution Profile ◽  
Friction Forces ◽  
Stiffness Analysis ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Load Distributions ◽  
Fixed End

This paper presents a theoretical model of corrugated foil strip (bump foil) deformation in compliant foil bearings and dampers. The friction forces between bump foils and the housing or the top foil, local interaction forces, variable load distributions, and bump geometries are taken into consideration. Following the trend of earlier published experimental data, the bumps near the fixed end have a much higher predicted stiffness (lower deflection) than those near the free end. Higher friction coefficients tend to increase stiffness and may pin down bumps near the fixed end. An increase in the friction coefficient between the top foil and the bump is a more effective method of achieving both Coulomb damping and higher stiffness. In addition to bump geometry, the load distribution profile greatly influences bump stiffness. A follow-up paper will present the experimental verification and discuss the comparison between theoretical and experimental results.

Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Sébastien Le Lez ◽  
Mihaï Arghir ◽  
Jean Frêne
Keyword(s):  
Dry Friction ◽  
Stability Limit ◽  
Time Step ◽  
Structural Dynamic ◽  
Friction Forces ◽  
Foil Bearings ◽  
Mass Unbalance ◽  
Foil Bearing ◽  
Highly Nonlinear ◽  
The Stability

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared with conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly nonlinear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these nonlinearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full nonlinear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared with rigid ones. Moreover, when friction is introduced, a new level of stability is reached, revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a nonlinear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

Link-Spring Model of Bump-Type Foil Bearings

2009 ◽  
Author(s):  
Kai Feng ◽  
Shigehiko Kaneko
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Wide Spectrum ◽  
Load Capacity ◽  
Ambient Air ◽  
Radial Clearance ◽  
Interaction Forces ◽  
Friction Forces ◽  
Foil Bearings ◽  
Foil Bearing

The field experiences of gas foil bearings (GFBs) from the 1960s prove that GFBs offer several advantages over traditional oil bearings and rolling element bearings. They have the potential to be applied in a wide spectrum of turbomachinery. Bump-type foil bearings, which are considered as the best structure for GFBs, can be simply described as a hydrodynamic bearing utilizing the ambient air as the lubricant and a smooth shell supported by a corrugated bump foil as the bearing surface. However, the performance predictions of bump-type foil bearings are difficult due to mechanical complexity of the support elastic structure, especially for the effects of four factors, elasticity of bump foil, interaction forces between bumps, friction forces at contact surfaces, and local deflection of top foil. In this investigation, an analytical model of bump-type foil bearings considering the effects of all above factors is presented. In this model, each bump of the bump strip is simplified to two rigid links and a horizontally spaced spring, whose stiffness is determined from Castigliano’ theorem. Then, interaction forces and friction forces can be coupled with the bump flexibility though the horizontal elementary spring. The local deflection of top foil is described using a Finite Element model and added to the film thickness for the pressure prediction with the Reynolds’ equation. The bump deflections of a strip with ten bumps under different load distributions are calculated with the presented model and the predictions show consistency with published results. Moreover, the predicted bearing load and film thickness of a full bump-type foil bearing using this model are very close to the experimental data. Also, radial clearance and friction force variations in the foil bearing are noted to change the stiffness of bump significantly. And the predictions from the calculation with a proper selection of radial clearance and friction coefficients show extremely good agreement with the experimental data. The assumption of minimum reachable film thickness is based on experimental data to determine the load capacity of bearing. The results demonstrate that the radial clearance of foil bearing has an optimum value for the maximum load capacity.

Compliant Foil Bearing Structural Stiffness Analysis—Part II: Experimental Investigation

1993 ◽  
Vol 115 (3) ◽  
pp. 364-369 ◽  
Author(s):  
C.-P. Roger Ku ◽  
Hooshang Heshmat
Keyword(s):  
Theoretical Model ◽  
Structural Characteristics ◽  
Tracking System ◽  
Operating Conditions ◽  
Optical Tracking ◽  
Design Parameters ◽  
Friction Forces ◽  
Foil Bearings ◽  
Light Load ◽  
Wide Range

This paper describes the second part of an investigation into the mechanism of deformation of the corrugated foil (bump foil) strips used in compliant surface foil bearings. In the earlier work, a theoretical model was developed to predict the structural characteristics of bump foil strips under various loads, including the effects of the friction forces between the compliant elements, local interaction forces, load distribution profiles, and bump configurations. In the experiments described here in, two-dimensional deflections of bump foils were recorded via an optical tracking system for a wide range of operating conditions to verify the feasibility of the theoretical model. Test results corroborate the theoretical model for the linear regions of load and the deflection parameters. The effects of the bearing design parameters, such as bump configuration, load profile, and surface coating and lubricant, on the structural characteristics of the bump foil strip were investigated. In addition, the source and mechanism of nonlinear behavior of the bump foil strips under light load conditions were examined, and more effective methods of achieving both Coulomb damping and optimum structural compliance were investigated. An understanding of the analytical and semi-empirical relations resulting from this work offers designers the potential for enhancing the design of high-performance compliant foil bearings.

Nonlinear Numerical Prediction of Gas Foil Bearings Stability and Unbalanced Response

2008 ◽  
Author(s):  
Se´bastien Le Lez ◽  
Mihai¨ Arghir ◽  
Jean Frene
Keyword(s):  
Dry Friction ◽  
Stability Limit ◽  
Time Step ◽  
Structural Dynamic ◽  
Friction Forces ◽  
Foil Bearings ◽  
Mass Unbalance ◽  
Foil Bearing ◽  
Non Linear ◽  
The Stability

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared to conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly non linear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these non linearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full non linear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared to rigid ones. Moreover, when friction is introduced, a new level of stability is reached revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a non linear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

Analytical Model of Bump-Type Foil Bearings Using a Link-Spring Structure and a Finite-Element Shell Model

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Kai Feng ◽  
Shigehiko Kaneko
Keyword(s):  
Finite Element ◽  
Film Thickness ◽  
Shell Model ◽  
Analytical Model ◽  
Load Capacity ◽  
Radial Clearance ◽  
Interaction Forces ◽  
Friction Forces ◽  
Foil Bearings ◽  
Foil Bearing

A complete analytical model of bump-type foil bearings taking into consideration the effects of four factors, i.e., the elasticity of bump foil, the interaction forces between bumps, the friction forces at the contact surfaces, and the local deflection of top foil, is presented in this investigation. Each bump is simplified to two rigid links and a horizontally spaced spring, the stiffness of which is determined from Castigliano’s theorem. The interaction forces and the friction forces are coupled with the flexibility of bumps through the horizontal elementary spring. The local deflection of the top foil is described using a finite-element shell model and added to the film thickness to predict the air pressure with Reynolds’ equation. The bump deflections of a strip with ten bumps calculated using the presented model under different load distributions are consistent with the published results. Moreover, the predicted bearing load and film thickness obtained from a foil bearing with a bump circumferential extend of 360 deg also agree very well with the experimental data, especially for predictions with a proper selection of radial clearance (preload of foil structure) and friction coefficients. In addition, the radial clearance and friction force variations in the foil bearing are noted to significantly change the performance of the foil bearing. The predictions demonstrate that the radial clearance of the foil bearing has an optimum value for the maximum load capacity.

Foil Gas Bearing With Compression Springs: Analyses and Experiments

2007 ◽  
Vol 129 (3) ◽  
pp. 628-639 ◽  
Author(s):  
Ju-ho Song ◽  
Daejong Kim
Keyword(s):  
Loss Factor ◽  
Load Capacity ◽  
Underlying Structure ◽  
Equivalent Viscous Damping ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Different Types ◽  
Structural Loss ◽  
Compression Springs ◽  
Gas Bearing

A new foil gas bearing with spring bumps was constructed, analyzed, and tested. The new foil gas bearing uses a series of compression springs as compliant underlying structures instead of corrugated bump foils. Experiments on the stiffness of the spring bumps show an excellent agreement with an analytical model developed for the spring bumps. Load capacity, structural stiffness, and equivalent viscous damping (and structural loss factor) were measured to demonstrate the feasibility of the new foil bearing. Orbit and coast-down simulations using the calculated stiffness and measured structural loss factor indicate that the damping of underlying structure can suppress the maximum peak at the critical speed very effectively but not the onset of hydrodynamic rotor-bearing instability. However, the damping plays an important role in suppressing the subsynchronous vibrations under limit cycles. The observation is believed to be true with any air foil bearings with different types of elastic foundations.

Static Determinacy in the Theory of Finite Width Foil Bearings

1974 ◽  
Vol 41 (1) ◽  
pp. 51-54 ◽  
Author(s):  
W. E. Langlois
Keyword(s):  
Force Balance ◽  
Finite Width ◽  
Foil Bearings ◽  
Lubrication Equation ◽  
Foil Bearing ◽  
Edge Conditions ◽  
Single Force ◽  
Static Determinacy ◽  
Force Balance Equation ◽  
Determinate Problem

The assumption of “perfect flexibility” is shown to be self-consistent in an important class of finite-width foil bearing problems. When the membrane equations are written in the “stretched coordinates” of foil bearing theory, the usual edge conditions on the tape result in a statically determinate problem. The tape dynamics couples to the Reynolds lubrication equation through a single force-balance equation which does not entail the elastic strain.

Experimental Evaluation of the Structure Characterization of a Novel Hybrid Bump-Metal Mesh Foil Bearing

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Kai Feng ◽  
Yuman Liu ◽  
Xueyuan Zhao ◽  
Wanhui Liu
Keyword(s):  
Excitation Frequency ◽  
Structure Characterization ◽  
Viscous Damping ◽  
Metal Mesh ◽  
Equivalent Viscous Damping ◽  
Foil Bearings ◽  
Damping Characteristics ◽  
Foil Bearing ◽  
Mesh Density ◽  
Load Tests

Rotors supported by gas foil bearings (GFBs) experience stability problem caused by subsynchronous vibrations. To obtain a GFB with satisfactory damping characteristics, this study presented a novel hybrid bump-metal mesh foil bearing (HB-MMFB) that consists of a bump foil and metal mesh blocks in an underlying supporting structure, which takes advantage of both bump-type foil bearings (BFBs) and MMFBs. A test rig with a nonrotating shaft was designed to estimate structure characterization. Results from the static load tests show that the proposed HB-MFBs exhibit an excellent damping level compared with the BFBs with a similar size because of the countless microslips in the metal mesh blocks. In the dynamic load tests, the HB-MFB with a metal mesh density of 36% presents a viscous damping coefficient that is approximately twice that of the test BFB. The dynamics structural coefficients of HB-MFBs, including structural stiffness, equivalent viscous damping, and structural loss factor, are all dependent on excitation frequency and motion amplitude. Moreover, they exhibit an obvious decrease with the decline in metal mesh density.

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