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.

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.

Theoretical Study on Static Performance of Double-Bump Foil Bearings

2021 ◽  
Author(s):  
Fangcheng Xu ◽  
Jianhua Chu ◽  
Wenlin Luan ◽  
Guang Zhao
Keyword(s):  
Finite Element ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Static Characteristics ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Static Performance ◽  
Initial Clearance

Abstract In this paper, single-bump foil models with different thickness and double-bump foil models with different initial clearances are established. The structural stiffness and equivalent viscous damping of double-bump foil and single-bump foil are analyzed by finite element simulation. The results show that the double-layer bump foil has variable stiffness and the displacement of the upper bump is greater than the initial gap when the two-layer bumps contact. A model for obtaining static characteristics of aerodynamic compliant foil thrust bearing is established on the basis of the stiffness characteristics of the double-bump foil. This paper solves gas Reynolds equation, the gas film thickness equation and the foil stiffness characteristic equation via the finite element method and the finite difference method. The static characteristics of the thrust bearings including the bearing pressure distribution, the gas film thickness and the friction power consumption have been obtained. The static characteristics of two kinds of foils have been compared and analyzed, and the effect of initial clearance on the static performance of double-bump foil bearings is studied. The results show that the double-bump foil structure can effectively improve the load capacity of thrust bearing. In addition, the static performance of double-bump foil thrust bearings is between the performance of the single-bump foil bearing and the double-bump foil bearing whose foil’s clearance is zero. The smaller the initial clearance is, the easier it will be to form a stable double-bump foil supporting structure.

Influence of geometric parameters on the bump foil bearing performance

2019 ◽  
Vol 234 (7) ◽  
pp. 1017-1026
Author(s):  
Sadanand Kulkarni ◽  
Soumendu Jana
Keyword(s):  
Carrying Capacity ◽  
High Speed ◽  
System Development ◽  
Load Capacity ◽  
Radial Clearance ◽  
Load Carrying Capacity ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Load Carrying ◽  
Lift Off

High-speed rotating system development has drawn considerable attention of the researchers, in the recent past. Foil bearings are one of the major contenders for such applications, particularly for high speed and low load rotating systems. In foil bearings, process fluid or air is used as the working medium and no additional lubricant is required. It is known from the published literature that the load capacity of foil bearings depend on the operating speed, viscosity of the medium, clearance, and stiffness of the foil apart from the geometric dimensions of the bearing. In case of foil bearing with given dimensions, clearance governs the magnitude of pressure developed, whereas stiffness dictates the change in radial clearance under the generated pressure. This article deals with the effect of stiffness, clearance, and its interaction on the bump foil bearings load-carrying capacity. For this study, four sets of foil bearings of the same geometry with two levels of stiffness and clearance values are fabricated. Experiments are carried out following two factor-two level factorial design approach under constant load and in each case, the lift-off speed is measured. The experimental output is analyzed using statistical techniques to evaluate the influence of parameters under consideration. The results indicate that clearance has the maximum influence on the lift-off speed/ load-carrying capacity, followed by interaction effect and stiffness. A regression model is developed based on the experimental values and model is validated using error analysis technique.

Investigation of Structural Conformity in a Three-Pad Adaptive Air Foil Bearing With Regard to Active Control of Radial Clearance

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Hossein Sadri ◽  
Henning Schlums ◽  
Michael Sinapius
Keyword(s):  
Shape Control ◽  
Degrees Of Freedom ◽  
Load Capacity ◽  
Radial Clearance ◽  
Foil Bearings ◽  
Compliant Structure ◽  
Foil Bearing ◽  
Points Of View ◽  
Lift Off ◽  
Structural Conformity

Abstract Various solutions for the design of oil-free bearings are discussed in the literature. Adding hydrodynamic preload to the foil bearings by profiling the inner bore of the bearing is one of the most frequently investigated methods for improving the bearing stability and damping character of the entire system. However, this approach leads to a reduced load capacity and thus to an increased lift-off speed of the foil bearings. Observations of this kind lead to the presentation of various solutions for active bearing contour adjustment, which benefits from different profiles of the lubricant film. Most of these concepts use piezoelectric stack actuators to generate the required alternating force, although the influence of the stiffness of adaptive elements on bearing performance is not fully discussed in the literature. The focus of this study is on the investigation of structural conformity, i.e., the harmonization of stiffness with respect to the requirements for shape control and load capacity of an adaptive air foil bearing (AAFB). The result may be a basis for the consideration of additional degrees of freedom in any concept with shape control as the main design framework in interaction between the lubricant and compliant structure in an air foil bearing from both static and dynamic points of view.

Effect of Foil Geometry on the Static Performance of Thrust Foil Bearings

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Gen Fu ◽  
Alexandrina Untaroiu ◽  
Erik Swanson
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Optimization Technique ◽  
Three Dimensional ◽  
Leading Edge ◽  
Numerical Approach ◽  
Sensitivity Study ◽  
Rotating Speed ◽  
Foil Bearings ◽  
Foil Bearing

Gas foil bearings can operate in extreme conditions such as high temperature and high rotating speed, compared to traditional bearings. They also provide better damping and stability characteristics and have larger tolerance to debris and rotor misalignment. Gas foil bearings have been successfully applied to micro- and small-sized turbomachinery, such as microgas turbine and cryogenic turbo expander. In the last decades, a lot of theoretical and experimental work has been conducted to investigate the properties of gas foil bearings. However, very little work has been done to study the influence of the foil bearing pad configuration. This study proposes a robust approach to analyze the effect of the foil geometry on the performance of a six-pad thrust foil bearing. In this study, a three-dimensional (3D) computational fluid dynamics (CFD) model for a parallel six-pad thrust foil bearing is created. In order to predict the thermal property, the total energy with viscous dissipation is used. Based on this model, the geometry of the thrust foil bearing is parameterized and analyzed using the design of experiments (DOE) methodology. In this paper, the selected geometry parameters of the foil structure include minimum film thickness, inlet film thickness, the ramp extent on the inner circle, the ramp extent on the outer circle, the arc extent of the pad, and the orientation of the leading edge. The objectives in the sensitivity study are load capacity and maximal temperature. An optimal foil geometry is derived based on the results of the DOE process by using a goal-driven optimization technique to maximize the load capacity and minimize the maximal temperature. The results show that the geometry of the foil structure is a key factor for foil bearing performance. The numerical approach proposed in this study is expected to be useful from the thrust foil bearing design perspective.

A Fully Coupled 3D Finite Element Analysis for a Bump-Type Compliant Foil Bearing

2011 ◽  
Author(s):  
Serdar Aksoy ◽  
M. Bulut Coskun ◽  
Mahmut F. Aksit
Keyword(s):  
Finite Element ◽  
Film Formation ◽  
Load Capacity ◽  
Foil Surface ◽  
Element Analysis ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Element Approach ◽  
The Stability ◽  
Fully Coupled

A bump-type foil bearing consists of a compliant corrugated sheet metal supporting structure that is covered by a thin top foil surface. Bumps serve as stiffener and damping elements to increase the stability of the system while top foil creates necessary wedge surface for aerodynamic film formation. Foil bearings are hard to analyze as flexible foil surface deforms and changes shape while aerodynamic film pressure forms. Fully coupled finite element approach is presented. To increase the accuracy, the geometry is discretized with quadratic hexagonal elements. The gas film is modeled by compressible Reynolds equation. The effect of velocity on load capacity will be investigated to reveal the performance of the code.

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.

Rotordynamics Performance of Hybrid Foil Bearing Under Forced Vibration Input

2017 ◽  
Author(s):  
Daejong Kim ◽  
Brian Nicholson ◽  
Lewis Rosado ◽  
Garry Givan
Keyword(s):  
Impulse Response ◽  
High Speed ◽  
Load Capacity ◽  
Supply System ◽  
Forced Response ◽  
Experimental Results ◽  
Lateral Acceleration ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Gas Supply

Foil bearings are one type of hydrodynamic air/gas bearings but with a compliant bearing surface supported by structural material that provides stiffness and damping to the bearing. The hybrid foil bearing (HFB) in this paper is a combination of a traditional hydrodynamic foil bearing with externally-pressurized air/gas supply system to enhance load capacity during the start and to improve thermal stability of the bearing. The HFB is more suitable for relatively large and heavy rotors where rotor weight is comparable to the load capacity of the bearing at full speed and extra air/gas supply system is not a major added cost. With 4,448N∼22,240N thrust class turbine aircraft engines in mind, the test rotor is supported by HFB in one end and duplex rolling element bearings in the other end. This paper presents experimental work on HFB with diameter of 102mm performed at the US Air force Research Laboratory. Experimental works include: measurement of impulse response of the bearing to the external load corresponding to rotor’s lateral acceleration of 5.55g, forced response to external subsynchronous excitation, and high speed imbalance response. A non-linear rotordynamic simulation model was also applied to predict the impulse response and forced subsynchronous response. The simulation results agree well with experimental results. Based on the experimental results and subsequent simulations, an improved HFB design is also suggested for higher impulse load capability up to 10g and rotordynamics stability up to 30,000rpm under subsynchronous excitation.

On the Axisymmetric Response of a Damaged Flexible Pipe

2014 ◽  
Author(s):  
José Renato M. de Sousa ◽  
Carlos Magluta ◽  
Ney Roitman ◽  
George C. Campello
Keyword(s):  
Finite Element ◽  
Analytical Model ◽  
Load Capacity ◽  
High Stress ◽  
Experimental Tests ◽  
Theoretical Models ◽  
Experimental Measurements ◽  
Fe Model ◽  
Flexible Pipe ◽  
High Stress Concentration

This work focuses on the structural analysis of a damaged 9.13″ flexible pipe to pure and combined axisymmetric loads. A set of experimental tests was carried out considering one up to ten broken wires in the outer tensile armor of the pipe and the results obtained are compared to those provided by a previously presented finite element (FE) model and a traditional analytical model. In the experimental tests, the pipe was firstly subjected to pure tension and, then, the responses to clockwise and anti-clockwise torsion superimposed with tension were investigated. In these tests, the induced strains in the outer armor were measured. Moreover, the axial elongation of the pipe was monitored when the pipe is subjected to tension, whilst the twist of the pipe was measured when torsion is imposed. The experimental results pointed to a slight decrease in the stiffness of the pipe with the increasing number of broken wires and, furthermore, a redistribution of forces among the intact wires of the damaged layer with high stress concentration in the wires close to the damaged ones. Both theoretical models captured these features, but, while the results obtained with the FE model agreed well with the experimental measurements, the traditional analytical model presented non-conservative results. Finally, the results obtained are employed to estimate the load capacity of the pipe.

Hybrid Air Foil Bearings With External Pressurization

Tribology ◽  
2006 ◽  
Author(s):  
Daejong Kim ◽  
Soonkuk Park
Keyword(s):  
Load Capacity ◽  
Experimental Studies ◽  
Axial Flow ◽  
Steel Tube ◽  
Operating Conditions ◽  
Drag Torque ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Hybrid Operation ◽  
Lift Off

Foil bearings are widely used for oil-free microturbomachinery. One of the critical technical issues related to reliability of the foil bearings is a coating wear on the top foil and rotor during start/stops. Especially for heavily loaded foil bearings, large start torque requires a large drive motor. Bearing cooling is also mandatory for certain applications because the foil bearings can generate significant amount of heat depending on operating conditions. Usually axial flow is used through the space between the top foil and bearing sleeve. In this paper, a hybrid air foil bearing with external pressurization is introduced. A flexible steel tube is attached to the backside of the top foil with orifice holes, and externally pressurized air is directly supplied to the bearing clearance to lift off the rotor before rotor spins. The hybrid operation eliminates the coating wear during start/stop cycles, reduces drag torque during starts, and eliminates axial flow cooling. The hybrid foil gas bearing was constructed using a multiple compression springs to demonstrate a feasibility of the concept. A simple analytical model to calculate top foil deflection under hydrostatic pressurization has been developed. Predictions via orbit simulations indicate the hybrid air foil bearings can have much higher critical speed and onset speed of instability than hydrodynamic counter part. Measured load capacity was slightly higher than hydrodynamic bearing even under smaller amount of air flow. In addition, the hybrid operation was very effective for bearing cooling even if the cooling flow rate was lower than hydrodynamic counterpart. The measured very small drag torque during the start/stop demonstrates the hybrid foil bearing can have near-infinite life time without wear of the bearing and rotor surface. The experimental studies show high potential of the hybrid air foil bearings for various oil-free turbomachinery, especially for heavily loaded high temperature applications.

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