Free Linear Vibration of Self-Pressurized Foil Bearings

1993 ◽  
Vol 115 (2) ◽  
pp. 145-151 ◽  
Author(s):  
J. A. Wickert
Keyword(s):  
Elastohydrodynamic Lubrication ◽  
Air Pressure ◽  
Mode Shapes ◽  
Illustrative Case ◽  
Recording Head ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Generalized Matrix ◽  
Axially Moving ◽  
The One

A foil bearing is formed when a flexible medium travels across a stationary rigid surface and entrains a thin layer of fluid that lubricates the relative sliding motion. Such bearings are used in magnetic tape drives to prevent excessive wear of the recording head and tape interface. In the one-dimensional model considered here, the tape is approximated as an axially-moving Euler-Bernoulli beam under tension, and the air pressure in the bearing region satisfies Reynolds equation for unsteady compressible flow. To the extent that transverse deformation of the tape couples with the air pressure, the “foil bearing problem” falls within the discipline of elastohydrodynamic lubrication. The governing equations for the tape and recording head are linearized about the equilibrium displacement and pressure fields, and the two resulting coupled partial differential equations with nonconstant coefficients describe the linear response. Following global discretization through Galerkin’s method, the natural frequencies, damping, and mode shapes of the tape and recording head system are determined through numerical solution of the generalized matrix eigenvalue problem. The coupled displacement and pressure modes depend on the transport speed, and they are complex because of viscous dissipation of the air and convection of the tape. For the illustrative case of a semicircular recording head, the dependence of the system’s eigenvalues on the transport speed, and on the location of the recording head within the tape’s span, is discussed.

On the Vibration of Coupled Traveling String and Air Bearing Systems

1996 ◽  
Vol 118 (3) ◽  
pp. 398-405 ◽  
Author(s):  
A. V. Lakshmikumaran ◽  
J. A. Wickert
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Nodal Point ◽  
Fold Increase ◽  
Computational Effort ◽  
Air Pressure ◽  
Mode Shapes ◽  
Air Bearing ◽  
Design Variables ◽  
Axially Moving

Air bearings are used to position and guide such axially-moving materials as high speed magnetic tapes, paper sheets, and webs. In each case, vibration of the moving medium couples with the air bearing’s dynamics, and techniques are developed here to reduce the computational effort that is required to predict the natural frequencies, damping ratios, and vibration modes of the prototypical traveling string and self-pressurized air bearing model. Automatic nodal point allocation reduces the number of nonlinear equations that arise in finding the equilibrium string displacement and air pressure, and in subsequent vibration analysis, the response is obtained in closed form by using the Green’s function for the traveling string. Global discretization of the air pressure alone then yields a matrix eigenvalue problem which is simpler than that obtained through previous methods which required discretization of both displacement and pressure. Overall, essentially a five-fold increase in computational speed is achieved, thus facilitating design and parameter studies. Changes in the natural frequencies, damping ratios, and coupled displacement-pressure mode shapes with respect to several design variables are discussed and compared with experiments.

An Experimental Study of Elastohydrodynamic Lubrication of Foil Bearings: Part 1—Displacement in the Central Zone

1968 ◽  
Vol 90 (1) ◽  
pp. 199-220 ◽  
Author(s):  
L. Licht
Keyword(s):  
Central Zone ◽  
Elastohydrodynamic Lubrication ◽  
Rotating Cylinder ◽  
Air Gap ◽  
Finite Width ◽  
Transition Zones ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Theoretical Predictions ◽  
Gap Width

An elastic foil under tension is wrapped partly around a rotating cylinder and is supported on a thin film of air. Capacitance probes, coincident with the surface of the cylinder, scan the air gap along the arc of wrap. The cylinder can be traversed across the width of the stationary foil, so that the topography of the air gap can be determined from a series of circumferential scans. Experimental results are compared quantitatively with theoretical predictions for the perfectly flexible and for the elastic foil bearing of infinite width [8, 12]. A comparison is also made with theory, for the case when the angle of wrap is small and the entrance and exit transition zones merge [9]. The effect of foil and gap width on side leakage is illustrated. The last part of this study deals with elastic foil bearings of finite width and with the characteristic “edge effect” in particular. The influence of various parameters on the nature of the displacement field of foils is demonstrated and related to recent analyses [13].

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.

Lateral Vibration of Two Axially Translating Beams Interconnected by a Winkler Foundation

2006 ◽  
Vol 129 (3) ◽  
pp. 380-385 ◽  
Author(s):  
Mohamed Gaith ◽  
Sinan Müftü
Keyword(s):  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Mode Shapes ◽  
Winkler Foundation ◽  
Axial Tension ◽  
Winkler Elastic Foundation ◽  
Critical Tension ◽  
Divergence Instability ◽  
Axially Moving Beams ◽  
Axially Moving

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. The natural frequencies and associated mode shapes are obtained. The natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at a critical velocity and a critical tension; and, divergence and flutter instabilities coexist at postcritical speeds, and divergence instability takes place precritical tensions. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams are presented.

Comparative Evaluation of Foil Bearings With Different Compliant Structures for Improved Manufacturability

2017 ◽  
Author(s):  
K. Shalash ◽  
J. Schiffmann
Keyword(s):  
Cantilever Beam ◽  
Static Load ◽  
Measurement Tool ◽  
Reduced Order ◽  
Foil Bearings ◽  
Compliant Structure ◽  
Foil Bearing ◽  
Local Stiffness ◽  
Beam Foil ◽  
Bearing System

Potential geometrical deviations in bump foil bearings due to manufacturing uncertainty can have significant effects on both the local stiffness and clearance, and hence, affecting the overall bearing performance. The manufacturing uncertainty of bump type foil bearings was investigated, showing large geometrical deviations, using a developed measurement tool for the formed bump foils. A reduced order foil bearing model was used in a Monte Carlo simulation studying the effect of manufacturing noise on the onset of instability, highlighting the sensitivity of the rotor-bearing system to such manufacturing deviations. It was found that 30% of the simulated cases resulted improvements in stability, the remaining cases underperformed. Attempting to increase the robustness of the bearing, two other compliant structures replacing the classical gen-II bump foils were investigated from a manufacturing perspective. The first is a modified bump type Sinusoidal foil, and the second is the Cantilever beam foil. Consequently, quasi-static load-displacement tests were executed showing deviations in local clearance and stiffness for the classical bump type compliant structure compared to the other designs. It was found that the Cantilever beam foils yield more robustness compared to the bump type foils. Finally, an analytical model for the sequential engagement of the compliant structure is presented and validated with experimental measurements for both bump type and Cantilever structures.

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.

Evaluation of DLC Coatings for High-Temperature Foil Bearing Applications

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Said Jahanmir ◽  
Hooshang Heshmat ◽  
Crystal Heshmat
Keyword(s):  
Carbon Film ◽  
Dlc Coatings ◽  
Foil Bearings ◽  
Dlc Coating ◽  
Foil Bearing ◽  
Flat Disk ◽  
Wide Range ◽  
Diamondlike Carbon ◽  
Powder Lubrication ◽  
Foil Thrust Bearing

Diamondlike carbon (DLC) coatings, particularly in the hydrogenated form, provide extremely low coefficients of friction in concentrated contacts. The objective of this investigation was to evaluate the performance of DLC coatings for potential application in foil bearings. Since in some applications the bearings experience a wide range of temperatures, tribological tests were performed using a single foil thrust bearing in contact with a rotating flat disk up to 500°C. The coatings deposited on the disks consisted of a hydrogenated diamondlike carbon film (H-DLC), a nonhydrogenated DLC, and a thin dense chrome deposited by the Electrolyzing™ process. The top foil pads were coated with a tungsten disulfide based solid lubricant (Korolon™ 900). All three disk coatings provided excellent performance at room temperature. However, the H-DLC coating proved to be unacceptable at 300°C due to lack of hydrodynamic lift, albeit the very low coefficient of friction when the foil pad and the disk were in contact during stop-start cycles. This phenomenon is explained by considering the effect of atmospheric moisture on the tribological behavior of H-DLC and using the quasihydrodynamic theory of powder lubrication.

Rotordynamic Performance of a Shaft With Large Overhung Mass Supported by Foil Bearings

2016 ◽  
Vol 139 (4) ◽  
Author(s):  
Nguyen LaTray ◽  
Daejong Kim
Keyword(s):  
High Speed ◽  
Foil Bearings ◽  
Speed Test ◽  
Foil Bearing ◽  
Stable Conditions ◽  
Bending Mode ◽  
Mode Vibration ◽  
Lift Off ◽  
Compact Design ◽  
Bearing System

This work presents the theoretical and experimental rotordynamic evaluations of a rotor–air foil bearing (AFB) system supporting a large overhung mass for high-speed application. The proposed system highlights the compact design of a single shaft rotor configuration with turbomachine components arranged on one side of the bearing span. In this work, low-speed tests up to 45 krpm are performed to measure lift-off speed and to check bearing manufacturing quality. Rotordynamic performance at high speeds is evaluated both analytically and experimentally. In the analytical approach, simulated imbalance responses are studied using both rigid and flexible shaft models with bearing forces calculated from the transient Reynolds equation along with the rotor motion. The simulation predicts that the system experiences small synchronous rigid mode vibration at 20 krpm and bending mode at 200 krpm. A high-speed test rig is designed to experimentally evaluate the rotor–air foil bearing system. The high-speed tests are operated up to 160 krpm. The vibration spectrum indicates that the rotor–air foil bearing system operates under stable conditions. The experimental waterfall plots also show very small subsynchronous vibrations with frequency locked to the system natural frequency. Overall, this work demonstrates potential capability of the air foil bearings in supporting a shaft with a large overhung mass at high speed.

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