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].

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.

Preliminary Experiments With Foil Bearings

1966 ◽  
Vol 88 (1) ◽  
pp. 1-3 ◽  
Author(s):  
L. Licht
Keyword(s):  
Rotating Cylinder ◽  
Air Gap ◽  
Exit Region ◽  
Foil Bearings ◽  
Capacitive Probe ◽  
Experimental Values

A capacitive probe, coincident with the surface of a revolving drum, scans the air gap between a flexible foil and the rotating cylinder. Preliminary measurements of foil displacement are made and compared with results obtained by other investigators. The experiments confirm the existence of an undulating, and sometimes unstable foil configuration in the exit region. A comparison is made between theoretical and experimental values of local amplitude and wavelength of the undulation. The effect of side leakage on displacement is demonstrated.

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.

An Experimental Study of High-Speed Rotors Supported by Air-Lubricated Foil Bearings—Part 1: Rotation in Pressurized and Self-Acting Foil Bearings

1969 ◽  
Vol 91 (3) ◽  
pp. 477-493 ◽  
Author(s):  
L. Licht
Keyword(s):  
Experimental Study ◽  
Temperature Rise ◽  
High Speed ◽  
Air Gap ◽  
The Self ◽  
Wear Characteristics ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Mode Of Operation

A high-speed rotor, supported by an air-lubricated foil bearing, is rotated in both the vertical and horizontal attitudes at speeds in excess of 60,000 rpm. The rotor is stable and free from “half-frequency” or “fractional-frequency” whirl instability encountered in conventional gas bearings. External pressurization is applied to separate the foil surfaces from the journal during the initial and final stages of rotation, with adequate self-acting support and foil separation established at relatively low transition speeds. In the pressurized mode of operation, the system is characterized by a series of ultra-harmonic resonances, of sharply defined frequencies, related by fractions to speeds of synchronous resonance. In the self-acting mode of operation, the response of the system to residual imbalance is influenced by both the foil bearing and by the pressurized thrust bearings. The magnitude of the air gap (clearance) is determined at various rotational speeds and compared with theoretically predicted results. The temperature rise of the foil with speed is measured at various locations in order to assess its contribution to clearance growth. The journal and foil surfaces are examined and it is found that the foil bearing is endowed with excellent wipe-wear characteristics.

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.

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.

scholarly journals Triadic resonances in precessing rapidly rotating cylinder flows

2015 ◽  
Vol 778 ◽  
Author(s):  
T. Albrecht ◽  
H. M. Blackburn ◽  
J. M. Lopez ◽  
R. Manasseh ◽  
P. Meunier
Keyword(s):  
Rotating Cylinder ◽  
Direct Numerical Simulations ◽  
Mode Shapes ◽  
Resonance Model ◽  
Rapid Rotation ◽  
Nutation Angle ◽  
Resonant Instability ◽  
Theoretical Predictions ◽  
Long Time ◽  
Good Agreement

Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with $45^{\circ }$ nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.

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.

Sign in / Sign up

Export Citation Format

Share Document