Asymptotic Methods for an Infinitely Long Slider Squeeze-Film Bearing

1968 ◽  
Vol 90 (1) ◽  
pp. 173-183 ◽  
Author(s):  
R. C. DiPrima
Keyword(s):  
Thrust Bearing ◽  
Relative Rate ◽  
Asymptotic Methods ◽  
Squeeze Film ◽  
Singular Perturbation Theory ◽  
Slider Bearing ◽  
Approach Infinity ◽  
Bearing Number ◽  
Squeeze Number ◽  
Gas Bearing

The application of the techniques of singular perturbation theory (boundary layer theory) to several problems in gas bearing lubrication is discussed. The leading terms in asymptotic expansions for the pressure are obtained for the cases: A slider bearing with large bearing number, a squeeze-film thrust bearing with large squeeze number, and a combined slider squeeze-film bearing with large bearing number and/or large squeeze number. For the latter problem it is necessary to distinguish several cases depending upon the relative rate at which the bearing number and squeeze number approach infinity

Compressible Squeeze Films and Squeeze Bearings

1964 ◽  
Vol 86 (2) ◽  
pp. 355-364 ◽  
Author(s):  
E. O. J. Salbu
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Journal Bearings ◽  
Squeeze Film ◽  
Thrust Bearings ◽  
Finite Difference Solution ◽  
Squeeze Number ◽  
Gas Bearing ◽  
Compressibility Effects ◽  
Piezoelectric Devices

Experimental agreement with a finite-difference solution of the isothermal squeeze film equation was obtained for steady-state sinusoidal squeeze motion of parallel, coaxial disks. At low squeeze number, the film force is in phase with the velocity; at high squeeze number, with the displacement. Compressibility effects at high squeeze number introduce a superambient mean film pressure, so that it is possible to operate a gas bearing on squeeze effects alone. Thrust bearings, spherical bearings, and journal bearings have been successfully operated as squeeze bearings, using both electromagnetic and piezoelectric devices to generate the squeeze motion.

The one-dimensional gas-lubricated slider bearing

1980 ◽  
Vol 22 (1) ◽  
pp. 75-97
Author(s):  
J. J. Shepherd
Keyword(s):  
Singular Perturbation ◽  
Pressure Distribution ◽  
Singular Perturbation Theory ◽  
Slider Bearing ◽  
Perturbation Problem ◽  
Jump Discontinuities ◽  
Uniqueness Results ◽  
The One ◽  
Bearing Number ◽  
Film Profile

AbstractUnder the appropriate physical hypotheses, the problem of determining the pressure distribution in a gas-filled slider bearing becomes a singular perturbation problem as Λ, the bearing number, tends to infinity. This paper extends the results of an earlier one by the author to consider the case where the film profile has jump discontinuities in slope at points interior to the bearing. Application of the methods of general singular perturbation theory establishes the appropriate existence-uniqueness results for this problem, and a means is devised by which uniformly valid asymptotic approximations to the pressure distribution may be obtained for large values of Λ.

On the Physical Meanings of Λ/Q˜p0 and σ/Q˜p0 in Molecular Gas Film Lubrication Problems

1996 ◽  
Vol 118 (2) ◽  
pp. 364-369 ◽  
Author(s):  
S. Fukui ◽  
R. Matsuda ◽  
R. Kaneko
Keyword(s):  
Flow Rate ◽  
Squeeze Film ◽  
Molecular Gas ◽  
Thrust Bearings ◽  
Molecular Gas Film Lubrication ◽  
Lubrication Characteristics ◽  
Bearing Number ◽  
Squeeze Number ◽  
Film Lubrication ◽  
The Continuum

To estimate molecular gas film lubrication (MGL) characteristics, we propose a modified bearing number Λ′ and a modified squeeze number σ′, which are, respectively, the conventional bearing Λ and squeeze number σ divided by the relative Poiseuille flow rate Q˜p0. Using Λ′ and σ′, the linearized MGL problem can be reduced to the continuum gas film lubrication problem and the MGL characteristics can be exactly estimated, if the characteristic flow rate corresponding to the spacing, Q˜p0, is known. For nonlinear MGL problems, the lubrication characteristics can be verified to be roughly estimated by Λ′ and σ′ both in rectangular slider bearings and in circular squeeze-film thrust bearings.

Asymptotic Methods for a General Finite Width Gas Slider Bearing

1978 ◽  
Vol 100 (2) ◽  
pp. 254-260 ◽  
Author(s):  
J. A. Schmitt ◽  
R. C. DiPrima
Keyword(s):  
Film Thickness ◽  
Asymptotic Expression ◽  
Asymptotic Methods ◽  
Finite Width ◽  
Slider Bearing ◽  
Sliding Direction ◽  
Special Cases ◽  
Load Carrying ◽  
The Individual ◽  
Bearing Number

The method of matched asymptotic expansions is used to develop an asymptotic expression for the load-carrying capacity of a finite width gas slider bearing for large bearing numbers and for film thicknesses varying both in the sliding and transverse directions. The individual terms in the formula for the load are independent of the bearing number and are related to the interior portion, the side edge boundary layers, and the trailing edge boundary layer of the bearing. Only the terms associated with the side leakage phenomena must be computed numerically. Two special cases are discussed: (i) the film thickness varying only in the sliding direction, and (ii) the film thickness having linear or parabolic variation in the sliding direction and parabolic variation in the transverse direction.

Additively Manufactured Compliant Hybrid Gas Thrust Bearing for SCO2 Turbomachinery: Design and Proof of Concept Testing

2021 ◽  
Author(s):  
Bugra Ertas
Keyword(s):  
Thrust Bearing ◽  
Nonlinear Behavior ◽  
Squeeze Film ◽  
Outer Diameter ◽  
Proof Of Concept ◽  
Unit Load ◽  
Rotating Speed ◽  
Load Carrying ◽  
New Type ◽  
Turbomachinery Design

Abstract The following paper presents a new type of gas lubricated thrust bearing fabricated using additive manufacturing or direct metal laser melting (DMLM). The motivation for the new bearing concept is derived from the need for highly efficient supercritical carbon dioxide turbomachinery in the mega-watt power range. The paper provides a review of existing gas thrust bearing technologies, outlines the need for the new DMLM concept, and discusses proof of concept testing results. The new concept combines hydrostatic pressurization with individual flexibly mounted pads using hermetic squeeze film dampers in the bearing-pad support. Proof-of-concept testing in air for a 6.8" (173mm) outer diameter thrust bearing was performed; with loads up to 1,500 lbs (6.67kN) and a rotating speed of 10krpm (91 m/s tip speed). The experiments were performed with a bent shaft resulting in thrust runner axial vibration magnitudes of 2.9mils (74microns) p-p and dynamic thrust loads of 270 lbs (1.2kN) p-p. In addition, force deflection characteristics of the bearing system are presented for an inlet hydrostatic pressure of 380psi (2.62MPa). Results at 10krpm show that the pad support architecture was able to sustain high levels of dynamic misalignment equaling 6 times the nominal film clearance while demonstrating a unit load carrying capacity of 55psi (0.34Mpa). Gas-film force-deflection tests portrayed nonlinear behavior like a hardening spring, while the pad support stiffness was measured to be linear and independent of film thickness.

Flow Characteristics of a Powder Lubricant in a Slider Bearing

2001 ◽  
Author(s):  
Manjunath Pappur ◽  
M. M. Khonsari
Keyword(s):  
Slip Velocity ◽  
Thrust Bearing ◽  
Volume Fraction ◽  
Flow Characteristics ◽  
Slider Bearing ◽  
Systematic Development ◽  
Powder Lubrication ◽  
Insight Into ◽  
Theory And Experiment ◽  
Good Agreement

Abstract This paper deals with a systematic development of theory of powder lubrication with the appropriate formalism based on the fundamentals of fluid mechanics. The theory is capable of predicting flow velocity, fluctuation (pseudo-temperature), powder volume fraction, and slip velocity at the boundaries. An extensive set of parametric simulations covering particle size, surface roughness, volumetric flow, load and speed are performed to gain insight into the performance of a powder lubricated thrust bearing. The results of simulations are compared to the published experimental results. Good agreement between the theory and experiment attests to the capability of the model and its potential for design of powder lubricated bearings.

Asymptotic Methods for an Infinite Slider Bearing With a Discontinuity in Film Slope

1976 ◽  
Vol 98 (3) ◽  
pp. 446-452 ◽  
Author(s):  
J. A. Schmitt ◽  
R. C. DiPrima
Keyword(s):  
Boundary Layer ◽  
Film Thickness ◽  
Asymptotic Expansions ◽  
Asymptotic Expression ◽  
Asymptotic Methods ◽  
Matched Asymptotic Expansions ◽  
Slider Bearing ◽  
Trailing Edge ◽  
Slider Bearings ◽  
Special Cases

The method of matched asymptotic expansions is used to develop an asymptotic expression for the pressure for large bearing numbers for the case of an infinite slider bearing with a general film thickness that has a discontinuous slope at a point. It is shown that, in addition to the boundary layer of the pressure at the trailing edge, there is also a boundary layer in the derivative of the pressure at the point of discontinuity. The corresponding load formula is also derived. The special cases of the taper-flat and taper-taper slider bearings are discussed.

Asymptotic Analysis of a Narrow Gas-Lubricated, Flat Sector Thrust Bearing

1988 ◽  
Vol 110 (3) ◽  
pp. 427-433 ◽  
Author(s):  
J. J. Shepherd
Keyword(s):  
Steady State ◽  
Numerical Methods ◽  
Power Loss ◽  
Thrust Bearing ◽  
Center Of Pressure ◽  
Operating Conditions ◽  
Load Bearing Capacity ◽  
Steady State Operation ◽  
Bearing Number ◽  
Continuous Range

The method of matched expansions is employed to analyze the steady state operation of a finite gas-lubricated flat sector bearing for the case where the ratio of radial to circumferential dimensions is small and the relevant bearing number, Λ, is moderate. This technique yields general expressions for the pressure distribution, load bearing capacity, power loss and center of pressure location that are valid for a significant and continuous range of bearing dimensions, orientations and operating conditions. Comparisons are made, where possible, with the existing results from the literature obtained by numerical methods.

Squeeze Film Dampers: Amplitude Effects at Low Squeeze Numbers

1975 ◽  
Vol 97 (4) ◽  
pp. 1366-1370 ◽  
Author(s):  
Martin H. Sadd ◽  
A. Kent Stiffler
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Squeeze Film ◽  
Periodic Disturbance ◽  
Squeeze Film Dampers ◽  
Parallel Surfaces ◽  
Load Characteristics ◽  
Squeeze Number ◽  
Stiffness And Damping ◽  
Film Stiffness

Gaseous squeeze film dampers are analyzed to determine the effect of periodic disturbance amplitude on the dynamic performance. Both circular and rectangular parallel surfaces are investigated. A solution of the nonlinear Reynolds equation is obtained by expanding the pressure in powers of the squeeze number σ, retaining up to and including terms 0(σ2). The time dependent load characteristics are found. The effect of disturbance amplitude on the film stiffness and damping is given.

The Effect of Two Sided Surface Roughness on Ultra-Thin Gas Films

1983 ◽  
Vol 105 (1) ◽  
pp. 131-137 ◽  
Author(s):  
J. W. White
Keyword(s):  
Surface Roughness ◽  
Current Method ◽  
Solution Procedure ◽  
Lubrication Equation ◽  
Write Heads ◽  
Stationary Surface ◽  
Simple Geometry ◽  
Load Carrying ◽  
Bearing Number ◽  
Gas Bearing

The influence of two sided striated surface roughness on bearing load carrying capacity is analyzed for very low clearance gas films. As was done for the case of stationary surface roughness [1], a model lubrication equation appropriate for extremely high gas bearing number films is solved analytically for several simple geometry bearings. The analytic solution provides information on the exact relationship between pressure and roughness which makes it possible to ensemble average the lubrication equation before solution, greatly simplifying the solution procedure. It is found that the translating surface roughness has an influence on load similar to that caused by the stationary surface. Exact solutions with the current method are compared with those of the theory attributed to Christensen and To̸nder. The results are strikingly different and serve to bring attention to the fact that for high bearing number compressible lubrication, the Christensen-To̸nder theory is inappropriate. The results reported here should find application in the computer peripherals area where read/write heads now routinely hover over a spinning disk at clearances of 0.25 micron.

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