Asymptotic Analysis of a Finite Gas Slider Bearing of Narrow Geometry

1983 ◽  
Vol 105 (3) ◽  
pp. 491-495 ◽  
Author(s):  
J. J. Shepherd ◽  
R. C. DiPrima
Keyword(s):  
Steady State ◽  
Asymptotic Analysis ◽  
Pressure Distribution ◽  
Asymptotic Expansions ◽  
Matched Asymptotic Expansions ◽  
Slider Bearing ◽  
Load Bearing ◽  
Bearing Number ◽  
Isothermal Gas ◽  
State Pressure

The method of matched asymptotic expansions is used to analyze the steady state pressure distribution and load bearing properties of a finite rectangular isothermal gas slider bearing when ε, the ratio of transverse to longitudinal dimensions of the bearing, is small and the bearing number Λ is moderate. General expressions for the pressure and load are obtained. Specific results are given for bearings with shallow crowning. The effects of the bearing number becoming large and the interaction between the two effects ε→0 and Λ→∞ are discussed.

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.

scholarly journals Poisoning-induced exchange of steady states in a catalytic chemical reactor

1980 ◽  
Vol 22 (2) ◽  
pp. 237-253 ◽  
Author(s):  
D. D. Do ◽  
R. H. Weiland
Keyword(s):  
Steady State ◽  
Asymptotic Expansions ◽  
Phase Plane ◽  
Exchange Process ◽  
Chemical Reactor ◽  
Matched Asymptotic Expansions ◽  
Catalyst Poisoning ◽  
Independent Variables ◽  
Sudden Failure ◽  
Reactor Operating

AbstractSlow catalyst poisoning can result in the sudden failure of a chemical reactor operating isothermally with substrate-inhibited kinetics. At failure, a satisfactory steady state is exchanged for one of low conversion. The method of matched asymptotic expansions is used to give a detailed description of the exchange process in the phase plane. The structure of the jump is ascertained by separate asymptotic expansions across two adjoining transition regions in which the independent variables contain unknown shifts.

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.

scholarly journals Measurement of Steady State Pressure Distribution and Dynamic Pressure Fluctuations During Sputtering Process

2017 ◽  
Vol 60 (6) ◽  
pp. 220-227
Author(s):  
Shuichi TAJIRI ◽  
Takanori ONISHI ◽  
Yukiko OKANO ◽  
Soichi OGAWA ◽  
Hiroshi MIMA
Keyword(s):  
Steady State ◽  
Pressure Distribution ◽  
Dynamic Pressure ◽  
Pressure Fluctuations ◽  
State Pressure

Free Fall of a Sphere in a Partially Lubricated Cylinder

1991 ◽  
Vol 58 (3) ◽  
pp. 812-819
Author(s):  
Roger F. Gans
Keyword(s):  
Contact Force ◽  
Closed System ◽  
Experimental Verification ◽  
Asymptotic Expansions ◽  
Total Mass ◽  
Free Fall ◽  
Matched Asymptotic Expansions ◽  
Biological Applications ◽  
Slider Bearing ◽  
Acceleration Of Gravity

The entrainment of lubricant at the entrance of a lubrication zone, such as that of a partially starved slider bearing, is analyzed in a closed system using the method of matched asymptotic expansions. A sphere falling together with a small lens of lubricant in a closely fitting tube is shown to fall under gravity at a speed V=(Mg−Fc)√[(RC−RS)/RC]/(16π2μRC), where M denotes the total mass of the system, sphere plus lubricant, g the acceleration of gravity, Fc the differential contact force, μ the viscosity of the lubricant, and RC and RS the radii of the tube and the sphere, respectively. Potential biological applications and experimental verification are discussed.

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