A new modified Reynolds equation is derived based on physical principles for rarefied gas for compressible and extremely thin layer gas lubrication. For the one-dimensional problem, theoretical analysis and numerical simulation are employed to show that the new equation does not predict an unphysical unbounded pressure singularity in the limit of contact between the bearing surface and the moving surface. We also show the same is true for other existing models with higher than first order slippage correction, which introduce additional diffusion terms that are functions of the spacing with similar order to that of the convection terms. These developments remove the ambiguity of some previously published analyses and correct prior erroneous statements that all existing generalized Reynolds equation models predict nonintegrable singular pressure fields in the limit of contact. The asymptotic analysis also supplies a means for deriving the needed additional boundary condition at the boundary of a contact region. For the two-dimensional problem, we show by numerical analysis that there are also no unbounded contact pressure singularities for the new model and other models with corrections higher than first order, and that the singularity is weaker than in the one-dimensional case for these lower order correction models due to the cross diffusion effect introduced by the additional dimension.

Topics
Computer simulation, Vector fields, Rarefied gas dynamics
1.
A.
Burgdorfer
, “
The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearing
,”
ASME J. Basic Eng.
81
,
94
(
1959
).
Google Scholar
Crossref
Search ADS
 
2.
Y. T.
Hsia
and
G. A.
Domoto
, “
An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances
,”
ASME J. Lubr. Technol.
105
,
120
(
1983
).
Google Scholar
Crossref
Search ADS
 
3.
Y.
Mitsuya
, “
Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient
,”
ASME J. Tribol.
115
,
289
(
1993
).
Google Scholar
Crossref
Search ADS
 
4.
S.
Fukui
and
R.
Kaneko
m, “
A database for interpolation of Poiseuille flow rates for high Knudsen number lubrication problems
,”
ASME J. Tribol.
110
,
335
(
1988
).
Google Scholar
 
5.
M.
Anaya-Dufresne
and
G. B.
Sinclair
, “
On the breakdown under contact conditions of Reynolds equation for gas lubricated bearings
,”
ASME J. Tribol.
119
,
71
(
1997
).
Google Scholar
Crossref
Search ADS
 
6.
W.
Huang
and
D. B.
Bogy
, “
An investigation of a slider air bearing with a asperity contact by a three dimensional direct simulation Monte Carlo method
,”
IEEE Trans. Magn.
34
,
1810
(
1998
).
Google Scholar
Crossref
Search ADS
 
7.
W.
Huang
,
M.
Honchi
, and
D. B.
Bogy
, “
An asperity contact model for the slider air bearing
,”
ASME J. Tribol.
122
,
436
(
2000
).
Google Scholar
Crossref
Search ADS
 
8.
M. Anaya-Dufresne, “On the development of a Reynolds equation for air bearings with contact,” Doctoral dissertation, Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, 1996.
9.
E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938).
10.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77 (Cambridge University Press, Cambridge, 1992).
11.
S. V. Patankar, Numerical Heat Transfer and Fluid Flow (McGraw-Hill, New York, 1980).
This content is only available via PDF.
© 2001 American Institute of Physics.
2001
American Institute of Physics
You do not currently have access to this content.