This paper presents a novel finite element elastohydrodynamic lubrication analysis appropriate for gas journal bearings under dynamic conditions. The method employs gas pressure as a state variable, and structural sleeve deformation is represented by a linear combination of pre-selected mode shapes obtained from a related eigenvalue problem. The method takes into account temporal variation of journal position and velocity, and second-order slip flow boundary effects are included at no additional computational cost. The formulation is subsequently applied to a particular example (flexible large-aspect ratio, high-speed, MEMS-scale journal microbearing), where it is shown that a judicious choice of structural sleeve elasticity can significantly improve bearing performance (as measured by pressure distribution and load capacity) when compared with results obtained using rigid bearing surfaces.

Keywords:
electrohydrodynamics, lubrication, machine bearings, finite element analysis, deformation, eigenvalues and eigenfunctions, micromechanical devices
Topics:
Bearings, Pressure, Journal bearings, Slip flow, Eigenvalues, Deformation, Steady state, Stress
1.
Epstein, A. H. et al., 1997, “Micro Heat Engines, Gas Turbines, and Rocket Engines—The MIT Microengine Project,” 28th AIAA Fluid Dynamics and 4th AIAA Shear Flow Control Conference, Paper AIAA 97-1773.
2.
Nguyen
,
N.-T.
,
Huang
,
X.
, and
Chuan
,
T. K.
,
2002
, “
MEMS-Micropumps: A Review
,”
ASME J. Fluids Eng.
,
124
, pp.
384
–
392
.
3.
Garcia
,
E. J.
, and
Sniegowski
,
J. J.
,
1995
, “
Surface Micromachined Microengine
,”
Sens. Actuators, A
,
48
, pp.
203
–
214
.
4.
Hara
,
M.
,
Tanaka
,
S.
, and
Esashi
,
M.
,
2003
, “
Rotational Infrared Polarization Modulator Using a MEMS-Based Air Turbine With Different Types of Journal Bearing
,”
J. Micromech. Microeng.
,
13
, pp.
223
–
228
.
5.
Tanner, D. M. et al., 1998, “The Effect of Frequency on the Lifetime of a Surface Micromachined Microengine Driving a Load,” Proc. 1998 IEEE International Reliability Physics Symposium, pp. 26–35.
6.
Tanner, D. M. et al., 1999, “The Effect of Humidity on the Reliability of a Surface Micromachined Microengine,” Proc. 1999 IEEE International Reliability Physics Symposium, pp. 189–197.
7.
Piekos
,
E. S.
, and
Breuer
,
K. S.
,
2002
, “
Manufacturing Effects in Microfabricated Gas Bearings: Axially Varying Clearance
,”
ASME J. Tribol.
,
124
, pp.
815
–
821
.
8.
Heshmat
,
H.
,
1994
, “
Advances in the Performance of Aerodynamic Foil Journal Bearings: High Speed and Load Capability
,”
ASME J. Tribol.
,
116
, pp.
287
–
295
.
9.
Gross, W. A., 1962, Gas Film Lubrication, Wiley, New York.
10.
Pan, C. H. T., 1981, “Gas Bearings,” Tribology: Friction, Lubrication, and Wear, A. Z. Szeri, ed., McGraw-Hill, New York.
11.
Faria
,
M. T. C.
, and
San Andre´s
,
L.
,
2000
, “
On the Numerical Modeling of High Speed Hydrodynamic Gas Bearings
,”
ASME J. Tribol.
,
122
, pp.
124
–
130
.
12.
Miller
,
B. A.
, and
Green
,
I.
,
2001
, “
Numerical Formulation for the Dynamic Analysis of Spiral-Grooved Face Seals
,”
ASME J. Tribol.
,
123
, pp.
395
–
403
.
13.
Kumar
,
A.
,
Goenka
,
P. K.
, and
Booker
,
J. F.
,
1990
, “
Modal Analysis of Elastohydrodynamic Lubrication: A Connecting Rod Application
,”
ASME J. Tribol.
,
112
, pp.
524
–
534
.
14.
Boedo
,
S.
, and
Booker
,
J. F.
,
1997
, “
Surface Roughness and Structural Inertia in a Mode-Based Mass Conserving Elastohydrodynamic Lubrication Model
,”
ASME J. Tribol.
,
119
, pp.
449
–
455
.
15.
Boedo
,
S.
, and
Booker
,
J. F.
,
2000
, “
A Mode-Based Elastohydrodynamic Lubrication Model With Elastic Journal and Sleeve
,”
ASME J. Tribol.
,
122
, pp.
94
–
102
.
16.
Booker
,
J. F.
, and
Boedo
,
S.
,
2001
, “
Finite Element Analysis of Elastic Engine Bearing Lubrication: Theory
,”
Rev. Europe´enne des Ele´ments Finis
,
10
, pp.
705
–
724
.
17.
Boedo
,
S.
, and
Booker
,
J. F.
,
2001
, “
Finite Element Analysis of Elastic Engine Bearing Lubrication: Application
,”
Rev. Eur. Ele´ments Finis
,
10
, pp.
725
–
740
.
18.
Szeri, A. Z., 2000, Fluid Film Lubrication, Cambridge University Press, Cambridge, p. 396.
19.
Booker
,
J. F.
, and
Huebner
,
K. H.
,
1972
, “
Application of Finite Element Methods to Lubrication: An Engineering Approach
,”
ASME J. Lubr. Technol.
,
94
, pp.
313
–
323
.
20.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1989, Numerical Recipes, Cambridge University Press, Cambridge, pp. 554–560.
21.
Fuller, D. D., 1984, Theory and Practice of Lubrication for Engineers, Wiley, New York, pp. 502–509.
22.
Johnson, K. L., 1987, Contact Mechanics, Cambridge University Press, New York, p. 413.
Copyright © 2005
 by ASME
You do not currently have access to this content.