In this paper, a multigrid technique is applied to the compressible Reynolds equation discretized by the divergence formulation in order to analyze both static and dynamic characteristics of herringbone-grooved gas-lubricated journal bearings. The developed code demonstrates quicker convergence than an optimized successive over-relaxation scheme, and the dominance in numerical efficiency is especially remarkable at higher values of bearing number where slow convergence is generally observed. Comparisons between the present nonlinear orbit solutions and previously published experimental results show reasonable agreement in both steady-state and dynamic stability performances.

1.
Bonneau
D.
, and
Absi
J.
,
1994
, “
Analysis of Aerodynamic Journal Bearings with Small Number of Herringbone Grooves by Finite Element Method
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
116
, pp.
698
704
.
2.
Brandt
A.
,
1977
, “
Multi-Level Adaptive Solutions to Boundary Value Problems
,”
Mathematics of Computation
, Vol.
31
, pp.
333
390
.
3.
Castelli
V.
, and
Elrod
H. G.
,
1965
, “
Solution of the Stability Problem for 360 Deg Self-Acting, Gas-Lubricated Bearings
,”
ASME Journal Of Basic Engineering
, Vol.
87
, pp.
199
212
.
4.
Castelli
V.
, and
Pirvics
J.
,
1968
, “
Review of Numerical Methods in Gas Bearing Film Analysis
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
90
, pp.
777
792
.
5.
Castelli, V., and Vohr, J. H., 1967, “Performance Characteristics of Herringbone-Grooved Journal Bearings Operating at High Eccentricity Ratios with Misalignment,” Proceedings Gas Bearing Symposium, University of Southampton, Paper 14.
6.
Coleman
R. L.
,
1972
, “
A Brief Comparison of the Accuracy of Time-Dependent Integration Schemes for the Reynolds Equation
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
94
, pp.
330
334
.
7.
Cunningham
R. E.
,
Fleming
D. P.
, and
Anderson
W. J.
,
1969
, “
Experimental Stability Studies of the Herringbone-Grooved Gas-Lubricated Journal Bearing
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
91
, pp.
52
59
.
8.
Cunningham
R. E.
,
Fleming
D. P.
, and
Anderson
W. J.
,
1971
, “
Experimental Load Capacity and Power Loss of Herringbone Grooved Gas Lubricated Journal Bearings
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
93
, pp.
415
422
.
9.
Fleming, D. P., and Hamrock, B. J., 1974, “Optimization of Self-Acting Herringbone Journal Bearings for Maximum Stability,” Proceedings of the 6th International Gas Bearing Symposium, Southampton, Coles, N. G., ed., pp. C1-C11.
10.
Foster
D. J.
,
Carow
D.
, and
Benson
D.
,
1969
, “
An Approximate Theoretical Analysis of the Static and Dynamic Characteristics of the Herringbone Grooved, Gas Lubricated Journal Bearing, and Comparison With Experiment
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
91
, pp.
25
36
.
11.
Ghia, K. N., and Ghia, U., 1988, “Elliptic Systems: Finite-Difference Method III,” Handbook of Numerical Heat Transfer, W. J. Minkowycz et al., ed., John Wiley & Sons, New York, pp. 310–315.
12.
Hamrock, B. J., and Fleming, D. P., 1971, “Optimization of Self-Acting Herringbone Journal Bearings for Maximum Radial Load Capacity,” 5th International Gas Bearing Symposium, University of Southampton, Paper 13.
13.
Kawabata
N.
,
Ashino
I.
,
Tachibana
M.
, and
Fujita
K.
,
1988
, “
Numerical Analysis of Reynolds Equation for Gas-Lubrication at a High A Region, 2nd Report, A Highly Precise Upstream Scheme
,”
Transactions of the Japan Society of Mechanical Engineers (in Japanese)
, Vol.
54
, C., pp.
1911
1918
.
14.
Kobayashi
T.
,
1996
, “
Fast Numerical Approach for Analyzing Self-Acting Gas-Lubricated Bearings Using a Multigrid Method
,”
Transactions of the Japan Society of Mechanical Engineers (in Japanese)
, Vol.
62
, C., pp.
4636
4643
.
15.
Lubrecht
A. A.
,
ten Napel
W. E.
, and
Bosma
R.
,
1987
, “
Multigrid, an Alternative Method of Solution for Two-Dimensional Elastohydrodynamically Lubricated Point Contact Calculations
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
109
, pp.
437
443
.
16.
Malanoski
S. B.
,
1967
, “
Experiments on an Ultrastable Gas Journal Bearing
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
89
, pp.
433
438
.
17.
Michael
W. A.
,
1963
, “
Approximate Methods for Time-Dependent Gas-Film Lubrication Problems
,”
ASME Journal of Applied Mechanics
, Vol.
30
, pp.
509
517
.
18.
Pan
C. H. T.
, and
Sternlicht
B.
,
1964
, “
Comparison Between Theories and Experiments for the Threshold of Instability of Rigid Rotor in Self-Acting, Plain Cylindrical Journal Bearings
,”
ASME Journal of Basic Engineering
, Vol.
86
, pp.
321
327
.
19.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992a, Numerical Recipes in FORTRAN Second Edition Cambridge University Press, New York, p. 866.
20.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992b, Numerical Recipes in FORTRAN Second Edition, Cambridge University Press, New York, pp. 708–716.
21.
Raimondi
A. A.
,
1961
, “
A Numerical Solution for the Gas Lubricated Full Journal Bearings of Finite Length
,”
ASLE Transactions
, Vol.
4
, pp.
131
155
.
22.
Vohr
J. H.
, and
Chow
C. Y.
,
1965
, “
Characteristics of Herringbone-Grooved, Gas-Lubricated Journal Bearings
,”
ASME Journal of Basic Engineering
, Vol.
87
, pp.
568
578
.
23.
Vohr, J. H., and Pan, C. H. T., 1963, “On the Spiral-Grooved, Self-Acting Gas Bearings,” MTI Technical Report, MTI63TR52.
24.
Wildmann
M.
,
1968
, “
On the Behavior of Grooved Plate Thrust Bearings With Compressible Lubricant
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
90
, pp.
226
232
.
25.
Woods
C. M.
, and
Brewe
D. E.
,
1989
, “
The Solution of the Elrod Algorithm for a Dynamically Loaded Journal Bearing Using Multigrid Techniques
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
111
, pp.
302
308
.
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