## Abstract

Aerostatic porous bearings are becoming important elements in precision machines due to their inherent characteristics. The mathematical modeling of such bearings depends on the pressure-flow assumptions that are adopted for the flow in the porous medium. In this work, one proposes a nondimensional modified Reynolds equations based on the quadratic Forchheimer assumption. In this quadratic approach, the nondimensional parameter $Φ$ strongly affects the bearing load capacity, by defining the nonlinearity level of the system. For values of $Φ>10$, the results obtained with the modified Reynolds equation with quadratic Forchheimer assumption tend to those obtained with the linear Darcy model, thus showing that this is a more robust and global approach of the problem, and can be used for both pressure-flow assumptions (linear and quadratic). The threshold between linear and quadratic assumptions is numerically investigated for a bronze sintered porous bearing, and the effects of bearing geometry are discussed. Numerical results show that $Φ$ strongly affects the bearing loading capacity and stiffness coefficients.

1.
Beavers
,
G. S.
, and
Joseph
,
D. D.
, 1967, “
Boundary Conditions at Naturally Permeable Wall
,”
J. Fluid Mech.
0022-1120,
30
(
1
), pp.
197
207
.
2.
Andrisano
,
A.
, and
Maggiore
,
A.
, 1978, “
Theoretical and Experimental Analysis of an External Pressurized Porous Gas Thrust Bearing
,”
Tribol. Int.
0301-679X,
11
(
5
), pp.
285
288
.
3.
Bhatt
,
B. S.
, and
Verma
,
R. L.
, 1980, “
Generalized Reynolds Equation for Porous Bearings
,”
Wear
0043-1648,
59
, pp.
345
354
.
4.
Pal
,
D. K.
, and
Majumdar
,
B. C.
, 1984, “
Stability Analysis of Externally-Pressurized Gas-Lubricated Porous Bearings with Journal Rotation—Part 1: Cylindrical Whirl
,”
Tribol. Int.
0301-679X,
17
(
2
), pp.
83
91
.
5.
Shih
,
Y.-D.
, and
Yang
,
J.-Y.
, 1990, “
Analysis of Narrow Rectangular Aerostatic Porous Thrust Bearings Moving With a Uniform Transverse Velocity
,”
Wear
0043-1648,
141
, pp.
125
136
.
6.
Bujurke
,
N. M.
, and
Patil
,
H. P.
, 1992, “
The Effect of Variable Permeability and Rotation on the Performance Characteristics of Porous Bearings
,”
Wear
0043-1648,
155
, pp.
7
14
.
7.
Luong
,
T. S.
,
Potze
,
W.
,
Post.
,
J. B.
,
Van Ostayen
,
R. A. J.
, and
Van Beek
,
A.
, 2004, “
Numerical and Experimental Analysis of Aerostatic Thrust Bearings With Porous Restrictors
,”
Tribol. Int.
0301-679X,
37
(
10
), pp.
825
832
.
8.
Fourka
,
M.
, and
Bonis
,
M.
, 1997, “
Comparison Between Externally Pressurized Gas Thrust Bearings With Different Orifice and Porous Feeding Systems
,”
Wear
0043-1648,
210
, pp.
311
317
.
9.
Yoshimoto
,
S.
, and
Kohno
,
K.
, 2001, “
Static and Dynamic Characteristics of Aerostatic Circular Porous Thrust Bearings
,”
ASME J. Tribol.
0742-4787,
123
(
3
), pp.
501
507
.
10.
Plante
,
J. S.
,
Vogan
,
J.
,
El-Aguizy
,
T.
, and
Slocum
,
A. H.
, 2005, “
A Design Model for Circular Porous Air Bearings Using the 1D Generalized Flow Model
,”
Precis. Eng.
0141-6359,
29
(
3
), pp.
336
346
.
11.
Su
,
J. C. T.
, and
Lie
,
K. N.
, 2006, “
Rotor Dynamic Instability Analysis on Hybrid Air Journal Bearings
,”
Tribol. Int.
0301-679X,
39
, pp.
238
248
.
12.
Belforte
,
G.
,
Raparelli
,
T.
,
Viktorov
,
V.
, and
Trivella
,
A.
, 2006, “
Feeding System of Aerostatic Bearings With Porous Media
,”
Proceedings of ESDA 2006—Eighth Biennial ASME Conference on Engineering Systems Design and Analysis
,
Torino, Italy
, July 4–7, pp.
1
9
.
13.
Cieslicki
,
K.
, 1994, “
Investigations of the Effect of Inertia on Flow Air Through Porous Bearing Sleeves
,”
Wear
0043-1648,
172
, pp.
73
78
.
14.
Darcy
,
H.
, 1856,
Les Fontaines Publiques de la Ville de Dijon
,
Dalmont
,
Paris
.
15.
Forchheimer
,
P.
, 1914,
Hydraulik
,
Teubner
,
Leipzig
.
16.
Cieslicki
,
K.
, 1993, “
Static and Dynamic Evaluation of Permeability of Porous Bearing Sleeves
,”
Wear
0043-1648,
167
, pp.
69
72
.
17.
Allaire
,
P. E.
,
Parsell
,
J. A.
, and
Barrett
,
L. E.
, 1981, “
A Perturbation Method for the Dynamic Coefficients of Tilting-Pad Journal Bearings
,”
Wear
0043-1648,
72
, pp.
29
44
.