A detailed analysis of the effective thermal resistance for the bump foil of air foil bearings (AFBs) is performed. The presented model puts emphasis on the thermal contact resistances between the bump foil and the top foil as well as between the bump foil and the base plate. It is demonstrated that most of the dissipated heat in the lubricating air film of an air foil bearing is not conducted by microcontacts in the contact regions. Instead, the air gaps close to the contact area are found to be thin enough in order to effectively conduct the heat from the top foil into the bump foil. On the basis of these findings, an analytical formula is developed for the effective thermal resistance of a half bump arc. The formula accounts for the geometry of the bump foil as well as for the surface roughness of the top foil, the bump foil, and the base plate. The predictions of the presented model are shown to be in good agreement with measurements from the literature. In particular, the model predicts the effective thermal resistance to be almost independent of the applied pressure. This is a major characteristic property that has been found by measurements but could not be reproduced by previously published models. The presented formula contributes to an accurate thermohydrodynamic (THD) modeling of AFBs.

References

References
1.
Heshmat
,
H.
,
Walton
,
J. F.
, and
Tomaszewski
,
M. J.
,
2005
, “
Demonstration of a Turbojet Engine Using an Air Foil Bearing
,”
ASME
Paper No. GT2005-68404.
2.
Kim
,
D.
,
Lee
,
A. S.
, and
Choi
,
B. S.
,
2013
, “
Evaluation of Foil Bearing Performance and Nonlinear Rotordynamics of 120 kw Oil-Free Gas Turbine Generator
,”
ASME J. Eng. Gas Turbines Power
,
136
(
3
), p.
032504
.
3.
Lee
,
Y.-B.
,
Kwak
,
Y.-S.
,
Chung
,
J. T.
, and
Sim
,
K.
,
2011
, “
Microturbocharger With Air Foil Bearings for a 100-w Class Micro Power System and Improvement of Rotordynamic Performance
,”
Tribol. Trans.
,
54
(
6
), pp.
939
948
.
4.
Sim
,
K.
,
Yong-Bok
,
L.
,
Ho Kim
,
T.
, and
Lee
,
J.
,
2012
, “
Rotordynamic Performance of Shimmed Gas Foil Bearings for Oil-Free Turbochargers
,”
ASME J. Tribol.
,
134
(
3
), p.
031102
.
5.
Xiong
,
L.-Y.
,
Wu
,
G.
,
Hou
,
Y.
,
Liu
,
L.-Q.
,
Ling
,
M.-F.
, and
Chen
,
C.-Z.
,
1997
, “
Development of Aerodynamic Foil Journal Bearings for a High Speed Cryogenic Turboexpander
,”
Cryogenics
,
37
(
4
), pp.
221
230
.
6.
Howard
,
S. A.
,
2009
, “
Misalignment in Gas Foil Journal Bearings: An Experimental Study
,”
ASME J. Eng. Gas Turbines Power
,
131
(
2
), p.
022501
.
7.
Ryu
,
K.
, and
San Andres
,
L.
,
2013
, “
On the Failure of a Gas Foil Bearing: High Temperature Operation Without Cooling Flow
,”
ASME J. Eng. Gas Turbines Power
,
135
(
11
), p.
112506
.
8.
Ku
,
C.-P. R.
, and
Heshmat
,
H.
,
1994
, “
Structural Stiffness and Coulomb Damping in Compliant Foil Journal Bearings: Parametric Studies
,”
Tribol. Trans.
,
37
(
3
), pp.
455
462
.
9.
Ryu
,
K.
, and
Ashton
,
Z.
,
2016
, “
Bump-Type Foil Bearings and Flexure Pivot Tilting Pad Bearings for Oil-Free Automotive Turbochargers: Highlights in Rotordynamic Performance
,”
ASME J. Eng. Gas Turbines Power
,
138
(
4
), p.
042501
.
10.
Ryu
,
K.
,
2011
, “
Effect of Cooling Flow on the Operation of a Hot Rotor-Gas Foil Bearing System
,”
Ph.D. thesis
, Texas A&M University, College Station, TX.
11.
Radil
,
K.
, and
Zeszotek
,
M.
,
2004
, “
An Experimental Investigation Into the Temperature Profile of a Compliant Foil Air Bearing
,”
Tribol. Trans.
,
47
(
4
), pp.
470
479
.
12.
San Andrés
,
L.
,
Ryu
,
K.
, and
Kim
,
T. H.
,
2011
, “
Thermal Management and Rotordynamic Performance of a Hot Rotor-Gas Foil Bearings System—Part I: Measurements
,”
ASME J. Eng. Gas Turbines Power
,
133
(
6
), p.
062501
.
13.
Salehi
,
M.
,
Swanson
,
E.
, and
Heshmat
,
H.
,
2001
, “
Thermal Features of Compliant Foil Bearings—Theory and Experiments
,”
ASME J. Tribol.
,
123
(
3
), pp.
566
571
.
14.
Dowson
,
D.
,
1962
, “
A Generalized Reynolds Equation for Fluid-Film Lubrication
,”
Int. J. Mech. Sci.
,
4
(
2
), pp.
159
170
.
15.
Lehn
,
A.
, and
Schweizer
,
B.
,
2015
, “
Generalized Reynolds Equation for Fluid Film Problems With Arbitrary Boundary Conditions: Application to Double-Sided Spiral Groove Thrust Bearings
,”
Arch. Appl. Mech.
,
86
(
4
), pp.
743
760
.
16.
Mahner
,
M.
,
Lehn
,
A.
, and
Schweizer
,
B.
,
2016
, “
Thermogas- and Thermohydrodynamic Simulation of Thrust and Slider Bearings: Convergence and Efficiency of Different Reduction Approaches
,”
Tribol. Int.
,
93
, pp.
539
554
.
17.
Dykas
,
B. D.
,
2006
, “
Factors Influencing the Performance of Foil Gas Thrust Bearings for Oil-Free Turbomachinery Applications
,”
Ph.D. thesis
, Case Western Reserve University, Cleveland, OH.
18.
San Andres
,
L.
, and
Kim
,
T.
,
2010
, “
Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data
,”
ASME J. Eng. Gas Turbines Power
,
132
(
4
), p.
042504
.
19.
Lee
,
D.
, and
Kim
,
D.
,
2010
, “
Thermohydrodynamic Analyses of Bump Air Foil Bearings With Detailed Thermal Model of Foil Structures and Rotor
,”
ASME J. Tribol.
,
132
(
2
), p.
021704
.
20.
Bouchehit
,
B.
,
Bou-Saïd
,
B.
, and
Garcia
,
M.
,
2016
, “
Static and Dynamic Performances of Refrigerant-Lubricated Bearings
,”
Tribol. Int.
,
96
, pp.
326
348
.
21.
Peng
,
Z.
, and
Khonsari
,
M.
,
2006
, “
A Thermohydrodynamic Analysis of Foil Journal Bearings
,”
ASME J. Tribol.
,
128
(
3
), pp.
534
541
.
22.
Sim
,
K.
, and
Kim
,
T. H.
,
2012
, “
Thermohydrodynamic Analysis of Bump-Type Gas Foil Bearings Using Bump Thermal Contact and Inlet Flow Mixing Models
,”
Tribol. Int.
,
48
, pp.
137
148
.
23.
Yovanovich
,
M. M.
,
1981
, “
New Contact and Gap Conductance Correlations for Conforming Rough Surfaces
,”
AIAA
Paper No. 81-1164.
24.
Lee
,
D.
, and
Kim
,
D.
,
2011
, “
Three-Dimensional Thermohydrodynamic Analyses of Rayleigh Step Air Foil Thrust Bearing With Radially Arranged Bump Foils
,”
Tribol. Trans.
,
54
(
3
), pp.
432
448
.
25.
Marotta
,
E.
, and
Fletcher
,
L.
,
1998
, “
Thermal Contact Conductance for Aluminum and Stainless-Steel Contacts
,”
J. Thermophys. Heat Transfer
,
12
(
3
), pp.
374
381
.
26.
Sridhar
,
M.
, and
Yovanovich
,
M.
,
1994
, “
Review of Elastic and Plastic Contact Conductance Models—Comparison With Experiment
,”
J. Thermophys. Heat Transfer
,
8
(
4
), pp.
633
640
.
27.
Yovanovich
,
M.
, and
Rohsenow
,
W.
,
1967
, “
Influence of Surface Roughness and Waviness Upon Thermal Contact Resistance
,” Massachusetts Institute of Technology, Cambridge, MA, Report No.
76361-48
.
28.
Greenwood
,
J. A.
, and
Williamson
,
J.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc.
,
295
(
1442
), pp.
300
319
.
29.
Bhushan
,
B.
,
2013
,
Introduction to Tribology
,
Wiley
,
New York
.
30.
Timoshenko
,
S.
, and
Goodier
,
J.
,
1951
,
Theory of Elasticity
,
Mcgraw-Hill Book Company
,
New York
.
31.
Ruscitto
,
D.
,
Mc Cormick
,
J.
, and
Gray
,
S.
,
1978
, “
Hydrodynamic Air Lubricated Compliant Surface Bearing for an Automotive Gas Turbine Engine. I—Journal Bearing Performance
,” Mechanical Technology, Inc., Latham, NY, Technical Report No.
NASA-CR-135368
.
32.
Iordanoff
,
I.
,
1999
, “
Analysis of an Aerodynamic Compliant Foil Thrust Bearing: Method for a Rapid Design
,”
ASME Tribol. Trans.
,
121
(
4
), pp.
816
822
.
33.
Wang
,
L.
,
Zhou
,
X.
, and
Wei
,
X.
,
2008
,
Heat Conduction
,
Springer
,
Heidelberg, Germany
.
34.
Radil
,
K. C.
, and
DellaCorte
,
C.
,
2002
, “
The Effect of Journal Roughness and Foil Coatings on the Performance of Heavily Loaded Foil Air Bearings
,”
Tribol. Trans.
,
45
(
2
), pp.
199
204
.
35.
Bruckner
,
R. J.
,
2004
, “
Simulation and Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings
,”
Ph.D. thesis
, Case Western Reserve University, Cleveland, OH.
36.
Dykas
,
B.
,
Bruckner
,
R.
,
DellaCorte
,
C.
,
Edmonds
,
B.
, and
Prahl
,
J.
,
2008
, “
Design, Fabrication, and Performance of Foil Gas Thrust Bearings for Microturbomachinery Applications
,” NASA Glenn Research Center, Cleveland, OH, Technical Report No.
TM-2008-215062
.
You do not currently have access to this content.