The complexities of analyzing rolling element bearings vary. Vendors offer cataloged solutions comprised of limiting loads and speeds, bearing life, and lubricant recommendations. These guidelines meet the needs of most customers; however, more demanding applications warrant advanced analyses. This work focuses on thermal management. Current literature offers system level solutions using either resistance methods or finite element analysis (FEA). Resistance methods have rapid computation time, yet lack accuracy. Finite element methods improve the accuracy, but are computationally cumbersome. This work proposes an integral transform method. The rapidly computed solution yields accurate results. The methodology and results of this work are presented in a three-part series. Part I details existing literature and provides the framework for a new heat transfer model. This model describes rolling-element bearing systems containing a shaft, housing, and numerous bearing raceways. It also includes gears, cooling jackets, and is applicable for several methods of lubrication. The model consists of solid component partial differential equations (PDEs) in conjunction with analytic expressions for fluid temperatures, convection equation, and mass flow. Part II presents the housing, shaft, and bearing raceway PDE solutions. Part III offers experimental validation, as well as observations from experiments on fluid flow within the bearing.

References

References
1.
Canter
,
N.
, “
Key Trends in Bearing Lubrication
”, Tribology and Lubrication Technology, Apr. 2012, pp.
2
11
.
2.
Pinel
,
S. I.
,
Singer
,
H. R.
, and
Zaretsky
,
E. V.
,
2001
, “
Comparison Between Oil-Mist and Oil-Jet Lubrication of High-Speed, Small-Bore, Angular-Contact Ball Bearings
,”
Tribol. Trans.
,
44
(
3
), pp.
327
338
.10.1080/10402000108982465
3.
Zaretsky
,
E. V.
,
Singer
,
H. R.
, and
Bamberger
,
E. N.
,
1974
, “
Operating Characteristics of 120 mm Bore Ball Bearings at 3 × 106 DN
,” Report No. NASA TN D-7837.
4.
Singer
,
H. R.
,
Bamberger
,
E. N.
, and
Zaretsky
,
E. V.
,
1974
, “
Parametric Study of the Lubrication of Thrust Loaded 120 mm Bore Ball Bearings to 3 Million DN
,”
ASME J. Lubr. Technol.
,
96
(
3
), pp.
515
525
.10.1115/1.3452031
5.
Harris
,
T.
,
1964
, “
Prediction of Temperature in Rolling Bearing Assembly
,”
Lubr. Eng.
,
20
(2), pp.
145
150
.
6.
Harris
,
T.
, and
Kotzalas
,
M. N.
,
2007
,
Advanced Concepts of Bearing Technology
,
4th ed.
,
CRC
,
Boca Raton
, Vol.
2
, pp.
191
208
.
7.
Witte
,
D.
,
1976
, “
Predicting Bearing Temperature
,”
Mach. Des.
,
48
, pp.
110
115
.
8.
Schrand
,
J. B.
,
1977
, “
Computer Program Operation Manual on “SHABERTH.” A Computer Program for the Analysis of Steady State and Transient Thermal Performance of Shaft-Bearing Systems
,” Technical Report No. AFAPL-TR-76-90.
9.
Hadden
,
G. B.
,
Kleckner
,
R. J.
,
Ragen
,
M. A.
, and
Sheynin
,
L.
,
1981
, “
The SHABERTH Program—Steady State and Transient Thermal Analysis of a Shaft Bearing System Including Ball, Cylindrical and Tapered Roller Bearing
,” Report No. NASA-CR-165365.
10.
Pinel
,
S. I.
,
Singer
,
H. R.
, and
Zaretsky
,
E. V.
,
1998
, “
Design and Operating Characteristics of High-Speed, Small-Bore, Angular-Contact Ball Bearings
,” Report No. NASA/TM 1988-206981.
11.
Winer
,
W. O.
,
Bair
,
S.
, and
Gecim
,
B.
,
1986
, “
Thermal Resistance of a Tapered Roller Bearing
,”
Am. Soc. Lubr. Eng.
,
29
(
4
), pp.
539
547
.10.1080/05698198608981718
12.
Gupta
,
P. K.
,
2002
, “
Thermal Interactions in Rolling Bearing Dynamics
,” U.S. Department of Commerce, Report No. ADA409914, Clifton Park, NY.
13.
Blok
,
H.
,
1937
, “
Theoretical Study of Temperature Rise at Surfaces of Actual Contact Under Oiliness Lubrication Conditions
,”
Proceeding of the Institute of Mechanical Engineers General Discussion of Lubrication
, Institute of Mechanical Engineers, London, pp. 222–235.
14.
Changenet
,
C.
,
Oviedo-Marlot
,
X.
, and
Velex
,
P.
,
2006
, “
Power Loss Predictions in General Transmissions Using Thermal Newtons-Applications to a Six-Speed Manual Gearbox
,”
ASME J. Mech. Des.
,
128
(
3
), pp.
618
625
.10.1115/1.2181601
15.
Changenet
,
C.
,
2006
, “
Modelisation du Comportement Thermique des Transmissions par Engrenages
,” Ph.D. thesis, INSA Lyon, France.
16.
Bairi
,
A. A.
,
2004
, “
Three Dimensional Stationary Thermal Behavior of a Ball Bearing
,”
Int. J. Therm. Sci.
,
43
(
6
), pp.
561
568
.10.1016/j.ijthermalsci.2003.10.008
17.
Fischer
,
F. D.
,
Werner
,
E.
, and
Knothe
,
K.
,
2000
, “
The Surface Temperature of a Half-Plane Subjected to Rolling/Sliding Contact With Convection
,”
ASME J. Tribol.
,
122
(
4
), pp.
864
866
.10.1115/1.1288927
18.
Fischer
,
F. D.
,
Werner
,
E.
, and
Knothe
,
K.
,
2000
, “
The Surface Temperature of a Half Plane Heated by Friction and Cooled by Convection
,”
J. Appl. Math. Mech.
,
81
(
2
), pp.
75
81
.10.1016/j.ijthermalsci.2003.10.008
19.
Fischer
,
F. D.
,
2004
, “
Temperature and Stress Fields Due to Contact With Friction, Surface Heat Treatments, Welding, and Cutting
,”
Surface Modification and Mechanisms
,
G. E.
Tolten
, and
H.
Liang
, eds.,
2nd ed.
,
CRC
,
Boca Raton
, pp.
1
16
.
20.
Brown
,
J. R.
, and
Forster
,
N. H.
,
2003
, “
Carbon-Phenolic Cages for High-Speed Bearings
,” Report No. AFRL-PR-WP-TR-2003-2033.
21.
Hoeprich
,
M. R.
,
1996
, “
Rolling-Element Bearing Internal Temperatures
,”
Tribol. Trans.
39
(
4
), pp.
855
858
.10.1080/10402009608983605
22.
Jaeger
,
J. C.
,
1942
, “
Moving Sources of Heat and the Temperature at Sliding Contacts
,”
J. Proc. R. S. New South Wales
,
76
, pp.
203
224
.
23.
Tian
,
X.
, and
Kennedy
,
F. E.
,
1993
, “
Temperature Rise at the Sliding Contact Interface for a Coated Semi-Infinite Body
,”
ASME J. Tribol.
,
115
(
1
), pp.
1
9
.10.1115/1.2920976
24.
Tian
,
X.
, and
Kennedy
,
F. E.
,
1994
, “
Maximum and Average Flash Temperatures in Sliding Contacts
,”
ASME J. Tribol.
,
116
(
1
), pp.
167
174
.10.1115/1.2927035
25.
Cameron
,
A.
,
1966
,
Principles of Lubrication
,
Wiley
,
New York
, p.
42
.
26.
Parker
,
R. J.
,
1984
, “
Comparison of Predicted and Experimental Thermal Performance of Angular Contact Ball Bearing
,” Report No. NASA Technical Paper No. 2275.
27.
Incropera
,
F. P.
, and
Dewitt
,
D. P.
,
1985
,
Introduction to Heat Transfer
,
3rd ed.
,
Wiley
,
Jefferson City, MO
.
28.
Bejan
,
A.
, and
Kraus
,
A.
,
2003
,
Heat Transfer Handbook
,
Wiley
,
Hoboken, NJ
.
29.
Krieth
,
R.
,
1968
, “
Convection Heat Transfer in Rotating Systems
,”
Advances in Heat Transfer
,
Academic Press
,
New York
, Vol.
5
, pp.
129
251
.10.1016/S0065-2717(08)70130-8
30.
Houpert
,
L.
,
1999
, “
Numerical and Analytical Calculations in Ball Bearings
,”
Symposium Presented at the 8th European Space Mechanism and Tribology
,
Toulouse
, France, Sept. 29.
31.
Houpert
,
L.
,
2002
, “
Ball Bearing and Tapered Roller Bearing Torque: Analytical, Numerical and Experimental Results
,”
STLE Tribol. Trans.
,
45
(
3
), pp.
345
353
.10.1080/10402000208982559
32.
Biboulet
,
N.
, and
Houpert
,
L.
,
2010
, “
Hydrodynamic Force and Moment in Pure Rolling Lubricated Contact—Part I: Line Contacts
,”
Proc. Inst. Mech. Eng. J. Eng. Tribol.
,
224
(
8
), pp.
765
775
.10.1243/13506501JET790
33.
Biboulet
,
N.
, and
Houpert
,
L.
,
2010
, “
Hydrodynamic Force and Moment in Pure Rolling Lubricated Contact—Part II: Point Contacts
,”
Proc. Inst. Mech. Eng. J. Eng. Tribol.
,
224
(
8
), pp.
777
787
.10.1243/13506501JET791
34.
Clarke
,
A.
,
Sharif
,
K. J.
,
Evans
,
H. P.
, and
Sindle
,
R. W.
,
2006
, “
Heat Partition in Rolling/Sliding Elastohydrodynamic Contacts
,”
ASME J. Tribol.
,
128
(
1
), pp.
67
78
.10.1115/1.2125867
35.
Evans
,
H. P.
,
Clarke
,
A.
,
Sharif
,
J. J.
, and
Sindle
,
R. W.
,
2010
, “
The Role of Heat Partition in Elastohydrodynamic Lubrication
,”
Tribol. Trans.
,
53
(
2
), pp.
179
188
.10.1080/10402000903097452
36.
Hannon, W. M., 2015, “Rolling-Element Bearing Heat Transfer—Part III: ExperimentalValidation,“
ASME J. Tribol.
,
137
(3), p. 031103.10.1115/1.4029734
37.
Crook
,
A. W.
,
1961
, “
The Lubrication of Rollers
,”
Philos. Trans. A
,
250
, p.
387
.
38.
Crook
,
A. W.
,
1961
, “
The Lubrication of Rollers III. A Theoretical Discussion of Friction and the Temperatures in the Oil Film
,”
Philos. Trans. A
,
254
, p.
237
.10.1098/rsta.1961.0016
39.
Bloch
,
H.
, and
Shamim
,
A.
,
1988
,
Oil Mist Lubrication: Practical Applications
,
Fairmont, Inc
, Liburn.
40.
Freestone
,
R. E.
, III
,
1968
, “
Mist Lubrication
,”
A Technical Publication Devoted to the Selection and Use of Lubricants
,
Texaco
,
TX
, Vol.
54
, No.
10
, pp. 117–128.
41.
Weck
,
M.
, and
Koch
,
A.
,
1993
, “
A Spindle-Bearing Systems for High-Speed Applications in Machine Tooles
,”
Ann. CIRP
,
42
(
1
), pp.
445
448
.10.1016/S0007-8506(07)62482-2
42.
Zenker
,
J. S.
,
1993
, “
Design and Application of High-Speed Spindles for High-Speed Machining
,”
Society of Manufacturing Engineers Conference Division
, High Speed Machining Clinic, Apr., Chicago, IL.
43.
Riddle
,
J.
,
1955
,
Ball Bearing Maintenance
,
University of Oklahoma
,
Norman, OK
, p.
143
.
44.
Levy
,
S.
,
1999
,
Two-Phase Flow in Complex Systems
,
Wiley, Inc.
,
New York
, p.
252
.
45.
Hannon, W. M., 2015, “Rolling-Element Bearing Heat Transfer—Part II: Housing, Shaft, and Bearing Raceway Partial Differential Solutions,”
ASME J. Tribol.
,
137
(3), p. 031102.10.1115/1.4029733
46.
Siegal
,
R.
, and
Howell
,
J.
,
1981
,
Thermal Radiation Heat Transfer
,
2nd ed.
,
McGraw-Hill Book Company
,
New York
.
You do not currently have access to this content.