A brief review of finite element contact and friction theory is presented for low-speed bearing operations. A three-dimensional finite element model is developed to realistically characterize the friction experienced by a coated ball bearing element. The finite elements results, which are obtained for various normal loads and ball materials, are verified using Hertzian contact theory and previous experimental tests performed by the authors. From the results, general trends for the frictional behavior of coated bearing surfaces are established and implications to the field of controls, as applied to precision positioning and tracking instruments are discussed.

1.
Bergmann
G. M.
,
Muller
C.
, and
Simon-Vermot
A.
,
1981
, “
Friction Properties of Sputtered MoS2 Thin Films
,”
Tribology International
, Vol.
14
, pp.
329
332
.
2.
Bhargava
V.
,
Hahn
G. T.
, and
Rubin
C. A.
,
1985
, “
An Elastic-Plastic Finite Element Model of Rolling Contact
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
52
, pp.
67
75
.
3.
Buck
V.
,
1983
, “
Morphological Properties of Sputtered MoS2 Films
,”
Wear
, Vol.
91
, No.
3
, pp.
281
288
.
4.
Chen
W. T.
,
1971
a, “
Computation of Stresses and Displacements In A Layered Elastic Media
,”
International Journal of Engineering Science
, Vol.
9
, pp.
775
800
.
5.
Chen
W. T.
, and
Engel
P. A.
,
1971
b, “
Impact and Contact Stress Analysis in Multilayer Media
,”
International Journal of Solid Structures
, Vol.
8
, pp.
1257
1281
.
6.
Chiu
Y. P.
, and
Hartnett
M. J.
,
1983
, “
A Numerical Solution For Layered Solid Contact Problems With Application to Bearings
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
5
, pp.
585
590
.
7.
Christy
R. I.
, and
Ludwig
H. R.
,
1979
, “
R. F. Sputtered MoS2 Parameter Effects On Wear Life
,”
Thin Solid Films
, Vol.
64
, pp.
223
229
.
8.
Cole
S. J.
, and
Sayles
R. S.
,
1992
, “
A Numerical Model for the Contact of Layered Elastic Bodies with Real Rough Surfaces
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
114
, pp.
334
340
.
9.
Dahl, P. R., 1968, “A Solid Friction Model,” AFO 4695-67-C-D158, Aerospace Corporation.
10.
Dahl, P. R., 1978, “Measurements of Solid Friction Parameters of Ball Bearings,” Aerospace Corporation, pp. 49–60.
11.
Dimigen
H.
,
Hubsch
H.
,
Willich
P.
, and
Reichelt
K.
,
1985
, “
Stoichiometry and Friction Properties of Sputtered MoS2 Layers
,”
Thin Solid Films
, Vol.
129
, pp.
79
91
.
12.
Fleischman
P. D.
,
1984
, “
Effects of Crystallite Orientation On Environmental Stability and Lubrication Properties of Sputtered MoS2 Thin Films
,”
ASLE Transactions
, Vol.
27
, No.
1
, pp.
82
88
.
13.
Ford
I. J.
,
Cunningham
J. M.
,
Ogilvy
J. A.
,
Roberts
E. W.
,
1994
, “
Interpretation of Friction and wear Properties of MoS2 Coated Steel Substrates
,”
Wear
, Vol.
177
, No.
1
, pp.
93
101
.
14.
Gardos, M., 1990, “On the Elastic Constants of Thin Solid Lubricant Films,” Mechanics of Coatings, Elsevier, Amsterdam, The Netherlands, pp. 3–13.
15.
Keer
K. L.
, and
Mowry
D. B.
,
1979
, “
The Stress Field Created by a Circular Sliding Contact on Transversely Isotropic Spheres
,”
International Journal of Solid Structures
, Vol.
15
, pp.
33
39
.
16.
Kemure
M.
,
Okada
K.
,
Mogami
A.
,
Kitsu
A.
,
1987
, “
Friction and wear of Sputtered MoS2 Films in Sliding Contact
,”
Lubrication Engineering
, Vol.
158
, pp.
128
138
.
17.
King
R. B.
, and
O’Sullivan
T. C.
,
1987
, “
Sliding Contact Stresses In A Two-Dimensional Layered Elastic Half-Space
,”
International Journal of Solid Structures
, Vol.
23
, pp.
581
597
.
18.
Komvopoulos
K.
,
1988
, “
Finite Element Analysis of a Layered Elastic Solid in Normal Contact With A Rigid Surface
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
110
,
477
485
.
19.
Komvopoulos
K.
,
1989
, “
Elastic-Plastic Finite Element Analysis of Indented Layered Media
,”
Trans. ASME
, Vol.
111
,
430
439
.
20.
Leonard, N. E., and Krishnaprasad, P. S., 1992, “Adaptive Friction Compensation For Bi-Directional Low-Velocity Position Tracking,” Proceedings of the 31st Conference on Decision and Control, Tucson, Arizona, pp. 267–273.
21.
Lin
W.
,
Kuo
C. H.
, and
Keer
L. M.
,
1991
, “
Analysis of A Transversely Isotropic Half Space Under Normal and Tangential Loadings
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
113
, pp.
335
338
.
22.
Lovell
M. R.
,
Khonsari
M. M.
, and
Marangoni
R. D.
,
1993
a, “
Ultra Low-Speed Friction Torque On Balls Undergoing Rolling Motion
,”
STLE Tribology Transactions
, Vol.
36
, pp.
290
296
.
23.
Lovell
M. R.
,
Khonsari
M. M.
, and
Marangoni
R. D.
,
1994
, “
Experimental Measurements of the Rest Slope and Steady Torque on Ball Bearings Experiencing Small Angular Rotations
,”
STLE Tribology Transactions
, Vol.
37
, No.
2
, pp.
261
268
.
24.
Lovell
M. R.
,
Khonsari
M. M.
, and
Marangoni
R. D.
,
1993
b, “
The Response of Balls Undergoing Oscillatory Motion: Crossing From Boundary to Mixed Lubrication Regimes
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
115
, pp.
261
266
.
25.
Lovell, M. R., Khonsari, M. M., and Marangoni, R. D., 1995a, “Dynamic Friction Measurements of MoS2 Coated Ball Bearing Surfaces,” presented at the ASME/STLE Joint Conference, Orlando, FL, October, 1995, to appear in ASME JOURNAL OF TRIBOLOGY.
26.
Lovell, M. R., Khonsari, M. M., and Marangoni, R. D., 1995b, “A Finite Element Analysis Of The Frictional Forces Between A Cylindrical Bearing Element and MoS2 Coated and Uncoated Surfaces,” to appear in Wear.
27.
Lovell
M. R.
,
Khonsari
M. M.
, and
Marangoni
R. D.
,
1996
, “
Comparison of the Ultra-Low-Speed Frictional Characteristics of Silicon Nitride and Steel Balls Using Conventional Lubricants
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
118
, pp.
43
51
.
28.
Martin
J. M.
,
Donnet
C.
,
Le Mogne
Th.
,
1993
, “
Superlubricity of Molybdenum Disulphide
,”
Physical Review B
, Vol.
48
, No.
14
, pp.
10583
10586
.
29.
Mikkelsen
N. J.
,
Sorensen
G.
,
1992
, “
Solid Lubricating Films Produced By Ion Bombardment of Sputter Deposited MoS2 Films
,”
Surface and Coatings Technology
, Vol.
51
, pp.
118
123
.
30.
Nurre, G. S., 1974, “An Analysis of the Dahl Friction Model and Its Effects on a CMG Gimbal Rate Controller,” NASA-TMX 64934.
31.
Ovaert
T. C.
,
1993
, “
On the Indentation of a Transversely Isotropic Half-Space With Application to Thin Solid Lubricant Films
,”
Trans. ASME
, Vol.
115
, pp.
650
657
.
32.
Roberts, E. W., 1986, “Towards an Optimized MoS2 Lubricant Film,” Proc. 20th Aerospace Mech. Symposium, NASA CP-2423, pp. 103–119.
33.
Roberts, E. W., 1987, “The Tribology Of Sputtered Molybdenum Disulfide Films,” Proc. Inst. Mech. Engr. Tribology—Friction Lubrication and Wear, Fifty Years On, Vol. I, pp. 503–510.
34.
Spalvins
T.
,
1978
, “
Coatings For Wear and Lubrication
,”
Thin Solid Films
, Vol.
53
, pp.
285
300
.
35.
Stevens, K. T., and Todd, M. J., 1978, “Friction Torque of Angular Contact Ball Bearings with Different Conformities,” First Tribology Symposium, ESA Trib/1.
36.
Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, New York, McGraw-Hill, pp. 409–414.
37.
Todd
M. J.
, and
Johnson
K. L.
,
1987
, “
A Model For Coulomb Torque Hysteresis In Ball Bearings
,”
International Journal of Mechanical Science
, Vol.
29
, pp.
339
354
.
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