Wherever friction occurs, mechanical energy is transformed into heat. The maximum surface temperature associated with this heating can have an important influence on the tribological behavior of the contacting components. For band contacts the partitioning of heat has already been studied extensively; however, for circular and elliptic contacts only approximate solutions exist. In this work a numerical algorithm is described to solve the steady state heat partitioning and the associated flash temperatures for arbitrary shaped contacts by matching the surface temperatures of the two contacting solids at all points inside the contact area. For uniform and semi-ellipsoidal shaped heat source distributions, representing EHL conditions and dry or boundary lubrication conditions respectively, function fits for practical use are presented giving the flash temperature as a function of the Pe´clet numbers of the contacting solids, the conductivity ratio, and the aspect ratio of the contact ellipse. These function fits are based on asymptotic solutions for small and large Pe´clet numbers and are valid for the entire range of Pe´clet numbers. By comparison with numerical results they are shown to be accurate within 5%, even for the situation of opposing surface velocities.

Issue Section:
Research Papers
Topics:
Heating, Tribology, Heat, Temperature, Solids, Algorithms, Boundary lubrication, Electrical conductivity, Friction, Steady state, Thermal conductivity
1.
Abramowitz, M., and Stegun, I. A., (eds.), 1965, Handbook of Mathematical Functions, New York.
2.
Allen
D. N. de G.
,
1962
, “
A Suggested Approach to Finite-Difference Representation of Differential Equations, With an Application to Determine Temperature-Distribution Near a Sliding Contact
,”
Quart. J. Mech. and Applied Math.
, Vol.
15
, pp.
11
–
33
.
3.
Archard
J. F.
,
1959
, “
The Temperature of Rubbing Surfaces
,”
Wear
, Vol.
2
, pp.
438
–
455
.
4.
Blok, H., 1937a, “The Surface Temperatures Under Extreme Pressure Lubricating Conditions,” Contributions by the Delft Laboratory of the Royal Dutch/Shell to the 2nd World Petroleum Congress, Paris 1937, The Hague 1939, pp. 151–182.
5.
Blok, H., 1937b, “Theoretical Study of Temperature Rise at Surface of Actual Contact Under Oiliness Lubricating Conditions,” Instn. Mech. Engrs., Proceedings of General Discussion on Lubrication and Lubricants, Vol. 2, pp. 222–235.
6.
Bos, J., and Moes, H., 1993, “Frictional Heating of Elliptic Contacts,” Proc. of the 20th Leeds-Lyon Symposium on Tribology, Lyon, France, to appear.
7.
Brandt, A., 1984, “Multigrid Techniques: 1984 Guide With Applications to Fluid Dynamics,” available as G.M.D.-Studien No. 85, from G.M.D.-FIT, Postfach 1240, D-5205, St. Augustin 1, Germany.
8.
Cameron
A.
,
Gordon
A. N.
, and
Symm
G. T.
,
1965
, “
Contact Temperatures in Sliding/Rolling Surfaces
,”
Proc. Roy. Soc.
A, Vol.
286
, pp.
45
–
61
.
9.
Carleman
T.
,
1922
, “
U¨ber die Abelsche Integralgleichung mit konstanten Integrationsgrenze
,”
Mathematisch Zeitschrift
, Vol.
15
, pp.
111
–
120
.
10.
Carlsaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, 2nd ed., Oxford.
11.
Francis
H. A.
,
1970
, “
Interfacial Temperature Distribution Within a Sliding Hertzian Contact
,”
ASLE Trans.
, Vol.
14
, pp.
41
–
45
.
12.
Greenwood
J. A.
,
1991
, “
An Interpolation Formula for Flash Temperatures
,”
Wear
, Vol.
150
, pp.
153
–
158
.
13.
Jaeger
J. C.
,
1943
, “
Moving Sources of Heat
,”
J. and Proc. Roy. Soc. N.S.W.
, Vol.
76
, pp.
203
–
224
.
14.
Kennedy
F. E.
,
1984
, “
Thermal and Thermomechanical Effects in Dry Sliding
,”
Wear
, Vol.
100
, pp.
453
–
467
.
15.
Kuhlmann-Wilsdorf
D.
,
1986
, “
Sample Calculations of Flash Temperatures at a Silver-Graphite Electric Contact Sliding Over Copper
,”
Wear
, Vol.
107
, pp.
71
–
90
.
16.
Kuhlmann-Wilsdorf
D.
,
1987
, “
Temperatures at Interfacial Contact Spots: Dependence on Velocity and on Role Reversal of Two Materials in Sliding Contact
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
109
, pp.
321
–
329
.
17.
Lubrecht
A. A.
,
ten Napel
W. E.
, and
Bosma
R.
,
1986
, “
Multigrid, an Alternative Method for Calculating Film Thickness and Pressure Profiles in Elastohydrodynamically Lubricated Line Contacts
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
108
, pp.
551
–
556
.
18.
Lubrecht
A. A.
, and
Ioannides
E.
,
1989
, “
A Fast Solution of the Dry Contact Problem and the Associated Sub-Surface Stress Field Using Multilevel Techniques
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
113
, pp.
128
–
133
.
19.
Tian
X.
, and
Kennedy
F. E.
,
1994
, “
Maximum and Average Flash Temperatures in Sliding Contacts
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
116
, pp.
167
–
174
.
20.
Venner, C. H., and Lubrecht, A. A., 1993, “Multilevel Solvers for Integro and Integro-Differential Problems in Contact Mechanics and Lubrication,” Proceedings 4th European Multigrid Conference, Amsterdam, The Netherlands, pp. 111–127, Editors Hemker, P. W., and Wesseling, P., published by Birkhauer Verlag.
21.
Winter, A. de, 1967, “De berekening van de flitstemperatuurverdelingen in en aan weerszijden van een bandvormig contactvlak (tevens warmtebron) tussen twee over elkaar glijdende loopvlakken,” Masters thesis (in Dutch), Technical University of Delft.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.