The analysis of the elastic contact of ideal rough surfaces is presented in this paper. The rough asperities are assumed to be spherical with the same vertical height and spatial distance. The mutual influence of asperities is considered. Numerical results show that for the same load, the contact area is less than the Hertzian prediction, while the pressure distribution is still of a Hertzian type, but is increased to some extent. We find that the asperity interaction is associated with a parameter, called the “loading level,” which combines the surface texture, mechanical properties, and the nominal mean pressure. Of significant importance is the discovery of the variation of the reference plane position with the contact load. In the classical theory of rough contact (Greenwood and Williamson, 1966), the reference plane was in fact assumed to be in the mean line position. We prove that the location of the reference plane is determined by the number of contacting asperities and the loading level, thus making the analysis of the contact of rough surfaces somewhat complex.

1.
Bhushan
B.
,
1984
, “
Analysis of the Real Area of Contact Between a Magnetic Medium and a Rigid Surface
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
106
, pp.
26
34
.
2.
Greenwood
J. A.
, and
Williamson
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. Roy. Soc. London
, Vol.
A295
, pp.
300
319
.
3.
Greenwood, J. A., and Tripp, J. H., 1967, “The Elastic Contact of Rough Spheres,” ASME Journal of Applied Mechanics, Mar., pp. 153–159.
4.
Goryacheva
I. G.
, and
Dobychin
M. N.
,
1991
, “
Multiple Contact Model in the Problems of Tribomechanics
,”
Tribology International
, Vol.
24
, No.
1
, pp.
29
35
.
5.
Johnson
K. L.
,
Greenwood
J. A.
, and
Higginson
J. G.
,
1985
, “
The Contact of Elastic Regular Wavy Surfaces
,”
Int. J. Mech. Sci.
, Vol.
27
, No.
6
, pp.
383
396
.
6.
Johnson, K. L., Contact Mechanics, Cambridge University Press, 1985.
7.
Leng
Y. S.
,
Xian
L.
,
Huang
Y.
, and
Zheng
L. Q.
,
1990
, “
Elastic Contact of Asperities on the Rough Surfaces
,”
Journal of Tsinghua University
, Vol.
30
, No.
S1
, pp.
94
106
(in Chinese).
8.
Leng
Y. S.
,
Wang
G. C.
, and
Huang
Y.
,
1992
, “
Non-Hertzian Contact of Infinite Asperity Group on the Nominal Flat
,”
Journal of Tsinghua University
, Vol.
32
, No.
5
, pp.
95
100
(in Chinese).
9.
Nowell
D.
, and
Hills
D. A.
,
1989
, “
Hertzian Contact of Ground Surfaces
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
111
, pp.
175
179
.
10.
Paul, B., and Hashemi, J., 1977, “An Improved Numerical Method for Counterformal Contact Stress Problems,” Technical Report No. 3, FRA-ORD-78–26, Contract DOT-OS-60144, Federal Rail Administration (PB 286 228).
11.
Poon
C. Y.
, and
Sayles
R. S.
,
1989
, “
Frictional Transitions in Boundary Lubrication Sliding
,”
Proc. IMech. E.
,
C375
, pp.
109
124
.
12.
Sayles
R. S.
,
De Silva
G. M. S.
,
Leather
J. A.
,
Anderson
J. C.
, and
Macpherson
P. B.
,
1981
, “
Elastic Conformity in Hertzian Contacts
,”
Tribology International
, Vol.
14
, pp.
315
322
.
This content is only available via PDF.
You do not currently have access to this content.