This paper presents a simple method that may be used to calculate the pressures and surface displacements in contacts of rough surfaces. A main feature of the method is that the pressure is calculated (updated) individually at each surface location rather than simultaneously at all locations by solving a system of equations. The pressure update at a given location is computed solely based on the surface interpenetration at that location; consequently, both 2-D and 3-D contact problems are solved in exactly the same way. Furthermore, this scheme of calculation does not produce negative pressures in the solution process, which is a main source of numerical instability in other types of methods of solution. The method is conceptually simple and easy for computer implementation. It is numerically stable and can solve various types of problems of high contact severity. Measured roughness data can be used directly without any mathematical treatment such as filtering or frequency decomposition. The method is also computationally efficient and requires minimum computer storage, making it suitable for integration into computer programs for design-analysis calculations of practical contact/lubrication problems.

1.
Chang
L.
,
Webster
M. N.
, and
Jackson
A.
,
1994
, “
A Line-Contact Micro-EHL Model with Three-Dimensional Surface Topography
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
116
, No.
1
, pp.
21
28
.
2.
Conry, T. F., and Seireg, A., 1971, “A Mathematical Programming Method for Design of Elastic Bodies in Contact,” ASME Journal of Applied Mechanics, June, pp. 387–392.
3.
Dahlquist, G., and Bjorck, A., 1974, Numerical Methods, Prentice-Hall, New Jersey.
4.
Houpert
L. G.
, and
Hamrock
B. J.
,
1986
, “
Fast Approach for Calculating Film Thickness and Pressures in Elastohydrodynamically Lubricated Contacts at High Loads
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
108
, No.
4
, pp.
411
420
.
5.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press.
6.
Ju
Y.
, and
Farris
T. N.
,
1996
, “
Spectral Analysis of Two-Dimensional Contact Problems
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
118
, No.
2
, pp.
320
328
.
7.
Kalker
J. J.
, and
Vanranden
Y.
,
1972
, “
A Minimum Principle for Frictionless Elastic Contact with Application to Non-Hertzian Half-Space Contact Problems
,”
Journal of Engineering Math
, Vol.
6
, pp.
193
206
.
8.
Lai
W. T.
, and
Cheng
H. S.
,
1985
, “
Computer Simulation of Elastic Rough Contacts
,”
ASLE Transactions
, Vol.
28
, No.
2
, pp.
172
180
.
9.
Lee
S. C.
, and
Cheng
H. S.
,
1992
, “
On the Relation of Load to Average Gap in the Contact Between Surfaces with Longitudinal Roughness
,”
Tribology Transactions
, Vol.
35
, No.
3
, pp.
523
529
.
10.
Lubrecht
A. A.
, and
Ioannides
E.
,
1991
, “
A Fast Solution of the Dry Contact Problem and the Associated Sub-surface Stress Field, Using Multilevel Techniques
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
113
, No.
1
, pp.
128
133
.
11.
Nogi
T.
, and
Kato
T.
,
1997
, “
Influence of a Hard Surface Layer on the Limit of Elastic Contact—Part I: Analysis Using a Real Surface Model
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
119
, No.
3
, pp.
493
500
.
12.
Stanley
H. M.
, and
Kato
T.
,
1997
, “
An FFT-Based Method for Rough Surface Contact
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
119
, No.
3
, pp.
481
485
.
13.
Sui, P. C., 1997, “An Efficient Computational Model for Calculating Surface Contact Pressures Using Measured Surface Roughness,” Tribology Transactions, Vol. 40, No. 2.
14.
Tian
X.
, and
Bhushan
B.
,
1996
, “
A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
118
, No.
1
, pp.
33
42
.
15.
Webster
M. W.
, and
Sayles
R. S.
,
1986
, “
A Numerical Model for the Elastic Frictionless Contact of Real Rough Surfaces
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
108
, No.
3
, pp.
314
320
.
16.
Wolfe
P.
,
1959
, “
The Simplex Method for Quadratic Programming
,”
Econometrica
, Vol.
27
, pp.
382
398
.
This content is only available via PDF.