117 .
1
61 .
1
KE KE
ep
Y p
for
110 6
1
KE
where Y is the yield strength of the material.
While the relationship between surface areas in contact in the interference functions of elastic-plastic contact is given in the equation:
136 .
1 1
93 .
KE c
KE ep
A A
for
6 1
1
KE
........................................2.24
146 .
1 1
94 .
KE c
KE ep
A A
for
110 6
1
KE
A
c-KE
is critical contact area when
KE
1
.
2.2 Surface Topography: Surface Texture, Roughness, Waviness
Surface topography is the three-dimensional representation of geometric surface irregularities. A surface can be curvy, rough or smooth depending upon the magnitude
and spacing of the peaks and valleys and also depending upon how the surface is produced. Surface texture refers to the locally limited deviation of a surface from the
ideal intended geometry of the part. A realistic characterization of surface roughness is required to analyze the effect of surface roughness on different tribological parameters.
Roughness relates to the closely-spaced irregularities left on a surface from a production process. It is a measure of the fine, closely spaced, random irregularities or surface
texture. Waviness is the component of texture upon which roughness is superimposed. It relates to the more widely-spaced irregularities than roughness caused by vibration,
chatter, heat treatment, or warping strains [16]. Surface roughness cannot be easily defined by a single parameter. In fact, there are several ways to represent roughness. All
rough surfaces having height and wavelength, with the former measured at right angle
to the surface and the latter in the plane of the surface. The distribution of height is measured from a reference plane say, mean plane.
The characterization of a surface may be one dimensional 1-D or two dimensional 2-D depending upon the machining and finishing process. For 1-D case,
height z varies with one of the coordinates, whereas in other coordinate there exists a lay where variation of z is comparatively small. But for surfaces made by conventional
manufacturing processes, when 1-D characterization is not proper, 2-D surface roughnesses description is required. Atomic Force Microscope AFM and 3D surface
profilometer are used to improve the resolution and accuracy of the roughness measurement. Typical 1-D and 2-D representation of nominally flat surfaces polished
are shown in Figure 2.2. a and 2.2. b. Scale used for the height is much larger than that for the wavelength because the height of the asperities from the mean plane is very
less compared to their wavelengths [16].
Figure 2.2: Typical representation of a surface: a one-dimensional b two-
dimensional [16].
2.3 Contact Problem of Smooth Surfaces
