Page 104 - Tribology in Machine Design

90 Tribology in machine design

standard deviation, cr, the distribution of summit heights is very nearly
Gaussian with a standard deviation

The mean height of the summits lies between 0.5cr and 1.5cr above the
mean level of the surface. The same result is true for peak heights in a
profilometer trace. A peak in the profilometer trace is identified when,
of three adjacent sample heights, z,-_ t and z f+1 , the middle one z, is
greater than both the outer two.
(ii) the mean summit curvature is of the same order as the r.m.s. curvature
of the surface, i.e.

(iii) by identifying peaks in the profile trace as explained above, the number
of peaks per unit length of trace rj p can be counted. If the wavy surface
were regular, the number of summits per unit area q s would be ^. Over
a wide range of finite sampling intervals

Although the sampling interval has only a second-order effect on the
relationship between summit and profile properties it must be
emphasized that the profile properties themselves, i.e. o k and cr p are
both very sensitive to the size of the sampling interval.

3.8.2. Contact of nominally flat rough surfaces
Although in general all surfaces have roughness, some simplification can be
achieved if the contact of a single rough surface with a perfectly smooth
surface is considered. The results from such an argument are then
reasonably indicative of the effects to be expected from real surfaces.
Moreover, the problem will be simplified further by introducing a
theoretical model for the rough surface in which the asperities are
considered as spherical cups so that their elastic deformation charac-
teristics may be defined by the Hertz theory. It is further assumed that there
is no interaction between separate asperities, that is, the displacement due
to a load on one asperity does not affect the heights of the neighbouring
asperities.
Figure 3.11 shows a surface of unit nominal area consisting of an array of
identical spherical asperities all of the same height z with respect to some
reference plane XX'. As the smooth surface approaches, due to the

Figure 3.11