Page 101 - Tribology in Machine Design

Elements of contact mechanics 87

where

3.8. Contact between There are no topographically smooth surfaces in engineering practice. Mica
rough surfaces can be cleaved along atomic planes to give an atomically smooth surface
and two such surfaces have been used to obtain perfect contact under
laboratory conditions. The asperities on the surface of very compliant
solids such as soft rubber, if sufficiently small, may be squashed flat
elastically by the contact pressure, so that perfect contact is obtained
through the nominal contact area. In general, however, contact between
solid surfaces is discontinuous and the real area of contact is a small fraction
of the nominal contact area. It is not easy to flatten initially rough surfaces
by plastic deformation of the asperities.
The majority of real surfaces, for example those produced by grinding,
are not regular, the heights and the wavelengths of the surface asperities
vary in a random way. A machined surface as produced by a lathe has a
regular structure associated with the depth of cut and feed rate, but the
heights of the ridges will still show some statistical variation. Most man-
made surfaces such as those produced by grinding or machining have a
pronounced lay, which may be modelled, to a first approximation, by one-
dimensional roughness.
It is not easy to produce wholly isotropic roughness. The usual procedure
for experimental purposes is to air-blast a metal surface with a cloud of fine
particles, in the manner of shot-peening, which gives rise to a randomly
cratered surface.

3.8.1. Characteristics of random rough surfaces

The topographical characteristics of random rough surfaces which are
relevant to their behaviour when pressed into contact will now be discussed
briefly. Surface texture is usually measured by a profilometer which draws a
stylus over a sample length of the surface of the component and reproduces
a magnified trace of the surface profile. This is shown schematically in Fig.
3.9. It is important to realize that the trace is a much distorted image of the
actual profile because of using a larger magnification in the normal than in
the tangential direction. Modern profilometers digitize the trace at a
suitable sampling interval and send the output to a computer in order to
extract statistical information from the data. First, a datum or centre-line is
established by finding the straight line (or circular arc in the case of round
components) from which the mean square deviation is at a minimum. This
implies that the area of the trace above the datum line is equal to that below
it. The average roughness is now defined by

Figure 3.9