Chapter 2 Review of Forces and Moments - Brown University

(1) All surfaces are rough;
(2) All surfaces are covered with a thin film of oxide, an adsorbed layer of water, or an
organic film.
Surface roughness can be controlled to some extent – a cast
surface is usually very rough; if the surface is machined the
roughness is somewhat less; roughness can be reduced further
by grinding, lapping or polishing the surfaces. But you can’t get
rid of it altogether. Many surfaces can be thought of as having a
fractal geometry. This means that the roughness is statistically
self-similar with length scale – as you zoom in on the surface, it
always looks (statistically) the same (more precisely the
surfaces are self-affine. When you zoom in, it looks like the
surface got stretched vertically – surfaces are rougher at short
wavelengths than at long ones).
Of course no surface can be truly fractal: roughness can’t be
smaller than the size of an atom and can’t be larger than the
component; but most surfaces look fractal over quite a large range of lengths. Various statistical
measures are used to quantify surface roughness, but a discussion of these parameters is beyond the scope
of this course.
Now, visualize what the contact between two rough surfaces looks like. The surfaces will only touch at
high spots (these are known in the trade as `asperities’) on the two surfaces. Experiments suggest that
there are huge numbers of these contacts (nobody has really been able to determine with certainty how
many there actually are). The asperity tips are squashed flat where they contact, so that there is a finite
total area of contact between the two surfaces. However, the true contact area (at asperity tips) is much
smaller than the nominal contact area.
N
Nominal contact area A nom
True contact
area A true
The true contact area can be estimated by measuring the surface roughness, and then calculating how the
surfaces deform when brought into contact. At present there is some uncertainty as to how this should be
done – this is arguably the most important unsolved problem in the field. The best estimates we have
today all agree that:
The true area of contact between two rough surfaces is proportional to the normal force pressing them
together.
Atrue
= CN