Chapter 2 Review of Forces and Moments - Brown University

When we do engineering calculations involving friction forces, we always want to calculate the forces
that will cause the two contacting surfaces to slip. Sometimes (e.g. when we design moving machinery)
we are trying to calculate the forces that are needed to overcome friction and keep the parts moving.
Sometimes (e.g. when we design self-locking joints) we need to check whether the contact can safely
support tangential force without sliding.
2.5.1 Experimental measurement of friction forces
To do both these calculations, we need to know how to determine the critical tangential forces that cause
contacting surfaces to slip. The critical force must be determined experimentally. Leonardo da Vinci was
apparently the first person to do this – his experiments were repeated by Amontons and Coulomb about
100 years later. We now refer to the formulas that predict friction forces as Coulomb’s law or Amonton’s
law (you can choose which you prefer!).
The experiment is conceptually very
simple – it’s illustrated in the figure.
We put two solids in contact, and push
them together with a normal force N. We
then try to slide the two solids relative to
each other by applying a tangential force
T. The forces could be measured by force
transducers or spring scales. A simple
equilibrium calculation shows that, as long
as the weight of the components can be
neglected, the contacting surfaces must be
subject to a normal force N and a tangential force T.
N
contact, area A
T
N
T
N
N
T
T
In an experiment, a normal force would first be applied to the contact, and then the tangential force would
be increased until the two surfaces start to slip. We could measure the critical tangential force as a
function of N, the area of contact A, the materials and lubricants involved, the surface finish, and other
variables such as temperature.
You can buy standard testing equipment for measuring friction
forces – one configuration is virtually identical to the simple
experiment described above – a picture (from http://www.plinttribology.fsnet.co.uk/cat/at2/leaflet/te75r.htm
) is shown below.
This instrument is used to measure friction between polymeric
surfaces.
There are many other techniques for measuring friction. One
common configuration is the `pin on disk’ machine. Two examples
are shown below. The picture on the left is from
www.ist.fhg.de/leistung/gf4/ qualitaet/bildgro4.html , and
shows details of the pin and disk. The picture on the right, from www.ulg.ac.be/tribolog/ test.htm
shows a pin on disk experiment inside an environmental chamber. In this test, a pin is pressed with a
controlled force onto the surface of a rotating disk. The force required to hold the pin stationary is
measured.