Friction and wear - Orthopaedic Biomaterials in Research and Practice - page 258

Friction

Coefficients of
friction

If two bodies are placed in contact under a normal force W , both chemi-
cal and mechanical interactions may occur. This produces a net attraction
between the surfaces. If we now try to slide one surface over the other, we
find that there is an initial force, F i , needed to start motion, and then to main-
tain a constant velocity, a smaller steady-state force, F s , is required.
Both of these forces are related to the interfacial load:

F i = μ S ∙ W

F s = μ D ∙ W

where μ S and μ D are called the static and dynamic coefficients of friction.
It is usual for μ D < μ S ; thus, it is easier to maintain motion in the presence
of friction than to initiate it.

PROBLEM 11.1
Find the values of μ S and μ D from Figure 11.1.

ANSWER:
The force perpendicular to the interface is the gravitational force acting
on 5 kg of mass, which equals 9.8 × 5 or 49 N. Thus, μ S = 15/49 or 0.31,
whereas μ D = 10/49 or 0.20.
Thorough investigations of frictional phenomena have resulted in the
recognition of more or less two universal rules:

1. The frictional coefficients depend on load , W , rather than upon
stress ; that is, they are independent of the area of the interface (this
statement is sometimes referred to as the “law of friction”).

2. Over broad ranges of interfacial loads, the coefficients of friction
are linear; that is, they are independent of W .

Origin of frictional
forces

Frictional forces depend on both the roughness of the opposed surfaces
and their chemical composition. Of these two effects, the role of rough-
ness is the easier to understand. Surfaces show a wide range of rough-
nesses, defined as the average height of local elevations or “asperities”

F i = µ S W F S = µ D W

F i F S

M = 5 kg

1 cm = 5 N

FIGUre 11.1 Production of frictional resultant force.