Page 52 - Tribology in Machine Design

Basic principles of tribology 39

2.11.5. Adhesive wear equation
Theoretically, the volume of adhesive wear should strictly be a function of
the metal-metal contact area, A m, and the sliding distance. This hypothesis
is central to the model of adhesive wear. Thus, it can be written as

where k m is a dimensionless constant specific to the rubbing materials and
independent of any surface contaminants or lubricants.
Expressing the real area of contact, A T, in terms of W and P and taking
into account the concept of fractional surface film defect, /?, eqn (2.83)
becomes

where Wis the load supported by the contacting asperities and P is the flow
pressure of the softer material in contact. Equation (2.84) contains a
parameter k m which characterizes the tendency of the contacting surfaces to
wear by the adhesive process, and a parameter P indicating the ability of the
lubricant to reduce the metal-metal contact area, and which is variable
between zero and one.
Although it has been customary to employ the yield pressure, P, which is
obtained under static loading, the value under sliding will be less because of
the tangential stress. According to the criterion of plastic flow for a two-
dimensional body under combined normal and tangential stresses, yielding
of the friction junction will follow the expression

where P is now the flow pressure under combined stresses, S is the shear
strength, P m is the flow pressure under static load and a may be taken as 3.
An exact theoretical solution for a three-dimensional friction junction is not
known. In these circumstances however, the best approach is to assume the
two-dimensional junction.
From friction theory

where F is the total frictional force. Thus

and eqn (2.84) becomes

Equation (2.87) now has the form of an expression for the adhesive wear of
lubricated contacts which considers the influence of tangential stresses on
the real area of contact. The values of W and ft can be calculated from the
equations presented and discussed earlier.