Page 36 - Tribology in Machine Design

Basic principles of tribology 23

A simple model of chemical wear can be used to estimate the amount of
material loss

where k is the velocity factor of oxidation, d is the diameter of asperity
contact, p is the thickness of the reaction layer (Fig. 2.10), £ is the critical
thickness of the reaction layer and H is the hardness.
The model, given by eqn (2.18), is based on the assumption that surface
layers formed by a chemical reaction initiated by the friction process are
removed from the contact zone when they attain certain critical thicknesses.

2.9. Sliding contact The problem of relating friction to surface topography in most cases
between surface reduces to the determination of the real area of contact and studying the
asperities mechanism of mating micro-contacts. The relationship of the frictional
force to the normal load and the contact area is a classical problem in
tribology. The adhesion theory of friction explains friction in terms of the
formation of adhesive junctions by interacting asperities and their sub-
sequent shearing. This argument leads to the conclusion that the friction
coefficient, given by the ratio of the shear strength of the interface to the
normal pressure, is a constant of an approximate value of 0.17 in the case of
metals. This is because, for perfect adhesion, the mean pressure is
approximately equal to the hardness and the shear strength is usually taken
as 1/6 of the hardness. This value is rather low compared with those
observed in practical situations. The controlling factor of this apparent
discrepancy seems to be the type or class of an adhesive junction formed by
the contacting surface asperities. Any attempt to estimate the normal and
frictional forces, carried by a pair of rough surfaces in sliding contact, is
primarily dependent on the behaviour of the individual junctions. Knowing
the statistical properties of a rough surface and the failure mechanism
operating at any junction, an estimate of the forces in question may be
made.
The case of sliding asperity contact is a rather different one. The practical
way of approaching the required solution is to consider the contact to be of
a quasi-static nature. In the case of exceptionally smooth surfaces the
deformation of contacting asperities may be purely elastic, but for most
engineering surfaces the contacts are plastically deformed. Depending on
whether there is some adhesion in the contact or not, it is possible to
introduce the concept of two further types of junctions, namely, welded
junctions and non-welded junctions. These two types of junctions can be
defined in terms of a stress ratio, P, which is given by the ratio of, s, the shear
strength of the junction to, k, the shear strength of the weaker material in
contact