Page 48 - Tribology in Machine Design

Basic principles of tribology 35

the load-bearing surfaces, then the probability of forming an adhesive wear
particle is reduced. Figure 2.13 is an idealized representation of two
opposing surface asperities and their adsorbed species coming into contact.
At slow rate of approach the adsorbed molecules will have ample time to
desorb, thus permitting direct metal-metal contact (case (b) in Fig. 2.13). At
high rates of approach the time will be insufficient for desorption and
metal-metal contact will be prevented (case (c) in Fig. 2.13).
In physical terms, the fractional film defect, /?, can be defined as a ratio of
the number of sites on the friction surface unoccupied by lubricant
molecules to the total number of sites on the friction surface, i.e.

Figure 2.13
where A m is the metal metal area of contact and A r is the real area of
contact. The relationship between the fractional film defect and the ratio of
the time for the asperity to travel a distance equivalent to the diameter of the
adsorbed molecule, f z , and the average time that a molecule remains at a
given surface site, r r, has the form

Values of Z - the diameter of a molecule in an adsorbed state - are not
generally available, but some rough estimate of Z can be given using the
following expression:

Taking the Avogadro number as N a=6.02 x 10 23

where V m is the molecular volume of the lubricant. It is clear that /?->1.0 if
f, M r. Also, j8-»0 iff, <^f r . The average time, r r, spent by one molecule in the
same site, is given by the following expression:

where £ c is the heat of adsorption of the lubricant, R is the gas constant and
T s is the absolute temperature at the contact zone. Here, f 0 can be
considered to a first approximation as the period of vibration of the
adsorbed molecule. Again, f 0 can be estimated using the following formula:

where M is the molecular weight of the lubricant and T m is its melting point.
Values of T m are readily available for pure compounds but for mixtures
such as commercial oils they simply do not exist. In such cases, a