Page 96 - Tribology in Machine Design

82 Tribology in machine design

The ratio of Q l and Q 2 is

Equation (3.17) gives the relationship between the heat dissipated to the
substrates and the location of the slip plane. Temperatures of the substrates
will increase as a result of heat generated in the slip plane. Thus, the increase
in temperature is given by

where Q(t — £) is the flow of heat during the time (t — £), k { is the thermal
conductivity, c { is the specific heat per unit mass and p- t is the density.

3.7.5. Critical temperature for lubricated contacts

The temperature rise in the contact zone due to frictional heating can be
estimated from the following formula, proposed by Bowden and Tabor

where J is the mechanical equivalent of heat and g is the gravitational
constant. The use of the fractional film defect is the simplest technique for
estimating the characteristic lubricant temperature, T c, without getting
deeply involved in surface chemistry.
The fractional film defect is given by eqn (2.67) and has the following
form

If a closer look is taken at the fractional film defect equation, as affected by
the heat of adsorption of the lubricant, £ c, and the surface contact
temperature, T c, it can be seen that the fractional film defect is a measure of
the probability of two bare asperital areas coming into contact. It would be
far more precise if, for a given heat of adsorption for the lubricant-substrate
combination, we could calculate the critical temperature just before
encountering /?>0.
In physical chemistry, it is the usual practice to use the points, T cl and
T c2, shown in Fig. 3.6, at the inflection point in the curves. However, even a
small probability of bare asperital areas in contact can initiate rather large
regenerative heat effects, thus raising the flash temperature T f . This
substantially increases the desorption rate at the exit from the conjunction
zone so that almost immediately ($ is much larger at the entrance to the
conjunction zone. It is seen from Fig. 3.6 that when T c is increased, for a
given value £ c, /? is also substantially increased. It is proposed therefore,
Figure 3.6 that the critical point on the jS-curve will be where the change in curvature