Page 95 - Tribology in Machine Design

Elements of contact mechanics 81

of temperature. Assuming the same frictional energy dissipation, at low
sliding speeds, the surface temperature is unchanged by the presence of the
film. At high sliding speeds, the layer influence is determined by its thickness
relative to the depth of heat penetration, JC P, where

2 l
a T = thermal diffusivity of the solid, (m s ) and t = w/F = time of heat
application, (sec).
For practical speeds on materials and surface films, essentially all the
heat penetrates to the substrate and its temperature is almost the same as
without the film. Thus, the thermal effect of the film is to raise the surface
temperature and to lower or leave unchanged the temperature of the
substrate. The substrate temperature will not be increased by the presence
of the film unless the film increases the friction. A more likely mechanism by
which the surface film will influence the surface temperature increase, is
through the influence the film will have on the coefficient of friction, which
results in a change in the amount of energy being dissipated to raise the
surface temperature. The case of a thin elastohydrodynamic lubricant film
is more complicated because it is both a low thermal conductivity film and
may be thick enough to have substantial temperature gradients. It is
possible to treat this problem by assuming that the frictional energy
dissipation occurs at the midplane of the film, and the energy division
between the two solids depends on their thermal properties and the film
thickness. This results in the two surfaces having different temperatures as
long as they are separated by a film. As the film thickness approaches zero
the two surface temperatures approach each other and are equal when the
separation no longer exists.
For the same kinematics, materials and frictional energy dissipation, the
presence of the film will lower the surface temperatures, but cause the film
middle region to have a temperature higher than the unseparated surface
temperatures. The case of a thin elastohydrodynamic film can be modelled
using the notion of a slip plane. Assuming that in the central region of the
film there is only one slip plane, y = h l (see Fig. 3.5), the heat generated in
this plane will be dissipated through the film to the substrates.
Because the thickness of the film is much less than the width of the
contact, it can therefore, be assumed that the temperature gradient along
the x-axis is small in comparison with that along the y-axis. It is further
assumed that the heat is dissipated in the y direction only. Friction-
generated heat per unit area of the slip plane is

where T S is the shear stress in the film and Vis the relative sliding velocity. If
all the friction work is converted into heat, then

Figure 3.5