Page 98 - Tribology in Machine Design

84 Tribology in machine design

stationary heat source case. Therefore

where Q 2 is the rate of frictional heat supplied to body 2 and k 2 is the
thermal conductivity of body 2.
The speed criterion used for the analysis is the dimensionless parameter,
L, called the Peclet number, given by eqn (3.9e). For L<0.1, eqn (3.22)
applies to the moving surface. For larger values of L (L>5) the surface
temperature of the moving surface is

where x is the distance from the leading edge of the contact. The average
temperature over the circular contact in this case then becomes

The above expression can be simplified if we define:

Then, for L<0.1, eqns (3.21) and (3.22) become

and for high speed moving surfaces, (L>5), eqn (3.24) becomes

and for the transformation region (0.1 ^L^5)

where it has been shown that the factor ft is a function of L ranging from
about 0.85 at L=0.1 to about 0.35 at L = 5. Equations (3.25-3.27) can be
plotted as shown in Fig. 3.8.
To apply the results to a practical problem the proportion of frictional
heat supplied to each body must be taken into account. A convenient
procedure is to first assume that all the frictional heat available (Q =fWV}
is transferred to body 1 and calculate its mean temperature rise (T ml ) using
NI and L!. Then do the same for body 2. The true temperature rise T m
(which must be the same for both contacting surfaces), taking into account
the division of heat between bodies 1 and 2, is given by

To obtain the mean contact surface temperature, T c, the bulk temperature,
Figure 3.8 T b, must be added to the temperature rise, T m.