Page 90 - Tribology in Machine Design

Elements of contact mechanics 77

The time for the point on the surface to move through half the contact
width, vv/2, is

and therefore the Peclet number, eqn (3.9e), can be written as

Hence the Peclet number (or dimensionless speed parameter) can be
interpreted as the ratio of the time required for the friction heat to penetrate
the surface a distance equal to half the contact width, divided by the time in
which a point on the surface travels the same distance.
Equations (3.9a) to (3.9d) assume that both surfaces are moving and that
the Peclet number of each surface is at least 5 to 10. The analysis prediction
accuracy will increase as the Peclet number increases beyond these values.
The flash temperature, T f , is the maximum temperature rise on the surface
in the contact region above the bulk temperature. For the assumption
underlying the theory and given above, the maximum temperature will be
located at about
X«0.825w,
where X is measured from the contact edge at which the material enters the
contact region.
The analysis presented above can be illustrated by the following
numerical example. Consider two steel (1 per cent chrome) cylinders each
100 mm diameter and 30 mm long rotating at different speeds such that the
l
l
surface velocities at the conjunction are V ^ — 3.0 m s~ and V 2 = 1.0 m s~ .
5
6
The contact load is 10 N or 3.33 x 10 N/m and the bulk temperature of
each roller is 100 °C.
The thermal properties of the material (see Table 3.3 or ESDU-84041 for
a more comprehensive list of data) are

therefore

2
11
The Young modulus E 1 -2.068 x 10 N/m and v^O.30, thus