Page 89 - Tribology in Machine Design

76 Tribology in machine design

If both bodies are of the same material, the maximum flash temperature
can be written in one of the following three forms in commonly available
variables:

In addition to the previously defined variables we have

2
p H = Hertzian (maximum) pressure in the contact, N/m .
The numerical factors, 1.11, 0.62 and 2.45 are valid for a semi-elliptical
(Hertzian) distribution of the frictional heat over the contact width, w. This
would be expected from a Hertzian contact with a constant coefficient of
friction, or an elastohydrodynamic contact for a lubricant with a limiting
shear stress proportional to pressure. Obviously, a consistent set of units
must be chosen to give T { in units of degrees centigrade.
The Blok flash temperature formulas apply only to cases for which the
surface Peclet numbers, L, are sufficiently high. This is generally true for
gear contacts which were the focus of Blok's experiments.
The Peclet number, or dimensionless speed criterion, is defined as

where the variables involved are defined above. An interpretation of the
Peclet number can be given in terms of the heat penetration into the bulk of
the material.
We now consider the instantaneous generation of energy at the surface of
body / at a time zero. At a depth of half the contact width, vv/2, below the
surface, the maximum effect of this heat generation occurs after a time f l 5
where