Page 296 - Tribology in Machine Design

Lubrication and efficiency of involute gears 281

As a first approximation, the value of P e may be assumed to be equal to
the full load on the tooth. When certain conditions are met, that is, spacing
accuracy is perfect and the profile of the tooth is very accurate and modified,
then jP e may be taken to be equal to 60 per cent of P. Equation (8.8) was
formulated with the assumption that the tooth surface roughness is in the
range of 0.5 to 0.7jum.

8.4.2. Minimum film thickness factor
Figure 8.4 illustrates the contact zone conditions on the gear teeth when the
running velocity is low and consequently the thickness of an elastohydro-
dynamic film is not sufficient to completely separate the interacting
surfaces. The idea of the minimum thickness of the lubricant film is based on
the premise that it should be greater than the average surface roughness to
avoid scuffing. Conditions facilitating scuffing are created when the
thickness of the lubricant film is equal to or less than the average surface
roughness. It is customary to denote the ratio of minimum thickness of the
film to surface roughness by

Figure 8.4
where R a = (R l + R 2)/2,R l is the root mean square (r.m.s.) finish of the first
gear of a pair and R 2 is the finish in r.m.s. of a second gear of a pair.
The minimum thickness of the lubricant film created between two teeth
in mesh is calculated using elastohydrodynamic lubrication theory de-
veloped for line contacts (see Chapter 6). Contacting teeth are replaced by
equivalent cylinders (see Chapter 3) and the elastic equation together with
the hydrodynamic equation are solved simultaneously. Nowadays, it is a
rather standard problem which does not present any special difficulties.
For spur or helical gears the following approximate formula can be
recommended

where

54
L t = lubricant factor = (a£')°- ,
a = lubricant pressure-viscosity coefficient,
E'= effective modulus for a steel gear set,

v = the Poisson ratio =0.3 for steel,