Page 290 - Tribology in Machine Design

Lubrication and efficiency of involute gears 275

might be expected to alter the situation drastically, but it does not, simply
because the oil film assumes the form of an extremely thin film of almost
constant thickness.
In view of all these qualifying remarks, it is hardly to be expected that we
could design gear teeth.on the basis that the maximum shear stress is equal
to 0.3/? max and has to equate to the shear strength of the material in fatigue.
Nevertheless, the Hertz analysis is of vital qualitative value in indicating the
parameter P/R, which, for any given material, can be taken as a criterion of
the maximum stress, the actual value to be allowed being determined
experimentally.
lgure
' In order to proceed, we have to determine the minimum value of R when
only a single pair of teeth is in contact, as shown in Fig. 8.1. It is known that
for involute teeth the radius of curvature is the length of the generating
tangent, so, with reference to Fig. 8.1, we can write for contact at X

R will have a minimum value at either E or F, depending on which is nearer
the adjoining base circle. In this case the critical point is E, and R can be
calculated. If the permissible surface stress factor determined experiment-
ally is denoted by S c, then

and the permissible tangential load at the pitch circle on a unit width of the
tooth will be

Again, as in the case of bending stresses the need, for the individual designer,
to work out each particular case is obviated by the provision of a factor Z
which corresponds to (Rcos</>) for the meshing teeth of module 1, and a
speed factor X c accounting for impact and dynamic loads. In fact, tables
containing Z and X c, given in many books on gears, are based on a slightly
0 8
more empirical approach, which suggests that (R) ' gives better agreement
1
with practice than (R) °. The final simple form of the critical factor S c for
surface wear is

0 8
where K is not directly proportional to (1/m) but to (1/m) ' , where m
denotes module. Values of S c for commonly used gear materials can be
found in books on gears.

8.3. Lubrication There are three clearly distinguishable regimes of operation for gears with
regimes regard to lubrication. They may be described and defined as follows:
(i) Boundary lubrication. This regime of lubrication is characterized by a
velocity so low that virtually no elastohydrodynamic lubricating film