Page 305 - Tribology in Machine Design

290 Tribology in machine design

between them, it can be shown that the total friction loss and the power
input to the driven gear during the engagement of one pair of mating teeth
are the same as when one pair of mating teeth carry the entire load
throughout their period of engagement.
During approach, considering any position of contact as at x (see Fig.
8.7), the normal force W opposes the rotation of the driver, while the
frictional force (fW) assists rotation. The torque exerted by the driver at
any approach position is as follows:

but

thus

Figure 8.7
The work output for the driver during approach is as follows

During recess, the direction of sliding between the teeth is reversed, so that

and the work output for the driver during recess

Now, turning to the driven gear, during approach the normal force and the
frictional force oppose one another. Thus

Expressing

the work output for the driven gear during approach is given by

During recess, both the normal force and the tangential force assist the
rotation of the driven gear, therefore

but