Page 304 - Tribology in Machine Design

Lubrication and efficiency of involute gears 289

order of only 1 per cent or less of the power transmitted at full load. To this,
the losses due to oil churning and bearing friction have to be added. In such
gears, there is inevitably, sliding at all points in the path of contact, except at
the pitch point, and it can be deduced that the coefficient of friction is low
and that lubrication must therefore be effective in spite of the extremely
high contact pressures.
In the case of skew, and more particularly worm, gearing, sliding occurs
not only as in spur gears but, much more importantly, in a direction at right
angles to this. In fact, we can obtain a sufficiently close approximation to
the situation in a worm gear by ignoring the pressure angle of the thread
and thinking of this thread as perpendicular to the axis. We can then regard
the thread as an inclined plane which moves relatively to the surface of the
worm wheel; and the analogous situation of a block being pushed up an
inclined plane by a horizontal force is quite common in mechanics. Thus,
the expression for efficiency can be written as

where a is the inclination of the plane, or in this case the pitch angle of the
worm, and (j> is the angle of friction. For the case of the worm-wheel driving
the worm the expression for efficiency is

Now, in the case of a single-tooth worm, a may be only a few degrees, and if
the surfaces are dry or poorly lubricated ^ may well exceed a; in this case rj
will be less than 0.5 and r\' will be negative. In other words, the drive will be
irreversible. Such a gear has its uses, but would be unthinkable for power
transmission. For multi-start worm gears, however, a can be made of the
order of 45°, and if the gears are well lubricated, 0, under running conditions,
particularly at high speeds, may well be of the order of 1° or less. The
efficiency is then of the order 0.97-0.98, i.e. of the same order as that for spur
gears. As far as power loss is concerned, the difference is probably negligible
but it should be noted that the losses have to be dissipated as heat, and since
the amount of heat which has to be expended is almost directly propor-
tional to the effective coefficient of friction, it is vital to ensure that the best
possible lubrication is maintained, and in the case of highly loaded gears
that sufficient cooling is provided.

8.8.1. Analysis of friction losses
In Fig. 8.7, one gear rotating clockwise drives another. Subscript 1 is used
on the symbols for the driver and the subscript 2 is used on those for the
driven gear. All the parameters used in the following analysis are clearly
defined in Fig. 8.7. Using the assumption that when two or more pairs of
teeth carry the load simultaneously, the normal pressure is shared equally