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76
between the mating surfaces. This mean coefficient of friction is a
function of the acting tooth forces, gear material, contact surface
condition, and the velocity of relative motion of these surfaces in the
different phases of engagement. The last factor is also a function of
geometry of the gearing.
Although analytical expressions have been developed for
determination of tooth mesh loss, the relationships involved are rather
complex and not always reliable. They appear to be best suited for
comparative evaluation of different gear-tooth forms rather than for
calculation of absolute values of gear
losses. Available experimental
data offer a more reliable source of information on tooth mesh power
losses in gears than do the theoretical expressions. The following
conclusions can be made:
1. Tooth mesh losses in internal gears are somewhat less than those
in external gears.
2. Pitch-line velocity has small influence on gear efficiency.
3. With the exception of light load conditions, it may be assumed
that the ratio, ∆, of tooth mesh loss to input power does not depend
upon this power.
4. The difference in losses for several standard tooth forms in
common use is so small that the same values of efficiency may be
assumed for various tooth forms.
5. Losses from oil churning are independent of the load transmitted,
but depend upon gear velocities, gear-drive design, and viscosity of
lubricants. It seems that these losses can be neglected for gear
trains which transmit relatively large power, but must be taken into
account in the total efficiency of high-velocity, low-power gear
systems.
6. For practical purposes, the loss in a pair of spur gears may be
assumed to be proportional to the product of the pitch-line velocity
and the tangential force acting at the pitch circle of the driving
gear.
Merritt
2
has developed a chart, Fig. 1, which gives the value of ∆
for external and internal gear pairs as a function of the speed ratio of the
two gears. In this chart, the abscissas represent the ratios between the
numbers of teeth on pairs of gears; the numerator of the ratio is always
the number of teeth on the smaller gear. Range of chart values includes
pinions varying in size from 10 to 90 teeth. Plots are based on the
sliding friction between a pair of spur gears of British Standard form
having 20-degree pressure angle and full depth. A mean coefficient of
friction equal to 0.08 is assumed. Fig. 1 may be used for a first
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