the errors in manufacturing and assembling. Since
the amount of the decrease in tooth thickness depends upon the accuracy of machining, the
allowance for a specified backlash will vary according to the manufacturing conditions.
It is customary to make half of the allowance for backlash
on the tooth thickness of each gear of a pair, although there are exceptions. For example,
on pinions having very low numbers of teeth, it is desirable to provide all of the
allowance on the mating gear so as not to weaken the pinion teeth.
In spur
and helical gearing, backlash allowance is usually obtained by sinking the hob deeper into
the blank than the theoretically standard depth. Further, it is true that any increase or
decrease in center distance of two gears in any mesh will cause an increase or decrease in
backlash. Thus, this is an alternate way of designing backlash into the system.
In the following we give the fundamental
equations for the determination of backlash in a single gear mesh. For the determination
of backlash in gear trains, it is necessary to sum the backlash of each mated gear pair.
However, to obtain the total backlash for a series of meshes it is necessary to take into
account the gear ratio of each mesh relative to a chosen reference shaft in the gear
train. For details see Reference 5.
Backlash is defined in
Figure 1.20a as the excess thickness of tooth space over the thickness of the mating
tooth. There are two basic ways in which backlash arises: Tooth thickness is below the
zero-backlash value; and the operating center distance is greater than the zero-backlash
value.
If the tooth thickness of
either or both mating gears is less than the zero-backlash value, the amount of backlash
introduced in the mesh is simply this numerical difference:
B = Tstd - Tact = DT
(20)
where:
B = linear backlash measured
along the pitch circle (Figure 1.20b)
Tstd = no backlash tooth thickness on the operating-pitch circle, which is the
standard teeth
thickness for ideal
gears
Tact = actual tooth thickness