T-120
In order to obtain the amount of backlash
desired, it is necessary to decrease tooth
thickness. See Figure 14-1. This decrease
must almost always be greater than the
desired backlash because of 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 10 at the end of
the technical section.
14.1 Definition Of Backlash
Backlash is defined in Figure
14-2(a) 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:
j = sstd – sact = D s
(14-1)
Figure 14-1
Backlash (j ) Between
Two Gears
Angular Backlash of
j
Gear
= jq1 = –––
R
j
Pinion = jq2 = –––
r
Linear Backlash = j = ss – s2
j
R
Fig. 14-2(a)
Geometrical Definition of
Angular Backlash
jq2
jq1
r
R
Base Circle
Base
Circle
Pinion
Gear
s1
s2
ss
O1
O2
