T-121
where:
j
= linear backlash measured
along the pitch circle
(Figure 14-2(b))
sstd = no backlash tooth
thickness on the operating
pitch circle, which is the
standard tooth thickness
for ideal gears
sact = actual tooth thickness
Fig. 14-2(b) Geometrical Definition of Linear Backlash
When the center distance is increased by a relatively small amount, Da, a backlash
space develops between mating teeth, as in Figure 14-3. The relationship between center
distance increase and linear backlash jn along the line-of-action is:
jn
= 2 D a sina
(14-2)
Figure 14-3 Backlash Caused by Opening of Center Distance
(a)
Gear Teeth in Tight Mesh
No Backlash
(b)
Gear Mesh with Backlash
Due to Da
a
Da
Linear
Backlash Along
Line-of-Action
Backlash, Along Line-of-Action = jn = j cosa
Base
Circle
Base
Circle
r
jq2
jq1
j
jn
R
Line-of-Action
a
