T-41
There are several theories concerning how to distribute the sum of coefficient of
profile shift (x1 + x2) into pinion (x1) and gear (x2) separately. BSS (British) and DIN
(German) standards are the most often used. In the example above, the 12 tooth pinion
was given sufficient correction to prevent undercut, and the residual profile shift was given
to the mating gear.
4.7 Rack And Spur Gear
Table 4-6 presents the method for calculating the mesh of a rack and spur gear.
Figure 4-9a shows the pitch circle of a standard gear and the pitch line of the rack.
One rotation of the spur gear will displace the rack (l) one circumferential length of
the gear's pitch circle, per the formula:
l = pmz
(4-6)
Figure 4-9b shows a profile shifted spur gear, with positive correction xm, meshed
with a rack. The spur gear has a larger pitch radius than standard, by the amount xm.
Also, the pitch line of the rack has shifted outward by the amount xm.
Table 4-6 presents the calculation of a meshed profile shifted spur gear and rack. If
the correction factor x1 is 0, then it is the case of a standard gear meshed with the rack.
The rack displacement, l, is not changed in any way by the profile shifting. Equation (4-6)
remains applicable for any amount of profile shift.
Table 4-6 The Calculation of Dimensions of a Profile Shifted Spur Gear and a Rack
3
20°
Item
Symbol
Formula
No.
1
Module
m
2
Pressure Angle
a
3
Number of Teeth
z
4
Coefficient of Profile Shift
x
5
Height of Pitch Line
H
6
Working Pressure Angle
aw
7
Center Distance
ax
zm
–––– + H + xm
2
zm
8
Pitch Diameter
d
9
Base Diameter
db
10
Working Pitch Diameter
dw
11
Addendum
ha
12
Whole Depth
h
13
Outside Diameter
da
14
Root Diameter
df
d cosa
m(1 + x)
2.25m
d + 2ha
da – 2h
db
––––
cosaw
Example
Spur Gear Rack
––
12
0.6
–– 32.000
20°
51.800
36.000
33.829
––
––
36.000
4.800 3.000
6.750
45.600
32.100
