T-40
In the meshing of profile shifted gears, it is the operating pitch circles that are in
contact and roll on each other that portrays gear action. The standard pitch circles no
longer are of significance; and the operating pressure angle is what matters.
A standard spur gear is, according to Table 4-4, a profile shifted gear with 0 coefficient
of shift; that is, x1 = x2 = 0.
Table 4-4 The Calculation of Positive Shifted Gear (1)
Table 4-5 is the inverse formula of items from 4 to 8 of Table 4-4.
Table 4-5 The Calculation of Positive Shifted Gear (2)
h
da
df
x1 + x2
2 tana (––––––) + inv a
z1 + z2
Find from Involute Function Table
z1 + z2 cosa
–––––– (––––– – 1)
2 cosaw
z1 + z2
(––––– + y)m
2
zm
d cosa
db
–––––
cosaw
(1 + y — x2)m
(1 + y — x1)m
[2.25 + y – (x1 + x2)]m
d
+ 2ha
da – 2h
m
a
z1, z2
x1, x2
inv aw
aw
y
ax
Module
Pressure Angle
Number of Teeth
Coefficient of Profile Shift
Involute Function aw
Working Pressure Angle
Center Distance Increment Factor
Center Distance
Item
Symbol
Formula
No.
Example
Pinion Gear
5
6
7
8
11
9
1
2
3
4
13
14
15
10
12
Pitch Diameter
Base Diameter
Working Pitch Diameter
Addendum
Whole Depth
Outside Diameter
Root Diameter
ha1
ha2
d
db
dw
3
20°
12 24
0.6 0.36
0.034316
26.0886°
0.83329
56.4999
36.000 72.000
33.8289 67.6579
37.667 75.333
4.420 3.700
6.370
44.840 79.400
32.100 66.660
Item
Symbol
Formula
No.
Example
ax
y
aw
x1 + x2
x1 , x2
1
2
3
4
5
Center Distance
Center Distance Increment Factor
Working Pressure Angle
Sum of Coefficient of Profile Shift
Coefficient of Profile Shift
ax z1 + z2
––– – –––––––
m 2
(z1 + z2)cosa
cos–1[–––––––––––– ]
2y + z1 + z2
(z1 + z2 ) (invaw – inv a)
–––––––––––––––––––
2 tana
56.4999
0.8333
26.0886°
0.9600
0.6000 0.3600
