T-35
Table 4-2 The Calculation of Teeth Number
Note that the numbers of teeth probably will not be integer values by calculation with
the formulas in Table 4-2. Then it is incumbent upon the designer to choose a set of
integer numbers of teeth that are as close as possible to the theoretical values. This will
likely result in both slightly changed gear ratio and center distance. Should the center
distance be inviolable, it will then be necessary to resort to profile shifting. This will be
discussed later in this section.
4.2 The Generating Of A Spur Gear
Involute gears can be readily generated by rack type cutters. The hob is in effect a rack cutter.
Gear generation is also accomplished with gear type cutters using a shaper or planer machine.
Figure 4-2 illustrates how an involute gear tooth profile is generated. It shows how the pitch
line of a rack cutter rolling on a pitch circle generates a spur gear.
Fig. 4-2 The Generating of a Standard Spur Gear
(a = 20°, z = 10, x = 0)
No.
Item
Symbol
Formula
Example
1
2
3
4
5
Module
Center Distance
Speed Ratio
Sum of No. of Teeth
Number of Teeth
m
a
i
z1 + z2
z1 , z2
3
54.000
0.8
36
16 20
2a
–––––
m
i(z1 + z2) (z1 + z2)
––––––––––– –––––––
i + 1 i + 1
Rack Form Tool
a
O
db
d
d
–– sin2a
2
I
