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Gear Module

What is the module of a gear ?

In general, the size of a gear tooth is expressed as its module.
The sizes of gear teeth using the module system are indicated with the symbol m followed by numerals such as m1, m2, and m4 where the teeth sizes get larger as the numerical value increases.

two different module
Figure 1 - The comparison of teeth sizes between Module 1.5 (left) and module 4 (right)

In order for the gears to mesh, the space between the gear teeth of each gear, in other words the pitch (p) must be equal.
The pitch of a gear indicates the size of the gear tooth, but because the pitch contains the circular constant π (3.1415…), it is not a convenient number.
Therefore, by dividing the pitch by π, π can be eliminated. The remaining value is named the module and represents the tooth size.
(The unit of module is mm.)

The relationship is shown as the following formula.

m = p / π

meshed gears with same module
Figure 2 - Two gears of module 2
They mesh together correctly because their modules are equal.

By the way, the pitch circle diameter of a spur gear (d) can be obtained by multiplying the module (m) and the number of teeth (z).
Expressed as a formula, it is d = m x z.

In the ISO system, the unit to indicate the size of gear tooth is specified as module. In reality, there are others such as CP (circular pitch) which expresses pitch in integer and DP (diametral pitch) which is mainly used in the US, etc.

The chart shown in Table 1 compares the equivalent values of module (m), circular pitch (CP) and diametral pitch (DP).

Module
m
Pitch
CP
Diametral Pitch
DP
0.39688 1.24682 64
0.5 1.57080 50.8
0.52917 1.66243 48
0.6 1.88496 42.33333
0.79375 2.49364 32
0.79577 2.5 31.91858
0.8 2.51327 31.75
1 3.14159 25.4
1.05833 3.32485 24
1.25 3.92699 20.32
1.27000 3.98982 20
1.5 4.71239 16.93333
1.59155 5 15.95929
1.58750 4.98728 16
2 6.28319 12.70
2.11667 6.64970 12
2.5 7.85398 10.16
2.54000 7.97965 10
3 9.42478 8.46667
3.17500 9.97456 8
3.18310 10 7.97965
4 12.56637 6.35
4.23333 13.29941 6
4.77465 15 5.31976
5 15.70796 5.08
5.08000 15.95929 5
6 18.84956 4.23333
6.35000 19.94911 4
6.36620 20 3.98982
8 25.13274 3.175
8.46667 26.59882 3
10 31.41593 2.54

Table 1 - Comparison of various pitch measurements

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