What is modulus?
Generally speaking, the size of the gear teeth is expressed by the modulus.
When the size of the teeth is expressed by the module, it is generally expressed by symbols and numbers such as m1, m2, and m4.The higher the number, the larger the size of the teeth.
Figure 1 - Size comparison of teeth of module 1.5 (left) and module 4 (right)
In order for the gears to mesh, the spacing, or pitch (p), of the individual gear teeth must be the same.
Although the pitch (p) indicates the size of the teeth, the pitch is calculated from the pi, and it looks complicated as a number.Therefore, the quotient obtained by dividing the pitch of the teeth by the pi is called the modulus, which is used as a way of marking the size of the teeth. (The unit of modulus is mm)
It can be expressed by the formula as follows.
m = p / π
Figure 2 - Two mod 2 gears
The modules are the same and can be meshed normally
In addition, the pitch circle diameter (d) of a spur gear is the product of the module (m) and the number of teeth (z).Formulated as d = mxz.
In the international standard, the size unit of teeth is expressed by modulus, but in fact, there are also CP (circular pitch) that converts the pitch to an integer, and DP (diameter pitch), which is mainly used in the United States.
Table 1 is a comparison of modulus (m), circumferential pitch (CP), and diameter pitch (DP).
| Modulus m |
Weekly Festival CP |
and diameter section 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 |