# planetary gear - number of teeth

I created the following planetary gear in FreeCAD.

I calculated number of teeth using formula R = 2*P+S. In my case R = 75 P = 5 (there are 3 of them) S = 45.

Also all gear have the same pitch of 2.5 mm. However picture has huge gap. I can not figure out what could be wrong. Here is link to FreeCAD file link

• what is the actual problem? ... what is your question? Nov 5, 2021 at 1:37

The following image explains where the formula $$R=2P+S$$ comes from.

Figure: Planetary gear with 4 planets (https://woodgears.ca/gear/planetary.html)

Although it has 4 planets the spacing will be the same with 2 or more planets. (Three is used for optimal balance and redundancy).

Essentially, the diameter of the Ring $$d_R$$ should be equal to the Diameter of the sun $$d_S$$ plus 2 diameters of the planets $$d_p$$. I.e. :

$$d_R = 2d_P+ d_S \tag{eq:1}$$

However for gears, the diameter of a gear ($$d$$) and the number of teeth ($$z$$) are proportional.

• in the metric system usually the module m is used, $$d= m\cdot z$$
• in the US system usually the Diametral Pitch (P) is used, $$d= \frac{z}{P}$$

In both cases, the equation 1 becomes:

$$z_R = 2z_P + z_S$$

So for $$z_R=75$$ and $$z_S=5$$, the correct number for the teeth of sun is $$z_S = 75-2*5=65$$

You are almost there. Except you need to use $$2p=10. \\ not\ \ 2*3*p=30$$

You use the number of the gears of one of the middle planetary gears no matter how many are there.

As you can see adding more P gears would not change the ratio, it probably reduces the stress on the gears.

Then you would have

• R=75
• S= 65
• P= 5