# Number of Teeth for Planetary Gear Train Question

1. Aug 9, 2012

### StephenD420

Hello all:

I have a quick question concerning a variation of a planetary gear train I am working on.
If I want a sun gear and then two planetary gears in between the sun and ring gear (like is shown in the attached picture), how do I find the number of teeth for the ring gear? Would the number of teeth still follow the formula R = 2P + S ?
Or would more gear teeth need to be added, and if so how many?

Example:
If the sun gear has say 94 teeth and the planetary gears have just 4 teeth would the ring gear have 102 teeth? or 104 teeth or some other number of teeth?

Thank you guys so much for the help.
Stephen

#### Attached Files:

• ###### GearPic.jpg
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2. Aug 10, 2012

### Pkruse

I've never seen a ring gear that was not round.

3. Aug 10, 2012

### Pkruse

Any of the gears can have any number of teeth within the physical constraints of your application. I start with the desired gear ratio. Then I decide if I want to fix the ring or the planet carrier. Then I work backwards to see how many teeth I need, making sure that I remain within the stress limits of the material. Then I start looking at lubrication and cooling. Lastly, I check vibrational modes and fatigue. All such designs are iterative, and at any point in this process I may find a reason to stop and start another iteration. Pratt is just now selling their first geared turbofan engine after 15 years of iterations. That was a very difficult gear design and they seem to have finally succeeded after many have failed over the last 4 or 5 decades.

4. Aug 10, 2012

### StephenD420

But I have read that the number of teeth in the ring gear has to equal R = 2P + S where P is the number of teeth in the planet gears and S is the number of teeth of the sun gear. Is this not true?

And yes the gears are circular just my drawing skills in paint leaves much to be desired.

Stephen

5. Aug 10, 2012

### Pkruse

That may be true. I seem to remember something like that from my training many decades ago. It was derived from the basic geometric relations that enable the gears to mesh correctly. But your application is not the common one. You have an extra planet. So I would not use any standard derived formula unless I went thru the derivation again to make sure it applied to this specific case. But then by the time I did that, I could have the design substantially complete. That is what I meant when I said they could have any number within the physical constraints of your application.

I'll go back and check my notes to see what else might apply to your example.

Last edited: Aug 10, 2012
6. Aug 10, 2012

### StephenD420

Using the equations from http://blog.makezine.com/2010/06/28/make-your-own-gears/

I found that using 40 teeth for the sun gear, 18 teeth for the planet gears and 80 teeth for the ring gear gives the following outer diameter values in inches using a diametrical pitch of 8.835729338

sun gear: 4.753427634
planet gears: 2.263536968
ring gear: 9.280501571

so adding 2* outer diameter of P + outer diameter of S gives 9.280501571 which would be the outer diameter of the ring gear, thus adding the outer diameter of the sun gear and the two planet gears gives the outer diameter of the ring gear.
so I believe that this is correct, right?
So it seems you use 2P + S, where here P is the number of teeth of planetary gears and S is the number of teeth of the sun gear, and then add 4 to this to get the number of teeth for the ring gear. Does this sound right?

Thanks for the help.
Stephen

Last edited: Aug 10, 2012