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• # Planetary gear calculations, true?

Discussion in 'The main mechanical design forum' started by jawnn, Mar 20, 2018.

1. ### jawnnWell-Known Member

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In regards to the cyclone mid drive kit; I do not understand this at all. So I hope that some one can tell me if it is correct.

I did not write this:

“Okay, first off somewhere I read that the planetary reduction on this kit had a 4.91-to-1 gear down ratio. This did not sound right to me. Picture on the first page of this thread shows a simple single stage planetary reduction unit with an input sun gear will 11-teeth and three planet gears with 22-teeth each. Its difficult to count the ring gears teeth but careful scrutiny of the image and counting gives me a 55-teeth ring gear which mathematically makes sense, because on a simple planetary gearing system without complex two stage planets the following formula is used: (sun gear teeth count) + 2 x (planet gear teeth count) = (ring gear teeth count)

Thus with the input being the sun gear and the output being the planet carrier and the ring gear being fixed the reduction ratio must be 6-to-1
(ring gear teeth count) / (sun gear teeth count) + 1 = (reduction ratio)

I think someone made two mistakes in their math. First they forgot that with a planetary reduction gear box with a sun gear input and planetary carrier output and fixed ring gear you get a full extra rotation of "bonus" reduction due to the over-running orbits the planets make. Accounting for an incorrect 5-to-1 vs. correct 6-to-1 calculation. And then by miscounting the ring gear teeth by one less, AKA counting 54 rather then 55 teeth on the ring gear that would give them an incorrect reduction of 4.909090909090909---> repeating pattern which rounds down to a two decimal (incorrect) result of a 4.91-to-1 reduction ratio”

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3. ### s.weinbergWell-Known MemberEngineeringClicks Expert

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I'd want to see the diagram in question, but when I googled, "cyclone mid drive kit" the links said that the gear ratio is 6:1, as your contact writes. I'm not sure the source for the 4.91:1 ratio, nor do I have access to the information required to tell if it's accurate.

4. ### jawnnWell-Known Member

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well I just wanted to know if the math is corect. if it is then the rest maybe also. Luna cycles has not changed their statement that it is 4.91 to ! ratio....

5. ### s.weinbergWell-Known MemberEngineeringClicks Expert

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Again, I don't know the particulars of the system. The math is correct, assuming it's a single stage planetary gear, the sun gear is the input, the planetary carrier is the output, and the gears are the size described.

If, for example, the sun was the input and the ring gear the output, and the ring gear has 54 teeth (planetary sets often have a gear with a tooth count one off from what you'd expect based on center to center distances), then their ratio would be correct (though the output would spin in the opposite direction of the input, which should be easy to check, I imagine).