Differential planetary gearing 2

[Capstan]

I am in the process of developing a light duty winch with very high reduction (around 250:1) in the lighest and most compact fashion. I have been looking at some cheap electrical winches that are usiong a so-called Differential planetary gearbox in which:
1) The planet carrier is located halfway between two ring gears, one is fixed on the input side, the other one is driving the load but has fewer teeth than the fixed one, allowing it to turn slowly.
2) The input is the sun gear.

Does anyone know how to calculate the ratios in such a gearbox?

Thanks!

 

[williedawg]

Here's some info that may be what you're looking for....

http://en.wikipedia.org/wiki/Epicyclic_gearing

Note this paragraph under Compund planets;

> During World War II, a special variation of epicyclic gearing was developed for portable radar gear, where a very high reduction ratio in a small package was needed. This had two outer annular gears, each half the thickness of the other gears. One of these two annular gears was held fixed and had one tooth fewer than did the other. Therefore, several turns of the "sun" gear made the "planet" gears complete a single revolution, which in turn made the rotating annular gear rotate by a single tooth. <

The article continues with formulae for different gear arrangements

 

[Capstan]

Thanks Williedawg for pointing me in the right direction.

The calculation works like this:
Ring gear (fixed) : 63T
Ring gear output: 66T
Sun gear: 6T
Planet gear: 29T
So the formula is (1+R/S) * (R(fixed)/(R(fixed)-R(output))
In this case: 1+(63/6) * 66/3
The ratio is 253:1

I have a couple other questions however:

Does anyone have any experience with calculating the life expectancey of such systems?

Also, is there any reason why it would not work if the annulus with fewer teeth was fixed? That would make our design simpler with the standard components available.

Thank you!

 

[tbuelna]

Capstan,

AGMA 6123-B06 will give you all the design guidance you need for your compound-coupled planetary.

carburized makes an excellent point about bearing life vs. gear life (specifically the planet pins).

Section 8 of AGMA 6123-B06 describes the problem of "circulating power" in the particular type of planetary you are considering, and its significant impact on efficiency. Definitely worth reading.

Good luck.
Terry

 

[Capstan]

Thank you very much Terry I have purchased the AGMA 6123-B06 standard and started studying it!
Thanks also to Carburized for your input, i will be contacting you directly via your webite.

 

[Windward]

tbuelna, glad to know that AGMA discusses circulating power. I read about this problem in a very interesting paper by G. White, "Early Epicyclic Reduction Gears", written when he was working for the Western Gear Corporation. The paper is not dated, but it was probably written in the 1960's.

He provides an example of a "differential combination of wheels" that was invented by the Englishman James White in the late 1700's. G. White says that this is the earliest use of "differential" in this sense that he had found. The ratio is 1:99495. Assuming a 1% loss at each mesh, of which there are only four, it would have had an efficiency of 0.25%. That is, 1/4 of one percent, because of the high recirculating power.

Although this is an extreme example, G. White writes elsewhere in the paper, "In this way did the pioneers of power transmission epicyclic gears discover that any advantage in respect of high reduction ratio is invariably accompanied by the drawback of reduced efficiency."

 

[tbuelna]

Windward,

I worked for Western Gear/Lucas Western/Rolls-Royce Geared Systems for a few years back in the early 90's. Being a novice gear designer, it was a great place to work because the company (at that time) had some sharp gear guys, including one Mr. Graham White. Sadly, the company went through a rough period (financially) after I left. I saw Graham about 2 years ago, so he's still around, but I think he is now retired.

I have fond memories of Western Gear. I initially got the job at Western Gear because I had some experience with casting design, and not because I knew anything about gears at the time. But once there, I quickly decided I was going to learn everything I could about gears. Western Gear was a perfect place for it, because I got a paid, 40-hour-per-week education in gear design from world-class experts. As long as I worked hard and paid attention, those guys were happy to teach me everything they knew.

Terry

 

[Windward]

tbuelna,

Just saw your post, glad to have the information about Western Gear and Graham White. His paper saved me a lot of grief.