## Planetary Gear Torque Output & Distribution

## Planetary Gear Torque Output & Distribution

(OP)

I am admittedly a rookie when it comes to planetary gear trains, so bear with me. I am unsure how to determine the strength of a given planetary gear train. I don't understand the dynamics of power distribution in them. Determining the strength of a given gear is one thing, but I don't know how they all share the power transmitting duties. Is there a formula or so to determin the strength? Also, this gear train will be operated manually, so it is difficult to base anything on horsepower ratings because of RPM fluctuation. This unit will need to generate around 600 ft. lb. of torque at extremely slow RPM. Any help is much appreciated.

## RE: Planetary Gear Torque Output & Distribution

## RE: Planetary Gear Torque Output & Distribution

## RE: Planetary Gear Torque Output & Distribution

Thread406-59082

## RE: Planetary Gear Torque Output & Distribution

Assuming you have decided upon the basic arrangement, ratio, numbers of teeth, helical or spur etc, the next thing you need to do is to figure out the torques and then the forces.

When figuring the pitting fatigue strength, the multiple meshes need to be taken into account.

Just as in designing any other gearbox, it is frequently possible to get balanced strength on both teeth of a mesh by adjusting the addenda. On the other hand, one might decide to adjust the addenda to give mimimum slide/roll ratios.

One thing to remember is that the planet gears will experience reverse bending, like any idler gear, and will need to be derated because of that.

The degree to which load sharing needs to be considered depends on what steps you have taken, if any, to ensure it.

Some people use a de-rating factor. It depends on the design.

Sometimes, a good way to picture a sun and ring gear planetary when you are figuring out torques, ratios etc is to imagine that you are viewing the train from a reference frame that is rotating at the same speed as the planet carrier. That way, the train appears as a simple non-planetery, and you can figure things out more easily..

For a low speed such as you appear to have, you really shouldn't have to contend with "dynamics" as you put it.

## RE: Planetary Gear Torque Output & Distribution

## RE: Planetary Gear Torque Output & Distribution

Assuming perfect load sharing, if the input torque on the sun gear is Ti and its radius is Ri, then:

The tangiential loads on the three meshing teeth on this gear will be Ti/(3*Ri).

The three planet gears will each see these same tangiential loads on one of their teeth, and the same load on a diametrically opposed tooth, in the same absolute direction.

The planet bearings will each see twice this load in a tangiential direction.

The internal gear will also see tangiential loads on three teeth of Ti/(3*Ri).

If we agree so far - what exactly are you asking beyond that ?

By the way - I would recommend ANSI/AGMA 6123-A88 - Design manual for Epicyclic Gear Drives.

## RE: Planetary Gear Torque Output & Distribution

## RE: Planetary Gear Torque Output & Distribution

## RE: Planetary Gear Torque Output & Distribution

You might want to consider using a 50 percent

long addendum for the sun, 25 percent long for

the idler and a special pitch diameter for the

internal gear to balance the strengths.

If you submit the number of teeth and dp and

pressure angle, I will be glad to offer several

center distance options and still hold the 4:1

ratio for the system. If your center distance

is fixed for the Sun and Annulus, you can drop

one tooth in the idler and still use some

combination on long addendums on the sun and

idler to arrive at the same center distance.

You might also look at shaving the addendum on

the internal annulus to prevent any involute

interference between the idler and the annulus.

Just a few ideas to balance the system.

My email is J.GEISEY@juno.com

## RE: Planetary Gear Torque Output & Distribution

## RE: Planetary Gear Torque Output & Distribution

Out of the loop?! Says who? You have been most helpful to me. I was planning on using 18 teeth for the sun & planet gears, 54 for the ring. This unit is going to see very little action(2 output revolutions per day would be a lot), so wear is not even an issue. Diamond Jim's idea (thanks for the input Jim!) would be great if useage was going to be much higher, but since it's not I want to keep things simple. Getting back to an earlier post of yours, using the formula Ti/(3*Ri), if input torque is 100 ft-lb and the sun & planet gears have a 1-1/2" PD, then each tooth in the 6 mesh points on all gears will experience a tangential force of 44.44? What unit of measure is this answer in? If I seem a little incoherant, it's just one of those days for me where I feel like the proverbial chicken without a head...

## RE: Planetary Gear Torque Output & Distribution

And he got the star ! (You see, I want to get tipster of the week, and put it on my resume so I can find a job !

Actually, kidding aside, Diamondjim's design is no more complicated or expensive to make, once you have designed it - just a little more design work that's all. But you are probably smart to keep it simple in this case.

Now :

If the input torque is 100 lbf.ft, that's 1200 lbf.in.

That means that, if the pitch radius of the input pinion is 3/4", you will have a force of 533.33 lbf at each of three equispaced teeth on the input pinion. On the planets, each will have a force of 533.33 lbf on one tooth, and 533.33 lbf on a diametrically opposed tooth. So each planet gear exerts a force of 2*533.33 lbf on the planet carrier, at a radius of 1.5 ins. Thats a total output torque of 6*533.33*1.5 lbf.in = 4800 lbf.in, which lo and behold is exactly 4 times the input torque as it should be. Hope that helps. By the way, I have no clue at this point whether those forces are reasonable.

## RE: Planetary Gear Torque Output & Distribution

Your last post just earned a star from me because it finally pulled the concept of power distribution into focus for me. Thanks again for your help. I must confess that although I liked Diamond Jim's idea, I was not the person who gave his post a star. Someone else must have done it.

Please don't drop out of the loop. You never know what I'll come up against next. ;o)

## RE: Planetary Gear Torque Output & Distribution