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# Two output Epicyclic Gear Train Calculations

## Two output Epicyclic Gear Train Calculations

(OP)
Hello All,

I've been tasked to develop a generalized model for calculating speeds/torques etc. of a new series of epicyclic gear trains we are developing. This is new territory for the company I am with so there is not any tribal knowledge for me to go on here.

I have a pretty good grasp in calculating everything when I have two inputs (which is typical, as I believe for calculating an epicyclic, and for most modes of operation for the line we are developing). One mode, however, has only one input and two outputs. Input torque into the spider, and I am trying to figure out how to calculate speeds for the sun AND the ring gear.

When I setup my table I am left (as expected) with 3 equations and 4 unknowns. I am guessing my best bet is to do a conservation of power? I have been unable to find anything similar in text books or online, with the exception of a brief schematic in a dissertation of how a Toyota Prius drive train works, but the dissertation did not delve into that portion.

Does anyone have any experience in this type of analysis that can point me in the right direction?

Thank you!

### RE: Two output Epicyclic Gear Train Calculations

It's a differential.

When you drive the spider, the sun and the ring both rotate at the same speed.

Unlike a bevel-gear diff, the torque split is not necessarily equal.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Two output Epicyclic Gear Train Calculations

(OP)
Thank you, Mike! That sea to jive with what I've been finding. Do you know how to determine analytically or how to design it to be a particular split? That's where I was thinking conservation of power but I'm just not certain how to go about designing or calculating what percentage goes in which direction.

Thank you again!

Ryan

### RE: Two output Epicyclic Gear Train Calculations

I think you can figure the torque split by considering each gear as a lever, and doing a free body diagram of the geartrain, using pitch radii or number of teeth.

Expanding a bit...
You know the radius to the center of the planets, so you can resolve an arbitrary input torque to a force at that radius.
If the planet is not rotating on the spider pin, that force must be applied equally to the pitch radius of the sun gear, and to the pitch radius of the ring gear, from each of which, knowing the radius, you can derive a torque.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Two output Epicyclic Gear Train Calculations

(OP)
Thanks all for the help! This link is also very helpful for this type of device if ever you find yourself in a similar situation. It appears this is technically called a "Power Split Device". Very interesting read!

http://prius.ecrostech.com/original/Understanding/...

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