Planet gear efficiency. Need help

[anticz]

I'm having a bit of difficulty figuring out the theoretical efficiency of a compound epicyclic gear train. The math involved is a bit over my head. This train is meant to run at very slow speed under light load. I want to find the theoretical efficiency of the design so I can determine if it is feasible to build. Here are the details.

(A) sun gear = 17 teeth
(B) Planet gear = 51 teeth
(C) Ring gear = 119 teeth
(D) Planet gear = 52 teeth
(E) Ring gear = 120 teeth
.25 module (metric)
input torque = 5 to 10 [N*mm]

Input is Ring (E) rotating counter-clockwise once every 6 hours
Output is Sun (A) rotating clockwise once every 30 seconds
720:1 total reduction

Ring (E) meshes with Planet (D) which is compounded to planet (B). Planet (B) meshes with ring (C) [locked] giving a -90:1 reduction on the arm (Arm spins clockwise). Compound planets spin 2.333333:1 relative to carrier. Planet (B) meshes with Sun (A) giving an 8:1 ratio for a total ratio of 720:1.

I'm guessing this is going to be very inefficient do to the high reduction but, I have no Idea how to find out how much energy is being lost or how to figure out how much torque is actually needed to run this. I've found several methods for calculating efficiency of an epicyclic train but I'm completely lost on the math. I'd describe myself as more of an amateur inventor than a mechanical engineer. Any help would be greatly appreciated.

 

[anticz]

BTW,

I just need a bit of help understanding the order to go about this and what parameters I need to solve for. I understand how to find the efficiency of a simple epicyclic but this is over my head right now.

 

[MikeHalloran]

Assume a tiny bit of torque at A, e.g. the miniscule torque required to rotate a shaft within a seal, and you'll need 720 X that to drive it at E, ignoring all losses.

Put an escapement at A, and a constant torque, e.g. a plumb bob with its string wrapped on a pulley at E, and you've got a clock.

Speaking of rotation rate, you've stated the speeds of input and output as if both are driven by some other means at known rates... and both are stated at very unusual rotation rates. So the first obvious question is, where/what is the prime mover for this mechanism? Second obvious question, where/what is the load?





Mike Halloran
Pembroke Pines, FL, USA

 

[tbuelna]

anticz,

With that 17T sun gear, you'll probably need to tweak your addendum, pitch diameters, and use tip mods to get good efficiency and smooth meshing. You also probably want to design your planetary meshes for what is called "recess action", in order to minimize sliding losses.

Good luck.
Terry

 

[anticz]

Mike,
As you said, it should be obvious what is driving this and what the load is. Just re-read your own post.

Terry,
Thanks for the tips. I have a profile shift on the sun and mating wheels to get rid of the interference but I'm not sure I understand what you mean by tip mods and designing the planets for recess action. The 51 tooth planet is driving the sun but being driven by the 119 tooth ring. If I change the tip on this planet for better recess action on the sun wouldn't this cause more approach action at the ring?

 

[FeX32]

anticz-
That's not what Mike means by "what is the load". What are you driving?
Have you thought of the torque to get the gear train moving? (ie. the inertial torque on initial transient start-up)



Fe

 

[MikeHalloran]

I regret that I've lost track of my friend Wayne, who spent WW2 rebuilding supercharger gearboxes, high ratio planetary speed increasers. I don't think they had the extreme ratio you're trying to make, but they were plenty tricky.

Maybe rebuilding is not the right word. According to Wayne, when they blew up, which was often, there was very little left worth salvaging; he was making replacements from scrounged used parts, repaired parts, and the few new parts he could get.

He said he had to select planet gears to build sets with matching (by 'tenths') tooth thickness so they might share the load as the designers intended.

I get the impression that Detroit has made some progress in that area, not by making gears any better, but by engineering limited but controlled flexibility into the planet carriers, so that imperfectly matched imperfect planet gears can share the load by differential precession. Or, I could be wrong; it happens a lot.

My point here is that making real epicyclic geartrains is much more difficult than textbooks make it appear. You might be better off just buying a gearbox from, e.g. Sumitomo.



Mike Halloran
Pembroke Pines, FL, USA

 

[anticz]

Thanks Mike,

I'm not at all concerned that this will explode. The loads are so light I don't think there's much chance of that happening. My main concern is efficiency. I only need about .2 millinewtons of force out at the Sun. I could easily do this with a simple inline compound train but I have a special requirement that necessitates an epicyclic train. Buying an existing gearbox isn't an option as this all has to fit inside a volume 4cm in diameter and 1cm in height.

Any one know where I might find information on asymmetric gear teeth?

 

[MikeHalloran]

( Eight days to get a load and an envelope is unfortunately not a record here. )

Since the load is very light, and the rotation speed is very low, balance and load sharing are unimportant, so just forget about them... by eliminating all but one planet gear in each set.

That means that the sun gears do see a radial load, but it's computable, and not dependent on tolerances or stiffnesses in parallel load paths. I.e., it becomes a regular compound gear train, just wrapped in a circle... sort of.



Mike Halloran
Pembroke Pines, FL, USA

 

[anticz]

Thanks again Mike,
I appreciate you kindness and time. Sorry it took so long. I've been reading furiously to figure this out on my own and I appreciate your (and everyone else here) advice.