high mechanical ratios

[darryl]

I've been thinking about friction drives lately. One of the methods of providing such a drive is through a planetary set, where a ring race has some planetary balls orbiting in it, and a central shaft acts to turn the balls by friction. The ball carrier is the output shaft. The setup is identical to a planetary gearset in operation, except that instead of gear teeth, there are only smooth surfaces under contact pressure. I did some measuring with steel balls and found that by having three balls in the race, the smallest central shaft that could be used would be about 1/6 the diameter of any one ball. The overall maximum ratio for such a setup seems to be about 13 to 1. If two balls were used instead, that ratio would become very much higher, as the center shaft could then be made very much smaller and still have contact with the balls to transmit torque. Someone with better math skils would be able to compute the theoretical maximum ratio obtainable with the three ball planetary drive, and that would be interesting to know. Hopefully, to more than just me.
As far as the two ball planetary setup, theoretically, if there's any diameter to the central shaft at all, there will be some drive, such that the smaller the shaft, the higher is the drive ratio. Of course, at some small diameter, the shaft will not have enough strength to hold together and the device will fail. I don't know of any math that can predict the limit to this.


In any event, I'm going to propose a project: fabricate a working model friction drive designed to give the highest possible ratio between input and output shafts. This would be a single stage only, such as one planetary set, or one shaft driving a disc through rim drive- whatever method is chosen, three rules apply: the device must be a single stage, it must work and be able to show the turns of the input and the output shafts, and it must be friction drive. This last rule eliminates gears, cogs and toothed belts, but not ordinary belts. I can see someone wanting to make a worm gear with 300 teeth per millimeter driving a 6 ft diameter disc with 2 million teeth, but that doesn't qualify for this project, though it could be another challenge in itself.
You may use steel balls, string, rollers, rubber, razor blades, pins, whatever- you may use bearings, bushings, jewels, magnets- anything your design needs for support for it's parts, as long as it meets the three criteria. If you can use fluid in some way- as long as the drive is through touching surfaces.
I think it's reasonable to suggest a size limit to any one component part, to make this fair and practical. If for instance your design calls for a disc, it can be no larger than say 1 foot in diameter. Same for any shaft, no longer than 1 foot. A belt, wire, or loop of any material can be any length useable in your particular design.
The aim of this project is to demonstrate the highest input to output ratio possible in a single stage friction drive. The amount of torque transferred is not important, but it must work. If you come up with a design that has more than say, a 500 to 1 ratio, you may use a small motor to turn the input shaft, as long as the number of turns can be counted somehow. Similarly, if the output shaft can be clocked at say, quarter turn increments, then you could demonstrate the device without having to crank the input several hundred or thousand times to show the ratio you've achieved. Cranking it until the output has turned a quarter turn will be fair enough to demonstrate the ratio.
Somebody might want to use the two ball idea, while others might want to use the finest diameter guitar string as a shaft driving the rim of a 1 ft disc- whatever method you can come up with as long as it obeys the rules.

It might be that your skill as a machinist enables you to achieve a higher ratio than anyone else, or it may be your brighter idea that does that. It could be your knowledge of metallurgy enables you to demonstrate a superior device.

Anybody interested?

[bikepete]

Sorry, not much tempted to build one (needs a PRIZE - even if it's only a wall-mountable Round Tuit :-), but seems to me that a friction version of a harmonic drive might be a good way to go: e.g.

http://www.berton.com.sg/bapl/hds/mechanism.shtml

[This message has been edited by bikepete (edited 07-26-2005).]

[This message has been edited by bikepete (edited 07-26-2005).]

[andy_b]

darryl,

i'm confused by your description. wouldn't the gear ratio of the drive be determined by the diameter of the BALLS and not the input shaft? the balls are running on the surface of the input/drive shaft. the speed of the surface of this shaft will determine the speed of the surface of the balls. the speed of the ring being driven by the balls will be determined by the diameter (i guess more appropriately the radius) of the balls. if you had a large "gear reduction" ring drive, i guess someone could say you have big balls.

andy b.

[J Tiers]

You might look through a book on "computing mechanisms". There are a number of drives for that purpose, wheel and disc type, with input shaft speed and disc position as inputs, resolvers with balls as intermediary elements, etc, etc. I have an old Radiation Laboratory book on them. Lots of interesting drives.

Computing devices need a large ratio, in general, to allow the largest range of input and outputs without "mechanical clipping" of the "signal". Good source, therefore.

Old drill presses often had disc and wheel drives. Depending on relative sizes, you could go from higher through same to lower speed of disc vs input wheel. Ultimate ratio is the difference in disc vs wheel diameter.

Seems mo particular reason it couldn't be as high as 25 or 30 or even more.

The three planet drive is as you say, limited by interference. But it is balanced and stable, even with no support of pinion shaft.
With two balls or planet gears, it is not stable, they want to "squirt out", and the shafts must be held rigidly.

[lenord]

Funny the topic of friction drives should come up. I've been making the rods and disks for a friction drive for a telescope. All aluminum, 4.250 to 4.50" OD disks driving .500" shafts. All the disks have to be press fit to the shafts, PITA. I'll only do this again with hubs on the disks.

This is a 5 stage friction gearbox though. The guy wants no PE and a high gear ratio in 2 gearboxes for a telescope. He plans on hooking each box up to a stepper motor.

FWIW
Lenord

[Wirecutter]

Have you seen this old thread?

http://bbs.homeshopmachinist.net//Forum1/HTML/012578.html

Sounds like the transmission I was asking about is just what you described. Am I missing something here?

-M


[This message has been edited by Wirecutter (edited 07-27-2005).]

[Paul Alciatore]

The ratio of a sun and planet system is given by one of these two formulae:

For stationary planetary rollers or gears:

R = Do/Ds

For stationary outer race:

R = Do/Ds + 1

Where Do is the diameter (or tooth count for a gear) of the outer race and Ds is the diameter (or tooth count for a gear) of the sun wheel/gear. The diameter of the planet gears/wheels is related by the following formula:

Dp = 1/2(Do - Ds)

Where Dp is the diameter of the planet gears/wheels.

In either case, the ratio is only limited by physical and engineering restraints. With three or more planets, the physical fit comes into play. Since the diameter of the outer race is related to the diameter of the sun and planets by a slight rearrangement of the above formula (Do = Ds + 2*Dp), the limits on the size of the planet gears will limit the outer race size and hence the ratio.

With three balls or cylinders, the biggest planets that will fit on a unit size sun are 6.464" in diameter. So the outer race will be 2 * 6.464 + 1 = 13.928. The ratios for such a system will be 13.928 for stationary planets and 14.928 for stationary outer race. That's the limit for more than two planets your 13 figure is close to that. That is the limit and it is a limit that you can not actually ever reach as the planets would be rubbing. So in practice, the ratio must always be just a bit smaller. It appears that the engineering problems (strength of materials, getting sufficient friction, etc.) are easily overcome in a three or more planet system.

When you go to a two planet system the geometric limit disappears as you can place two planets of any size, even infinite size, on opposite sides of any size sun. So the theoretical limit is infinity. But now engineering problems come into play. The sun must be large enough to resist the forces acting on it.

With two planets, the forces on the sun are balanced (at least to a first approximation). So you can apply as much pressure as you like (within limits) to gain additional friction. Frictional forces in the practical relm are directly proportional to the normal (perpendicular) force between the surfaces. But any real material will have limits. Soft steel will crush at fairly low pressures. Hardened tool steel will hold up longer but will also have it's limits.

How fast can you spin a 0.1" shaft? A 0.01" one? Sooner or later, as you reduce the shaft size, you will reach a point where even very slight differences in the forces from the two planets will start pushing it sideways and it will bend or break. Balance may become the main factor. Any imbalance at tens of thousands of RPMs or higher can be fatal to both the mechanism and the operator. And any friction in the sun will be amplified by that ratio. Friction in the planets by a lesser amount, perhaps the square root of the ratio or some such number. It is not just math, it is the practical balanceing of all the factors. 20, 30, even 50 to 1 are certainly possible. Higher ratios are likely and the exact limit may never be known as it is always possible to improve a system.

Paul A.

[Ryobiguy]

Check this out, the Torofluxus:

http://www.grand-illusions.com/torofluxus.htm

It hit me that this could almost (but not quite) be adapted into the basis of a potential solution to Darryl's high ratio single stage friction drive challenge.

Neat to watch, maybe there's some principle that could be borrowed for a unique friction drive... Think display model, not anything practical.

[darryl]

Thanks for the responses. Paul, your math goes further than mine did, and confirms my rough calculations. Some other ideas/questions are interesting as well. How fast can you spin a .1 diameter shaft, how fast a .01 diameter, etc. I can see another math solution using the strength of material, the rpm, and the diameter- we would just assume that suitable bearings are able to allow the shaft to speed until it flies apart from rotational stresses. Sometimes I wonder just how many rpm a steel ball is doing inside a high speed ball bearing- must be way up there. I know, I need to get a life.
Wirecutter, your mentioning the ball riding down two rods is interesting. If we imagine that the ball has two very small indents in it at opposite sides- if an axle were to be in place it would go through these indents- this is the balls rotational axis. As it rolls down the two diverging rods, the point of contact between the ball and the rods gets closer to this axis, and at some point it goes right to it. This is where the ball falls through.

Before this happens, the ball has to speed up on it's axis in order to travel down the rods at an even speed. Turn those rods into loops, vary the spacing of the loops, and there's the basis of a cvt. In fact, there's the basis for a variable inertial transmission, using the weight of the balls spinning as well as travelling around the loops as the storage medium. Probably some homework to be done on this concept, but it could be viable given the right application.

Still relying on friction though to transfer torque, and it seems part of the problem with this is that if more than just a point of contact is made between parts, then some scrubbing is going to go on, which is what polishes the parts (read that as wear) and wastes some energy.
The cvt friction drives I've looked at all have this problem, to a greater or lesser degree, and it makes the old belt in variable sheaves system look pretty good still.

Anyway, back to the 'challenge'. One really simple idea is to taper an input shaft to a point, then touch this point to a rim on the output shaft. Theoretically, if that point is zero atoms wide, then it will not turn the rim at all, but in real life the point will have some diameter. This should mean that it will turn the rim, and the diameter of the point can be calculated on the basis of the step-down ratio observed, and the diameter of the rim.