Ball bearings and friction.

Some time ago I made a double, or chaotic, pendulum for my own satisfaction. My wife showed a video of the thing to a friend of hers, and now I'm instructed to make another one.

I didn't worry myself too much about the bearings first time round- the device ran for about 30 seconds from an initial shove, which was long enough to display chaotic behaviour. But I'd like to make the MKII run longer if I can.

So to my question - how do the sizes of the bearings affect frictional loss? I had a look round and found, to my surprise, that bearing types are characterised by a single scalar  coefficient of friction - about 0.01 for deep groove rollers. If I take as true that bearings behave like that , the frictional loss should scale with the diameter of of the bearing - the frictional torque should be the load times the coefficient of friction times the distance of the race from the centre of the torque? And the energy loss (torque times angular velocity) should be directly proportional to that? If so I guess I should be going for infinitesimally small bearings. Or take up knitting - knit one, purl one must be easier than this!

Robin

Edited By Robin Graham on 02/10/2020 00:37:32

Edited By Robin Graham on 02/10/2020 01:13:37

It sounds like your alternative has to be to just use the lowest friction bearing type. That lead me down the rabbit hole from simple ceramic bearings through magnet bearings to air foil bearings....presumably you can also do something to the shape of the pendulums to reduce their air resistance... which you keep them runnng longer but may reduce 'chaos-icity' (I think that's a new word)..

pgk

.

Two thoughts, which may lead you in different directions, Robin

1. Have a look at the way John Harrison supported a clock arbor in the ‘vee’ between two large diameter wheels
2. Also study the ‘unipivot’ arrangement : both the hypothetical version and practical approximations like this: **LINK**

https://www.genuin-audio.de/en/produkte/point/

Have fun !

MichaelG.

Don't both of those work in one direction using gravity to keep the parts in place? would have thought the arms flailing about on on this pendulum would see it flying off or at the very least not keep bearing contact through the whole 360 deg rotation?

.

Does a ‘chaotic pendulum’ need to ‘flail about’ at levels greater than 1G ?

... I’m not sure.

MichaelG.

.

Edit: ... My suggestions were just  ‘lines of investigation’ for Robin to follow, on the matter of friction in bearings

Edited By Michael Gilligan on 02/10/2020 08:08:11

I would have thought that as the pendulum gets vertical at very slow speeds then gravity will try to push the contacts apart, just think of the direction of the arrows being reversed on your unipivot link

The ‘detailed technical drawing’ at this Harvard page isn’t much help: **LINK**

https://sciencedemonstrations.fas.harvard.edu/presentations/chaotic-pendulum

MichaelG.

.

Very likely, Jason ... but the Unipivot concept can be extended to involve a pair of opposed bearings, acting like the cones on the ‘scape wheel of a traditional Alarm Clock. ... It was really the question of bearing friction that I was trying to discuss.

MichaelG.

.

P.S. ___ Likewise, Harrison’s pair of wheels could be increased to a trio ... it’s his use of ‘leverage’ that interests me.

Edited By Michael Gilligan on 02/10/2020 08:25:12

Avoid bearings altogether by using flexures, i.e. threads, wires, etc?

.

Sounds a very good idea ... but given the unpredictable motion, I suppose there is a risk that they would ‘wind-up’

[ or do you have a devious work-around for that ? ]

MichaelG.

Ah, now I've seen a couple of videos, I understand the problem. I was thinking that only small arcs had to be accommodated - as in a complex-pendulum harmonograph. Clearly flexures aren't appropriate for multiple complete-circle rotations. Not very bright to offer a solution before understanding the problem... [shuffles off stage, head hung low].

But the bright bit was thinking about alternative low-friction bearing configurations

... Even if they are impractical for this particular device, all variants are useful waypoints on Robin’s road to enlightenment.

MichaelG.

Michael, once you start to add a couple of balls to the opposite side you have in effect created a ball race with 4 balls.

If Robin does not want to spend much then unshielded bearings or popping the seals out of 2RS ones then flushing out the heavier lubricant would be best like the stirling engine builders do to get minimal drag

I think the same general rules apply to chaotic pendulums as those for normal clock pendulums in that air and bearing frictional losses determine the system Q. Given the degree of freedom needed ball races are probably the the simplest bearing arrangement. However to reduce the effects of air friction, like the Shortt clock, the pendulum needs to operate in a low air pressure or vacuum environment which has its implications. So why not apply the same method of maintaining oscillation as a pendulum clock by giving the pendulum an occasional impulse. This can be done electro-magnetically, in a similar way to that being devised by SOD for his pendulum clock. For a conventional pendulum clock the impulse is usually provided on a regular basis with a defined amount of energy added to maintain pendulum amplitude and precise timing. However for a chaotic pendulum the impulse energy can be varied to give different levels of excitement to its movement.

Clive

.

Yes, I know that Jason ... I was trying to help Robin with his actual question

”So to my question - how do the sizes of the bearings affect frictional loss? ”

MichaelG.

Edited By Michael Gilligan on 02/10/2020 10:12:36

As we are no longer treating this as an academic problem ... The most practical and cost-effective ‘production engineering’ solution would probably be to base the design on a cheap bought-in bearing assembly

... a ‘Fidget Spinner’

MichaelG.

Would bigger balls, with more stored kinetic energy ( cf big flywheel) extend the run time?

Rod

I think the coefficient of friction will be much the same whatever the size of the bearing (of the same design, materials and tolerances)

What is different is the amount of energy needed to overcome inertia and the amount of metal in contact. A big bearing is sized to manage bigger loads as much as it is to reduce friction. As a percentage of the total energy in the system, the friction of a car wheel bearing is low, but the bearing would be unsuitable in a fine clock because it's far too heavy. Conversely jewelled spindle bearings are far too light for rough work.

The cheap bearings I initially fitted to my Ridder's Coffee Cup Stirling engine were significantly stiffer than expensive ones of the same size. Removing the seals to reduce friction helped, but allowed dirt into the bearing - they soon stiffened up agaoin. On a low-power engine, better bearings are essential. Probably the same applies to Chaotic Pendulum bearings. The smallest good bearing that will do the job.

Taking a cheap bearing apart didn't reveal obvious defects, so I think the difference is due to better tolerances all round in the 3x more expensive version. I bet Ketan knows!

Dave

That's what steel shielded bearings are for. The steel shields do not quite touch the inner race so there is not the friction of the rubber sealed types where the rubber rubs on the inner race and causes friction. The tiny gap on the steel shielded bearings keeps most of the muck out without creating friction.

Commonly used on drill presses and bench grinders to cater for low-torque on start-up while protecting the bearings as much as possible. I once made the mistake of fitting all new bearings to a drill press spindle, pulley shaft and motor with rubber seals both sides all round. Thing would not start unless the chuck was spun by hand. Doh!

And yes, cheap bearings are a bit like cheap machine tools. They simply are not made to the same standards as the expensive stuff. Well worth paying the little bit extra for SKF, FAG, Timken, Koyo or Naachi etc if you want something that works well.

Edited By Hopper on 02/10/2020 12:32:23

Thanks for replies.I'm not sure if my question has been answered though, probably because I didn't frame it clearly enough. My bad. After further thought I'm pretty sure that all other things being equal a large diameter bearing will dissipate more energy through friction than a smaller one. That's assuming that bearings can be characterised by a single (velocity independent) coefficient of friction, as with sliding surfaces - which surprised me at first, but I think I now understand.

MichaelG - thanks for the links. It may take me a while to get my head around that stuff . The Unipivot designers claim that their arrangement is 'extremely damped' which may not be what I want.

This is a rough sketch of what I'm proposing:

Yeah, I'm no good at technical drawing, it's just an aide-mémoire . The whole thing pivots about the central disc, and the secondary pendulum about the disc on the right arm. Something I have found when making prototypes is that the bearings need to be 'tight' in the sense of keeping all the moving parts coplanar. Any wobble and parasitic vibrations set in which sap the energy surprisingly quickly. I guess there is a trade-off between that and friction. I imagine people making Stirling engines must face the same sort of challenge.

Robin.

Edited By Robin Graham on 03/10/2020 02:07:02

Edited By Robin Graham on 03/10/2020 02:16:06