Precision pendulum techniques

[SillyOldDufferModerator @sillyoldduffer]

Posted by S K on 30/03/2023 15:07:21:

… Is there more to the spring being a spring than providing a pivot?

Yes. Bearings waste energy because of friction, plain bearings being particularly bad at stop/starting. Knife edges are low friction, but the pressure on the edge is very high and they tend to cut into the support and/or go blunt. Thread and chain hung pendulums avoid friction and wear but are liable to wander because there's nothing to keep the swing straight; a disturbed bob will fly in ellipses. There are good reasons for avoiding all of the above.

On the other hand, springs are the simplest, cheapest way of getting a robust low-friction support and they keep the swing straight. Low friction because there are no sliding parts plus they're a low-loss way of storing and returning energy to the bob. Hard to better springs for suspending a reciprocating pendulum swinging a few degrees, and they're easy.

Dave

[Michael GilliganParticipant @michaelgilligan61133]

Posted by S K on 30/03/2023 15:07:21:

[…]

I think I'll just use it as-is. At least it should be robust, as I had wished when I initially laid it out. I'll make a better-thought-out Version 2 if I get that far.

[…]

.

A alternative approach is to locally ‘thin’ the spring

Wrap it round a suitably sized cylinder and take a few strokes with a stone, or a diamond hone [keeping the hone horizontal]

Turn it over and repeat.

Yes, obviously they are unlikely to be identical profiles … but with care and a good ‘eye’ they should be pretty close.

MichaelG.

[S KParticipant @sk20060]

Posted by SillyOldDuffer on 30/03/2023 15:38:43:

…. plus they're a low-loss way of storing and returning energy to the bob.

Dave

A spring can do that, but the "storing and returning energy" part is supposed to be done by exchanging potential and kinetic energy through the force of gravity.

It seems to me that this aspect of a spring is at best a distraction and at worst an influence that corrupts the natural behavior of a pendulum. So, shouldn't this particular quality of a spring be minimized, e.g. via a spring that is as thin, narrow and short as practical given it's other jobs (to support the pendulum, minimize twisting, etc.)?

Edit: Now I'm thinking of starting over. 🤔

 

Edited By S K on 31/03/2023 17:37:45

[duncan webster 1Participant @duncanwebster1]

The spring absorbs energy because of hysteresis, and so thin is good. It also prevents the pendulum swinging out of plane, so 2 narrow springs widely spaced is good. It will have a very small effect on period, but as that is constant I don't think it matters. You can after all have a mass on spring oscillator, otherwise known as a balance wheel.

[SillyOldDufferModerator @sillyoldduffer]

Posted by S K on 31/03/2023 17:35:10:

Posted by SillyOldDuffer on 30/03/2023 15:38:43:

…. plus they're a low-loss way of storing and returning energy to the bob.

Dave

A spring can do that, but the "storing and returning energy" part is supposed to be done by exchanging potential and kinetic energy through the force of gravity.

It seems to me that this aspect of a spring is at best a distraction and at worst an influence that corrupts the natural behavior of a pendulum. …

Whilst I don't disagree, I take a less purist view. Looking at the pendulum as an oscillator, all I require is that it store and return energy by one means or another, and that all energy losses be minimised, whatever the cause. I'm after high Q rather than exchanging potential and kinetic energy through the force of gravity. If part of the potential energy is provided by elasticity, I don't care, especially as springs are maybe the most efficient way of storing energy available. (But only in tiny quantities.)

Might even build a clock with a spring powered balance wheel where gravity isn't used at all and call it a chronometer!

But it's not that I expect a suspension spring to power the clock, it's that the spring doesn't lose energy whilst doing it's job.

Unless one of the real experts knows better, I think the spring need only be strong enough to support the weight without exceeding it's elastic limit. If the elastic limit is exceeded it ceases to be a spring and work will be done on the metal, dropping the Q, and perhaps the bob too!

A stiff spring would be bad too, because the return action would be too violent or the rod might bend before the suspension, altering the period and requiring different maths. Even that doesn't worry me much: I've made a pendulum where the entire rod was used as a spring, I called it a 'sprod'. The rod was 1mm diameter carbon fibre – worked fairly well, but Q was low, it was humidity sensitive, and the bob was prone to swing in ellipses. Trying a steel-spring-rod is on my to do list. I still think it could be made to work well.

The natural behaviour of pendulums is already corrupt: they aren't isochronous and behave badly as timekeepers if swung more than a few degrees! As far as I know springs are less disturbing to the existing faults than most alternatives, and I don't recall any negative aspects of spring suspensions requiring the attention of designers. Could be wrong – anyone else know?

Dave

[S KParticipant @sk20060]

Posted by duncan webster on 31/03/2023 18:28:07:

The spring absorbs energy because of hysteresis, and so thin is good.

Some springs with designed-in hysteresis have been used in things like old-school keyboards to provide a tactile sensation by buckling under load. But a spring exhibiting any noticeable hysteresis (i.e., one that doesn't obey Hooke's law) would be very poor for a pendulum application.

My gut and my limited experience tells me that knife edges are about as good as it gets – and superior to springs – for pendulums, at least when their finicky nature isn't an obstacle. That's rare, though. For example, I live in earthquake country, and I'd never propose using knife edges as a long-term solution, as sooner or later it would be jostled out of position.

I fully expect my spring-mounted pendulum to have lower Q than my knife-edge version, all else being equal.

 

Edited By S K on 31/03/2023 22:26:11

[duncan webster 1Participant @duncanwebster1]

All springs display hysteresis. I'm not talking about overcentre type things, just flexing within the elastic range. It's very small, but real. Cycling quickly within the elastic range will cause a spring to get warm. Google elastic hysteresis.

[S KParticipant @sk20060]

Well, yes, I'm sure all materials will exhibit some elastic hysteresis, but it would be very hard to measure any in a nice thin strip of well-tempered spring steel or beryllium copper, etc., and when flexed only slightly.

My query was whether the "spring" in a spring is actually beneficial at all to a pendulum, or whether it's a detriment that's only used because it's functional and convenient in other ways. I think the latter.

Anyway, the adverse effects of a spring are likely minimal compared to air friction (like maybe 1% of air friction), and the ancillary benefits (support and some anti-twist) are useful. Alternatives such as silk threads or knives have their own problems that are typically worse. But you still want a spring that presents as little interference with the motion of the pendulum as possible, including by being thin, narrow (including when split in two) and short.

[Martin KyteParticipant @martinkyte99762]

Posted by S K on 01/04/2023 02:13:03:

Well, yes, I'm sure all materials will exhibit some elastic hysteresis, but it would be very hard to measure any in a nice thin strip of well-tempered spring steel or beryllium copper, etc., and when flexed only slightly.

My query was whether the "spring" in a spring is actually beneficial at all to a pendulum, or whether it's a detriment that's only used because it's functional and convenient in other ways. I think the latter.

Anyway, the adverse effects of a spring are likely minimal compared to air friction (like maybe 1% of air friction), and the ancillary benefits (support and some anti-twist) are useful. Alternatives such as silk threads or knives have their own problems that are typically worse. But you still want a spring that presents as little interference with the motion of the pendulum as possible, including by being thin, narrow (including when split in two) and short.

It depends if you are trying to minimise the spring effect or use it to balance out other causes of period error.

Youngs modulus decreases with temperature so the restoring force of the suspension will also decrease with temperature. Shaped cheeks have been employed (notably by John Harrison) to create an additional control factor by shortening the effective length with increasing angular displacement and so balancing environmental changes with modified circular error.

Best if you realise and quantify at least in order of magnitude all the factors that effect the motion of the pendulum.

[SillyOldDufferModerator @sillyoldduffer]

Posted by S K on 01/04/2023 02:13:03:

…

Anyway, the adverse effects of a spring are likely minimal compared to air friction (like maybe 1% of air friction), and the ancillary benefits (support and some anti-twist) are useful. Alternatives such as silk threads or knives have their own problems that are typically worse. But you still want a spring that presents as little interference with the motion of the pendulum as possible, including by being thin, narrow (including when split in two) and short.

Agreed except perhaps the 'narrow' bit. I think of it this way: the bob of a perfect pendulum should always travel in a straight line. Real pendulums rarely do, instead describing an ellipse, shallower the better. Many reasons for deviations: air currents, earth tremors, building movement, impulse twisting or twanging the rod, unbalanced bob, brownian motion, vibration due to humans, molecular changes in the metal work (notably Invar), stress relief after temperature changes, frame not stiff enough, and probably many others, mostly small.

Some are easier to fix than others. Air currents in the room are a major risk, but easily avoided by encasing the pendulum. However, this causes new air-currents inside the case due to the bob stirring air in a confined space: these can be eliminated by evacuating the case so the bob swings in a vacuum. The vacuum also eliminates inconsistency due to buoyancy changing with barometric pressure.

A broad rather than narrow spring suspension is a fix because it tends to resist the bob and rod twisting sideways. If something deviates the bob, the spring will store energy from the torque and return it in the opposite sense to straighten the rod. Thus the minimum energy path (straight) is positively encourages by the spring, broader the better within reason. There's advantage in slotting a broad spring because the removed central slice adds weight and doesn't help keep the spring straight much.

Is it a fix or a problem? An issue with springs occurs when the impulse is misaligned with the bob. Then the impulse can torque-oscillate the spring resulting in the bob flying in the ellipse we're so keen to avoid! May not matter to other than perfectionists though, because the induced ellipse likely to be in phase with the period. The error is corrected by tweaking the rate in the normal way, and the pendulum owner probably won't notice (or need to care) that a small part of his rate error is caused by off-centre pulsing.

Deviation effects are much more obvious in my lightweight experimental pendulum clock than big ones. An advantage of building big, heavy and rigid in the time-honoured way is that such errors become proportionally less troublesome.

What fascinates me about precision pendulum clocks is the huge range of interacting design choices available. There isn't a simple black-and-white answer. Instead there are thousands of compromises to explore, where we find that the result can always be improved.

Pendulum development largely stopped a century ago because quartz-electronics provided better accuracy for less money and opened the door to even better methods. However, that change of course left amateurs with the highly tantalising prospect of being able to make the best pendulum clock ever. Difficult but not unrealistic, and packed with surprising interest.

Dave

[duncan webster 1Participant @duncanwebster1]

The springiness of the suspension will change the period, I think it will reduce it. However I don't think it matters as long as it's constant. The effect will be very small. As Martin points out, the Young's modulus will reduce with temperature, but over the range we are talking about that will be a very small change, and as the spring is metal, it will get longer with temperature and so slow down the pendulum, but as the spring is very short this again will be very small. A potential downside is that the top of the pendulum is less rigid in the plane of swing, but if the impulse is applied at the right point, there is little or no force at the top.

Quartz crystals are effectively a mass on a spring, and they keep very good time, similarly balance wheels in chronometers. I think the mass on spring system is independant of amplitude, and so isochronous (as long as the spring is linear)

[John HaineParticipant @johnhaine32865]

The best things to read about suspension springs are Philip Woodward and Kenneth James. PW wrote some articles in HSN that also reference James, HSN 1998 No. 5 and 2001 No. 4. A chap called Alan Emmerson has looked at solving the exact equations for a compound pendulum on a spring suspension, it is a horrendous problem and the answer is of little practical interest. As far as I can make out one of the main conclusions is that there is an additional pendulum mode where it rotates around a transverse axis at a frequency determined by the moment of inertia and the spring rate and dimensions.

Watch and chronometer balance wheels have carefully designed "terminal curves" to make them isochronous. Philip Woodward also looked at the theory of this and wrote a 6 part article in HJ.

Compared to springs, pendulums are easy!

[Tony JeffreeParticipant @tonyjeffree56510]

I remember Dick Stephen doing some measurements on suspension springs Vs small ball races for pendulum suspension and concluding that there wasn't much to choose between them – the frictional losses in the ball race were comparable to the hysteresis loss in a spring. I don't know whether he published any results – he was certainly writing on & off for HJ and ME at the time.

[SillyOldDufferModerator @sillyoldduffer]

I found this paper on elastic hysteresis in steel, dated 1912. The effect is small:

The difference of length to be measured is not more than one hundredth of the total variation of strain, and on apiece 4 inches long amounts to but 1/50000 inch, so that the measurement is a very delicate one, an error of one-millionth of an inch in absolute length being equivalent to 5 per cent, in the result. The test piece was loaded to 10 tons per square inch and oscillated at 120Hz – much faster than clock pendula.

I doubt it matters. Any evidence hysteresis effects time-keeping? Sure it will cause the spring to lose a little energy, but nothing is 100% efficient. I think it's a molecular effect, see list below.

Be useful to create a scaled list of things that cause pendulums to misbehave.

My guess for my geologically stable quiet part of the world, most serious first, unfortunately without numbers:

• Non-rigid frame and loose connections absorbing energy
• Unstable pendulum rod: one that bends, twists, stretches, sensitive to wet, decomposes etc
• Impulse faults
• Excessive amplitude
• Draughts
• Suspension faults – misalignment, high friction, asymmetry, too many degrees of freedom etc
• Uncompensated Temperature changes
• Aerodynamic effects inside the case – turbulence, drag
• Uncompensated Barometric changes
• Man-made Vibration
• Seismic effects
• Molecular effects
• Atomic effects

Any comments?

Dave

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 01/04/2023 18:45:07:

[…]

Any comments?

Dave

.

Three disruptive comments, from a sedentary position:

1. your list looks like a good start … it could take a lifetime to quantify and rank the entries
2. please excuse the pedantry, but I think we need to note the distinction between effect and affect
3. possibly irrelevant, or possibly fundamental: Time is not what it was … so are we chasing the recorded performance of the best existing pendulum clocks, or the Caesium second ?

MichaelG.

[S KParticipant @sk20060]

By "narrow," I meant the net width of the spring material, not the spacing between springs in a two-spring configuration. So, using two of the thinnest, shortest and narrowest springs (spaced apart appropriately) that can hold the weight and not permanently deform under abuse, etc., are likely to be best.

It's clear that a lot of clock-making black magic is in trying to balance one unavoidable adverse effect against another opposing adverse effect. But I'm not patient enough to fuss with all that. I just want to do a respectable job based on good materials and straight-forward techniques, maybe with a touch of artistic flair, and hopefully get decent results.

[S KParticipant @sk20060]

• Relativistic space-time effects. There is no such thing as "time" as a stand-alone feature of the universe. There is only unified space-time. My "time" and yours are necessarily different, and it doesn't even make complete sense to speak of time as a discrete thing. So what does your pendulum even measure, really? 😛🙃

[SillyOldDufferModerator @sillyoldduffer]

Posted by Michael Gilligan on 01/04/2023 19:21:21:

Posted by SillyOldDuffer on 01/04/2023 18:45:07:

[…]

Any comments?

Dave

.

Three disruptive comments, from a sedentary position:

1. your list looks like a good start … it could take a lifetime to quantify and rank the entries
2. please excuse the pedantry, but I think we need to note the distinction between effect and affect
3. possibly irrelevant, or possibly fundamental: Time is not what it was … so are we chasing the recorded performance of the best existing pendulum clocks, or the Caesium second ?

MichaelG.

Apologies for affect and effect; I hit those rocks every time. Can't do nine sevens, or righty tighty / leftie loosie either.

I'm chasing the recorded performance of the best existing pendulum clocks, and what ever I build has to depend on a pendulum too.

As to SK and the nature of time, it's remarkable time is measured so incredibly accurately even though no-one understands what it is!

Dave

[duncan webster 1Participant @duncanwebster1]

Well my time varies at random, but keeps exactly in step with my pendulum. That's my truth and I'm sticking to it (as a certain prince of the realm said)😂

Edited By duncan webster on 01/04/2023 22:52:25

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 01/04/2023 22:36:42:

[…]

As to SK and the nature of time, it's remarkable time is measured so incredibly accurately even though no-one understands what it is!

.

Ah – but, they can only measure ‘time’ so accurately because they have defined it [as being the thing they can measure accurately] … very convenient.

MichaelG.

[Martin KyteParticipant @martinkyte99762]

Ah the old nature of reality question. Who knows what anything is ‘really’. All we have is what our senses and sensors tell us. Back to Plato and the cave. We get a little further with instrumentation in as far as building spectrometers allows us to agree what we mean by Yellow for example but still we cannot be sure that what I ‘see’ as yellow is the same as what you see. Past and Future are emergent from conscienceness but the equations don’t differentiate and can run both ways. All we can do is trust our instruments and leave the rest to the philosophers cos it ain’t physics.
regards Martin

Edited By Martin Kyte on 02/04/2023 09:31:38

Edited By Martin Kyte on 02/04/2023 09:32:43

[John HaineParticipant @johnhaine32865]

Somewhere I read that the very latest atomic clocks can detect the difference in time running at head height compared to foot height due to gravitational time dilation. Whether your feet or your head gets older first I can't recall!

[david bennett 8Participant @davidbennett8]

Posted by S K on 14/03/2023 18:31:50:

Except for sheer convenience, I'd avoid USB power supplies, including battery-based ones, as they are all "switching" supplies (for cost and efficiency reasons). These are very noisy.

You want a nice, quiet linear supply with good regulation, like a decent laboratory bench supply, but those are somewhere around the $300-500+ U.S. mark.

A suitable battery followed by a common "LM"-type regulator would be quiet too, though long-term regulation would be an issue as the battery runs down, temperature changes, etc.   – – —

Isn't this what you would effectively have if a battery was connected via a d.c to usb cable, relying on the arduino voltage regulator for control?

dave8

 

Edited By david bennett 8 on 06/04/2023 20:36:22

[SillyOldDufferModerator @sillyoldduffer]

Posted by david bennett 8 on 06/04/2023 20:26:19:

Posted by S K on 14/03/2023 18:31:50:

…

You want a nice, quiet linear supply with good regulation, like a decent laboratory bench supply, but those are somewhere around the $300-500+ U.S. mark.

A suitable battery followed by a common "LM"-type regulator would be quiet too, though long-term regulation would be an issue as the battery runs down, temperature changes, etc. – – —

Isn't this what you would effectively have if a battery was connected via a d.c to usb cable, relying on the arduino voltage regulator for control?

dave8

Not quite, but I believe it's close enough for my purposes.

All power supplies are noisy, some worse than others. Even the best mains powered supplies are vulnerable to muck arriving over the line – switching transients, solar activity, distant lightning strikes, radio signals, mush generated by appliances. Many sources: motors with faulty suppressors, unfiltered VFDs, and – very common – switch-mode power supplies.

The latter are wonderfully power efficient, but difficult to suppress properly. Too cheap models just dump spikes on both input and output. Better made units are much cleaner, but still electrically noisy. For most applications noise below a certain level doesn't matter, but for others it does.

Audiophiles claim to be able to hear switched mode noise on their amplifiers, discuss! More to the point, noise spikes on the power supply can upset communications systems, computers, and sensors. It's possible that electrical noise on the supply to a beam-break IR sender and IR receiver could cause slightly early or late detects. So with a 1 second pendulum a poorly decoupled sensor might report 1.0000, 1.0000, 1.0003, 1.0000, 0.9999, 1.0000, 0.9997 In the example, the mean is 1.0000s, with ±0.3mS noise, but spikes could bias away from the mean, hence it's good to problematic noise.

Actually, in my set-up, which has a noisy pendulum, ie the period varies, I don't have any evidence, yet, that power supply noise is the cause. Power is from a reasonably clean wall-wart USB PSU via an Arduino's regulator, and the sensor electronics are decoupled. No obvious difference running the pendulum with a linear power supply (which I have available).

In the event switched mode power was confirmed to be causing period noise, the obvious first step is a linear power supply. In the unlikely event the sensor was so sensitive that a linear supply upset it, batteries are as low noise as power gets. A battery is on the cards already – not to clean up the power supply, but trickle charged to keep the clock going during power cuts.

The most likely cause of my clock's noisy period is its faulty suspension and whippy rod. They have to be fixed before I look for anything else.

Dave

[BazyleParticipant @bazyle]

If you are that worried about psu noise you would have to make sure you were using the battery voltage direct, ie not through a regulator. And if using a trickle charger not have it on permanently but eg 7 hours on, 7 hours off so that you can compare any anomalies for coincident with the charger, and not use a sub multiple of 24hrs to progressively move through day/night variations, and use a prime number of time units.

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