JoNo's Pendulum

Excellent!

Though I too would have expected a higher number, the Q-factor is 'about right'. That said, it suggests something can be improved, as does the way Q increases as the pendulum decays.

The Q-factor calculation assumes a particular exponential decay, which may not be achieved in practice. Check the graph's curve to see how close the curve is to theoretical. Could be the Q is higher. (I can't look up the maths now - have to go out.)

I'd start by suspecting the suspension. What could possibly go wrong with a knife pivot? Could be the edge is rounded - not a point or a circle, or it slips sideways at high amplitudes, or is cutting a groove. Might be a 'running in' fault that diminishes as the edge wears into a comfy shape.

Next suspect is the bob shape because air resistance increases with speed. Although the rugby football shape should perform well, maybe it's construction edges or curves cause excessive turbulence. A smoking joss-stick might provide a clue.

Dave

Edited By SillyOldDuffer on 30/08/2023 09:39:46

In case there's any remaining confusion about how to calculate Q with this sort of run-down test, maybe you should state how you calculated it at each interval.

(It's not surprising that Q improves with lower amplitudes due to lower losses from air resistance per swing. Also, knife edges are cool and may be a bit superior to spring hinges, but air friction almost completely dominates Q at normal atmospheric pressure, as seen by the dramatic improvements in Q in a vacuum.)

Your work is an amazing effort!

If only!

Seriously though, I'd expect your pendulum to do better than 12000. The build quality is high, the measurement method seems sound (best amplitude measurement yet), and the graph looks right.

Other possibilities: swinging in a draught; frame flexing; floor not solid; suspension not level; elliptical path; external vibration; rod bending...

I've found pendulums to be very sensitive to tiny faults.

Dave

Dave:

I have made best effort to ensure the pendulum is in a stable system. Floor is 16 inches of concrete. The pendulum frame is very stiff and the A frames were welded at the base under sprung stress, so the frame is quite rigid - 20mm x1.5mm wall square tube, with a heavy base.

No draughts during the tests, all leveled up as best I can - Not sure how the rod could bend - only if there were resistance to pivot?

Temperatures, pressure, etc were very constant.

Ambient temp - 26-27deg, Rod : 23-24deg, Bob:22-23deg, Pressure 1014.4mb, Humidity - 44%

The Q's reported in the previous post have an error in the '31.8%' Q computation ( the Q of 14514)

The logged data is a large file, and during the latter portions of that log, 'someone' must have bumped the pendulum and buried in the data I found this:

That jump up in Q was to suspicious and when digging minute by minute in the file I found what had happened, so that Q computation is invalid.

I ran the test again today - twice, with consistent results both times , using all the variations of Q computations already discussed :

This is the plot of the last run-

It ran for 3hours 33minutes, with sample rate @ 20ms.

Q's computed :

@ 61% - 1940 beats * 2 * pi - Q = 12200

@ 50% - 2850 beats *4.5324 - Q = 12900

@ 36% - 4100 beats * pi Q = 12880

@ 21% - 6313 beats * 2.013 Q = 12714

There is a small improvement in Q from the 50% amplitude reduction onwards, and not what was indicated in the erroneous post. This is encouraging as it does indicate that the aerodynamic effects are not hugely impacting the bob, since there is little improvement at the lower amplitudes ( less moving air mass, but not a great Q improvement).

As more data becomes available for analysis, more improvements are made, and the cycle repeated...I have now discovered an oscillation in the stable system condition( pendulum running with amplitude loop locked) - logging the angle sensor data shows a variation of the peaks of the 0.5Hz period. It is very small - the peak to peak voltage is 1944mv, and the oscillation is 4mv. The peak angle is 1deg, so around 1000mv/deg. 4mV = 4milli degrees!

The total control loop time constant is around 60minutes, so it seems impossible that the pendulum is being forced to oscillate like this.

I do suspect it has to do with aliasing during the sampling of the voltage by the DAC.

When I sample at 200Hz (5ms), the oscillation period is 12 seconds ; at 20ms sample rate ( 50Hz) the period is 15 seconds - I suspect a software sampling cycle that is being interrupted by serial comms at a rate that causes a repeating delta in the sampling rate, and that manifests as an aliase...What fun.

Fascinating. I love this stuff.

Graphing, zooming in and doing the statistics revealed many anomalies in the data collected by my Mark 1 pendulum, which had many mechanical and electronic shortcomings compared with yours. Though the latest build is better made, I'm still getting odd patterns and events, especially over long runs. For example, seems the Q-factor of my pendulum varies significantly during runs. May be my methodology is faulty - forum peers haven't approved my way of measuring Q.

I sample every beat, about 0.933s and after 46 days the log file is up to 370Mb. Loaded for statistical analysis into my computer, a 370Mb input file eats nearly 4Gb of RAM. A 20 millisecond sample rate is scary.

Dave

Data analysis is an Art itself. The size of the file and how much space it needs in RAM is no longer an issue these days, but I have yet to find Non-Rockefeller SW tools able to process such large files without needing a shave between runs!

The core sample rate of the ADC data for the angle sensor is 200Hz ( 5ms) - because I eventually want to use that to generate the phase offset for the coil drive, and to be able to adjust the phase in small angles - maybe 0.1deg or better. The Temps/pressure, etc I sample at 2sec intervals, and will probably push that out to 30sec.

You do seem reluctant to stem the Q tide against you - is it not practical on your setup to do a 'normal' run-down data log?

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At the risk of putting my foot into it [ I have already lost track of whom I am quoting]

The exponential decay is quite well described in something I recently referenced:

https://www.model-engineer.co.uk/forums/postings.asp?th=187595&p=4

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[quote]

Edit: __ in the case for the prosecution, I present this [found after I posted] well-documented, and easily replicated, experiment: **LINK**

Edited By Michael Gilligan on 18/08/2023 20:32:22

[/quote]

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MichaelG.

Edited By Michael Gilligan on 30/08/2023 19:45:57

Partly other things to worry about, partly measuring Q isn't vital to my project, partly I'm not quite fully convinced I'm doing it wrong yet, partly because I don't want to stop the current test run, plus a technical issue to solve.

My electronics produce a relative measure of amplitude, so in theory I could simply change the governor values so the pendulum is never impulsed, which can be done by remote control.

Unfortunately, SK questioning IR sensor performance led me to check how well my cheap Arduino comparator performs. It's good on beam-break detect, but the beam-open detect timing is delayed. Thus my relative amplitude value is wrong, possibly by a constant, not confirmed. Doesn't affect clock operation, but it means the decay curve can't be trusted. Unhelpfully, my amplitude measure is low resolution because the code clips the logged amplitude value to 4 places of decimals to save space. Needs a recompile and install to fix.

Often wish I'd built two clocks, one for long test runs and the second for testing new ideas on. As it is, I don't want to touch the clock until the present test comes to an end. Been running for 43days, 22 hours. During that time I've not been able to apply any hardware or software upgrades. At the moment the clock is 6.297933s slow.

Looking at the data I'm 99% certain there's an error in the way I calculate temperature/pressure compensation, cause unknown. And a suspicion the Arduino applying compensation with single precision floating point numbers is losing accuracy.

Just for laughs here's the Allan Deviation.

If I drew the graph correctly and understand Rawlings/Bateman it means 'Progressive change ins system parameters' with 'Normal type of rate fluctuation. Could be horribly wrong - I don't have the right sort of brain for maths and statistics!

Dave

Thanks Michael - I read through briefly and will try study in depth, as I still do not follow - I understand the exponential decay - that applies to all oscillators, so in the realm of electronic oscillators, with transistors and coils and capacitors, I am comfortable in predicting and calculating the curve for a set of parts - But I am lost with the pendulum. I don't see how to compute the exponential decay without either knowing Q ( and then I have the decay anyway) or a plethora of other data - pivot friction, air resistance to the bob/rod, etc - all damping factors that would change the curve.

6sec in 44 days is rather impressive - 1.6us/sec slow....Not sure my approach will be as good.

Dave, that ADEV graph bothers me - it is shown reversed to the norm, ie, starts hi and drops, stabilises and then turns up again. Also, way down below 10 minus 13...! That's good GPSDO territory and I am afraid, not possible. Even the Shortt is around 10 minus 8 @ 10 ^5 sec.

Unless I misunderstand this curve completely, is looks like the curve you get when you do ADEV measurement on an oscillator using a time reference that is derived from the same oscillator - somewhat incestuous...doing so gives a curve that just keeps going down, almost forever - looks good, but is a lie.

EDIT : is your pendulum running in a vacuum on this test? 

Edited By Joseph Noci 1 on 30/08/2023 22:08:31

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I think you may already be ‘ahead of the game’ Jo

The recent papers I have found cover fairly simple experimental set-ups, and are pretty-much ‘demonstration of concept’ exercises … I wonder whether there is actually any current ‘Academic research’ on pendulums, or whether they are considered passé

MichaelG.

Dynamic analysis of simple pendulum model under variable damping

This is recent, and freely downloadable: **LINK**

https://www.sciencedirect.com/science/article/pii/S1110016822002393

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MichaelG.

Well, a few points.

First Joe, I think your Q is very respectable. Of the same order that a Synchronome has if not having to operate its count wheel. My 'Nome derivative is about 12,000, and Doug Bateman's clock is similar.

Looking back through this thread I don't see a mention of your bob mass. Q is defined in the simple model as "w*M/k" where w is angular resonant frequency, M the mass, and k the resistance constant. Your shape will have a lower k but mass is equally important.

Nome bobs are usually about 7kg (as is mine being a hefty chunk of CI). They are however blunt cylinders so aerodynamically not so good. If you can increase your bob density (fill it or make it from lead?) that should be a direct was to get higher Q. My tungsten bob is somewhat smaller in mass (5.2kg) but 52mm diameter rather than 80mm, and has chamfered and rounded ends. I think its relatively smaller size and high density is what gives it the higher Q.

You plot the decay I think on a linear amplitude scale. It would be interesting to plot it on a log (ln) scale which is more natural for exponential decay. But it's fairly clear that there is a "break point" where the slope decreases. If you are seeing essentially an exponential shape it's a good indication that the loss is primarily aerodynamic - other forms of loss give different shapes. My pendulum test showed exactly such a break point, with a somewhat higher Q for that part of the decay above it. At very low speeds the loss is viscous drag which is proportional to velocity and gives the "ideal" decay shape. As amplitude increases the flow gets more complex and the loss moves towards a square-law with velocity. Douglas Drumheller in the US does a lot of work in this area and you can see some discussion at here. (By the way please feel free to join the HSN forum!) In an HSN article IIRC, Doug links this towards flow vortices detaching from the bob at higher speeds.

I am also reaching the limits of the pendulum's environment now..

In my setup, looking at the bob period index pulse, referenced to the GPSDO 0.5Hz reference, on a 'scope is the quickest way of seeing what the pendulum period is doing.

After many hours of running and adjusting the weights I have it reasonably stable @ 0.5Hz with a 100us or so jitter. However, simply opening a 800mmx300mm cupboard door, 3 meters from the pendulum, causes a 3-400us jump within 1/2 a second of opening the door. The pendulum is in the study ( 2nd storey of the house..), on a thick concrete floor, but walking slowly on the floor 1 meter from the pendulum causes a similar jump - maybe motion, maybe air movement, or both. Also, I have the Atlantic ocean crashing 50 meters from the house...Perhaps Fishing would be a more successful pastime?

John, Is this 'log' plot format what you mean?

Yeah, that Allan graph bothers me too! I added the code long before the performance of the clock justified it, and strongly suspect something is wrong with my implementation. Not chased it much because other graphs show worrying about Allan is premature. There's nothing legitimate in what I've done to justify 10⁻¹². Got the bits needed to install the vacuum system, not done it yet. At the moment the bob swings uncased in air.

6 seconds in 44 days would be impressive if it were consistent. Boo, hoo the graph of clock time vs NTP is less impressive because the rate wanders:

X-axis is in millions of beats, but the grid verticals are midnights, red Sundays. Sync error is the difference between clock start and NTP, another bug in my clock setting code.

Apart from the large wander, the blue line also has a daily ripple corresponding to temperature change. I'm hoping both are due to an error in my temperature and pressure compensation system.

I'm letting the clock run in hope more data will explain why the rate changes. Doesn't seem to have an environmental cause.

Dave

Edited By SillyOldDuffer on 31/08/2023 11:28:06

Dave:

One needs other hobbies when playing with pendulums, that's for sure. Everything takes a very long time - days or weeks to evaluate any changes, while the environment changes as well. In one of the papers I read , the fellow took 7 years (!) to evaluate a specific element on his pendulum. And as I said in my last post, my environment prevents me progressing further now, so short of moving home....

Or knitting!

Don't despair, these misbehaviours are good news I think the better made a pendulum is, the more likely it is to pick up environmental events. And your monitoring system is detecting them.

Houses aren't particularly stable, even concrete ones. I'm hard put to find a good place for my clock. At the moment, it's on a 1st floor window sill on an external cavity wall (breeze blocks). The clock and wall catch the sun in the afternoon, and I'd be surprised to find the wall isn't moving due to thermal changes. The room has a wooden suspended floor and walking on it upsets the pendulum slightly: I try to keep out of the room. The wall is parallel and to and only 3 metres away from a narrow residential road, light slow traffic only, but vibration is detectable.

The rest of my home is even more unstable plus there's a clumsy cat! Understairs is a possibility, but people crash about on the stairs. Bathroom and kitchen are out - too wet and busy. Workshop full of vibrating tools. Dining room busy. Far corner of living room is a possibility, hidden behind the visitors only sofa, except I do have visitors. Downstairs toilet is a maybe too - I could lock the door! I've thought of using 3 big concrete sewage pipes on end to sink a shaft in my back garden, putting the pendulum on a concrete block at the bottom.

I don't have to worry about the sea, but what's the tidal range on your beach? Several parts of the UK foreshore sink noticeably when the tide comes in - millions of tons of water push the geology down, and the ground springs back when the tide goes out. Lots of energy in big waves too!

There's no end to the torture. You detect a slight problem with a pendulum clock and find you have to move house to fix it.

Dave

So why do we do this?