Arduino Pendulum Clock Design – Comments Welcome

[SillyOldDufferModerator @sillyoldduffer]

Posted by Joseph Noci 1 on 24/10/2020 09:05:55:

Posted by SillyOldDuffer on 23/10/2020 21:26:53:

Posted by John Haine on 20/10/2020 17:07:30:

 

Also been looking into Allan Deviation and Variation. Thick fog ahead!

Dave

 

Been there, still there, and the more I learn the more I realise that mostly I learn how little I know…

…

The one major discovery has been where the 'Nuts' comes from in the Forum name..

Sorry, nothing to add that helps you Dave, but beware of the road ahead!!!

Joe

No comfort from Joe, I have all the symptoms of TimeNut Syndrome albeit on a smaller scale!

My set-up at the moment is this:

 

Supported with a Frequency Counter, oscilloscope and computer with an extensive scientific maths capability doing the statistics and graphs. Chief flaw is me, because the gap between what I'm doing and understanding it is much larger than expected. As you say 'the more I learn the more I realise that mostly I learn how little I know' : exactly!

Made some progress with Allan though. I've found a Python software module that does the hard work provided I can understand it! I was able to graph white noise and brownian motion.

I understand White Noise to represent a perfect pendulum, one influenced only by truly random variations due to natural noise at the atomic level. The ideal slope is a nice straight diagonal line falling 45° to the right, shown in Blue.

Real oscillators suffer other effects. For example, Invar alloy is unstable over time in that microscopic structural changes cause tiny increases and decreases of rod length. These movements alter the period of each swing causing the clock to go on a random walk that frequency modulates the period, oh dear. The orange line demonstrates Brownian motion which is characteristic of random walk error. Compared with white noise the slope and shape is different.

This and other defects can be detected by taking many samples from the test clock and comparing them statistically with a better one. A promising technique, except toddlers need to learn to walk properly before trying to sprint! At the moment my pendulum has more serious defects.

One thing Joe or another expert might know the answer to? In so far as I understand it, Allan requires me to generate a list of phase differences between the test clock and its reference. The Allan examples assume test and reference are both outputting 1 pulse per second (so calculating small phase differences is easy). Unfortunately my GPS reference is 1 pulse per second while the pendulum is about 0.883 pulses per second. How do I normalise the data-sets?

Dave

 

Edited By SillyOldDuffer on 24/10/2020 13:18:47

[John HaineParticipant @johnhaine32865]

No, Allan compares the test clock with itself. If you use the TimeLab package you just give it a big file list of successive period readings and it does the rest (IIRC).

Here is an Adev plot of my "Arduinome" clock I just generated to remind myself.

It takes the whole file of which only the first column are period measurements and ignores the rest. So far I haven't really worked out what it means but generally the trend is sort of diagonally downwards though with some flattening off. What the little wiggles result from I don't know. Good explanation here. If you explore that site you can read about Tom's adventures testing General Relativity on a camping trip.

[SillyOldDufferModerator @sillyoldduffer]

Posted by John Haine on 24/10/2020 14:02:26:

No, Allan compares the test clock with itself. If you use the TimeLab package you just give it a big file list of successive period readings and it does the rest (IIRC).

Here is an Adev plot of my "Arduinome" clock I just generated to remind myself.

It takes the whole file of which only the first column are period measurements and ignores the rest. So far I haven't really worked out what it means but generally the trend is sort of diagonally downwards though with some flattening off. What the little wiggles result from I don't know. Good explanation here. If you explore that site you can read about Tom's adventures testing General Relativity on a camping trip.

John, you are my hero. I had the fixed idea Allan analysed phase differences between clocks and managed to spin my reading of the documentation to cement the misunderstanding. Might have taken me weeks to get back on track. Thanks to you sorting me out it's easy to to apply any of the methods provided in Python's Allantools module.

Interpreting the graphs is another walk in the dark, but I read your Arduinome chart thus:

• The line generally falls from left to right, which is good.
• The wave like wiggles in the first 100 seconds could be settling errors, maybe due to the pendulum vibrating after start-up, or the clock being bumped whilst the measurement was set up.
• Y axis values are small, which I think indicates good stability.

My clock's chart:

• The tick shaped line is bad – rising to the right indicates a consistent rate error. Sharp falls are characterised by Rowland as observation error. In my case, pretty certain the observations are OK, and the real cause is pendulum bounce due to restarting the clock from scratch for each test.
• Y-axis values are big, which I think indicates poor stability.

Could be wrong!

Meanwhile, I broke the pendulum rod again. I frayed the rod and made a brass clamp to hold the fibres OK but got clumsy reassembling the clock. Showstopper – looks like I've run out of 0.5mm rod and will have to order more.

Dave

[Joseph Noci 1Participant @josephnoci1]

Posted by John Haine on 24/10/2020 14:02:26:

No, Allan compares the test clock with itself. …………..If you use the TimeLab package you just give it a big file list of successive period readings and it does the rest (IIRC).

 

John, please explain..Allen deviation is re result of a mathematical/statistical process applied to a set of data that comprises the sample interval and the phase difference between the measured clock time interval and the reference clock time interval. It cannot be the phase delta in the interval between the measured clock and itself…Then there will never be a phase delta…

Eg, A total of N time interval measurements are taken at a 1 second rate. That is, the time (aka phase) of an oscillator is compared against the time (aka phase) of a reference standard once a second for NX1s . That data is then used to determine the Allan Deviation and Variation.

 

Joe

Edited By Joseph Noci 1 on 24/10/2020 17:39:44

[John HaineParticipant @johnhaine32865]

The comparison to a reference is already done by measuring the period. AV is a measure of how the period varies with time.

[Joseph Noci 1Participant @josephnoci1]

Posted by John Haine on 24/10/2020 18:08:10:

The comparison to a reference is already done by measuring the period. AV is a measure of how the period varies with time.

Agreed, but somewhere in there is an accurate 'clock' is required – and that is the clock that is used to measure the period. THAT clock has to be stable, accurate, etc. So there is the accurate reference…You cannot get away from that – the comparison is not with the clock itself, it is the variation of the clock period against an accurate reference – the timebase used to measure the period.

[John HaineParticipant @johnhaine32865]

Yes, which in my case is a 10 MHz OCXO, and (I think) for Dave it is the Arduino clock. But the AV is a variance – it is a measure of how the samples of period depart from some sort of mean. A simple variance would just take the long term average and the sum of squares of the deviation from that average, but for some types of variation the variance gets larger and larger without limit as the number of readings increases. Once you have some sort of timebase to measure the period you don't need another one to compare with.

[Joseph Noci 1Participant @josephnoci1]

I think we vehemently agree…The 'another one' you talk of would be a THIRD – thats NOT at all what I suggested…..The Timebase is the second ( the reference, same as your 10MHz OCXO.)..My point was that you are not measuring the clock variance against ITSELF, but measuring its variance referred to the 'accurate' timebase, the reference…

[SillyOldDufferModerator @sillyoldduffer]

Joe & John's Q&A has clarified my thinking. What I need to do is upgrade my Arduino code to compensate for the deficiencies of its resonator. I can continually re-measure how many Arduino ticks are in a GPS second and use the info to adjust the pendulum measurement. Doing so will compensate for temperature and resonator drift, at least within the 4uS resolution of the Arduino timer plus however long it takes to service the interrupt.

A Nucleo would squeeze a little more accuracy than a Nano. 3x faster and they have a 20ppm crystal oscillator too.

Dave

[Joseph Noci 1Participant @josephnoci1]

Dave, I get a bit lost with the size of the numbers we are dealing with here – I am chasing down in the 10 minus 12/13 arena, and this is way overkill for what you are measuring – I don't yet have a handle on what the real effect will be of, say, a 1ppm osc versus your, what, maybe 30ppm one? Also, what is the effect of the 4us jitter, and the interrupt jitter..I suspect that the oscillator stability effects will be drowned in the noise of the rest..Trying to model this a little and see…Lament the day I discovered TimeNuts…

BTW, 1ppm TCXO's are easily available from Digikey and Mouser for under $3.00 – easy to fit.

Joe

[John HaineParticipant @johnhaine32865]

Posted by SillyOldDuffer on 24/10/2020 17:31:23:

Posted by John Haine on 24/10/2020 14:02:26:

……………

Interpreting the graphs is another walk in the dark, but I read your Arduinome chart thus:

• The line generally falls from left to right, which is good.
• The wave like wiggles in the first 100 seconds could be settling errors, maybe due to the pendulum vibrating after start-up, or the clock being bumped whilst the measurement was set up.
• Y axis values are small, which I think indicates good stability.

My clock's chart:

• The tick shaped line is bad – rising to the right indicates a consistent rate error. Sharp falls are characterised by Rowland as observation error. In my case, pretty certain the observations are OK, and the real cause is pendulum bounce due to restarting the clock from scratch for each test.
• Y-axis values are big, which I think indicates poor stability.

Could be wrong!

Meanwhile, I broke the pendulum rod again. I frayed the rod and made a brass clamp to hold the fibres OK but got clumsy reassembling the clock. Showstopper – looks like I've run out of 0.5mm rod and will have to order more.

Dave

Just to clarify, my plot is of a set of measurements taken when the clock is in equilibrium, not from the start of the run. I don't know where the wiggles come from – there is one key periodicity in the clock which is the impulsing, which during that run was probably happening every 40 swings or 80 seconds. (Currently I impulse every 30 swings.) Another option in TimeLab is "Modified Allan Variance" – if I choose that the wiggles go away.

What it means I still have to figure out!

You can buy this stuff which might be an alternative to burning the resin out of the composite?

[John HaineParticipant @johnhaine32865]

Today's job is to move the Arduinome back an hour – currently manual, really I ought to add a couple of commands to deal with DST/UTC shifting. Would need to generate 400 pulses to step the dial backwards or forwards, +/- an adjustment to allow for the time taken.

[Joseph Noci 1Participant @josephnoci1]

Posted by John Haine on 25/10/2020 06:30:35:

Just to clarify, my plot is of a set of measurements taken when the clock is in equilibrium, not from the start of the run. I don't know where the wiggles come from – there is one key periodicity in the clock which is the impulsing, which during that run was probably happening every 40 swings or 80 seconds. (Currently I impulse every 30 swings.) Another option in TimeLab is "Modified Allan Variance" – if I choose that the wiggles go away.

John, do you have Adev's for longer periods? – 10 hours plus? Interested to see that – if so maybe we should PM so as not to hijack this thread any further..

My GPSDO Adev for approx 12-1/2 hours @ 1 sec samples:

[John HaineParticipant @johnhaine32865]

Not yet, I haven't properly understood how to use TimeLab so far. I have been posting some results here – may be aa better place as it isn't precious about file formats?

[SillyOldDufferModerator @sillyoldduffer]

A surprising result from yesterday's endeavours.

First, my attempts to fray and hold the 0.5mm rod in a clamp failed miserably. Superglue wicks into the fibres, making them stiff and easily snapped. I'm completely out of 0.5mm rod now.

Needing to test a software upgrade, I fitted a 0.3mm diameter rod. (No 0.3mm drills available but I was able to shim the thinner rod with some 0.5mm O/D, 0.3mm I/D brass tube bought for another purpose.) Also took the opportunity to fit a slightly bigger bob, foolishly forgetting to weigh or measure it before putting the shield back.

Dropping the rod from 0.5 to 0.3mm made a big improvement. Q about 3000 and it takes much less power to impulse the bob. Currently getting about 20 swings per impulse. Zooming in on an undisturbed section of the run (I was working outside, so no vibration indoors) shows the Period holding steady while the amplitude sawtooths between impulses. The period can just be seen to jump when the impulse is applied.

I guess the 0.5mm rod was acting as an inefficient spring and absorbing a lot of energy. Presumably the 0.3mm rod being about 1/3rd the weight and much less stiff makes it more efficient. Still surprised a small change made such a big difference.

Dave

[Sam StonesParticipant @samstones42903]

Roughly 1/8 as stiff?

i.e. D^4

However, I can't be sure about resin composites.

Sam

[John HaineParticipant @johnhaine32865]

Is it 0.3mm CF or steel?

[duncan webster 1Participant @duncanwebster1]

It will undoubtedly be less stiff, and Sam's calculation is right, but if the springiness were 'ideal' I don't think it would make any difference to Q as it wouldn't absorb any energy. However even steel has (mechanical) hysteresis, that's why springs get hot if rapidly cycled. Stress/strain curves are done slowly to allow time for things to recover. I have no evidence for this but I suspect harder steel is better than soft. I can't find any information on CF/resin composites, but it would be interesting to try a steel rod of the same stiffness. There is some info about mechanical hysteresis at Royal Society

The best of the best clocks use knife edge suspension, Is this why?

My theory of 'do what you like, but do it every time' says SOD should now turn the wick down on the impulser so that it impulses nearly every time. No doubt the clever software could change the impulse so that it missed one in 100.

In passing my clock is now stopped, I stopped it as it had gained a couple of minutes (been cold) intending to start it when it got correct, but got distracted and forgot, so I'm waiting until it's correct again.

[John HaineParticipant @johnhaine32865]

Posted by duncan webster on 26/10/2020 20:23:15:

….

The best of the best clocks use knife edge suspension, Is this why?

…

Do they? Not Harrison, or Clock B, or the Shortt Synchronome, or the Riefler.

[duncan webster 1Participant @duncanwebster1]

Well I thought they did, shows how wrong one can be

According to this Riefler has both knife edges and a spring suspension

Edited By duncan webster on 27/10/2020 00:13:43

[John HaineParticipant @johnhaine32865]

Ah, you're right, the upper spring chop pivots on a knife edge to do the impulsing.

[Martin KyteParticipant @martinkyte99762]

John Harrisons RAS regulator also had the pendulum suspended on a knife edge.

regards Martn

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 27/10/2020 06:52:59:

Ah, you're right, the upper spring chop pivots on a knife edge to do the impulsing.

.

Nicely illustrated in this Meccano version **LINK**

http://www.meccanotec.com/riefler%20borrill.htm

… and detailed in his patent: **LINK**

https://worldwide.espacenet.com/patent/search/family/002577589/publication/US508760A?q=sigmund%20riefler

MichaelG.

[John HaineParticipant @johnhaine32865]

Posted by Martin Kyte on 27/10/2020 07:58:12:

John Harrisons RAS regulator also had the pendulum suspended on a knife edge.

regards Martn

Actually no. Key to that clock, as also to Clock B, is the use of circular chops round which the suspension spring wraps to give partial compensation of circular deviation. This is obvious from the published descriptions of the RAS clock (The Lost Science of John "Longitude" Harrison), Clock B and the series on the RAS Regulator replicas in HJ at the moment. They do use knife-edge suspension, hard brass on glass blocks, for the crutch but that carries much less load than the main suspension, and arguably friction doesn't matter since the crutch is driven by the train.

[duncan webster 1Participant @duncanwebster1]

I think this is where I got the idea that knife edge was good Knife Edge. If you go to Q3 there is a good description. However reading it again, he had a problem with the knife edge slowly walking sideways.

Mine's going again!

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