Arduino Pendulum Clock Design - Comments Welcome

Hi Martin,

Thanks for your comments.

Is it a spring or a pendulum? I think it's both, but mainly a pendulum. The version I've readying for test has a 0.5mm diameter carbon fibre rod, so it's very light compared with the bob. At the suspension end, it's definitely as spring, at the bob it's a rod. I should be able to get a feel for which is which by comparing actual period to theoretical compound pendulum time.

Various notions behind the light bob. As I can control the impulse, it can be set close to the minimum needed to maintain the pendulum and so reduce variations in period. Originally I intended to run the clock in a vacuum, further reducing the energy input. And a light bob won't stretch the thin rod, I hope! Could all be rubbish - I'm not any kind of expert.

I haven't measured Q yet and there's a lot I don't know starting with my ebay carbon fibre: does it stretch; how much does temperature effect springiness (and does that matter if it's more rod than spring); unknowns galore! I knew pressure changes would alter buoyancy, but not that temperature changes air viscosity. Perhaps the answer to that is to temperature control the interior at just above UK maximum, say 41°C. At the moment, I've veered towards correcting rate after in line with measured pressure. That's assuming I can correlate the two!

Dave

Dave, just to confirm, the rod is CF / resin composite, correct?

On the question of Bob mass, the required impulse depends not on the mass but the loss. The two are connected but a more dense Bob of the same size as a less dense will have the same air loss and need the same impulse. Generally speaking more mass = higher Q = lower sensitivity to impulse variations in time and amplitude.

The viscosity change with temperature is quite small.

You've got me thinking, I have some thin CF rod, about 1 mm I think.  I can feel an experiment coming on...

If you are reading Rawlings, I recommend the notes inserted by the editors, especially Philip Woodward and Doug Bateman, for much of the theory of impulsing pendulums. PW especially if you can get copies of his two books is in my opinion much clearer than Rawlings.

Edited By John Haine on 07/09/2020 22:25:28

Ah, 0.5mm is a little smaller than I imagined. You could measure restoring force at your design amplitude simply with a weight on a thread round a pully attached to the bob.

It would be interesting to compare various sytems with different dia rods giving succesively stiffer spring constants (more spring less pendulum).

Co-incidently I learned yesterday that LeRoy (of chronometer fame) discovered that for every balance spring there was an ideal length that produced isochronism (Period independent of amplitude). I wonder if that is true for springs in the form of rods.

I would suggest that you could do a lot worse than losing the spring componant by suspending the rod on a knife edge thus removing the bending moment on the rod entirely and restoring the system to that of a pure pendulum.

You may like to visit the Trinity Clock website for a vast amount of interesting data on penedulum clocks and their gravity escapement pendulum clock project. The 2nd graph down on this page

**LINK**

shows a daily ripple in rate caused unless I'm mistaken by the addition and subtraction of solar and lunar gravity as the Earth spins.

regards Martin

The suspension spring on my clock is 0.006" thick and 0.5" wide. The second moment of area is thus 9 e-9 in^2. SODs carbon rod is 7.85 e-9 in^4. The moduli of elasticity are much the same, but it's too late in the evening to start working out the difference in bending forces for a long thin string subject to axial force compared to a stiff rod with a short bendy bit. A blind guess says that the short spring is stiffer, and so SOD more nearly approaches a knife edge. There will also be less windage on the rod itself. I've read contrary arguments on the shape of the bob itself, some argue that a lenticular bob has less frontal area therefore less resistance from pushing air out of the way, others say lenticular has more surface area parallel to the travel and so more skin friction.

Realised last night I hadn't mentioned the main reason for a light bob. It reduces the force applied to the frame, meaning it too can be relatively lightly built. I haven't attempted sums, instead I'll bounce a laser pointer off a mirror on the top cap while the clock is running to see if the projected dot moves on a distant wall. With luck it will be rock steady. Don't bet the farm on it.

John asked if the rod is carbon fibre / resin composite. I assume so, but don't know. I'll have to trace the order back but I don't recall it having a specification. To find the rod's properties it will probably be necessary to measure them.

Picking up on Martin's knife edge suggestion, I got into this after noticing a very crude and simple pendulum knocked on this principle to test another project kept amazingly good time, similar to a digital watch. Compared with the high-end engineering needed to make a good conventional pendulum clock, the approach seems ridiculously straightforward. The good performance could have been down to pure luck, and I'm chasing a red-herring, or was due to:

• Carbon fibre having low temperature expansion characteristics - comparable to Invar
• Nothing intrusive at the suspension. The thin carbon rod is it's own spring at the join, and there is no escapement adding and subtracting energy.
• The lightweight bob and 'rod' don't shake the frame much.
• It's a 'free pendulum' clock. Ticks are detected optically at the bob, and impulses are provided by an electromagnet.
• The electromagnet tends to keep the pendulum running straight.
• Straightforward to fine tune what happens between detect and impulse when the impulse is generated by a microcontroller. The impulse can be accurately timed relative to detect and it's power accurately adjusted by altering the length of the output pulse. Slightly analogous to the Shortt Clock's pair of pendulums except the Arduino's clock, (good at microsecond and milliseconds, not so accurate over days) provides precision control over the impulse, and applies it non-intrusively.
• As ticks are processed by the microcontroller, the actual period of the pendulum doesn't matter much.  I guess it doesn't matter if the rod is a suspension or spring or both provided it's consistent.  It's not necessary to provide mechanical adjustments to set the pendulum to time. Instead, the period can be measured and rate adjusted in software. The 'gear-train' is implemented in software with whatever 'ratio' is needed to convert ticks into human time.

Doing stuff in software opens up other opportunities. Whilst counting and maintaining ticks, the microcontroller can also monitor temperature, air pressure and humidity. It should be possible to correct errors in pendulum time caused by these factors.

Apart from mechanical simplicity, the clock is advantageously small because it doesn't depend on a long pendulum (or does it?), and the shield could be evacuated without much bother.

I'm finding the comments very helpful: please keep 'em coming. Off to see if I can find any of the books recommended by John. Research & Development is expensive.

How well any of this will work in practice is an open question. So far ignorance is bliss. I'm sure my design can be improved, not least because there's so much I don't know. This fool is going where angels fear to tread!

Dave

Edited By SillyOldDuffer on 08/09/2020 10:33:37

Philip Woodward:

My Own Right Time

Woodward on Time

Thanks John, found a copy of My Own Right Time for sale and ordered it. Listed next to the 'Skin Two Fetish Yearbook', which is worrying! Also a cheap Grimethorpe on offer so got that too.

Cheers,

Dave

MORT is a great read, the book that got me started on horology. WOT is a compilation of all Woodward's articles in Horological Journal and Horological Science News - some of the ground is covered in MORT.

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Try the twang test, Dave

... Remember the school ruler, cantilevered over the edge of a desk ?
... You have the technology to measure its frequency : the rest is basic math.

MichaelG.

I guess if it isn't composite it would just CF strands and would be floppy like a string?

Not string-like at all, which I why I'm fairly sure it's a composite. If I get the chance I'll take a microphotograph and try Michael's twang test.

Dave

Just hold it horizontal? It should sag slightly but be relatively stiff. If you can hold it at one end and have enough to measure the "sag" at the other, if you know its weight you could calculate its YM I think.

Can you come up with a way of demonstrating that the pendulum period is not being 'regulated' by the Arduino timing in the sense of a phase locked loop. As I understand your system there is a fixed delay between the beam break and the impulse which is generated by the arduinino. During the delay the pendulum has moved a distance S. The magnetude of the impulse will depend on S (pendulum further or closer to the electromagnet). Say S is smaller the pendulum will get a bigger impulse which increases the amplitude and slows the pendulum. This makes S larger as the bob is moving faster so the impulse is less which allows the pendulum to slow down. Could you perhapse write some code to modulate the delay and compare the period. I'm concerned that the Arduino is driving the timing rather than the pendulum. It would be easier to see with a high mass bob perhaps so you could allow the pendulum to swing free for many oscillation between impulses.

regards Martin

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Very true, John ... ‘though would suspect it difficult to do accurately on CRP, as the specific modulus [stiffness to weight] is high.

You are effectively measuring a ‘freeze-frame’ of the peak deflection in vibration at 1g

MichaelG.

.

My guess is that it’s a pultrusion [but other composite constructions are available]
.

If you want to go beyond doing a ‘twang test’ for the first mode : this is a handy one-page reference.

https://autofem.com/examples/determining_natural_frequencie.html

... unlikely to be relevant, but curiosity leads us ...

MichaelG.

Edited By Michael Gilligan on 08/09/2020 14:14:03

Now that's a darned good question! Vital to prove that's not happening. Hmmm.

Working on the electromagnet now. Once it's in place and the clock is ticking, I have to show I'm measuring a pendulum rather than the Arduino's crystal oscillator. Could be a show-stopper. Eek.

Ta,

Dave

A quick test on my 2mm rod 1m long shows that its sag is ~20mm over the length under its own weight. Weight goes down as the square of radius and YM as the cube or something? So as long as Dave has enough length it should be possible.

On the question of locking to the digital controller, there's been quite a lot of discussion about this. One way to ensure it isn't happening is to make the pendulum period asynchronous to the Arduino - you may find that its period "beats" but the effect should cancel out on average. You could put some variable delay in the arduino code to show that the pendulum period is not locked?

As an aside, the Shortt-Synchronome system operate like this (I think I have it right). The Synchronome is used to time the impulse of the Shortt free pendulum with the period of the Synchronome set slightly longer than that of the Shortt. Timing pulses from the Shortt pendulum are used to operate a hit and miss synchroniser where once the Synchronome is sufficiently 'retarded' it receives an additional push from the synchroniser spring which advances it a little. Thus the period of the Shortt pendulum regulates the period of the Synchronome which generates the timings signals.

To remain true to this system assuming you have produced a high quality free pendulum, that pendulum should be arranged to adust the oscillator frequency of the Arduino which is then divided down to generate the required period to match the period of the free pendulum. The arduino needs to predict where in time the beam break occurs and compare predicted with actual. If the predicted is earlier than the actual the oscillator needs to slow down and vice versa. The Arduino timebase can then be used to time the impulse point and by normal counting generate the TIME. This also ensures that the timing of the impulse comes from the Free Pendulum and not the arduino and is independent of the point in the oscillation where the impulse occurs.

Note: The Trinity clock group used a pulse decay system and level sensing to achieve sub sampling period accuracy on their sensor. See Instrumentation on their website.

regards Martin

WRT magnetic excitation of a pendulum - and not being familiar with the field at all - I can accept that the 'sharp' impulse can perturb the pendulum in modes additional to the desired one - what about this -

Place the electromagnet at the one end of the pendulum swing and use an optical sensor to detect the pendulum position as it approaches the magnet. Have the magnet ALWAYS energised, the level of to be determined while tuning the setup. Then as the opto is triggered, linearly reduce the magnetic field ( current through the coil) to zero, with the zero achieved at some adjustable distance before the pendulum turns around in its swing.

To try have a 'sufficient' magnetic field lying in wait for the pendulum's approach, and as it enters the (now very gentle) tug of the field reduce the field to zero as the pendulum approaches end of swing.

I believe this would impart very little undesired perturbation to the pendulum, and any second order effect should terminate before the pendulum turns around.

Joe

edit: - remove an errant 'n'...

Edited By Joseph Noci 1 on 08/09/2020 15:38:53

Dave, would the frequency locking concept used in many GPSDO's not work here ?- where they lock to the GPS 1Hz time clock -

The GPSDO I built uses the 1Hz time stamp from the GPS, which has a lot of jitter and short term inaccuracies, and the rising edge of that is clocked by the reference oscillator we are trying to stabilize, and then into a phase detector whose output is filtered in software - often a 32 to 64 tap IIR filter, easy on an Arduinio at 1Hz...This then locks the reference oscillator.

So, if you get two of those medium class GPSDO's , available relatively cheaply, and use one as your reference - then use the second one as the clock lock - instead of the 1PPS GPS time stamp feeding the phase detector, feed it from the pendulum opto detector. Then lock THAT GPSDO's reference oscillator to the pendulum period, and compare the reference GPSDO oscillator clock to the pendulum locked clock by means of another phase detector. That way there is no chance of locking to any obscure reference.

Maybe I'm just blowing smoke..

Joe