Precision pendulum techniques

JH - thanks for the links - very interesting articles.

Seems to me that there have historically been two rather different extremes in the approaches taken to building a precision pendulum clock - the Harrison approach, where he accepted that there were environmental and mechaninal effects that would affect the timekeeping and carefully balanced them in order to create an accurate clock, and the Shortt et al approach, where the pendulum was as far as possible isolated from mechanical and environmental effects and mostly left free to vibrate as it will.

My own rather amateurish messing around with a "free" pendulum that is electromagnetically impulsed under the control of a single board computer has led me to start thinking about a third possible approach which takes advantage of the processing power and electronic sensors that could be applied to the problem - measure the environmental factors that could affect the pendulum (temperature, pressure, humidity,...), feed those measurements into the SBC, and use its processing power to determine how much impulse to give to the pendulum in order to correct for the environmental effects. Even for the lowly BBC Micro Bit that I am using has add-on boards that will measure temperature, pressure, and humidity. Obviously the calculation is probably going to be non-trivial, and the details specific to a particular pendulum, but in principle...?

...or are you all way ahead of me...?

Edited By Tony Jeffree on 11/02/2023 12:13:30

I looked into the mathematics of larger amplitude pendulums. I'm still taking the paracetamol, very much more difficult than the usual approach. A previous thread has mentioned a 'eureka synchroniser' where the amplitude of a balance wheel is controlled to make it keep pace with a quartz crystal, so the principle is sound. However, I think the difficulty might be that the pendulum will take time to react both to environmental changes and to impulse changes. No doubt someone cleverer than me can sort it out

To digress slightly, magnetic impulse by attraction speeds a pendulum up, by repulsion slows it down, at least I think it does. Synchronomes and Pulsynetics drop their weights such that impulse is equal either side of centre. Anyone fancy a 3 phase linear motor with an aluminium vane on the end of the pendulum?

Yes, I think that's the problem. A high-Q pendulum can take hours to settle to the new amplitude you wanted to compensate for a time error, by which time it's too late! Better to have a system that directly "tunes" the pendulum like Robertson's regulator or the "ball chain" idea mentioned on here recently.

How impulsing affects rate depends on where it's done in the cycle. Whether you attract the bob to the right of repel it from the left, if you do so before BDC it speeds up the pendulum, if after it slows it down.

For larger amplitudes, to all intents and purposes you can ignore elliptic integrals and stuff (I've done so all my life!) and just use the rate proportional to 1+A^2/16 correction where A is the angle in radians - pretty accurate up to 10 degrees or so. Or Tom Van Baak gives a wonderfully easy and to all intents and purposes exact method of calculation here:

**LINK**

Similar to what I'm doing in the 'Experimental Pendulum' thread. My method:

1. Build attempts a high Q pendulum without mechanical temperature or barometric compensation, that isn't designed to beat at a particular frequency. The bob is impulsed by an electromagnet, triggered by the bob breaking an infra-red beam, so there's nothing mechanical apart from my bad design and workmanship to spoil the pendulum. Not tried yet, but the pendulum is designed to run in a vacuum.
2. Logs temperature, air pressure and humidity on every beat, also measuring period at high resolution for external statistical analysis.
3. The statistical analysis quantifies the relationship between temperature, pressure, and humidity (if any). My clock isn't noticeably effected by humidity, so that's been dropped. The relationship between period, temperature and air pressure is quantified numerically by doing a 'Multivariable Regression', on the log.
4. The regression results are loaded into the clock, where the microcontroller uses them to turn mechanical ticks into microsecond accurate 'should be values'. When time-keeping independently, the actual pendulum period isn't measured. Instead the tick event causes the microcontroller to calculate the 'correct' period from temperature and pressure, and it counts that rather than actual pendulum time. Very different from other clocks I believe!

The log looks like this, millibars, humidity, and temperature in bold, actual period and corrected period in italics:

13277507 0.4059 0.3600 36 1024.02 73.72 13.55 823472 1676117346 766006 1676118087 862746
13279885 0.4059 0.3600 36 1024.02 73.72 13.55 823472 1676117347 589478 1676118088 688123

Note that the microcontroller corrects both actual tick periods into the same value in microseconds based on temperature and pressure. The smoothing is aggressive, and may be cheating!

The maths is easy enough, when you know how, because someone else did all the hard work! I'm using python with numpy and sklearn, both modules built by experts! Numpy is designed to make working with numeric arrays easy, whilst sklearn is a machine learning module that includes multi-variable regression. The two are compatible.

Mult-vartiable regression may be complicated behind the scenes but the Python code needed to use it as a tool is simple:

X = np.column_stack((pressures, temps)) # Combine pressure and temperature arrays
regr = linear_model.LinearRegression() # Create an object that does regression sums
regr.fit(X, ticks) # Get relationship between ticks( aka period), temperature and pressure

intercept = regr.intercept_ # The answer is in three parts
pressureCoef = regr.coef_[0]
tempCoef = regr.coef_[1]

Regression results loaded into the clock, the microcontroller uses the intercept, pressure and temperature coefficients to do a simple sum:

Written in C because I'm using an Arduino, but nothing other languages couldn't do just as well.

Example values:

What I hadn't thought of doing is computing the impulse power as necessary to adjust Amplitude - an idea I shall certainly steal!

Thanks,

Dave

Edited By SillyOldDuffer on 11/02/2023 15:16:06

Interesting stuff Dave, thanks - there's plenty there for me to steal too!

Cheers,

Tony

This is something I have a hard time believing. Sure, in the days of "Electric Clocks" (no copyright page shown, but I'm guessing it was from the '40's), that was no-doubt true. Maintaining fine regulation of voltages and currents and impulse durations was very difficult back then, which would lead to horrible long-term performance. In addition, I think light detection with selenium elements was known back then, but that too would likely have been too slow and inaccurate for good timing.

But do you believe that's somehow always going to be the case, even with modern electronics? If so, what specific issues do you think remain potentially worse about electronic measurement and impulsing than mechanical?

I have barely any experience with clocks, but a fair amount of experience with electronics. My opinion would be that if the very best (electro-) mechanical clocks of old are still better than amateur attempts of today, that was likely due to the extraordinary skills of the best practitioners of the day, not the inherent superiority of mechanical impulsing.

Edited By S K on 12/02/2023 01:20:27

Different technologies usually come with a different list of virtues and vices. I don't see this as a straight competition, rather an opportunity for the designer to mix and match for best effect. For example, firearm design calls for materials expertise, mechanical engineering and energetic chemistry. The motor on my lathe calls for materials expertise, mechanical engineering, and electrical engineering. A lathe could be driven by an IC engine, but there are a long list of disadvantages.

An advantage of impulsing with a falling weight is the force delivered can be determined very accurately. My experimental clock uses an electronic timer to deliver an ultra-accurate timed pulse to an electromagnet that then attracts the bob. Although the pulse is super-accurate, the resulting force applied to the bob is hard to guarantee, for example:

1. The voltage applied to the electromagnet's coil may sag under load, causing the magnetic field to vary
2. The coil's impedance effects the shape of the pulse, causing the field to vary
3. The strength of the magnetic field weakens rapidly with distance, so the force applied to the pendulum depends on timing
4. In my clock the bob is made of mild-steel, which is likely to become slowly magnetised itself by impulses. I think the change will alter when each impulse reaches the bob, causing a drift. I don't know how big the change will be, or how long it will take to appear.

In practice, I dodge the first three by adjusting for best results, but I don't know how much force each super accurate pulse applies to the bob. Thus I can't give any sensible advice on how to wind an electromagnet from first principles, and the set-up doesn't provide much insight into the actual force applied to the pendulum. All I can do at the moment is give the part number of the 5V relay I cannibalised, describe it's physical position, state the pulse length, and graph various effects on period and overall time-keeping.

In contrast, a dropped weight is less accurate in terms of 'when' the impulse force is applied, but much more predictable and measurable in terms of effect. Both are important if the aim is to explain why things work and why they fail so that the next design will be an improvement. My ideal system would be accurately predictable in terms of time and force, but I'm nowhere near achieving that! Hence much fumbling in the dark!

Dave

My comments regarding falling mass impulsing was really just a gut reaction and you would have to look at the data to say for certain. Mass impulsing will be affected by changing gravity from tidal effects but they are small and predictable. Again a gut feeling but I would think it would be easier to do without introducing a wobble to the pendulum especially if the electromagnetic impulse was at the bottom of the bob.
Im also twitchy about having a magnet on the bob with the system sitting in a varying magnetic field. The earth field varies and there are other sources of magnetic disturbance potentially on a more local level. Quite how much this would effect things I have no idea.

Part of it is taste. I like mechanical solutions.

For an electronically compensated clock I’m not sure it matters much anyway as the feedback from the amplitude input will compensate for any variation in impulse.

regards Martin

For my first clock I decided to use a gravity escapement based on the Synchronome for the reasons that Martin suggested. In fact I used an old 'Nome as a basis though the only parts retained are the cast frame and the gravity arm, and the dial mech (it came without a pendulum). The arm is lifted by a small stepper driving a snail cam, the pendulum sensed by an opto, and all controlled by an Arduino - hence "Arduinome". I used the stepper for the arm because it can be much better controlled, and the pallet design is based on the raised-cosine shape that Shortt proposed. In principle you can set up the clock so that the gravity roller is just half-way down the cam when the pendulum is stationary so the impulse should be exactly symmetric and centred. In practice that does not give an actual central impulse and looking at detailed timing measurements there is a distinct phase step on each impulse. Correcting this needs a real-time measurement of the time shift which is hard to do though I did kluge the control software to do it. Whether the adjustment survived the clock being moved from workshop to kitchen I don't know!

I also found that I had to be very careful about setting the pallet exactly in the plane of swing to avoid imparting a twisting motion to the pendulum. The rod is carbon fibre and so very light, and the impulse also imparts a distinct "wobble" to the rod because the CoP is virtually at the bob CoG. So though in principle I think mechanical impulsing could be better (and in fact can be as in Clock B), I don't think it's any easier to set up than electromagnetic.

Of course the Fedchenko clock shows that EM impulsing can be very precise and that has no amplitude control, instead a special spring design that corrects for circular deviation.

There's no need to have a magnet on the bob - mine has a soft iron armature attached which the electromagnet attracts. I do use a very small magnet for the Hall effect sensors though - but as others have done, optical sensors could be used.

I thought that the pallet was meant to be the segment of a circular cone with the proper profile if that makes any sense. Think of a sectioned bell perhaps. That way the slope is always radial to the rod so provided the roller is square to the swing there should not be any twist. I made mine like that but as it’s not finished I cannot comment on the outcome.

regards Martin

Fair comment.

My pallet is just 1/8" wide so not much opportunity to shape it.

That would explain it John. Mine looks nothing like that.

regards Martin

.

Putting my head briefly above the parapet … may I refer to my post on 01-Feb, here at 17:18:26  **LINK**

https://www.model-engineer.co.uk/forums/postings.asp?th=184659&p=2

MichaelG.
[ exits before the flak starts flying ]

Edited By Michael Gilligan on 12/02/2023 18:53:45

Thats what mine looks like. Made with a form tool with the pallet on an arbor in the chuck to generate the circular arc. That way if the pallet is slightly skew it doesn't matter.

regards Martin

Well, strictly the pallet face isn't circular! Mine is CNC profile milled, such that a follower roller of the right diameter follows a path that gives a raised-cosine force, just like the red curve in the picture you posted Michael. Probably a circular arc isn't far off though.

Am I correct in thinking that Michael's red curve doesn't allow for the roller diameter? The scan appears more sharply curved at the top

As I understand it only the length of a pendulum rod and the restoring force exerted by gravity determine the frequency of oscillation of a pendulum.

Variations in rod length due to temperature can be reduced by using a rod of Invar, fused quartz or other slow thermal expansion materials. Variations in the restoring force acting on the bob mass caused by air pressure/density may be offset by a barometric compensator or operating the pendulum in a controlled atmosphere.

Both of these are both simple and effective to implement.

However for a simple pendulum the issue of circular error and the need to stabilise amplitude is a difficult issue to solve if the history of clock development so far and the discussions here are anything to go by. Numerous escapements, drive train improvements and increasing levels of pendulum detachment have been devised to help produce a stable amplitude.

Fedchenko side stepped the problem by using a suspension design that eliminated or at least substantially reduced circular error and therefore reduced the need to stabilise amplitude.

There have been several methods devised to reduce the effects of circular error such as the spring used on the Bulle electric clock that compensated for the reduction of battery voltage over time and reduced impulse energy.

Although this method doesn't reduce circular error to the extent the Fedchenko's design does it will go some way to reduce the need for highly accurate impulsing. Also on an electrically impulsed pendulum one can easily change the impulse energy to see if such a method makes the pendulum more isochronous.

CS