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An accurate regulator for a pendulum clock
I have a clock that's around 150 years old. It's what's known as a "Black Forest Clock" and pendulum. I like the clock but I don't like that it never keeps accurate time.
Many people enjoy constantly tinkering with an old clock: winding it and adjusting its time or speed. Others want an old clock that is as hassle-free and accurate as a modern clock. The obvious solution for them is to add an auto-winder and a regulator.
Auto-winders are fairly common in church clocks but are rare in domestic clocks. An auto-winder for a weight-driven clock is described here.
Currently, this project exists as a prototype. I'll replace this webpage when the final version is complete.
An electronic regulator seems to be an obvious addition to a pendulum clock but I can't find any references to one anywhere. (Electronic drivers for a free-running pendulum are common in "fake" pendulum clocks.) Why does no-one do it? It turns out, it's surprisingly hard to get it right.
|The obvious arrangement is to have a
coil which attracts a magnet attached to the pendulum.
The pendulum is synchronised by pulsing the coil with the correct period. The pulse is generated by counting cycles of the mains supply (50Hz or 60Hz).
The mains frequency may drift by a fraction of a percent at different times of day as the district's load varies. However, during the night, it is adjusted so that there are exactly the right number of cycles during each 24 hours. In the USA, at different times of the day, a typical 60Hz mains supply will vary between 59.95Hz and 60.05Hz (i.e. +/- 1%) and is usually within 0.5%. Typically in europe, it is accurate to 0.2% and is usually within 0.1%. For comparison, a pendulum clock which is accurate to 15min/day is 1% accurate. During the day, as the weight or spring runs down, the the clock's period may vary by more that that.
In 1665 Huygens discovered how easy it is to get two clocks to synchronise their pendulums. You just put them on the same shelf. So you'd think it would be easy to synchronise a pendulum to a coil. It isn't.
What are we trying to achieve? We want the pendulum to be synchronised to the pulses in the coil. We want that synchronistaion to be maintained even if the natural period of the pendulum is, say, 2% more or less than the period of the pulses. What can be varied? The strength of the magnetic field; the percentage of the period that the coil is switched on; the strength of the magnet; the horizontal position of the coil and the vertical position of the coil.
The usual arrangement for a coil-driven pendulum is to put the magnet near the pendulum bob. In that way, the force due to the coil has the greatest torque and so should have the greatest effect. The axis of the coil can point outwards from the wall and the coil can be either in the centre of the swing or to one side. Or the axis of the coil can point towards the pendulum (as shown above) and the coil is at one side of the swing.
|I first tried the coil attached to the wall behind the bob at the centre of the swing. It had very little effect on the pendulum.|
|So I moved the coil to the end of the swing. Again, it had very little effect.|
|I presumed that it wasn't very effective
because the coil was facing outwards and the pendulum slid past it.
(That's the arrangement of many electrically driven pendulums.) So I
turned the magnet and the coil sideways. Yet again, it had very little
Perhaps the coil should repel the magnet rather than attract it. Nope, that didn't work.
Why on earth wasn't it working? Huygens had shown that even imperceptibly small movements of the shelf were enough to synchronise a pendulum yet the coil and magnet were quite powerful.
What's going wrong is this. Huygen's shelf always applied a (small) force to the pendulum with a fixed period. But the coil doesn't do that. The coil is always pulsed with a fixed period but the force is only applied when the magnet is near the coil. The force due to the magnet has quite a short range. (Magnetism is extremely complicated but, as a rough approximation, the force decreases with the cube of the distance. Imagine pulling a piece of iron off a strong magnet.)
So the pendulum was only affected when the bob was near the coil and the coil was being pulsed.
Let's say the clock is running a little fast and the pendulum is near the coil just as the coil is pulsed. The coil and pendulum are in sync - great. But the natural period of the pendulum is slighly too short. So the pendulum tries to move "ahead". The pulse now occurs as the pendulum is moving away. It ought to slow the pendulum to keep it in sync. But to do that requires quite a big force - more than the coil can supply. So on the next swing, the pendulum move slightly further ahead and, as a result, the force is weaker and the pendulum is affected even less. And so on. That's different from Huygen's shelf where the size of the force is aways the same.
The pendulum will stay in sync for a while but if it ever get's a little "ahead" it will excape and lose sync.
A further problem is that when the pendulum and the pulse are in sync, the swing of the pendulum is larger so the pendulum comes closer to the coil. If it goes out of sync even slightly, the swing becomes slightly smaller and the force decreases.
It's difficult to prove all this theoretically. The maths is very tricky but it's simple enough to simulate on a computer. The simulation shows all the effects described above. It requires an enormously strong coil to force the pendulum into sync. The force due to the coil is similar to the force trying to centre the pendulum when it's at the end of its swing. That's totally unlike the tiny effects Huygens saw.
The root of the problem is that the magnetic force has a very short range. How can we make it longer?
|If the coil and magnet are moved up
towards the pendulum pivot then the coil will have an effect over a much
greater pendulum angle. When the coil is at the bottom, the magnet will
be within range over only a few degrees but when the coil is at the top,
the magnet is in range over a lot of the pendulum's cycle.
Of course, when the coil is near the top, its torque is much smaller (torque = force x distance) so you'd expect its influence to be less not more. But the effect extends over much more of the pendulum's cycle and so it's very much easier to achieve sync. That observation applies both to the simulation and to the real clock.
|Here is a prototype with
the coil Blu-Tacked just under the clock.
The magnet is 9mm dia and 1mm thick. It came from a badge.
It has kept "perfect" time over the last week.
I'll now try moving the coil further up inside the clock.
The circuit is pretty straightforward:
9VAC is obtained from a transformer - use a cheap "swinging brick" (known as a "wall wart" in the USA). It's half-wave rectified to power both the auto-winder and the regulator; the positive half powers the regulator and the negative half powers the auto-winder. The idea is to isolate changes in the voltage when the the winder operates. (On reflection, it may be better to operate both from the positive half. I'll check that.) The diode supplying the winder has to take a few hundred mA so a 1N4007 is used. The motor generates a lot of electrical noise so several capacitors are used to smooth the power to the PIC.
The rectified 9VAC is reduced to 5V to power a small PIC processor. The AC is also fed to the PIC so the PIC can count the mains cycles.
Counting the number of teeth on the clock's gears allows us to calculate how many ticks per hour and hence how many mains cycles per tick.
The answer is 3168 ticks per hour (36 * 66/6 * 72/6 * 24/36). Which is 625/11 cycles per tick (3600*50/3168). The PIC uses a DDA algorithm to do the arithmetic. The PIC "de-bounces" the mains to eliminate any noise generated by the winder motor.
Each pulse is 5 mains cycles long (i.e. 100mS). Perhaps longer would be better.
|Neodymium disc magnets are ideal - they are small and strong.|
|The coil should have lots of windings (a few thousand?) and a fairly high resistance (at least 1k?). You're unlikely to want to wind your own but coils like that are hard to buy. I got mine from an old fashioned battery operated clock (the sort with a balance wheel) and is fairly flat in shape. A good coil can be found in a modern battery operated clock but they're long and thin. You could also buy a small 5V or 12V relay for pound or two and extract the coil. The shape of the coil that you need depends on the layout of your clock. It is probably better if the coil does not have an iron core - the core should be empty. An iron core "concentrates" the magnetic field but would attract the magnet even when the coil is switched off.|
There's a diode across the coil so that the spike generated when it is turned off doesn't damage the PIC.
|A small piezo speaker clicks when the coil is pulsed.
It allows you to tell whether the pendulum is in sync - the click should
always occur at the same place in the pendulum's cycle. Once the
regulator is operating properly, the piezo speaker can be removed.
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