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DonCorson
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Resonance Watches, a First Approach

Resonance Watches, a First Approach
by Don Corson

Resonance watches are rare and when discussed the resonance effect is often not accepted.  Always looking for a challnge, I have decided to make my next watch a resonance watch to see what is real and what is only talk.  While the mechanical design of the movement has slowly been advancing I have also been interested in the theoretical side of the phenomenon of resonance.  In other domains we use resonance daily without even knowing it probably, why shouldn’t it work in mechanical watches?  (Note that I realise that resonance is the wrong term technically.  We should be talking about synchronisation of coupled oscillators.  I will, however, retain the term resonance for historical reasons.  Antide Janvier and A.L. Breguet called their clocks and watches with coupled oscillators resonant timekeepers.  Journe and Haldimann do too.  So will I.)

The only modern resonance watches that I know of are the F.-P. Journe Chronomètre à Résonance  and the Haldimann H2 Flying Resonance.  There are several other recent multi-oscillator watches such as the new MB&F Legacy 2 and the Dufour Duality, but these watches do not try and make use of the resonance effect, they simply average the rate of the two or more oscillators.

The energy added by the impulse keeps the amplitude from falling off.  The amplitude stabilises at about 280 degrees.

This model has a problem for with I have not seen a solution in the literature.  The anchor is not only a means for adding energy to the balance wheel through the impulse, but if external forces act on the balance so it has a high amplitude or speed the anchor also serves to slow the balance down, to stabilise the amplitude in a normal region.  For the moment I have added a feature to the model so that if the speed of the balance is faster than for a 300° amplitude the impulse is not given.  This does not correspond well with reality which actually slows the balance, but is a first step in that direction.  I will think about this problem some more to make a more realistic simulation in the future.

Now that I have an oscillating system that corresponds more or less to a real balance wheel/ hairspring oscillator it is time to see how it is affected by oscillations coming from an external source.  How will this model act as a part of a resonant system?  I will make this first simulation with a simple sine wave generator and couple the energy from this source into the balance wheel.  There will be no feedback from the balance wheel to the sinus generator as there would be in a resonance watch.  But we want to take small steps and try to understand things on the way.

What do I expect?  Well, I expect that at frequencies far from the natural oscillating frequency of the balance the external excitation will have little influence on the balance wheel.  At frequencies near or at the balances natural oscillating frequency there will be a big increase in the amplitude of the balance as the balance resonates with the external excitation.

To do this simulation have reduced the impulse so the amplitude does not become excessive.  I will run the model with several external excitation frequencies with an energy somewhat less to that used for the excitation from the anchor and note the amplitude of the balance wheel when it has arrived at a stable state.

Here are the results.  The horizontal axis shows the frequency of the external excitation, the vertical axis the amplitude after the system stabilised.  The model needs about 60 seconds to stabilise. It will be interesting to see if the real watch has the same behaviour.  The values were taken after 120 seconds.

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