Paradoxical rate increase over mainspring power reserve decrease; coaxial double barrel movement

jtfreelancer · Aug 6, 2020

A few months ago I purchased a used 8906 GMT Black and White 215.30.44.22.01.001 cir 2019. I'm happy with the accuracy etc. This is not a post about METAS gripes with the rate being less than 0. I have read many of those posts. My curiosity, which I have yet to assuage despite endless internet searches, is why my watch continues to have a positive rate change while the mainsprings unwind. This inquiry did spring, no pun intended, from the fact I noticed the watch was losing time about 0.5-1s per day over a month. When I started monitoring it on the time grapher I noticed as it sat in a stationary position the rate was increasing over time as the mainsprings unwound. I know very little about watch movements, but from what I do know I thought rate would decrease as mainspring potential energy decreases. Based on reading about how the double barrel setup works, my hypothesis is that because the first barrel acts alone at full wind lower torque is put out thus resulting in a lower rate. As the first barrel's energy equals the second and they work in concert a greater amount of energy is available so the rate increases. Here is my time graph data. I have run this twice with similar results. The watch was worn for a day. Then taken off the wrist and placed dial up. It sat stationary for 53 hours. I then hand wound it and checked the rate again.

Aug 03 4:00 pm -1.4 s/d
7:00 pm -1.0 s/d
Aug 04 9:00 am 0.6 s/d
6:30 pm 1.3 s/d
Aug 05 8:30 am 2.4 s/d
9:00 pm 3.7 s/d

Full manual wind after 9:00 pm rate dropped to -1.1 s/d.

Thoughts? I assume all Omega double barrel coaxial movements exhibit this behavior so it must be a feature of the design.

Dan S · Aug 6, 2020

My understanding is that there's no hard and fast rule about how a watch will deviate from isochronism. Some will get faster and some slower, depending on the details of the mechanism and how it has been adjusted.

tritto · Aug 6, 2020

Think about it this way - as there is less power imparted from the mainspring through the gear train to the pallet fork and on to the balance, the amplitude of the balance decreases and therefore the period between the balance swinging back and forth decreases. Thus the rate increases.

Archer · Aug 7, 2020

tritto
Think about it this way - as there is less power imparted from the mainspring through the gear train to the pallet fork and on to the balance, the amplitude of the balance decreases and therefore the period between the balance swinging back and forth decreases. Thus the rate increases.

In theory this is correct, in practice there are many things that can affect whether the watch speeds up or slows down as the torque delivered by the mainspring drops. The resistance to rate/frequency change when amplitude changes is called isochronism, and watch companies spend a lot of resources making sure it affects the timekeeping as little as possible as the torque varies.

jtfreelancer
Based on reading about how the double barrel setup works, my hypothesis is that because the first barrel acts alone at full wind lower torque is put out thus resulting in a lower rate. As the first barrel's energy equals the second and they work in concert a greater amount of energy is available so the rate increases.

Starting from a fully wound state, initially the torque in barrel 2 (auto barrel) is higher, not lower. It's only once that torque drops to meet the level in barrel 1 (manual barrel) that they both operate together, so your theory is backwards.

Cheers, Al

Dan S · Aug 7, 2020

tritto
Think about it this way - as there is less power imparted from the mainspring through the gear train to the pallet fork and on to the balance, the amplitude of the balance decreases and therefore the period between the balance swinging back and forth decreases. Thus the rate increases.

For an ideal harmonic oscillator, the frequency is obviously independent of the amplitude. Clearly, an actual balance deviates from ideality, but why do you assume that the frequency would increase with decreased amplitude? You seem quite certain, and Al says that you're correct, so I'm curious where this intuition came from.

M'Bob · Aug 7, 2020

tritto
Think about it this way - as there is less power imparted from the mainspring through the gear train to the pallet fork and on to the balance, the amplitude of the balance decreases and therefore the period between the balance swinging back and forth decreases. Thus the rate increases.

Dan S
You seem quite certain, and Al says that you're correct, so I'm curious where this intuition came from.

Now you have me curious: I thought his statement was a generally accepted watchmaking principal, all other things being equal. Where in his statement was the Indication that it was intuition, rather than simply providing retained information?

Dan S · Aug 7, 2020

M'Bob
Now you have me curious: I thought his statement was a generally accepted watchmaking principal, all other things being equal. Where in his statement was the Indication that it was intuition, rather than simply providing retained information?

It's not a generally accepted principle to my knowledge. In practice, some watches slow down and some speed up. And as I mentioned, there is no general connection between amplitude and frequency of an oscillating system. A harmonic system has no such connection, and in an anharmonic system the connection will depend on the details. @tritto didn't provide a scientific reason for the coupling of amplitude and frequency. So I'm inferring that he has some intuition about it, and I'm curious where it came from.

janice&fred · Aug 7, 2020

All this technical stuff makes my head hurt. I'm gonna wear me a quartz watch for the rest of the day!

M'Bob · Aug 7, 2020

Dan S
It's not a generally accepted principle to my knowledge.

I speak from no expertise personally. I was told by a watchmaker that, in principle, when the mainspring winds down and the amplitude decreases, that rate would increase. If, in practice, this happens either a majority or minority or the time, I can’t say. But if I heard it, he could have too.

Nobel Prize · Aug 7, 2020

As I read a post this technical and well discussed all I can say is:

What is better Rolex or Omega? And why are Rolex owners fat?

M'Bob · Aug 7, 2020

Nobel Prize
And why are Rolex owners fat?

?

Archer · Aug 7, 2020

Well, the answer is always "it depends"....and in this case it depends on how much the Rolex owner eats. 😉

Deafboy · Aug 7, 2020

In a standard mechanical wristwatch (swiss lever escapement), the escapement error causes the watch to run slower when the amplitude drops. Watch designers (and adjusters) can compensate for this by hairspring design. Ideally, if the compensation is perfect then the watch's rate doesn't vary with amplitude. In the real world the watch may be undercompensated (watch slows down) or overcompensated (watch speeds up). So it depends....

I don't know if the co-axial escapement has a similar escapement error as a swiss lever escapement so your mileage may vary.

M'Bob · Aug 7, 2020

Deafboy
In a standard mechanical wristwatch (swiss lever escapement), the escapement error causes the watch to run slower when the amplitude drops. Watch designers (and adjusters) can compensate for this by hairspring design. Ideally, if the compensation is perfect then the watch's rate doesn't vary with amplitude. In the real world the watch may be undercompensated (watch slows down) or overcompensated (watch speeds up). So it depends....

I don't know if the co-axial escapement has a similar escapement error as a swiss lever escapement so your mileage may vary.

What is “escapement error” and how does it cause the watch to run slower when the amplitude drops?

Archer · Aug 7, 2020

If I had to guess (as I don't keep track) I would say that more watches in my shop gain as the balance amplitude drops, then those that slow when the amplitude drops. But of course where the amplitude starts and where it drops to is important, because there are for example amplitudes where positional variation that might be present in vertical positions essentially goes away. This is a complex system, and not something simple like a pendulum.

This isn't really a subject that can be distilled into a couple of lines or paragraphs. The variables that can affect this are numerous, such as the balance being free sprung or with regulating pins, how those pins are spaced and how they interact with the balance spring as the amplitude drops. If the balance is free sprung what are the damping factors involved (how much drag is there on the balance) and is it a smooth balance, onw with screws that protrude, or are the adjustable masses made in a way that creates little in the way of drag. What is the Q factor of the balance. All these things can play a part in how the timekeeping is affected when amplitude drops, so really any simple statement isn't telling you anywhere near the full story.

I have two watches in the shop right now using the same caliber, and one slows when the amplitude drops, and one gains. Very small things can have a huge impact here.

YY77 · Aug 7, 2020

Nobel Prize
As I read a post this technical and well discussed all I can say is:

What is better Rolex or Omega? And why are Rolex owners fat?

I knew there was a reason why I'm not eligible to buy a Rolex. ::rimshot::

Deafboy · Aug 7, 2020

M'Bob
What is “escapement error” and how does it cause the watch to run slower when the amplitude drops?

Ideally you want to drive the balance wheel assembly exactly at the location where it normally is at rest (equilibrium position). Escapement error occurs when it is driven before or after. There is a loss of rate when it is driven after the swing passes equilibrium position, and a gain when driven before. Because of the mechanics of a swiss lever escapement it is not possible to drive it at the equilibrium position; most of the drive is after. If amplitude of motion would stay constant then the rate of would be constant but because amplitude of motion drops when the mainspring unwinds the effect of the escapement error increases so the watches "loses" when it unwinds.

BTW, this phenomenon is applicable to any oscillator, not just wristwatch balances. Look at the following bode plots of an electronic oscillator. The oscillator only oscillates at its natural frequency when the drive phase is 0 degrees.

a-A-simple-series-resonant-oscillator-schematic-b-Bode-plot-for-a-low-Q-tank.png

M'Bob · Aug 7, 2020

Archer
If I had to guess (as I don't keep track) I would say that more watches in my shop gain as the balance amplitude drops, then those that slow when the amplitude drops

Deafboy
If amplitude of motion would stay constant then the rate of would be constant but because amplitude of motion drops when the mainspring unwinds the effect of the escapement error increases so the watches "loses" when it unwinds.

Interesting.

Archer · Aug 7, 2020

M'Bob
Interesting.

Again, this isn't really a subject that can be distilled into a couple of lines or paragraphs...

jtfreelancer · Aug 7, 2020

As they say, the devil is in the details. Thank you so much for all the great information!