mapping mainspring torque and fusees

[JGrainger]

Hello,

It feels a bit like I've been doing a bit of work on fusee watches lately, it can get the mind wondering about the modern problems for vintage fusee rates of spiral, and the theoretical optimum for modern springs.

I wondered if anyone has measured the torque amount and curve for a as-close-to-new-as-possible blued steel spring, and also for a modern unbreakable mainspring?  A couple of things come to mind, such as being able to produce a new fusee cone for a modern spring.. Guessing that any measurements would have to apply to a specific spring and barrel combination which really suits batch or mass production requirements - but that doesn't put me off.. Is there a good device for measuring the torque at such a low strength - weight attached to a pulley wheel?

Additionally, is there a good formula for calculating the length of the path for the chain on the fusee cone at the design stage - perhaps something which takes the rate of decreasing diameter, start diameter, and number of turns.. or would the average diameter in each rotation just be simple and accurate enough?

 

 

[spectre6000]

I'm no rocket surgeon.... but

t = rFsin0 

0 is supposed to be theta, but I can't figure out how to type it...

t = torque

r = radius

F = force

0 (theta) = angle between F and the lever arm

 

There was a video I posted in another thread here recently where the subject was isochronism. I think the model used was a pocket watch with its original mainspring. Lots of representative curves used in the presentation.

I think this is the lecture:

 

Edited June 11, 2020 by spectre6000

[jdm]

1 hour ago, spectre6000 said:

 0 is supposed to be theta, but I can't figure out how to type it...

Simple way, copy from a page that has it, paste here. More sophisticated https://www.codecogs.com/latex/eqneditor.php

[JGrainger]

Thank you, I don't know why that didn't occur to me before, I've got it in books but must have had a brain fart in making the link between engineering and horology

[FLwatchguy73]

20 hours ago, JGrainger said:

Additionally, is there a good formula for calculating the length of the path for the chain on the fusee cone at the design stage - perhaps something which takes the rate of decreasing diameter, start diameter, and number of turns.. or would the average diameter in each rotation just be simple and accurate enough?

Back in the day there was specialized tooling required to manufacture the fusee cones. Those tools are incredibly rare and a usually museum pieces.  Nowadays many cnc mills and lathes can perform these operations, but the engineering needs to be completed ahead of time to get the proper dimensions. There has been a verge fusee manufacturing book floating around on eBay occasionally, but I cant find it naturally. It describes all the principles of a verge escapement and the math needed to build a fusee cone, if memory serves.

Specialized Fusee cone tools below.

[JGrainger]

I did briefly consider trying to build one of the fusee engines but I may be able to do it on my lathe once I've measured the pitch and made a few bits.

Thank you for the heads up on the book, I'll try and find some reference to it's name.

[FLwatchguy73]

9 minutes ago, JGrainger said:

I did briefly consider trying to build one of the fusee engines but I may be able to do it on my lathe once I've measured the pitch and made a few bits.

Thank you for the heads up on the book, I'll try and find some reference to it's name.

I found it online. It's a free download. This is there direct download for it, here.

It's quite long and very detailed. The vernacular is a bit difficult because it was originally written in French.... In the late 1700's!!! but the principles have not changed in all that time.

Edited June 11, 2020 by FLwatchguy73

[JGrainger]

Thank you, that's great. The old books are always interesting and it should be a good read

[JohnR725]

There's another minor problem with this. Properly made modern mainsprings have a back curve. My understanding is the back curve is to equalize the force to give a more constant running as it unwinds. That means your not just dealing with a strength issue you're dealing with the curvature of the mainspring changing things.

Then the principal should still apply you should seek out the books of John Wilding they're not on watchmaking there on clock making.  The reason is a couple of his books tell how to make a  fusee.

Then I have this vague memory that one of my books has the device for measuring mainspring power but conveniently I don't remember which one. But one of the other books does show a chart and suggests that you need a force gauge or a dynamometer Conveniently no pictures provided but there is a curve but it doesn't say what kind of a spring it is.

 

[nickelsilver]

I used to use a manually operated machine for measuring mainspring force, can't find a pic but nowadays there are more compact electronic devices for that.

 

You might notice a trend in some modern ultra high end pieces using fusees. The fusee form is noticeably less conical than the old ones that worked with steel springs. The old fusees all look more or less similar, they figured out a general form that worked most of the time and used that. In a special piece the fusee would be adjusted to the spring; here, a bar with a sliding weight was fixed to the square on the mainspring arbor in lieu of the ratchet and click. The arbor would be turned to the desired pre-tension, then the bar positioned horizontally, and the weight moved to a position that maintained the power in the barrel (a "gravity click"). The fusee would then be wound. If the form was good, the bar/weight would remain in position. If the bar lifted up, the fusee needed to be cut down there. If the bar went down, the fusee was too small there. Obviously this was a tedious process and would have been implemented on only the finest pieces, or when developing a new fusee.

 

In modern times, to make a fusee is fairly simple if you have a screwcutting lathe. The cross slide screw is removed and a tracer attachment is used to determine the conical form. No need for a dedicated machine.

[spectre6000]

If the goal is better isochronism with a modern unbreakable/back curve mainspring by mining the archeological depths of horology, you might be better served with a Geneva stop. The whole point of the metallurgy and geometry of the modern mainsprings is to compensate for torque delivery differences across the winding length of the spring. This obviates the need for a fusée and the Geneva stop for practical purposes, but if you're trying to get super accurate isochronism on top of that, your torque delivery error zones are still at the ends of the spring, and the middle is pretty flat. A Geneva stop removes those error prone regions from play, and is much easier to make. Old school Geneva stops would allow something like 4-5 turns of the barrel, but a modern spring would allow a bit more since the error prone regions are much tighter at the ends.

[nickelsilver]

I agree stopworks are a great way of keeping power pretty even. But the timepiece has to be "globally" designed for them; a typical watch has 6 turns of wind on the barrel to give a power reserve of perhaps 40-44 hours. A typical ratio from barrel to center pinion is 7.5, i.e. 7.5 hours per turn of barrel. The most often seen stopworks do 4 turns, so that gives a relatively small power reserve of 30 hours. Generally in a watch equipped with stopworks the barrel:center pinion ratio will be upped to 9, giving 36 hours- but those are good hours.

Upping the ratio effectively decreases the overall power delivered though. If going with a 5 turn stopwork a thinner and longer spring will be needed to avoid the dead and super charged zones at each end of wind (develop 7 turns of wind).

I worked on a small series of watches where the (very clever) designer used a barrel with a spring that developed 15 turns of wind, and quite unique stopworks that allowed 7.5 turns for a 60 hour reserve. The result was a watch that had a difference of amplitude of 5 to 10 degrees between one click of wind and full wind. Effectively a constant force without resorting to remontoire d'égalité systems or special escapements or fusees.

[JGrainger]

John R, thank you for the suggestion of the John Wilding book, I shall be able to find that.

 

Spectre, Geneva stop work is a nice option but I'd like to eventually do something with a fusee parts movement which could be updated and completed.. I like to start planning some months in advance.

 

Nickelsilver, the method you describe with a weighed bar, you've given me a flashback to a book I've read in the past, will have a search through a couple I have - from memory I think it may have been suggested (in servicing) for setting the barrel tension so that the spring tension is the most even at both extremes of wind when the watch is reassembled.

I don't have a tracer or cnc but hopefully it will be possible to produce a fusee cone my lathe with a thread chasing attachment which fits into a t-slot on the back of the machine. There's a striker plate on the lathe bed which the handle rests on when pulled down to take a cut, there are some examples of a tilting striker plate produced to enable tapered threads, so it should be possible to produce a profile piece for the handle to rest on during the cut.. luckily this is much more likely to succeed with the shallower angle needed for a modern spring - I'm actually in the process of making an indexing plate to produce the missing change gears - so will have a quick play with the idea when I can.

The 7.5 turn watch sounds like a superb execution of the Geneva stop mechanism.

[spectre6000]

4 hours ago, nickelsilver said:

I worked on a small series of watches where the (very clever) designer used a barrel with a spring that developed 15 turns of wind, and quite unique stopworks that allowed 7.5 turns for a 60 hour reserve. The result was a watch that had a difference of amplitude of 5 to 10 degrees between one click of wind and full wind. Effectively a constant force without resorting to remontoire d'égalité systems or special escapements or fusees.

I don't know what the design was (do tell!), but in my mind I was thinking of a gear train between the ratchet wheel and the stop (which is not on the barrel or lid as per a conventional Geneva stop). Sounds like I was at least in the ballpark from that angle.

Mental exercises like this are gold in this pandemic...