Selecting components to assemble a balance complete

[Shane]

I have a movement that, when acquired, did not have a balance cock or balance.  I found a replacement cock among my many piles of miscellany and would now like to start searching them for a balance wheel and hair spring.  Most of the wheels I have are used and require repivoting, truing, poising or all three.  I have a new replacement staff on order and its diameter will yield the first number to start my search.  Some of these wheels have salvageable hair springs, some do not but I am sure that I have plenty to work with (or at least keep me busy).

My question is can anyone point me at an article/page or book that discusses the relevant points of mass, diameter, beat rate, spring tension, ect and how they interact to form a working balance, of the correct beat.   Vibrating it when assembled should be the least of my problems.

Yes, purchasing a balance complete would be easier, faster and if I assigned a reasonable value to my time, also cheaper.

My goal is the process not a working movement.  I welcome any and all questions or comments.

Thanks in advance.

Shane

Edited July 20, 2022 by Shane

[JohnR725]

you might try George Daniel's book on watchmaking although I'm not sure it's going to have enough theory for you. You want some of the vintage books on watch design watchmaking. For instance there's a link below there is a book the first one that popped up where I did a search then you want to search there for a variety of figure out the keywords as a bunch of vintage books that might find helpful

then you didn't give enough specifications. Over coil are flat hairspring for instance? Flat hairspring is typically vibrated to that specific balance wheel. We've had this discussion before on the group there are basically no more raw hairsprings so finding a hairspring to vibrate for your balance wheel will be challenging. Over a coil hairspring is easier as they were meant to be replaceable. But that manger balance wheel has to have screws on it because you'll have to match the balance wheel to the hairspring.

Oh then there's the other minor thing for the hairspring just as a reminder in addition to timekeeping purposes the energy of the hairspring is used to unlock the escapement so they hairspring does have some other properties they have to be right they can't just visually look right

https://archive.org/details/treatiseonclock00reidgoog

 

 

 

 

[nickelsilver]

I don't know of a resource that gives all the math to determine hairspring CGS to a given balance except for perhaps Theorie Generale de L'Horlogerie by Leopold Defossez, which I think is only found in French and rather expensive. The list below I've found is pretty good for getting in the ballpark to size a spring. If you get a spring of a specific CGS that's close, you can calculate the actual spring needed with the formula

 

K=K' (D/D')²

where

K= CGS to find

K'=CGS of test spring

D= diameter of spring wanted

D'= diameter of test spring at vibration point

[dadistic]

Here is my rough translation from French of the paper that explains what the C.G.S. number is.  As far as I know, it's the only English translation that exits.

My math is not strong, so I may have mangled some equations in my attempt at translation, if you find something that not right please let me know and I'll fix it.

Cheers!

1934AFChr___4__233DTranslated.pdf 

[praezis]

Happy owners of the  electronic hairspring box for Luthys can use this tool in its evaluating program.
Determines the CGS number of hairsprings (same what nickelsilver already described) and determines the moment of inertia of a balance wheel.

The book that I know containing the theory is in German, sorry.

Frank

[TimeWerks]

Hi Shane, 

When it comes to the theory and formulas, the book that I found that provides some of this  is "The Theory of Horology".  Chapter 7 in particular.  AWCI has English copies of it on hand since it was out of stock for some time, but they are not cheap. 

Mathematical formula for a balance and hair spring

T = 2 * pi * sqr root ( I / C)

T = period, I = moment of inertia of balance around axis, C = spring stiffness.

It goes on to provide formulas for hairspring CGS (same formula NickleSilver mentioned), stiffness,  proportionality factor, variation of length, terminal curve ...

This link has some information that might be useful as well (where he suggests getting a test spring with a known CGS and experimenting with it) https://www.watchprozine.com/watchtech/a-day-in-watch-school-part-six-hairsprings-/6112423/1223/

Cheers

Terry

[JohnR725]

Another way to do this would be to look at the old school rule of thumb on how to make a watch. This way it save yourself a lot of math physics and possibly computer simulation which I'm sure exist today. Don't know which book I read this in but basically repeated diameter for your watch which you already have. The mainspring barrel is supposed to be as big as possible to fit in one half of that diameter and still mesh with the center wheel pinion. The balance wheel is supposed to fit into the rim of the mainspring barrel. Seeing as how you already have a watch you have a barrel and you know how much space your balance wheel supposed to fit in that will get you really close to the diameter the balance.

Then because you going to pick and choose from an existing balance wheel that's going to narrow things down considerably. Versus if you were making a custom balance wheel but you can have anything you want.

Then the hairspring is relatively easy will need some math but not as much as you're probably thinking. If you have an existing balance wheel with no hairspring no problem just grab the hairspring and vibrate. Yes ill be totally wrong but we don't care is a formula I'm sure someone will come along and supply it to you shortly. Once you have a hairspring vibrated that's wrong you can do the math the calculated what you're supposed to have. Then with that new hairspring you can vibrate it to your balance wheel.

 

 

 

[Shane]

Thanks guys.  This has given me a significant amount of information to go through.  If anything else comes to mind, I would appreciate you dropping it off here or PM me.

Thanks again.

Shane

[praezis]

13 hours ago, TimeWerks said:

Mathematical formula for a balance and hair spring

T = 2 * pi * sqr root ( I / C)

T = period, I = moment of inertia of balance around axis, C = spring stiffness.

You may substitute flexural stiffness C by the often available CGS of the hairspring:

  C = CGS / (D^2 - d^2)
D and d according my picture above

Frank

[KarlvonKoln]

20 hours ago, praezis said:

The book that I know containing the theory is in German, sorry.

Frank

 

May I ask for the name of the German book?  I was curious about it.

[Nucejoe]

Some previous discussions on CGS.

https://www.watchrepairtalk.com/topic/20376-sourcing-hairspring/page/2/#

And 

https://www.watchrepairtalk.com/topic/12492-hairspring-cgs-specifications/?do=findComment&comment=111751

 Notice CGS N is by convention defined as springness per unit area. 

Regds 

Joe

[praezis]

2 hours ago, KarlvonKoln said:

May I ask for the name of the German book?  I was curious about it

Sure. it is "Lexikon der Uhrentechnik" by Prof. Glaser.

Horological science very very compressed.

Frank