A Day in Watch School Part Six - Hairsprings.

Nov 01, 2013,11:31 AM

A Day in Watch School Part 6


by ei8htohms
© 8-29-2003
a raw hairspring

Ok, I've put it off long enough, I think I've finally recovered from the Post Traumatic Stress Syndrome and am ready to talk about hairspringing.

Forget everything I've said before about how important the barrel is, the train wheels, lubrication, the escapement, blah, blah, blah.  The hairspring is the watch.  No kidding.  If your hairspring is not near perfect (or a perfect blend of chaotic and miraculously counteracting errors, don't laugh, it happens), the watch is not gonna keep time.  Sure, sure, it needs a smooth, even flow of power, a poised balanced and all that other stuff (they call it watchmaking I believe), but if that wonderful little spiral wrapped around the heart of the movement is not right, forget about it.

We had been innoculated somewhat to "hairspring induced dementia" in our fourth quarter and had increasingly long wrestling matches with them on an individual basis trying to keep our kit watches runnning in the fifth quarter (hmm, is this a sports metaphor forming?), in the sixth quarter we tackled them with tweezers in both fists.  It was a knock-down drag-out fight of epic proportions and, although it was not a clear victory, I think a mutual respect was established on both sides.  We of course learned to respect (and fear) hairsprings in all their power and glory, but I think a few hairsprings learned to fear us as well.  God knows I left a few of them with a severe limp or a black eye.

The art of vibrating hairsprings involves first and foremost some mysterious mathematics.  Some combination of the mass of the balance and it's radius (the moment of inertia I hear tell) and the frequency of the movement is used to determine the size and elastic couple of the hairspring which are encapsulated and represented by its CGS number.  More specifically, the CGS (K in (N x mm^3)/rad) is equal to M (the elastic couple of the spring in ((N x mm^2)/rad)) times (the quantity) the square of the external diameter of the spring minus the square of the internal diameter of the spring or the diameter of the collet. Of course to use this formula with any success you have to first establish the necessary elastic couple of the hairspring: M (units listed above) is equal to E (the modulus of elasticity of the spring in ((N x mm)/rad) times h (height of spring in mm) times e^3 (where e is the thickness of the spring in mm) (the quantity) divided by 12L (where L in the length of the spring in mm).  Of course to find the elastic couple from a known balance and beat rate, it's necessary to apply the formula: T (the period in seconds) equals 2 times Pi times the square root of (the quantity) I (the moment of inertia of the balance in (kg x m^2)) divided by M (the restoring couple of the hairspring in (N x m)).

Hmm this has gotten a little off track. Let's just say it involves some mysterious mathematics and leave it at that.  This stuff is all very important when designing a balance assembly from scratch for a given movement but, for the practicing watchmaker, it's a little too much information.  Let me not discourage you math whizzes from pursuing this number dance to its many wonderous conclusions, but let me not kid you about how much of the above anyone in our class actually knows how to apply in the real world.

For watchmakers, the most common way to use the CGS of the hairspring (and to find it) is to use a test spring of a known CGS to experimentally establish the CGS needed for the replacement hairspring for a given balance.  Frankly even this is more math than most practicing watchmakers would do.  It's most common to just eyeball the spring and balance and try out the combination to see if it might work (crude, but usually effective).

For our first foray into the fine art of vibrating hairsprings, we were simply given a balance and a hairspring with the appropriate CGS (whew!).  Ok, really we were given several of the aforementioned balances (in two different sizes/frequencies), a slew of hairsprings, some collets, some studs and some brass taper pins.  Although the supply of collets was severely limited (they were pretty beat up looking for the most part), thankfully we had a seemingly never ending supply of hairsprings.  It seems the road to good springing is littered (at least ankle deep) with mangled bits of wire.

At the Collet

Since we're starting out with a hairspring of the appropriate CGS for our balance, the first thing to do is temporarily attach the hairspring to the collet so we can find the initial vibrating point.  We need to have the hairspring attached securely enough so that we can put the collet on the balance and suspend the balance by the hairspring in the vibrating tool but we don't want to make it a particularly permanent atachment because we're going to want to adjust where it is attached in the near future.

A raw hairspring comes with a fairly tight innermost coil and a little straight part at the very middle.  This is a bi-product of the manufacturing process which just happens to look a little like the straight part we're going to need in the innermost coil in order to pin the hairspring to the collet.  One way to go about the initial atachment is to pin the hairspring to the collet.  To do this we need to cut off some of the innermost coil and form a little straight portion that we can slide into the hole in the collet.  Then we can push a taper pin into the hole to hold the hairspring in place and snip off the ends of the taper pin so that they don't interfere with the first coil of the spring.  It's a good idea to do this initial pinning with the smallest first coil possible so that when we repin it later we won't be left with an excessively large first coil (more on this later).

Another method of making the initial attachment (and the one I prefer) is to simply wrap the very tight first coil around the collet.  This will stretch out the first coil enough to make it hold the collet fairly securely, but not so much as to ruin any of the useful portion of the spring.  The trick to this method comes later when we're trying to determine exactly where the active portion of the hairspring leaves the collet (more on this later as well).  Once we've temporarily attached the hairspring to the collet (and slid the collet onto the balance staff), we can hang the combination from the tweezer-like scaffold on the vibrating tool and commence to vibrate the spring.

A hairspring vibrating tool consists of a platform with a reference balance and hairspring, over top of which is a scaffold from which to dangle the balance and hairspring to be vibrated to time.  The whole platform and scaffold can rotate some 90 degrees or so and is held in its rest position be a restoring spring somewhere in the base of the tool.

Once the test balance has been suspended from the scaffold directly over the reference balance, it is arranged so that one of the arms of the test balance is directly in line with one of the arms of the reference balance. Then the whole platform and scaffold can be rotated from its rest position (by means of a lever) and allowed to return (under the restoring force of the hidden spring).  This action creates some motion in both the reference balance and the test balance which continue to vibrate back and forth due to the restoring force of their respective hairsprings.

Now that both balances are vibrating back and forth, the extent to which they are (or are not) in time with each other can be determined by observing the arms of the two balances and seeing how long they remain in synch with each other and/or how long it takes them to return to a synchronized state.  The effective length of the test hairspring can then be made shorter or longer by changing where it is gripped in the "tweezers" and the comparison to the reference can be performed again.  This continues until the two balances vibrate at very nearly the same frequency (we were instructed to aim for approximately 20 seconds of observable synchronization or more), thus determining the initial vibrating point.

Of course getting this far is not as easy as I've made it sound, but I don't want to bore you with the many pitfalls and secret tricks we learned along the way.  I'm sure the rest of this extended dissertation will be adequately excruciating as it is.

So now that we've determined the initial vibrating point (that word "initial" has a sense of foreboding about it, doesn't it?), we cut off the outer portion of the hairspring at a point exactly one coil out from the vibrating point.  This is done so that the initial vibrating point can be spotted easily while still leaving us plenty of hairspring to use for the terminal curve and studding procedures.

At this point we must undo everything that we've done.  Believe it or not, we're going to repin the hairspring at the collet and revibrate the spring.  We do this not because we are masochistic SOB's (or at least not solely because of this), but because we want our hairspring to be poised.

As you might remember from the Watch School article that dealt with poising the balance (Part 5), it is critical for the balance to be in poise (the weight evenly distributed about the axis of rotation) in order for it to keep good time in the vertical positions.  Likewise, the hairspring can also be poised by ensuring that its vibrating point lines up with the point of attachment at the collet.  This means that the active length of the hairspring consists of whole coils, thus being more or less evenly distributed with regards to mass.

There are a variety of different theories on points of attachment and the pursuit of poise of the hairspring is only one of them.  Another approach is to attempt to align the vibrating point approximately 90 degrees (86.5 degrees I believe) from the point of attachment at the collet and in this way ensure a flatter isochronism curve (the graph of the rate against amplitude).  The tradeoffs of positional performance versus isochronism can probably be debated ad infinitum, but most modern watches are pinned at whole coils in my experience.

To poise the hairspring we must first determine the angle between the point of attachment at the collet and the initial vibrating point.  One of the ways to determine the angle is to lay out the hairspring and collet on a protractor-like scale.  By lining up the point of attachment at the collet with the zero angle, the angle to the vibrating point can be read off the scale and used to determine how much of the hairspring must be cut off the innermost coil in order to repin it "in poise".  If you're using the "wrap method" initially, establishing what constitutes the initially point of attachment (to line up with the zero angle on the scale) requires some experience and some guesswork.  Since the hairspring leaves the collet fairly smoothly, deciding at what point it first starts vibrating is not cut and dried.


The formula for determining how much to cut off is:  A (the angle between the two points) plus (the quantity) A over 3 minus 60 degrees equals B (the number of degrees to be cut off from the intial point of attachment).  This allows for 60 degrees of the remaining spring to be tucked into the whole in the collet for pinning.  The thought behind this formula is that a length of spring on the innermost coil is equal to a length of spring on the outermost coil that represents one third of the angular value of the portion at the innermost coil.  This is only approximately true given the general geometry of hairspring coils but it's close enough to allow us to come within 15 degrees or so of pinning the hairspring in poise.

Ok, pinning the hairspring at the collet and then later at the stud requires the utmost precision and care.  Not only is it incredibly easy to ruin the hairspring with a slight slip of the tweezers, but if it is not pinned flat, it'll create a world of troubles for you trying to make it that way.  Also, if you pin it without the right amount of spring in the sharp curve where it enters the first coil (at the collet), it will resist centering vigorously.

It is absolutely critical that the hairspring be perfectly centered and perfectly flat at the collet if you cant to get anything like good performance out of it.  As Henry Hatem (the first year instructor) said to me when he saw us struggling with this aspect, "That first coil is your whole world."  He couldn't have been more right.

Each of us developed our own methods for holding the collet and spring, inserting the taper pin, cutting it to the right length and pushing it in firmly enough to hold the spring.  For a little while I thought that holding the collet in a collet closing tool at precisely the correct height to let the spring lie flat as it enters the hole in the collet could insure a reasonably flat initial pinning.  The problem being that the taper pin itself pushes the hairspring out of flat.  There's really no perfect way to do it so you just have to practice, practice, practice until you can figure out a series of steps that works for you.

So after the spring has been pinned at the collet and made as flat as possible, we must shape the innermost curve to make the hairspring coils centered around the collet.  This is incredibly difficult if the first coil is very tight (because you don't have room to get your tweezers in between the collet and the hairspring) and is also not at all easy if the first coil is very large (because it's hard to see how well centered it is).  The actual size of the first coil is somewhat arbitrary as it is determined by the poising process.


One of the ways to check if the spring is properly centered and flat is to place the balance in the figure 8 calipers and spin it slowly.  From the side, a slight up and down motion of the hairspring will indicate it is out of flat.  From above, a perfectly centered hairspring will have coils that appear more or less stationary as it spins (or at least they will progress very evenly).  One of the joys of this part of the process is that making corrections in the flat usually throws off the centering and vice versa.

At the Stud


Once we're convinced that the spring is perfectly flat and centered, why not let's form a dogleg and terminal curve?  It's not a whole lot of fun but at least it's easier than forming an overcoil.  A little anyway.

After much experimentation, this is how I ultimately ended up forming the dogleg and terminal curve.  With the hairspring off the balance, I picked a spot about 80 degrees or so in from the new vibrating point (on the outermost coil, directly in line with the spot where the hairspring exits the collet thanks to our poising efforts).  I make a nice sharp outward bend here.  Then at some randomly chosen and aesthetically pleasing spot a little ways out on that bend, I make a sharp inward bend.  If I've chosen the location of the two bends properly, the second bend will be approximately 60 degrees from the vibrating point.


Now the exact alignment and shape of the dogleg is a source of some mystery.  I've been told (by those who should definitely know) that the shape and location of the dogleg can play a critical role in improving isochronism and positional performance.  The specifics however are completely unknown to me.  Apparently this analysis is a fairly recent (and probably ongoing) development or else a pretty well-kept secret.  This did not stop me from experimenting a little though.  My one radical experiment (a little on this later) proved to be a complete functional failure.  It properly demonstrated that there is something to the whole dogleg issue, but offered no real basis for further experimentation.

So now that we have our somewhat randomly formed dogleg, we need to form a terminal curve.  The portion of the spring from the second bend of the dogleg out is already curved, but more tightly than we need it to be.  We need it to be curved along a radius that's at least three or four coils larger than it is currently.  The final shape of its sweep will have to be formed on the balance cock in relation to the arc of the regulator pins, but I found it much easier to loosen it up before pinning it to the stud by "stroking" it with some fine tweezers (using the word "fine" here is a little silly, all the tweezers that touch hairsprings are pretty darn "fine").

This stroking/curling is accomplished by grasping the hairspring firmly at the second bend with one pair of tweezers and stroking the length of the hairspring with a second pair turned to the side as one might curl a ribbon with a pair of scissors when wrapping presents.  No kidding, this really wrks pretty well.  If either of the bends of the dogleg or the stroking/curling occurs at anything but an exact right angle to the length of the hairspring, more flattening fun will commence.  In truth, more flattening fun is always either commencing or in varying degrees of needing to commence.  Sigh.

So now that we've got a rough approximation of a dogleg and a rough approximation of a terminal curve, let's attach the hairspring to the balance cock via the stud to see where we're at.  While some people prefer to pin the hairspring to the stud on a studding table, I found it easiest to put the stud in the stud carrier (held with the stud screw) and pin the hairspring in situ.  By doing it this way, any out of upright issues that might exist between the stud and the stud carrier can be accounted for from the get-go.

If the location of the dogleg has been estimated correctly, the hairspring can be pinned to the stud approximately 120 degrees from the dog-leg.  Ideally this will put the vibration point directly between the stud and the dogleg, giving it 60 degrees of freedom on either side for rate adjustment.

As with pinning the hairspring at the collet, it is crucial that it is pinned to the stud at precisely the correct angle to make the coils parallel with the underside of the bridge.  This can and will be adjusted somewhat after the balance has been installed, but if it's not flat to begin with, you'll be creating a lot more headaches down the road than you need to.

I like to do this by screwing the balance cock upside down onto a largish piece of brass.  This gives me something to hold onto while I'm pinning and otherwise manipulating the hairspring.  To pin the hairspring at the stud, I hold the piece of brass vertically and coax the hairspring into hanging vertically from the stud while I push the taper pin in.   It's never as smooth or straight forward of a procedure as it sounds, but with some fussing I could usually manage to get it pretty flat before pushing the taper pin home.  Once the taper pin is snugly in place, you can cut or break off the ends of the taper pin and cut off the excess hairspring as well.  It's best to leave a little bit of extra hairspring sticking out just in case though.  You never know when you might need to repin it.

So now we need to adjust our terminal curve.  The idea here is to make a circular curve between the stud and the dogleg that is exactly concentric with the balance pivot jewels and exactly as far from the center as the curb pins.  When the curb pins are as close to the stud as they can get, the hairspring should be exactly centered between them, and it should stay there regardless of how far towards the dogleg the curb pins are moved.  Oftentimes, in order to get the terminal curve to line up with the regualtor sweep, a tiny little dogleg bend is necessary right at the stud.

I won't try to kid you, the process of making the terminal curve line up with the regulator sweep is excruciating.  Theoretically, an infinite number of tiny bends are necessary to ensure that the terminal curve is perfectly smooth and concentric with the regulator sweep (assuming an act of God has not granted you a perfectly formed terminal curve based on the stroking you did previously).  In practice, I found that making 6 or 8 very small bends was typically enough to get it pretty darn close without visibly distorting the spring from its rounded shape and then a number of smaller bends in between could correct for any small errors that still might be present ("might be present" that's a good one, of course there are still errors!).  Here again, if the bends are not made at precisely a right angle to the length of the hairspring, you'll be throwing it out of flat, much to your chagrin.

Now we simply need to manipulate the two bends of the dogleg to center the collet directly over the balance pivot jewels.  Then we can put the hairspring back on the balance and do it all over again.  Invariably, a perfect looking spring when attached to the balance cock without the balance will still need some further adjustment once the balance is in place.  It's at this juncture that our supreme care in making sure the hairspring is perfectly flat throughout the process pays off.  Trying to correct subtle flatness issues with the balance in place is an exercise in futility for the most part.

Here's one of the fun tricks that I found helped me to get the hairspring perfectly centered on the balance cock.  Once you've basically got the balance and hairspring combination well adjusted, that is, it's as flat centered and true as you can get it by eye, take the balance cock off the movement and turn it upside down and screw it onto the brass plate we used for pinning the hairspring at the stud.  Make sure that the balance cock is perfectly flat on the plate and that the plate is perfectly flat (use a level to be sure) and then observe the balance.  If the hairspring is perfectly centered, it will hold the balance perfectly upright, without leaning in any direction.  This only works on movements with fairly stiff hairsprings (the tiny hairsprings in ladies movements or ultrathins won't hold the balance up no matter how perfectly centered they are), but it can help you to get the hairspring very well centered in those cases.

So then we took an exam on vibrating hairsprings where we had to do this from start to finish in four hours.  The time was not really a huge problem on this test, the problem was getting a proper looking (and performing) hairspring in that time period.  A simple mistake or two early in the process could easily ruin your chances of getting it done in the time allotted.  In fact, most of our class had to take this exam twice before getting a passing grade.

I really love fitting hairsprings.  It's very challenging but also very rewarding and seeing your efforts translating directly into timing performance is most satisfying.  I had a little fun along the way too.

Having heard that a properly formed and correctly positioned dogleg could significantly effect positional performance but not being able to find any reference material that pertained, I decided to experiment a little.  As we were forming our umpteenth hairspring for a Unitas 6497, I made some of the doglegs pretty sharp and some of them pretty loose to see if I could tell the difference in how they behaved.  As you can probably imagine, with such a small sample, no control for the various shapes and fighting all the other student induced errors along the way, I wasn't able to get any feel for how the different shapes were affecting the performance (if at all).  Just to make sure there was some significance to the shape of the dogleg, I made one like this one day.  It performed so miserably as to assure me that the shape of the dogleg is critical, even if I don't yet understand how or why.

Some other fun hairspring projects included vibrating a hairspring for a tiny ladies watch.  It had a 5 1/2 by 6 3/4 ligne A. Schild 1012 movement. It was running miserably and no amount of adjustment, pivot polishing or black magic could seem to get the positional variation closer than about 50 seconds or so.  Finally, in an act of desperation I decided just to vibrate a new hairspring for it (reasoning that the old hairspring was just too mushy to hold adjustment and was sagging into itself in various positions).

Remarkably we had some raw hairsprings that happened to be the right size (or close enough to work anyway) and, after a few days or cursing, I was able to get a positional performance on the order of 20 seconds between positions.  Not stellar performance, but given all the other shortcomings of the movement, I was delighted to say the least.  I think my teacher was a little shocked that my efforts had succeeded at all.  Although not the only one to say it, she was clearly heard to pronounce me insane at some point along the way.

A little later I also got the chance to vibrate a new hairspring for this IWC ultrathin pocket watch.  It's beautiful, blued steel hairspring had some rust on it and, with Curtis Thomson's help finding me a raw replacement spring, I was able to fit a new blued steel hairspring for it.  This also gave me the chance to learn how to form and adjust an overcoil.  It's a lot more straightforward than I might've guessed initially but getting it adjusted to perform well was enormously challenging (now I know why they aren't used too often these days!).

Vibrating a hairspring from scratch is not the kind of thing that most watchmakers will ever do in their lives.  Even if you can find the right spring, it is very time consuming and, outside of a few specialists in restoration work, it's just not done that often.  Learning how to do it has given us a much greater respect for and deeper understanding of hairspring adjustment in general though, and that alone is well worth the effort.  If you know that you have the skill to fit a hairspring from scratch if need be, making a simple tweak here or there to correct a damaged hairspring is not nearly as daunting as it might be otherwise.


For more information about career opportunities in watchmaking, check out the Watch Technology Institute at North Seattle Community College.
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Copyright March 2002 - Mr. John Davis and ThePuristS - all rights reserved


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Comments: view entire thread


Crystal clear explanation ...

 By: nilomis : November 1st, 2013-15:52
John, Your statement " forget everything I've said before about how important the barrel is, the train wheels, lubrication, the escapement, blah, blah, blah. The hairspring is the watch. " is a big eye opener. I always paid much more attention to those it... 

a little tongue-in-cheek...

 By: ei8htohms : November 2nd, 2013-03:12
Thanks Nilo, I meant that to be a little tongue-in-cheek in my effort to capture the extent to which each and every part is critical to the proper functioning of a watch and that each and every part SEEMS to be the absolute most important when you're focu...