Came back to this watch and have been trying a couple of things. That spring above was a long way out of true in many places and was also conical to some degree so has been badly treated.
I thought this was beyond my ability to recover so, sourced a new balance spring for a 354. I was lucky to get this. Fitted this to the balance and with the regulator right over to slow, the best result I could get was this:
This is very fast and is even more when the regulator is in its neutral position so, the spring is too strong for my balance. Springs are specified with a stiffness (strength) and you choose these to suit the mass of your balance and its radius of gyration. So, out of interest, sizing a spring for a balance goes like this:
Let's say the mass of the balance, m = 0.75 grams
and the
Radius of gyration, k = 9.0 mm = 0.9 cm
Then the balance "
Moment of inertia", I = m.k^2 = 0.75*0.9^2 = 0.608 g.cm^2
I can't do the "squared" in this editor so, I have used ^2 for that. That is a big balance with a diameter of about 20 mm which is far larger than the balance I have here but, the logic is the same. You size the spring for a given train count (19800 in this case) to fit this balance and there's a specific equation for that but, basically, the spring stiffness varies linearly with the balance moment of inertia - that is, if you double the balance moment of inertia, you need to double the spring stiffness.
The situation I have here is that I have a given spring but my balance inertia is too small so, I need to adjust either the balance mass (by adding mass at the balance screws using timing washers) or increase the radius of gyration which I can do temporarily by unscrewing the screws a little. It's clear that adding the washers will also increase the radius of gyration a little as well but, ignoring that effect:
There are 86400 seconds in a day and with the regulator in the middle, I'm about 450 seconds fast which is 450/86400 = 0.52% fast. So, I can increase the mass of the balance by 0.5% which is significant or I can increase the radius of gyration by about 7% (because it's a squared effect).
It's not easy to do the latter in a permanent way but, let's try it as a temporary solution. I loosened all the balance screws by a half a turn and end up with this where it might just be possible to see all the screws are not tight to the wheel. There's a lot of mass in these screws so, it might just increase my balance radius of gyration and so the inertia sufficiently.
Pop this back in and now with the regulator fully slow, I have this:
It's still not enough as the regulator is hard over on slow and leaves me nowhere to go but, it shows that there would be a way forward with this spring. I can get the timing washers out but, I'm not sure I have any small enough and don't really want to add mass to the balance if I don't need to.
So, with some encouragement (from Al) I put this spring back in its container and go back to the original spring. I'm starting with the one on the right and aiming for something close to the one on the left.
First thing I do is try and get the centre closer to where it should be as it's clearly not in the middle of the spiral and get to this:
That's a bit closer and in the range that I would normally be able to correct it - difficult to get all of this right when it's not mounted so, this is an exercise in getting the spring to where I feel it's adjustable and then tweaking it when it's fitted.
Next, that outer coil is hopeless out of plane and looks like this:
So, I work to get that closer to in plane with the rest of the coils and end up with this:
This is in a range I can tweak on the movement so, I work on the outer coil in the other plane and get the spring to look like this. I also slightly straighten the collet relative to the spring as it was not quite at 90 degrees which you can see above. Still, I don't think the collet is exactly centred as it looks fine left to right but still a bit high vertically - it's hard to judge this so, I'll solve that when I put it in the cock and can use the features of the cock to help me.
I still don't have perfect concentricity of every coil but, it's workable with and I can put it on the cock and see how it lines up. Again, there's a bit of tweaking to get to this but, it's now close to lining up with the jewel and it's between the regulator pin and boot.
I give it a few more tweaks in the centre and especially in the outer coil where I'm trying to get it centred between the regulator pin and boot for the regulator range of movement which goes right down to the lower of the picture and a bit higher than where it is. Then it's mounted on the balance and put back into the cock and everything back into the movement. Now, my result with the regulator in the middle of its range (not at it's slowest point) is this
This is fine but, over six positions, I have a 50 second variation which is too much for me. That's not an issue as I can work on it now to solve that as it's back to the range I would usually deal with. There is still a little "coning" of the spring but it works well in all positions.
Overall, it's not bad but, I could do better. It's just a case of deciding where to stop and for this movement, apart from reducing the delta, I probably won't do anything else. It's quite intense work this as the spring is only about 5 mm in diameter....
Cheers, Chris