Staff on the staking set...Notice I don't use the staff removing tool with the set...I just use a hollow stump and a centering punch...

Tapped the punch a couple of times in the center of the hub and staff is out..The staff broke away and the small washer is left on the bottom of the balance wheel

Here is what the upper part of the staff and washer looks like when it is out...

I measured the remainder of the staff and the thickness of the hub that was left on the bottom..

Staff on the riveted side..1.35mm
Staff that on the side I pushed out from the bottom..1.26mm
Thickness of hub that was left after grinding was .16mm
I know that this doesn't answer all your questions but this is the method I use for removing a staff..

Gary, Have you used other methods for comparison, does the hub method cause less distortion and require less truing effort ?

For the preservation of the bore and flatness of surrounding material, this seems the best and least stressful, unless you forgot you needed a pattern .

Respectfully, Paul

Gary, how did you measure the diameter of the rivet side with the rivet still present?

How hot does the staff get while you are grinding it?

A good collet and sharp carbide could make quick work of hub with little heat , a cross slide might be better. "Important" to remember not much meat would be in collet.

I'll let thread rest

Paul and Jim,
I will try to answer your questions this morning. First, yes I have tried the two other methods that have been mentioned in the post and this works best for me. It is fast and I get very little distortion in the balance wheel. If I were to say I didn't get any I would not be truthful. I have had some that when I was finished I didn't have to touch. Most though and I am not sure if it is taking the staff out or installing the new one you always have to check them and do a little something to them. I am not sure what you meant about needing a pattern. Jim, you asked about how I measured the riveted end, well I just measured what is in the picture that was left after I removed it. (I measured the mushroom end and the end that I ground down) Maybe it was not real accurate but it was all I had that I could measure. You asked about heat, grinding does produce heat but I take my time and try to produce as little heat as possible to not damage anything..

Paul,
You are right a good sharp graver and you could do the same work on your lathe. I guess I am just lazy because I can grind it at my bench and not have to get up...LOL..I forgot to mention I am old too..

Thanks Gary, Measuring the remainder with the rivet still in place will make it difficult to get an accurate measurement of one sides diameter vs the other. Im not sure if the difference in diameter you mentioned in a previous post is because the staff is tapered in the hole in the balance arms or that there is a flange created during riveting that is over the arms, and that is a little bigger.
The reason I asked about heat is I was wondering if the heat generated could remove some of the hardening of the staff. That would make it much easier to tap out the staff without warping the arms.

Jim,
The heat that is generated from the grinding might have something to do with the temper of the staff making it easier to remove but I can't say for sure..

Thanks to the excellent instructions here I was able to change my balance staff on my 18 size 17 jewel Bunn, she's now running like a top! I'll never be afraid to do this job now, this opens up a whole new spectrum of watches I would be afraid to buy because of a broken staff. Thanks to all who contributed to this thread

I'm definitely going to try Gary's method. I have always been a cut off man as punching can be destructive.
But then they make a tool called a caliper that can fix the misalignment of balance wheels. To each his own. What works for you is what you should stick with.