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That looks sad.
I would make a heavy version of some woodworking "cauls" - one with the interior diameter and one with the exterior diameter. I probably go about 7-8 inches wide. Ideally, the one that goes on the inside would be made of steel and pretty stout. The receiving side or the outside could be made of hardwood with steel behind that.
You might be able to find some random object like a brake rotor with the correct diameter for the interior.
Ultimately you're going to do some press work here so you need to plan how you're going to do the squeezing. Maybe a big hydraulic Arbor press. That's pretty common in most machine shop so if you get yourself ready go take a visit to one of those guys.
Instead of doing one squeeze directly on the worst part, I'd work my way in from the side making the correction as I go.
Btw, Since the opposite side of the Ring is going to be in the way you have to figure out how to offset that load on the inside.
Get a block of scrap wood, lay the good side on it and draw a radius. Band saw the radius so it will match the inside curve. That makes a backing block to put inside the ring. Then, put the bent part of the ring on the block and pound away on the outside with a rubber mallet. I bought mine at Harbor freight but you can also find them at home supply stores and hardware stores.
That's kind of a redneck way to do the job but it works. Just take your time and you can get the ring to fit the rim. It may or may not be perfect but it will work.
OP Dustyman Vince has an interesting repair/re-truing issue there that could be a fun challenge. I also see several satisfactory techniques to make the fix although each approach calls for varying/different pre-planing and execution. Above all, promise yourself to be patient and nudge the skirt by a few thousandths at a time.
Now, it's +3:00AM right now and I could draw you a sketch of another fix possibility but I won't - you could work that out on your own but the idea is to use a fulcrum.
Case in point: having recently watched a Scotty Kilmer video of removing a tire from a rim, a thought snuck up on me of using a similar technique of breaking a tire bead but sort of applying the bar force in reverse.
In short, you would make a "core" (similar to as mentioned in a post above) and the well-bolted down leverage bar would rotate around a center point. When the leverage bar is slightly slotted at the center then you could make small 'sliding' adjustments of the bar by increments of a couple-three thousandths at a time that would enable you to re-true the skirt.
Some type of lubrication, applied to the inside rim skirt, would be necessary in particular, to prevent spalling.
At this time of the morning I can't tell if this idea is even worth my time to explain it or should be discarded entirely.
With the right thinking, and lathe swing capacity, the differently same technique could be performed repeatedly, but very very slowly by hand, on a wood or metal lathe.
Edited by - banjoT1 on 04/29/2025 02:40:38
Never having worked on a banjo tone ring, I'm probably as well qualified to comment on this as a lot of the other things I comment on.
Could the outside ^^ caul be shimmed at the ends to allow the ring to go out a hair farther at the middle part? Would C or bar clamps [pull] be worth considering instead of block/hammer [push]?