At twelve inches to the foot scale, boiler plates were bent in a machine variously described as a rolling mill or bending rolls, and we can use a small scale version of that. (To forestall the pedants, I know bending rolls come in different types, not all similar to what I shall describe, but let us move quickly on). The photos show that it consists of two pinch rollers and a bending roller. The plate to be bent is trapped between the two pinch rollers. The lower one is turned by the handle and the upper one is forced against the plate using the screws on each side. It is not essential, but it helps to have the two rollers geared together so that the top one cannot slip. If it is not geared, it has to be screwed down harder to ensure that it rotates.
So by turning the handle, the plate is moved through the rollers. The bending roller is set high enough in relation to the other two to cause the plate to bend, and the higher it is set, the sharper the bend. The height of this roller therefore needs to be adjustable, and that is the function of the two lower screws. There is some trial-and-error involved in getting the right bend radius, and in general, it is good practice to start off with the bending roller set fairly low and roll a gentle radius, then gradually increase the height of the bending roller, moving the plate backwards and forwards by turning the pinch rollers, until the radius is tight enough.
For a boiler, or any other cylindrical part, you end up with the plate wrapped around the top roller. It can often be sprung off, but if not, the top roller can be removed in order to release it. You can roll conical as well as circular boilers by setting one end of the bending roller higher than the other. Again, some trial-and-error is required to get the correct bend radius at both ends of the boiler.
The technical stuff
If mechanics is not your thing, skip this paragraph, but I promise to keep it simple. The stiffness of a roller, i.e. its resistance to bending, depends very strongly on its diameter, and less strongly but still importantly on its length. That means the rollers should be as large a diameter and as small a length as possible. If the rollers bend significantly, they will pinch the plate at the edges but not in the middle, and you end up with a barrel shape rather than a true cylinder. It is worse for thick plates than thin plates because so much more force is required to make the bend. My rollers are 12mm diameter. That is a lot smaller than a typical boiler diameter, even for some of the early locos that I make, but I wanted to be able to roll other things like cylinder wrappers as well. And they are about 120mm long, which I decided was long enough for the largest boiler I was likely to make. But of course if you want to roll a boiler for a “Big Boy”, you will need something about twice as long and twice, if not more times, the diameter.
Where do you get bending rolls?
A good question - at one time, Metalsmith sold bending rolls of about the right size for O Gauge, but they seem to have disappeared, and I don't know of any other commercial source at present. I made my own (of course!), based on a design by G. H. Thomas that appeared in Model Engineer back in the 1970s and republished in The Model Engineer's Workshop Manual (TEE Publishing). It can also be downloaded as a PDF here. Thomas's design was too big for my needs, so I scaled it down to about 50% size (without being slavish about the non-critical dimensions, and working with stock size materials).
A few related points worth mentioning
I never anneal the material for this or any other purpose. For most work I use nickel silver that is described as “half hard”, and with the bending rolls I have no trouble getting it into shape. Curved shapes are always more difficult to get right than flat ones, and wherever possible I make parts slightly oversize and trim them back after fitting. A little bit of forethought often makes this possible to do. And surprising as it may sound, you can roll plates that have had rivets impressed. I put it down to two things. The act of pressing the rivet probably work hardens the material locally (have you ever tried to press out a rivet that you put in the wrong place?) so that they do not get crushed by the pinch rollers. And the rivets make the plate less likely to slip in the rollers, so that less pinching force is required anyway.