I have performed similar by using appropriate hole-saws readily available from the builders'-merchants, with their normal arbor held in the bench-drill, to cut discs and rings with sufficient if not sometimes rather generous turning allowances for finishing.
This does make a quarter-inch hole in the centre which may or may not matter.
However you don't need worry about the arbor thread, nor the pilot-drill, because those are supplied.
You do need to clear the chips frequently, and lubricate the tool well. (Use an old paint- or tooth- brush.)
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For trepanning in the lathe I'd suggest a circular-section tool ground so the top of the cutting edge is on or slightly below the centre line, then a small clearance along each flank.
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If the work-piece is fairly hefty, then if possible I bolt the plate to the faceplate both inside and outside the annulus – the "if possible" is if holes in the central disc are either needed or permissible. I try to use tapped holes and set-screws from behind the face-plate, to minimise projections.so allow minimum tool overhang.
This approach allowed me to machine a thin-walled annular channel about 8" and 7" dias, from half-inch thick hot-rolled steel plate. I'd backed the plate with coloured plastic shims, (more building-site parts) so pretty-coloured swarf indicated starting to break through. That rigid mounting method and very light cuts at the end, allowing the springing to work out, meant a gentle break-through with no fraught tool-snagging or great lumps of steel crashing about. (The work was rotating at roughly 70rpm.)
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Beware – all trepanning / hole-drilling is liable to leave razor-sharp edges, even blades.
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Chain-drilling is something I see as a last resort but have used it a few times. It's best to file or grind down the worst of the teeth this process leaves, to limit the horrible hammering action they give to the tool and lathe.