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Looks like a practical solution to me. A couple of thou though? That ain't squat.
I have to confess to a bit of embarrassment giving you advice Canuck, but here goes...You will have a lot of trouble getting the drum to spin with the axle remaining in line by regular chuck mounting.It is possible to get it into a chuck and put a clock on it, but that is not the best way.The real solution is to put the axle in the lathe and put a small centre in each end. The axle can then be placed between centres in the lathe with the drum spinning on its own axle. It will need to be dogged so as to be able to be driven.Needless to say, if you do not do it this way, you will almost certainly have a few thou of run out, and the lever will pulse like buggery.Chuck suggests that a couple of thousand is acceptable, but I'd wager that 1/2" of lever travel equates to something like that amount at the shoes, so conversely, if you are out by 2 thou' the lever will move considerably in use.No bloody good...
Rough Edge is correct, the wheel should be assembled then the drum trued, find an auto repair shop with a brake drum lathe, I have an old Bear unit that I regularly turn motorcycle drums on, even with the tire mounted. DonG