Really not a good idea. It *can* be done, and I have done it, using a shaft which is already round, and back before I had a lathe, I took a 1/4" shaft down to about 1/8" (I forget the precise diameter, I was making a capstan for a tape deck which I was building, and it needed to be the right diameter to produce 3-3/4 inches per second. I spent a lot of time with the file and a micrometer checking as I went.
I'll bet that you would have the choice of not progressing very fast at all, or having enough of a drop to give problems. And you would want your support bolted to the motor but easy to adjust.
Assume that it is the full length of the motor housing, plus the visible extension as a worst case.
Not collets for this. You put a dead center (solid) in the headstock taper, with a drive plate (perhaps a faceplate with a bolt sticking out to drive a lathe dog). You put the live center in the tailstock, and support the rotor and shaft between centers. A lathe dog (something which clamps onto the short shaft near the headstock) engages the pin or a slot in the faceplate, so as the lathe spindle turns, it turns the shaft.
You will be doing your machining near the tailstock end, where the live center is supporting the shaft.
Probably run at one of the slower speeds, because the dog and driving bolt will probably unbalance the rotating mass, and your lathe would otherwise be hopping all over the workbench -- or off it. :-)
Then supporting it between centers is the right way to do the job. The OD of the shaft was turned based on those center holes, so supporting with the live center and turning should produce something concentric. It is up to you to stop at the right point for a good fit. And if you are going to be using just a setscrew -- no keyway -- mill a flat on the shaft when you have the diameter right. This is for the setscrew to press upon, so it does not raise burrs on the shaft and prevent the pulley from being removed at a later date.
Oh yes -- while the shaft and rotor are in the lathe, use a file to turn a bevel on the shoulder left by turning down the shaft diameter. This will remove the burr which was left by the machining, and which would likely burr the bearing as you reassembled.
Yes -- but even better is getting another motor based on what you show me later on in this article.
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O.K. But probably the second step would be better -- it would be about half-way along the length of the bore.
From the photos (which of course are not the same as having the object in hand) it looks as though the inside end of the bushing expands to a good percentage of the larger bore. This would mean that it would have to be pushed out by pushing from the small end.
Or perhaps *two* sets. What are the odds that the setscrew is metric?
Ball-end Allen keys are very convenient for some things, but a straight-sided one is easier to use for starting a setscrew in the bottom of a groove.
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That is what key stock is -- square rod in the common key sizes. Likely a little oversized so you can file them down to a precise fit. :-)
Actually -- looking at the photos -- the motor mount slides on two pins which are secured by screws with flapping wings (common China/Taiwan import construction). Those slides need to be cleaned of rust and properly lubricated. And typically, there is a lever on the right side of the drill press -- but I don't see it on this. It normally runs a link to push or pull the motor during belt changes. And I don't see the scew you mention. But the motor does *not* pivot -- the entire mount slides in and out.
Anyway -- you have the motor slid as close to the column as can be done I think, and it is already close to where the edge of the pulley would rub on the belt guard when it is closed.
I hope the bearings are better than some of the external surfaces -- including the rust on the chuck.
You will need to clean off the rust on the column and the motor adjusters, and oil them. Looks like it stood out in the back yard for a few years. :-)
And I note that the spindle is a fixed Jacobs taper on the end (a JT-2), instead of having a Morse taper in the spindle. This limits your ability to use it for some tasks.
Just out of curiosity -- what does the motor nameplate say about the horsepower? And what is the shaft RPM?
Don't! Get a smaller motor -- with a shaft which fits the current pulley. Be prepared to measure the shaft when you go out shopping for a used motor.
Depends on where you are. Medium sized three-phase motors are often available from places which do heating/air-conditioning work, from when they pulled out industrial units to replace them with larger ones.
I sometimes find motors at hamfests. (Think a large electronic flea market). You might be able to find them at flea markets locally.
New York City and environs are really an unknown to me.
Do you have a local Craigslist?
How about a Freecycle?
Well ... if you could make a bushing to fit it to the 5/8" shaft, and then drill and tap for a setscrew, it might be more appropriate to that motor size. But you would need to know the RPM of the motor -- with the larger pulley, the spindle speeds would likely be too high. (And they seldom are slow enough for the size chuck supplied when drilling steel. :-)
Enjoy, DoN.