If you want to do the job on your lathe for the sake of a lathe job, here are a few thoughts:
1. cheap screwdrivers can be relied upon to have shanks that are likely NOT of any consistent diameter, and may not even be straight.
2. That being said, we then get into the hardness of the screwdrivers. Before you do anything else, check the hardness of the screwdriver shanks with a file. It is unlikely they will be hardened, but, it never hurts to check hardness
before proceeding. If hardened, then you can try annealing the shanks with a torch. Heat to a dull red heat from the tip back up the shank for as far as you want to machine, and keep the heat on for maybe a minute, then stick into a can
of DRY sand or ashes. Let cool slowly.
3. Using a hacksaw, cut off the tip of the screwdriver and file a chamfer on the end of the shank. Learn the hand "bench" skills that are part and parcel of doing machine shop work.
4. I would make a fixture to hold the screwdriver shanks in the lathe. Sometimes, this type of fixture is called a "cat head". It is a kind of chuck in its own right. I'd get a piece of round stock, say 1 1/4" diameter (or bigger than the
screwdriver handles) x 2" long for the cat head. Face both ends square, length not critical. Centerdrill the second end after you have faced it, doing this in the lathe. Drill a hole down the center of the round stock about 1/16-1/8 larger in
diameter than the screwdriver shank. Countersink or break the corners of the drilled hole so no burr is left.
5. Take the stock out of the lathe and layout and drill for setscrews. You will need four (4) set screws at 90 degrees to each other, maybe 3/8" in from each end. These set screws must be in line at 12:00, 3:00, 6:00 & 9:00 so you have,
in essence, two sets of "chuck jaws" in line with each other.
6. Drill the holes for a 10-32 tap. You will need to look up the tap drill size for 10-32, then tap the (8) holes 10-32. I chose 10-32 as it will bear on the screwdriver shank without interfering with the adjacent setscrew.
7. Get (8) 10-32 x 1/2" set screws and screw them into the holes. Stick the screw driver thru the cat head and run the setscrews in so the front row of screws chucks the screwdriver shank approximately centered in the cathead. Let the back
row barely touch the the shank as you will need some adjustment room. Leave about 1" of screwdriver sticking out of the cathead. Any longer, unsupported, and it will bend when you get to turning it in the lathe.
8. Chuck the cathead and screwdriver in the lathe so the front row of set screws is exposed beyond the front of the chuck jaws. If you are lucky, the back row of set screws will be lined up to clear the chuck jaws and you can reach in with
a long hex key (Allen wrench) to get to them.
9. With the lathe belt slacked and a toolholder in the toolpost upside down and backwards, toolpost screw just finger tight:
-roll the chuck so one jaw is approximately level with the toolholder bottom (which is now the top surface). Mark this jaw with chalk or Sharpie or a piece of tape. It is your "home jaw".
-crank the carriage and toolholder in so the toolholder is about 1/8" from the screwdriver shank.
-roll the chuck by hand thru 360 degrees and note where the screwdriver shank is running closest to the toolholder and furthest from it. Adjust the setscrews in the cathead, moving them about half of what the runout of
the screwdirver shank is.
-keep doing this until the screw driver shank appears to be running true.
-When you have trued the screwdriver shank, run the toolholder in so it just touches the screwdriver shank. Roll the chuck over slowly by hand and see if the screwdriver shank is pushed out from its position.
If it is, you will see a gap 180 degrees opposite that location. Adjust the corresponding setscrews to move the shank about half this amount.
-When you have the screwdriver running as true as you can get it, mark the cathead relative to the chuck and remove it from the lathe. TIGHTEN the back row of setscrews AFTER you have tightened the front row, and only get them
snug to avoid cocking the screwdriver in the cathead.
-Put the cathead back in the lathe, orienting your marks on the cathead and chuck. Tighten the chuck.
If you want to make yourself crazy, put a dial indicator on the screw driver shank. Chances are a runout check or straightness check will send the indicator needle into orbit. For what you are trying to do with a cheap screwdriver,
using your eyes and simple adjustments are about all you can do to get things running relatively true.
-Turn your marlin spike or awl. Use your compound rest and a properly ground toolbit. Very light cuts, toolbit must be set exactly on center of the work or it will grab and climb and bend.
-After you play with the toolbit, you will probably say a few choice things and take a file and emery cloth to the spinning screwdriver shank.
-Other method: make a bushing out of round stock, as above, but drill for a snug fit on the screwdriver shank. Take a hacksaw and slit the bushing lengthwise so it has a slit from the outer circumference into the hole on one side only. This allows the bushing to spring. You have now made a collet of sorts. Stick the screwdriver in it, chuck it in the lathe so the saw slot is between two chuck jaws. Tighten the chuck and start the lathe. You will see the shank of the screw driver wobbling like a dog's hind leg, and wonder why you ever undertook this project. Turn an awl point and finish with a file and emery cloth as it will likely need some blending due to runout and dogleg in the screwdriver shank.
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