I have recently acquired a Sherline lathe, and I am learning how to use
it. I have run into a problem that I sure those of you with more
experience (or practically any experience) can help me solve. I needed
to center a 3/8"-16 threaded hole in a Delrin cylinder.

The first couple of times that I did this, it worked great. I put the
workpiece in a 3 jaw chuck, faced each end, and then used a center drill
in the tailstock to make a small hole. Then I used a 5/16" twist drill
in the tailstock to enlarge the hole, and then used a 3/8"-16 tap. The
first two times that worked well, I was doing this to a cylinder that
was only about 3/4" long.

Then I tried to center a hole in a 3" long cylinder, using the exact
same mechanism--and it didn't work. The hole was way off--about .05"
difference from one side to the other.

Possible sources of difficulty:

1. I know that twist drills are intrinsically less accurate than center
drills. Should I look for a 5/16" center drill to make the pilot hole
for the twist drill? Or should I start with a twist drill the diameter
(or slightly smaller) than the pilot hole of the center drill, and
gradually move up in size?

2. Is it possible that that the 3 jaw chuck can't hold a piece of Delrin
that long without high speed rotation causing it to wiggle slightly
off-center? Is the solution to drill the center drill and/or twist
drill at very low speed?

Clayton E. Cramer