I want to drill a hole accurately in the end of a shaft so that I can clamp a tool in the manner of a collet.
This is a simple job to fit a centre drill to a Morse taper blank but every attempt so far has come out crooked.

Here is a sketch, of course the male bit has a saw cut so that it can compress somewhat as it is screwed into the shaft.

I drilled the hole with the two bits screwed together and mounted in the lathe spindle taper.