I made a new arbor, straight shank. I pressed it in with some Loctite after heating the drill chuck body with a heat gun to about 250-300. I used a +.002 interference fit.
Let it cool, and it seems pretty tight.
I put it into the lathe, and put an indicator on the chuck body, and got it to run to within .0005 of perfectly true. Then I center drilled (#3) the arbor end, and put in a live center for support.
Oddly, I couldn't keep the chuck body true when the live center was in place - I was off by .002-.003. I took a few cuts, just to get the arbor CLOSE to concentric with the chuck body.
Any idea what I may be doing wrong? or is introducing a few .001 when using a live center considered normal?
I have enough length on the arbor that I can face it off and try again, but I wanted to get some ideas here first.
-Tom