I recently bought a Super Chuck model 14N for a floor drill press. This
chuck has a capacity of 0" to 1/2 ". I have been checking the TIR using
jobber length drill bits in the 1/8" to 1/4" diameter range. I noticed
the TIR seems to depend on how hard I tighten a drill bit in the chuck.
For example, if I tighten it just using my hands without the key, the
TIR is under 0.001, but if I fully tighten it using the chuck key the
TIR climbs up to 0.004 or so. If use a #1 drill+countersink bit instead
of a jobber drill bit, the TIR change is even more dramatic with a
shift from under 0.001" to about 0.008". These measurements are all at
the top end of the bit, just under the chuck jaws. Is this normal
behavior for these chucks, or perhaps I got a lemon?

The point of the ball-bearing chucks is higher gripping capacity on account
of reduced friction in the tightening works. The jaws fit looser than in
precision keyless chucks so there's bound to be more slop. Also the high
gripping capacity makes it easy to spring and permanently damage the jaws by
over-tightening the jaws on a bit that doesn't reach all the way to the back
of the jaws. If your chuck is not new it has probably suffered that abuse.

I'm sure happy with them though and would not use anything else for heavy
drilling.

It should not be a problem with a #1 center drill but the larger
double-ended ones are a problem, as the smooth part of the body doesn't
reach the back of the jaws.

Bob