VERY few 3 jaw chucks will hold anything absolutely concentric, even if very accurately matched to a backplate that has been finish turned and face on the lathe in question.
Expect something of the order of 0.075mm eccentricity for a good one, when new.. The concentricity will vary according to the diameter being held.
You are depending upon:
the accuracy of the scroll location within the chuck body,
the accuracy of pitch the scroll,
and the accuracy of the jaw face relative to the "teeth" that engage the scroll,
not to mention all the clearances.involved
Start adding up clearances, of say 0.012 mm, at each interface, and the tolerances on the dimensions of each part. You should be agreeably surprised at what you have found for concentricity!
(I have only ever seen one 3 jaw that held work truly concentric ).
A chuck that has seen a lot of use / abuse, may well have jaws that are bell mouthed and gripping less well. or accurately.
Bar may well not be truly round. It is not unknown for centreless ground bar to be trilobular, rather than absolutely round. Check some with a DTI when resting in a Vee block
If it has been ground between centres you stand a much better chance.
If you hold the work in a 4 jaw, independent, chuck the eccentricity will depend on the operator; on how much trouble and time they are prepared to devote to bringing the work to run concentric.
Generally, if it is within 0.012 mm near the chuck jaws, I am satisfied.
Also, remember that most of us have hobby, abused ex college, or worn ex Industry lathes, rather than a well cared for toolroom machine.
Howard