South Bend lathe 13 in.

And don't discount heat. Straight cuts need ample cooling on the tool bit and the work piece. .003 on three inches could be the result. Roughly speaking each 100 degree rise in temp gives .0005 diameter or length increase per inch of material.

My post below should have stated clearly that the chuck itself AND the chuck mount have nothing to do with taper in the workpiece once you have made cuts on it, asumming the cuts were deep enough to emove material all the way around the bar. It of course does effect how concentric the bar is to the lathe centers before you start to machine the part. Your problem could be in head stock and bed alinement, flimsy mountings, flimsy work piece. or head stock bearings. (I assumed you would have checked them with an idicator and bar). Being as it has just been moved, leveling and footing problems would be my first guess. Messing with the head alignment is something you realy should not attempt, especialy untill all other possibilities are eliminated. The novice can realy screw up a lathe when he starts to "adjust" his head stock alignment. Things change in ways that you dont expect and get screwed up real fast. Also when talking "level" we are not talking "Stanley" level, but "Starett" level. A presision level is needed.