Just to add a little detail to the process for the less initiated. Not better, but may add some comprehension in doing this quickly.
There is no better chuck for rework and repair than a set true. A 4 jaw will do, but the part shifts around too much while getting it aligned.
I use a dial test indicator but a travel indicator would work. With a ground pin in chuck jaws, indicate on pin OD, and adjust 4 setscrews on chuck periphery, until runout=0 (adjust 1 screw, then adjust screw @180 degrees opposite)
With the indicator set some where between 10 and 12 O-clock on the test piece OD. Find the highest point in the runout. Now sight an imaginary line from the OD of the chuck, through the point that the indicator is touching to the center line of the spindle axis. Observe where the "set true screws" are at in relation to that imaginary line. Loosen the closest one a tad and mental note the indicator needle position. Now rotate the chuck 180 and observe the total difference on the indicator, and tighten this opposite screw now pointing at you 1/2 that reading. REPEAT and rinse until all runout is gone to your satisfaction.
Usually within about 4 tests, you can have it running true at the position of the rod being checked. Keep in mind, you may want perfection, but if the part being trued is not round, split the differences and call it good-nuff. Another fact in truing a chuck. It will only run true for the diameter being gripped. Do not expect other size bars to run true. Slight deformations in the scroll shift each jaw. Abused chucks are worse for this, but even new chucks need checking when the grip diameter will be used untouched, but critical to the part function.
Further more, for a new chuck. I wouldn't blindly trust the jaws or the mount as it fits your lathe nose compared to the factory running alignment. At least check it out for your own peace of mind. First indicate in the OD of the chuck body true. Then compare this to a ground test rod gripped in the jaws for runout. Check the rods runout near the jaws and 4-6" out from the jaws. If the runout is greater than .003 and worse as you travel away, I would grind the jaws true to the chuck body centerline as it is mounted. The mount should have an arrow or a zero marker so it is mounted in the same position each time on the spindle nose. If it is missing, add your own at the time the jaws are ground in place on the lathe. If you do not have the capability to grind, beg, buy, borrow or steal a set of soft jaws in the same config as your hard jaws. Mill and turn them to suit. I won't go into all the details of grinding or turning soft jaws. There are plenty of those procedures to peruse as needed.
For 3 jaw secondary operations or reworking of a part that needs to be cleaned up with minimal material removal or mod'ing features. Grip the part in the chuck and align its face or 2 ends of the bore to set the part true to the spindle centerline first. Using known good surfaces that have the least amount of wear or use selective reasoning of the original machined surface. Say a step or a grove or the end face, flange etc. Once the part is confirmed parallel to the spindle axis, then use the set-true screws to bring the OD or ID on center as detailed above. Again, the idea here is slelecting the best surface alignment reference that everything else on the part needs to be true to.
If all else fails. The best plan to keep a turned part true, is to turn all accessible features BEFORE the part is parted off. Secondary operations for OD work can be completed on another part(like a spud, mandrel or shank) turned to size regardless where the runout of the chuck is at, within reason.
I only use a 7x12, and keep my cuts within the limits of the machine.
