The chuck
There are a few things that you can do to the chuck itself to improve its accuracy.
Make sure the jaws are registered to each other. When attaching them, just take the slack out of the thread when you first insert the screws. Then completely close the jaws until they are snug together, and tighten all of the screws. The jaws need to be clean so they will close on each other rather than on all of the finish and gunk that may be on them. It may also be necessary to take a flat file across the side of the face-jaw to remove any machining burrs that were left there by the manufacturer.
The accuracy of the "jaw circle" can change slightly as they are moved from closed to wide open. Look for a "sweet spot" where the chuck is a more accurate circle, and then make all of chucking spigots this diameter. It will be a spot where they wiggle the least and all four feel the same, and that will usually close to where jaw profile forms a true circle. Experience with the chuck will find the diameter where it is the most accurate, if there is one.
Most jaw sets will have a preferred arrangement on the chuck where they will make a truer circle. It may be different from what is marked on them, if they are marked at all. Try different locations for the jaws until the most accurate arrangement is found, and then mark them so you can replace them in the same places.
Maintain a Center Reference
It is always a good idea to have center-point references in both ends of the piece of wood. That will allow the tail-stock center to be used to "center" the wood on the chuck before tightwening the jaws.
Chucking Wet Wood
We can't expect much accuracy from the chuck for holding wet wood. The wood is constantly moving as new surfaces are exposed and start to dry. The chucking spigot or recess itself will be moving and changing shape as it dries and shrinks. Fortunately, wet turning is usually "rough turning". There are no finish dimensions and a high degree of accuracy isn't as important as strength of the grip.
We should be checking the tightness of the chuck on the spigot as we turn away the block of wet wood. If there is a spigot, it is drying and shrinking as time passes, and the wood can become loose in the chuck.
If it is held by a recess, remember that shrinking wood will make the recess smaller, and the chuck tighter. We may have to relieve the grip of the chuck to prevent breakout in the wood block.
Chucking Dry wood
The accuracy of the chuck is important for turning dry wood, because dry wood is turned to the finished form and dimensions. There can still be problems with wood movement because the wood may not be as dry as you thought.
If you are drilling a center hole, collect some of the hot shavings from the drill, and squeeze them in your hand. If there is any feeling of moistness in the warm chips, the wood could be your problem because it is drying and moving as you are turning.
Feel the wall inside of the drilled hole. Heat brings moisture to the surface, and the wood will feel moist if there is any present. This ability to check for moisture inside the wood is a good reason for drilling a center hole before starting the hollowing.
Chucking from the Tail-Stock
An old idea that has been rejuvenated is to mount the chuck on the tail-stock and clamp it to the wood before ratating the piece in the lathe. That insures that the chuck is lined up with the wood before, rather than after, it is reversed in the lathe. Oneway makes an adapter for their tail-center to allow doing this.
Stresses
This not a chuck related problem, but it is often the reason for questions about the accuracy of chucks.
Besides the changing moisture content, wood moves because the internal stresses are relieved as it is turned down to a smaller size and a different shape. These changing stresses cause movement in the wood, and it is always in the direction of no longer being round. This can happen in rough turned forms as well as those being turned from a large block of wood. It is a particular problem with thin turnings and things like boxes where lids must be fitted.
The solution is to stop short of making those final finishing cuts, remove the piece from the lathe, and let it sit for a few days to allow the wood to get used to its new shape.
The Chucking Spigot (or Recess)
The spigot may not be as round as you think it is because of the differential between end and side grain. Check it for "round" with a pair of calipers. I have had better luck with spigots and recesses being round by cutting them with a plunge cut made with a sharp parting tool.
There will always be less chance of wood distortion when the chuck is gripping a spigot or recess that is the same diameter as the "true circle" of the jaws. All chuck jaws have an opening where the shape of the jaw forms a circle. This is the "true circle" of the jaws. At this diameter, the jaws are gripping !00% around the circle of the jaws profile, and less pressure is required to hold the wood. At all other jaw openings the wood in held by either a 4 point contact in the center of each jaw, or by the 8 corners of the jaws. Neither is as accurate nor a strong as holding with 100% jaw contact. The chuck jaws get a better grip with less pressure on the wood, and less distortion of the wood, when they are gripping on a spigot or recess that is the same diameter as the "true circle" of the jaws.
The only exception to this is the Oneway jaws that have a profile that exerts a broad 8-point contact with the wood area over a wide diameter range. These jaws were designed for gripping power. The downside is that they may not be as accurate as the other jaw profiles.
Note that there are several inexpensive chucks being imported whose "true circle" is with the jaws fully closed. They will always be holding the wood with the corners of the jaws.
Position of wood in chuck
You may be getting some differential "squeeze" on the chucking spigot or recess that you turned on the wood because of the differences in compressibility between end and side grain. You will get a more uniform grip if you line up the grain with the line between the chuck jaws, rather across the centers of the opposing jaws. This will give the closest thing that you can get to the same grain orientation in the grip area of all four jaws.
Clean
Always make sure that the gripping area of the jaws are clean. Remove all of the old finish and gunk that gets in them. Soaking the jaws in lacquer thinner can do wonders for chucking accuracy. If the jaws have teeth, they can't get a good grip if they are filled with gunk.
Take the chuck apart and clean the scroll when it gets hard to operate.
Tightening the chuck
Always tighten the jaws on the wood by going around the scroll. Tightening the jaws from just one place pulls all of the clearance between the back of the base-jaws and the scroll in one direction. The best way to insure a concentric grip is to bring the jaws up to snug enough to hold the piece, jam the tail center into it to keep it there, and then rotate to the opposite side and tighten the chuck again. Then go back and tighten again, and then do it again. Do this a couple times. This progressive tightening insures that the jaws are concentric with the scroll, and that all jaws equally compress the wood.
You will have to repeat this tightening several times if you are turning wet wood because the wood in the spigot will relax as it dries.
Do a spin check
Now is the time to do a “spin check” for roundness. In spite of all of this care, there will still times when it will be necessary to take another finish cut on the outside of the piece after you have reversed it. You may have to learn to turn with the opposite hand. And you may have discovered the reason that many turners turn the entire bowl, inside and out, from one setting.
All of this may sound like a lot of fooling around just to chuck a piece of wood, but good work habits are just as fast as bad ones.
It is always possible that you are expecting too much from the chuck. Some chucks are just more accurate than others.
