I've noticed some +/- runout repeatability variations on my 3-jaw chuck too. Its a Bison 6", jaws & scroll in good shape, never abused or crashed or overtightened etc. Always mounted on same marked (lowest runout) D1-4 orientation. Same dowel which is hardened, known circular tolerance. The resultant indicator deviation range is typically 0.001 to 0.0015" runout which is pretty good for 3-jaw. So when I get a rogue reading like 0.003" it stands out for further investigation. Assuming all the obvious things like debris, I find I can usually make it revert to the mean by re-inserting & gradually tightening all the jaws in progressive succession and to the same (hand estimated) torque. Over-gronking or worse yet gronking on one jaw only is not good practice IMO. I know there is some kind of primary or dominant jaw, but I've found equal tightening to be better. Shorter length dowels that don't fully contact the jaws fully might be another discrepancy source. Measuring close or further from jaws is another variable. The dowel could be circular, but is it perfectly straight?
I think there a few subtleties to testing runout that people may not think of as important but may actually may be in the range. IE blaming the chuck, but it could be external factors. I've heard countless times something to effect: I chucked a shiny ground piece of O1 tool steel and.... Hope this isn't stating the obvious but Tool steel in its typical annealed ready-to-machine form is no harder than most other common alloys, so may as well say I chucked a piece of stainless or 4140. The hardness only comes after heat treating. Also, every tool steel bar I've had varies by 0.0005"-0.001" across the axis (non circular) which is actually stated by specs if they can be found. So right off the bat there will be at least this runout to contend with in otherwise perfect jaws. But this eccentric shape will present itself differently to the 3 jaws as a function of shape & orientation. If you rotate it slightly & re-grip, runout will be different again. Insertion: if the jaws are wide open and you 'drop' the bar kind of in between 2 supporting jaws & start scroll tightening, the jaws could be squeezing up the bar OD differently until fully tangent contacted. VS. getting the jaws close to OD & lightly turning the dowel as you tighten. I do this spin thing routinely on drills as I tighten chuck. Its how I discovered the crazy raised stamped marks on the shank affecting grip It probably pays to have some known (hardened) dowel standard for testing, ideally of a few different diameter ranges. Maybe the jaws faces are OK but scroll is worn or distorted in different areas? Not sure what can be done about that but at least you aren't chasing your tail fixing the wrong perceived problem source.
I haven't actually purchased a set of jaws for a chuck yet, but I've heard of people who did & majority of headaches went away assuming that's all it was. May not be the answer but something to compare as baseline cost to alternatives assuming the chuck body, scroll & slide ways are good. I'm a fan of Set-True type chucks where you can tweak the chuck axis relative to spindle axis. Unfortunately the backplate adapters & chucks themselves can add considerable cost. This discussion is related to repeatability issues of typical 3-jaw. Many will advocate getting a collet chuck for precision work. That may be helpful, but maybe not, depends on quality of chuck, collets & same axis orientation issues. And a 5C or ER collet chuck wont do us much good if we need repeatability on parts outside the typical range of collets.
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