I use my ER25 collet chuck quite regularly, generally because it's more accurate than the three jaw chuck. It's a morse taper fit in the lathe spindle and consequently has a very short capacity - you can't fit more than about 50 mm into the collet holder before the work bottoms out.
Therefore, I thought I'd buy a flange mounted collet holder which would allow me to pass the workpiece right into the lathe spindle. You can buy a lot of stuff online, usually made in China, for little money these days and to be honest that's what's enabled me to develop my machining skills without breaking the bank. However sometimes these things are not quite the quality you would want.
Here's a little video. Look at the dial test indicator needle waving around all over the place:
The whole collet retaining assembly has a 0.4 - 0.5 mm runout compared to the spindle locating feature on the back.
To fix this little problem I initially removed the collet nut. The first step was to rebore the 16° cone that receives the collet; that helped a little bit but didn't give me the accuracy that I was looking for.
The cone in the faceplate is mirrored by another cone in the nut. The collet itself is suspended effectively between these two cones centralising the collet to the lathe, so the concentricity of the nut becomes critical - and was eccentric by something like 0.5 mm. I'd have to recut the thread and hope it would retain enough strength.
I used the Little Machine Shop gear calculator to set up the lathe gear train and set about cutting the thread. The first attempt didn't make enough difference - I still had something like 0.25 mm run-out.
I changed tools and turned the outside diameter such that it was concentric, taking the minimum amount off, and recut the thread again.
By the time I'd finished I had taken 0.5 mm out of the thread diameter, biased to one side as I expected. Another test showed it could be improved a bit more, and I removed another 0.05 mm to get this:
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