what are possible causes/solutions to reduce/eliminate runout in machining a shaft.
Part is chucked with a tailcenter and steadyrest. I read previous post of the 30... 80 microns of that shaft. Could someone also define the value of a micron.

Something that you can relate to 0.0005" = 12.7 microns. That's 1/2 of a thousanth of an inch.

Not sure you can "eliminate" runout - at least not economically on a mass production basis since that would imply perfection of each part. "Minimizing" runout, is a different thing.

Is "no runout" a real mating part or functional requirement (e.g. a gage)? Or is it an arbitrary dimensional requirement from the part designer not related to a real need. It's amazingly easy to dimension a part such that it is not feasible to produce.