[gimpo]

With respect of the motor axis?

[deadlykitten]

if you refer to something like a damaged chuck cone, for example, let's say that the tool got stuck, and the collet rotated like crazy inside the cone ... then the cone should be refreshed

take away the part, corect it, put it back
... or
corect directly on the machine

hmm ... do you wish to know if your chuck cone is tilted ? or you are sure that is tilted, and wanna know how to corect it ? i think the 1st one is that you are after

All was going fine (0.004-0.005 mm of runout) until... I picked the ER20 collet for 4mm dia tools.
Bang!
Runout between 0.07 and 0.11 mm!

this shows a problem with a collet; i would check the o4mm collet

if chuck cone was &^&**&(, then you would have not noticed those 4-5um runouts, but bigger values