Critical speed of the shaft of a rotating shaft is the speed at which the shaft starts vibrating violently in transverse direction.
At critical speed amplitude of vibrations will build up continuously and system may break into pieces.
This applies to bots with high speed system elements only. Obviously. And can be ignored. :)
In drum bots, material of the shaft of the drum can be chosen wisely using this understanding.
Cure to this disease is
(1) to provide damping at the ends of the shaft or
(2) to use properly aligned shaft in which the geometric centre, COG of shaft and bearing centre line are in line.
Here is the link of pdf file on how to calculate critical speed of the shaft.
Critical Speed of the shaft
On a side not...Read this
A Practical Review of Rotating Machinery Critical Speeds and Modes
