Since the critical speeds are excited by the unbalance which is present on the rotor, and as we have shown in Jeffcott rotor, the vibration amplitude is directly proportional to the unbalance, so in all rotors the unbalance has to be reduced to very small amounts. This can be performed with the balancing procedures.
If the rotor can be considered rigid, the actual distribution of inertia forces can be substituted by their resultant force and moment, as shown in figure, where also the further equivalent force system composed of two forces acting in correspondence of the balancing planes is represented. It is obvious that we need two balancing planes in order to balance both the resultant force and the resultant moment. As shown in the Figure it is sufficient to fix on the balancing planes two masses at a fixed radial distance, so that their centrifugal forces are equal and opposite to the force system due to the unbalance.
Rotors can be considered rigid if their maximum operating speed is below their first critical speed at least by a 30%. Most electric motors have rigid rotors, some single stage compressors or pumps and small single stage steam turbines also.