I guess you should have to better specify your question. However, on the basis of your contributions it looks like that you are an electrical engineer and usually, in this field, there is a distinction between static and dynamic eccentricity. Actually this distinction is meaningful only if the rotor is rigid, i.e. it is rotating far below its first critical speed.
Anyway, for electrical engineers, eccentricity is:
• static, when the position of minimum radial length of the air gap is fixed in the space; in this case the rotor axis coincides with the shaft axis, but does not coincide with the stator axis. So, the rotor is symmetrical with respect to its axis and rotates about this one; moreover, the rotor axis is parallel to the stator axis. Static eccentricity may be due to manufacturing tolerances or bearing wear;
• dynamic, when the position of minimum radial length of the air gap rotates with the rotor; in this case the shaft axis does not coincide with the rotor axis (the rotor does not rotate about its axis). This situation occurs if there is looseness in the bearings so that the centre of the rotor traces an orbit about the axis of the stator bore and could be produced by manufacturing tolerances, by rotor whirl close to a critical speed or by a bending of the shaft.
Considering rigid rotors and different types of electrical machines, current or vibration spectra can be employed to determine also the type (static or dynamic) and the severity of the eccentricity. There is a rich literature about, an overview is given in the the paper here in attachment.
Conference Paper Detection and modelling of rotor eccentricity in electrical ...
Thank you for your interest in my question. Behind the naive question, I have a practical problem as follows. Please consider the following: a 2MVA four-pole 50Hz low-voltage synchronous generator with suspected eccentric-rotor (the rotor is rigid). By applying the SPCSA (split-phase current signature analysis, which is based on simple measurements of internal currents in armature windings with parallel connections) I can assess, say, a 6% of static and 1% of dynamic components on the working machine. Now I'm searching for a method, possibly based on just mechanical measurements (vibrations), to verify the assessment.
A very naive solution can be the accurate amplitude estimation of the rotational frequency component at (fo + k*fr) and (fo + k*fr) from stator current.
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