I am so glad that I stumbled across this forum. I am dealing with rotordynamics and balancing of large turbines and generators in power plants for over forty years. Last five years I am working hard to resolve the long outstanding quarrel between Bishop and Kellenberger of whether for a proper balancing of eccentric rotors it is necessary to consider "rigid modes" and resolve developed forces in bearings first, in a rotor speed range below the first system "critical", with so called N+2 planes, or not. As a proponent of N+2 methods I have developed an advanced 2N+1 balancing method, but, although I found in literature ample of similar methods, no one so far had explained why that method is more successful, specially when rotors with significant eccentricities are involved. I am finding out that the culprit is in simplified mathematical explanation of some true physical events, and which also exclude some of of those events, which occur in real life on real life flexible rotor constrained in bearings.
The problem with properly interpreting the "phase lag" observed and measured with non-contact sensors, is the result of developed equations of motions based on rotors modeling as a closed systems. A true presentation of physics events of rotating flexible bowed or eccentric rotor can only be done by considering a rotor -bearings system as an open system model, with continuous power input. This does not claim that mathematical approach is wrong, because it derives the solutions applicable in design of rotors and rotating machines, and is valid for rotors with minimum allowable eccentricities, but it acts as a handicap when diagnosing root causes of rotors responses in real life.
How a phase angle is created between reactive centrifugal force developed from torque input "spin" in a "rigid" body mode of the rotor, and elastic deflection (reaction force of rotor "spring") as a "precession in space" of the rotor constrained in bearings, is nowhere explained in literature. I have attempted to explain just that in my paper "Behavior of eccentric rotor passing through the critical speed". I would be grateful to get some feedback on the topic.