Torsional Vibration of Rotor-Shaft

[chinmay]

I have developed a mathematical model to study the dynamic behavior of rotor (with 6 dof). It is assumed that rotor is rigidly mounted at the mid point of shaft, and both end of the shaft is attached to ball bearing.

I have developed the FE model for it too, and the frequencies in X, Y, Theta, Phi (in plane translation & rotation) is same in analytical & FE model. However for Psi (out of plane rotation),I assumed that the restoring moment will be provided by the torsional stiffness of shaft (G.J/L) and got a frequency; but in FE model I got a rigid body mode for this dof.

My doubt is, for a shaft whose one end is attached to a bearing, will there be any torsion / or in other words will it provide any restoring moment ?

 

[JBA]

Unless there is any significant weight associated with the inside races of the end bearings, the shaft has a very long length, or there is an additional mass or restraint connected to one or both ends of the shaft beyond the bearings, it is hard to see how any there would be any measurable torsional restoring moment from the shaft ends.

 

[Dr.D]

A rigid body mode is associated with a zero natural frequency. The system you describe is a free-free system from a torsional perspective; it is able to displace angularly without any strain energy. This is what gives rise to the zero natural frequency and the rigid displacement. The system is strain free in this mode.

 

[Dr.D]

Just to clarify, the zero natural frequency in rotation results in gross rigid body motion with no restoring moment at all. This is common to most motor driven machinery systems that rotate endlessly.