On the Instability of Rotating Shafts Due to Internal Damping

Internal damping in rotating shafts can lead to dynamic instability — the unbounded growth over time of the off-axis displacement of the spinning shaft in whirl. In analyzing this phenomenon, some authors have phrased the instability criterion in terms of energies dissipated through internal and external damping. One such study has claimed that instability ensues when the rate of work done by internal damping equals that done by external damping. This analysis shows that this criterion is wrong and explains why it fails. It also provides a clear picture of how internal forces can act to produce instability by coupling the motion of spin with motion in whirl.