The physical reason and the analytical condition for the onset of dry whip in rotor-to-stator contact systems

Dry whip is an instability of rotor-to-stator contact systems and may lead to a catastrophic failure of rotating machinery. The physical reason for the onset of dry whip in rotor/stator systems with imbalance is not yet well understood. This paper explores the development of the rotor response into dry whip of a specific rotor-to-stator contact model and finds that the rotor in resonance at a negative (natural) frequency of the coupled nonlinear rotor/stator system is the physical reason for the onset of dry whip with imbalance. Based on this find, the equations of motion of the rotor/stator system are formulated in a different way that includes the dynamic characteristics in the vicinity of the onset point of dry whip. The onset condition of dry whip with imbalance is then derived by using the multiple scale method. As shown by examples, the analytical onset condition of dry whip agrees well with the numerically simulated one. In addition, the results are consistent with phenomena observed in tests.