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.

In this paper the global response characteristics of a piecewise smooth dynamical system with contact, which is specifically used to describe the rotor/stator rubbing systems, is studied analytically. A method to derive the global response characteristics of the model is proposed by studying each piece of the equations corresponding to different phases of the rotor motion, i.e., the phase without rubbing, the phase with rubbing and the phase of self-excited backward whirl. After solving the typical responses in each phase and deriving the corresponding existence boundaries in the parameter space, an overall picture of the global response characteristics of the model is obtained. As is shown, five types of the coexistences of the different rotor responses and deep insights into the interactive effect of parameters on the dynamic behavior of the model are gained. Nomenclature AAmplitude of the synchronous no-rub motion BAmplitude of synchronous full annular rub solution

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