The Physical Reason and the Analytical Condition for the Onset of Dry Whip in Rotor-to-Stator Contact Systems

Abstract

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.

The forward and the backward full annular rubbing dynamics of a coupled rotor-casing/foundation system

“…As observed in tests and simulations [6,14], the response of the dry friction backward whirl is generally composed of a backward whirl motion with a negative super-synchronous whirl frequency and a forced forward whirl motion with a synchronous whirl frequency whose amplitude is usually negligible. Accordingly, the solutions of dry friction backward whirl of Eq.…”

“…There are a great number of papers in the literature studying on the rubbing behavior of this model. Various rubbing responses are found through theoretical analyses, numerical simulations and experimental investigations, such as the jump phenomenon [4], the synchronous full annular rubs [5][6][7], the partial rubs in sub-and super-synchronous whirl [8][9][10], the partial rubs in quasi-periodic whirl [11,12], the chaotic motion [13] and dry friction backward whirl [14,15]. The third rotor/stator model takes the stator as an elastically supported rigid ring with mass, and is also widely used in modeling the retainer bearings [16][17][18][19][20].…”

Control Methods Using Cross-Coupling Effects for Suppression of Rotor/Stator Rubbing System

“…the rotor/stator system is a linear system without rubbing, this governing equation has steady-state periodic solution, but the cross-coupling stiffness may induce the instability of the system when the cross-coupling stiffness goes above a critical value. From reference [12], it has been shown that for a rotor system with rubbing, the dry friction at the contact surface can induce the instability of the rotor/stator system when the dry friction exceeds a critical value.…”

“…The schematic of the rotor/stator model studied in this paper [12] is shown in Figure 1. A weightless shaft supported by two ideal bearings has effective transverse stiffness k r and rotates at an angular speed Z.…”

“…It becomes well known that rotor/stator rubbing can induce different kinds of dynamical behaviours, the periodic synchronous full annular rubs [1][2][3][4], sub-and super-harmonic motions [5,6], the quasi-periodic partial rubs [7,8], chaotic responses [9,10], as well as the destructive self-excited dry friction backward whirl [2,11,12].…”