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TECHNICAL PAPERS

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

[+] Author and Article Information
Jun Jiang

State Key Laboratory of Mechanical Structural Strength and Vibration, Xi’an Jiaotong University, 710049 Xi’an, Chinajun.jiang@mail.xjtu.edu.cn

Heinz Ulbrich

Institute of Applied Mechanics, Department of Mechanical Engineering, Technical University of Munich, 85748 Garching, Germanyulbrich@amm.mw.tu-muenchen.de

J. Vib. Acoust 127(6), 594-603 (Dec 01, 2004) (10 pages) doi:10.1115/1.1888592 History: Received February 24, 2003; Revised December 01, 2004

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.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

(a) Schematic diagram of the Jeffcott rotor with the stator clearance. (b) The forces applied on the rotor during the backward whirl of the rotor, where the unbalance excitation lags behind the rotor response (a positive phase angle) to produce an unbalance excitation as if the rotor were rotating in the negative (clockwise) direction.

Grahic Jump Location
Figure 2

Rotor orbits, phase angles, and full spectrum at different rotating speeds where ζ=0.05, β=0.10, R0=1.05, and μ=0.15. (a) The synchronous full annular rub; (b) the forward partial rub; (c) the backward partial rub; and (d) dry whip, where it is supposed that the radius of disk Rdisk=20R0. The circle with dashed line represents the stator clearance.

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Figure 3

Campbell diagram to show the mechanism of the onset of dry whip, where ζ=0.05, β=0.10, R0=1.05, and μ=0.15, and the rotating speed, Ω, varies from 0 to 0.80.

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Figure 5

Rotor response characteristics on the plane of Ω-μ, where ζ=0.05, β=0.10, and R0=1.05. Lines LCl and LCr indicate the rotating speed where the linear rotor starts to contact the stator. Curve HP is the stability boundary of the synchronous full annular rub (Refs. 5-6). Curve DW is the boundary of dry whip obtained from 26,27 and “∇” indicates the onset point of dry whip determined by the numerical simulations.

Grahic Jump Location
Figure 6

Rotor response characteristics on the plane of Ω-μ, where ζ=0.05, β=0.04, and R0=1.05. Lines LCl and LCr indicate the rotational speed where the linear rotor starts to contact the stator. Curve HP is the stability boundary of the synchronous full annular rub. Line JP represents the boundary of the existence of the synchronous full annular rub solution (Refs. 5-6). Curve DW is the boundary of dry whip obtained from 26 and “∇” indicates the onset point of dry whip determined by the numerical simulations.

Grahic Jump Location
Figure 4

The best value of ε versus the coefficient of friction obtained through the error and trial program with ζ=0.05 and R0=1.05: there are two cases for β=0.10, with the solid line determined by using 26 and the dashed line by using 27, and one case for β=0.04.

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