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Technical Brief

Effects of Forward/Backward Whirl Mechanism on Nonlinear Normal Modes of a Rotor/Stator Rubbing System

[+] Author and Article Information
Yanhua Chen

State Key Laboratory for Strength and Vibration,
Xi'an Jiaotong University,
Xi'an 710049, China;
Graduate School at Shenzhen,
Tsinghua University,
Shenzhen 518055, China
e-mail: cyh0623@126.com

Jun Jiang

State Key Laboratory for Strength and Vibration,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: jun.jiang@mail.xjtu.edu.cn

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 29, 2014; final manuscript received April 3, 2015; published online May 20, 2015. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 137(5), 054503 (Oct 01, 2015) (7 pages) Paper No: VIB-14-1408; doi: 10.1115/1.4030347 History: Received October 29, 2014; Revised April 03, 2015; Online May 20, 2015

In this paper, the effects of forward and backward whirl mechanism on the existence and the stability of multiple nonlinear normal modes (NNMs) in a four degree-of-freedom (DOF) rotor/stator rubbing system with cross-coupling stiffness and dry friction are investigated analytically. The NNMs may possess either positive or negative modal frequencies, corresponding, respectively, to the inherent motions of forward or backward whirl, and can be either stable or unstable. The relationship between the NNMs, regarding to their stability, and the forced system responses of the system is of great interest. It is found that a stable NNM corresponds to a forced harmonic response with the same whirl direction and frequency as the NNM, and an unstable NNM may still influence some forced system responses by contributing a frequency component equal to the modal frequency to the response spectrum.

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References

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Figures

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Fig. 1

(a) Schematic plot of the rotor/stator system. (b) Side view of the system to show the forces applied on the rotor during the rubbing condition.

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Fig. 2

Existence regions and stability of NNMs when βsr = 2.0 and βcr = 200.0. (a) The negative modes, NUi, i=1, 2, 3, that are unstable and (b) the positive modes PSi and PUi, i=1, 2, for stable and unstable regimes.

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Fig. 3

Modal frequencies ωn's of the NNMs on plane of κr-μ as shown by Fig. 2. (a) First negative NNM, (b) second and third negative NNMs, and (c) first and second positive NNMs.

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Fig. 4

Existence regions and stability of NNMs when βcr = 200 and κr = 0.2. (a) Negative NNMs with NUi and NS2, i=1, 2, 3, for unstable and stable regimes and (b) first positive NNM with PS1 and PU1 for stable and unstable regimes.

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Fig. 5

Mode shapes of NNMs when βcr = 200, βsr = 2.0, and κr = 0.2, where short (blue online) curve stands for stable NNM and long (red online) curves for unstable one. (a) and (c) for first positive NNM; (b) and (d) for first negative NNM. Panels show the orbits of the rotor (black; blue online) and the stator (gray; green online).

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Fig. 6

Response-1 in case B. Left: orbit of difference between rotor and stator with clearance marked by dashed circle; right: spectrum of forced system responses (dot marked frequencies are listed in Table 1).

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Fig. 7

(a) Response-1 and (b) response-2 in case C. Left: orbit of difference between rotor and stator with clearance marked by dashed circle; right: spectrum of forced system responses (dot marked frequencies are listed in Table 1).

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