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Research Papers

Stochastic Dynamics of a Nonlinear Misaligned Rotor System Subject to Random Fluid-Induced Forces

[+] Author and Article Information
Zigang Li

State Key Laboratory for Strength and Vibration,
Xi'an Jiaotong University,
No. 28, Xianning West Road,
Xi'an 710049, Shannxi, China
e-mail: lzghsfy@hotmail.com

Jun Jiang

State Key Laboratory for Strength and Vibration,
Xi'an Jiaotong University,
No. 28, Xianning West Road,
Xi'an 710049, Shannxi, China
e-mail: jun.jiang@mail.xjtu.edu.cn

Zhui Tian

State Key Laboratory for Strength and Vibration,
Xi'an Jiaotong University,
No. 28, Xianning West Road,
Xi'an 710049, Shannxi, China
e-mail: tianzhui@mail.xjtu.edu.cn

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 6, 2015; final manuscript received July 3, 2016; published online September 1, 2016. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 12(1), 011004 (Sep 01, 2016) (13 pages) Paper No: CND-15-1356; doi: 10.1115/1.4034124 History: Received November 06, 2015; Revised July 03, 2016

In this paper, stochastic responses and behaviors of a nonlinear rotor system with the fault of uncertain parallel misalignment and under random fluid-induced forces are investigated. First, the equations of motion of the rotor system are derived by taking into account the nonlinear journal bearings, the unsymmetrical section of the shaft, and the displacement constraint between the two adjacent rotors. Then, the modeling on uncertainties of misalignment and random fluid-induced forces are developed based on the polynomial chaos expansion (PCE) technique, where the misalignment is modeled as a bounded random variable with parameter η distribution and the fluid-induced force as a random variable with standard white noise process. Finally, examples on the stochastic dynamic behaviors of the nonlinear generator-rotor system are studied, and the influences of the uncertainties on the effects of shaft misalignment, the stochastic behaviors near bifurcation point as well as the distribution of the system responses are well demonstrated.

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References

Figures

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Fig. 1

Schematic diagram of the generator rotor system with a parallel misalignment fault

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Fig. 2

Schematic diagram of the motion relationship between the adjacent rotors with the parallel misalignment

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Fig. 3

η-PDF curves with respect to different η

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Fig. 6

Rotor trajectories for the different misalignment

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Fig. 8

Bifurcation diagram of steady-state response for x-direction with V0 = 313 ∼ 316 (m/s) when γv = 0, Δ = 0.10.

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Fig. 9

Time histories at same initial conditions and parameters

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Fig. 10

Statistics of the period-4 and the period-2 motions with the parameter V0 = 313–316 (m/s)

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Fig. 5

Influences of the misalignment on the system responses with γv = 0.010, V0 = 290 m/s, Δ = 0.10

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Fig. 4

Influences of the misalignment on the system responses with γv = 0.010, V0 = 290 m/s, Δ = 0.01

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Fig. 7

Influences of the stochastic fluid-induced forces on the system responses with γv = 0.001, V0 = 290 m/s, Δ = 0.10

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Fig. 11

MAV of steady-state response for x-direction with the parameter f = 0.30–1.45

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Fig. 12

Rotor orbit of EMR and response PDFs at f = 0.5

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Fig. 13

Rotor orbit of EMR and response PDFs at f = 1.0

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Fig. 14

Schematic diagram of the oil film bearing

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