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Research Papers

Numerical Method and Bifurcation Analysis of Jeffcott Rotor System Supported in Gas Journal Bearings

[+] Author and Article Information
Jiazhong Zhang1

School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, Shaanxi Province, P.R.C.jzzhang@mail.xjtu.edu.cn

Wei Kang

School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, Shaanxi Province, P.R.C.

Yan Liu

Mechatronic Engineering College, Northwestern Polytechnical University, Xi’an 710072, Shaanxi Province, P.R.C.

1

Corresponding author.

J. Comput. Nonlinear Dynam 4(1), 011007 (Nov 12, 2008) (9 pages) doi:10.1115/1.3007973 History: Received August 27, 2007; Revised July 01, 2008; Published November 12, 2008

From the viewpoint of nonlinear dynamics, the stability and bifurcation of the rotor dynamical system supported in gas bearings are investigated. First, the dynamical model of gas bearing-Jeffcott rotor system is given, and the finite element method is used to approach the unsteady Reynolds equation in order to obtain gas film forces. Then, the method for stability analysis of the unbalance response of the rotor system is developed in combination with the Newmark-based direct integral method and Floquet theory. Finally, a numerical example is presented, and the complex behaviors of the nonlinear dynamical system are simulated numerically, including the trajectory of the journal and phase portrait. In particular, the stabilities of the system’s equilibrium position and unbalance responses are studied via the orbit diagram, phase space, Poincaré mapping, bifurcation diagram, and power spectrum. The results show that the numerical method for solving the unsteady Reynolds equation is efficient, and there exist a rich variety of nonlinear phenomena in the system. The half-speed whirl encountered in practice is the result from Hopf bifurcation of equilibrium, and the numerical method presented is available for the stability and bifurcation analysis of the complicated gas film-rotor dynamic system.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of a gas bearing

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Figure 2

Local coordinates in a rectangle element

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Figure 3

Pressure distribution of the gas film

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Figure 4

Model of a Jeffcott rotor

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Figure 5

Trajectory of the rotor system at 12,300rpm

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Figure 6

Phase portrait in the x direction at 12,300rpm

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Figure 7

Time history of the rotor system at 12,300rpm

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Figure 8

Trajectory of the rotor system at 14,500rpm

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Figure 9

Phase portrait in the x direction at 14,500rpm

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Figure 10

Time history of the rotor system at 14,500rpm

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Figure 14

Phase portrait in the x direction at 10,000rpm

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Figure 15

Poincaré section of the rotor system at 10000rpm

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Figure 16

Trajectory of the rotor system at 14,900rpm

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Figure 17

Phase portrait of the rotor system in the x direction at 14,900rpm

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Figure 18

Poincaré section of the rotor system at 14,900rpm

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Figure 20

Phase portrait of the rotor system in the x direction at 23,000rpm

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Figure 21

Poincaré section of the rotor system at 23,000rpm

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Figure 22

Power spectrum of displacement in the x direction at 10,000rpm

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Figure 23

Power spectrum of displacement in the x direction at 14,900rpm

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Figure 24

Power spectrum of displacement in the x direction at 23,000rpm

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Figure 25

Bifurcation diagram in the x direction

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Figure 11

Power spectrum of displacement in the x direction at 14,500rpm

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Figure 12

Bifurcation diagram of displacement in the x direction

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Figure 13

Trajectory of the rotor system at 10,000rpm

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Figure 19

Trajectory of the rotor system at 23,000rpm

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