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Research Papers

Nonlinear Dynamics of the Rod-Fastened Jeffcott Rotor

[+] Author and Article Information
Qi Yuan

School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: qyuan@mail.xjtu.edu.cn

Jin Gao

School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: gaojin1985@stu.xjtu.edu.cn

Pu Li

School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: phililplee@stu.xjtu.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 20, 2012; final manuscript received November 28, 2013; published online January 15, 2014. Assoc. Editor: Yukio Ishida.

J. Vib. Acoust 136(2), 021011 (Jan 15, 2014) (10 pages) Paper No: VIB-12-1184; doi: 10.1115/1.4026241 History: Received June 20, 2012; Revised November 28, 2013

Rod-fastened rotors are composed of some disks clamped together by a central tie rod or several tie rods distributed along the circumference. Due to the nonlinear flexural stiffness of the contact interfaces in disks, especially when the contact surfaces are partially separated, the dynamics of the rod-fastened rotors are potentially different from that of the solid rotors. In this paper, the nonlinear flexural stiffness of a rod-fastened Jeffcott rotor is calculated by the finite element method (FEM). Then the harmonic balance method is adopted to analyze the dynamics of the rotor. The flexural stiffness of a rod-fastened Jeffcott rotor dramatically decreased with the increase of the dimensionless load γ1 from 1 to 2.5. Thus, the dynamics of the rotor were nonlinear when it was subjected to a large unbalance force. The response of the rotating rotor contains a predominantly forward 1X component or both forward 1X component and backward 1X components. However, the rotor may settle in a state depending upon both the operating parameters and its history.

Copyright © 2014 by ASME
Topics: Rotors , Stiffness , Disks
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References

Figures

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Fig. 1

Structure of a rod-fastened Jeffcott rotor

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Fig. 2

Flexural stiffness model of a rod-fastened Jeffcott rotor

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Fig. 3

Disk segment with separated zone

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Fig. 4

Platelike deformation in the hub

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Fig. 5

Uniform distribution of the tie rods

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Fig. 6

Rotating and inertial reference system

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Fig. 7

Flow chart for calculating Δr∧

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Fig. 8

Lateral stiffness of the rod-fastened rotor

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Fig. 9

The vibration amplitudes for type A (the amplitudes of ±3X and −2X are equal to zero, ωn is the natural frequency of the rotor before separating, λn = Δr∧n/r∧s, n = ±3, ±2, ±1,0): (a) the vibration amplitude of 1X (ζ = 0.02), and (b) the vibration amplitudes of −1X, 0X, and 2X (e = 50 μm, ζ = 0.02)

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Fig. 10

The test rig and vibration amplitudes of the tested rod-fastened Jeffcott rotor [3]: (a) the test rig, and (b) the vibration amplitudes of the tested rod-fastened Jeffcott rotor

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Fig. 11

Influence of the damping ratio ζ on the stability of the vibration of type A

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Fig. 12

The vibration amplitude for type B: (a) the vibration amplitudes of ±1X (ζ = 0.02), and (b) the vibration amplitudes of ±3X, ±2X, and 0X (e = 50 μm, ζ = 0.02)

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Fig. 13

The stability of the vibration of type B (ζ = 0.02)

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Fig. 14

The orbit of vibration type B and the decrease of the flexural stiffness within one rotating period (e = 50 μm, ω0 = 1.0, and ζ = 0.02), (a) the orbit of vibration type B, and (b) the decrease of the lateral stiffness within one rotating period

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Fig. 15

The modulus of the dynamic stiffness (e = 50 μm, ζ = 0.02)

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Fig. 16

Real and bilinear stiffness models of the rod-fastened rotor

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Fig. 17

Comparison of the vibrations of the real and bilinear stiffness models (e = 100 μm, ζ = 0.02): (a) the vibration amplitudes for type A, and (b) the vibration amplitudes for type B

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Fig. 18

The type A vibration of the bilinear stiffness models (e = 100 μm, ζ = 0.02)

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