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Radial and torsional vibration characteristics of a rub rotor

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Abstract

The nonlinear dynamics characteristics of a vertical Jeffcott rotor with radial rub-impact are investigated in this paper. Considering the influence of speed whirling, the radial-torsional coupling model of the rub rotor in polar coordinate system is established. With the improved model, the dynamics characteristics of radial vibration, whirl and torsional vibration are analyzed under no rub, full annual rub and partial rub conditions. The radial harmonic frequency is obtained by the harmonic balance method. The torsional vibration has the harmonic frequency component similar to the radial vibration. The new harmonic frequency is useful to help diagnose the occurrence of rub fault. A reasonable explanation of backward whirl instability is presented in this paper. With development of partial rub, the backward whirl will occur. When the backward whirling frequency is near the natural frequency, the instability is observed. The numerical method gives the quantitative results and reveals the backward whirl instability process of rub.

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Abbreviations

r :

Radial displacement

θ :

Whirling phase angle

ϕ 0 :

Initial imbalance phase angle

ϕ :

Rotational angle

e :

Imbalance eccentricity

k r :

Lateral stiffness of rotor

c r :

Lateral damping coefficient

α :

Torsional phase angle

Ω :

Rotating speed

μ :

Friction coefficient

m :

Mass of rotor

c α :

Torsional damping coefficient

k α :

Torsional stiffness

k s :

Stator stiffness

δ :

Clearance between rotor and stator

F N :

Normal rub force

F T :

Tangent rub force

ω n :

Natural frequency of non-rub system

ρ :

Non-dimensional radial displacement

ε :

Non-dimensional imbalance eccentricity

v :

Non-dimensional lateral damping coefficient

ω :

Non-dimensional rotating speed

J p :

Moment of inertia

v t :

Non-dimensional torsional damping coefficient

ω t :

Non-dimensional torsional natural frequency

k :

Non-dimensional stator stiffness

f N :

Non-dimensional normal rub force

f T :

Non-dimensional tangent rub force

ω ρ :

Radial vibration feature frequency of rub system

ω ρst :

Onset radial vibration feature frequency of partial rub system

ω ρend :

Onset radial vibration feature frequency of dry friction backward whirl

ω θ :

Whirling frequency of rub system

ω θ0 :

The constant term of ω θ

α 0 :

The constant term of torsional phase angle

θ 0 :

The constant term of whirling phase angle

ρ 0 :

The constant term of non-dimensional radial displacement

ρ ia :

The ith harmonic cosine coefficient of ρ

ρ ib :

The ith harmonic sine coefficient of ρ

θ ia :

The ith harmonic cosine coefficient of θ

θ ib :

The ith harmonic sine coefficient of θ

α ia :

The ith harmonic cosine coefficient of α

α ib :

The ith harmonic sine coefficient of α

s 1 :

The attenuation coefficient

ρ 1 :

The first-order coefficient of ρ

θ ρ :

The phase of the first-order term of ρ

X :

Rotating frequency, 1X means one time of rotating frequency, 1/2X means half of rotating frequency

ω b :

Backward whirling frequency of rub system

ω b0 :

Backward whirling frequency when dry friction backward whirl occurs (backward whirl natural frequency of coupled rubbing system)

ω b1 :

Backward whirling frequency after the occurrence of dry friction backward whirl

Z :

Complex deflection of the rotor

Z 1 :

Solution parts of the self-excited backward whirl motion

Z 2 :

Solution parts of the forced forward whirl motion

σ :

Real part of exponent of the solution part of backward whirling motion

A :

Amplitude of Z 1

B :

Amplitude of Z 2

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Acknowledgements

This research is supported by National Natural Science Foundation of China (Grant No. 51175279), Beijing Natural Science Foundation (Grant No. 3112013) and the Key Lab of Health Maintenance for Mechanical Equipment of Hunan Province in Hunan Science and Technology University (Grant No. KFJJ0903).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, P.R. China

    Wenxiu Lu & Fulei Chu

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  1. Wenxiu Lu
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  2. Fulei Chu
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Correspondence to Wenxiu Lu.

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Lu, W., Chu, F. Radial and torsional vibration characteristics of a rub rotor. Nonlinear Dyn 76, 529–549 (2014). https://doi.org/10.1007/s11071-013-1147-6

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