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Nonlinear Dynamics

, Volume 76, Issue 1, pp 529–549 | Cite as

Radial and torsional vibration characteristics of a rub rotor

  • Wenxiu Lu
  • Fulei Chu
Original Paper

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.

Keywords

Radial-torsional vibration Rotor–stator rub Whirl Fault diagnostics Radial harmonic frequency 

Nomenclature

r

Radial displacement

θ

Whirling phase angle

ϕ0

Initial imbalance phase angle

ϕ

Rotational angle

e

Imbalance eccentricity

kr

Lateral stiffness of rotor

cr

Lateral damping coefficient

α

Torsional phase angle

Ω

Rotating speed

μ

Friction coefficient

m

Mass of rotor

cα

Torsional damping coefficient

kα

Torsional stiffness

ks

Stator stiffness

δ

Clearance between rotor and stator

FN

Normal rub force

FT

Tangent rub force

ωn

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

Jp

Moment of inertia

vt

Non-dimensional torsional damping coefficient

ωt

Non-dimensional torsional natural frequency

k

Non-dimensional stator stiffness

fN

Non-dimensional normal rub force

fT

Non-dimensional tangent rub force

ωρ

Radial vibration feature frequency of rub system

ωρst

Onset radial vibration feature frequency of partial rub system

ωρend

Onset radial vibration feature frequency of dry friction backward whirl

ωθ

Whirling frequency of rub system

ωθ0

The constant term of ω θ

α0

The constant term of torsional phase angle

θ0

The constant term of whirling phase angle

ρ0

The constant term of non-dimensional radial displacement

ρia

The ith harmonic cosine coefficient of ρ

ρib

The ith harmonic sine coefficient of ρ

θia

The ith harmonic cosine coefficient of θ

θib

The ith harmonic sine coefficient of θ

αia

The ith harmonic cosine coefficient of α

αib

The ith harmonic sine coefficient of α

s1

The attenuation coefficient

ρ1

The first-order coefficient of ρ

θρ

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

ωb

Backward whirling frequency of rub system

ωb0

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

ωb1

Backward whirling frequency after the occurrence of dry friction backward whirl

Z

Complex deflection of the rotor

Z1

Solution parts of the self-excited backward whirl motion

Z2

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

Notes

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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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTsinghua UniversityBeijingP.R. China

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