Skip to main content
SpringerLink
Log in

Nonlinear dynamics of a cracked rotor in a maneuvering aircraft

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The nonlinear dynamics of a cracked rotor system in an aircraft maneuvering with constant velocity or acceleration was investigated. The influence of the aircraft climbing angle on the cracked rotor system response is of particular interest and the results show that the climbing angle can markedly affect the parameter range for bifurcation, for quasiperiodic response and for chaotic response as well as for system stability. Aircraft acceleration is also shown to significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for on-line rotor crack fault diagnosis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

c m :

Mass center of disk

D :

Dimensionless external damping ratio (=2ε/Ω)

e :

Unbalance eccentricity of disk

K:

Stiffness of uncracked rotor

K ν :

Stiffness of cracked rotor in crack direction

ΔK ν :

The largest stiffness change in crack

ΔK :

Stiffness change ratio (=ΔK η/K)

m :

Mass of disk

O 1 :

Center of the line connecting the two bearing centers

O 3 :

Center of disk

r :

Deflection of disk center

r nmax :

Maximum amplitude of per revolution

r v :

Static weight deflection (=mg/K)

t :

Time

U :

Unbalance parameter (=e/r v)

(x, y, z) :

Inertial co-ordinates

x, y, z :

Displacements of the center of the line connecting two bearing centers in coordinates(x, y, z)

x ′nO ,z ′nO :

Dimensionless initial velocity of aircraft before acceleration

x ′n ,z ′n ,x ′'n ,z ′'n :

Dimensionless velocity and acceleration of the aircraft

(x 1,y 1,z 1), (x n,y n,z n):

Deflection and dimensionless deflection of disk center in coordinatesO 1 X 1 Y 1 Z 1(x n=x 1/r v,Yn=y 1/r v,zn=z 1/r v)

\(\bar x_n \) :

Mean value of the displacement inX 1

α:

The obliquity of aircraft, i. e. the angle between the line connecting two bearing centers and the horizontal line

β:

The angle between the crack center line and unbalance direction (crack angle)

ε:

External damping ratio (=c/2mω c)

ϕ 0 :

Initial whirl angle

ϑ:

Rotating angle of co-ordinates (σ, η, ξ)

θ 0 :

Initial unbalance angle

τ:

(=ωt)

τ 1 :

Cycles of rotor

τ r :

(=ω rt)

ϕ:

The angle between crack center line and the line connecting the bearing center and disk center, angle determining degree of opening of crack

ω:

Rotation speed

ω c :

Critical speed of uncracked rotor (\( = \sqrt {{K \mathord{\left/ {\vphantom {K m}} \right. \kern-\nulldelimiterspace} m}} \))

ω f :

Response angular frequency

ω r :

Whirl speed

(σ,η,ξ):

Body fixed rotating co-ordinates

(σ′,η′,ξ′):

Rotating co-ordinates parallel to (σ,η,ξ)

Ω:

Speed ratio (=ω/ωc)

Ωf :

Dimensionless response angular frequency ratio (=ωf/ωc)

·:

d/dt

':

d/dτ

References

  1. Wauer J. On the dynamics of cracked rotors: A literature survey[J].Applied Mechanics Reviews, 1990,43(10):13–17.

    Google Scholar 

  2. Wu M C, Huang S C. Vibration and crack detection of a rotor with speed-dependent bearings[J].International Journal of Mechanical Sciences, 1998,40(6):545–555.

    Article  MATH  Google Scholar 

  3. Kicinski J, Ostachowicz W M. Nonlinear analysis of cracked rotors with multiple supports[J].ASME, Design Engineering Division, 1995,84(3):1283–1292.

    Google Scholar 

  4. Prabhu B S, Sekhar A S. Severity estimation of cracked shaft vibrations within fluid film bearings [J].Tribology Transactions, 1995,38(3):583–588.

    Google Scholar 

  5. Sekhar A S, Prabhu B S. Condition monitoring of cracked rotors through transient response [J].Mechanism & Machine Theory, 1998,33(8):1167–1175.

    Article  MATH  Google Scholar 

  6. Prabhakar S, Sekhar A S. Detection and monitoring of cracks using mechanical impedance of rotorbearing system[J].Journal of the Acoustical Society of America, 2001,110(5):2351–2359.

    Article  Google Scholar 

  7. Ratan S, Baruh H, Rodrigucz J. On-line identification and location of rotor cracks[J].Journal of Sound and Vibraton, 1996,194(1):67–82.

    Article  Google Scholar 

  8. Zheng J B, Mi Z, Meng G. Bifurcation and chaos of a nonlinear cracked rotor[J].International Journal of Bifurcation and Chaos, 1998,8(3):597–607.

    Article  MATH  Google Scholar 

  9. Gasch R. Dynamic behavior of a simple rotor with a cross-sectional crack[A]. In: I Mech E Ed.Proceeding of the Conference on Vibration in Rotating Machinery[C]. London: University of Cambridge, 1976, 123–128.

    Google Scholar 

  10. Meng G, Gasch R. The nonlinear influences of whirl speed on the stability and response of a cracked rotor[J].Journal of Machine Vibration, 1992,4(2):216–230.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiaotong University, 200030, Shanghai, P.R. China

    Lin Fu-sheng Associate Professor, Doctor

  2. Department of Electromechanical Engineering, Wuhan University of Science and Engineering, 430073, Wuhan, P.R. China

    Meng Guang Professor, Doctor

  3. School of Mechanical and Manufacturing Engineering, The University of New South Wales, 2052, Sydney, Australia

    Eric Hahn

Authors
  1. Lin Fu-sheng Associate Professor, Doctor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meng Guang Professor, Doctor
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eric Hahn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Li Li, Original Member of Editorial Committee, AMM

Foundation items: the National “863” Project of China (2002AA412410); the National Natural Science Foundation of China (10325209,50335030)

Biographies: Lin Fu-sheng (1965≈)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fu-sheng, L., Guang, M. & Hahn, E. Nonlinear dynamics of a cracked rotor in a maneuvering aircraft. Appl Math Mech 25, 1139–1150 (2004). https://doi.org/10.1007/BF02439866

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02439866

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation