Skip to main content
SpringerLink
Log in

Effect of localized faults on chaotic vibration of rolling element bearings

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper investigates the effect of localized faults on the chaotic vibration of rolling element bearings. The presence of chaotic behavior is demonstrated using experimental vibration data. A nonlinear mathematical model is developed that captures bearing dynamics. The numerical simulations of the model agree with the experimental evidence and provide insight into the bearings chaotic response in a wide range of rotational speeds. The bearing chaotic behavior is quantified using the Lyapunov exponent and correlation dimension. It is further shown that these measures can be exploited in detecting bearing failure.

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.

Similar content being viewed by others

Abbreviations

δ i , δ(θ i ):

Deformation of ith rolling element

θ i :

Angular position of ith rolling element

N :

Number of rolling elements

E :

Elastic module

ν :

Poisson ratio

Q :

Compressive force in Hertzian deformation

Γ :

Hertzian deformation constant

D b :

Ball diameter

D m :

Pitch diameter

r i , r o :

Inner/outer race groove radius

R i , R o :

Inner/outer race radius

k c :

Coefficient of equivalent nonlinear stiffness

e :

Internal clearance

l c :

Length of roller

r c :

Radius of roller edge

τ :

Time delay

ε :

Scale of covering elements

dg :

Correlation dimension

N d :

Number of digitized data

C d :

Average fraction of points

α :

Vector spacing

ω r , f r :

Shaft rotational speed, frequency

Q x , Q y :

External load

m :

Mass of rotating components

c :

Internal damping of bearing

References

  1. Meyer, L.D., Ahlgren, F.F., Weichbrodt, B.: An analytical model for ball bearing vibrations to predict vibration response to distributed defects. J. Mech. Des. 102, 205–210 (1980)

    Google Scholar 

  2. Sunnersjö, C.S.: Varying compliance vibration of rolling bearing. J. Sound Vib. 58(3), 363–373 (1978)

    Article  Google Scholar 

  3. Mevel, B., Guyader, J.L.: Routes to chaos in ball bearings. J. Sound Vib. 162(3), 471–487 (1993)

    Article  MATH  Google Scholar 

  4. Harsha, S.P., Kankar, P.K.: Stability analysis of a rotor bearing system due to surface waviness and number of balls. J. Mech. Sci. 46, 1057–1081 (2004)

    Article  MATH  Google Scholar 

  5. Golnaraghi, M.F., Lin, D.C., Fromme, P.: Gear damage detection using chaotic dynamics techniques: a preliminary study. In: Proc. of the 1995 ASME Design Engineering Technical Conferences, Symposium on Time-Varying Systems and Structures, Boston MA, DE-vol. 84-1, vol. 3, Part A, pp. 121–127 (1995)

  6. Logan, D., Mathew, J.: Using the correlation dimension for vibration fault diagnosis of rolling element bearings, I: basic concepts. Mech. Syst. Signal Process. 10(3), 241–250 (1996)

    Article  Google Scholar 

  7. Choy, F.K., Zhou, J., Braun, M.J., Wang, L.: Vibration monitoring and damage quantification of faulty ball bearings. J. Tribol. 127(4), 776–783 (2005)

    Article  Google Scholar 

  8. Eschmann, P.: Ball and Roller Bearings-Theory, Design, and Application. Willey, New York (1985)

    Google Scholar 

  9. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)

    MATH  MathSciNet  Google Scholar 

  10. Moon, F.C.: Chaotic Vibrations—An Introduction for Applied Scientists and Engineers. Willey, New York (1987)

    MATH  Google Scholar 

  11. Ruelle, D.: Deterministic chaos: the science and fiction. Proc. R. Soc. Lond. A 427, 241–248 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  12. Simm, C.W., Sawley, M.L., Skiff, F., Pochelon, A.: On the analysis of experimental signals for evidence of deterministic of chaos. Helv. Phys. Acta 60, 510–551 (1987)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    S. H. Ghafari, F. Golnaraghi & F. Ismail

Authors
  1. S. H. Ghafari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Golnaraghi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Ismail
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Golnaraghi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghafari, S.H., Golnaraghi, F. & Ismail, F. Effect of localized faults on chaotic vibration of rolling element bearings. Nonlinear Dyn 53, 287–301 (2008). https://doi.org/10.1007/s11071-007-9314-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-007-9314-2

Keywords

Search

Navigation