Skip to main content
SpringerLink
Log in

A dynamic model of ball bearing for simulating localized defects on outer race using cubic hermite spline

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

In this paper a dynamic model is presented for predicting the vibration behavior of a ball bearing under the influence of localized defects on the outer race. The calculation of contact force is based on Hertzian contact deformation theory. The pulse generated by the ball striking the defect on outer race is modeled by using the blending functions of the cubic hermite spline. The effect of change in the angular position of the defect, size of the defect on outer race, multiple defects on outer race and the variation of load on the vibration amplitude is predicted by this model. A computer program in MATLAB is developed and the governing equation of motion is solved by Euler’s method. The numerical results are presented as a function of variation of the geometry of the outer race due to the impact at the defect and normal race contact w.r.t. time and the conclusion about the health of the bearing is determined by the spectral analysis. To validate the results, experimentation has also been performed.

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

References

  1. C. S. Sunnersjo, Varying compliance vibrations of rolling bearings, Journal of Sound and Vibration, 58 (3) (1978) 363–373.

    Article  Google Scholar 

  2. T. A. Harris, Rolling bearing analysis, Third Ed. John Wiley and Sons, New York, USA (2001).

    Google Scholar 

  3. T. S. Nisbet and G. W. Mullett, Rolling bearings in service: Interpretation of types of damage, Hutchinson (1978).

    Google Scholar 

  4. N. Tandon and A. Choudhury, A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings, Tribology International, 32 (1999) 469–480.

    Article  Google Scholar 

  5. P. D. McFadden and J. D. Smith, Model for the vibration produced by a single point defect in a rolling element bearing, Journal of Sound and Vibration, 96 (1) (1984) 69–82.

    Article  Google Scholar 

  6. P. D. McFadden and J. D. Smith, Model for the vibration produced by multiple point defects in a rolling element bearing, Journal of Sound and Vibration, 98 (2) (1985) 263–73.

    Article  Google Scholar 

  7. Y. T. Su and S. J. Lin, On initial fault detection of a tapered roller bearing: frequency domain analysis, Journal of Sound and Vibration, 155 (1) (1992) 75–84.

    Article  MATH  Google Scholar 

  8. N. Tandon and A. Choudhury, An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect, Journal of Sound and Vibration, 205 (3) (1997) 275–92.

    Article  Google Scholar 

  9. N. Sawalhi and R. B. Randall, Simulating gear and bearing interactions in presence of faults: Part I. The combined gear bearing dynamic model and the simulation of localized bearing faults, Mech. Syst. Signal Process, 22 (2008) 1924–1951.

    Article  Google Scholar 

  10. V. N. Patel, N. Tandon and R. K. Pandey, A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races, Journal of Tribology, 132 (2010) 041101-1-10.

    Google Scholar 

  11. M. S. Patil, Jose Mathew, P. K. Rajendrakumar and Sandeep Desai, A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing, International Journal of Mechanical Sciences, 52 (2010) 1193–1201.

    Article  Google Scholar 

  12. S. P. Harsha, K. Sandeep1 and R. Prakash, Non-linear dynamic behaviors of rolling element bearings due to surface waviness, Journal of Sound and Vibration, 272 (2004) 557–580.

    Article  Google Scholar 

  13. R. K. Purohit and K. Purohit, Dynamic analysis of ball bearings with effect of preload and number of balls Int. Journal of Applied Mechanics and Engineering, 11 (1) (2006) 77–91.

    MATH  Google Scholar 

  14. Yi Guo and Robert G. Parker, Stiffness matrix calculation of rolling element bearings using a finite element/contact mechanics model, Mechanism and Machine Theory, 51 (2012) 32–45.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, PVG’s COET, Pune, 411009, India

    P. G. Kulkarni

  2. College of Engineering, University of Pune, Pune, 411005, India

    A. D. Sahasrabudhe

Authors
  1. P. G. Kulkarni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. D. Sahasrabudhe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. G. Kulkarni.

Additional information

Recommended by Associate Editor Cheolung Cheong

A. D. Sahasrabudhe did his Bachelor of Engineering Degree in Mechanical Engineering with a Gold Medal from Karnataka University followed by Master of Engineering and Ph.D. from Indian Institute of Science, Bangalore with UGC fellowship.

P. G. Kulkarni is currently a Ph.D. student of COEP, University of Pune, India. He did his Master of Engineering in Mechanical Engineering from Walchand College of Engineering, Sangli. His research interests include condition monitoring and signal analysis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kulkarni, P.G., Sahasrabudhe, A.D. A dynamic model of ball bearing for simulating localized defects on outer race using cubic hermite spline. J Mech Sci Technol 28, 3433–3442 (2014). https://doi.org/10.1007/s12206-014-0804-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-014-0804-0

Keywords

Search

Navigation