Dynamical Response of a Planetary Gear System with Faults Using Recurrence Statistics

  • B. Ambrożkiewicz
  • Y. Guo
  • G. Litak
  • P. WolszczakEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 228)


Recurrence plots and recurrence plots quantification analysis were applied to the planetary gears system to identify faults in the system. In this chapter the recurrence rate parameter adopted in the gear fault detection is presented. It is indicated in terms of recurrence statistics that the response of the gears system with faults is more periodic. This is caused by selected harmonics which are more pronounced in system with faults. Usefulness of other recurrence parameters is also discussed.


Planetary gear Recurrence analysis Faults monitoring 


  1. 1.
    F. Chaari, T. Fakhfakh, M. Haddar, Dynamic analysis of a planetary gear failure caused by tooth pitting and cracking. J. Fail. Anal. Prev. 6, 73–78 (2006)CrossRefGoogle Scholar
  2. 2.
    Z. Cheng, N. Hu. Quantitative Damage Detection for Planetary Gear Sets Based on Physical Models. Chin. J. Mech. Eng. 25(1), 190–196 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    M.I. Friswell, G. Litak, J.T. Sawicki, Crack identification in rotating machines with active bearings, in Proceedings of ISMA (Leuven, Belgium, 20–22 September, 2010), pp. 2843–2855Google Scholar
  4. 4.
    Y.C. Guo, R.G. Parker, Analytical determination of mesh phase relations in general compound planetary gears. Mech. Mach. Theory 46, 1869–1887 (2011)CrossRefGoogle Scholar
  5. 5.
    C. Hu, W.A. Smith, R.B. Randall, Z. Peng, Development of a gear vibration indicator and its application in gear wear monitoring. Mech. Syst. Signal Process. 76–77, 319–336 (2016). Scholar
  6. 6.
    Y.G. Lei, M.J. Zuo, Z.J. He et al., A multidimensional hybrid intelligent method for gear fault diagnosis. Expert Syst. Appl. 37, 1419–1430 (2010)CrossRefGoogle Scholar
  7. 7.
    Y.G. Lei, J. Lin, M.J. Zuo, Z. He, Condition monitoring and fault diagnosis of planetary gear boxes: a review. Measurement 48, 292–305 (2014)CrossRefGoogle Scholar
  8. 8.
    G. Litak, M.I. Friswell, Dynamics of a gear system with faults in meshing stiffness. Nonlinear Dyn. 41, 415–421 (2005). Scholar
  9. 9.
    G. Litak, J.T. Sawicki, R. Kasperek, Cracked rotor detection by recurrence plots. Nondestruct. Test. Eval. 24(4), 347–351 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    G. Litak, M. Wiercigroch, B.W. Horton, X. Xu, Transient chaotic behaviour versus periodic motion of a parametric pendulum by recurrence plots. ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik 90(1), 33–41 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    N. Marwan, J. Kurths, Nonlinear analysis of bivariate data withcross recurrence plots. Phys. Lett. A 302, 299–307 (2002)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    N. Marwan, M.C. Romano, M. Thiel, Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329 (2007)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    N. Marwan, CRP Toolbox for MATLAB v.5.19, Potsdam Institute for Climate Impact Research (PIK) (2016).

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • B. Ambrożkiewicz
    • 1
  • Y. Guo
    • 2
  • G. Litak
    • 1
  • P. Wolszczak
    • 1
    Email author
  1. 1.Faculty of Mechanical Engineering, Department of AutomationLublin University of TechnologyLublinPoland
  2. 2.Faculty of Mechanical and Electrical EngineeringKunming University of Science and TechnologyKunming CityChina

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