Skip to main content
SpringerLink
Log in

Nonlinear friction dynamics on fibrous materials, application to the characterization of surface quality. Part II: local characterization of phase space by recurrence plots

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

Abstract

As has been shown in the first part of this series of papers, the global analysis of phase spaces does not allow one to access topographies of attractors, generated by the singular dynamic contacts between MODALSENS and our evaluated fibrous surfaces. By using the same time series from MODALSENS, this second paper presents a local exploration of the recurrences of the phase spaces. As a complement of the results from Part I, we propose, in this part of the work, a finer analysis of the vibrations of MODALSENS. Therefore, this part of the work aims at tracing friction dynamics cartographies of fibrous surfaces with the help of Recurrence Plots. This tool allows one to obtain images of recurrences in the space portraits. Hence, by regarding passages between strong and low magnitudes of vibrations, it is possible to take into account strong heterogeneities of relief and also the various mechanical and frictional behaviors of the asperities encountered during friction. Finally, Recurrence Quantification Analysis is performed in order to discuss the relationship between expected performances of the tested surfaces and their friction dynamics behaviors.

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. Riley, M.A., Balasubramaniam, R., Turvey, M.T.: Recurrence quantification analysis of postural fluctuations. Gait Posture 9, 65–78 (1999)

    Article  Google Scholar 

  2. Dingwell, J.B., Cumsumano, J.P.: Nonlinear time series analysis of normal and pathological human walking. Chaos 10(4), 973–977 (2000)

    Article  Google Scholar 

  3. Zbilut, J., Thomasson, N., Webber, C.: Recurrence quantification of non stationary cardiac signals. Med. Eng. Phys. 24, 53–60 (2002)

    Article  Google Scholar 

  4. Perc, M.: Nonlinear time series analysis of the human electrogram. Eur. J. Phys. 26, 757–768 (2005)

    Article  MathSciNet  Google Scholar 

  5. Feucht, M., Moller, U., Witte, H., Schmidt, K., Arnold, M., Benniger, F., Steinberger, K., Friedriech, M.H.: Nonlinear dynamics of 3 Hz spike-and-wave discharges recorded during typical absence seizure in children. Cereb. Cortex 8(6), 525–533 (1998)

    Article  Google Scholar 

  6. Ouyang, G., Dang, C., Richard, D.A.: Using recurrence plot for determinism analysis of EEG recordings in genetic absence epilepsy rats. Clin. Neurophysiol. 119, 1747–1755 (2008)

    Article  Google Scholar 

  7. Babinec, P., Jakubilova, E., Leszczynski, J.: Recurrence plot analysis of non linear vibrational dynamics in H3+ molecule. Chaos Solitons Fractals 17, 981–984 (2003)

    Article  MATH  Google Scholar 

  8. Perc, M., Green, A.K., Dixon, J., Marhl, M.: Establishing the stochastic nature of intracellular calcium oscillations from experimental data. Biophys. Chem. 132, 33–38 (2008)

    Article  Google Scholar 

  9. Ahlborn, A., Parlitz, U.: Experimental observation of chaotic phase synchronization of a periodically modulated frequency-doubled Nd:YAG laser. Opt. Lett. 34(18), 2754–2756 (2009)

    Article  Google Scholar 

  10. Krese, B., Perc, M., Govekar, E.: The dynamics of laser droplet generation. Chaos 20, 013119 (2010)

    Article  Google Scholar 

  11. Trauth, M.H., Bookhagen, B., Marwan, N., Strecker, M.R.: Multiple landslide clusters record quaternary climate changes in the northwestern Argentine Andes. Palaeogeogr. Palaeoclimatol. Palaeoecol. 194, 109–121 (2003)

    Article  Google Scholar 

  12. Marvan, N., Trauth, M.H., Vuille, M., Kurths, J.: Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods. Clim. Dyn. 21, 317–326 (2003)

    Article  Google Scholar 

  13. Barkoulas, J.T.: Testing for deterministic monetary chaos: Metric and topological diagnostics. Chaos Solitons Fractals 38, 1013–1024 (2008)

    Article  Google Scholar 

  14. Benko, T.P., Perc, M.: Nonlinearities in mating sounds of American crocodiles. Biosystems 97, 154–159 (2009)

    Article  Google Scholar 

  15. Eckmann, J.P., Oliffson Kamphorst, S., Ruelle, D.: Recurrence plots of dynamical systems. Europhys. Lett. 9(4), 973–977 (1987)

    Article  Google Scholar 

  16. Nichols, J.M., Trickey, S.T., Seaver, M.: Damage detection using multivariate recurrence quantification analysis. Mech. Syst. Signal Process. 20, 421–437 (2006)

    Article  Google Scholar 

  17. Marwan, N., Romano, C.M., Thiel, M., Kurths, J.: Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329 (2007)

    Article  MathSciNet  Google Scholar 

  18. Casdagli, M.C.: Recurrence plots revisited. Physica D 108, 12–44 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  19. Sun, R., Wang, Y.: Predicting termination of atrial fibrillation based on the structure and quantification of the recurrence plot. Med. Eng. Phys. doi:10.1016/j.medengphys.2008.01.008

  20. Thiel, M., Romano, C.M., Kurths, J., Meucci, R., Allaria, E., Arecchi, F.T.: Influence of observational noise on the recurrence quantification analysis. Physica D 171, 138–152 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gao, J., Cai, H.: On the structures and quantification of recurrence plots. Phys. Lett. A 270, 75–87 (2000)

    Article  Google Scholar 

  22. Strozzi, F., Zaldivar, J.M., Zbilut, J.: Application of nonlinear time series analysis techniques to high frequency currency exchange data. Physica A 312, 520–538 (2002)

    Article  MATH  Google Scholar 

  23. Zbilut, J.P., Giulani, A., Webber, C.L.: Recurrence quantification analysis as an empirical test to distinguish relatively short deterministic versus random number series. Phys. Lett. A 267, 174–178 (2000)

    Article  Google Scholar 

  24. Thiel, M., Romano, C.M., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dyn. 44, 299–305 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LPMT—Laboratoire de Physique et de Mécanique Textiles, EAC CNRS 7189, University of Mulhouse, Mulhouse, France

    Stéphane Fontaine, Seydou Dia & Marc Renner

  2. Institut National des Sciences Appliquées, Strasbourg, France

    Marc Renner

Authors
  1. Stéphane Fontaine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seydou Dia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marc Renner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stéphane Fontaine.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fontaine, S., Dia, S. & Renner, M. Nonlinear friction dynamics on fibrous materials, application to the characterization of surface quality. Part II: local characterization of phase space by recurrence plots. Nonlinear Dyn 66, 647–665 (2011). https://doi.org/10.1007/s11071-011-9968-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-9968-7

Keywords

Search

Navigation