Advertisement

Friction

, Volume 7, Issue 5, pp 432–443 | Cite as

On the boundedness of running-in attractors based on recurrence plot and recurrence qualification analysis

  • Guodong Sun
  • Hua ZhuEmail author
  • Cong Ding
  • Yu Jiang
  • Chunling Wei
Open Access
Research Article
  • 68 Downloads

Abstract

A feature parameter was proposed to quantitatively explore the boundedness of running-in attractors; its variation throughout the friction process was also investigated. The enclosing radius R was built with recurrence plots (RPs) and recurrence qualification analysis (RQA) by using the time delay embedding and phase space reconstruction. Additionally, the typology of RPs and the recurrence rate (RR) were investigated to verify the applicability of R in characterizing the friction process. Results showed that R is larger at the beginning, but exhibits a downward trend in the running-in friction process; R becomes smooth and trends to small steady values during the steady-state friction period, and finally shows an upward trend until failure occurs. The evolution of R, which corresponded with the typology of RPs and RR during friction process, can be used to quantitatively analyze the variation of the running-in attractors and friction state identifacation. Hence, R is a valid parameter, and the boundedness of running-in attractors can offer a new way for monitoring the friction state of tribological pairs.

Keywords

running-in attractor boundedness enclosing radius recurrence plot dynamic evolvement 

Notes

Acknowledgments

This work is carried out within the projects supported by the National Natural Science Foundation of China (Nos. 51775546 and 51375480) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

References

  1. [1]
    Blau P J. The significance and use of the friction coefficient. Tribol Int 34(9): 585–591 (2001)CrossRefGoogle Scholar
  2. [2]
    Blau P J. A model for run-in and other transitions in sliding friction. J Tribol 109(3): 537–543 (1987)CrossRefGoogle Scholar
  3. [3]
    Xie Y B. Theory of Tribo-systems. In Tribology-Lubricants and Lubrication. Kuo C H, Ed. InTech, 2011.Google Scholar
  4. [4]
    Urbakh M, Klafter J, Gourdon D, Israelachvili J. The nonlinear nature of friction. Nature 430(6999): 525–528 (2004)CrossRefGoogle Scholar
  5. [5]
    Xia X T, Chen L, Fu L L, Li J H. Information mining for friction torque of rolling bearing for space applications using chaotic theory. Res J Appl Sci Eng Technol 5(22): 5223–5229 (2013)CrossRefGoogle Scholar
  6. [6]
    Vitanov N K, Hoffmann N P, Wernitz B. Nonlinear time series analysis of vibration data from a friction brake: SSA, PCA, and MFDFA. Chaos Solit Fract 69: 90–99 (2014)CrossRefGoogle Scholar
  7. [7]
    Enns R H, McGuire G C. Nonlinear Physics with Mathematica for Scientists and Engineers. Boston: Birkhäuser, 2001.CrossRefzbMATHGoogle Scholar
  8. [8]
    Zhou Y K, Zhu H, Zuo X. Dynamic evolutionary consistency between friction force and friction temperature from the perspective of morphology and structure of phase trajectory. Tribol Int 94: 606–615 (2016)CrossRefGoogle Scholar
  9. [9]
    Zhu H, Ge S R, Li G, Lv L. Test of running-in process and preliminary analysis of running-in attractors. Lubr Eng 32(1): 1–3 (2017)Google Scholar
  10. [10]
    Grassberger P, Procaccia I. Characterization of strange attractors. Phys Rev Lett 50(5): 346–349 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Lopes R, Betrouni N. Fractal and multifractal analysis: a review. Med Image Anal 13(4): 634–649 (2009)CrossRefGoogle Scholar
  12. [12]
    Wolf A, Swift J B, Swinney H L, Vastano J A. Determining Lyapunov exponents from a time series. Phys D: Nonlinear Phenomena 16(3): 285–317 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Fraser A M. Information and entropy in strange attractors. IEEE Trans Inf Theory 35(2): 245–262 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Manuca R, Savit R. Stationarity and nonstationarity in time series analysis. Phys D: Nonlinear Phenomena 99(2–3): 134–161 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Zhou Y K, Zhu H, Zuo X. The behavior of intrinsic randomness and dynamic abrupt changes of friction force signal during the friction process. J Tribol 138(3): 031605 (2016)CrossRefGoogle Scholar
  16. [16]
    Zhu H, Ge S R, Lv L, Lu B B. Evolvement rule of running-in attractor. Chin J Mech Eng 44(3): 99–104 (2008)CrossRefGoogle Scholar
  17. [17]
    Sun D, Li G B, Wei H J, Liao H F. Experimental study on the chaotic attractor evolvement of the friction vibration in a running-in process. Tribol Int 88: 290–297 (2015)CrossRefGoogle Scholar
  18. [18]
    Zhou Y K, Zhu H, Zuo X, Yang J H. Chaotic characteristics of measured temperatures during sliding friction. Wear 317(1–2): 17–25 (2014)CrossRefGoogle Scholar
  19. [19]
    Liu T, Li G B, Wei H J, Sun D. Experimental observation of cross correlation between tangential friction vibration and normal friction vibration in a running-in process. Tribol Int 97: 77–88 (2016)CrossRefGoogle Scholar
  20. [20]
    Jiang Y, Zhu H, Li Z, Peng Z. The nonlinear dynamics response of cracked gear system in a coal cutter taking environmental multi-frequency excitation forces into consideration. Nonlinear Dyn 84(1): 203–222 (2016)CrossRefGoogle Scholar
  21. [21]
    Manevitch L I, Kovaleva A S, Manevitch E L, Shepelev D S. Limiting phase trajectories and non-stationary resonance oscillations of the Duffing oscillator. Part 1. A non-dissipative oscillator. Commun Nonlinear Sci Numer Simul 16(2): 1089–1097 (2011)CrossRefzbMATHGoogle Scholar
  22. [22]
    Manevitch L I, Kovaleva A S, Manevitch E L, Shepelev D S. Limiting phase trajectories and nonstationary resonance oscillations of the Duffing oscillator. Part 2. A dissipative oscillator. Commun Nonlinear Sci Numer Simul 16(2): 1098–1105 (2011)CrossRefzbMATHGoogle Scholar
  23. [23]
    Zhang F C, Shu Y L, Yang H L. Bounds for a new chaotic system and its application in chaos synchronization. Commun Nonlinear Sci Numer Simul 16(3): 1501–1508 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Gao J B. Detecting nonstationarity and state transitions in a time series. Phys Rev E 63(6): 066202 (2001)CrossRefGoogle Scholar
  25. [25]
    Marwan N, Wessel N, Meyerfeldt U, Schirdewan A, Kurths J. Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. Phys Rev E 66(2): 026702 (2002)CrossRefzbMATHGoogle Scholar
  26. [26]
    Jackson R L, Green I. Study of the tribological behavior of a thrust washer bearing. Tribol Trans 44(3): 504–508 (2001)CrossRefGoogle Scholar
  27. [27]
    Boudraa A O, Cexus J C. EMD-Based signal filtering. IEEE Trans Instrum Meas 56(6): 2196–2202 (2007)CrossRefGoogle Scholar
  28. [28]
    Peng Z K, Tse P W, Chu F L. An improved Hilbert-Huang transform and its application in vibration signal analysis. J Sound Vibr 286(1–2): 187–205 (2005)CrossRefGoogle Scholar
  29. [29]
    Takens F. Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics, vol 898. Rand D, Young L S, Eds. Berlin, Heidelberg: Springer. 1981: 366–381.CrossRefGoogle Scholar
  30. [30]
    Kim H S, Eykholt R, Salas J D. Nonlinear dynamics, delay times, and embedding windows. Phys D: Nonlinear Phenomena 127(1–2): 48–60 (1999)CrossRefzbMATHGoogle Scholar
  31. [31]
    Piórek M. Mutual information for quaternion time series. In Computer Information Systems and Industrial Management. CISIM 2016. Lecture Notes in Computer Science, vol 9842. Saeed K, Homenda W, Eds. Cham: Springer, 2016: 453–461.CrossRefGoogle Scholar
  32. [32]
    Fraser A M, Swinney H L. Independent coordinates for strange attractors from mutual information. Phys Rev A 33(2): 1134–1140 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    Kennel M B, Brown R, Abarbanel H D I. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45(6): 3403 (1992)CrossRefGoogle Scholar
  34. [34]
    Liu L J, Fu Y, Ma S W. Wind power short-term prediction method based on multivariable mutual information and phase space reconstruction. In Intelligent Computing in Smart Grid and Electrical Vehicles. ICSEE 2014, LSMS 2014. Communications in Computer and Information Science, vol 463. Li K, Xue Y, Cui S, Niu Q, Eds. Berlin, Heidelberg: Springer, 2014: 1–12.Google Scholar
  35. [35]
    Eckmann J P, Kamphorst S O, Ruelle D. Recurrence plots of dynamical systems. EPL (Europhys Lett) 4(9): 973–977 (1987)CrossRefGoogle Scholar
  36. [36]
    Marwan N, Kurths J, Saparin P. Generalised recurrence plot analysis for spatial data. Phys Lett A 360(4–5): 545–551 (2007)CrossRefGoogle Scholar
  37. [37]
    Addo P M, Billio M, Guégan D. Nonlinear dynamics and recurrence plots for detecting financial crisis. North Amer J Econ Finance 26: 416–435 (2013)CrossRefGoogle Scholar
  38. [38]
    Llop M F, Gascons N, Llauró F X. Recurrence plots to characterize gas-solid fluidization regimes. Int J Multiph Flow 73: 43–56 (2015)CrossRefGoogle Scholar
  39. [39]
    Oberst S, Lai J C S. Chaos in brake squeal noise. J Sound Vibr 330(5): 955–975 (2011)CrossRefGoogle Scholar
  40. [40]
    Marwan N, Romano M C, Thiel M, Kurths J. Recurrence plots for the analysis of complex systems. Phys Rep 438(5–6): 237–329 (2007)MathSciNetCrossRefGoogle Scholar
  41. [41]
    Marwan N, Kurths J, Foerster S. Analysing spatially extended high-dimensional dynamics by recurrence plots. Phys Lett A 379(10–11): 894–900 (2015)CrossRefzbMATHGoogle Scholar
  42. [42]
    Marwan N, Kurths J. Line structures in recurrence plots. Phys Lett A 336(4–5): 349–357 (2005)CrossRefzbMATHGoogle Scholar

Copyright information

© The author(s) 2018

Open Access: The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Guodong Sun
    • 1
  • Hua Zhu
    • 1
    Email author
  • Cong Ding
    • 1
  • Yu Jiang
    • 1
  • Chunling Wei
    • 1
  1. 1.School of Mechatronic EngineeringChina University of Mining and TechnologyXuzhouChina

Personalised recommendations