, 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


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.


running-in attractor boundedness enclosing radius recurrence plot dynamic evolvement 



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.


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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

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