Characteristic parameter extraction of running-in attractors based on phase trajectory and grey relation analysis

  • Guodong Sun
  • Hua Zhu
Original Paper


The coefficient of friction signals were extracted throughout the friction process, and the morphology of phase trajectory reconstructed from the obtained scalar time series was analysed. Experimental results show that the morphology of the phase trajectory follows the evolution rule of “convergence–stabilization–divergence”. To characterize the convergence degree of the phase trajectory, a brand new parameter named “grey phase density \(d_{\mathrm{G}}\)” was defined using the grey relation analysis. It was found that \(d_{\mathrm{G}}\) shows significant advantages with regard to the robustness against noise and the friction state identification, suggesting that the convergence degree of the phase trajectory can describe the change in friction states. Hence, the results indicate that grey phase density \( d_{\mathrm{G}}\) is amenable for characterizing the friction process.


Coefficient of friction Running-in attractor Phase trajectory Grey relation analysis Characteristic parameter 



This project is supported by the National Natural Science Foundation of China (Grant No. 51775546) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Compliance with ethical standards

Conflict of interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, and there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mechatronic EngineeringChina University of Mining and TechnologyXuzhouChina

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