, Volume 5, Issue 2, pp 194–206 | Cite as

Reduction of friction by normal oscillations. II. In-plane system dynamics

  • Xinyu Mao
  • Valentin L. Popov
  • Jasminka Starcevic
  • Mikhail Popov
Open Access
Research Article


The influence of out-of-plane oscillations on friction is a well-known phenomenon that has been studied extensively with various experimental methods, e.g., pin-on-disk tribometers. However, existing theoretical models have yet achieved only qualitative correspondence with experiment. Here we argue that this may be due to the system dynamics (mass and tangential stiffness) of the pin or other system components being neglected. This paper builds on the results of a previous study [19] by taking the stiffness and resulting dynamics of the system into account. The main governing parameters determining macroscopic friction, including a dimensionless oscillation amplitude, a dimensionless sliding velocity and the relation between three characteristic frequencies (that of externally excited oscillation and two natural oscillation frequencies associated with the contact stiffness and the system stiffness) are identified. In the limiting cases of a very soft system and a very stiff system, our results reproduce the results of previous studies. In between these two limiting cases there is also a resonant case, which is studied here for the first time. The resonant case is notable in that it lacks a critical sliding velocity, above which oscillations no longer reduce friction. Results obtained for the resonant case are qualitatively supported by experiments.


sliding friction out-of-plane oscillation stiffness system dynamics macroscopic friction coefficient 



The authors would like to thank Juliane Wallendorf and Qiang Li for their help with preparing figures for the paper. This work was supported in part by Tomsk State University Academic D.I. Mendeleev Fund Program (No.


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© The author(s) 2017

Open Access: The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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

  • Xinyu Mao
    • 1
    • 2
  • Valentin L. Popov
    • 1
    • 3
    • 4
  • Jasminka Starcevic
    • 1
    • 4
  • Mikhail Popov
    • 1
    • 3
    • 4
  1. 1.Technische Universität BerlinBerlinGermany
  2. 2.Tsinghua UniversityBeijingChina
  3. 3.Tomsk Polytechnic UniversityTomskRussia
  4. 4.Tomsk State UniversityTomskRussia

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