, Volume 5, Issue 1, pp 45–55 | Cite as

Reduction of friction by normal oscillations. I. Influence of contact stiffness

  • M. PopovEmail author
  • V. L. Popov
  • N. V. Popov
Open Access
Research Article


The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane. In contrast to previous works we analyze the influence of the stiffness of the tribological contact in detail and also consider the case of large oscillation amplitudes at which the contact is lost during a part of the oscillation period, so that the sample starts to “jump”. It is shown that the macroscopic coefficient of friction is a function of only two dimensionless parameters—a dimensionless sliding velocity and dimensionless oscillation amplitude. This function in turn depends on the shape of the contacting bodies. In the present paper, analysis is carried out for two shapes: a flat cylindrical punch and a parabolic shape. Here we consider “stiff systems”, where the contact stiffness is small compared with the stiffness of the system. The role of the system stiffness will be studied in more detail in a separate paper.


sliding friction out-of-plane oscillation contact stiffness coefficient of friction active control of friction 



This work was supported in part by the Ministry of Education of the Russian Federation, by COST Action MP1303 and the Deutsche Forschungsgemeinschaft.


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© The Author(s) 2016

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

  1. 1.Berlin University of TechnologyBerlinGermany
  2. 2.Tomsk Polytechnic UniversityTomskRussia
  3. 3.Tomsk State UniversityTomskRussia

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