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Analytical Expression for the Atomic Friction of a Single Asperity Based on the Prandtl–Tomlinson Model

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Abstract

The Prandtl–Tomlinson (PT) model has been widely applied to interpret the atomic friction mechanism of a single asperity. In this study, we present an approximate explicit expression for the friction force in the one-dimensional PT model under quasi-static conditions. The ‘stick–slip’ friction curves are first approximated properly by sawtooth-like lines, where the critical points before and after the ‘slip’ motion are described analytically in terms of a dimensionless parameter η. Following this, the average friction force is expressed in a closed form that remains continuous and valid for η > 1. Finally, an analytical expression for the load dependence of atomic friction of a single asperity is derived by connecting the parameter η with the normal load. With the parameters reported in experiments, our prediction shows good agreement with relevant experimental results.

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Acknowledgements

The support from the National Natural Science Foundation of China (Grant Nos. 12302141, 12372100, and 12102322), the China Postdoctoral Science Foundation (Grant No. 2023M732799), and the General Research Fund (Project No. CityU 11302920) from the Research Grants Council of the Hong Kong Special Administrative Region is acknowledged.

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Authors and Affiliations

  1. Department of Engineering Mechanics, SVL, MML, Xi’an Jiaotong University, Xi’an, 710049, China

    Weike Yuan, Yue Ding & Gangfeng Wang

  2. Department of Mechanical Engineering, City University of Hong Kong, Hong Kong SAR, 999077, China

    Xinrui Niu

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  1. Weike Yuan
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  2. Yue Ding
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  3. Gangfeng Wang
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  4. Xinrui Niu
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Correspondence to Gangfeng Wang or Xinrui Niu.

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Yuan, W., Ding, Y., Wang, G. et al. Analytical Expression for the Atomic Friction of a Single Asperity Based on the Prandtl–Tomlinson Model. Acta Mech. Solida Sin. (2024). https://doi.org/10.1007/s10338-024-00488-2

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  • DOI: https://doi.org/10.1007/s10338-024-00488-2

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