Skip to main content
SpringerLink
Log in

A Multi-Scale Stiffness Fractal Model of Joint Interfaces

  • Published:
Russian Physics Journal Aims and scope

Stiffness characterization of mechanical interfaces is quite crucial for the analysis of several tribological behaviors. In the research of industrial robots, joints exist universally. The stiffness of different machine tools varies greatly, particularly for computer numerical control machine. Therefore, this research aims at providing an assessment of influence factors for stiffness of joint interfaces theoretically. Based on fractal roughness parameters independent of scale and contact mechanics theory, the contact area of joint interface is studied, and a multi-scale normal contact stiffness model and a multi-scale tangential contact stiffness model are proposed. Meanwhile, the problem of the deformation of any contact asperity is considered as three separate regimes. The laws of area-displacement and force-displacement under elastic-plastic regime are established. The transition which is in the deformation mechanism of asperity from elastic to plastic is consistent with classical contact mechanics. The analysis of numerical calculation results indicates the approximate linear relation among dimensionless normal load and key parameters. Moreover, these key parameters have been divided into two main categories for the multiscale model of joint interfaces, namely, fractal parameters, such as fractal dimension D and fractal roughness parameter G, and interfacial parameters. In addition, tangential load and friction factor are two important factors of the tangential stiffness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Y. C. Zhou, Y. Xiao, Y. He, et al., Compos. Struct., 236, 111874 (2020).

  2. X. Guo, B. B. Ma, and Y. C. Zhu, J. Mech. Phys. Solids, 133, 103724(2019).

  3. X. Zhang, N. Wang, G. Lan, et al., J. Tribol.-T. ASME, 136, 1–10 (2014).

    Article  Google Scholar 

  4. W. J. Pan, X. P. Li, L. L. Wang, et al., Eur. J. Mech. A/Solids, 66, 94–102 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  5. W. W. Liu, J. J. Yang, et al., J. Adv. Mech. Des. Syst. Manuf., 9, No. 5, 70–82 (2015).

    Article  Google Scholar 

  6. D. Y. Zhang, Y. Xia, F. Scarpa, et al., Sci. Rep., 7, 12874 (2017).

    Article  ADS  Google Scholar 

  7. J. Shen, X. Zhang, et al., Therm. Sci., 23, 2849–2856 (2019).

    Article  Google Scholar 

  8. J. A. Greenwood and J. Williamson, Proc. R. Soc. Lond., Ser. A, 295, 300–319 (1966).

  9. D. J. Whitehouse and J. F. Archard, Proc. R. Soc. Lond., Ser. A, 316, 97–121 (1970).

  10. A. Majumdar and B. Bhushan, J. Tribol.-T. ASME, 113, 1–11 (1991).

    Article  Google Scholar 

  11. B. Bhushan and A. Majumdar, Wear, 153, 53–64 (1992).

    Article  Google Scholar 

  12. M. V. Berry and Z. V. Lewis, Proc. R. Soc. Lond., Ser. A, 370, 459–484 (1980).

  13. A. Majumdar and B. Bhushan, J. Tribol.-T. ASME, 112, 205–216 (1990).

    Article  Google Scholar 

  14. A. Majumdar and C. L. Tien, Wear, 136, 313–327 (1990).

    Article  Google Scholar 

  15. S. Wang, K. Komvopoulos, and B. Bhushan, J. Tribol., 117, 203–215 (1995).

    Article  Google Scholar 

  16. S. Wang and K. Komvopoulos, J. Trib.-T. ASME, 116, No. 4, 824–832 (1994).

    Article  Google Scholar 

  17. W. Yan, K. Komvopoulos, J. Appl. Phys., 84, 3617–3624 (1998).

    Article  ADS  Google Scholar 

  18. Y. Morag and I. Etsion, Wear, 262, 624–629 (2007).

    Article  Google Scholar 

  19. X. M. Miao and X. D. Huang, Wear, 309, 146–151 (2013).

    Article  Google Scholar 

  20. W. J. Pan, X. P. Li, and G. Na, Adv. Mech. Eng., 9, No. 3, 1–11 (2017).

    Article  Google Scholar 

  21. Y. S. Zhao, J. J. Xu, and L. G. Cai, ProIMechE, Part C, J. Mech. Eng. Sci., 231, No. 2, 279–293 (2017).

  22. T. Jana, A. Mitra, and P. Sahoo, Appl. Surf. Sci., 392, 872–882 (2017).

    Article  ADS  Google Scholar 

  23. J. F. Shen, S. Xu, W. W. Liu, et al., Mechanika, 23, No. 5, 703–713 (2017).

    Article  Google Scholar 

  24. R. Q. Wang, L. D. Zhu, and C. X. Zhu, Int. J. Mech. Sci., 134, 357–369 (2017).

    Article  Google Scholar 

  25. Q. Chen, J. J. Zhou, A. Khushnood A, et al., AIP Adv., 9, No. 1, 1–13 (2019).

  26. S. Xi and A. A. Polycarpou, J. Vib. Acoust., 127, 52–60 (2005).

    Article  Google Scholar 

  27. W. P. Fu, Q. Guo, Y. M. Huang, et al., J. Vib. Acoust., 122, 393–398 (2000).

    Article  Google Scholar 

  28. M. Eriten, C. Lee, and A. A. Polycarpou, Tribol. Int., 50, 35–44 (2012).

    Article  Google Scholar 

  29. L. Kogut and I. Etsion, J. Appl. Mech.-T. ASME, 69, 657–662 (2002).

    Article  ADS  Google Scholar 

  30. L. P. Lin and J. F. Lin, J. Tribol.-T. ASME, 127, 666–672 (2005).

    Article  Google Scholar 

  31. W. J. Stronge, in: Impacts in Mechanical Systems, B. Brogliato, Ed., Springer, Berlin; Heidelberg; Cambridge (2000), pp. 189–234.

    Chapter  Google Scholar 

  32. K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge (1985).

    Book  Google Scholar 

  33. D. Josheski, E. Karamazova, and M. Apostolov, AMNS, 4, No. 2, 331–350 (2019).

    Article  Google Scholar 

  34. L. Li, Y. Wang, and X. Li, AMNS, 5, No. 1, 55–60 (2020).

    Article  Google Scholar 

  35. J. L. Liou and J. F. Lin, J. Tribol.-T. ASME, 128, 515–524 (2006).

    Article  Google Scholar 

  36. J. L. Liou and J. F. Lin, J. Tribol.-T. ASME, 74, 603–613 (2007).

    Google Scholar 

  37. W. Chang, I. Etsion, and D. B. Bogy, J. Tribol.-T. ASME, 110, 57–63 (1988).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. China Electronic Product Reliability and Environmental Testing Research Institute, Guangzhou, China

    Wenwei Liu

  2. College of Sciences, Huazhong Agricultural University, Wuhan, China

    Jingfang Shen, Sijie Cheng & Siyan Wang

Authors
  1. Wenwei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingfang Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sijie Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Siyan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenwei Liu.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 81–95, July, 2021.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, W., Shen, J., Cheng, S. et al. A Multi-Scale Stiffness Fractal Model of Joint Interfaces. Russ Phys J 64, 1261–1280 (2021). https://doi.org/10.1007/s11182-021-02453-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11182-021-02453-9

Keywords

Search

Navigation