Skip to main content
Log in

Static friction coefficient model of joint surface based on the modified fractal model and experimental investigation

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

It has been widely recognized that there are influences of static friction characteristics in a bolted joint on pre-tightening and service reliability. This study proposed a static friction coefficient model of joint surfaces based on the modified three-dimensional fractal model. A method of measuring the static friction coefficient of joint surfaces was investigated to verify the accuracy of model. The results showed that calculated value of the model and measured value of experiment are highly matched. Furthermore, the influential mechanisms of material, pressure, and surface topography were investigated. The relative error between experimental results and model calculations are all less than 15%. This research provides a theoretical basis for subsequent research on the friction characteristics of joint surfaces and connection reliability of bolted joints.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Availability of data and materials

Not applicable.

References

  1. Liu Z, Wang Y, Dong X et al (2022) A novel model for evaluating preload based on spectral problem in system with double-bolted connections. Appl Math Model 102:21–34

    Article  Google Scholar 

  2. Li Y, Liu Z, Wang Y et al (2020) Experimental study on behavior of time-related preload relaxation for bolted joints subjected to vibration in different directions. Tribol Int 142:106005

    Article  Google Scholar 

  3. Zhang Y, Zhang C, Yan J et al (2022) Rapid construction method of equipment model for discrete manufacturing digital twin workshop system. Robot Comput Integr Manuf 75:102309

    Article  Google Scholar 

  4. Li L, Wang J, Shi X et al (2021) Contact stiffness model of joint surface considering continuous smooth characteristics and asperity interaction. Tribol Lett 69(2):1–12

    Article  Google Scholar 

  5. Popov V (2010) Contact between rough surfaces. Springer, Berlin, Heidelberg

    Book  Google Scholar 

  6. Greenwood J, Williamson J (1966) Contact of nominally flat surfaces. Proc R Soc Lond 295(1442):300–319

    Google Scholar 

  7. Chang W, Etsion I, Bogy D (1988) Static friction coefficient model for metallic rough surfaces. J Tribol 110(1):57–63

    Article  Google Scholar 

  8. Sheng X, Luo J, Wen S (1998) Static friction coefficient model based on fractal contact. China Mech Eng 9(7):16–18

    Google Scholar 

  9. Majumdar A, Bhushan B (1991) Fractal model of elastic-plastic contact between rough surfaces. J Tribol 113(1):1–11

    Article  Google Scholar 

  10. Kogut L, Etsion I (2004) A static friction model for elastic-plastic contacting rough surfaces. J Tribol 126(1):34–40

    Article  Google Scholar 

  11. You J, Chen T (2010) A static friction model for the contact of fractal surfaces. Proc IMechE Part J J Eng Tribol 224:513–518

    Article  Google Scholar 

  12. Tian H, Zhu D, Qin H (2011) Fractal model of static friction coefficient of joint interface and its simulation. Chinese J Appl Mech 28(2):158–162

    Google Scholar 

  13. Tian H, Zhao C, Fang Z et al (2013) Predication investigation on static tribological performance of metallic material surfaces—theoretical model. J Vibration Shock 32(12):40–44, 66

  14. Tian H, Liu F, Zhao C et al (2014) Prediction of surface static tribological properties of metallic materials—experimental support. J Vibration Shock 33(1):209–220

    Google Scholar 

  15. Tian H, Zhao C, Fang Z et al (2013) Mathematical model of nonlinear friction based on anisotropic fractal geometric theory. J Vibration Shock 32(23):135–144

    Google Scholar 

  16. Zhang Y, Zhang X, Jiang L et al (2014) Fractal model of static frictional coefficient on joint surface considering elastic-plastic deformation. J Taiyuan Univ Sci Technol China 25(4):294–301

    Google Scholar 

  17. Lan G, Sun W, Zhang X et al (2021) A three-dimensional fractal model of the normal contact characteristics of two contacting rough surfaces. AIP Adv 11(5):055023

    Article  Google Scholar 

  18. Li X, Wang Z, Wang X et al (2019) Research on static friction coefficient of joint surfaces considering elastic-plastic deformation based on fractal model. Int J Ind Syst Eng 32(1):32–55

    Google Scholar 

  19. Pan W, Li X, Wang X (2020) Contact mechanics of elastic-plastic fractal surfaces and static friction analysis of asperity scale. Eng Comput 38(1):131–150

    Article  Google Scholar 

  20. Zhang X, Zhang W, Wen S et al (2021) Three-dimensional fractal model with scale correlation for static friction factor of joint interfaces. J Mech Eng 57(09):127–138

    Article  Google Scholar 

  21. Benabdallah H (2007) Static friction coefficient of some plastics against steel and aluminum under different contact conditions. Tribol Int 40(1):64–73

    Article  Google Scholar 

  22. Mandelbrot B (1982) The fractal geometry of nature. Freeman, New York

    MATH  Google Scholar 

  23. Mandelbrot B, Passoja D, Paullay A (1984) Fractal character of fracture surfaces of metal. Nature 308(5961):721–722

    Article  Google Scholar 

  24. Ji C, Zhu H, Jiang W (2013) Fractal prediction model of thermal contact conductance of rough surfaces. Chinese J Mech Eng English Ed

  25. Zhao Y, Xu J, Cai L et al (2017) Stiffness and damping model of bolted joint based on the modified three-dimensional fractal topography. Proc Inst Mech Eng C J Mech Eng Sci 231(2):279–293

    Article  Google Scholar 

  26. Zhao Y, Xu J, Cai L et al (2017) Contact characteristic analysis of spindle–toolholder joint at high speeds based on the fractal model. Proc Inst Mech Eng Part E J Process Mech Eng 231(5):1025–1036

    Article  Google Scholar 

  27. Ausloos M, Berman D (1985) A multivariate Weierstrass-Mandelbrot function. Proc Royal Soc London Ser A Math Phys Sci 400(1819):331–350

  28. Kogut L, Etsion I (2002) Elastic-plastic contact analysis of a sphere and a rigid flat. J Appl Mech 69(5):657–662

    Article  MATH  Google Scholar 

  29. Yuan Y, Cheng Y et al (2017) A revised Majumdar and Bushan model of elastoplastic contact between rough surfaces. Appl Surf Sci 425:1138–1157

    Article  Google Scholar 

  30. Zhang X (2002) Dynamic characteristics and application of mechanical joint surface. China Science and Technology Press, Beijing

    Google Scholar 

  31. Zhao B, Xu H, Lu X (2019) Sliding interaction for coated asperity with power-law hardening elastic-plastic coatings. Materials 12(15):2388–2388

    Article  Google Scholar 

  32. Kotov V, Linnik E, Sabaeva T (2021) Analyzing the problem of a spherical cavity expansion in a medium with Mohr-Coulomb-Tresca’s plasticity condition. Springer, Cham

    MATH  Google Scholar 

Download references

Funding

This work was sponsored by the National Natural Science Foundation of China (52175157, 51975019), the Beijing Natural Science Foundation (3192003), the General Project of Science and Technology Plan from Beijing Educational Committee (KM201810005013), the Tribology Science Fund of State Key Laboratory of Tribology (STLEKF16A02, SKLTKF19B08), and the training program of Rixin talent and outstanding talent from Beijing University of Technology.

Author information

Authors and Affiliations

Authors

Contributions

CZ and YL are responsible for providing overall research ideas. XL, JH, and ZL are responsible for the establishment of the theoretical model. YC and YL are responsible for experimental data analysis.

Corresponding author

Correspondence to Ying Li.

Ethics declarations

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, C., LI, X., He, J. et al. Static friction coefficient model of joint surface based on the modified fractal model and experimental investigation. Int J Adv Manuf Technol 124, 4415–4429 (2023). https://doi.org/10.1007/s00170-022-10063-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-022-10063-z

Keywords

Navigation