Advertisement

Fractal modeling of normal contact stiffness for rough surface contact considering the elastic–plastic deformation

  • Huifang Xiao
  • Yunyun Sun
  • Zaigang Chen
Technical Paper
  • 11 Downloads

Abstract

In this work, a new formulation of elastic–plastic contact model for the normal contact between rough surfaces is proposed based on the fractal theory. The surface topography is described using the modified one-variable Weierstrass–Mandelbrot fractal function. A new elastoplastic asperity contact model is developed based on the contact mechanics combined with the continuity and smoothness of mean contact pressure and contact load across different deformation regimes from elastic to elastoplastic, and from elastoplastic to fully plastic. The contact stiffness of a single asperity in the three deformation regimes of fully plastic, elastoplastic and elastic is derived, which changes smoothly at transit points between different deformation modes and overcomes the shortcoming of discontinuity derived from previous model. The contact stiffness and contact load of the whole surface in the three deformation regimes are formulated by integrating the micro-asperity contact. The difference between contact stiffness calculated from the plastic–elastoplastic–elastic three contact regimes and plastic–elastic two contact regimes is not obvious for surface with rougher topograph; however, for surface with smoother topograph, the two contact regimes predict a much smaller contact stiffness. The relationship of the normal contact stiffness and the normal contact force follows a power law function for the fractal surface contact considering three deformation regimes. The power exponent is nonlinearly dependent on the fractal dimension, which is different from the linear relationship for the purely elastic contact.

Keywords

Fractal rough surface Elastoplastic deformation Contact stiffness 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant Number 51775037] and Open Project Foundation of the State Key Laboratory of Traction Power in Southwest Jiaotong University [Grant Number TPL1713].

References

  1. 1.
    Gonzalez-Valadez M, Baltazar A, Dwyer-Joyce RS (2010) Study of interfacial stiffness ratio of a rough surface in contact using a spring model. Wear 268:373–379CrossRefGoogle Scholar
  2. 2.
    Du F, Hong J, Xu Y (2014) An acoustic model for stiffness measurement of tribological interface using ultrasound. Tribol Int 73:70–77CrossRefGoogle Scholar
  3. 3.
    Bazrafshan M, Ahmadian H, Jalali H (2014) Modeling the interaction between contact mechanisms in normal and tangential directions. Int J Non Linear Mech 58:111–119CrossRefGoogle Scholar
  4. 4.
    Zou HT, Wang BL (2015) Investigation of the contact stiffness variation of linear rolling guides due to the effects of friction and wear during operation. Tribol Int 92:472–484CrossRefGoogle Scholar
  5. 5.
    Oskar EL, Nordborg A, Arteaga IL (2016) The influence of surface roughness on the contact stiffness and the contact filter effect in nonlinear wheel-track interaction. J Sound Vib 366:429–446CrossRefGoogle Scholar
  6. 6.
    Greenwood JA (1966) Williamson JBP (1966) Contact of nominally flat surfaces. Proc R Soc Lond Ser A 295:300–319CrossRefGoogle Scholar
  7. 7.
    Nayak PR (1971) Random process model of rough surfaces. Trans ASME J Lubr Technol 93:398–407CrossRefGoogle Scholar
  8. 8.
    Nayak PR (1973) Some aspects of surface roughness measurement. Wear 26:165–174CrossRefGoogle Scholar
  9. 9.
    Chang WR, Etsion I, Bogy DB (1987) An elastic-plastic model for the contact of rough surfaces. ASME J Tribol 109:257–263CrossRefGoogle Scholar
  10. 10.
    Johnson KL (1985) Contact mechanics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  11. 11.
    Zhao YW, Maietta DM, Chang L (2000) An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow. J Tribol 122:86–93CrossRefGoogle Scholar
  12. 12.
    Brake MR (2012) An analytical elastic-perfectly plastic contact model. Int J Solids Struct 49:3129–3141CrossRefGoogle Scholar
  13. 13.
    Mandelbrot BB (1983) The fractal geometry of nature. Freeman, New YorkCrossRefGoogle Scholar
  14. 14.
    Majumdar A, Bhushan B (1990) Role of fractal geometry in roughness characterization and contact mechanics of surfaces. ASME J Tribol 112:205–216CrossRefGoogle Scholar
  15. 15.
    Yan W, Komvopoulos K (1998) Contact analysis of elastic–plastic fractal surfaces. J Appl Phys 84:3617–3624CrossRefGoogle Scholar
  16. 16.
    Hyun S, Pei L, Molinari JF et al (2004) Finite-element analysis of contact between elastic self-affine surfaces. Phys Rev E 70:026117-1–02611712CrossRefGoogle Scholar
  17. 17.
    Goerke D, Willner K (2008) Normal contact of fractal surfaces-experimental and numerical investigations. Wear 264:589–598CrossRefGoogle Scholar
  18. 18.
    Jiang SY, Zheng YJ, Zhu H (2010) A contact stiffness model of machined plane joint based on fractal theory. ASME J Tribol 132:011401CrossRefGoogle Scholar
  19. 19.
    Pohrt R, Popov VL (2012) Normal contact stiffness of elastic solids with fractal rough surfaces. Phys Rev Lett 108:104301CrossRefGoogle Scholar
  20. 20.
    Pohrt R, Popov VL, Filippov AE (2012) Normal contact stiffness of elastic solids with fractal rough surfaces for one-and three-dimensional systems. Phys Rev E 86:026710CrossRefGoogle Scholar
  21. 21.
    Pohrt R, Popov VL (2013) Contact stiffness of randomly rough surfaces. Sci Rep 3(3291):1–6Google Scholar
  22. 22.
    Liu YL, Guan BS, Xu ZL (2012) A friction contact stiffness model of fractal geometry in forced response analysis of a shrouded blade. Nonlinear Dyn 70:2247–2257MathSciNetCrossRefGoogle Scholar
  23. 23.
    Buczkowski R, Kleiber M, Starzynski G (2014) Normal contact stiffness of fractal rough surfaces. Arch Mech 66:411–428MathSciNetzbMATHGoogle Scholar
  24. 24.
    Xiao HF, Shao YM, Brennan MJ (2015) On the contact stiffness and nonlinear vibration of an elastic body with a rough surface in contact with a rigid flat surface. Eur J Mech A Solids 49:321–328CrossRefGoogle Scholar
  25. 25.
    Zhao YS, Song XL, Cai LG et al (2016) Surface fractal topography-based contact stiffness determination of spindle-toolholder joint. Proc Inst Mech Eng Part C J Mech Eng Sci 230(4):602–610CrossRefGoogle Scholar
  26. 26.
    Liou JL, Lin JF (2010) A modified fractal microcontact model developed for asperity heights with variable morphology parameters. Wear 268:133–144CrossRefGoogle Scholar
  27. 27.
    Kogut L, Etsion I (2002) Elastic-plastic contact analysis of a sphere and rigid flat. J Appl Mech 69:657–662CrossRefGoogle Scholar
  28. 28.
    Mandelbrot BB (1975) Stochastic models for the Earth’s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proc Natl Acad Sci 72(10):3825–3828MathSciNetCrossRefGoogle Scholar
  29. 29.
    Majumdar A, Bhushan B (1991) Fractal model of elastic-plastic contact between rough surfaces. J Tribol 113(1):1–11CrossRefGoogle Scholar
  30. 30.
    Yan W, Komvopoulos K (1998) Contact analysis of elastic-plastic fractal surfaces. J Appl Phys 84(7):3617–3624CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringUniversity of Science and Technology BeijingBeijingChina
  2. 2.Collaborative Innovation Center of Steel TechnologyUniversity of Science and Technology BeijingBeijingChina
  3. 3.State Key Laboratory of Traction PowerSouthwest Jiaotong UniversityChengduChina

Personalised recommendations