Investigation on Normal Dynamic Contact Characteristics of Mechanical Interface of Machine Tools


The dynamic contact characteristics of mechanical interface significantly impact the performance of machine tools. The static contact behaviors of mechanical interface have been studied. However, most mechanical interfaces are exposed to dynamic load. It is necessary to study the dynamic contact characteristics of mechanical interface. A normal dynamic microcosmic contact model is built using the statistical method, and the interactional effects of adjacent asperities are considered. The influences of the normal preload, vibrational frequency and displacement amplitude on normal contact stiffness and damping of mechanical interface are revealed. The predicted contact stiffness and damping of mechanical interface are verified by a series of simulations and experiments.

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  1. 1.

    Burdekin M, Back N, Cowley A. Analysis of the local deformations in machine joints. J Mech Eng Sci. 1979;21:25–32.

    Google Scholar 

  2. 2.

    Ren Y, Beards CF. Identification of ’effective’ linear joints using coupling and joint identification techniques. J Vib Acoust. 1998;120:331–8.

    Google Scholar 

  3. 3.

    Kono D, Nishio S, Yamaji I, Matsubara A. A method for stiffness tuning of machine tool supports considering contact stiffness. Int J Mach Tools Manuf. 2015;90:50–9.

    Google Scholar 

  4. 4.

    Kono D, Inagaki T, Matsubara A, Yamaji I. Stiffness model of machine tool supports using contact stiffness. Precis Eng. 2013;37:650–7.

    Google Scholar 

  5. 5.

    Shimizu S, Nakamura K, Sakamoto H. Quantitative measurement method of contact stiffness of the joint with different material combination, 2010

  6. 6.

    Greenwood JA, Williamson JBP, Bowden Frank P. Contact of nominally flat surfaces. Proc R Soc Lond A. 1966;295:300–19.

    Google Scholar 

  7. 7.

    Chang WR, Etsion I, Bogy DB. An elastic–plastic model for the contact of rough surfaces. J Tribol. 1987;109:257–63.

    Google Scholar 

  8. 8.

    Zhao Y, Maietta DM, Chang L. An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow. J Tribol. 1999;122:86–93.

    Google Scholar 

  9. 9.

    Kogut L, Etsion I. A finite element based elastic–plastic model for the contact of rough surfaces. Tribol Trans. 2003;46:383–90.

    Google Scholar 

  10. 10.

    Etsion I, Kligerman Y, Kadin Y. Unloading of an elastic–plastic loaded spherical contact. Int J Solids Struct. 2005;42:3716–29.

    MATH  Google Scholar 

  11. 11.

    Kadin Y, Kligerman Y, Etsion I. Unloading an elastic–plastic contact of rough surfaces. J Mech Phys Solids. 2006;54:2652–74.

    MATH  Google Scholar 

  12. 12.

    Tian H, Li B, Liu H, Mao K, Peng F, Huang X. A new method of virtual material hypothesis-based dynamic modeling on fixed joint interface in machine tools. Int J Mach Tools Manuf. 2011;51:239–49.

    Article  Google Scholar 

  13. 13.

    Mao K, Li B, Wu J, Shao X. Stiffness influential factors-based dynamic modeling and its parameter identification method of fixed joints in machine tools. Int J Mach Tools Manuf. 2010;50:156–64.

    Article  Google Scholar 

  14. 14.

    Zhao Y, Chang L. A model of asperity interactions in elastic–plastic contact of rough surfaces. J Tribol. 2000;123:857–64.

    Article  Google Scholar 

  15. 15.

    Knowles JK. On Saint-Venant’s principle in the two-dimensional linear theory of elasticity. Arch Ration Mech Anal. 1966;21:1–22.

    MathSciNet  Article  Google Scholar 

  16. 16.

    Love Augustus Edward H. The stress produced in a semi-infinite solid by pressure on part of the boundary. Philos Trans R Soc Lond Ser A. 1929;228:377–420.

    Article  Google Scholar 

  17. 17.

    Ciavarella M, Greenwood JA, Paggi M. Inclusion of “interaction” in the Greenwood and Williamson contact theory. Wear. 2008;265:729–34.

    Article  Google Scholar 

  18. 18.

    Jeng Y-R, Peng S-R. Elastic–plastic contact behavior considering asperity interactions for surfaces with various height distributions. J Tribol. 2005;128:245–51.

    Article  Google Scholar 

  19. 19.

    Jackson RL, Green I. A finite element study of elasto-plastic hemispherical contact against a rigid flat. J Tribol. 2005;127:343–54.

    Article  Google Scholar 

  20. 20.

    Jackson RL, Green I. A statistical model of elasto-plastic asperity contact between rough surfaces. Tribol Int. 2006;39:906–14.

    Google Scholar 

  21. 21.

    Johnson KL. Contact mechanics. Cambridge: Cambridge University Press; 1985.

    Google Scholar 

  22. 22.

    Dimarogonas AD. The origins of vibration theory. J Sound Vib. 1990;140:181–9.

    MathSciNet  MATH  Google Scholar 

  23. 23.

    Wu C-Y, Li L-Y, Thornton C. Energy dissipation during normal impact of elastic and elastic–plastic spheres. Int J Impact Eng. 2005;32:593–604.

    Google Scholar 

  24. 24.

    Greenwood JA, Tripp JH. The contact of two nominally flat rough surfaces. Proc Inst Mech Eng. 1970;185:625–33.

    Google Scholar 

  25. 25.

    Nayak PR. Random process model of rough surfaces. J Lubr Technol. 1971;93:398–407.

    Google Scholar 

  26. 26.

    Nayak PR. Random process model of rough surfaces in plastic contact. Wear. 1973;26:305–33.

    Google Scholar 

  27. 27.

    McCool JI. Predicting microfracture in ceramics via a microcontact model. J Tribol. 1986;108:380–5.

    Google Scholar 

  28. 28.

    Fu WP, Huang YM, Zhang XL, Guo Q. Experimental investigation of dynamic normal characteristics of machined joint surfaces. J Vib Acoust. 2000;122:393–8.

    Google Scholar 

  29. 29.

    Shi X, Polycarpou AA. Measurement and modeling of normal contact stiffness and contact damping at the meso scale. J Vib Acoust. 2005;127:52–60.

    Google Scholar 

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The authors gratefully acknowledge the financial support provided by the China Postdoctoral Science Foundation (No. 2019M663782), the Shaanxi Natural Science Basic Research Project (No. 2020JQ-629), the Special scientific research project of Shaanxi Provincial Department of Education (No. 20JK0800), the Open project of State Key Laboratory of Power System of Tractor (AKT2020002) and the project supported by scientific research program of Key Laboratory of Shaanxi Provincial Department of Education (13JS070).

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Correspondence to Weiping Fu.

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Gao, Z., Fu, W., Wang, W. et al. Investigation on Normal Dynamic Contact Characteristics of Mechanical Interface of Machine Tools. Acta Mech. Solida Sin. 34, 104–123 (2021).

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  • Dynamic
  • Stiffness
  • Damping
  • Asperity interaction
  • Experiment