Archive of Applied Mechanics

, Volume 88, Issue 4, pp 525–541 | Cite as

Influence of contact stiffness of joint surfaces on oscillation system based on the fractal theory

  • Wujiu Pan
  • Xiaopeng Li
  • Linlin Wang
  • Na Guo
  • Zemin Yang


In this paper, in view of microscopic surface topography characteristic, the relationship of microscopic surface topography characteristic and the dynamic characteristic of macroscopic system is established, and the influence of fractal contact stiffness on the stability and nonlinearity of modal coupling system is studied based on microscopic surface topography. According to the fractal characteristic of metal surface machined, the normal and tangential contact stiffness fractal models of joint surfaces are established and verified. In this paper, a critical two-degree-of-freedom modal coupling model is listed, the fractal contact stiffness obtained is embedded into oscillatory differential equation to study the influence of the coupling between friction coefficient and stiffness ratio of joint surfaces and the coupling between natural frequency and stiffness ratio of joint surfaces on the system stability, and the influence of fractal contact stiffness on the limit cycle of system is further analyzed. The above theoretical analysis can provide a reference for the design of suitable surface topography in the engineering.


Joint surfaces Contact stiffness Fractal theory Oscillation system 



The authors greatly appreciate the reviewers’ suggestions and the editor’s encouragement. This work was supported, in part, by a Grant from National Natural Science Foundation of China (Nos. 51275079 and 51575091) and Fundamental Research Funds for the Central Universities (N160306003).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Wujiu Pan
    • 1
  • Xiaopeng Li
    • 1
  • Linlin Wang
    • 1
  • Na Guo
    • 1
  • Zemin Yang
    • 1
  1. 1.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangPeople’s Republic of China

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