Tribology Letters

, Volume 51, Issue 3, pp 513–523 | Cite as

A Multistate Friction Model Described by Continuous Differential Equations

Original Paper


This paper proposes a multistate friction model derived from a set of differential-algebraic inclusions. This model is described as a set of continuous differential equations that describe both the presliding and sliding regimes in a unified expression. It reproduces major features of friction phenomena reported in the literature, such as the Stribeck effect, nondrifting property, stick–slip oscillation, presliding hysteresis with nonlocal memory, and frictional lag. Moreover, the new model does not produce unbounded positional drift or nonsmooth forces, which are major problems of previous models due to the mathematical difficulty in dealing with transitions between the presliding and sliding regimes. The model is validated through comparison between its simulation results and empirical results in the literature.


Dynamic modeling Static friction Stick-slip 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Kyushu UniversityFukuokaJapan

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