The frequency response of dynamic friction: Enhanced rate-and-state models

Significance Statement

Friction plays a major role in vibration engineering and earthquake mechanics.  Dynamic friction needs to be understood to make progress in these fields, and many models have been proposed to characterize the friction force. In applications like vehicle brake squeal, undesirable brake noise arises when there is instability in the steady sliding state between brake liner and brake disc. Similarly, earthquake processes are studied by mapping the frictional instability regime. For both applications there are many possible mechanisms leading to instability, but the natural starting point for study is instability based on linearised theory.

Within a linearised framework, it is clear what information is required about friction: it is a kind of frequency response function for sliding friction. Professor Jim Woodhouse and Dr Alessandro Cabboi from the University of Cambridge in collaboration with Dr Thibaut Putelat from the University of Bristol have studied this response function both experimentally and theoretically.  A pin-on-disc test rig has been designed to allow measurements of the frictional frequency response. A hemispherical pin sample made from a chosen test material is brought in contact with a disc of the other chosen material. The sample is attached to a dynamometer unit, containing sensors to measure the friction force, normal force, and relative motion between pin and disc. A spring system is used to control the normal force. Rotation of the disc provides a steady sliding speed between pin and disc, and a piezo-electric actuator allows the relative speed to be modulated dynamically.

Using a range of sliding speeds and normal forces, the dynamic responses were collected for pins of nylon or polycarbonate against a glass disc.  The most complete results were for nylon. For this case, the main conclusions were:

(i) The frictional frequency response can be measured reliably and repeatably.

(ii) The results show non-trivial dependence on frequency, sliding speed and normal force.

(iii) The results conflict with many traditional friction models from the literature.

(iv) When compared with a family of rate-and-state models extended to include allowance for the contact stiffness, good agreement was demonstrated, and the measurements could be used to discriminate between the variant models.

(v) The best-fitting model was able to match successfully the observed variations with sliding speed and normal load.

With the polycarbonate pin similar results were obtained, but thermal effects caused changes in the contacting surfaces so that only a limited number of measurements were possible. Repeatable results were still obtained for the frictional frequency response for the cases that could be tested, even though the steady-sliding coefficient of friction was found to vary by up to a factor of 2 between tests under nominally identical conditions

The authors have succeeded in demonstrating the robustness of measurements of the newly-proposed frictional frequency response, and also in identifying an extension to existing theoretical model that gives an excellent match to the measurements.  The way is thus open to extend this test methodology to tribological characterization in industrially-important applications such as design to eliminate brake squeal.  The identified theoretical model could be incorporated in computer codes for performing squeal predictions.  

Frequency response of dynamic friction: Enhanced rate-and-state models. Advances in Engineering

About the author

Thibaut Putelat graduated from the Ecole Normale Superieure of Lyon (France) in Earth Sciences and received his PhD degree in Theoretical Mechanics from the University of Lyon (France), in 2002.

His research interests deal with nonlinear solid mechanics and applied nonlinear dynamics spanning engineering and natural sciences, including friction-induced vibration such as earthquakes or brake squeal, stability of structures, geodynamics and cell motility. His contribution to tribology concerns the theoretical study and experimental identification of rate-and-state friction models with non-monotonic characteristics and its consequences on the sliding stability of frictional systems.

 

About the author

Dr. Alessandro Cabboi received his Masters (2010) and Ph.D. (2014) at the University of Cagliari in Structural Engineering. Between 2011-2013 he was a visiting student at the Polytechnic of Milan and the University of Porto working on vibration-based monitoring of Civil Structures.

In 2014, he joined the Dynamics and Vibration Research Group at the University of Cambridge as a Research Associate, working on modelling and experimental characterization of the frictional force at a sliding interface. The research was funded by the “Engineering Nonlinearity” project. Between September and December 2016, he was appointed as Research Associate at the Vibration University Technology Center at Imperial College London. The work was focused on experimental characterization and numerical modelling of linear and nonlinear dynamic responses of fuel manifold pipes in lean burn engines.

His research interests covers structural dynamics in general, with a particular focus on friction-induced vibration, experimental and operational modal analysis and condition monitoring.  

About the author

Jim Woodhouse studied mathematics in Cambridge for his undergraduate and PhD work.  After a spell with a consultancy company, he joined the Engineering Department of Cambridge University in 1985, and has worked there ever since.

His research interests cover a range of topics in vibration: prediction methods for complex structures, modelling and characterisation of structural damping and of frictional interfaces, and the mechanics of musical instruments such as the violin. 

Journal Reference

Alessandro Cabboi1,  Thibaut Putelat2, Jim Woodhouse1, The frequency response of dynamic friction: Enhanced rate-and-state models, Journal of the Mechanics and Physics of Solids, Volume 92, 2016, Pages 210-236.

[expand title=”Show Affiliations”]
  1. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK.
  2. Department of Engineering Mathematics, University of Bristol, Queen’s Building, University Walk, Bristol BS8 1TR, UK.
[/expand]

 

 

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