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.
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”]- Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK.
- Department of Engineering Mathematics, University of Bristol, Queen’s Building, University Walk, Bristol BS8 1TR, UK.
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