Pearson, S.R. and Shipway, P.H.
Is the wear coefficient dependent upon slip amplitude in fretting?: Vingsbo and Söderberg revisited.
More than 25 years ago, Vingsbo and Söderberg published a seminal paper regarding the mapping of behaviour in fretting contacts (O. Vingsbo, S. Söderberg, On fretting maps, Wear, 126 (1988) 131–147). In this paper, it was proposed that in the gross-slip fretting regime, the wear coefficient increased by between one and two orders of magnitude as the fretting displacement amplitude increased from around 20 µm to 300 µm (defined as the limits of the gross-slip regime).
Since the publication of this paper, there have been many papers published in the literature regarding fretting in the gross-sliding regime where such a strong dependence of wear coefficient upon fretting displacement has not been observed, with instead, the wear coefficient being shown to be almost independent of fretting amplitude. Indeed, many researchers have demonstrated that there is a good correlation between wear volume and frictional energy dissipated in the contact for many material combinations, with the additional insight that a threshold in energy dissipated in the contact exists, below which no wear is observed (experimental data relating to fretting of a high strength steel is presented in the current paper which supports this concept).
It is argued that in deriving a wear coefficient in fretting, there are two key considerations which have not always been addressed: (i) the far-field displacement amplitude is not an adequate substitute for the slip amplitude (the former is the sum of the latter together with any elastic deformation in the system between the contact and the point at which the displacement is measured); and (ii) there is a threshold in the fretting duration, below which no wear occurs and above which the rate of increase in wear volume with increasing duration is constant (this constant may be termed the wear coefficient, ktrue). Not addressing these two issues results in the derivation of a nominal wear coefficient (knominal) which is always less than ktrue. A simple analysis is presented which indicates that
knominal / ktrue = 1 - A - B
where A is associated with erroneously utilising the far field displacement amplitude in place of the contact slip amplitude in the calculation of the wear coefficient and B is associated with the failure to recognise that there is a threshold in fretting duration below which no wear occurs.
A and B are shown to depend upon the tractional force required to initiate sliding (itself dependent upon the applied load and coefficient of friction), the system stiffness, the applied displacement amplitude, the threshold fretting duration below which no wear occurs and the number of fretting cycles in the test. Using typical values of these parameters, the ratio of knominal to ktrue has been shown to be strongly dependent upon the applied displacement amplitude over the range addressed by Vingsbo and Söderberg (with the ratio rapidly decreasing by an order of magnitude over this range). As such, it is argued that ktrue shows no strong dependence on slip amplitude in fretting, and that the strong dependence of knominal upon displacement amplitude presented by Vingsbo and Söderberg does not imply a change in ktrue as is often inferred.
The routine recording of force–displacement loops in fretting is a major experimental advancement which has taken place since the publication of the paper by Vingsbo and Söderberg. It is argued that this technique must be routinely used to allow the correct interpretation of wear data in terms of the actual slip amplitude (or energy dissipated); moreover, a range of conditions should be experimentally examined to allow the threshold fretting duration below which no wear has occurred to be evaluated and its significance assessed.
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