There is a very lengthy discussion on fretting in the following reference:
"Electrical Contacts : Fundamentals, Applications and Technology" by Milenko Braunovic´, Valery V. Konchits, and Nikolai K. Myshkin (2006, Taylor and Francis)
ISBN:9781574447279
He talks about a minimum slip amplitude delta for fretting to occur as follows:
delta = 2*(2-nu)*(1+nu)*mu*P*[1-(1-T/<mu*p>)^(2/3) / 8Ea
where a is the diameter of the contact outer radius, E is the Young modulus, nu is Poisson’s ratio, P is
the normal force, mu is the static coefficient of friction between the contact surfaces and T is the
tangential force (T<<mu*P).
Then later he talks about frequency dependence of fretting:
"6.4.4.5 Frequency of Motion
Because fretting is a rate-dependent phenomenon, the contact resistance will be affected by the
frequency of oscillations. The results in Figure 6.17 show the variation of the number of fretting
cycles required to attain a predetermined contact resistance value as a function of the oscillating
frequency. The data shown are for copper vs. copper26 and aluminum vs. tin-plated copper
contact combinations. It is clear that the lower the frequency, the shorter the time to reach a
given level of elevated contact resistance. The observed effect of frequency can be explained in
terms of oxidation factor of fretting. Because oxidation is time dependent, at lower frequencies for a
longer time the contact zone will be exposed by fretting to oxidation as a result of which an increasing number of conducting spots in the contact zone will be closed, thus increasing the contact resistance."
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