It is shown that the exhibition of smooth sliding and relaxation oscillations, or ‘stick-slips’, under conditions of boundary lubrication, when frictional forces are measured by the deflexion of an elastic system, may be explained as due to the dependence of kinetic friction on velocity. In the cases giving smooth sliding, kinetic friction decreases as velocity decreases, at very low speeds; for the cases giving relaxation oscillations kinetic friction increases as velocity decreases. That is, sliding under boundary conditions is not inherently discontinuous, any discontinuous motion being due to the dynamics of the measuring instrument, and is the result of kinetic friction increasing as velocity decreases. Curves of boundary friction against velocity, using various slicing surfaces, have been determined for a number of lubricants, which show both the above-mentioned types of friction-velocity relationship; and the dependence is shown of kinetic boundary friction on molecular weight for a series of esters of the fatty acids, on percentage of fatty oil in a compounded lubricant (actually oleic acid in mineral oil) and on temperature for a pure substance and a mineral oil. The measurements with the series of esters show some agreement with results given by Fogg (1940). The mixtures of oleic acid with mineral oil give decreasing kinetic friction with increasing percentage of oleic acid right up to 100% oleic acid. The effect of temperature on the dependence of friction in velocity shows that the temperature at which relaxation oscillations first occur depends on the speed of sliding, from which it appears that measurements of the temperature at which relaxation oscillations start at constant sliding speed (Frewing 1942) are not a measure of the temperature at which there is a discontinuity in the properties of the boundary layer.
BEYOND SLOW-FAST: RELAXATION OSCILLATIONS IN SINGULARLY PERTURBED NONSMOOTH SYSTEMS
