Characteristics of Fibre Friction

Abstract

AMONTONS'S classical law of friction, as explained by the cohesion theory, accounts satisfactorily for most cases of metallic friction. For non-metallic materials, however, and in particular the elastic solid field of polymeric monofilaments and natural fibrous materials, many exceptions to his law have been reported^1–4. In these cases it has been observed that over an appreciable load range, the frictional coefficient (µ) does not remain a constant but decreases as the load increases, which suggests that local deformation occurs at the interface between the polymer and friction object. To explain the variability of µ, it has been proposed⁵ that the true area of contact and the shear strength vary with the load. For this to be true, Howell^6,7 has shown that the frictional force must be related to the load by F = KWⁿ, where K and n are constants. (The value of K depends on the properties of the surface materials while n is independent of these and is dependent only on the mechanism of deformation, that is, n is an indicator of the visco-elastic properties of the material under test.) For a fibre or a yarn travelling at a constant speed over a cylindrical object, the change in tension developed in the fibre or yarn is therefore found from the following equation where T₂ and T₁ are the output and input tensions, respectively, θ is the angle of yarn wrap, and R is the radius of curvature of the test object.