Study of the Friction Interaction between a Filament and a Cylindrical Surface.

An analysis of literature sources on the friction of flexible elements attests to the fact that Euler's formula used in engineering calculations does not take into account the real friction patterns and the process of formation of the virtual area of contact between a filament and a sheave with allowance for the structure of the filament, using Hertz' formula and a binomial expression for the adhesion component of the friction force, and assuming a condition of equilibrium of an element of the filament on the sheave, a new formula is derived which takes into account the effect of a number of parameters not figuring in Euler's formula on the friction of the filament. The use of the new formula makes it possible to determine the molecular constants of the law of friction of a filament without resorting to measurement of the virtual contact area.