Analytical Method for Studying the Force Interaction of Elements of Steel Ropes when Working on Blocks

Abstract

The paper considers the issue of force interaction of elements of steel ropes (wire, strands, etc.) when working on blocks. Initially, the issue of mutual relative movement of wires during bending is investigated, this phenomenon is more commonly known as the deployment of a cross section of a wire rope. When determining the additional displacements, it was taken into account that the extension of the rope elements occurs on both sides of the point of incidence of the rope on the block (both in straight and curved sections of the rope). Additional displacements occurring in the curved part of the rope are also taken into account. Next, the problem of the analytical determination of the friction forces between the wires of a rope running onto a rotating block is solved. The approach used is based on solving the Euler equation for a thread bent on a drum. At the final stage, the dependences for the operation of the friction forces are established depending on the coefficient of friction between the contacting surfaces, due to the type of cable lubricant. In particular, it follows from the expressions obtained that with a decrease in the coefficient of friction between the elements of the rope, the work performed by the forces of friction will decrease. The results obtained confirm that the use of effective wire rope lubrication will contribute to energy saving and extend the life of the steel wire rope.