On the boundaries of the region of stress variation in a hoisting rope

Abstract

The problem of determining the stresses in a hoisting rope during the lifting and lowering of a load suspended from it is divided into two. For small lifting and lowering heights, we neglect the mass and weight of the rope. For large heights, both are taken into account. In the first case, the question is reduced to integrating an ordinary differential equation and in the second, a partial differential equation. This paper is devoted to the first case and, thus, is an introduction to the general formulation of the question. For practical purposes, it is of interest to find the value of the tension T of the rope as a function of time t. In what follows, we assume that the linear velocity diagram v (t) on the drum circumference is trapezoidal. The analytical dependence T = T (t) was obtained by us earlier for each of the three periods of the above-mentioned diagram.