Determination of elastic deformations in a cable rope when lowering a load

Abstract

The problem of mathematical physics considered in this work is of great importance in mining; it is in matters of mine lifting that it requires further development. Previously, the function e(s), which characterizes the law of change in relative elongation for the part of the rope wound on a drum, was considered arbitrarily specified. Due to the arbitrary assignment of this function, the elements of the above-mentioned part of the rope, passing through position C, undergo an impact at the moment of their inclusion in the vertical part of the BC rope, so the relative elongation and speed of these elements, generally speaking, do not coincide, respectively, with the relative elongation and speed of the part of the BC rope at point C. Note here that the speed values differ from each other by a small amount on the order of relative elongation (see below). The problems of lowering and raising a load lead, generally speaking, to various forms of the second boundary condition. The coincidence of these forms occurs only in one particular case, which requires a special specification of the function e(s). Finally, in conclusion, we examine, as an example, the nature of elastic deformations of the rope for the initial period of rotation of the drum (see article).