Determination of elastic deformations in the rope when lowering a load

Abstract

The problem of mathematical physics considered in this work is of great importance in mining, specifically in matters of shaft hoisting, and requires further development. Previously, the function e(s), which characterizes the law of variation of relative elongation for the part of the rope wound onto the drum, was considered arbitrarily assigned. Due to this arbitrary assignment, the elements of the aforementioned part of the rope, when passing through position C, undergo an impact at the moment they are incorporated into the vertical part BC of the rope, so that the relative elongation and velocity of these elements do not, generally speaking, coincide with the relative elongation and velocity of the part BC of the rope at point C, respectively. Note here that the values of the velocities differ from each other by a small amount of the order of relative elongation (see below). The problems of lowering and raising a load lead, generally speaking, to different forms of the second boundary condition. The coincidence of these forms occurs only in one special case, which requires a specific assignment 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 drum rotation (see the article).

Read more

None