Considerations of mine hoisting rope contraction

Hoisting ropes are constructed of wires and strands positioned helically around the axis. This helical positioning is such that, for a rope loaded at the end with weight Q, the longitudinal displacement u, axial force P, torsional displacement v and constant torsional moment M are generated. Moreover, the self weight of the rope q gives a force acting along the axis of the rope. This force changes its value from 0 at the bottom to qL at the top. Additionally, this force causes, along the rope length, a variable torsional moment which will make the rope rotate. During the movement of the conveyance downwards, the descending part of the rope rotates, which causes it to untwist on the section up to the half-depth of the shaft and twist up on the other half-depth. As the result, the twisting lay of the rope changes, increasing in the upward direction and decreasing downwards. The angle of twist of the strands changes in an opposite way. When moving upwards, the uplifted rope does not twist and retains its state of deformation up to the moment when it passes over the pulley. Next, the cycle of untwisting and twisting repeats during the movement of the other conveyance downwards. This phenomenon has been observed in practice in mines, and has been analysed, in the works of Glushko (1966} and Popowicz (1963)
 Author(s): Hankus, J.