Some Stochastic Aspects of Safety Work of Steel Wire Ropes Used in Mining-Shaft Hoists

In most rope transport devices, the used steel wire ropes are replaced with new ones after working for a certain period of time, or after reaching the acceptable level of wear. The operational safety of the entire system depends on the correct diagnosis of the condition of the working wire rope. This is not easy, because the working lives of the ropes are varied, and their wear depends on many factors, including random ones. This article presents three different aspects of the work of steel ropes in mining-shaft hoists. What they have in common is a stochastic approach to interpreting the level of rope wear. The process of progressive wear due to fatigue breaking of wires is presented as the first example. This process is non-linear with a strong upward trend, which, in the final stage, turns into a phase often referred to as “explosive”. The rate at which subsequent wire breaks appear is influenced by numerous random factors, e.g., in the form of different methods and materials from which a given rope is constructed. However, the character of the progressing wear process is most affected by the random distribution of stresses experienced by individual wires and the randomly variable nature of the working environment. The second aspect presented in this article is an attempt to determine the probability of wire breaks of the rope. This was presented on the example of wear of the hoisting rope of a mining-shaft hoist. The last aspect of a stochastic nature, which is discussed in the article, is the issue of separating individual components of this distribution from the multimodal distribution describing the tensile strength of the rope wires, possibly of a normal character. Modern methods of analysis allow such distributions to be assigned to specific structural elements of the wire rope. This gives information about which structural elements of the rope wear faster or unusually and, consequently, determine its strength. This was presented on the basis of the results of strength tests of the wires of the mining-shaft hoist rope, which broke due to excessive corrosion wear of the inner strands. The presented examples explain only a short part of randomness in the description of working ropes, but the intention of the authors is to draw the attention of the personnel responsible for their safe operation to unavoidable random factors.