Strength Degradation and Dynamic Reliability of Damaged Wires in Mine Hoisting Ropes Under Time-Varying Tension

Mine hoisting ropes are subjected to time-varying tension, inertial loads, and constraints imposed by their helical structure during service. These factors readily induce normal compression and slight relative sliding between internal wires, thereby causing surface damage, residual strength degradation, and reduced reliability. In this paper, the internal wires of an 18 × 7 + IWS (Independent Wire Strand Core) mine hoisting rope are taken as the research object. A dynamic model of the hoisting rope and an analytical method for the contact load between internal wires are established. Tensile fracture tests are carried out to develop a residual strength degradation model for damaged wires, and a stress-strength interference reliability model is constructed to analyze the dynamic reliability evolution of damaged wires under different transverse loads. The results show that the rope tension fluctuates significantly with the operating stages during hoisting, and the internal wire forces exhibit marked positional differences. The core strand and interlayer contact regions are identified as potential damage-sensitive zones. As the transverse load increases from 80 N to 320 N, the breaking force of damaged wires decreases approximately linearly with increasing fretting cycles, and the strength degradation slope increases from -9.8 to -21.5, indicating that higher transverse contact loads significantly accelerate wire strength degradation. The working stress of the in-service wires approximately follows a normal distribution, with a mean value of 241.63 MPa and a standard deviation of 26.61 MPa. Under transverse loads of 80, 160, 240, and 320 N, the critical cycles at which the wire reliability begins to decrease rapidly are approximately 1.65 × 10⁶, 1.57 × 10⁶, 1.14 × 10⁶, and 7.38 × 10⁵, respectively.