Nonlinear dynamics of time-varying curvature balance rope coupled with time-varying length hoisting rope in friction hoisting system

Mine friction hoisting system is a typical multi-body system composed of traction sheave, conveyance, hoisting rope, and balance rope. Hoisting rope is of large-scale and flexible tension, leading to large amplitude elastic vibration and huge tension fluctuation during hoisting movement. Balance rope is of small tension amplitude and bending modulus, undergoing significant curvature changes, large displacement, and large deformation. Considering the complex coupling vibrations between the moving hoisting rope and balance rope in the ultra-kilometer-deep shaft, a coupling modeling method of the variable-length hoisting rope with the variable-curvature balance rope is proposed. Based on the absolute nodal coordinate formulation(ANCF), the balance rope is modeled by non-equal-length and variable-number elements, and the hoisting ropes on both sides are modeled by variable-length and variable-number elements. A flexible rope vibration experiment platform is built in the laboratory to verify correctness of the proposed theoretical model.The experimental results are in good agreement with those in theoretical simulation. Besides, the nonlinear coupling dynamic behaviors of hoisting rope and balance rope in an ultra-kilometer-deep well are studied. It reveals the non-stationary phenomenon of hoisting rope and balance rope with a long-time range. Both sides of flat balance rope undergo large bending deformation and non-stationary response when transient resonance occurs in hoisting ropes.

Automated summary

Mine friction hoisting system is a multi-body system consisting of traction sheave, conveyance, hoisting rope, and balance rope. The hoisting rope experiences large amplitude elastic vibration and tension fluctuation during hoisting movement due to its large-scale and flexible tension. The balance rope undergoes significant curvature changes, large displacement, and large deformation due to its small tension amplitude and bending modulus. A coupling modeling method of the variable-length hoisting rope with the variable-curvature balance rope is proposed, and its correctness is verified through experiment and theoretical simulation. The nonlinear coupling dynamic behaviors of the hoisting rope and balance rope in an ultra-kilometer-deep well are studied, revealing non-stationary phenomena and large bending deformation when transient resonance occurs.