Three-Dimensional Dynamic Modelling and Analysis of a Dual-Cable Winding Hoisting System

In this paper, a three-dimensional dynamic model of a dual-cable winding hoisting system is presented to simulate and analyze its coupled vibrations. The equations of motion of this system are derived based on a substructure method and Lagrange’s equations of the first kind, in which the longitudinal–torsional coupled mechanical characteristics of the hoisting cables are considered. Longitudinal and transverse natural frequencies of the system are obtained and studied, and its dynamic responses due to some assumed displacement excitations are calculated. Numerical results agree well with those from ADAMS simulation, and the results have shown that longitudinal and transverse resonances are inevitable, but the transverse resonance has little effect on the conveyance; Slow longitudinal excitations should be avoided, thus avoiding the first-order longitudinal resonance since the system longitudinal vibration is dominated by its first-order mode; the torque in the hoisting cable is mainly induced by its tension under longitudinal–torsional coupled mechanical characteristics of the cable, and a torque release device is suggested to protect the hoisting cable from torsion failure; Torsional and transverse vibrations of the conveyance are been well restricted by the guiding cables even when the guiding cable pre-tension is zero. The results of this paper can be used to improve the parameter design of the ultra-deep shaft hoisting systems.