Coupled vibration of hoisting cable in cable-guided hoisting system with different swivels

In most cases, the hoisting cable in the cable-guided hoisting system is connected to the hoisting bucket with the swivel. The coupled longitudinal-torsional responses of the hoisting cable with time-varying length are investigated. The hoisting cable and two guiding cables are discretized by employing the assumed modes method, while the equations of motion are derived using Lagrange equations of the first kind, where a coefficient λ varying from 0 to 1 is introduced to represent the free spinning, proportional and self-locking swivels. The longitudinal and torsional displacements with different swivels are obtained. The results indicate the torsional displacement in the free spinning swivel is much larger than that in the proportional and there is one resonance in the former, while the longitudinal resonance in the free spinning swivel occurs earlier than that in the other two, which implies the system frequencies decrease. In addition, the presented model could also be used to describe the coupled vibration in the rigid rail-guided hoisting system but needs more modes.