Lateral and torsional vibrations of cable-guided hoisting system with eccentric load

Theoretical investigation of the lateral and torsional vibrations of the hoisting cage in the cable-guided hoisting system caused by the eccentric load and the flexibility of the guiding cable is presented in this paper. The assumed modes method (AMM) is adopted to discretize the hoisting cable and two guiding cables, then Lagrange equations of the first kind are used to derive the equations of motion, while the geometric relationships between the hoisting cage and the cables are accounted for by the Lagrangian multiplier. Considering all the geometric matching conditions are approximately linear, the differential algebraic equations (DAEs) are transformed to the ordinary differential equations (ODEs). The dynamic responses of the hoisting cage are calculated, and especially the lateral displacements of the guiding cable and the constraints forces at the interfaces are obtained. Preload plays a vital role in affecting the cage vibration, thus, the effects of the total preload and the tension difference are analyzed. The numerical results indicate increasing the total preload can decrease the vibration displacements, while the tension difference has little impact on the vibration but can obviously change the constraint forces. In addition, the vibration displacements are directly proportional to the eccentric load, but less sensitive to the hoisting mass.