Abstract
During the high speed of the mine hoisting system, external excitation will produce large transverse vibrations on the vertical rope, which may eventually lead to dynamic instability. In this paper, the Hamiltonian principle is used to establish the partial differential equations transverse vibration of the vertical rope. By using the Finite Difference Method, the differential vibration control equation under lateral excitation is discretized and solved, and the transverse vibration characteristics of the vertical rope are improved. Taking the multi-cable winding hoisting system as an example, the effect of external excitation on the transverse vibration of the vertical rope was simulated and analysed. The simulation results show that the solution of vertical rope vibration equations based on the Finite Difference Method can improve the vibration results of the system.
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