Longitudinal vibration characteristics of multi-rope friction hoisting system by the finite difference method

Considering the impact of the balance of wire rope to the mine hoisting system and using Hamilton principle to establish the variable length of steel rope longitudinal vibration dynamic model of mine hoisting system.The finite difference method was used to discretize the partial differential equation to ordinary differential equation.The mine hoisting system was used to the example to analysis the regular of the longitudinal vibration of wire rope，the Hilbert marginal spectrum and the energy diagram of the system are plotted.The simulation results showed that the elongation of mine hoisting rope system is increasing in the descending process of mine hoisting system，which is unrecoverable deformation；during the whole process of operation，the frequency of 2Hz is the largest，according to the parameters of the multi rope friction hoisting system，it cannot produce resonance phenomenon；in the process of mine hoist system，the energy is almost 0 in downlink，while in the uplink process，the energy of the system increases with the time increasing，the most dramatic increase in pithead.Therefore，it can provide an idea for energy analysis and dynamic tension analysis of multi rope friction hoisting system.