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In this paper, the transverse vibration displacement, velocity and acceleration of the wire rope of deep mining hoisting system is acquired by establishing a mathematical model and solving it by Galerkin discrete method. The results show that: for the deep mining hoisting system with hoisting depth of 1000m and hoisting load of 25 t, when there is an excitation with amplitude of 0.002 m and frequency of 10 Hz at one end, the transverse vibration displacement of the wire rope at 200 m is between -0.015 m and 0.015 m, the transverse vibration velocity is between –0.05 m/s and 0.05 m/s, and the transverse vibration acceleration is between –0.5 m/s2 to 0.5 m/s2. Meanwhile, it can be found that different loads, accelerations and mass of wire rope per unit length have little influence on the transverse vibration displacement of the wire rope, but different external excitation frequency have an impact on the transverse vibration displacement of the wire rope. Then the vibration energy and natural frequencies are analyzed. And the maximum vibration energy and 30 natural frequencies are obtained. Finally, the mathematical model is verified through the experiment and the validity of the mathematical model is proved.

Transverse vibration analysis of wire rope in deep mining hoisting system