Coupled Extensional-torsional Vibration Frequency of Hoisting Rope in Tower-type Friction Drive Hoist System

In order to avoid resonance, and to enhance safety of hoisting system and monitoring reliability, an impact mechanical model of mine hoisting rope for friction drive hoist system was built. According to Hamilton principle and considering the effect of oriented pulley and hoisting rope string, coupled extensional-torsional and extensional only mathematical models of hoisting rope were deduced. Mode shape and transcendental equation of angular frequency were obtained based on the hypothesis that the wave of vibration propagated with sine shape. With numerical calculation, results show that the frequency considering the effect of oriented pulley and hoisting rope string was slightly lower comparing with the frequency ignoring the effect at the bottom of shaft, but much different at the mouth; and there is significant difference between coupled frequency and extensional vibration only. Thereby, to make the design and monitoring of mine hoisting much more reliably, it is suggested that the extensional-torsional coupled vibration of hoisting rope, oriented pulley and hoisting rope string should be considered.