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Modeling and Natural Frequency Characteristics of Coupled Vibration with Varying Length of Hoisting Rope in Drum Winding System

In order to avoid resonance and enhance safety during designing hoist control method for mine hoisting system, the model of drum winding system guided by a head heave with varying length of hosting rope was established by the method of moving frame approach. According to Hamilton principle, the extensional, torsional and lateral coupled mathematical model with the effect of a concentrated mass was described to investigate the natural frequency characteristics. The mode shape and transcendental equation of angular frequency were obtained by supposing that the wave of vibration propagated with sine shape and using characteristic of the Heaviside function. By taking the scanning method of frequency and the hypothesis of transient, all vibration frequencies of the transcendental equation during drum winding could be calculated numerically, and frequencies at the bottom of shaft during the drum winding were given as a calculation example.