Coupled vibration of hoisting rope during tramcar pushing into or out cage in winding hoist system

In order to evaluate the vibration characteristics reasonably during the tramcar pushing into or out cage, the coupled vibration characteristics of hoisting rope was investigated. According to Hamilton principle and considering the effect of torsional movement of wire rope, head sheave and hoisting rope string, the extensional-torsional coupled mathematical models during the cage supporting on the swing deck and the elastic supporting device was built. Based on the property of step function, the mode of hoisting rope was obtained and the method of numerical solution and approximately analytical expressions for displacement, tension and torque were proposed. The results show that the descendent distance of cage by using the elastic supporting device is much less than the swing deck, whereas the tension and torque of rope are slightly lower, but the cage deceleration peak is approximately equal. Consequently, it is suggested that the elastic supporting device should be used while the cage deceleration is limited to the allowable scope of the coal mine safety regulation, which favors to enhance the safety during tramcar pushing into or out cage.