The nonlinear dynamic responses of a wire rope under periodic excitation in a friction hoisting system are investigated. Longitudinal excitation experiments of different periodic excitation frequencies are performed. The nonlinear dynamic characteristics of the rope, including transverse, longitudinal, and coupled vibrations, are discussed with time-frequency analysis. The results show that the transverse vibration is a forced vibration following the excitation, while the longitudinal vibration shows a complex, random vibration state. The vibration amplitude and intensity deviate significantly from their linear trend (superharmonic resonance) at some excitation frequencies, and this deviation indicates the typical nonlinear multiorder natural frequency characteristics. The lifting motion can lead to additional corrugated high-order harmonics and cause a fundamental wave distortion of low-frequency excitation. Experimental evidence for the coupling characteristics of the transverse-longitudinal rope vibration in the lifting process is found.

A new transmission theory of “global dynamic wrap angle” for friction hoist is proposed. The theory is based on a mine hoist simulation model which combines the suspended rope with the wrapped rope. Rope dynamics in a suspended section are verified by the field experiment results. The theory holds that the mechanical state of wire rope is dynamic through the whole wrap angle, including deformation, contact and friction. When the rope enters the wrap angle, it provides positive friction and changes direction at a certain boundary point. The demarcation of the boundary depends on the rope load on both sides of the friction pulley. The theory is suitable for accurately analyzing the kinetics of high-speed and heavy-load friction hoisting.

Based on the rigid finite element method and multibody dynamics, a discrete model of a flexible conveyor belt considering the material viscoelasticity is established. RFE (rigid finite element) and SDE (spring damping element) are used to describe the rigidity and flexibility of a conveyor belt. The dynamic differential equations of the RFE are derived by using Lagrange’s equation of the second kind of the non-conservative system. The generalized elastic potential capacity and generalized dissipation force of the SDE are considered. The forward recursive formula is used to construct the conveyor belt model. The validity of dynamic equations of conveyor belt is verified by field test. The starting mode of the conveyor is simulated by the model.

The dynamic distribution of contact stress of friction lining in the process of deep coal mine friction transmission was investigated in this study. Rope tensions during lifting and lowering were obtained using Simulink simulation models first. Then, correlation model of contact stress of friction lining was established. Subsequently, effects of the friction coefficient, lifting load, terminal mass ratio, maximum speed, maximum acceleration and acceleration rate on the dynamic distribution of contact stress were explored. The results show that the wrap angle of the friction pulley is divided into three, i.e. static, mixed, and friction angles, respectively. Furthermore, the friction angle decreases with the increasing coefficient of friction, and the increases of the terminal mass ratio induce expanding trends of overall ranges of the friction angle, which could result in rope skid accidents and unpredictable failure of friction lining.