Large deformation of longitudinal-torsional-lateral coupled effect of round balance rope in mine friction hoisting system

Torsion deformable spatial beam and Costello theory are used to establish longitudinal-torsional-lateral coupled model of round balance rope. Based on Coulomb’s friction law and longitudinal-torsional-lateral coupled model, the nonlinear coupled dynamic model with friction constraint of round balance rope is established. Meanwhile, time-varying multi-segments non–equal-length element transformation method (TMN-ETM) is proposed to save computation time. Then, natural frequencies, lateral responses are calculated when the coupled stiffness coefficient is zero. And the calculations are compared with traditional solution method. The results show that only about few areas in the round balance rope loop have large stress norm value, while the rest parts have small stress values. Besides, dynamic responses of the balance rope with balance rope suspension rotor releasing are conducted. When the static friction is converted to dynamic friction, the friction torque and angle acceleration will be mutated at the switching instants, and slip-stick transition in angle acceleration occurs.