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 model, the nonlinear dynamic with constraint rope is established. Meanwhile, time-varying multi-segments non–equal-length element transformation method (TMN-ETM) proposed save computation time. Then, natural frequencies, lateral responses calculated when stiffness coefficient zero. And calculations compared traditional solution method. The results show that only about few areas in loop have large stress norm value, while rest parts small values. Besides, suspension rotor releasing conducted. When static converted friction, torque angle acceleration will be mutated at switching instants, slip-stick transition occurs.