Theoretical and Experimental Study on Tension–Torsion Coupling Vibration for Time-Varying Elevator Traction System

Elevators used in ultra-high buildings are prone to vibrating due to their ultra-long traction ropes, which significantly affects the comfort and safety of high-speed elevators. Therefore, vibration of the elevator has always been a topic of research interest. This paper presents a theoretical model for analyzing the tension–torsion coupling vibration of the time-varying elevator traction system. The constitutive relations with the tension–torsion coupling effect of the wire rope are reduced by analyzing the deformation mechanism of the spiral winding wire rope. Based on Hamilton’s principle, the equations of motion and corresponding boundary conditions for the tension–torsion coupling vibration of the elevator traction system are derived. The Galerkin method is employed to account for the influence of nonlinear boundary conditions and to transform the equations of motion into discrete ones with variable coefficients of time, which are solved using the Newmark-β method. The accuracy of the proposed model is justified by the good agreement between theoretical predictions and experimental results, following which, the influence of the operation status and structural parameters of the elevator traction system on its vibration performance is discussed in detail.