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.

超高层建筑使用的电梯由于曳引绳超长，容易产生振动，严重影响高速电梯的舒适性和安全性。因此，电梯的振动一直是人们研究兴趣的课题。本文提出了分析时变电梯曳引系统拉扭耦合振动的理论模型。通过分析螺旋缠绕钢丝绳的变形机理，简化了与钢丝绳拉扭耦合效应的本构关系。基于哈密顿原理，推导了电梯曳引系统拉扭耦合振动的运动方程及相应的边界条件。采用 Galerkin 方法来考虑非线性边界条件的影响，并将运动方程转化为具有可变时间系数的离散方程，并使用 Newmark-β 方法进行求解。理论预测与实验结果良好吻合，证明了该模型的准确性。随后，详细讨论了电梯曳引系统的运行状态和结构参数对其振动性能的影响。