Characteristics of Concomitant Lateral Vibration Under Longitudinal Excitations in Parallel Wire Ropes Vertical Hoisting System

Abstract The parallel wire ropes vertical hoisting system (PRHS) is widely used in mine hoists and elevators. Existing models typically attribute the longitudinal–lateral coupled vibration to the concurrent longitudinal and lateral excitations at the drive end or to the kinematic coupling of individual ropes as described by the nonlinear string theory. However, even when drive end defects generate solely longitudinal disturbance excitation (LDE), the PRHS still exhibits complex longitudinal–lateral coupled vibration responses due to geometric constraints between the parallel wire ropes and the cage. To address this, a rigid-flexible coupled dynamic model of the PRHS that explicitly incorporates geometric constraints is established. A set of differential-algebraic equations (DAEs) describing the PRHS is formulated based on the first-kind Lagrange equations and solved using the generalized-α algorithm. By integrating noise reduction, filtering, and fast Fourier transform (FFT) analysis of the cage vibration signals, a multisource LDE equation for the drive drum end is constructed and validated experimentally. Simulation studies reveal that asymmetric LDE at the drive drum end causes asynchronous motion among the parallel wire ropes, triggering synchronous longitudinal–lateral coupled vibration of the cage, with the lateral amplitude exceeding the longitudinal by 39.4%; applying 6.78 Hz lateral excitation resonantly amplifies cage lateral vibration, while longitudinal vibration remains largely unaffected.