Coupled dynamic modeling and nonstationary vibration analysis of a double-cable hoist under rigid guide-roller contact excitation

Guoying Wang; Dongyue Li; Wanqiang Chen; Yongtao Wang; Chengshuang Zhang; Guoying Wang; Dongyue Li; Wanqiang Chen; Yongtao Wang; Chengshuang Zhang

doi:10.3934/era.2026274

Electronic Research Archive

2026, Volume 34, Issue 9: 6249-6285. doi: 10.3934/era.2026274

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Research article

Coupled dynamic modeling and nonstationary vibration analysis of a double-cable hoist under rigid guide-roller contact excitation

1.
School of Machinery and Automation, Weifang University, Weifang 261061, China
2.
Department of Advanced Manufacturing and Robotics, College of Engineering, State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, China
3.
Shandong Key Laboratory of Intelligent Manufacturing Technology for Advanced Power Equipment, Weifang 261061, China
4.
Service Development Advancement Center of Science and Technology Shandong Province, Jinan 250101, China

Received: 07 May 2026 Revised: 16 June 2026 Accepted: 24 June 2026 Published: 16 July 2026

In this paper, a comprehensive coupled dynamic model was developed for a double-cable mine hoisting system to investigate nonstationary vibration responses induced by rigid-guide imperfections. The spatial motions of the cables in the longitudinal, transverse, and lateral directions were described by nonlinear partial differential equations (PDEs), whereas the cage dynamics and guide-roller interactions were formulated as coupled ordinary differential equations (ODEs). By incorporating time-varying cable lengths and rigid guide-roller contact excitation, the governing equations were transformed into a finite-dimensional ODE system using a normalized spatial coordinate and Galerkin projection. The numerical implementation was verified through modal, time-step, and no-guide-deviation benchmark analyses. Numerical simulations were then conducted to characterize the nonstationary dynamic behavior of the system under guide curvature and verticality deviations, with particular emphasis on tension inconsistency between the suspension strings. The model-based reference deviation amplitudes were further identified, providing a theoretical basis for assessing the influence of guide-structure geometric deviations on hoisting-operation safety.
- double-cable hoist,
- nonlinear partial differential equations,
- rigid guide,
- coupled dynamic model,
- tension inconsistency
Citation: Guoying Wang, Dongyue Li, Wanqiang Chen, Yongtao Wang, Chengshuang Zhang. Coupled dynamic modeling and nonstationary vibration analysis of a double-cable hoist under rigid guide-roller contact excitation[J]. Electronic Research Archive, 2026, 34(9): 6249-6285. doi: 10.3934/era.2026274

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Abstract

In this paper, a comprehensive coupled dynamic model was developed for a double-cable mine hoisting system to investigate nonstationary vibration responses induced by rigid-guide imperfections. The spatial motions of the cables in the longitudinal, transverse, and lateral directions were described by nonlinear partial differential equations (PDEs), whereas the cage dynamics and guide-roller interactions were formulated as coupled ordinary differential equations (ODEs). By incorporating time-varying cable lengths and rigid guide-roller contact excitation, the governing equations were transformed into a finite-dimensional ODE system using a normalized spatial coordinate and Galerkin projection. The numerical implementation was verified through modal, time-step, and no-guide-deviation benchmark analyses. Numerical simulations were then conducted to characterize the nonstationary dynamic behavior of the system under guide curvature and verticality deviations, with particular emphasis on tension inconsistency between the suspension strings. The model-based reference deviation amplitudes were further identified, providing a theoretical basis for assessing the influence of guide-structure geometric deviations on hoisting-operation safety.

References

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