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This investigation was primarily to establish assessment criteria for axial fluctuations of head sheaves in a multi-rope friction mine hoist. Large axial fluctuating displacements of head sheaves can excite intense transverse vibrations in inclined ropes, which can result in dangerous collision between two adjacent ropes. A coupled dynamic model was established and then validated by experimental tests and numerical simulations. In this case, it can be concluded that double rotational frequency of head sheave is the primary excitation frequency and rope tension can change the resonance frequency range. Finally, to avoid large transverse displacements of inclined ropes in a multi-rope friction hoist, based on response–excitation displacement curves, assessment criteria for axial fluctuating displacements of head sheaves were established. [ABSTRACT FROM AUTHOR]

• The calculation equation with correction efficient and particle swarm optimization can improve the inversion accuracy of compressive modulus of the bottom aquifer. • The variation law of the elastoplastic interface of the vertical additional force with the bottom aquifer waterhead is deduced. • The interaction between the shaft and guide rail changes with the guide rail position due to the vertical additional force acting on the shaft. • The guide rail deformation can reflect the deformation trend of the shaft and the connection state between them under non-mining action. To lay the foundation for monitoring the mine vertical shaft deformation and mitigating its influence on the guide rail, this paper studies the deformation law of the guide rail and its interaction mechanism with the shaft under non-mining action. Firstly, the correction coefficient is introduced into the settlement equation, and its compression modulus is inverted by the particle swarm optimization (PSO). Secondly, the relationship between the elastoplastic interface of the vertical additional force (VAF) and the bottom aquifer (BA) water head is deduced, and then its distribution law varied with water head is obtained. Finally, a finite element model using spring elements to simplify the interaction between the shaft and surrounding rock-soil body is established to analyze the shaft deformation law, its interaction mechanism with the guide rail, and the guide rail deformation rule in different connection states. It can be obtained from the analysis results that using the improved settlement equation as the PSO objective function weakens the influence of compressive modulus with the change of soil settlement, and enhances the calculation precision on the BA settlement, so that the deduced relationship between the bottom aquifer water head and the elastoplastic interface of the VAF is consistent with the actual soil settlement and deformation laws. The spring element can effectively simulate the interaction between the shaft and rock-soil body, which makes the action mechanism between them to consistent with the actual situation. Owing to the vertical compression deformation of the shaft, the force direction on the guide rail subjected to the shaft varies with the position, which bears the vertical upward force in the upper section, the vertical downward force in the middle section and the vertical upward force in the lower section. There are obvious differences in the deformation laws of the guide rail corresponding to different connection states, disconnected positions and non-mining shaft deformation, which exist a certain regularity corresponding their respective states. The guide rail mainly produces the fluctuating deformation along the bunton direction, and its amplitude and range increase with the non-mining shaft deformation. All in all, the guide rail deformation can reflect the state of itself, the shaft and the connection between them, which can provide reference and guidance for the monitoring of the shaft deformation and the safety of the mine hoisting system. [ABSTRACT FROM AUTHOR]