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In order to analyse the system spatial vibration of compound biaxial and inter-shaft bearings during unbalanced excitation, the theory of rotor dynamics and bearing contact deformation are combined to establish a coupling system model of compound biaxial and inter-shaft bearings. Considering the moment of inertia, gyro effect, and structural damping, a one-dimensional beam model is used to perform the MATLAB numerical calculation of the coupling system to obtain the modal characteristics of the system, and based on the ANSYS simulation analysis of the three-dimensional model, a modal test is used to obtain the system modal shape and test frequency response function to verify the rationality of the coupling system model. Based on the Runge-Kutta iterative method and Hamilton's principle, the nonlinear amplitude-frequency response of the system is calculated while taking into account the influence of the compound biaxial eccentricity, as well as the stiffness and radial clearance of the inter-shaft bearing. The results show that the changes in the eccentricity of the compound biaxial and the structural parameters of the inter-shaft bearing cause the unbalanced excitation of the system, additional external load changes, and different coupled vibrations between the composite compound biaxial and inter-shaft bearings. Therefore, it is reasonable to match the structural parameters of the coupling system and improve the dynamic performance to avoid system resonance. [ABSTRACT FROM AUTHOR]

Traction systems are a good choice for high-rise lift systems, especially in deep wells. With increasing lift depth and weight, rope-guided traction systems have become an essential design methodology in the mine lift field. In this paper, a comprehensive mathematical model is established to simulate the dynamical responses of a rope-guided traction system with different terminal tensions acting on the compensating rope. The results and analysis presented in this paper reveal dynamical responses in terms of longitudinal and transverse vibration. Additionally, a wide range of resonances occurs in the target system. Differences in the dynamical responses between a traditional traction system and tensioned traction system are analysed in detail. Through comparison and analysis, it is determined that terminal tension plays an important role in the suppression of longitudinal vibration in a system. However, changes in the amplitude of longitudinal vibration are independent of terminal tension, which only affects longitudinal elastic elongation and does not affect the basic shape of longitudinal and transverse vibrations. Based on this analysis, it can be concluded that longitudinal vibration suppression can be achieved by applying proper tension on the compensating rope to ensure that it reaches a tensioning state. Continuing to increase terminal tension is not beneficial for the vibration suppression of a system. The results presented in this paper will serve as a valuable guide for the design and optimisation of traction systems. [ABSTRACT FROM AUTHOR]

The dynamic responses of parallel hoisting system with time-varying length and rigid guidance under drive deviation are investigated considering tension and torsion characteristics of the ropes. The variable-domain three-node elements of rope are employed and the corresponding differential algebraic equations (DAEs) are derived using Lagrange’s equations of the first kind. The slack situation of the rope is considered, and the dynamic equations which are systems of DAEs are transformed to ordinary differential equations (ODEs). The dynamic responses of tension, torsion, and acceleration are analyzed considering radius’ error of the drums, which indicates that the drive deviation between ropes can cause large influence on the tension difference and even cause one of the ropes to slack. However, the torsion of the corresponding rope is active. And unreasonable discordance between ropes should be controlled for the design and manufacture of drum on super deep parallel hoisting system. [ABSTRACT FROM AUTHOR]

The flexibility of the suspension multicables and driven length difference between two cables cause the translation and rotation of the platform in the incompletely restrained cable-suspended system driven by two cables (IRCSWs2), which are theoretically investigated in this paper. The suspension cables are spatially discretized using the assumed modes method (AMM) and the equations of motion are derived from Lagrange equations of the first kind. Considering all the geometric matching conditions are approximately linear with external actuator, the differential algebraic equations (DAEs) are transformed to a system of ordinary differential equations (ODEs). Using linear boundary conditions of the suspension cable, the current method can obtain not only the accurate longitudinal displacements of cable and posture of the platform, but also the tension between the platform and cables, and the current method is verified by ADAMS simulation. [ABSTRACT FROM AUTHOR]