Abstract
Axial wobbles of the head sheave due to manufacturing accuracy and installation technology can exert periodic lateral excitations to the winding hoisting rope. A hoisting rope consists of a constant catenary rope from the drum to the head sheave and a variable vertical rope from the head sheave to the conveyance. The longitudinal and lateral vibration responses of the hoisting rope are coupled to each other. In this paper, the coupled lateral-longitudinal governing equations of the winding hoisting system under the axial wobble excitations of the head sheave are established by the Hamilton principle. The governing equations are nonlinear infinite-dimensional partial differential equations, which are discretized into the finite-dimensional ordinary differential equations through the Galerkin method. The dynamic responses of the hoisting rope under the head sheave axial wobbles are given by MATLAB simulation when the winding hoist is lifting or lowering. The results show that lateral vibration displacements of the vertical rope under the head sheave axial wobbles are larger than those of the catenary rope. The axial wobble amplitude range of the head sheave is given to limit the lateral vibration displacements of the hoisting rope.
Highlights
In order to increase production power, coal is being mined from strata at ever-increasing depths. e safety and reliability of the ultradeep mine hoist are becoming increasingly significant [1]
E lateral vibration characteristics of axially moving strings are reviewed [13]. e dynamic responses of the string under a single motion force are given through the perturbation and numerical methods [2]. e dynamic behavior of the winch rope during winding or unwinding is given, which is verified with a new software toolbox [3]. e bending moment expression of the catenary rope is derived from the bending moment equation, and its large sag and bending stiffness are obtained [14]. rough the Galerkin method, the nonlinear dynamic characteristics of axially moving viscoelastic strings are given [4]. e steady-state periodic lateral behaviors of axially accelerating viscoelastic cables are given through the Hamilton principle and the Kelvin viscoelastic method [5]
A spatial discretization method is given in order to predict dynamic characteristics of a timevarying rope system [7, 8]. e integrated model of the highlevel building elevator is given. e research results show that nonlinear dynamic behaviors entering the various parts of a building elevator are mutually influential [9]. e nonlinear lateral vibration behaviors of the flexible elevator cable with variable length are given by the Hamilton principle [10]. e autoresonance characteristics of the
Summary
Nonlinear Dynamic Behavior of Winding Hoisting Rope under Head Sheave Axial Wobbles. Axial wobbles of the head sheave due to manufacturing accuracy and installation technology can exert periodic lateral excitations to the winding hoisting rope. The coupled lateral-longitudinal governing equations of the winding hoisting system under the axial wobble excitations of the head sheave are established by the Hamilton principle. E dynamic responses of the hoisting rope under the head sheave axial wobbles are given by MATLAB simulation when the winding hoist is lifting or lowering. E results show that lateral vibration displacements of the vertical rope under the head sheave axial wobbles are larger than those of the catenary rope. E axial wobble amplitude range of the head sheave is given to limit the lateral vibration displacements of the hoisting rope The coupled lateral-longitudinal governing equations of the winding hoisting system under the axial wobble excitations of the head sheave are established by the Hamilton principle. e governing equations are nonlinear infinite-dimensional partial differential equations, which are discretized into the finite-dimensional ordinary differential equations through the Galerkin method. e dynamic responses of the hoisting rope under the head sheave axial wobbles are given by MATLAB simulation when the winding hoist is lifting or lowering. e results show that lateral vibration displacements of the vertical rope under the head sheave axial wobbles are larger than those of the catenary rope. e axial wobble amplitude range of the head sheave is given to limit the lateral vibration displacements of the hoisting rope
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