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. 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.