Dynamic analysis of balance rope under multiple constraints with friction

Abstract

Dynamic model of balance rope under multiple constraints with friction is established via using non-equal-length element division method (NEL-EDM) based on absolute nodal coordinate formulation. Then, the natural frequency of balance rope under multiple constraints is derived by the proposed method. The KDP generalized-alpha scheme is expanded to differential algebraic equations (DAEs) with friction constraint equations and used to solve the DAEs proposed by this paper. Compared with the frequencies, lateral vibration displacements at four observation points, the analysis of the NEL-EDM is carried out by MATLAB, ANSYS, and RECURDYN software, and the feasibility of NEL-EDM is verified. The frequencies of balance rope with installed bushing constraints will occur frequency veering phenomenon when the balance rope moves up and down with the conveyance. Last, free responses of the balance rope under multiple constraints due to the effects of conveyance vertical motion, and those of in-plane excitation on forced responses of balance rope under multiple constraints with friction are investigated.