An efficient model for dynamic analysis and simulation of cable-pulley systems with time-varying cable lengths

A cable-pulley system is composed of several segments of cables, winches and different types of pulleys. Modeling the motion of the flexible cable with time-varying length and the coupling motions between the cable and the winches or the pulleys are the major difficulties of its dynamic analysis. In this paper, an efficient model is presented for dynamic analysis of the cable-pulley system. Material coordinates and spatial coordinates are explicitly distinguished due to the flow of the cable. In order to improve computational efficiency, the axial instant strain of the cable is replaced by the axial time-averaged strain in a short time to filter out high frequency components. The flexible cable is discretized by cubic spline interpolation and the virtual powers of axial tensile strain, inertia and gravity forces are formulated. The governing equations of the cable-pulley system are assembled in terms of all description parameters of the cable, the winches and two different types of pulleys. The degrees of freedom (DOFs) of the internal nodes on the cable elements are reduced. At last, three typical numerical examples are demonstrated to prove the validity of this method.