Dynamic simulation of reeving systems with the extension of the modal approach in the axial direction

Abstract

In this work, the simulation of reeving systems has been studied by including axial modes using the Arbitrary Lagrangian-Eulerian (ALE) description. The reeving system is considered as a deformable multibody system in which the rigid bodies are connected by the elastic wire ropes through sheaves and reels. A set of absolute nodal coordinates and modal coordinates is employed to describe the motion and deformation in the axial direction. This new method allows the analysis of elements with non-constant axial strain along its length. In addition, modal coordinates are employed to describe the dynamic motion in the transverse direction. The non-constant axial displacement within the wire rope is computed in terms of the absolute position coordinates, longitudinal material coordinates, and modal deformation coordinates. To derive the governing equations of motion, Lagrange's equation is employed. The formulation is validated for a simple pendulum-like motion actuated by an initial velocity. The simulation results are provided to trace the movements of the payload. It can be seen that by adding modal coordinates, the axial force within the element changes. Moreover, the effects of modal coordinates in the axial direction are presented for a different number of nodes, and the resulting axial forces are compared with reference solution.