An arbitrary Lagrangian-Eulerian discretization method for modeling and simulation of reeving systems in multibody dynamics

This paper presents an efficient discretization method for the modeling and simulation of reeving systems using multibody dynamics. Reeving systems are assumed to include rigid bodies connected by a set of sheaves or reels and wire ropes. The method is based on line-parametrized Absolute Nodal Coordinate Formulation (ANCF) defined in the framework of an Arbitrary Lagrangian-Eulerian (ALE) description. In the ALE description the element nodes have variable material coordinates thus allowing the element to change its position within the flexible body. This property is very convenient to model wire ropes rolled in sheaves or reels that have variable-length free spans, as usually occurs in reeving systems. Axial-torsion elastic coupling of the wire ropes is also a very important effect to be considered in reeving systems. A set of locally defined cross-section rotation angles is introduced to describe this effect thus abandoning the ANCF formalism. This paper presents different options for the wire rope modeling depending on the problem dimension (1, 2 or 3D) and the assumed elastic force model. Depending on the application the method offers elements that can show axial, torsion and bending deformation energies or any combination of them. This paper presents a general procedure to model reeving systems and the numerical calculation of the resulting equations of motion. Two examples are presented: the dynamic model of a 2:1-suspended electrically-driven elevator and a quasi-static model of a large crane.