Efficient and accurate simulation of the rope–sheave interaction in weight-lifting machines

Abstract

This article presents different approaches that can be used for modelling wire ropes in weight-lifting machines. It is shown that modelling the rope as a linear spring, although very simple and efficient, is energetically inconsistent and produces spurious terms in the equations of motion if the rope deformation along the segment in contact with the sheave is not considered. In order to overcome this problem and obtain an efficient yet accurate method for the simulation of such systems, a semi-analytical method is derived by introducing an analytical model of the rope–sheave interaction in the system, and the obtained results are compared with a finite-element numerical model. The semi-analytical model is based on a continuum mechanics approach of the rope; it assumes Coulomb friction between the sheave and the rope and neglects the centrifugal force of the segment of rope in contact with the sheave while accounting for tangential inertia forces in the rope. The numerical model is based on the Absolute Nodal Coordinate Formulation, and accounts for both the inertia forces and the bending and axial deformation of the rope.