Computer modelling of wire strands and ropes Part I: Theory and computer implementation

In this paper the mathematical geometric models of the single-lay wire strands and double-lay wire ropes with defined initial parameters are presented. The present geometric models fully consider the single-helix configuration of individual wires in the strand and the double-helix configuration of individual wires within the wound strands of the ropes. The mathematical representation of the single and double helixes is in form of parametric equations with variable input parameters which determine the centreline of an arbitrary circular wire of the right hand lay and left hand lay strands and ropes of the Lang lay and regular lay construction. The concrete forms of the parametric equations are derived and presented. The application of the derived geometric analytical model is illustrated by numerical examples. Techniques for the implementation of the derived mathematical models in CATIA V5 software and procedures for the generation of the rope model are briefly presented. Correctness of the derived parametric equations and a performance of the generated rope model are controlled by visualizations. The application of the derived mathematical model and the development of a finite element model for the numerical simulation of the multi-layered strand under tension tests are treated in the second part of the paper [1]. (C) 2011 Elsevier Ltd. All rights reserved.