Mathematical modeling and geometric analysis for wire rope strands

Parametric models of round wire rope structures in arbitrary centerlines were presented and their geometrical features were analyzed based on enveloping theory. Especially concerning on strand directions and types such as right/left Lang lay and on strand wire structures as single-helixes, double-helixes and super-coiled configurations, a series of recursive formulas of spatial enwinding equations of wires and strands were derived. Geometrically configuring accurate wire radii of multiple strands in undeformed way in which all wires touch the core wire and the adjacent one in Seals and Warrington, mathematical optimal models derived from envelopment were presented. Through analyzing the density of space curve groups, the geometric features in which they are usually in point contact between adjacent wires and strands rather than in line were expressed qualitatively. The curvature of wire surface stretching and warping was demonstrated by orthogonal parameterized curve nets. The modeling process was implemented on CATIA and MATLAB platforms. And mathematical representation of geometric features of wire strands was shown in detail. The results may support parametric modeling platform of wire ropes for fast indeterminate contact analysis statically and dynamically.