A precise mathematical model for geometric modeling of wire rope strands structure

• Published in: Applied Mathematical Modelling Vol. 76; pp. 151 - 171
• Main Authors: Zhang, Peng, Duan, Menglan, Ma, Jianmin, zhang, Yu
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.12.2019; Elsevier BV
• Subjects: Algorithms; Core wire; Cross section method; Cylinders; Geometric modeling; Graphical representations; Mathematical analysis; Mathematical models; Particle swarm optimization; PSO; Spiral mathematical model; Strands; Wire; Wire rope; Wire rope strands; Cross section method; Geometric modeling; Spiral mathematical model; PSO; Wire rope strands
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.06.005

•A general mathematical spiral model is deduced for forming the skeleton of rope.•Costello's conclusion is extended to suit universal cases with rigorous proofs.•A novel cross section method (SCM) is put forward and proofed strictly for solving adjacent wires overlapping problem.•A precise geometric modeling of wire rope strands procedure is proposed.•The critical graph of wire radius determination is obtained for simple straight strand. Based on the Frenet frame, this paper proposes a general mathematical spiral model with an arbitrary smooth space curve as the center path, which can accurately build complex skeleton lines of wire rope strands. From the aspect of geometry, all the wires are spatial cylinders and must meet the actual geometric requirements: 1. The center cylinder is tangent or separated from the spiral cylinder; 2. The adjacent spiral cylinders do not overlap each other. For requirement 1, Costello’ conclusion is referenced and extended universally to suit an arbitrary smooth space central curve case with rigorous proofs. For requirement 2, the overlapping problem is described as obtaining the minimum distance between the two adjacent spatial path curves, which is deduced by a novel cross section method (SCM) with rigorous proofs and solved by the General Particle Swarm Optimization (PSO) algorithm. Based on the above models, the geometric modeling of wire rope strands procedure is proposed and implemented on the platforms of MATLAB and SolidWorks. Validations are conducted through geometric graphical representations, compared with those from some previous researches. For the simple straight strand case, when the number of spiral cylinders and spiral radius are given, the critical relationship between the ratio of spiral wire radius to spiral radius and the spiral angle is firstly obtained, which can be a precise dimension design reference of simple straight strand for eliminating initial geometric overlap. Further, to show the advance, some precise graphical examples of complex wire rope strands like independent wire rope core (IWRC) and multilayered rope are presented. The wire rope strands geometric modeling method proposed in this paper is precise enough averting initial geometric overlap between the wires for the benefit of subsequent mechanical computation accuracy and efficiency.