Three-Dimensional Determination of Superposed Helical Wires Constraint Ability

Abstract

A three-dimensional theoretical model for predicting the maximum force sustained by a flexible line wound around a rigid cylindrical body is developed based on Clebsch-Kirchhoff equilibrium equations, considering its bending rigidity, no sliding, modified non-linear frictional law in terms of stress and an external pressure exerted on the line. Likewise, this model is extended to solve the constraint problem of superposed counter wound helical wires. Results given by 4 th order Runge-Kutta numerical algorithm show that, except for the line thickness, the constraint ability grows with an increase of other geometric parameters and external pressure. However, it cannot be significantly enhanced by applying external pressure for large initial forces, especially when there is an initial binormal force.