Abstract
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 4th 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.
Highlights
Flexible lines, such as wires, ropes or fibers, wound around cylindrical body, are capable of making up some useful devices in engineering applications
On basis of Clebsch‐Kirchhoff equilibrium equations, a new three‐dimensional model accurately taking into account the bending rigidity, non‐linear frictional law and external pressure has been proposed for capstan problem, suitable for a wide range of engineering applications
According to the formulation of this three‐dimensional model, many parameters which are relevant to geometry, friction law and initial force conditions can be important to determine the constraint ability
Summary
Flexible lines, such as wires, ropes or fibers, wound around cylindrical body, are capable of making up some useful devices in engineering applications. The most likely device called capstan is used aboard ships or rope rescue systems, see Figure 1‐A, to control a rope under significant tension Another very common device is thermoplastic wire hose which is unique in its ability to undergo large internal pressure. Similar constructions can be found in flexible pipes which are widely used in the offshore industry for oil and gas extraction from subsea reservoirs, and many efforts have been carried out to deal with the structural analysis of the armor layers of flexible pipes 1‐4 For all these kinds of structures, estimating the constraint force and evaluating the constraint ability are important to ensure their functional integrity
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