Constraint ability of superposed woven fabrics wound on capstan

• An improved model for predicting the constraint ability of woven fabric wound on capstan is presented.
• Non-dimensional analytical solutions about tension transmission related to constraint ability are proposed.
• The constraint ability of sets consisting of two overlapped woven fabrics is obtained.
• Some insights into the effect on constraint ability induced by some parameters are captured.

Existing capstan equations cannot describe engineering applications where an external pressure is applied. This paper aims at improving available formulations for predicting the constraint ability of woven fabrics wound on capstans. A rigorous and comprehensive model for the capstan effect is proposed taking into account local external pressure and non-linear frictional behavior. In this model, a modified version of Howell's equation in terms of stress is used in combination with the existence of local external pressure. Non-dimensional analytical solutions for tension transmission as well as the maximum tension force held by woven fabric are derived. A model for the constraint ability of an original woven fabric overlapped by another one is also developed and solution is numerically obtained. It is clear that some parameters such as frictional coefficient, tension force applied on initial position, localization and magnitude of external pressure play important roles on achieving optimum constraint ability. Among those parameters, the interaction of initial tension force and external pressure as well as the frictional coefficient dominate the constraint ability effectiveness. The constraint ability is shown to be maximized when local external pressure is applied close to the initial position.