The equilibrium of the convergence point in two-strand yarn plying

Abstract

In this paper the theory of the bending and twisting of thin rods of uniform circular cross-section is used to find the relationships between the ply-helix angle, the strand convergence angle, and the applied tensions and torques required to hold the plied strands illustrated in Fig. 1 in equilibrium.The solution of this problem is of importance to the textile yarn manufacturing industry where singles yarns, made from long staple fibres, such as wool, are plied together in order to bind the surface fibres more effectively into the plied yarn structure. This produces warp yarns that are more abrasive resistant.A formula for the relationship between the pre-twist in two initially straight strands, and the helix angle of the plied structure obtained when they are allowed to twist together into a balanced ply structure is also derived in Section 4. A balanced two-ply structure is one that will maintain its configuration without the application of external tension or torque. Balanced ply structures are also important in textile manufacturing processes.