On the Twist of Yarns. (1 st Report)

概要

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A twist structure is a basic element found in yarn and fabrics. Every mechanical property of yarn can be traced into it. How it is formed by a force and what kind of moments should be applied to it has been statically analyzed. A solid streight thread is considered wound around a cylinder with the radius of R and the herieal angle φ. (Fig. 1) In order that the thread may keep a twisted form, torsion and bending must occur in it, the longitudinal angle of tortion being a=sin φ cos φ/R, and the curvature of bending, β=sin2φ/R. The circutnferential force in equilibrium with the resistance caused by the distortion has been solved to be : f' = sinφ/ R2 · {sin2φ(EI)2-cos2φ(GIp)2}1/2, in the direction of an angle which satisfies the relation tan φ'=tan φ·EI/GIp, (Fig. 2) Thus, it would be pointed out that tortional rigidity G as well as elastic modulas E is essential to solve the properties of a yarn. Optimum ratio between torsion and twist which would give the yarn a saturated twist has been derived to be cos2φ, and its theoretical shrinkage rate, 1-cosφ.
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