On the basis of a fact that the conditions of spinning processes through which a spun yarn has been produced are reflected on the slipping behavior of the component fibers of the spun yarn, to elucidate the relationship between the region of slip and the dimensions, frictional property and compressibility of the assemblage of the component fibers of the yarn. On an assumption with regard to the fiber parallelism in a fiber assembly, the region of slip for spun yarns has been estimated on the

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... is of studies performed by D. R. Oox, P. A. Smith and M. Hannah. The estimated region of slip dt (t/cm) is represented by the following parametric equation employing the assemblage density 9"o under a pressure of I (gf/cm2) as a parameter: dt=2 (K,b. pvo Kz-cLN z,+_b; PsK, LNd u where d = fiber diameter (cm), L = fiber length (cm), N = number of component fibers existing in cross-section of a yarn, fl = coefficient of inter-fiber friction (nondimension), c = constant for interfiber friction (gf/cm), p .r = fiber density (gf/cm3), Pvo = apparent density of fiber assembly under a pressure of I gf/cm2, b = coefficient of compressibility of fiber assembly (nondimension), Kl = 22rf/P, K2 = 6f, K3 = 47rf, f = maximum drafting force when a yarn is in the slipping state during the untwisting and drafting operation and in this paper, f = 20 gf, and Po = standard pressure and in' this paper Po -1 gf/cm. The values of the region of slip for spun yarns of polyester of 1.5d x 38 mm and 1.5 x 44 mm and also acrylic of 1.5 d x 38 mm and 3 d x 44 mm obtained through experiments performed using an untwisting-drafting machine developed by one of the authors were in good agreement with the estimated values when a suitable values of p"o was selected; pvo = 0.03 to 0.05 for polyester yarn and 0.06 to 0.12 for acrylic yarn.