Unevenness of Appearance of Spun Yarns Area : Part 2 : Theory on the Length Distribution of an Uneven Area

概要

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Some theoretical equations about the length distribution of a uneven area in an ideal yarn have been induced. The ideal yarn was defined in part. 1. The purpose of this inducement is to find the characteristics of the apparent uneven area in arbitrary yarns. The following results have been obtained : 1. The probability ψ(1) that unevenness begin in position a and extends to position α + l, is derived as follows : ψ / (l)= e -(λ+μ)l {1+ 1/ 2 (λ μl2)+ Σ∞k=2 (λ μ l2)k / 4(k!)2 √k(k - 1)}, where λ is the input density of fiber and μ is the output density. 2, The density function φ(l, l + Δl) = ∫ l+Δll ψ (l) dl / ∫∞o ψ(l) dl. 3, Under scene conditions, in which yarn counts, fiber fineness and fiber lengths are giver, the density function is calculated as an example. 4. Applying the above equations, we have obtain some information concerning the mean length of an uneven area, the relation between the length distribution and the over-level ratio, and the relation between the length distribution and the imperfection index IPI.