A Theory on Structure of Sliver Part 2:Irregularity in Thickness and Weight of Sliver.
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The authors have studied theoretically the relation between the arrangement of fiber leading ends and the irregularity of sliver. The results are as follows : <BR>(1) Let x be the distance measured parallel to the axis of sliver, C<SUP>2</SUP>(X) the relative variance of X, and X the mean of X. Then, approximately<BR>C<SUP>2</SUP>(S(x))≅C<SUP>2</SUP>(Sw(x))≅<SUP>2</SUP>(n(x, ι))…<BR><SUP>2</SUP>(W<SUB>t</SUB>(x<SUB>i</SUB>, y))≅<SUP>2</SUP>(W(x<SUB>i</SUB>, y))≅<SUP>2</SUP>(n(x<SUB>i</SUB>))…<BR>Here, S(x) is the number of fibers in the cross-sectiona at x, S<SUB>W</SUB>(x) is the weight of sliver per unit length, n (x, y) is the number of fiber leading ends between x and x+y, ι is the mean fiber length, W<SUB>t</SUB> (x<SUB>i</SUB>, y) and W( x<SUB>i</SUB>, y) are the weights of tuft and sliver at xj respectivelyt, h e length of them are y.<BR>(2) Let n(x) be the number of fiber leading ends per unit length at x, and<BR>n(x)=r(x)+n Σa<SUB>γ</SUB> sin 2π/λ<SUB>γ</SUB> (x+θ<SUB>γ</SUB>)<BR>Here, r(x) is the random variable of which variance is kn. Then the auto-correlation function p(r) and spectrum distribution function F(λ) of n(x, y) are formed approximately by the following equation :<BR>p(r)={2k(1-r/y)+nyΣ(a<SUB>γ</SUB>α<SUB>γ</SUB>)<SUP>2</SUP>cos(2πr/λγ)/2k+nyΣ(a<SUB>γ</SUB>α<SUB>γ</SUB>) (r≤y)…… nyΣ(a<SUB>γ</SUB>α<SUB>γ</SUB>)<SUP>2</SUP>cos(2πr/λ<SUB>γ</SUB>)/2k+nyΣ(a<SUB>γ</SUB>α<SUB>γ</SUB>)<SUP>2</SUP> (r≥y)……(c)<BR>F(λ)=1/2k+nyΣ(a<SUB>γ</SUB>α<SUB>γ</SUB>)<SUP>2</SUP>{2k/π<SUP>2</SUP>y ∫<SUB>0</SUB><SUP>λ</SUP>(1-cos2πy/p)dp+nyΣ(a<SUB>γ</SUB>α<SUB>γ</SUB>)<SUP>2</SUP>J<SUB>γ</SUB>}……(d)<BR>Here, J<SUB>γ</SUB> is 1 for λ<SUB>γ</SUB>≤λ 0 for λ<SUB>γ</SUB>>λ, and<BR>α<SUB>γ</SUB>=λ<SUB>γ</SUB>/πy sin πy/λ<SUB>γ</SUB><BR>(3) It may be suggested by equation (d) that the remarkable wave length in the variation of thickness and weight of sliver, y long, are 2ι and 2y respectively, except the drafting wave (for y much larger than ι).
- 社団法人 日本繊維機械学会の論文
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関連論文
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