Abstract
In actual slivers, there are groups (“Cluster”) of fibers which cannot be divided into single fibers in carding and behave like a single fiber. In the drafting zone, moreover, some of these groups (of fibers) may be divided into several smaller groups and some of groups or fibers may be united into a single group. In this paper, the effects of grouping of fibers and its division or combination in the drafting zone upon the irregularity of drafted sliver are studied. After theoretical studies, the following equations may be introduced. Here, V0(y, ∞) and V(y, ∞)are the relative variances of the number of fiber leading ends included in a piece of sliver y long, in in-going and drafted sliver respectively. D is the draft ratio, and _??_ is the mean density of fiber leading end in in-going sliver. K is the number of fibers which combine into a single group, _??_0 and _??_ are the means of K, and C20_??_K_??_and C2_??_K_??_are the relative variances of K in in-going and drafted sliver respectively. ατ is the relative amplitude of variation with wave length λτ in in-going sliver, which may be analysed into Fourier Series. I(y), A(λτ, D, σ) and α(λτ, D, y) are coefficients which vary with D, λτ, y and the shape of distribution of velocity change point of fiber leading end, as formulated in the previous paper. From these equations, several problems on actual drafting may be discussed.
