精紡における糸切れ数の理論的推定について

概要

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Ends-breakage are assumed to occur in the fiber bundle which forms a triangle zone between a front roller nip line and a twisting point. On this assumption a theoretical investigation into end-breakage produced during spinning has been made together with such factors as tension, yarn irregularity, number of fibers and fiber strength. The following equation for calculating absolute values of end-breakage rates during spinning has been derived : Q=∫TmaxTmin ∑∞n=0[∑nm=0{ncmpn-mqmλn∫∞0g(x)dx}]k(T)dT where Q is the end-breakage rate for a predetermined spun length ;mis the number of fibers which are caught simultaneously between the front rollers and the twisting point ;nis the cross sectional number of fibers ; λn is the probability that fibersnare caught between the front rollers ;Tis the tension exerting on the triangle zone, k(T) is the probability density function ofT; p=I-q, q is the probability that a fiber is caught simultaneously between the front rollers and the twisting point ; and g (x) is the probability density function of X in which X=T-S-R where S is the strength of the fiber bundle in the trianglezone and R is a mutual resistance agaisnt slippage. Since the values calculated by the equation lie substantially within the scope of the empiricallyknown end-breakage, it has been proved that the equation can be of practical use.
社団法人日本繊維機械学会の論文