Abstract
Variations in the fibre length distribution caused by the breakage process, which is assumed to be steady and continuous in time, are discussed generally.
Statistically, such a process is defined by three fractions: (a) the fraction α(l)Δt that a fibre of length l breaks in time Δt; (b) β(l)1; →lΔl that breakage occurs in l-1±Δl along a fibre axis having l1;; and (c) γ(l) Δl that fibre length l is lost in time Δt.
From those fractions an integro-differential equation has been derived giving the number-frequency distribution of fibre lengths at any instant. The equation is soluble by artbitrary functions
Assuming γ=0, methods to obtain α and β experimentally and the upper bound of total number at any instant have been investigated.
By applying the above results to breakage in roller carding, the following estimate of α and β has been obtained: α(l)=kl2.5 β(l1; →l)=6l/l21; -(1-l/l1;) Experimental and calculated distributions agree well if this estimate is used.
