Probabilistic Assessment of Irregularity in Random Fiber Arrays—Effect of Fiber Length Distribution on “Variance-Length Curve” 1

Abstract

The exact distribution and moments are derived for the length (mass) aggregate of fibers to be found within an interval L of a random fiber array as a direct function of the constituent fiber length distribution and the interval size L. The moments immediately facilitate computation of irregularity in terms of the coefficient of variation or the better-known “variance-length curve”, B(L), without using an autocorrelation function required by the traditional time-series approach. The B(L) curve thus obtained reflects the effects of fiber lengths and their orientation on irregularity of the fiber array in the absence of other contributing factors. For a population of uniform fiber lengths, the new results are shown to be compatible with that obtained by using the time-series method. Effects of fiber length and fineness on the resulting yarn irregularity are examined theoretically for a number of selected yarn counts.