# Rieter

### The unevenness limit

#### Index

The spinner tries to produce yarn with the highest possible degree of homogeneity. In this connection, evenness of the yarn mass is of the greatest importance. In order to produce an absolutely regular yarn, all fiber characteristics would have to be uniformly distributed over the whole thread. However, that is ruled out by the inhomogeneity of the fiber material and by the mechanical constraints. Accordingly, there are limits to achievable yarn evenness. Martindale indicates that, in the best possible case, if all favorable conditions occurred together, the following evenness limit could be achieved (for ring-spun yarn):

$U_{lim} \frac {80}{ \sqrt{n}} \times \sqrt{1 +0,0004{CV_D}^2$

or

$CV_{lim} \frac {100}{ \sqrt{n}} \times \sqrt{1 +0,0004{CV_D}^2$

where n is the number of fibers in the yarn cross section and CVD is the coefficient of variation of the fiber diameter. Since the variation in the diameter of cotton and man-made fibers is small enough to be ignored in industrial use, the equations reduce to:

$U_{lim} \frac {80}{ \sqrt{n}}$    or    $CV_{lim} \frac {100}{ \sqrt{n}}$

This can be expressed (admittedly to an approximation) as CV = 1.25U. The number of fibers can be estimated from the relation:

$n_F = \frac {tex_{yarn}}{tex_{fiber}}$

The unevenness index I is used in evaluation of the evenness achieved in operation. This is:

$I = \frac {CV_{actual}}{CV_{lim}}$