A Theoretical Approach to the Unstationary Roller Draft

Abstract

We have tried to approach theoretically the problem of the draft processes under the so-called unstationary condition, under which the peripheral velocity of rollers and the weight of fed sliver change at random. We haue then sought to clarify the qualitative trait with respect to the ralative correlations among three variables, namely, the peripheral velocity, the weight irregularity of fed sliver and the weight irregularity of spun sliver.
To sum up the results of our inquiry:
(1) Where peripheral velocity of rollers and the weight of fed sliver change at random, the weight of spun sliver is generally shown by the following formula:
(2) The weight irregularity of spun sliver is generally smaller where the peripheral velocity changes periodically than in the assumed case of draft in which the equation v₁(t)w₁(t)=v₂(t)w₂(t) is formed.
(3) The weight irregularity of spun sliver is generally greater where the weight of fed sliver changes periodically than in an assumed case of draft in which the equation v₁(t)w₁(t)=v₂(t)w₂(t) is formed.