Theoretical Approach to Sliver Irregularity Induced by Drafting

Abstract

To discuss the properties of sliver irregularity produced by roller drafting, the author has completed the following procedures: As the first step, stochastic treatment was made to analyze the behaviors of the fiber in the draft zone. By using this formula, the distribution of the velocity change point, ρ(x), was deduced as a special case of the general representation. As the second step, on the basis of the above-mentioned interpretation, a gene-ralized draft equation which is the differential equation for the fiber density of the front end, n(x t), was deduced. The two-velocity model method is considered an approximate equation constituting a simplified case of the generalized draft equation. By using those equations, the sliver irregularity of the weight per unit length was studied from two points of view. One is the causal interpretation. The other is the statistical interpretation. The causal interpretation means the “one to one correspondence” of the sliver irregualrity. As the last step, physical quantity representing the behavior of the fiber in the draft zone, was related to the spectral density used in the theory of the sliver structure.