Abstract
Mathematical model was introduced on calculation of size distribution of fiber in beating process, where some assumptions were based on the analysis of each elements of beating probability. Input and output size distribution were represented by vector form. When fiber length distribution was represented, these elements of vector might be given by cumulative frequency, which was calculated from the theoretical distibution curve considering weight. On the other hand, the theoretical distribution curve was not suitable enough to indicate denier distribution, so, these vector elements were calculated by smooth distribution curve (by fiber numbers).
(1) The relation of input vector vs. output one, which was suitably chosen for each distribution, was introduced into beating process, and it is expressed as
B(π·F)+(I-π)·F=F0
where
B: transfer matrix
π: probability matrix
F: input vector
I: unit matrix
F0: output vector
(2) This indication could be suitable for presumption of the change of fiber's configulation, particulary, for that of output denier frequency distribution.
(3) From the point of view of investigating the characteristics of beating process, waiting line-theory was applied, and the indication of output denier distribution was introduced.
(4) The systen of beating process could be evaluated in terms of probabilities.
