Abstract
We studied the transfer function between fed and delivered sliver thickness in drafting process in equilibrium and time-dependent states, and obtained the following results.
(1) The density function of fiber-leading-ends and the distribution function of fiber-length in draft process can be determined from the continuity relation and the probability of the velocity-change-point of fibers.
(2) When the fed sliver thickness does not change largely, the transfer function between the fed and the delivered sliver thickness is given as Gw(S)=fc(as) 1-f(s/Vf)/1-f(s/Vb) e-(ld/vf)s.
(3) Applying Pearson's function of the 1st type to the density functions of the velocity-change-point distribution and the fiber-length distribution, the effects of peakness and skewness of the density functions on the transfer function of sliver thickness are examined by use of Bode diagrams, and the following results are obtained; (a) The optimum density function for the velocity-change-point distribution is parabolic (β1=0, β2=2.1429). (b) The optimum density function for the fiber-length distribution is right triangled (β1=-0.32, β2=2.4).
