Numerical methods for the analysis of the behavior of a filament (i.e, displacement, stress, strain, etc.) which is pulled impulsively at constant velocity was derived.
Three-element visco-elastic model was adopted as the dynamical model of the filament.
An approximate solution by Laplace transform that is valid in a certain range was obtained. Comparison of its numerical results with those by the characteristic curve method and the direct difference method showed that they are practically in good agreement.

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The separation of a sliver, delivered from a pair of drafting rollers and opened by air flow, was evaluated experimentally by the following parameters:
(1) Sizes of separated fiber groups.
(2) Scatter of time interval of separation.
(3) Time dependent size variation of separated fiber groups.
The results are as follows.
(1) The sliver separation is considerably influenced by the air-speeds up to 30m/s. Larger group separation occurs periodically at low air speed.
(2) The slower the revolution of front rollers n, the better the separation of a sliver. The effect of n on fiber separation decreases with increasing air speed, and clear correlation is observed between n and the longest time interval of separated fiber groups.
(3) Draft ratio of drafting rollers D, affects the fiber separation when air-speed or n is low.
(4) The ratio of periodical group separation to total separation in quantity is very effective to evaluate the separation.
(5) The investigation of the periodicity of separation time verifies that a sliver is separated randomly.

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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 G_w(S)=f_c(as) 1-f(s/V_f)/1-f(s/V_b) e^-(l_d/v_f)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).

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