Studies on the Transfer Function of Drafting Process

Abstract

We made a study of the transfer function of drafting process, between fed and delivery sliver thickness, when the velocity-change-point and fiber-length density functions are no change with time. Following results are obtained : (1) The transfer function between fed and delivery sliver thickness is shown the following equation :Gω(s)=fc((D-1)/s/Vf)1-f(s/Vf)/1-f(s/Vb)e-lds/Vf where fc (p) is Laplace transform of fc (x), velocity-change-point density function, and f (p) is Laplace transform of f (l), fiber-length density function. (2) We were able to lead the transfer functions for the wide shape of density functions using the Pearson Ist type curve for the velocity-change-point and fiber-length density functions. (3) Comparing the transfer functions by Bode diagram to change the kurtosis and skewness of density functions, following results are obtained. (i) The greater the absolute value of skewness and the smaller the kurtosis of the velocity-change-point density function, the more desirable the drafting process property is. (ii) The smaller including sign the kurtosis and skewness of fiber length density function, the more desirable the drafting process property is.(iii) The most desirable drafting process is found when two constants of the Pearson Ist type curve, m1 and m2 are following; in the case of the velocity-change-point density function (m1 =0, m2=0) or (m1=1, m2=1), fiber-length density function (m1 =0, m2=1).