In an actual-drafting, capacitance of roller, which we defined in the previous report, varies with time. So,
c1 (
t), capacitance of front roller, and
c2 (
t), capacitance of back roller, have to beexpressed by the following equations;
c1(
t)=
c1+
Δc1(
t)
c2(
t)=
c2+
Δc2(
t)
In the above equations, unvariable values of the capacitance of roller, c, and
c2 are calculatedi by the following equations; where
X: position
L: length of draft-zone _??_: mean value of fiber length
lmax: maximum value of fiber length
f(
l): probability density function of fiber length in feed sliver
ρ(
x): probability density function of velocity-change-points As there is the next relation between
Δc1(
t) and
Δc2(
t),
Δc1(
t)=
Δc2(
t) we can express the change of the capacitance of roller only by
Δc2(
t).
From the differential equation of roller-drafting, we can express the relations among the variables-thickness of sliver produced, feed sliver thickness, surface velocity of front roller, and capacitance of back roller-in the following way.
From the above equations we can calculate the distributions of fiber length and velocity-change-points at the minimum change of the sliver thickness of sliver produced, that is the sharp distribution of fiber length (with the fibers of the same length) and the squeezed distribution of the velocity-change-points to the back roller side.
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