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# Force Analysis on Spinning Line in Wet Forming – Part 1: Axial Force Balance on the Spinning Line

Axial Force Balance on the Spinning Line

• The axial force analysis on the wet spinning line is basically the same as that of the melt spinning

• The balance of various forces on the spinning line should satisfy the following equation:

Fr(X) + Fg(X) = Fs(X) + Fi(X) +Ff(X) + Fc + Fr(0)

Fr(X) is the rheological force or tension of the spinning line at point X;

Fg(X) is the gravitational force received by the spinning line of length 0 to X;

Fs(X) is the surface tension that the spinning line needs to overcome;

Fi(X) is the inertial force that needs to be overcome for the spinning line from 0 to X to do the axial acceleration movement;

Ff(X) is the frictional resistance produced by the coagulation bath on the surface of the spinning line from 0 to X;

Fc(X) is the frictional resistance caused by the guide wire device to the spinning line;

Fr(0) is the rheological resistance of the spinning solution thin-stream at the exit of the spinneret hole.

The frictional resistance of the guide wire device is Fc.

F2 = F1exp(μdθ)

μd - surface kinetic friction coefficient, θ - wrap angle

FC = F2 – F1 = F1 [exp(μdθ) -1]  If the guiding device is guiding roller, Fc can be ignored.

When X<Xc (distance between the wire guide rod and the spinneret ), Fc can be ignored.

Thus the force balance equation can be simplified to:

Fr(x) = Ff(0-x) + Fr(0)

Fr(x) - Rheological force or spinning tension at x, can be directly measured;

Fr(0) - The rheological resistance at the exit of the spinneret hole can be calculated from Fr(x)-x;

Ff(0-x) - The frictional resistance of the filament in the medium, discussed in the next section.