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.