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:

F_r(X) + F_g(X) = F_s(X) + F_i(X) +F_f(X) + F_c + F_r(0)

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

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

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

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

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

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

F_r(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 F_c.

F₂ = F₁exp(μ_dθ)

μ_d - surface kinetic friction coefficient, θ - wrap angle

F_C = F₂ – F₁ = F₁ [exp(μ_dθ) -1]

If the guiding device is guiding roller, F_c can be ignored.

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

Thus the force balance equation can be simplified to:

F_r^(x) = F_f^(0-x) + F_r⁽⁰⁾

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

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

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