TY - JOUR

T1 - Traveling waves along viscous filaments

AU - Aarts, A.C.T.

AU - Eijndhoven, van, S.J.L.

AU - Zavinska, O.

PY - 2012

Y1 - 2012

N2 - In this article, deflections of a viscous filament in a classical fiber spinning set-up are analyzed. The deflections are considered in a direction perpendicular to the vertical equilibrium state of the spin line. The result is a traveling wave equation with non-uniform coefficients representing the non-uniform filament velocity and non-uniform tension in the spin line. Under neglect of air drag, the system is conservative with respect to an energy functional, so that its eigenmodes have purely imaginary characteristic values. A numerical analysis of the eigenmodes of the system reveals that deflections propagate from take-up wheel to spinneret, with frequencies being multiples of a basic frequency and amplitudes sinus shaped with the maximum being shifted toward the spinneret. From the numerical results, a formula is derived, which approximates the basic frequency and traveling wave velocity directly in terms of the spinning process parameters.
Keywords: Deflection – Eigenmode – Fiber spinning – Frequency – Traveling wave – Viscous filament – Viscous string model

AB - In this article, deflections of a viscous filament in a classical fiber spinning set-up are analyzed. The deflections are considered in a direction perpendicular to the vertical equilibrium state of the spin line. The result is a traveling wave equation with non-uniform coefficients representing the non-uniform filament velocity and non-uniform tension in the spin line. Under neglect of air drag, the system is conservative with respect to an energy functional, so that its eigenmodes have purely imaginary characteristic values. A numerical analysis of the eigenmodes of the system reveals that deflections propagate from take-up wheel to spinneret, with frequencies being multiples of a basic frequency and amplitudes sinus shaped with the maximum being shifted toward the spinneret. From the numerical results, a formula is derived, which approximates the basic frequency and traveling wave velocity directly in terms of the spinning process parameters.
Keywords: Deflection – Eigenmode – Fiber spinning – Frequency – Traveling wave – Viscous filament – Viscous string model

U2 - 10.1007/s10665-011-9466-4

DO - 10.1007/s10665-011-9466-4

M3 - Article

SN - 0022-0833

VL - 72

SP - 107

EP - 124

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

IS - 1

ER -