Geometry of Bent Continuous-Filament Yarns1

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Abstract
Expressions are derived for determining theoretically the number of filaments accommodatable in successive con centric rings in a multifilament yarn cross section as a function of yam twist and filament diameter. Increasing filament ellipticity with increasing twist is considered. Numerical values are tabulated for several typical filament diameters and a range of yam twists. The yarn packing factor is also given. Photomicrographs of model yarns illustrate that migra tion of filaments occurs with increasing twist; filaments are forced outward from one ring to the next as their ellipticity is increased.Photographs of bent, multifilament model yams show evidence of an increase in helix angle of the filaments on the inside of the bend and a decrease of those on the outside of the bend. A change of filament packing density upon bending is also evident. An increase in packing density on the inside of the bend and a decrease on the outside is observed for some degrees of bending; however, for severe bending the packing density appears to decrease throughout.Analytical results are presented graphically for the curvature and change in curvature of the filaments in a bent, twisted yam as a function of filament position in the yam cross section, yam twist, and radius of curvature. The most significant findings relate to the locations within the yam cross section of the maximum and minimum curvature and changes in curvature. A discussion of the classic geometrical model of a bent yarn as it relates to fiber mobility is included.