Three-Dimensional Geometry of Crimp

Abstract

Geometric torsion and curvature accurately describe three-dimensional forms of crimp. The usual parameters of crimp frequency and indices of amplitude or extensibility for idealized planar or helical crimp forms are expressible by specific relationships of geometric torsion and curvature. The more common, nonideal crimp forms are characterized by distribution statistics of these two fundamental parameters along the fiber. Mathematical techniques and analytical expressions were developed for describing crimp this way with data from an automatic crimp-measuring instrument and use of a digital computer. Examples are given from measurements made on several commercial man-made and natural fibers.

Geometrical and Mechanical Properties of Alkali-Treated Jute Filaments

“…Moreover, on one hand, a large re data are available in terms of hand, a large f of data are available in terms of hand, a large vo ' e of data are available in terms of crimp frequency an total crimp for wool, with which the alkali-treated jute is intended to be blended, and, on the other hand, no such~data, as far as our knowledge goes, are available for alkali-tteated jute. Brand and Scrub), [4] Hence, in the present s,tudy both the projected-image technique and the Instron techniques were employed to determine the'total crimp of the alkali-treated jute, while the crimp frequency was meatured from the projected image only.…”

“…The manual method of determining curvature and torsion is not only tedious and prone to error but also impractical. To overcome this difficult, Brand el aL [3,4] developed the Automatic Crimp Measuring Instruments (ACMI) in the , duPont laboratories, which not only determines the , distribution statistics of the crimp form in terms of geometric curvature andtorsion, but also provides data in terms of 'classical . imp parameters such as -crimp frequency a~d-.tota crimp.…”

Modeling and Computer Simulation of the Compressional Behavior of Fiber Assemblies

“…The fibers are assumed to each be a portion of a helix. The values of the helix angle a, defined as the angle between the tangent vector t and the centerline of the helix, and the helix radius Ro are chosen to be similar to those for Cantrece nylon, the most regularly helical fiber measured by Brand and Scruby [ 1 ]. Note that several authors define the helix angle as the complement of this definition.…”

Effects of Weft Count and Weft Density on Yarn Crimp% of Unbleached And Bleached 3/1(S) Twill Woven Fabrics

“…Also researchers have reported the effect of crimp on mechanical and physical properties of woven fabrics [17][18][19][20][21][22][23][24]. Studies of fabric geometry have played an important role in the mathematical description or prediction of crimp and a variety of models have been used by investigators [25][26][27][28][29][30]. Moreover, mathematical models for yarn shape in fabric structure are used for simulating plain woven fabric appearance [31].…”