Abstract
Problem statement: The objective of this study is to compare the methods for approximating the positions of twist fiber in yarn structures. Computer Aided Design (CAD) is applied using parametric equation, spline curve and NURBS curve. The ideal twist fiber and fiber migration are studied in 3 dimensions. Approach: The fiber positions in yarn structures were measured by trace fiber technique. The twist fiber in rayon yarn with 2.1, 3.0 and 6.0 twist factors was used as examples. The geometrical properties of twist fiber including curvature and torsion were applied in the analysis of all twist fiber examples. Each position was approximated along the length of yarn and then graphical representations of fiber are shown. Results: For ideal twist yarn, using parametric equation gives a smoother or better curve than when using the spline and NURBS curves. However, in the case of fiber migration, continuity of spline and NURBS curves are smoother than that of parametric equation. Conclusion/Recommendations: According to the comparison of the approximation method, parametric equation is most suitable for geometric modeling of ideal twist fiber, whereas the spline and NURBS curves were recommended for approximating the position of migrating fiber.
Highlights
The basic geometric properties of textiles such as fiber, yarn structures and fabric are related to the complexity in the arrangement of fiber in yarn structures and to the weaving of yarn structures when making fabric
Almost all of the theories studying and analyzing geometrical properties of single spun yarn structures depend on the geometry of ideal twisted yarn which was defined by Hearle et al.[3] based on the coaxial-helix model
All of the single spun yarn structures would not be perfectly like the ideal twist; that is, there would be a small change of the position of fiber radius from the center of yarn along its length
Summary
The basic geometric properties of textiles such as fiber, yarn structures and fabric are related to the complexity in the arrangement of fiber in yarn structures and to the weaving of yarn structures when making fabric. Almost all of the theories studying and analyzing geometrical properties of single spun yarn structures depend on the geometry of ideal twisted yarn which was defined by Hearle et al.[3] based on the coaxial-helix model. All of the single spun yarn structures would not be perfectly like the ideal twist; that is, there would be a small change of the position of fiber radius from the center of yarn (fiber migration) along its length. Tao[9] proposed a mathematical model of the helix as sine wave pattern with variable radius and this model was used in the analysis of the geometrical and mechanical properties of a migrating fiber. A fiber migration pattern of fiber in yarn structures was introduced by Neckar et al.[6] whose model was modified from that of Treloar[10]. Sriprateep and Bohez[8] modified the model of Tao[9] by extending parameters that can be applied to a wider variety of samples in the analysis of geometrical properties of fiber migration
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