Evaluating yarn crimp with fractal geometry

Abstract

Fractal geometry is used to evaluate the irregularities of crimped filament yarns. To measure the fractal dimension of textured filament yarns, methods based on the box counting dimension, the compass dimension, and the equipaced dimension are applied to digital images of the textured filament yarns, obtained using a charge coupled device (CCD) camera. For textured PET filament yarns, as the crimp and twist level increase, higher values of fractal dimension are obtained, confirming that the fractal dimension can be used to evaluate fiber crimp. The fractal dimension and crimp also show an exponential relationship, which is well verified experimentally. Therefore, time-consuming direct measurements of fiber crimp may be effectively replaced by this automatic process, based on the acquisition of crimp images and fractal dimension analysis. The ideal sine wave, which has an equal length, crimp, and twist per meter, is synthesized as a topological model to study the physical properties of crimped yarn. This sine wave study shows that the major parameter of the crimped structure is the period of the crimp, and the dominant effect of yarn shrinkage development in boiling water is the increment of crimp amplitude.