Evaluating yarn crimp with fractal geometry

Fractal geometry is used to evaluate the irregularities of crimped filament yarns. To measure the fractal dimension of textured filament yarns, method s based on the box counting dimension, the compass dimension, and the equip aced dimension are applied to digital images of the textured filament yarns , obtained using a charge coupled device (CCD) camera. For textured PET fil ament yarns, as the crimp and twist level increase, higher values of fracta l dimension are obtained, confirming that the fractal dimension can be used to evaluate fiber crimp. The fractal dimension and crimp also show an expo nential relationship, which is well verified experimentally. Therefore, tim e-consuming direct measurements of fiber crimp may be effectively replaced by this automatic process, based on the acquisition of crimp images and fra ctal dimension analysis. The ideal sine wave, which has an equal length, cr imp, and twist per meter, is synthesized as a topological model to study th e physical properties of crimped yam. This sine wave study shows that the m ajor parameter of the crimped structure is the period of the crimp, and the dominant effect of yarn shrinkage development in boiling water is the incr ement of crimp amplitude.