A theoretical model of maximum hairiness of staple ring-spun yarns

This paper proposes a theoretical model for maximum hairiness, defined as the number of fiber ends with a certain length in the surface layer of a unit length of ring-spun yarn. These fiber ends have the potential to become protruding hairs, that is, form hairiness of the spun yarn. With consideration of yarn twist, but excluding loops and wild fibers, this model predicts the maximum yarn hairiness or maximum numbers of potential fiber ends with various lengths, which is derived by employing kernel estimation of fiber length distribution. A hairiness contribution factor is introduced as the ratio between the number of fiber ends in the surface layer that potentially contribute to yarn hairiness and the total number of fiber ends in the yarn cross-section. Previous and the present models associated with hairiness or fiber ends are discussed and compared with the measured number of hairs to verify the proposed theoretical model for maximum hairiness of ring-spun yarn.