Hairiness of staple fiber yarns part I: mathematical modeling

Abstract

In this work, an attempt is made to create probabilistic models of yarn hairiness and verify them with experimental results. The first part of this work deals with model development, while the second part focuses on model validation. In this part, a set of generalized relationships on yarn hairiness are developed. Assuming only one type of hairs present in the yarns, a single exponential model of yarn hairiness is created. The number of protruding fibers is found to decrease exponentially with the increase in yarn radius. Under the consideration of two mutually independent types of hairs in the yarns, a double exponential model of yarn hairiness is developed. Further, the evaluation of yarn hairiness according to both the models is discussed. In the second part of this work, we make an attempt to validate the models with the experimental results and develop better understanding of the characteristics of yarn hairiness.

Keywords:

• hairiness
• single exponential model
• double exponential model
• blackening function

Disclosure statement

No potential conflict of interest was reported by the authors.