Improved Limiting Irregularity and Effective Fineness Models for Wool Yarn

The limiting irregularity of yarn is the minimum count variation expected from ideal yarn with a random fibre ends distribution. It can be calculated with the Martindale limiting irregularity model which takes into account the changes in the number of fibres in yarn crosssection and the variations in fibre cross-sectional areas. However, the variations in fibre cross-sectional areas are calculated from between-fibre diameter variations only, without considering the within-fibre diameter variations. Wool fibres exhibit diameter variations both between fibres and within fibres. Ignoring the within-fibre diameter variations may lead to an underestimation of yarn limiting irregularity. This paper reports an improved model for calculating the limiting irregularity of wool yarn, incorporating both between-fibre and within-fibre diameter variations of the constituent wool fibres. Experimental verification shows that this model can predict yarn limiting irregularity more accurately than the existing one. Based on this improved yarn limiting irregularity model, an improved effective fineness model which also incorporates both within-fibre and between-fibre diameter variations has been established.