A new approach to theoretical yarn unevenness: a binomial distribution model

This is the authors' abstract. We don't add key points for this paper.

For many decades, Martindale’s theory on yarn unevenness has been widely used as a reference for staple yarn production and its quality control. With the yarn count becoming higher and higher and with the decrease in the yarn irregularity, the index of irregularity (I), defined on the basis of Martindale’s limit yarn unevenness, could not be used as a fully effective yardstick for evaluating the yarn unevenness caused by a specific spinning process. This approach, under some plausible assumptions, constructs a new model with a binomial probability distribution that describes the status of the fiber array in a yarn. The analysis of the model is done with the simulation of the parameters and the calculation of cotton ring‐spun yarns is conducted. A newly defined parameter, δ, proves to be valid for evaluating the change in the number of fibers in a cross‐section of the yarn. This parameter, which describes the variation in the number of fibers, can be used as a fiber alignment index in assessing the yarn irregularity in terms of the change in the number of fibers in its cross‐section. The new model can serve as a semi‐empirical method for forecasting the yarn unevenness.