Theoretical expression and Monte Carlo simulation of longitudinal unevenness for batt used in yarn spinning

The batt is the first semiproduct in the yarn spinning process, and its longitudinal mass unevenness significantly affects the properties of the spun yarn. Therefore, establishing a theoretical model for batt unevenness is crucial for accurately predicting and controlling yarn quality. However, previous models only address cross-sectional unevenness and are not applicable to unevenness along the commonly used segment length (i.e. 1 m). Furthermore, these models are semiempirical and no longer valid because of the progress in both equipment and technology for yarn spinning. In this paper, we first derive an expression for batt unevenness caused by the random positional distribution of tufts—the constituent elements of the batt—that is valid for arbitrary segment lengths. Second, an improved expression is developed by incorporating tuft mass randomness via variance addition. Then, using MATLAB and the Monte Carlo method, the randomness of tuft number and mass was simulated to obtain the unevenness and mass variation of the batt. Finally, data from experiments with cotton, viscose, and polyester fibers for segment lengths ranging from 30 to 300 mm and from previous literature for a segment length of 1 m were used to verify the proposed expression and simulation method. Results show highly consistent trends between measured and predicted batt unevenness, with correlation coefficients exceeding 0.92 for cotton, exceeding 0.91 for viscose, and exceeding 0.94 for polyester, strongly confirming their effectiveness. This research provides a basis for predicting batt and yarn properties, and offers guidance for designing optimum process parameters in yarn production.