Theoretical Study of the Point Impact of a Fibrous Mass on a Shaped Grooved Surface for Environmentally Efficient Textile Processing

This study presents a theoretical and mathematical investigation into the cleaning dynamics of fibrous materials, with specific focus on the removal of fine foreign impurities in the pre- spinning processing stage. A mathematical model is developed to describe the motion and behavior of fibrous mass within the cleaning zone, where interactions with a shaped grooved surface lead to the fragmentation and separation of contaminants. From this model, a differential equation is derived to characterize the temporal and spatial variation in fiber mass flow through the cleaning zone. The results of numerical simulations and graphical representations provide insights into the behavior of fiber mass under varying degrees of mechanical opening. . The study shows that the degree of fiber opening has a significant impact on the efficacy of impurity removal, increasing the exposure of embedded pollutants and raising the cleaning process’s overall efficiency. This finding is significant not only for improving fiber quality in yarn production but also for reducing waste and energy consumption during mechanical cleaning. The outcomes of this work contribute to the development of environmentally responsible and energy-efficient textile processing systems, supporting sustainable manufacturing practices in the textile industry.