Theoretical Model of Cotton Fiber Waste Cleaning Process Using A Peg Screw and Mesh Surface

The article provides a theoretical analysis of the operating process of a spiked screw and hole-mesh cleaner used in the final stages of cotton ginning to remove small impurities from the lint, lint, and cyclone fluff. Based on the power-kinematic interaction of the working element with fibrous waste and a model of statistical (probable) separation of impurity particles along the fibrous flow, a unified engineering formula was obtained that links the cleaning efficiency with the structural and kinematic parameters of the working element: pile diameter, mesh hole size, rotation frequency, working slit, and screw pitch. Numerical calculation results showed that for the experimental sample with a peg diameter dk = 12 mm, a mesh hole of 6×50 mm, and a rotation speed n = 160 rpm, the cleaning efficiency ηo ≈ 92%; meanwhile, fiber loss is practically absent. The model quantitatively confirmed the existence of a technological optimum for hole size—decreasing it reduces efficiency, while increasing it sharply increases fiber loss.