DETERMINATION OF THE DEFLECTION ARC OF COTTON TUFTS CAUGHT BY THE PINS OF A LONG-PIN DRUM

Abstract

This paper presents a theoretical investigation of the interaction between a long-pin drum and cotton tufts and their oscillatory motion in a device designed to remove stones and other heavy impurities from raw cotton. A mathematical model was developed to determine the deflection angle of a cotton tuft captured by the pins of the long-pin drum, taking into account inertial, gravitational, and aerodynamic resistance forces. A differential equation describing the relative motion of the cotton tuft was formulated and solved numerically using the Runge-Kutta method. The effects of the angular velocity of the long-pin drum and the mass of the cotton tuft on its deflection angle and oscillation amplitude were investigated. The calculated results demonstrate that increasing the angular velocity of the drum leads to an increase in the deflection angle and expansion of the cotton tuft trajectory, while a decrease in tuft mass results in a greater oscillation amplitude. Based on the obtained results, an angular speed of approximately 800 rpm is considered appropriate for reducing the probability of cotton entering the waste discharge system and improving the efficiency of heavy impurity separation. The obtained results provide a scientific and practical basis for optimizing the structural and kinematic parameters of the proposed device and improving the cleaning efficiency of raw cotton.