Determination of the Axial Velocity of the Material Being Sorted in a Rotating Perforated Drum

This article provides a comprehensive investigation into the motion of bulk materials inside a perforated rotating drum separator, paying particular attention to the correlation between the kinematic characteristics of particles, the structural and geometric parameters of the drum, and the combined effects of gravitational and centrifugal forces. The study develops a theoretical model that captures the dynamics of axial velocity and the residence (exit) time of bulk materials as they move under the simultaneous influence of rotational motion, centrifugal action, and the inclination of the drum relative to the horizontal plane. To establish the governing relationships, Newton’s second law of motion is employed together with energy-based analytical formulations, which makes it possible to derive mathematical expressions describing both the axial displacement of the particles and the time required for their discharge from the drum. These analytical equations are subsequently solved numerically using Microsoft Excel across a wide range of operating conditions, including variations in rotational speed, inclination angle, drum diameter, and length. The numerical results reveal that the axial velocity of the bulk material reaches a stable value after a relatively short transient phase, indicating a quasi-steady state of motion within the drum. In addition, it is shown that the discharge or exit time of the material grows almost linearly with increases in drum length and other key operating parameters, which confirms the strong dependence of throughput capacity on design variables. The outcomes of the research clearly demonstrate that angular velocity of the drum and its inclination angle play a decisive role in governing the efficiency of the screening process. These parameters not only affect the residence time of particles but also determine the quality of separation and the overall performance of the equipment. The developed model and the obtained findings thus provide a reliable theoretical and numerical foundation for the scientific optimization of perforated drum separator design, enabling engineers to enhance process efficiency, reduce energy consumption, and improve the uniformity of material separation in industrial applications.

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