Development of an analytical model of the controlled movement of grain material on the bulk shelves of a loading-gravity-cascade unit

The object of research is the gravitational movement of grain along the transfer shelves and a cascade loading unit with two acceleration and two braking sections. The study of such movement is carried out to confirm theoretical studies on the development and justification of an analytical model of controlled gravitational movement of grain along transfer shelves. When loading grain, it can be injured when falling from a considerable height and hitting the bottom and walls of the container. This problem requires the development and study of a technical solution that would provide regulation of the velocity of grain movement when loading it into the container. Theoretical studies were carried out using the developed analytical model of grain movement and the proposed equations to find the relationships between the angles of inclination of the acceleration and braking shelves of the gravity-cascade unit. Based on the analytical model, an experimental unit was made of two acceleration and two braking shelves. The shelves can freely rotate on the axes to the required angle in the range from 0° to 90° relative to the horizontal plane. For the shelves of the acceleration sections, the angle of inclination α was chosen from the variable series of 45°, 50°, 60°. Based on the angle α, according to the model, the shelf of the first braking section was set at an angle of 20.43°, 20.48°, 20.32°, and the shelf of the second braking section was set at 38.46°, 35.28°, 29.32°. Experimental studies have shown that the velocity of grain movement is indeed regulated by a combination of the ratios of the angles of the acceleration and braking shelves. In this case, the velocity of grain in the last braking section is close to the initial flow velocity at the beginning of the first acceleration shelf. The values of the absolute and relative errors of the experiments of the experimentally determined velocities and the theoretical value of the velocity indicate quite acceptable limits of deviations for this multifactorial experiment. The relative deviation of the experimental from the theoretical velocity of movement of the grain mass does not exceed 12.76%. The results obtained and their analysis indicate that the presented analytical model and the designed gravity-cascade unit due to the braking and acceleration sections allow solving the problem of controlled movement of the velocity of grain for its loading into containers without injury, in particular into silo structures.