Building an analytical model of the gravitational grain movement in an open screw channel with variable inclination angles - Arendarenko, Volodymyr; Antonets, Anatoliі; Ivanov, Oleg; Dudnikov, Ihor; Samoylenko, Tetiana (Eastern-European Journal of Enterprise Technologies, 2021)
Existing technical means for loading silos with grain material do not fully meet the needs of production. The issue related to grain injury remains urgent, which predetermines the need to design a gravitational loader of another principle of operation with the appropriate theoretical justification for the movement of grain material in it. This paper has presented and substantiated the model of the gravitational movement of grain in the peripheral open screw channel with two variable angles of inclination. The model is based on the system of forces in the cylindrical coordinate system, acting on the volume of grain flow in the peripheral screw channel. The grain speed at the end of the braking section of the channel should be as low as possible but not less than the initial flow rate at the beginning of the acceleration section. The model takes into consideration this condition and ensures the optimal passage of grain along any part of the channel. The reported model makes it possible to obtain the speed of grain movement at any time, takes into consideration the height of the bunker hole and the dependence between the angles of inclination of the spirals of acceleration and brake sections. A mathematical dependence is given for these angles that ensures the passage of grain without its discharge and, at the same time, prevents injury to the grain mass due to a controlled decrease in the resulting speed. A separate dependence is provided to find the time at which the grain increases its speed on the acceleration section, reaching the maximum value. Based on the model, a peripheral open screw channel with two angles of inclination of spirals α and β has been proposed. For this channel, the relationships between its key parameters have been established, in particular, values have been substantiated for the recommended angles of 41°…45° for the acceleration section and 39°…35° for the brake section, respectively, as well as the hо/r ratio not less than 0.6...0.7.