IMPACT OF LOOSE MATERIALS ON TRACK HOPPER WALLS - S. S. Muradova; L. V. Fedoseeva (Вестник Дагестанского государственного технического университета: Технические науки, 2017)
Objectives. During the design of different types of devices it is important to obtain reliable information concerning both the pressure distribution along the device's walls and the pressure at the level of  the eduction gear. Differential equations for the equilibrium and  stationary states of the loose medium accounting for the forces of  dry friction between its particles are provided in the article.Methods. Both the vertical pressure component z P and its gradient along axis OZ are assumed to depend on the respective radius.  Consequently, different forces will act vertically on the neighbouring  elementary rings. This leads to the neighbouring outer ring being  shifted downwards relative to the one under consideration;  conversely the neighbouring inner ring, relative to the latter, will be  shifted upwards. Therefore, the forces of dry friction acting on the  inner and outer lateral surfaces of the elementary ring under consideration will be directed in opposite directions. The resultant force will be determined by the gradient of the pressure  component along the coordinate  P . The assumption that the  components of the pressure acting on the loose material depend on  the coordinates leads to the need to take this force into account.Results. The resulting differential equations are integrated by  successive approximation in the boundary conditions corresponding  to an extended track hopper; the derived analytical expressions for  the pressure components of loose material in the hopper are  illustrated with the help of graphs for the actual parameters of the  hoppers; the distribution of loose material pressure along the walls  of track hoppers is analysed on the basis of loose material concepts  as an easily deformed anisotropic medium, which differs in its  properties from a liquid and does not obey Pascal's law.Conclusion. The walls of the hopper take on all the load. To save the wall's material, its thickness can be considered not as a  constant, but rather as a variable, providing maximum strength at a  level of 2/3rds of the height at which vibrators are to be positioned  to ensure a continuous flow of loose material from the hopper.