IMPACT OF LOOSE MATERIALS ON TRACK HOPPER WALLS

Abstract

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.