Determination of characteristics of grain movement in the presence of dry friction forces and resistance of the environment

Abstract

Purpose. Determination of the effect of air resistance on the parameters of particle movement on rough surfaces and determination of the particle movement resistance coefficient. Methods. Based on the analysis of modern ideas about the mechanisms of the formation of hydrodynamic (aerodynamic) resistance of the environment during the movement of a solid body, the form of recording the resistance force (formalization of the resistance force) is determined, and in accordance with the accepted form of representation of the resistance force, which depends on the aerodynamic regime (Reynolds number), the equation of motion is formulated along the surface in a stationary or moving air environment according to the value of the active forces. To identify the constant coefficients of differential equations, their analytical (symbolic) solution is obtained in the form of dependences of displacement S on time t. The coefficients included in the equation are determined from the experimental data (direct measurements of S and t) from the dependences of S(t). The movement of a single particle or several connected particles along a real surface (smooth, artificially rough, perforated, etc.) of a plane inclined to the horizon at an angle α was used as a model of physical and virtual experiments. The size of the angle α changes the speed of movement of the particle and the time it stays on the plane. Results. Theoretical and experimental studies of the movement of particles of grain material along sloping surfaces (feeding device) were carried out, which made it possible to determine the characteristics of the movement of the material: speed of movement, speed of descent of the grain from the support surface, coefficients of friction and aerodynamic resistance for different groups of grain material. Conclusions. The coefficients of friction and aerodynamic resistance of the air medium determined by the proposed method make it possible to use known theoretical mathematical models to calculate the parameters of particle movement on an inclined plane with maximum accuracy. Keywords: grain material, support-slope surface, speed of grain movement, coefficient of friction, aerodynamic resistance, equation of dynamic movement of grain.