Movement of the top layer of the grain mixture on the vibrating grooved surface

The most unfavourable conditions for the implementation of separation arise in the case where the impurities and clean the grain evenly distributed. Therefore, a layer of granular grain mixture should be pre-prepared for participation in the process, which can be estimated by analyzing the kinematic parameters of the movement of grain particles, which is the purpose of this study. The description of the working body and the process of vibration movement of the grain mixture is given. To describe the vibrational movement of the grain mixture, a two-layer model is considered, in which changes are made due to the presence of riffles in the form of rectilinear plates on the support surface. In the study of the movement of the upper layer of the grain flow, we consider the movement of a material point on an inclined plane that makes horizontal harmonic oscillations perpendicular to the line of the greatest slope. Consideration of the scheme of forces acting on the particle in relative motion and the conditions of motion of the particle, made it possible to write the differential equation of relative motion in the projections on the coordinate axis. The transformations of the obtained dependences allowed us to determine the minimum force of inertia at which the relative motion will begin. By introducing the concepts and designations of the phase angles at which the relative sliding of a particle begins and ends, we determined the type of dependence of the particle velocity upon its sliding. The dependences of the particle movement in the positive and negative directions of the x and y axes, the dependence of the total displacements along the axes, as well as the average particle velocity along the x axis were obtained.the model of the two-layer vibrational movement of the grain flow along the surface with the riffles in the form of rectangular plates at their arrangement perpendicular to the direction of oscillations was Considered.