Theory of Heap Particle Motion in Vibration Cleaning of Potatoes

Abstract Theoretical research was conducted using the basic principles of higher mathematics and theoretical mechanics. Numerical calculations and graphical dependences are obtained using a PC based on developed and standard programs. The movement of the potato heap on the wing surface of the V-shaped heap distributor in the process of its distribution over the entire width of the separating conveyor was studied. An equivalent scheme of interaction of potato heap particle with the surface of the distributor wing is constructed, on the basis of which differential equations of its motion on the specified surface are made, taking into account the main constructive and kinematic parameters of the separating conveyor and V-shaped distributor. Based on the integration of the specified system of differential equations in quadratures, analytical expressions describing the laws of change of speed and movement of a particle of a potato heap in time at various values of constructive and kinematic parameters of the distributor and separating conveyor are received. Based on the obtained analytical expressions, calculations were performed and graphical dependences of heap velocity along the distributor wing on time at different values of the angle of distributor wings taking into account the oscillations of the separating conveyor blade were obtained. The allowable speed of movement of the heap along the wing of the distributor is determined from the condition of maintaining the equality of supply of the heap to the distributor and its ascent from the distributor. The specified speed is 1.62 m∙s −1 . The analysis of graphical dependences shows that the speed of the heap along the wing of the distributor decreases with increasing angle of the wing. If the speed is reduced to less than the allowable value, the heap will be unloaded on the wings of the distributor, which will lead to a disturbance of the technological process of the potato harvester. With the allowable time of movement of the heap along the distributor wing, the maximum allowable values of the deflection of the distributor wing are within 40–45°.