Particle Motion on the Surface of a Concave Soil-Tilling Disk

Abstract

Relative particle motion on the internal rough surface of a concave soil-tilling disk, which rotates around horizontal axis under a soil reaction force, has been considered. A disk blade is positioned in a vertical plane, which makes an incidence angle with the direction of the machine movement. This angle has its acceptable limit and when it exceeds the limit, it causes disk dragging. In the paper, it has been assumed that dragging was non-existent, the rotational rate of a disk is stable and it depends on stabilized velocity of the machine movement and on an incidence angle. When a machine is operated, soil particles get onto an internal disk surface and perform a relative motion, which determines the slipping trajectory of a particle on a disk surface. The trajectory of the absolute particle motion relative to a fixed coordinate system allows tracing the rise height of a particle after its gets onto a disk surface. Differential equations of particle motion have been developed and solved using numerical methods. A particle gets onto a disk with specified initial criteria, namely the direction of its entering on a disk and its initial velocity. Two models of particle motion on a disk have been considered. According to the first model, we assume that further particle motion after its getting onto a disk surface is performed due to the kinetic energy of a particle at the moment of its getting onto a disk surface. According to the second model, the backup force of other particles, which breaks the force of particle friction on a surface, is taken into account. Differential equations of particle motion have been developed in projections onto a fixed solid system of axes. Thus, the system includes three differential equations in three unknown functions. One of the unknown functions is the surface reaction force and the dependences, which describe relative particle motion on a disk surface. For the purpose of the quality of soil loosening, we conducted multivariate experiment to determine the area of the soil dissipation. On the basis of field experiments, it has been determined that the production process quality of tillage machine meets agrotechnical requirements.

Particle Motion Over the Edge of an Inclined Plane That Performs Axial Movement in a Vertical Limiting Cylinder

“…In this case, the angular velocity α of a particle sliding will be stable, but its angular acceleration α will be equal to zero. Having solved (5) for α at α = 0, we obtain:…”

“…Having substituted (31) and (32) into (30), after a simplification, we obtain the differential equation (5).…”

“…It considers relative particle motion at a wide range of inclination angles of a plane to the axis of rotation, beginning from a horizontal position and finishing by a vertical one. The development of a bladed operating element of a conveyer-mixer is considered in paper [5][6][7][8][9][10].…”

Management and Production Engineering Review

“…The obtained results ensure the fall of friction assembly normal operation and reduce the possibility of microfractures formation. Additionally, based on the experimental research [21], it has been determined that the production process quality during machining meets the requirements.…”

External Rolling of a Polygon on Closed Curvilinear Profile

“…Designing and calculation of soil-tilling implementation have been thoroughly studied by P. Zaika [7]. The analytical model of soil-tillage concave disks has been developed in order to determine their geometrical and technological characteristics [8][9][10][11][12]. Certain papers consider various aspects of the improvement of the quality of soil tillage performed by such tools [13][14][15][16][17][18][19][20].…”