Movement of soil particles on surface of developable helicoid with horizontal axis of rotation with given angle of attack
DOI:
https://doi.org/10.31548/machenergy2021.02.067Keywords:
developable helicoid, tillage body, angular velocity, parti-cle, slip, differential equations.Abstract
The interaction of the screw tillage body with soil particles is considered in the article. Due to its very wide application in engineering, the term "helical surface" is usually understood to mean the surface of a helical conoid or auger. The surface of the deployable helicoid, which is also linear, but significantly different from the auger, is considered in the work. The difference is not only in the geometric shape, but also in the manufacturing technology. If the auger is made by stamping or rolling a strip with significant deformations of the workpiece, then the deployable helicoid can be made by simple bending with a minimum of plastic deformation. From the point of view of the theory at zero thickness of preparation plastic deformations at its bending in general would be absent.
The working body for tillage consists of a strip of developable screw surface, in which the outer edge is pointed and acts as a blade, and the inner is rigidly attached to the lattice cylinder. The difference between the radius of the screw line of the blade and the cylinder determines the depth of processing. The lattice cylinder prevents clogging of interturn space and at the same time carries out additional function of a roller. The body works like a disk tool that is the profile of the treated field has ridges and depressions. At the time of contact of the blade with the surface of the field there are angles similar to the angles of attack and roll for disk guns. The design parameters that provide these angles can be calculated based on the analytical description of the surface.
The section, that is the drum with the turn of the screw working surface, is located so that its axis is a certain angle with the direction of movement of the unit. This cause the angle of attack and reaction forces that cause the drum to rotate with the surface. Based on the speed of the unit and taking into account the angle of attack, we can find the angular velocity of the section. Next, a differential equation of motion of the particle is formed after its entry on the rotating surface. The differential equation is painted in projections on three axes of a fixed coordinate system. It includes three unknown dependencies: two variables that describe the trajectory of the particle sliding on the surface and the reaction force of the surface. The system is solved by numerical methods. The trajectories of relative and absolute motion of a particle and graphs of changes in its relative and absolute velocities are constructed.
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