Mathematical modeling the process of forming a real tip of the blade edge for the knife of a screw grinder for solid materials
The article is devoted to a detailed analysis of the tip formation regularities for the cutting edge of the auger grinder knife blade. It is known that, as a result of sharpening, on the chamfer of the auger grinder knife blade a blade edge is produced, on the edge part of which a burr of theoretically ideal, absolute sharpness is formed with an infinitely small practically zero radius of curvature. This burr id of insufficient strength due to the small size of the cross-section, and when interacting with the crushed material it breaks off forming a sting, the radius of curvature of which is finite and is a real quantitative characteristic of the sharpness of the blade. Obviously, in order to reduce the energy consumption of the grinding process and improve the cutting quality, the sharpness of the cutting edge should be brought to the maximum possible, that is, the real radius of curvature of the tip - to the minimum achievable value. At the same time, it is quite clear that sharpening of the blade to very small values of the tip curvature radius is limited by the mentioned strength of the knife blade edge chamfer burr near its apex. In practice, there exist cutting tools with high sharpness determined by small radius of the tip curvature (of the order of several tens of angstroms). However, using a blade with such an extremely high sharpness when grinding solid materials leads to inevitable destruction of the burr that forms the sting and its breaking off due to the limited strength determined by the size of the cross section. The problem of determining the maximum achievable level of knife cutting edge sharpness by experimental methods has been considered and solved in a number of studies. The theoretical solution to the problem is also known. However, the existing work has a limited scope. This study examines mathematical modeling the deformation and destruction of the burr formed on the blade edge of the knife during sharpening. The tasks of the work are to develop an equation that establishes the dependence of the cutting edge sharpness on the geometric and strength characteristics of the blade, as well as the force factors and strength characteristics of the crushed material acting on the cutting edge. At the same time, both analytically in a general form and quantitatively, the maximum achievable sharpness of the blade is determined based on the condition for the strength of the burr, which is under the action of lateral pressure forces, as well as the compressive cutting force from the side of the material being crushed.