Stress state of the grinding tool loaded with tangential force

Abstract

Purpose. Determining the interaction mechanism of discrete grains through material that binds them in a tool for abrasive material processing in the case of its loading with a tangentially directed cutting force. Methodology. Development and analytical solution to a mathematical model formulated on the basis of static equilibrium of an abrasive grain as a system element of tool grains bound with a material with excellent mechanical characteristics. Findings. A mathematical model has been developed and an algorithm has been formulated to analytically determine the stress-strain state parameters of a tool for abrasive processing of materials, which is loaded with a discrete cutting force, tangential to its working surface. The nature of the dependence of stresses and deformations on mechanical parameters, the quantity of grains and the material binding them in an abrasive tool, loaded with a unit tangential force, has been determined. Originality. The loading of the extreme grains leads to greater displacements, tangents of the shear angles of the material binding the grains. They decrease with increasing quantity of grain rows in the tool or with increasing quantity of grains to the nearest tool edge. Practical value. The distribution of interaction forces of grains and stresses in the material binding them has been determined. The found distribution allows one in the process of developing the tool and technology, in which it is involved, to comprehensively assess the influence of tangential load value of the tool working grain on its stress state and the material containing the grains. The determined stress state makes it possible to predict the number of loading cycles until the simultaneous rational wear of the grain and the destruction of that part of the material that contains it. The linear formulation of the problem makes it possible to take into account the mutual influence of the tangential loads of several grains on the stress-strain state of the tool as a whole.