The effect of thermal expansion of abrasive grain on the stressed state of the tool

The purpose of the work is to develop a model and a method for determining the stress-strain state of the tool for abrasive processing of materials as an orthotropic composite with an arbitrary number of regularly spaced discrete grains connected by a bond material under the condition of a thermal increase in the size of an arbitrary grain of the working surface. The work establishes the following. The extreme shear stresses of the bond material in the plane normal to the working surface of the tool are almost twice as small as the corresponding stresses in the plane parallel to the working surface of the tool. The thermal increase in grain size, in accordance with the Saint-Venant’s principle, locally disturbs the stress-strain state of the tool. The size of the zone of local disturbance caused by the thermal expansion of the grain in the direction of expansion depends on the mechanical properties of the components of the tool (moduli of elasticity for the tension of the grain material and for the shear of the bond material). In all directions, the size of the disturbance zones of the stress-strain state depends on the number of grains in the tool in directions orthogonal to the direction of the thermal change in grain size. The obtained results make it possible to comprehensively take into account the composite orthotropic construction, the mechanical properties of the components of the tool in which, due to thermal expansion, the size of the arbitrary grain of the working surface has increased. The linearity of the problem statement allows, by summing up the results for the changes in the sizes of individual, several arbitrarily located grains, and at an arbitrary heating temperature of the grains, to determine the total stress-strain state. The obtained dependencies, at the stage of development of the processing technology, allow us to quantitatively estimate the stress level in the tool, to predict the likely number of load cycles before failure, to influence the value of stresses by selecting materials at the stage of tool manufacturing, to choose cutting modes at the stage of technology development, how to increase the efficiency of using the abrasive tool processing