Calculation of the components of cutting force on the front surface of the abrasive grain

Abstract

Purpose. The purpose of this paper is to develop the engineering methodology and derive a formula for direct calculation of the tangential and normal components of cutting force on the front surface of the abrasive grain based on the parameters of the grinding process. Methodology. The research methodology involves creating a calculation model of chip formation with a shearing surface from an abrasive grain, the main parameters of which included an equivalent radius of curvature of the upper base of the shearing surface (including the radius of the grain worn place on the rear surface), tilt angle of the shearing surface generator to the normal axis of the calculation pattern (directions of normal component of single-grain cutting force) and the angle of position of the projection of the resultant force of chip formation relative to the tangential axis (tangential component of cutting force). Results. The complex integral calculus of the shearing surface area during chip formation is substituted for the engineering calculation and an accessible search for the equivalent radius of an ellipse. The chief accomplishment of the invention is to derive a compact formula for direct calculation, which comprehensively includes all the output data of the chip formation process: thickness of cut; equivalent radius; radius of worn place; tilt angle of the shearing surface generator; angle of position of the projection of the resultant force of chip formation; intensity of tangential and normal stresses. Scientific novelty. The calculation was carried out on the basis of proposed real scheme of constrained single-grain cutting with a shearing surface during the chip formation and a worn place along the rear surface. The substitution of the radius of curvature of the ellipse of the upper base of the shearing surface for the equivalent radius of the circle is provided under condition of equality of the areas of an ellipse and a circle. The final accuracy of calculation is achieved by way of bringing the numerical value of the angle of position of the resultant force vector to conformity with the condition of canonical equation of an ellipse by the method of iterations. Practical importance. The components of the chip formation forces on the front surface together with the pressure force and friction force on the rear single-grain wearing surface afford an opportunity to determine the total tangential and normal components of cutting force during the grinding process as a whole, with due regard for the number of grains being in contact with a workpiece. This enables to substitute the cost-based dynamometry of the grinding force components for their analytical determination.