Mathematical models of cutting forces during turning

This paper considers the predictive determination of the cutting force components for non-free cutting during turning. It has been established that plastic deformation and friction along the rear surfaces adjacent to the main and auxiliary cutting edges of the tool influence the magnitude and direction of the action of the component . The resulting force is defined as the vector sum of the forces that occur on the main and auxiliary cutting edges. The authors propose to determine the direction of the force in non-free cutting as a vector in the chip flow direction relative to the main cutting edge. The chip deviation angle was fixed by photographing the cutting process. The authors confirmed that in free cutting, the chip flow direction is perpendicular to the main cutting edge. The machining of shaped surfaces on lathes with numeric control systems is accompanied by changes in the feed movement direction and, as a result, changes in the kinematic main and auxiliary angles in the plan of the cutting tool. The increasing active length of the main cutting edge leads to an increase in the contact area of the rear surface of the main cutting edge with the machinable surface, and, consequently, an increase in the force component . The experimental measurement of the cutting force components allowed the determination of the impact degree of the force components connected both to the plastic deformation of the machinable material and to the friction on the rear surfaces adjacent to the main and auxiliary cutting edges of the tool. The analytical dependencies express the functional relationship between the elements of cutting modes, the geometric parameters of the cutters, the degree of wear, the shape of the machinable surface, and the physical and mechanical properties of the machinable material. A large set of parameters included in the formulas for determining the cutting force components allows the adequate monitoring the nature of the force interaction of the technological system elements during machining.