Force of cutting by a single abrasive grain

Abstract

This paper investigates the cutting forces arising when using a single abrasive grain. Analytical studies were carried out using a model of a single abrasive grain in the form of a rod with a radiused apex acting on the workpiece material. The slip-line method (method of characteristics) was used to calculate the deformation intensity of a plastically edged workpiece material under the action of a single grain. Mathematical models were developed for the following factors: plastic deformation of the material, edging of the stagnated zone and its friction against the grain surface when moved upwards in the form of chippings, grain friction against the plastically deformed material, and the action of the dynamic component of plastic deformation. The significance of the dynamic component in the overall balance of forces related to plastic deformation was established by determining the ratio of dynamic stress on the break line and shear yield point. This dependence calculated for D16T and 30HGSA materials showed the feasibility of accounting for the dynamic component of the cutting force under the velocity of a single grain impacting the workpiece surface of above 50 m/s. Graphs depicting the relative grain force and the relative depth of grain penetration are given. The proposed calculation method for cutting forces using a single grain can be used to determine the total force of interaction between the single grain and the work-piece material. In order to adopt the defined processing method and the workpiece material, the number of grains in contact, the contact duration, and the cutting speed should be found. On this basis, the process performance and the quality of the workpiece surface can be calculated.