Probabilistic model of surface layer removal when grinding brittle non-metallic materials

OBRABOTKAMETALLOV Vol. 23 No. 2 2021 TECHNOLOGY average 15 ... 25% of the total cost of manufacturing products [1], when processing brittle materials, this fi gure increases signi fi cantly. Grinding processes have a complex stochastic nature [2], which leads to a scatter of product quality indicators, a decrease in the reliability, productivity and economy of the technological process. It is possible to reduce the scatter of product quality indicators when grinding brittle materials, as well as to increase the reliability and ef fi ciency of the operation, by choosing the optimal parameters of the technological system based on dynamic models of the process. A large number of studies are devoted to the development of dynamic models for various processes of abrasive processing [3-15]. However, to describe the regularities of the removal of particles of a brittle non-metallic material and the wear of the surface of the grinding wheel in the contact zone, the known models do not allow taking into account the peculiarities of the process in which micro-cutting-chipping and brittle volume fracture of the material are combined. In this regard, the aim of the work is to create a new probabilistic model for removing the surface layer when grinding brittle non-metallic materials. The task is to study the laws governing the removal of particles of brittle non-metallic material in the contact zone. Simulation of the process To obtain dependencies that allow calculating material removal when grinding holes in workpieces made of brittle non-metallic materials, consider the presented scheme (Fig. 1). Fig. 1. Scheme for calculating the probability of removing the surface layer when grinding the material In the period under consideration, the most protruding peaks of abrasive grains pass through the level of the surface of the workpiece, which, in contact with the treated surface, leave traces on it in the form of scratches. Moreover, the probability of its overlap can be full or partial. In most cases, incomplete contact is predominantly observed. Part of the grains of the abrasive tool can fall into the trail of the preceding grains, leaving no scratches. An analysis of the study of the mechanisms of material removal by a single grain shows that when passing through the contact zone, the grain can cut off the material when it hits the protrusion of the surface roughness, or it can not cut the speci fi ed material when passing through the cavity of the rough surface. Based on the analysis of the contact of the top of the abrasive grain with the material, a theoretical-probabilistic model is proposed in [16] that allows calculating the amount of material removal when grinding plastic materials. The probability is determined by the ratio of the unremoved part of the metal to the total length of the section under consideration (Fig. 1):