DETERMINING THE CHARACTER OF DISTRIBUTION THE CONTACTING VERTICES OF GRAINS AT THE SURFACE ON THE GRINDING WHEEL, TAKING INTO ACCOUNT THE MULTI-PASSAGE OF PROCESS

Abstract

The article is devoted to the method of determining the nature of distribution the contacting vertices of grains on the working surface of grinding wheel, depending on the grinding time. The number of contacting grains is determined by the probability of contact. A distinctive feature is the use of a mathematical model that takes into account the change in the distribution of grain vertices as a result of wear of the abrasive tool during the grinding period. Considered the probabilities in three types of wear: abrasion and spallation of the grain's vertices, pull-out grain from the bundles of the wheel. Changing the position of the grain’s vertices under the action of a particular type of wear is determined using random Markov’s processes. The method takes into account the influence of the following factors: characteristics of the abrasive tool, the grinding mode, the material to be processed, the initial distribution of grains on the abrasive tool working surface and the strength of their retention. The results of the study may be used to solve problems related to determining the intensity of heat generation in the contact zone of the grinding wheel and the billet, calculation of cutting power, tool wear and other issues related to the study of the grinding process.