Mathematical simulation of wear grains chipping using Markov processes

A mathematical model changes the distribution of grains on the working surface of the abrasive tool as a result of radial wear chipping during grinding. The model takes into account the displacement of the vertices of the periphery by the amount of wheel wear per revolution. All varieties of the wear surface of the abrasive tool combined into three types: mechanical abrasion of the top of the grain, chipping top, pulling the grain of the bunch. It is assumed that during the time of contact at one vertex can implement all three types of wear. Type of wear is determined by the maximum value of the radial wear during the reporting cycle. It is assumed that each grain during the period of interaction is exposed to only one type of wear, and the probability of these events, the composition-lyayut full group. The essential novelty of the project is to provide a process of wear of abrasive grains at the vertices of a single act of interaction as a Markov process with discrete time state, and the formation process of the working surface of the abrasive tool, such as a superposition of Markov processes. In the presented model, the transition probabilities were calculated from the experimentally obtained distribution law wear tops grains by cleaving. The technique and results of experimental study of wear in grinding grain chipping. Defined radial wear tops grains at mikrotsarapanii individual grains and cutting depth at which the shearing. It is proved that the distribution of the wear is most likely to obey the Weibull distribution. The functional dependence of the parameters of the distribution of the depth of spalling. The model can be used to study changes in the relief work surface for grinding abrasive tools in various grain sizes and material type.