Dynamic Modeling of the Grain Peak Distribution on the Working Surface of Abrasive Tools when Grinding Using Transition Probabilities

The grain peak distribution on the working surface of abrasive tools is formed by trueing. During grinding, the initial distribution changes due to wear.  The wear of grain peaks is regarded as a Markov’s process with discrete time and condition; the formation of a working surface of an abrasive tool, is regarded as a superposition of Markov’s processes. Three types of wear are investigated: attrition and chipping of the grain’s peak, and grain pull-out from the cluster. The probability of wear types is determined based on the cutting force, grain and bond strength. The mathematical models of transition probabilities for determining new position of the peaks, after a single act of interaction with the machined material at each turn of the grinding wheel, are determined. The mathematical model is presented in a matrix form. The main components of this model are matrices of probability of contact of the grain peaks with the machined material, probability of wear types, transition probabilities of wear due to attrition and chipping. The distribution of the grain peaks at different periods of grinding by abrasive tool is calculated.

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