Mathematical simulation of cutting force during grinding using theory of Markov processes

Abstract

The article presents a cutting force mathematical model which takes into account the grinding wheel working surface wear resulting from abrasion and chipping of grain vertices, pulling of grains out of the wheel bond depending on the grinding time. Wear of grain vertices is considered as a Markov process with discrete time and state, and the process of forming the grinding wheel working surface as a superposition of such Markov processes. The model allows to determine the nature of cutting force distribution in the grinding zone across the contact surface layers of the abrasive tool and the characteristics of changes in the distribution throughout the grinding period. The mathematical model 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 model includes the probabilities for types of grain vertice wear resulting from abrasion and chipping, pulling of grains out of the abrasive tool bond. The wear type probability calculation is determined by taking into account the actual cutting force of the grain vertex. A change in the grain vertex position resulting from various types of wear after each interaction with the processed material is determined by transition probabilities.