Variation of shape distribution of grain edge due to edge fracture was examined from the beginning to the steady state of belt grinding as a practical example of Markov process in grinding. The grain dislodgement, which often appear in heavy belt grinding, was also investigated experimentally and it was found that the flat type edge is in the majority of the dislodged grain edges. The sequence of the edge fracture, the grain dislodgement and the edge shape transition in the incipient stage of A#24 abrasive belt grinding were then simulated with Monte Carlo method as in the previous report. The calculated results of the transition of edge shape distribution, belt wear and the percentage of effective grain were verified to be in good agreement with experimental results. It was thus confirmed that grinding processes, in which the edge fracture plays a major role, can be predicted by applying the theory of Markov process. It was further made clear that “A” type grain is preferable for the belt grinding, because even in the flat type edge it has a great probability to fracture into other types, hence sharp edges are always kept up in the grinding action.

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Prior to the simulation, the edge fracture test of “A” type single grain was conducted and the fracture characteristics obtained were compared with those of “WA” type grain reported in the previous paper. The fracture onset probability is small for “A” grain regardless of edge shape, while it is large for “WA” grain except the flat type edge. Transition probability p₉₉ that the flat type edge changes again to the same one after fracture, is quite small for “A” grain in contrast with the value of almost unity for “WA” grain. Next, simulation analysis of the sequence of edge fracture and edge shape transition during surface grinding, in which grain depth of cut varies with time and location, was carried out with Monte Carlo method. Since the fracture onset and the edge shape transition have Markov property, they were determined independently of their history by generating random numbers in accordance with the probability distributions of the onset and the transition. In the analysis, the height loss of grain tip was also taken into account. For “WA” wheel, it is found that the grain depth of cut is reversely proportional to the fracture onset probability, hence the flat type edge exists in the outer layer of the wheel and contributes to the stock removal greatly. On the other hand, the edge sharpness is kept up for “A” wheel since the flat type edge often changes to other sharp edges due to the small p₉₉.

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In a grinding process in which the grain edge fracture predominates over its attritious wear, the dependence of the fracture characteristics upon the grain depth of cut must be taken into account for better understanding of the grinding process, since the depth is not constant but varies with relative location of the grain edges on the wheel surface. Therefore, the effects of grain depth of cut upon the onset probability of the edge fracture, the height loss of the grain tip, and the transition probability of the edge shape are investigated. From a fracture test of WA single grain, of which test method was reported in the previous paper, the probability density of the height loss for a constant grain depth of cut is found to be conformed with a gamma distribution. Another fracture test with a special model wheel having 125 abrasive grains on a certain circumferential line is also conducted, and it reveals that the fracture onset probability and the height loss are proportional to the grain depth of cut. Their proportional constants are obtained experimentally as the maximum likelihood estimator. Two series of fracture tests of single grain under the same grinding conditions but with different grain depth of cut are further conducted, and they reveal that the transition probabilities of the grain edge are independent of grain depth of cut.

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