Stochastic Modeling of Microgrinding Wheel Topography

Superabrasive microgrinding wheels are used for jig grinding of microstructures using various grinding approaches. The desire for increased final geometric accuracy in microgrinding leads to the need for improved process modeling and understanding. An improved understanding of the source of wheel topography characteristics leads to better knowledge of the interaction between the individual grits on the wheel and the grinding workpiece. Analytic stochastic modeling of the abrasives in a general grinding wheel is presented as a method to stochastically predict the wheel topography. The approach predicts the probability of the number of grits within a grind wheel, the individual grit locations within a given wheel structure, and the static grit density within the wheel. The stochastic model is compared to numerical simulations that imitate both the assumptions of the analytic model where grits are allowed to overlap and the more realistic scenario of a grind wheel where grits cannot overlap. A new technique of grit relocation through collective rearrangement is used to limit grit overlap. The results show that the stochastic model can accurately predict the probability of the static grit density while providing results two orders of magnitude faster than the numerical simulation techniques. It is also seen that grit overlap does not significantly impact the static grit density allowing for the simpler, faster analytic model to be utilized without sacrificing accuracy.