Modeling and analysis of dynamic cutting points density of the grinding wheel with an abrasive phyllotactic pattern

The model of dynamic cutting points density (N (d) ) using the grinding wheel with an abrasive phyllotactic pattern was established in this paper, which can be generalized to other engineered grinding wheels with orderly arrayed abrasive grains. The curves of N (d) over time of a grinding wheel with the abrasive phyllotactic pattern and two kinds of engineered grinding wheels were figured out at different wheel speeds, workpiece velocities, and grinding depths. The mathematical expectation, amplitude, and period of N (d) were compared and analyzed in different conditions based on the model. Results showed that N (d) of these engineered grinding wheels vary regularly according to process parameters. Also, N (d) of grinding wheel with the abrasive phyllotactic pattern has higher mathematical expectation and lower amplitude than that of the others. Finally, through analyzing the influence of the phyllotactic coefficient on N (d) based on the model, the change rule of N (d) is observed: N (d) decreases when the phyllotactic coefficient increases, but the decreasing rate will slow down gradually. This research is not only indispensable and fundamental for subsequent researches including grinding force, grinding and surface quality of workpiece, but also provides important information for a better understanding of the mechanism of grinding using engineered grinding wheels.