Modeling of Material Removal Rate for the Fixed-Abrasive Double-Sided Planetary Grinding of a Sapphire Substrate

Double-sided planetary grinding (DSPG) with a fixed abrasive is widely used in sapphire substrate processing. Compared with conventional free abrasive grinding, it has the advantages of high precision, high efficiency, and environmental protection. In this study, we propose a material removal rate (MRR) model specific to the fixed-abrasive DSPG process for sapphire substrates, grounded in the trajectory length of abrasive particles. In this paper, the material removal rate model is obtained after focusing on the theoretical analysis of the effective number of abrasive grains, the indentation depth of a single abrasive grain, the length of the abrasive grain trajectory, and the groove repetition rate. To validate this model, experiments were conducted on sapphire substrates using a DSPG machine. Theoretical predictions of the material removal rate were then juxtaposed with experimental outcomes across varying grinding pressures and rotational speeds. The trends between theoretical and experimental values showed remarkable consistency, with deviations ranging between 0.2% and 39.2%, thereby substantiating the model's validity. Moreover, leveraging the insights from this model, we optimized the disparity in the material removal rate between two surfaces of the substrate, thereby enhancing the uniformity of the machining process across both surfaces.