Due to their excellent physical and chemical properties, hard and brittle materials represented by the optical glass are massively used in high-end optoelectronic fields such as optical imaging, laser fusion, solar cells, space observation, and sensors. However, the ultra-high hardness, strength, brittleness, and chemical stability make such materials face significant challenges in practical processing and manufacturing. In response to these issues in precision and ultra-precision machining, in terms of grinding, lapping, and polishing, the material removal efficiency, and surface finish quality are brutal to ensure simultaneously. This work aims to ensure the machining efficiency and machined surface quality of the elastic grinding and polishing process by considering the influence of the abrasive particle motion trajectory according to the Hertz elastic contact model and Preston material removal mechanism. By derivating the movement function of effective working abrasive grains in the contact area between the tool and the workpiece, the effects of the precession angle, rotation speed, feed speed of the abrasive tool, and the concentration and arrangement characteristics of abrasive grains on the abrasive particle grinding trajectory were comprehensively analyzed. The grinding trajectory uniformity was characterized by the contact area share of the grain path and the coefficient of variation. The surface quality evaluation approach was developed on trajectory uniformity to guide the process parameters optimization. The simulation results indicated that the maximum area share of the abrasive particle trajectory was 96.46% and the minimum coefficient of variation was 0.375. It was achieved when the rotation speed was 300 r/min, the feed speed was 1 mm/s, the precession angle was 15°, and the abrasive grain spacing was 1 mm. For the experiment validation, the quartz glass was selected as the workpiece and processed by the polishing tool fabricated with silicone rubber as the bonding matrix and diamond grains as the abrasives. The effects of the kinematic parameters of the abrasive tool and the concentration and arrangement characteristics of abrasive grains on the surface quality of the workpiece were studied by orthogonal experiments. The surface roughness and micro-morphology of quartz glass were measured with a roughness tester and observed by a three-dimensional profiler. The material removal rate was calculated through the weight loss of the workpiece. The surface quality of the machined quartz glass before and after polishing was analyzed and compared. The experimental results showed that the optimal output was obtained by the process parameter combination where the rotation speed was 1 200 r/min, the feed speed was 1 mm/s, the precession angle was 15° to 20°, and the abrasive grain spacing was 1 mm. As a result, the surface roughness of the workpiece was decreased from 1.078 μm to 0.057 μm, and the material removal rate was 3.8×108 μm3/min. The practical application of elastic matrix tools in the precision machining of hard and brittle materials helps to obtain a smooth and uniform surface finish. In conclusion, to improve the workpiece's processing efficiency and surface quality, this study discussed the influence of the kinematic parameters of the polishing tool and its abrasive grains arrangement and trajectory. The theoretical analysis and modeling could be employed to develop high-efficiency and high-quality ultra-precision grinding and polishing technology. The density of abrasive grain trajectory is positively correlated with rotation speed, abrasive grain concentration and arrangement, and negatively correlated with feed speed. Considering the processing cost, dense and uniform abrasive grain trajectory can be obtained by adopting high rotation speed, high grain concentration, low feed speed and 15° to 20° precession angle, which improves the surface quality of workpiece and material removal efficiency. © 2022, Chongqing Wujiu Periodicals Press. All rights reserved.
