With the further development of precision optical systems such as space telescopes and high-power solid-state laser devices, high-efficiency and batch processing requirements for medium- and large-aperture optical planar elements are put forward. For common deterministic polishing methods such as small tool polishing and ion beam polishing, which have high machining accuracy and positive removal effect, there are still some shortcomings such as low removal efficiency and long processing period, and thus they fail to meet the urgent needs of the market for precise optical components. The ring-pendulum double-sided polishing has been a promising method due to its high convergence rate, short processing cycle, and easy batch production. However, during the process of ring-pendulum double-sided polishing, it is difficult to establish a stable removal function to predict the surface profile due to the constant changes in the contact area between the polishing disc and the workpiece surface, which thus makes it impossible to provide sufficient guidance for the polishing process. In order to solve this problem, a prediction model for the uniformity removal of ring-pendulum double-sided polishing based on the kinematics of abrasive particles is proposed, and it can be used to analyze the element surface uniformity removal under the influence of different process parameters and provide the optimization strategy of process parameters, so as to improve the convergence efficiency and controllability of surface accuracy.

A prediction model for the uniformity removal of ring-pendulum double-sided polishing based on abrasive particle kinematics is built. Firstly, the main factors influencing the removal distribution in the ring-pendulum double-sided polishing are explored according to the polishing mechanism and removal law following the Preston equation. Then the kinematic models of abrasive particles on the upper and lower surfaces of a workpiece are established respectively, in view of the differences in polishing methods between the upper and lower surfaces of the workpiece with ring-pendulum double-sided polishing. A prediction model for the uniformity removal of ring-pendulum double-sided polishing based on abrasive particle kinematics is presented, and its reliability is verified by simulation and actual machining results. Based on the machining prediction model, the distributions of removal amount and uniformity removal on the upper and lower surfaces of the workpiece are studied, and the abrasive track and the uniformity distribution of polishing removal under different polishing homogeneity influencing factors are analyzed. By changing parameters such as center eccentricity, radial swing distance, and radial swing speed, virtual machining experiments are carried out to find the mapping rules of surface removal distribution and these parameters. Finally, experiments are designed to verify that the ring-pendulum double-sided polishing uniformity removal method presented in this paper can achieve fast convergence of the surface pattern of optical elements.

The presented prediction model of ring-pendulum double-sided polishing can reflect the mapping of process parameters to the surface profile of the workpiece. Three groups of transparent fused quartz workpieces with different initial surface shapes and process parameters are selected to verify the processing prediction model. The prediction results are basically consistent with the actual machining results, which have the same removal characteristics of the surface (Fig. 4). The results have shown that the removal amount of the lower polishing plate is about 2-3 times that of the upper polishing plate, while the degree of removal irregularity of the upper polishing plate is 3-5 times that of the lower polishing plate (Fig. 6 & Fig. 7). Through simulation analysis, it is found that changes in parameters such as center eccentricity, radial swing distance, and radial swing speed will affect the homogeneity of workpiece surface removal. Experiments are designed according to the mapping between different process parameters and workpiece surface patterns. Finally, the experimental results show that the PV of 1# workpiece is 1.28λ (λ=632.8 nm), and that of 2# workpiece is 1.05 after machining (Fig. 12).

Based on the kinematic model of abrasive particles, a prediction model of the ring-pendulum double-sided polishing process is established. The simulation and actual machining experiments have verified that the model can correctly reflect the real machining surface profile results under different machining parameters. With the presented prediction model, the removal distributions of the upper and lower surfaces of the workpiece are studied. The simulation results show that although the removal amount of the lower surface is much larger than that of the upper surface of the workpiece, the non-uniform distribution of removal from the upper surface of the workpiece is the main source of the overall removal of the non-uniform distribution of the workpiece. By changing parameters such as center eccentricity, radial swing distance, and radial swing speed, the mapping of different process parameters to uniformity removal of the workpiece surface can be obtained, and then the purpose of even material removal of the workpiece surface can be achieved by combining the information of initial workpiece profile. The actual machining experiments show that the machining parameters are optimized under the guidance of the prediction model presented in this paper, which thus elevates the surface processing accuracy and provides a reliable solution for the machining efficiency of ring-pendulum double-sided polishing.