Validation and Analysis of Equal Arc Length Trajectory Point Planning Model

Projecting the commonly used equidistant grating scanning trajectory to the aspheric surface by projection method will lead to uneven distribution of trajectory points, excessive polishing or insufficient polishing of local areas, which will affect the accuracy of the polished surface. In order to solve this problem, an equal arc length trajectory point planning model is established, and the spatial interval transformation rate is introduced to quantitatively analyze the distribution of trajectory points. The spatial distance uniformity of any adjacent trajectory points on the aspheric surface is significantly improved. In order to make the model more intuitive in improving the uniformity of material removal, the removal efficiency of all trajectory points in the removal area at different residence points is calculated to obtain the correction matrix of the removal function. The distribution of material removal amount is obtained by combining the residence time distribution, and the correctness of the model is evaluated by the uniformity of the removal amount distribution. The simulation results show that the pv value of the material removal amount converges to the original 38.9 % 32.7%, and the rms value converges to the original 34.2 % 30.3 % by applying the equal arc length trajectory point planning model in the aspheric polishing process. This model is further verified to improve the uniformity of high-steep aspheric surface polishing.