High steepness aspheric polishing trajectory planning based on equal arc length sampling

As a kind of common aspheric element, high-gradient aspheric surface is more and more used in high-tech fields because of its advantages of improving system accuracy and optimizing system comprehensive performance. At the same time, it also has higher requirements for its surface processing quality. The trajectory planning in polishing is an important part that affects the surface quality of the component. Due to the continuous change of the curvature radius of the high-steep aspheric surface and the large change rate of the vector height, the commonly used planar equidistant grating scanning trajectory is projected onto its surface. The distribution of trajectory points on the surface is obviously uneven, resulting in overpolishing or underpolishing in some areas. In order to ensure the machining accuracy of high-gradient aspheric surface, the concept of “common equal arc length point” is proposed and the equal arc length trajectory point planning model is established to make the spatial distance of any adjacent trajectory points on the aspheric surface consistent, and the spatial interval change rate is introduced to quantitatively analyze the distribution of trajectory points. Several aspheric surfaces with different vector height change rates are sampled by the equal arc length trajectory point model. Under the same sampling accuracy as the plane equidistant grid scanning trajectory point model, the change rate of the trajectory point spacing to the surface shape is reduced from 70.72 % ~ 33.03 % to 25.18 % ~ 8.75 %. The simulation results show the effectiveness of the model.