Optimal polishing trajectory generation for complex optical surfaces modeled by meshes

The precision of polishing trajectories exerts a decisive impact on the final polishing quality of curved-surface components. The polishing process for complex surfaces necessitates not only solving the problem of polishing trajectory generation but also ensuring the uniformity of material removal between adjacent trajectories. This study first introduces linear constraints into the surface parameterization solution algorithm. This effectively mitigates distortion and stretching during the surface parameterization process, thereby obtaining a 2D parametric plane suitable for precision machining trajectory planning. By generating 2D polishing trajectory points on this parametric plane and employing affine transformations, the generation of polishing trajectories for complex surfaces is achieved. This resolves the challenge of generating polishing trajectories when the surface equation is unknown. Furthermore, to address the negative effects of over-polishing and under-polishing inherent in initial polishing trajectories on surface quality, this paper proposes an adaptive optimal polishing trajectory generation algorithm incorporating the material removal function. Dynamically adjusting the trajectory spacing significantly enhances the polishing quality of complex curved surfaces. Finally, polishing experiments validate the feasibility and practicality of the proposed adaptive optimal polishing trajectory optimization algorithm.