Uniform Coverage Trajectory Planning for Polishing of Equation-Free Surfaces

Conventional surface polishing trajectory generation relies on solving the plane trajectory equation in conjunction with the surface equation to obtain a surface polishing trajectory when the surface equation is known. However, in practical polishing processes, there exist equation-free surfaces which cannot be described by equations and the generation of polishing trajectories on equation-free surfaces cannot be realized by an equation-solving strategy. In this paper, a polishing trajectory generation method for equation-free surfaces modeled by meshes based on the trajectory mapping strategy is proposed. As the calculation process for the coverage area of polishing trajectories requires invoking surface curvature information, this paper proposes a mesh surface curvature fitting algorithm. Regarding the problem of non-uniformity in the coverage area of polishing trajectories caused by surface curvature fluctuations, an algorithm for adjusting the position of polishing trajectory points on mesh surfaces is proposed, which enables the mapped trajectory points to be adjusted according to the required overlapping coverage area of the adjacent polishing trajectories. The uniform coverage of multiple polishing trajectories for rotationally symmetric workpieces is achieved by the proposed trajectory point position adjustment algorithm. Through experiment and analysis, it is verified that the proposed algorithm for uniform coverage of polishing trajectories can obtain better polishing results with the same polishing time.