On the consistency of path smoothing and trajectory planning in CNC machining: A surface-centric evaluation

Path smoothing and trajectory planning are universally applied in computer-numerical-control (CNC) machining to avoid natural discontinuity of tangency and curvature at the junctions of G01 blocks. However, most existing methods primarily focus on path-centric indicators that consider the toolpath as a continuous curve, such as contour error and manufacturing efficiency, neglecting the global machining quality and failing to avoid surface inconsistencies, such as single tool marks. This paper establishes a theoretical framework to evaluate the global continuity of toolpaths and trajectories, proposing the consistency as a surface-centric evaluation that considers toolpaths as a surface in CNC machining. In this paper, the consistency is defined as similarity between adjacent toolpaths and trajectories when facing similar input fold-paths in single-point milling. The consistency of four typical existing methods representing a broad category of typical approaches is investigated based on the developed theory. As a theoretically ideal objective, the proposed strong consistency requires a path smoothing method robust to any positional disturbance on the input fold-paths, and this paper points out that few algorithms have achieved strong consistency so far. The proposed weak consistency focusing on the tangential disturbance is practical in the industry. Filtering-based methods without contour error limitations are proved to achieve weak consistency, and smoothing methods with explicit geometric constraints fail to achieve weak consistency. To facilitate evaluation on the consistency of more complex methods, this paper proposes numerical benchmarks and quantitative indicators which can determine whether a method is consistent by numerical experiments. Conducted on a 3-axis machine tool with a ball-end milling cutter, real-world experiments show that inconsistencies in toolpaths’ position and trajectories’ feedrate causes surface inconsistencies like single tool marks. The proposed consistency theory and the carefully designed benchmarks can serve as a novel evaluation for path smoothing and trajectory planning from a global perspective, and it can help to identify areas where inconsistencies may occur in single-point milling.