Geometry and tool motion planning for curvature adapted CNC machining

Abstract
CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing. We demonstrate this at hand of 5-axis machining of freeform surfaces, where the degrees of freedom in selecting and moving the cutting tool allow one to adapt the tool motion optimally to the surface to be produced. We aim at a high-quality surface finish, thereby reducing the need for hard-to-control post-machining processes such as grinding and polishing. Our work is based on a careful geometric analysis of curvature-adapted machining via so-called second order line contact between tool and target surface. On the geometric side, this leads to a new continuous transition between “dual” classical results in surface theory concerning osculating circles of surface curves and osculating cones of tangentially circumscribed developable surfaces. Practically, it serves as an effective basis for tool motion planning. Unlike previous approaches to curvature-adapted machining, we solve locally optimal tool positioning and motion planning within a single optimization framework and achieve curvature adaptation even for convex surfaces. This is possible with a toroidal cutter that contains a negatively curved cutting area. The effectiveness of our approach is verified at hand of digital models, simulations and machined parts, including a comparison to results generated with commercial software.

Citation
Bartoň, M., Bizzarri, M., Rist, F., Sliusarenko, O., & Pottmann, H. (2021). Geometry and tool motion planning for curvature adapted CNC machining. ACM Transactions on Graphics, 40(4), 1–16. doi:10.1145/3450626.3459837

Acknowledgements
This work was supported by the Spanish Ministry of Science, Innovation and Universities, grant No PID2019-104488RB-I00, BCAM “Severo Ochoa” accreditation (SEV-2017-0718), and by the European Union’s Horizon 2020 program under grant agreement No 862025. Michael Bartoň was supported by the Ramón y Cajal fellowship RYC-2017-22649. Michal Bizzarri was funded by KAUST under BRF grant No 3989 and by the project LO1506 of the Czech Ministry of Education, Youth and Sports. Florian Rist was supported by KAUST baseline funding.

Publisher
ACM

Journal
ACM Transactions on Graphics

DOI
10.1145/3450626.3459837

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