Combining physical shell mapping and reverse-compensation optimisation for spiral machining of free-form surfaces

Abstract

Machining of free-form surfaces has an important role in industrial manufacturing, but conventional tool-path generation strategies for free-form surfaces machining have the drawbacks of serious flattening distortion and poor tool-path continuity. Therefore, a novel method is developed to generate a spiral tool path for the machining of free-form surfaces by improving surface-flattening distortion and tool-path continuity. First, physical shell mapping is presented to flatten a free-form surface into a plane, which takes stretching energy, bending energy, and global energy into account. Then, the spatial spiral polyline is rounded to generate a spiral path by proposing reverse-compensation optimisation. Therefore, the free-form surfaces can be quickly flattened with less distortion, remaining free of overlap, and can in addition be machined at high speed along a C² continuous spiral tool path. Further, the flattening error, tool-path length, mean curvature, mean scallop-height error of the spiral path, machining time and surface roughness are obviously reduced. Finally, simulation results are given to show the effectiveness and feasibility of the presented strategy.

Keywords:

• physical shell mapping
• reverse-compensation optimisation
• less-distortion flattening
• C² continuous spiral tool path
• free-form surfaces machining

Acknowledgements

The authors would like to express their gratitude to Travis D. Ashworth for many useful comments on English writing. We also want to thank Professor Kazuhiro Saitou for discussing.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 51605495], the Fundamental Research Funds for the Central Universities of Central South University [grant number 2017zzts195], the International Postdoctoral Exchange Fellowship Program [grant number 2017[59]], and Research on Laboratory Construction and Management of Central South University Program number 201719.