Shape parameter optimisation of elliptic tool paths in trochoidal slot milling

Abstract. Trochoidal milling is a highly effective machining strategy for hard-to-reach areas like corners and slots. This strategy was initially developed using circular arc and cycloid-based tool paths. Recently, elliptic trochoidal tool path patterns have emerged as an even more efficient alternative. However, this advancement raises new questions as the analytical functions previously used to describe the cutter engagement will no longer be valid along the elliptic path. Additionally, changing the ellipse aspect ratio can completely alter the nature of tool load development. While there are examples of tool load modelling for the elliptic trochoidal strategy in scientific literature, there is still a need to directly connect these methods with productivity aspects. This study introduces a newly developed optimisation method that achieves two goals: (1) specifying the maximum permissible trochoidal step for a desired cutter engagement limit and (2) determining the optimal ellipse aspect ratio to achieve maximum material removal rate while respecting the boundary conditions. The presented optimisation method was validated by both experimental and simulation results. Although this algorithm is currently only applicable to trochoidal machining of straight slots, it has the potential to be extended to general shapes in the future.