Topology optimization is a powerful computational method for creating high-performance components that surpass conventional designs. However, the high degree of design freedom often results in complex, freeform geometries that are difficult to manufacture using practical subtractive methods such as multi-axis cutting. This study addresses this challenge by proposing a novel topology optimization framework that integrates a multi-stage machining process―comprising a roughing pass with a large-diameter face mill and a finishing pass with a small-diameter end mill. The framework employs a convolution-based filter to assess tool accessibility for each stage, modeled on different resolution grids to enhance computational efficiency. Building upon conventional methods for preventing inaccessible features such as internal voids, a key contribution of this study is the introduction and explicit formulation of an additional constraint to directly control the finishing cut volume. By imposing a constraint on this volume, the proposed method achieves a practical shape design that is optimized for the trade-off between structural performance and manufacturing cost. Numerical examples demonstrate the effectiveness of our approach in achieving this balance.
NOZAKI et al. (Wed,) studied this question.