Topology optimization for additive and subtractive manufacturing with multi-stage access directions and depth constraints based on coupled fictitious physical model

This paper proposes a topology optimization method that accounts for tool accessibility, including tool direction and depth constraints, in multistage machining processes. Although additive manufacturing provides a high degree of design freedom, it often produces rough surfaces. To overcome this limitation, a hybrid approach that appropriately integrates machining processes is advantageous. However, machining accessibility strongly depends on the timing of the deposition and removal operations in alternating stages. To model the multistage tool accessibility, a coupled fictitious physics formulation is introduced, which evolves with the manufacturing phase. This formulation captures the changes in the processing domain across successive stages, thereby representing tool accessibility through orientation and depth constraints. The proposed method was applied to a thermal diffusion problem in which the optimization was formulated under these constraints. A level set-based topology optimization algorithm was developed and its effectiveness was demonstrated through two- and three-dimensional numerical examples. • Topology optimization with tool accessibility constraints for additive manufacturing is proposed. • A fictitious physical model is introduced, considering tool direction and cutting depth. • Multi-stage tool direction is addressed through a coupled fictitious model approach. • Access depth constraints are represented and managed using a distance function. • Thermal diffusivity maximization is demonstrated as an illustrative example.