Topology optimization for hybrid additive-subtractive manufacturing incorporating dynamic process planning

A differentiable and geometry-controlled framework for hybrid additive-subtractive manufacturing structural topology optimization design method.

Shuzhi Xu 1 , Jikai Liu* 2 , Kentaro Yaji 1 , Lin Lu 3
1 Department of Mechanical Engineering, Graduate School of Engineering, Osaka University, Japan
2 Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University, China
3 School of Computer Science and Technology, Shandong University, China
Video Citation
Geometry-driven topology optimization overview

Our work achieves topology optimization design tailored for multi-axis hybrid additive and subtractive manufacturing. This enables the consideration of complex manufacturing constraints—inherent to multi-axis hybrid processes—at the design stage, thereby ensuring that structural manufacturing requirements are met while simultaneously optimizing structural performance.

Abstract

Hybrid additive–subtractive manufacturing (HASM) is a revolutionary technique that, the interplay between additive and subtractive processes within an integrated machine tool allows for the fabrication of traditionally challenging complex geometries with excellent quality. However, part design for hybrid manufacturing has mostly been done by experts with rare support from computational design algorithms. Hence, the primary contribution of this work is to propose a solution for HASM-oriented structural topology optimization that incorporates both dynamic process planning and accessibility constraints. This novel optimization algorithm is developed under a unified SIMP and magic needle framework. Two sets of design variables are proposed: one for the topological description while the other for identifying the printing stage-related subdivisions. Accordingly, a series of additive manufacturing (AM) and subtractive manufacturing (SM) dedicated geometric constraints are developed based on these design variables to enable the cutting tool and laser head accessibility. Supported by the sensitivities, the structural geometry and fabrication fields can be simultaneously optimized. The effectiveness of the algorithm is proved through several numerical and experimental case studies. All the factors of cutting tool directions, HASM stages, and specific tool shapes are thorough investigated.

Method

A cooperative optimization algorithm is proposed, primarily comprising the SM formulation, the AM formulation, and the HASM formulation.

Optimization pipeline

Fig.1 The whole optimization pipeline.

By employing a convolution algorithm to embed the tool shape into the convolution kernel, the non-machinable regions of the structure are determined.

Optimization pipeline

Fig.2 Illustration of the SM formulation.

For the additive manufacturing component, we introduce the "geodesic-in-heat" concept and leverage multiphysics coupling to achieve a differentiable representation of multi-axis slicing for curved surfaces.

Optimization pipeline

Fig.3 Illustration of the AM formulation.

Finally, we propose the "Magic Needle" algorithm. By integrating this with prior surface slicing techniques, we achieve a differentiable representation of regions designated for additive and subtractive manufacturing steps, while also enabling the number of regions to be treated as a differentiable variable. This allows for the simultaneous optimization of partition locations and the number of manufacturing steps.

Optimization pipeline

Fig.4 Illustration of the HASM formulation.

Qualitative Results

Optimization Processes

Two-dimensional optimization process

Two-Dimensional Example #1

2D heat sink design.

Two-dimensional optimization process

Two-Dimensional Example #2

2D heat sink design with another tool configuration.

Optimized Designs

Optimized result one

The optimized results for 2D heat sink.

Optimized result two

The optimized results for 3D heat sink

Optimized result two

The fabrication process for the optimized 3D heat sink

Quantitative Results

Optimized result one

In the ablation studies, we designed and compared the classic cantilever beam under various geometric constraints in both 2D and 3D settings.

Optimized result one

Comparison of AM and HASM Processing for Plastic and Metal Materials.

Finally, the optimized 3D heat sink components were fabricated using both plastic and metal materials, and the results obtained via HASM were compared with those from AM alone. It is evident that our designs could be successfully fabricated using both HASM and AM; notably, the surface roughness of the components produced via HASM was significantly better controlled.

Citation 

@article{xu2026geometry,
  title   = {Geometry-Driven Topology Optimization
             with B-Spline Geometric Features},
  author  = {Xu, Shuzhi and Others},
  journal = {Journal Name},
  year    = {2026}
}

Acknowledgements

Geometry-driven topology optimization overview

This work was supported by Shandong University and The University of Osaka.