Abstract
Self-supporting designs that eliminate the need for structural supports can reduce manufacturing complexity caused by overhanging parts in additive manufacturing (AM). Traditionally, 45° is the minimum overhang angle required to ensure that designs can be manufactured without requiring any supporting structure. In this paper, a new self-supporting design method of AM based on topology optimization with overhang angle constraint is proposed. A self-supporting index established using a continuous logistic aggregate function is introduced to assess the supporting status of the specimen for AM process. This proposed self-supporting index is continuous and can be directly differentiated for sensitivity analysis without further mathematical transformations in the optimization formulation. Furthermore, it can be easily extended to a high-dimension aggregate (i.e., it can easily adapt to different overhang angles or self-supporting design domains). Numerical and fused deposition modeling (FDM) of a cantilever and MBB beam reveal that the self-supporting design can satisfy either general overhang angles or arbitrary orientation of AM deposition direction.
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References
AM-Platform (2014) Additive manufacturing: strategic research agenda (release 2014). European technology sub-platform in additive manufacturing
Cheng L, Zhang P, Biyikli E, Bai J, Robbins J, To A (2017) Efficient design optimization of variable-density cellular structures for additive manufacturing: theory and experimental validation. Rapid Prototyp J 23(4):660–677. https://doi.org/10.1108/RPJ-04-2016-0069
Crucible Design Ltd. (2015) Design guidelines for direct metal laser sintering (DMLS). Crucible Design Ltd.
EOS GmbH Application Notes:Design Rules for DMLS. EOS GmbH
Guo X, Zhou J, Zhang W, Du Z, Liu C, Liu Y (2017) Self-supporting structure design in additive manufacturing through explicit topology optimization. Comput. Methods Appl Mech Eng 323:27–63
Gibson I, Rosen D, Stucker B (2015) Additive manufacturing technologies. Springer, New York
Gaynor AT, Guest JK (2016) Topology optimization considering overhang constraints: eliminating sacrificial support material in additive manufacturing through design. Struct Multidiscip Optim 54:1157–1172. https://doi.org/10.1007/s00158-016-1551-x
Huang Y, Leu MC, Mazumder J, Donmez A (2015) Additive manufacturing: current state, future potential, gaps and needs, and recommendations. ASME J Manuf Sci Eng 137(1):014001. https://doi.org/10.1115/1.4028725
Kuo YH, Cheng CC, Lin YS, San CH (2018) Support structure design in additive manufacturing based on topology optimization. Struct Multidiscip Optim 57(1):183–195. https://doi.org/10.1007/s00158-017-1743-z
Leary M, Merli L, Torti F, Mazur M, Brandt M (2014) Optimal topology for additive manufacture: a method for enabling additive manufacture of support-free optimal structures. Mater Des 63:678–690
Langelaar M (2016) Topology optimization of 3D self-supporting structures for additive manufacturing. Addit Manuf 12:60–70. https://doi.org/10.1016/j.addma.2016.06.010
Langelaar M (2017) An additive manufacturing filter for topology optimization of print-ready designs. Struct Multidiscip Optim 55:871. https://doi.org/10.1007/s00158-016-1522-2
Li D, Dai N, Zhou X, Huang R, Liao W (2018) Self-supporting interior structures modeling for buoyancy optimization of computational fabrication. Int J Adv Manuf Technol 95(1–4):825–834. https://doi.org/10.1007/s00170-017-1261-6
Mirzendehdel AM, Suresh K (2016) Support structure constrained topology optimization for additive manufacturing. Comput Aided Design 81:1–13
Panesar A, Abdi M, Hickman D, Ashcroft I (2018) Strategies for functionally graded lattice structures derived using topology optimisation for additive manufacturing. Addit Manuf 19:81–94. https://doi.org/10.1016/j.addma.2017.11.008
Petersson J, Sigmund O (1998) Slope constrained topology optimization. Int J Numer Methods Eng 41:1417–1434
Qian X (2017) Undercut and overhang angle control in topology optimization: a density gradient based integral approach. Int J Numer Methods Eng 111(3):247–272. https://doi.org/10.1002/nme.5461
Stratasys Ltd. (2018) Design considerations for FDM additive manufacturing tooling. Stratasys Ltd.
Strano G, Hao L, Everson RM, Evans KE (2013) A new approach to the design and optimisation of support structures in additive manufacturing. Int J Adv Manuf Technol 66:1247–1254. https://doi.org/10.1007/s00170-012-4403-x
Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4):401–424. https://doi.org/10.1007/s00158-006-0087-x
Ultimaker BV (2018) How to design for FFF 3D printing. Ultimaker B.V
van de Ven E, Maas R, Ayas C, Langelaar M, van Keulen F (2018) Continuous front propagation-based overhang control for topology optimization with additive manufacturing. Struct Multidiscip Optim 57(5):2075–2091. https://doi.org/10.1007/s00158-017-1880-4
Vanek J, Galicia JAG, Benes B (2014) Clever support: efficient support structure generation for digital fabrication. Eurogr Symp Geometry Process 33:117–125. https://doi.org/10.1111/cgf.12437
Wang W, Qian S, Lin L, Li B, Yin B, Liu L, Liu X (2017) Support-free frame structures. Comput Graph 66:154–161. https://doi.org/10.1016/j.cag.2017.05.022
Wang J, Dai J, Li KS, Wang J, Wei M, Pang M (2018) Cost-effective printing of 3D objects with self-supporting property. Vis Comput 1–13. doi: https://doi.org/10.1007/s00371-018-1493-y
Zhang W, Zhou L (2018) Topology optimization of self-supporting structures with polygon features for additive manufacturing. Comput Methods Appl Mech Eng 334:56–78
Zhao D, Li M, Liu Y (2017) Self-supporting topology optimization for additive manufacturing. arXiv Preprint arXiv:1708.07364
Acknowledgements
The author thanks Krister Svanberg for use of the GCMMA optimizer.
Funding
This study was supported by the Ministry of Science and Technology, Taiwan, ROC, under contract no. MOST 106-2622-E-194-003-CC2 and MOST 107-2634-F-194-001.
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Kuo, YH., Cheng, CC. Self-supporting structure design for additive manufacturing by using a logistic aggregate function. Struct Multidisc Optim 60, 1109–1121 (2019). https://doi.org/10.1007/s00158-019-02261-3
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DOI: https://doi.org/10.1007/s00158-019-02261-3