積層製造技術在現代已有許多先進技術被開發出來，其中以黏著劑噴塗成型最受矚目，其原理乃是利用驅動電壓及波形控制壓電噴頭，使其噴出黏著劑至粉床成型的技術，也是用於列印鑄造用砂模的主要技術，其顆粒性質、黏著劑種類等參數皆會影響砂模列印品質。
許多學者皆使用了這項技術進行製程上的突破，包括砂模形狀的幾何設計、砂模材料的選擇和改良、砂模製程的突破等等。其中影響砂模性質的要素為黏著劑和矽砂含硬化劑的結合反應、粒徑大小、黏著劑多寡等等。因此，有許多學者也針對砂模的強度、尺寸、透氣性等砂模檢驗進行優化改善。
常見的砂模機械性質如抗壓強度、抗彎強度、透氣性、成型性、尺寸精度、燒失量等為一個砂模是否良好的參考依據，機械性質又與墨量有關。因此，本研究透過理論方程式及數值分析探討單一墨滴於粉床中的滲透行為，並以ANSYS Fluent進行模擬分析證明了墨量和孔隙率等參數之間的關係，進而提出一種用以預測單一墨滴滲透深度和擴散直徑的簡易模型。此簡易模型可節省更多的運算資源和時間、更快速的知道單一墨滴在粉床中的滲透深度和擴散直徑，並且透過實驗得知，簡易模型和實驗所得的結果擁有相同趨勢，而實驗和模擬皆表示墨量以及孔隙率與擴散直徑和滲透深度成二次及一次函數關係。
接著，本研究將不同墨量以及孔隙率的成果用於列印中，發現機械性質與墨量之間的關係，表面硬度、抗壓和抗彎強度隨著墨量增加而增加，成型性也隨著更好，但在透氣性上和尺寸精度上表現越差。本研究提出一個製程改良－『灰階列印』，此方法透過調整壓電噴頭和切層軟體以不同墨量在不同位置噴印，我們在同一層中以不同墨量噴印，以及不同層中以不同墨量噴印，證明此方法可以兼顧高強度、高成型性、高透氣性、高尺寸精度的特點，透過此概念列印可在維持機械性質條件下，使尺寸誤差將至0.3%並同時兼具良好透氣性。
在了解墨量和孔隙率之間的關係是影響機械性質、尺寸精度和透氣性的主要變因後。本研究試圖在優化砂模列印品質的前提下，探討環保和永續使用的可能性。本研究提出使用回收砂進行砂模列印的概念，透過使用回收砂，不僅在砂粒、黏著劑和硬化劑的使用量大幅減少。並且我們發現矽砂在回收使用二至五次間的機械性質如抗壓強度、抗彎強度、表面硬度表現上，皆比使用新砂來得好，這是因為隨著矽砂的反覆使用會逐漸磨損，導致砂粒的尺寸變小。這個現象會使得粉床由單峰粒徑變為雙峰或是三峰粒徑，使得孔隙率發生變化，這也是使得砂模機械性質以及尺寸精度提高的原因之一，因此，我們得到一個結論，使用回收砂不僅比使用純新砂擁有更好的機械性質，在硬化劑和黏著劑的使用上皆遠小於使用純新砂石的用量。
透過以上研究，我們成功透過調整墨量、孔隙率來對砂模列印製程進行改良，使得砂模和砂心的列印品質得以優化。在砂模中我們能夠在維持高機械性質的前提下，使得透氣性和尺寸精度得以提升。在砂心以及砂型中較難透過後加工方式進行尺寸修正的地方，此製程改良的特色和優點更加放大，本文之研究成果適用於黏著劑噴塗成型在砂模列印中的改良，也期許此研究方法能使砂模列印品質更完善。

Additive Manufacturing, AM technologies have witnessed significant advancements in recent years, with particular attention given to binder jetting, a technique that utilizes a piezoelectric printhead driven by voltage and waveform control to deposit binder onto a powder bed for mold formation. This method is widely employed in the printing of sand molds for casting applications, where parameters such as particle properties and adhesive type significantly impact the quality of the printed molds.
Numerous researchers have made breakthroughs in process improvement using this technique, including geometric design of sand molds, selection and enhancement of sand mold materials, and process optimization. Factors affecting sand mold properties include the combination reaction between the binder and silica sand with hardener, particle size, and adhesive quantity. Therefore, many scholars have focused on optimizing the strength, dimensions, and permeability of sand molds through inspection and improvement.
Common mechanical properties used as references for evaluating sand molds include compressive strength, flexural strength, permeability, moldability, dimensional accuracy, and burnout. These properties are also influenced by the quantity of binder used. This study explores the permeation behavior of a single binder droplet in a powder bed through theoretical equations and numerical analysis. Using ANSYS Fluent, simulation analysis demonstrates the relationship between binder quantity, porosity, and diffusion diameter, leading to the proposal of a simplified model for predicting the penetration depth and diffusion diameter of a single binder droplet. This model saves computational resources and time, providing a faster estimation of penetration depth and diffusion diameter within a powder bed. Experimental results confirm that the simplified model exhibits similar trends to the experimental data, and both experiments and simulations indicate that binder quantity and porosity have quadratic and linear relationships with diffusion diameter and penetration depth, respectively.
Subsequently, the findings regarding binder quantity and porosity are applied to the printing process. The relationship between mechanical properties and binder quantity is examined, revealing that surface hardness, compressive strength, and flexural strength increase with increasing binder quantity, resulting in better moldability. However, permeability and dimensional accuracy are negatively affected. To address this, a process improvement technique called "gray-scale printing" is proposed. This method involves adjusting the piezoelectric printhead and slicing software to enable the deposition of varying binder quantities at different locations within the same layer and across different layers. The gray-scale printing approach balances high strength, moldability, permeability, and dimensional accuracy. By applying this concept, dimensional errors can be reduced to 0.3% while maintaining desirable mechanical properties.
Understanding the relationship between binder quantity, porosity, and their impact on mechanical properties, dimensional accuracy, and permeability, this study aims to explore possibilities for environmental sustainability and long-term usage improvement in sand mold printing. The concept of utilizing recycled sand for sand mold printing is proposed, resulting in significant reduction in the usage of sand grains, binder, and hardener. Furthermore, it is observed that the mechanical properties, such as compressive strength, flexural strength, and surface hardness, of recycled silica sand exhibit superior performance compared to using new sand. This is attributed to the gradual wear and reduction in sand particle size upon repeated use, leading to a transition from a unimodal to bimodal or trimodal particle size distribution, affecting the change in porosity. Therefore, it can be concluded that recycled sand not only possesses better mechanical properties but also requires smaller quantities of hardener and binder compared to using pure new sand.
Through the aforementioned research, improvements have been made in the sand mold printing process by adjusting the binder quantity and porosity, leading to optimized quality of sand molds and cores. While maintaining high mechanical properties, permeability and dimensional accuracy have been enhanced in sand molds. The advantages of this process improvement are particularly significant in areas where dimensional corrections through post-processing are challenging, such as sand cores and molds. The research outcomes presented in this paper are applicable to the improvement of binder jetting in sand mold printing, with the aim of further enhancing the quality of sand mold printing.

[1] Upadhyay M, Sivarupan T, El Mansori M. 3D printing for rapid sand casting—A review. J. Manuf. Process. 2017; 29:211-220; https://doi.org/10.1016/j.jmapro.2017.07.017.
[2] Hawaldar N, Zhang J. A comparative study of fabrication of sand casting mould using additive manufacturing and conventional process. Int. J. Adv. Manuf. Technol. 2018; 97:1037-1045; https://doi.org/10.1007/s00170-018-2020-z.
[3] Bourell, D., Kruth, J. P., Leu, M., Levy, G., Rosen, D., Beese, A. M., & Clare, A. (2017). Materials for additive manufacturing. CIRP annals, 66(2), 659-681; https://doi.org/10.1016/j.cirp.2017.05.009.
[4] Sivarupan T, Balasubramani N, Saxena P. A review on the progress and challenges of binder jet 3D printing of sand mould for advanced casting. J. Addit. Manuf. 2021; 40:101889; https://doi.org/10.1016/j.addma.2021.101889.
[5] Sachs E, Cima M, Cornie J. Three-dimensional printing: Rapid tooling and prototypes directly from a CAD model. Annals of the ClRP 1990; 39(1):201-204; https://doi.org/10.1016/S0007-8506(07)61035-X.
[6] Gilmer, D., Han, L., Hong, E., Siddel, D., Kisliuk, A., Cheng, S., ... & Saito, T. (2020). An in-situ crosslinking binder for binder jet additive manufacturing. Additive Manufacturing, 35, 101341
[7] Du, W., Ren, X., Pei, Z., & Ma, C. (2020). Ceramic binder jetting additive manufacturing: a literature review on density. Journal of Manufacturing Science and Engineering, 142(4), 040801.
[8] Barui, S., Ding, H., Wang, Z., Zhao, H., Marathe, S., Mirihanage, W., ... & Derby, B. (2020). Probing ink–Powder interactions during 3D binder jet printing using time-resolved X-ray imaging. ACS applied materials & interfaces, 12(30), 34254-34264.
[9] Bala Y, Rajendran DK, Rajagopal V. A review on binder jetting fabrication: Materials, characterizations and challenges. Advances in Additive Manufacturing Processes 2021; 121.
[10] Bai, Y., Wall, C., Pham, H., Esker, A., & Williams, C. B. (2019). Characterizing binder–powder interaction in binder jetting additive manufacturing via sessile drop goniometry. Journal of Manufacturing Science and Engineering, 141(1), 011005.
[11] Lu, K., & Reynolds, W. T. (2008). 3DP process for fine mesh structure printing. Powder technology, 187(1), 11-18;https://doi.org/10.1016/j.powtec.2007.12.017
[12] Sivarupan, T., El Mansori, M., Coniglio, N., & Dargusch, M. (2020). Effect of process parameters on flexure strength and gas permeability of 3D printed sand molds. Journal of Manufacturing Processes, 54, 420-437; https://doi.org/10.1016/j.jmapro.2020.02.043.
[13] Miyanaji, H., Momenzadeh, N., & Yang, L. (2018). Effect of printing speed on quality of printed parts in Binder Jetting Process. Additive Manufacturing, 20, 1-10; https://doi.org/10.1016/j.addma.2017.12.008.
[14] Tang, Y., Huang, Z., Yang, J., & Xie, Y. (2020). Enhancing the capillary force of binder-jetting printing Ti6Al4V and mechanical properties under high temperature sintering by mixing fine powder. Metals, 10(10), 1354.
[15] Løvoll, G., Méheust, Y., Måløy, K. J., Aker, E., & Schmittbuhl, J. (2005). Competition of gravity, capillary and viscous forces during drainage in a two-dimensional porous medium, a pore scale study. Energy, 30(6), 861-872; https://doi.org/10.1016/j.energy.2004.03.100
[16] Nguyen, T., Shen, W., & Hapgood, K. (2009). Drop penetration time in heterogeneous powder beds. Chemical Engineering Science, 64(24), 5210-5221.
[17] Adin, H. , Ergün, R. K. & Adin, M. Ş. (2022). Computer aided numerical damage analysis of the axle shaft . European Mechanical Science , 6 (3) , 201-206 . DOI: 10.26701/ems.1109917
[18] Adin, M. Ş. , Adin, H. & Ergün, R. K. (2022). Finite Element Analysis of Safety Pin in Snowplow Equipment . European Journal of Technique (EJT) , 12 (1) , 89-92 . DOI: 10.36222/ejt.1086422
[19] Rybdylova O, Qubeissi M. Al, Braun M, Crua C, Manin J, Pickett L.M., Sercey G. de, Sazhina E.M, Sazhin S.S, Heikal M. International Communications in Heat and Mass Transfer 2016; 76; 265-270; https://doi.org/10.1016/j.icheatmasstransfer.2016.05.032
[20] Hosseini S.A, Tafreshi H. V. Modeling particle-loaded single fiber efficiency and fiber drag using ANSYS–Fluent CFD code. Computers & Fluids 2012; 66(15); 157-166; https://doi.org/10.1016/j.compfluid.2012.06.017
[21] López A, Nicholls W, Stickland M.T, Dempster W.M. CFD study of Jet Impingement Test erosion using Ansys Fluent® and OpenFOAM®. Computer Physics Communications 2015; 197; 88-95; https://doi.org/10.1016/j.cpc.2015.07.016
[22] Yue C, Guo S, Li M. ANSYS FLUENT-based modeling and hydrodynamic analysis for a spherical underwater robot. IEEE International Conference on Mechatronics and Automation 2013; 1577-1581; doi: 10.1109/ICMA.2013.6618149
[23] Wang Y, Li S, Qin T, Yu Y, Xiao J. Concrete 3D Printing: System Development, Process Planning and Experimental Results. RILEM International Conference on Concrete and Digital Fabrication; DC 2020: Second RILEM International Conference on Concrete and Digital Fabrication 2020; 28; 998-1010; https://doi.org/10.1007/978-3-030-49916-7_97
[24] Gootjes D. Applying feedback control to improve 3D printing quality. Delft University of Technology 2017; Master Thesis; http://resolver.tudelft.nl/uuid:49a31f6e-5b28-48ce-b5f4-4e71fbf4009b
[25] Han Y, Wei C, Dong J. Droplet formation and settlement of phase-change ink in high resolution electrohydrodynamic (EHD) 3D printing. Journal of Manufacturing Processes 2015; 20(3); 485-491; https://doi.org/10.1016/j.jmapro.2015.06.019
[26] Raj R, Krishna S.V.V, Desai A, Sachin C, Dixit A.R. Print fidelity evaluation of PVA hydrogel using computational fluid dynamics for extrusion dependent 3D printing. Conf. Ser.: Mater. Sci. Eng 2022; 1225; 012009; DOI 10.1088/1757-899X/1225/1/012009
[27] López Martínez, J. A., Fernández, P., Mehrdel, P., & Casals Terré, J. (2020). 3D-printing and computational fluid dynamics" meet" paperbased microfluidics for enhanced flow control in difusive sensors. In µTAS 2020-The 24th International Conference on Miniaturized Systems for Chemistry and Life Science: October 4-9, 2020 (pp. 172-173); http://hdl.handle.net/2117/330613
[28] Bayat, M., Dong, W., Thorborg, J., To, A. C., & Hattel, J. H. (2021). A review of multi-scale and multi-physics simulations of metal additive manufacturing processes with focus on modeling strategies. Additive Manufacturing, 47, 102278; https://doi.org/10.1016/j.addma.2021.102278.
[29] Kattinger, J., Ebinger, T., Kurz, R., & Bonten, C. (2022). Numerical simulation of the complex flow during material extrusion in fused filament fabrication. Additive Manufacturing, 49, 102476; https://doi.org/10.1016/j.addma.2021.102476.
[30] Charles, A., Bayat, M., Elkaseer, A., Thijs, L., Hattel, J. H., & Scholz, S. (2022). Elucidation of dross formation in laser powder bed fusion at down-facing surfaces: Phenomenon-oriented multiphysics simulation and experimental validation. Additive Manufacturing, 50, 102551; https://doi.org/10.1016/j.addma.2021.102551
[31] Harris, M., Mohsin, H., Potgieter, J., Arif, K. M., Anwar, S., AlFaify, A., & Farooq, M. U. (2022). Hybrid deposition additive manufacturing: novel volume distribution, thermo-mechanical characterization, and image analysis. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 44(9), 432; https://doi.org/10.1007/s40430-022-03731-4
[32] Sadeghi, R., Shadloo, M. S., Hopp-Hirschler, M., Hadjadj, A., & Nieken, U. (2018). Three-dimensional lattice Boltzmann simulations of high density ratio two-phase flows in porous media. Computers & Mathematics with Applications, 75(7), 2445-2465; https://doi.org/10.1016/j.camwa.2017.12.028
[33] Nazari, M., Salehabadi, H., Kayhani, M. H., & Daghighi, Y. (2018). Predicting the penetration and navigating the motion of a liquid drop in a layered porous medium: viscous fingering vs. capillary fingering. Brazilian Journal of Chemical Engineering, 35, 731-744; https://doi.org/10.1590/0104-6632.20180352s20160318
[34] Deng, H., Huang, Y., Wu, S., & Yang, Y. (2022). Binder jetting additive manufacturing: Three-dimensional simulation of micro-meter droplet impact and penetration into powder bed. Journal of Manufacturing Processes, 74, 365-373; https://doi.org/10.1016/j.jmapro.2021.12.019
[35] Gao, X., Yang, W., Xian, H., Tu, X., & Wang, Y. (2020). Numerical Simulation of Multi-Layer Penetration Process of Binder Droplet in 3DP Technique. CMES-Computer Modeling in Engineering & Sciences, 124(1); doi:10.32604/cmes.2020.09923 .
[36] Miyanaji, H., Orth, M., Akbar, J. M., & Yang, L. (2018). Process development for green part printing using binder jetting additive manufacturing. Frontiers of Mechanical Engineering, 13, 504-512.
[37] Teunou E, Fitzpatrick JJ, Synnott EC. Characterisation of food powder flowability. J. Food Eng. 1999; 39(1):31-37.
[38] Balakrishnan A, Pizette P, Martin CL. Effect of particle size in aggregated and agglomerated ceramic powders. Acta Mater. 2010; 58:802–812.
[39] D. Snelling, CB. Williams, AP. Druschitz, A comparison of binder burnout and mechanical characteristics of printed and chemically bonded sand moulds, SFF Symp. (2014) 197-209.
[40] D. Snelling, H. Blount, C. Forman, K. Ramsburg, A. Wentzel, C. Williams, A. Druschitz, The effects of 3D printed molds on metal castings, in: Proceedings of the Solid Freeform Fabrication Symposium. (2013) 827-845.
[41] N. Coniglio, T. Sivarupan, M. El Mansori, Investigation of process parameter effect on anisotropic properties of 3D printed sand molds, The International Journal of Advanced Manufacturing Technology. 94 (5) (2018) 2175-2185. https://doi.org/10.1007/s00170-017-0861-5.
[42] S. Mitra, M. El Mansori, A. Rodríguez de Castro, M. Costin, Study of the evolution of transport properties induced by additive processing sand mold using X-ray computed tomography, J. Mater. Process. Technol. 277 (2020), 116495. https://doi.org/10.1016/j.jmatprotec.2019.116495.
[43] S. Mitra,A. Rodríguez de Castro, M. El Mansori, The effect of ageing process on three-point bending strength and permeability of 3D printed sand moulds, The International Journal of Advanced Manufacturing Technology. 97 (1) (2018) 1241-1251.
[44] Z. Shan, Z. Guo, D. Du, F. Liu, Coating process of multi-material composite sand mold 3D printing, China Foundry. 14 (6) (2017) 498-505.
[45] T. Sivarupan, M. El Mansori, N. Coniglio, M. Dargusch, Effect of process parameters on flexure strength and gas permeability of 3D printed sand molds, J. Manuf. Process. 54 (2020) 420-437. https://doi.org/10.1016/j.jmapro.2020.02.043.
[46] Sivarupan, T., Balasubramani, N., Saxena, P., Nagarajan, D., Mansori, M.E., Salonitis, K., Jolly, M., Dargusch M.S., 2021. A review on the progress and challenges of binder jet 3D printing of sand moulds for advanced casting. Additive Manufacturing. 40, 101889. https://doi.org/10.1016/j.addma.2021.101889.
[47] ENERGETICS, Inc, 2017. Energy and Environmental Profile of the U.S. Aluminum Industry, Columbia, Maryland, USA.
[48] Sa, A., Paramonova, S., Thollander, P., Cagno, E., 2015. Classification of industrial energy management practices. Energy Procedia. 75, 2581-2588. https://doi.org/10.1016/j.egypro.2015.07.311.
[49] Dalquist, S., Gutowski, T., 2004. Life Cycle Analysis of Conventional Manufacturing Techniques: Sand Casting, in: ASMEDC, International Mechanical Engineering Congress and Exposition, pp. 631-641.
[50] Huang, R., Riddle, M.E., Graziano, D., Das, S., Nimbalkar, S., Cresko, J., Masanet, E., 2017. Environmental and economic implications of distributed additive manufacturing: the case of injection mold tooling. Journal of Industrial Ecology. 21(1), 130-143. https://doi.org/10.1111/jiec.12641.
[51] Mitterpach, J., Hroncová, E., Ladomerský, J., Balco, K., 2017. Environmental analysis of waste foundry sand via life cycle assessment. Environ Sci Pollut Res. 24, 3153-3162. https://doi.org/10.1007/s11356-016-8085-z.
[52] Holtzer, M., Dańko, R., & Dańko, J., 2018. Thermal Utilization of the Post Reclamation Dust from Molding Sand with Furan Resin in Test Unit. Arch. Foundry Eng. 18(4), 15-18. doi:10.24425/123625.
[53] Tang, H.P., Qian, M., Liu, N., Zhang, X.Z., Yang, G.Y., Wang, J., 2015. Effect of Powder Reuse Times on Additive Manufacturing of Ti-6Al-4V by Selective Electron Beam Melting. JOM. 67, 555-563. https://doi.org/10.1007/s11837-015-1300-4.
[54] Delacroix, ,T., Lomello, F., Schuster, F., Maskrot, H., Garandet, J., 2022. Influence of powder recycling on 316L stainless steel feedstocks and printed parts in laser powder bed fusion. Additive Manufacturing. 50, 102553. https://doi.org/10.1016/j.addma.2021.102553.
[55] Zander, N.E., Gillan, M., Burckhard, Z., Gardea, F., 2019. Recycled polypropylene blends as novel 3D printing materials. Additive Manufacturing. 25, 122-130. https://doi.org/10.1016/j.addma.2018.11.009.
[56] Solodov, A.N., Shayimova, J., Balkaev, D., Nizamutdinov, A.S., Zimin, K., Kiiamov, A.G., Amirov, R.R., Dimiev, A.M., 2022. High-throughput, low-cost and “green” production method for highly stable polypropylene/perovskite composites, applicable in 3D printing. Additive Manufacturing. 59, Part A, 103094. https://doi.org/10.1016/j.addma.2022.103094.
[57] Singh, P., Katiyar, P., Singh, H., 2023. Impact of compatibilization on polypropylene (PP) and acrylonitrile butadiene styrene (ABS) blend: A review. Materialstoday: Proceedings. 78, Part 1, 189-197. https://doi.org/10.1016/j.matpr.2023.01.350.
[58] Liu, Q., Zhang, X., Jia, D., Yin, J., Lei, J., Xu, L., Lin, H., Zhong, G., Li, Z., 2023. In situ nanofibrillation of polypropylene/polyethylene/poly(ethylene terephthalate) ternary system: A strategy of upgrade recycling. Polymer. 269, 125729. https://doi.org/10.1016/j.polymer.2023.125729.
[59] Giani, N., Mazzocchetti, L., Benelli, T., Picchioni, F., Giorgini, L., 2022. Towards sustainability in 3D printing of thermoplastic composites: Evaluation of recycled carbon fibers as reinforcing agent for FDM filament production and 3D printing. Composites Part A: Applied Science and Manufacturing. 159, 107002. https://doi.org/10.1016/j.compositesa.2022.107002.
[60] Peng, T., Kellens, K., Tang, R., Chen, C., Chen, G., 2018. Sustainability of additive manufacturing: An overview on its energy demand and environmental impact. Additive Manufacturing. 21, 694-704. https://doi.org/10.1016/j.addma.2018.04.022.
[61] Voorde, B.V. de, Katalagarianakis, A., Huysman, S., Toncheva, A., Raquez, J., Duretek, I., Holzer, C., Cardon, Ludwig, Bernaerts, K.V., Hemelrijck, D.V., Pyl, L., Vlierberghe, S.V., 2022. Effect of extrusion and fused filament fabrication processing parameters of recycled poly(ethylene terephthalate) on the crystallinity and mechanical properties. Additive Manufacturing. 50, 102518.; https://doi.org/10.1016/j.addma.2021.102518.
[62] Fateri, M., Kaouk, A., Cowley, A., Siarov, S., Palou, M.V., González, F.G., Marchant, R., Cristoforetti, S., Sperl, M., 2018. Feasibility study on additive manufacturing of recyclable objects for space applications. Additive Manufacturing. 24, 400-404. https://doi.org/10.1016/j.addma.2018.09.020.
[63] 莊馥安，黏著劑噴印參數對3D砂模列印影響之研究，碩士論文，機械工程所. 2017, 國立臺灣科技大學
[64] 李坤泓，基於黏著劑噴印技術的多噴頭3D模具列印系統研究，碩士論文，自動化及控制研究所. 2017, 國立臺灣科技大學