在選擇性雷射熔融（SLM）的過程中，雷射光束照射於基板上的金屬粉末層，其能量通過吸收和散射兩種方式消散。因此，分析金屬粉末層的散射和吸收特性是選擇 SLM 工藝最佳參數的一項重要任務。本論文提出一種改進的順序添加方法來模擬選擇性雷射熔融（SLM）工藝中使用的金屬粉末層的沉積; 透過Monte Carlo 射線追踪模擬和灰度共生矩陣（GLCM）方法分析沉積層的散射特性。另透過比較點陣圖灰階特性的模擬結果和利用掃描雷射微投影（SLPP）檢測方法獲得的金屬粉末層的吸收係數和一些在論文中模擬的成果進行比較與驗證。然後進行進一步的模擬以研究金屬粉末堆積密度對金屬粉末層的散射特性和吸收的影響; 結果顯示，較高的填充密度導致較低的散射效應和較大的吸收率。另外，與具有不同尺寸分佈的金屬粉末層的散射和吸收的特性相比，顯示出粉末顆粒尺寸的雙峰分佈導致最低的散射效應和最高的吸收率; 因此，設計金屬粉末分佈參數的適當規格，可優化 SLM 中金屬粉末高堆疊緻密度的要求。
從分析金屬粉末層的散射和吸收特性的初步結果來看，可了解雷射和粉末顆粒之間的交互作用於SLM製程中熔池的形成產生顯著影響。因此，提出新的體積熱源進行三維有限元素傳熱模擬用以估計SLM期間熔池橫截面的尺寸; 該模擬基於新的體積熱源，並考慮了粉末粒徑分佈對雷射能量在金屬粉末層深度的傳播影響。在對體積熱源進行建模時，使用改良的序列疊加法來建立具有不同粉末粒度的金屬粉末層，然後通過蒙特卡羅射線追踪模擬來計算沿著粉末層深度的吸收率分佈。結果表示，本次模擬中得到的熔池最高溫度（3005 K）與實驗值比較，比現有團隊所提出模型之模擬結果更加吻合; 除此之外，峰值溫度低於粉末顆粒層的沸點，因此與實驗研究中報導的穩定熔體軌跡一致。為了進一步證實所提出有限元素傳熱模型的有效性，將熔池和基板之間的接觸寬度以及粉末消耗帶寬度的模擬結果與實驗結果和相關文獻模擬結果進行比較; 另進行模擬以預測 SLM 過程中單軌掃描熔體軌蹟的穩定性條件，其預測結果顯示與實驗結果一致。
最後，本研究提出了基於結合模擬和實驗方法以及SLM機器特性（例如，雷射功率，掃描速度，雷射光斑尺寸和雷射類型）及粉末材料和粒徑分佈等相關重要製程參數進行優化模擬。在所提出的方法中，採用圓形包裝設計算法(Circle Packing Design Algorithm) 來選取Nd：YAG SLM系統的雷射掃描速度和雷射功率的48個代表性組合; 並對於每個參數組合，進行有限元素熱傳導模擬以計算在316L基板上的316L不銹鋼粉末的熔池尺寸和最高溫度。以其模擬結果近一步用於訓練人工神經網路 (ANNs)， 訓練好的人工神經網絡將用於預測參數空間中3600個雷射功率和雷射掃描速度組合的熔池尺寸和最高溫度。依雷射功率與雷射掃描速度所得的SLM製程參數圖，以確定產生穩定的單掃描軌蹟特定參數組合，其對基板具有良好的結合性並且最高溫度低於SS316L粉末床的沸點; 最終，採用掃描雷射微投影（SLPP）來確認物件的表面粗糙度，以使 SLM 部件密度最大化的優化製程參數設置。實驗結果證明，所提出的 SLM 製程參數優化方法可以使最大工件緻密度達到99.97 ％，平均密度為99.89 ％，最大標準偏差為0.03 ％。

In Selective Laser Melting (SLM) process, the laser beam irradiates the metal powder layer deposited on the substrate, its energy is dissipated through two regimes which are absorption and scattering. Therefore, analyzing the scattering and absorption characteristics of metal powder layer is an important task in choosing the optimal parameters for SLM process. Accordingly, a modified sequential addition method is proposed for simulating the deposition of the metal powder layers used in SLM process. The scattering characteristics of the deposited layers are analyzed by means of Monte Carlo ray-tracing simulations and a gray-level co-occurrence matrix (GLCM) method. The validity of the proposed modeling approach is demonstrated by comparing simulation results for the gray-scale properties of the scattered image and the absorption coefficient of the metal powder layer with the experimental results obtained using a scanned laser pico-projection (SLPP) detection method and the simulation findings presented in the literatures, respectively. Further simulations are then performed to investigate the effect of the metal powder packing density on the scattering characteristics and absorption of metal powder layers. The results show that a higher packing density leads to a lower scattering effect and a greater absorptivity. In addition, as compared to the characteristics of scattering and absorption of metal powder layers with different size distributions, it is shown that a bimodal distribution of the powder particle size results in the lowest scattering effect and the highest absorptivity given an appropriate specification of distribution parameters for powder structures used in SLM.
From the preliminary results of analyzing the scattering and absorption characteristics of metal powder layer, it is postulated that the interaction between laser radiations and powder particles can have a significant effect of the formation of melt pool in SLM process. Therefore, three-dimensional finite element heat transfer simulations with new volumetric heat source are performed to estimate the size of the melt pool cross-section during SLM. The simulations are based on a new volumetric heat source which takes into account the effect of the powder size distribution on the propagation of the laser energy through the depth of the metal powder layer. In modeling the volumetric heat source, a modified sequential addition method is used to construct the metal powder layer with different powder particle sizes and the absorptivity profile along the depth of the powder layer is then calculated by means of Monte Carlo ray-tracing simulations. It is shown that the peak melt pool temperature obtained in the present simulations (3005 K) is in better agreement with the experimental value than that obtained in previous simulation studies. Furthermore, the peak temperature is lower than the evaporation point of the powder particle layer, and is hence consistent with the stable melt track reported in experimental studies. To further confirm the validity of the proposed finite element heat transfer model, the simulation results obtained for the contact width between the melt pool and the substrate and the width of the powder-consumed band are compared with the experimental results and simulation findings presented in the literature. Finally, simulations are performed to predict the stability condition of a single scan melt track in the SLM process. The prediction results are shown to be consistent with the experimental findings.
Finally, the present study proposes a systematic strategy based upon a combined simulation and experimental approach and a knowledge of the SLM machine characteristics (e.g., the laser power, scanning speed, laser spot size and laser type) and powder material and size distribution. In the proposed approach, a circle packing design algorithm is employed to identify 48 representative combinations of the laser scanning speed and laser power for a commercial Nd:YAG SLM system. For each parameter combination, finite element heat transfer simulations are performed to calculate the melt pool dimensions and peak temperature for 316L stainless steel powder deposited on a 316L stainless steel substrate. The simulated results are then used to train the artificial neural networks (ANNs). The trained ANNs are used to predict the melt pool dimensions and peak temperature for 3600 combinations of the laser power and laser speed in the design space. The resulting processing maps are then inspected to determine the particular parameter combinations which produce stable single scan tracks with good adhesion to the substrate and a peak temperature lower than the evaporation point of the 316L stainless steel powder bed. Finally, a Scan Laser Pico-Projection (SLPP) method is employed to characterize the quality of the surface roughness in order to confirm the optimized parameter settings which maximize the SLM component density. The experimental results show that the proposed approach results in a maximum component density of 99.97 %, an average component density of 99.89%, and a maximum standard deviation of 0.03%.

[1] I. Gibson, D. W. Rosen, and B. Stucker, Additive manufacturing technologies: Springer, 2010.
[2] N. K. Tolochko, S. E. Mozzharov, I. A. Yadroitsev, T. Laoui, L. Froyen, V. I. Titov, et al., "Balling processes during selective laser treatment of powders," Rapid Prototyping Journal, vol. 10, pp. 78-87, 2004.
[3] N. K. Tolochko, M. K. Arshinov, A. V. Gusarov, V. I. Titov, T. Laoui, and L. Froyen, "Mechanisms of selective laser sintering and heat transfer in Ti powder," Rapid Prototyping Journal, vol. 9, pp. 314-326, 2003.
[4] D. Becker and K. Wissenbach, Additive Manufacturing of copper components, Fraunhofer ILT annual report, Fraunhofer ILT, Aachen, Germany, 2009.
[5] D. Buchbinder and K. Wissenbach, Additive manufacturing of aluminum components with minimal distortion, Fraunhofer ILT annual report, Fraunhofer ILT, Aachen, Germany, 2008.
[6] A. Gusarov, I. Yadroitsev, P. Bertrand, and I. Smurov, "Model of radiation and heat transfer in laser-powder interaction zone at selective laser melting," Journal of heat transfer, vol. 131, p. 072101, 2009.
[7] C. Boley, S. Khairallah, and A. Rubenchik, "Calculation of laser absorption by metal powders in additive manufacturing," Applied optics, vol. 54, pp. 2477-2482, 2015.
[8] A. Streek, P. Regenfuss, and H. Exner, "Fundamentals of energy conversion and dissipation in powder layers during laser micro sintering," Physics Procedia, vol. 41, pp. 858-869, 2013.
[9] J. Zhou, Y. Zhang, and J. Chen, "Numerical simulation of laser irradiation to a randomly packed bimodal powder bed," International Journal of Heat and Mass Transfer, vol. 52, pp. 3137-3146, 2009.
[10] A. Gusarov and J.-P. Kruth, "Modelling of radiation transfer in metallic powders at laser treatment," International Journal of Heat and Mass Transfer, vol. 48, pp. 3423-3434, 2005.
[11] W. E. King, H. D. Barth, V. M. Castillo, G. F. Gallegos, J. W. Gibbs, D. E. Hahn, C. Kamath, A. Rubenchik, "Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing," Journal of Materials Processing Technology, vol. 214, pp. 2915-2925, 2014.
[12] S. A. Khairallah, A. T. Anderson, A. Rubenchik, and W. E. King, "Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones," Acta Materialia, vol. 108, pp. 36-45, 2016.
[13] S. A. Khairallah and A. Anderson, "Mesoscopic simulation model of selective laser melting of stainless steel powder," Journal of Materials Processing Technology, vol. 214, pp. 2627-2636, 2014.
[14] A. Foroozmehr, M. Badrossamay, and E. Foroozmehr, "Finite element simulation of selective laser melting process considering optical penetration depth of laser in powder bed," Materials & Design, vol. 89, pp. 255-263, 2016.
[15] J. Yin, H. Zhu, L. Ke, P. Hu, C. He, H. Zhang, X. Zeng , "A finite element model of thermal evolution in laser micro sintering," The International Journal of Advanced Manufacturing Technology, vol. 83, pp. 1847-1859, 2016.
[16] F. Klocke and C. Wagner, "Coalescence behaviour of two metallic particles as base mechanism of selective laser sintering," CIRP Annals-Manufacturing Technology, vol. 52, pp. 177-180, 2003.
[17] I. Yadroitsev, A. Gusarov, I. Yadroitsava, and I. Smurov, "Single track formation in selective laser melting of metal powders," Journal of Materials Processing Technology, vol. 210, pp. 1624-1631, 2010.
[18] C. Kamath, "Data mining and statistical inference in selective laser melting," The International Journal of Advanced Manufacturing Technology, vol. 86, pp. 1659-1677, 2016.
[19] F. Verhaeghe, T. Craeghs, J. Heulens, and L. Pandelaers, "A pragmatic model for selective laser melting with evaporation," Acta Materialia, vol. 57, pp. 6006-6012, 2009.
[20] I. Yadroitsev and I. Smurov, "Selective laser melting technology: from the single laser melted track stability to 3D parts of complex shape," Physics Procedia, vol. 5, pp. 551-560, 2010.
[21] C. Kamath, B. El-dasher, G. F. Gallegos, W. E. King, and A. Sisto, "Density of additively-manufactured, 316L SS parts using laser powder-bed fusion at powers up to 400 W," The International Journal of Advanced Manufacturing Technology, vol. 74, pp. 65-78, 2014.
[22] H.-C. Tran, Y.-L. Lo, and M.-H. Huang, "Analysis of Scattering and Absorption Characteristics of Metal Powder Layer for Selective Laser Sintering," IEEE/ASME Transactions on Mechatronics, vol. 22, pp. 1807-1817, 2017.
[23] H.-C. Tran and Y.-L. Lo, "Heat transfer simulations of selective laser melting process based on volumetric heat source with powder size consideration," Journal of Materials Processing Technology, vol. 255, pp. 411-425, 2018.
[24] J. Zhou, Y. Zhang, and J. Chen, "Numerical simulation of random packing of spherical particles for selective laser sintering applications," in ASME 2008 International Mechanical Engineering Congress and Exposition, 2008, pp. 327-336.
[25] D. Moser, S. Pannala, and J. Murthy, "Computation of Effective Radiative Properties of Powders for Selective Laser Sintering Simulations," Journal of Minerals,Metals & Materials Society, vol. 67, pp. 1194-1202, 2015.
[26] W. Jodrey and E. Tory, "Computer simulation of close random packing of equal spheres," Physical review A, vol. 32, p. 2347, 1985.
[27] Y. Shi and Y. Zhang, "Simulation of random packing of spherical particles with different size distributions," Applied Physics A, vol. 3, pp. 621-626, 2008.
[28] P. Meakin and R. Jullien, "Restructuring effects in the rain model for random deposition," Journal de Physique, vol. 48, pp. 1651-1662, 1987.
[29] G. Fu and W. Dekelbab, "3-D random packing of polydisperse particles and concrete aggregate grading," Powder Technology, vol. 133, pp. 147-155, 2003.
[30] C. Argento and D. Bouvard, "A ray tracing method for evaluating the radiative heat transfer in porous media," International Journal of Heat and Mass Transfer, vol. 39, pp. 3175-3180, 1996.
[31] M. Freeman, M. Champion, and S. Madhavan, "Scanned laser pico-projectors: seeing the big picture (with a small device)," Optics and Photonics News, vol. 20, pp. 28-34, 2009.
[32] F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd Edition by Frank L. Pedrotti, SJ, Leno S. Pedrotti New Jersey: Prentice Hall, 1993, vol. 1, 1993.
[33] A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Applied optics, vol. 37, pp. 5271-5283, 1998.
[34] P. Johnson and R. Christy, "Optical constants of transition metals: Ti, v, cr, mn, fe, co, ni, and pd," Physical Review B, vol. 9, p. 5056, 1974.
[35] R. M. Haralick, "Statistical and structural approaches to texture," Proceedings of the IEEE, vol. 67, pp. 786-804, 1979.
[36] X. Wang, T. Laoui, J. Bonse, J.-P. Kruth, B. Lauwers, and L. Froyen, "Direct selective laser sintering of hard metal powders: experimental study and simulation," The International Journal of Advanced Manufacturing Technology, vol. 19, pp. 351-357, 2002.
[37] C.-H. Chuang, T.-W. Sung, C.-L. Huang, and Y.-L. Lo, "Relative two-dimensional nanoparticle concentration measurement based on scanned laser pico-projection," Sensors and Actuators B: Chemical, vol. 173, pp. 281-287, 2012.
[38] T. Chen and Y. Zhang, "Three-dimensional modeling of laser sintering of a two-component metal powder layer on top of sintered layers," Journal of manufacturing science and engineering, vol. 129, pp. 575-582, 2007.
[39] A. Gusarov, T. Laoui, L. Froyen, and V. Titov, "Contact thermal conductivity of a powder bed in selective laser sintering," International Journal of Heat and Mass Transfer, vol. 46, pp. 1103-1109, 2003.
[40] L. Taylor and E. Howard, Metals Handbook Vol. 1: Properties and Selection of Metals: American Society for Metals, 1961.
[41] M. Rombouts, L. Froyen, A. Gusarov, E. H. Bentefour, and C. Glorieux, "Photopyroelectric measurement of thermal conductivity of metallic powders," Journal of applied physics, vol. 97, p. 024905, 2005.
[42] I. Roberts, C. Wang, R. Esterlein, M. Stanford, and D. Mynors, "A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing," International Journal of Machine Tools and Manufacture, vol. 49, pp. 916-923, 2009.
[43] F. L. Pedrotti and L. S. Pedrotti, "Introduction to optics 2nd edition," Introduction to Optics 2nd Edition by Frank L. Pedrotti, SJ, Leno S. Pedrotti New Jersey: Prentice Hall, 1993, 1993.
[44] A. Rubenchik, S. Wu, S. Mitchell, I. Golosker, M. LeBlanc, and N. Peterson, "Direct measurements of temperature-dependent laser absorptivity of metal powders," Applied optics, vol. 54, pp. 7230-7233, 2015.
[45] L. Han, K. Phatak, and F. Liou, "Modeling of laser cladding with powder injection," Metallurgical and Materials transactions B, vol. 35, pp. 1139-1150, 2004.
[46] C. Yunus and J. Afshin, Heat and Mass Transfer: Fundamentals and Applications, McGraw-Hill, New Delhi, India, 2011.
[47] C. Multiphysics and C. M. H. T. Module, COMSOL Multiphysics User's Guide, Version: COMSOL Multiphysics, vol. 3, 2014.
[48] L.-E. Loh, C.-K. Chua, W.-Y. Yeong, J. Song, M. Mapar, S.-L. Sing, Z.-H. Liu,D.-Q. Zhang, "Numerical investigation and an effective modelling on the Selective Laser Melting (SLM) process with aluminium alloy 6061," International Journal of Heat and Mass Transfer, vol. 80, pp. 288-300, 2015.
[49] N. Hodge, R. Ferencz, and J. Solberg, "Implementation of a thermomechanical model for the simulation of selective laser melting," Computational Mechanics, vol. 54, pp. 33-51, 2014.
[50] H.-C. Tran, Y.-L. Lo, and M.-H. Huang, "Analysis of Scattering and Absorption Characteristics of Metal Powder Layer for Selective Laser Sintering," IEEE/ASME Transactions on Mechatronics, 2017.
[51] A. Masmoudi, R. Bolot, and C. Coddet, "Investigation of the laser–powder–atmosphere interaction zone during the selective laser melting process," Journal of Materials Processing Technology, vol. 225, pp. 122-132, 2015.
[52] A. Spierings and G. Levy, "Comparison of density of stainless steel 316L parts produced with selective laser melting using different powder grades," in Proceedings of the Annual International Solid Freeform Fabrication Symposium, pp. 342-353, 2009.
[53] A. Gusarov and I. Smurov, "Modeling the interaction of laser radiation with powder bed at selective laser melting," Physics Procedia, vol. 5, pp. 381-394, 2010.
[54] C. Kamath and Y. Fan, Regression with Small Data Sets: A Case Study using Code Surrogates in Additive Manufacturing, Lawrence Livermore National Laboratory (LLNL), Livermore, CA2017.
[55] K.-T. Fang, R. Li, and A. Sudjianto, Design and modeling for computer experiments: CRC Press, 2005.
[56] M. Ma, Z. Wang, M. Gao, and X. Zeng, "Layer thickness dependence of performance in high-power selective laser melting of 1Cr18Ni9Ti stainless steel," Journal of Materials Processing Technology, vol. 215, pp. 142-150, 2015.
[57] D. Bergström, J. Powell, and A. Kaplan, "A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces," Journal of applied physics, vol. 101, p. 113504, 2007.
[58] C.-G. Ren and Y.-L. Lo, Measurement of melting pool temperature during selective laser melting process with stainless steel 316L, Master thesis, National Cheng Kung Universtiy, 2017.