本研究以三維數值模擬及無因次分析直接能量沉積(Directed Energy Deposition, DED)製程之熔池幾何。三維數值模型是以解析模型(analytical model)計算粉末顆粒在飛行過程的粉末流資訊，包括粉末流濃度、粉末顆粒溫度和粉末遮蔽率，再以單向耦合(One-way Coupling)方式將粉末資訊與熔池模型(cladding model)整合以計算流體力學(Computer Fluid Dynamic, CFD)運算。熔池模型配合了流體體積法(Volume of Fluid, VOF)，並考慮表面張力、馬倫格尼效應及粉末熱效應等物理現象，實現兩相交界面之流體動力學及金屬粉末之相變化過程。隨後數值模型與實驗驗證後，進行了一系列的數值實驗，並廣泛地蒐集文獻實驗，提供後續無因次分析可靠的採樣資料庫。
透過白金漢π定理發展無因次參數，並以數值方法驗證無因次參數滿足熔池幾何尺寸動態相似及流場分析，探討成長趨勢。與過往未適當無因次化之參數相比，以無因次參數建立之經驗方程式更能符合參數變動劇烈且材料繁雜之情況，不再被侷限於特定文獻之製程範圍與材料使用。研究發現熔池寬度主要受無因次雷射能量的正影響，增加無因次雷射能量和無因次粉末能量參數通常會使熔池高度增加，不過當粉末利用率(powder efficiency, ηp)或能量使用率(energy efficiency, ηe)趨近於100%時，熔池高度會隨雷射能量與粉末質量流率增加而趨緩或下降。此外，無因次參數分析提供了熔池接合度顯著增加之閥值，及接觸角與熔池結合度間之關係。以目前的熔池幾何尺寸經驗方程式搭配粉末利用率經驗方程式，可提供個別DED製程合理參數設計空間，使開發人員能快速預測製程結果，達到節省高額開發費用之目的。部分DED製程所使用之鍛鋼會存在一定含量之表面活性元素，使表面張力梯度轉為正值。由數值方法分析含硫金屬之燒熔動態行，發現因熔池流況相反，高溫能量往底部及高溫處匯聚顯著增加了熔池接合度，卻稍微減少了熔池寬度，而熔池高度並無顯著影響。

This study employs three-dimensional numerical simulation and dimensionless analysis to predict the melting geometry in Directed Energy Deposition (DED) process. The three-dimensional numerical model includes the powder stream and cladding model. The concentration, particle temperature, and shielding rate of the powder stream are treated by an analytical model. The information of the powder stream model is integrated into the cladding model by one-way coupling. The cladding model utilizes Computational Fluid Dynamics (CFD) technique with the VOF method, which considers the powder effect and surface tension, and the Marngoni effect.
Furthermore, this study applies Buckingham’s π theorem to develop the relationship between dimensionless parameters and the geometry of the final track. In contrast with the previous studies using dimension parameters, the dimensionless parameters better conform to the variations in different literature. The cladding width correlates positively with dimensionless laser power. Increasing laser power and powder mass flow rate generally results in higher cladding, but the trend reverses when the powder efficiency or laser energy efficiency approaches 100%. Additionally, the dimensionless parameters provide the sudden increasing threshold in dilution and the positive relationship between the contact angle and dilution. This study provides a reliable dimensionless empirical with sufficient generality, combining the empirical equations of cladding geometry with the equation of powder efficiency, which can optimize the process parameters for individual DED systems, enabling quickly predicting process outcomes and material resources.

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