本研究以三維數值模擬並搭配無因次參數，對積層製造中的直接能量沉積(Directed Energy Deposition, DED)進行全面的參數分析。首先以計算流體力學(Computation Fluid Dynamics, CFD)進行三維數值模擬，配合流體體積分率法(Volume of fluid, VOF)，並考慮表面張力(surface tension)、馬倫格尼效應(Marangoni effect)及粉末效應等物理現象，用於模擬金屬受雷射加工後之相變化(phase change)過程。三維數值模擬和實驗比對後，再以此模型架構，對不同加工參數或材料，進行一系列之數值實驗，並搭配文獻蒐集之實驗結果和無因次分析(dimensionless analysis)，找出無因次參數與熔池尺寸之經驗方程式。此經驗方程式有別於一般文獻，僅限於特定材料，並在限定之加工範圍內才可適用之有因次經驗方程式，本研究之方程式參數經過無因次化，故可針對大範圍的加工參數並可推及不同之材料。
針對數值模擬之結果，發現熔池寬度較不受粉末影響，由經驗方程式中亦可發現，無因次的熔池寬度主要受到無因次雷射能量的主宰，並且在寬度成長至雷射光斑大小之後，成長較為緩慢。無因次熔池高度較為複雜，跟無因次的雷射能量，粉末流量，傅立葉數，以及粉末利用率，皆有關聯。傅立葉數會影響熔池長度，進而改變粉末沉積時間長短。隨著無因次雷射能量增加，若粉末利用率接近百分之百，反將使無因次高先增後減；隨著無因次粉末流量增加，所需克服的潛熱會使得等效之雷射能量降低，使得熔池變短，反而讓無因次高下降。本研究所提供之無因次經驗方程式，對直接能量沉積最終燒結的尺寸可做一全面性的預測，用以提供最佳化設計，並可節省實際製程的成本。

This study presents a comprehensive investigation for direct energy deposition (DED), including three-dimensional numerical simulations and dimensionless analysis. The Computational Fluid Dynamics (CFD) together with volume of fluid (VOF) method is used to simulate the phase change of metallic material during laser cladding process, which includes the powder effect and interfacial dynamics such as Marangoni and surface tension effects. After validations with measured data, additional numerical experiments and data from previous literatatures have been collected to form emperical equations of sizes of melting pool. In contrast with previous studies that their emperical realtion can only be applied to a confined range of working conditions, the dimensionless empirical equations in this study can largely match the trends of measured data with noticeable variations of working conditions collected from several different literatures.
The dimensionless width of melting pool is found to less sensitive to the powder flow and dominated by the dimensionless laser energy. When the width grows larger than the laser spot size, the slope of width with respect to the laser energy becomes gentler. The characteristic of dimensionless height is more complex. It is influenced by the dimensionless laser energy and powder flow rate, Fourier number, and catchment efficiency. The Fourier number can change the length of the melting pool, which further influences the duration of powder deposition. When the catchment efficiency is close to unity, further increase of dimensionless laser power could even decrease the dimensionless height. As for excessive dimensionless powder flow rate, the effective laser power is possible to decline due to the larger amount of latent heat for the powder flow. Hence, the dimensionless height could also drop. The dimensionless empirical equations provided in this study can predict the scales of final products comprehensively, benefiting the optimal design and saving cost from the DED process.

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