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研究生:吳建彣
研究生(外文):Jian-WenWu
論文名稱:以有限元素法分析電子束熔融金屬積層製造之熱傳問題
論文名稱(外文):Finite Element Analysis of Heat Transfer in Additive Manufacturing Process Using Electron Beam Melting
指導教授:趙隆山
指導教授(外文):Long-Sun Chao
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工程科學系
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:中文
論文頁數:111
中文關鍵詞:積層製造電子束熔融技術EBM相變化熱傳潛熱
外文關鍵詞:additive manufacturingElectron beam meltingphase-changelatent heat
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  • 被引用被引用:1
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電子束熔融技術,是金屬積層製造成型技術的一種,而金屬積層製造目前所遇到的問題皆與溫度息息相關,因此探討金屬積層製造過程中相變化熱傳問題是本研究主要目的。本文採用鈦金屬作為本研究材料,並搭配有限元素法撰寫程式來分析電子束熔融製造之熱傳情況,並以等效比熱法來處理潛熱的效應,於處理潛熱部分加入鬆弛法及調整人工液固共存區的大小來協助收斂。本文研究方法分為兩部分,於測試部分為了確保所建立地數值模式的可行性,本文從一維熱傳問題、二維固定熱源、移動熱源到疊層一一探討,最後與模擬軟體COMSOL的結果做比對。確定建立的數值模型可行之後,再套入金屬中心提供的實際加工參數,模擬實際狀況的熱傳情形。由數值分析結果可發現,有無考慮潛熱的溫度分布有明顯的差異,因此不宜忽略潛熱的效應。電子束熱源瞬間功率極高可使鈦金屬迅速升溫熔化,熱源照射方向之溫度梯度大,故疊層厚度太厚使表層熱源無法讓上一層達熔點溫度,造成層與層無法有效熔接成型,易呈鬆散狀。經由實際條件測試發現經五次熱源加熱以及四次疊層,將每次加熱分別利用程式以及COMSOL所得到之溫度鋒值做比較,發現兩者最大誤差百分比為4.4%,最小誤差百分比為0.7%可知,兩者模擬結果相當一致!由這些結果可知經由數值模擬的探討,能預測加熱物件的暫態溫度場分布,希望有助於金屬積層製造之熱傳相關研究。
Electron beam melting (EBM) is one of the additive manufacturing processes. So far, most of the encountered problems of metal additive manufacturing are all related to the temperature field. Accordingly, the main purpose of this study is to analyze the heat transfer problem of phase change during the manufacturing process. The numerical method adopted in this study is finite element method. On the basis of the finite element method theory, the heat transfer problem of EBM process is analyzed by the self-writing programs in FORTRAN and simulated by the software, COMSOL, simultaneously. Next, the results calculated by the FORTRAN programs are compared to those simulated by COMSOL. In this thesis, the effective specific heat method is applied to deal with the effect of latent heat. Furthermore, the relaxation method and adjustable range of the artificial mushy zone is used to improve the convergence of temperature. The process of this study starts from the one-dimensional heat transfer problem, the two-dimensional one with fixed heat source or the mobile heat source to the layer-adding heat transfer problem. At last, the actual process parameters provided by the MIRDC are used to simulate the heat transfer problem of actual manufacturing process of EBM. The results reveal that whether consider the effect of latent heat or not makes significant difference to the temperature field; therefore the effect of latent heat should not be ignored. Besides, the thickness effect of the adding-layer should be considered. Because of the high temperature gradient in y-direction, too thick adding-layer easily causes the layers unable to fuse together effectively. Moreover, the minimum percent error between the FORTRAN programs and COMSOL is 0.7%, and the maximum percent error is 4.4%. This shows that the results analyzed by FORTRAN programs and simulated by COMSOL are consistent with each other and have the same trend. The results of this study are expected to be helpful to the additive manufacturing researchers.
摘要 I
Extended Abstract II
誌謝 XI
目錄 XII
表目錄 XV
圖目錄 XVI
符號說明 XXI
第一章 緒論 1
1-1 研究背景 1
1-2 研究動機與目的 1
1-2-1 為何需分析金屬積層製造之熱傳現象 2
1-2-2 為何使用有限元素法進行熱傳分析 2
1-2-3 為何選用鈦金屬 2
1-3 研究方法 3
第二章 文獻回顧 6
2-1 積層製造的簡介 6
2-1-1 積層製造的起源 6
2-2 積層製造種類 7
2-3 電子束熔融技術 9
2-3-1 電子束熔融技術原理 9
2-3-2 電子束熔融技術優勢 11
2-3-3 電子束熔融技術問題及改善 11
第三章 相變化熱傳問題之理論 14
3-1 暫態線性熱傳問題 14
3-1-1 初始邊界(x=0)為定溫邊界條件 14
3-1-2 初始邊界(x=0)為熱對流邊界條件 15
3-2 史蒂芬問題(Stenfan Problem) 16
3-3 紐曼問題(Neumann Problem) 18
3-4史蒂芬問題變形 19
3-5二維熱傳導暫態熱傳問題 20
3-6 等效比熱法(Effective specific heat method) 21
第四章 有限元素法理論 25
4-1 有限元素法基本概念 25
4-2 加權殘值法(Weighted residuals approach) 28
4-3 加勒金法(Galerkin’s method) 29
4-4 內插函數(Interpolation function) 29
4-4-1 內差函數廣義座標之形式 30
4-4-2 內差函數自然座標之形式 31
4-5 數值積分處理 33
第五章 有限元素法計算及數值分析 35
5-1 元素方程式 35
5-2 四邊形元素積分計算 39
5-2-1比熱項之元素矩陣 41
5-2-2傳導項之元素矩陣 42
5-3 邊界條件積分計算 42
5-3-1 直接積分 43
5-3-2 高斯點積分 44
5-4 求解聯立方程式 44
5-6 COMSOL Multiphysics軟體 50
第六章 結果與討論 58
6-1 測試結果與討論 58
6-1-1 潛熱效應測試 58
6-1-1-1一維無潛熱暫態熱傳 58
6-1-1-2史蒂芬問題(Stefan Problem) 58
6-1-1-3紐曼問題(Neumann Problem) 59
6-1-1-4潛熱測試討論 59
6-1-2一維暫態熱傳熱對流邊界測試 59
6-1-3二維固定熱源邊界測試 60
6-1-3-1 程式撰寫數值分析 60
6-1-3-2 熱源落於整個元素區間 60
6-1-3-3 熱源右移1/4個元素長度 60
6-1-3-4 熱源右移1/2個元素長度 61
6-1-3-5 熱源右移3/4個元素長度 61
6-1-3-6 COMSOL軟體模擬 61
6-1-3-7 程式撰寫數值與COMSOL數值比對 61
6-1-4二維移動熱源邊界測試 62
6-1-4-1程式撰寫數值分析 62
6-1-4-2 COMSOL軟體模擬 62
6-1-5二維疊層處理測試 63
6-1-6二維疊層後再掃描測試 63
6-2 實際條件結果與討論 63
第七章 結論 107
參考文獻 109

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