本研究以離散元素法(Discrete Element Method, DEM)雙向耦合(Two-way Coupling)計算流體力學(Computational Fluid Dynamics, CFD)進行數值運算，模擬 接觸以及分佈，更藉由滾鍍實驗量測表面電極厚度，進行實驗驗證。此方法將每 顆 LTCC 元件視為單獨元素，並將 LTCC 在電鍍液中所受到的不同作用力如拖曳 力(Drag Force)、虛擬質量力(Virtual Mass Force)、浮力(Bouyoug Force)等納入計 算，利用數值運算模擬其與鋼珠在滾桶中與有限時間下的接觸行為與 LTCC 元件 的分佈行為。結果顯示，隨著 LTCC 元件表面電極與鋼球接觸頻率的增加，以及 LTCC 元件在有效電鍍區中的滯留時間增加，鍍鎳速率隨之增加，但其厚度均勻 性降低。此外，隨著氧化鋯容積率與鋼球尺寸的增加，鍍鎳速率降低，然而其厚 度均勻性增加。而改變陶瓷珠密度，發現對鍍鎳速率以及表面電極厚度均勻性無 顯著影響。

The electroplating process of LTCC devices has been assessed by numerical simulation using discrete element method (DEM) with two-way coupling of computational fluid dynamics (CFD), and experimentally verified by barrel plating. The results show that the plating rate of Ni increases, but its thickness uniformity decreases with increasing contact frequency between the surface electrode of LTCC devices and steel balls. Moreover, the plating rate of Ni decreases, but its thickness uniformity increases with increasing ZrO2 bead loading, and steel ball size. However, insignificant correlation between the density of ceramic beads and plating rate of Ni and its thickness uniformity is found.

摘要..................................................................II Abstract.............................................................III 誌謝..................................................................IV
目錄..................................................................VI 表目錄..............................................................VIII 圖目錄................................................................IX
第一章 前言.............................................................1
第二章 耦合離散元素法與流體計算力學模擬方法..................................3
2.1 離散元素法(Discrete element method , DEM)...........................3 2.1.1 顆粒的控制方程式(Governing equations for particles) ...............4
2.2 流體的控制方程式(Governing equations for fluid) .....................7
2.3 顆粒與流體間交互作用力................................................8 2.3.1 拖曳力(Drag Force) ...............................................8
2.3.2 虛擬質量力(Virtual Mass Force) ...................................9
2.3.3 浮力(Buoyancy Force) ............................................9
第三章 實驗方法.........................................................10 3.1 DEM-CFD 模型......................................................10 3.2 模擬系統...........................................................10
3.3 實驗系統...........................................................11
3.3.1 表面電極鍍層厚度量測...............................................11 第四章 結果與討論.......................................................12
4.1 系統穩定測試(Benchmark test)........................................12 4.1.1 測試兩個圓形顆粒間之彈性正向接觸力...................................12
4.1.2 測試圓形顆粒與平板間之彈性正向接觸力.................................12
4.1.3 測試圓形顆粒與平板間之切向力........................................13
4.2 調降楊氏係數對雙向耦合模擬計算的影響...................................13
4.3 模擬結果與實驗結果..................................................14
4.3.1 氧化鋯容積佔比率對 LTCC 表面電極厚度與均勻性的影 響...................14
4.3.2 鋼珠粒徑對 LTCC 表面電極厚度與均勻性的影響...........................15
4.3.3 陶瓷珠密度對 LTCC 表面電極厚度與均勻性的影響.........................16
第五章 結論...........................................................18

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