本研究主要利用有限元素法模擬，分析不同操作條件與幾何參數，其對雷射二極體色輪模組中，螢光玻璃層之溫度與應力場的影響。雷射二極體色輪依照運作方式，可分為反射式與穿透式兩種。文中利用熱傳─結構間接耦合有限元素模式，配合以移動式熱源取代色輪旋轉的替代模型，分別探討腔體操作溫度、色輪轉速、藍光雷射照射功率、光腰大小等操作條件與玻璃螢光體厚度、基板厚度等幾何參數，進行一系列的分析，期找出影響可能色輪可靠度的關鍵因子。
文中因涉及部份新螢光玻璃材料，迄今尚無明確之機械性質資料，文中乃採用工程反算法，配合簡易之光熱轉化方程，分別所須之求取螢光體的轉化係數與熱傳導係數。同時，基於輸出均勻光場的需求，本文利用多個TEM00的雷射疊加，提出一具能量分布平坦化之雷射源設計，並依據此光場分佈，分析相關熱傳與熱應力效應。文中主要使用有限元素套裝軟體MSC.Marc，配合Fortran語法所編寫的子程式來做移動熱源之數值模擬。分析結果顯示本文提出之有限元素法分析模式，可成功應用於雷射二極體色輪，在各種工作狀態熱與應力場分析，希有助於開發與設計相關時分析之用。

A thermal-structural indirect coupling finite element model has proposed to simulate the thermal and stress distributions of the high power phosphor color transfer wheel. The effects of operating conditions, and the wheel dimension parameters, e.g. operating temperature, rotation speed of wheel, laser power, the geometric dimensions of phosphor glass, and the weight content concentration of phosphor, on the temperature and stress distributions have been simulated and evaluated in this study. A constant rotation speed moving laser source has also employed in this work to instead of the moving disk with a stationary laser in practice. A body force was introduced to include the centrifugal force in the disk.
In order to derive the required mechanical properties of different weight concentration phosphor glass, different engineering inverse approaches have been applied to estimate its possible values. A flat power density laser distribution was constructed by 64 lower power laser diodes. A normal distributed power density was assumed for each laser diode. Numerical results indicate that the proposed FEM model can simulate the temperature and stress fields of the moving high power phosphor color wheel successfully.

謝誌 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 ix
符號說明 x
第一章 緒論 1
1.1 研究背景與動機 1
1.2 文獻回顧 5
1.3 組織章節 7
第二章 基本理論 8
2.1螢光粉之光轉換原理 8
2.2 光激發熱效應 12
2.3 熱傳分析理論 15
2.4 固體力學分析理論 16
2.5 有限元素分析介紹 20
2.6 牛頓-拉佛森法(Newton-Raphson Method)與收斂判斷 22
第三章 玻璃與矽膠螢光體 27
3.1 螢光體介紹 27
3.2 螢光體性質 28
第四章 有限元素模型 46
4.1 雷射設定 46
4.2 色輪模型 48
第五章 結果與討論 63
5.1 參數規劃 63
5.2 矽膠與玻璃螢光體色輪之比較 65
5.3 反射式色輪 67
5.3.1 操作溫度 70
5.3.2 雷射功率 72
5.3.4 色輪轉速 77
5.3.4 螢光體厚度與基板厚度 79
5.3 穿透式色輪 82
第六章 結論與未來展望 91
6.1 結論 91
6.2 未來工作 92
參考文獻 93

[1] Kuo, C. P., Fletcher, R. M., Osentowski, T. D., Lardizabal, M. C., Craford, M. G., & Robbins, V. M., “High Performance AlInGaP Visible Light-emitting Diodes,” Applied Physical Letters, 57, pp. 2937-2939, 1990.
[2] 劉如熹、劉宇桓，發光二極體用氧氮螢光粉介紹，全華科技，台北，2006。
[3] Yi, X., Zhou, S., Chen, C., Lin, H., Feng, Y., Wang, K., & Ni, Y., “Fabrication of Ce:YAG, Ce,Cr:YAG and Ce:YAG/Ce,Cr:YAG duel-layered composite phosphor ceramics for the application of white LEDs,” Ceramics International, 40, pp. 7043-7047, 2014.
[4] Barton , D. L., “Degradation of Blue AlGaN/InGaN/GaN LEDs Subjected to High Current Pulses,” Reliability Physics Symposium, 1995. 33rd Annual Proceedings., IEEE International, pp. 191-199, 1995.
[5] Narendran, N., Gu, Y., Freyssinier, J. P., Yu, H., & Deng, L., “Solid-state Lighting: Failure Analysis of White LEDs,” Journal of Crystal Growth, 268(3-4), pp. 449-456, 2004.
[6] 林育寬，高功率發光二極體高溫加速老化之失效分析，碩士論文，國立中山大學機械與機電工程學系，高雄，2007。
[7] 鍾政勳，高功率白光發光二極體之玻璃螢光體製作及可靠度研究，碩士論文，國立中山大學光電工程研究所，高雄，2010。
[8] Tsai, C. C., Chen, G. H., Wang, J., & Cheng, W. H., “Thermal Test of Lumen Loss and Chromaticity Shift in Glass and Silicone Phosphor under Various Temperatures,” NSC, 2011.
[9] Nishiura, S., Tanabe, S., Fujioka, K., & Fujimoto, Y., “Properties of transparent Ce:YAG ceramic phosphors for white LED,” Journal of Optical Materials, 33, pp. 688-691, 2011.
[10] Samuel, P., Kumar, G. A., Yanagitani, T., Yagi, H., Ueda, K. I., & Babu, S. M., “Efficient energy transfer between Ce3+/Cr3+ and Nd3+ ions in transparent Nd/Ce/Cr:YAG ceramics,” Journal of Optical Materials, 34, pp. 303-307, 2011.
[11] Cheng, W. C., Tsai, C. C., Chang, J. K., Huang, S. Y., Chen, J. H., Hu, S. S., Huang, Y. C., & Cheng, W. H., “Fabrication of Low-Temperature Ce3+:YAG Doped Glass for Phosphor-Converted White-Light-Emitting Diodes,” 17th Opto-Electronics and Communications Conference, Korea, 2012.
[12] 蔡俊欽，高功率發光二極體模組光功率與光場高溫老化可靠度之研究，碩士論文，國立中山大學光電工程研究所，高雄，2009。
[13] Hecht, E., Optics, 4th edition, Addison-Wesley, USA, 2002.
[14] Beiser, A., Concepts of Modern Physics, McGrew-Hill, New York, 2003.
[15] Incropera, DeWitt, Bergmann, & Lavine, Fundamentals of Heat and Mass Transfer, 6th edition, John Wiley & Sons, Asia, 2007.
[16] Lurie, A. I., Theory of Elasticity, Springer, New York, 2005.
[17] Ugural, A. C., & Fenster, S. K., Advanced Strength and Applied Elasticity, 4th edition, Pearson, Taiwan, 2003.
[18] Chankrabarty, J., Theory of plasticity, 3rd edition, Elsevier, 2006.
[19] Meyer, M., Mechanical Behavior of Materials, Cambridge University Press, UK, 2009.
[20] Calister, W., Material Science and Engineering: An Introduction, John Wiley & Sons, USA, 2007.
[21] Turnes M. J., Clough R. W., Martin H. C., & Topp, J. L., “Stiffness and Deflection Analysis of Complex Structures,” Journal of Aeronautical Science, 23(9), pp. 805-824, 1956.
[22] Chandrupatla, T. R., & Belegundu, A. D., Introduction to Finite Elements in Engineering, Pearson, Taipei, 2010.
[23] 邱姵茹，雙雷射束畫線製程應用於薄膜太陽能電池之研究，碩士論文，國立中山大學機械與機電工程研究所，高雄，2013。
[24] MSC. Software Corporation, MSC. MARC Product Documentation Volume A: Theory and User Information, MSC. Software Corporation, 2010.
[25] Lee, H., & Neville, K., Handbook of Epoxy Resins, McGraw-Hill, Taipei, 1984.