在雷射加工玻璃的過程中，我們發現在切割邊緣常會發生裂紋、凸塊、殘留物與燒焦等現象。而實驗結果顯示，相較於直接在空氣中進行雷射加工，將玻璃板材置入水中再以雷射進行切割可大幅改善其切割品質，並提高切割速度。直觀而言，此乃因在水中進行雷射加工時引發較為旺盛之自然對流，故可以降低工件內部之溫度梯度和熱應力，從而減少裂痕產生；也可以更為有效地帶走材料剝蝕殘留物。
　　
　　本文建立水輔助雷射加工技術之熱流理論模型，在適當的假設下，除了利用溫度場之解析解檢討工件表面熱傳係數、雷射光加熱功率密度、切割半徑和切割速度等製程參數之間的相互影響，也利用數值方法模擬流場與各加工參數的相關連，並試圖以熔融區中自然對流所造成的表面變形解釋凸塊的生成。
　　
　　在不考慮流場的情況下，藉由解析解並以省能觀點出發，得ㄧ最佳切割速度。此外由數值模擬分析流場得知，在加工過程中液體對工件表面產生一最大剪切應力，此即為清潔能力，且此最大應力區隨著熱源移動，維持工件表面的品質。另外，模擬熔融區內的流場(忽略相變化)，求出因自然對流產生的表面變形，但其變形數量級極小。所以我們猜測除了自然對流外，相變化或其他機制的影響，如熱毛細現象，可能為凸塊生成的主因。

　　Experimental results suggest that, compared with laser cutting exercised in the air, both the cutting quality and speed are significantly increased when the material is submerged in the water. Intuitively, underwater laser cutting induces stronger natural convection than that in the air. The resulting greater heat loss then reduces the temperature gradient and thermal stress in the material, and the possibility of crack formation. Meanwhile, it also helps to remove the ablated debris from the substrate surface, and hence increases both the cutting depth and speed.
　　
　　In this thesis, a number of model problems are analyzed, aiming at explaining the basic mechanisms of water-assisted laser cutting. First, a two-dimensional (2D) model problem of heat conduction is analyzed. The model problem admits an analytic solution for the substrate temperature distribution, based on which we discuss the effects of heat loss on various process parameters such as the required laser power density, cut width and cutting speed. In particular, it is found that for prescribed cutting radius and heat loss, there exists an optimal (energy saving) cutting speed at which the energy required to remove a unit material mass reaches a local minimum.

　　Moreover, numerical methods are employed to solve the temperature and flow fields in two 2D model problems of water-assisted laser cutting. In the first model problem, natural convection due to laser heating is calculated. It is found that the water current induced by laser heating generally exerts a shear stress on the substrate surface, which is expected to be beneficial for ablated debris removal. In the second model problem, free surface deformation is taken into account (but neglecting phase change), and the numerical results suggest that natural convection alone may not be sufficient to cause bulge formation of the magnitude generally observed in practice. We conjecture that, in addition to natural convection, phase change and other effects such as thermocapillarity may work together to cause the bulge formation of such magnitudes.

1.A.Kruusing, “Underwater and Water- Assisted Laser Processing: Part 1–General Features, Steam Cleaning and Shock Processing.” Opt. Lasers Engrg. Vol. 41, pp. 307–327 (2004).
2.A.Kruusing, “Underwater and Water- Assisted Laser Processing: Part 2–Etching, Cuting and Rarely Used Methods.” Opt. Lasers Engrg. Vol. 41, pp. 329–352 (2004).
3.蘇志宏、楊天祥、陳國聲、鍾震桂, “水輔助雷射加工之理論分析與最佳切割速度計算。” 發表於中華民國第二十九屆全國力學會議(2005年12月16-17日).
4.張平昇、陳拓丞、陳國聲、楊天祥、鍾震桂, “CO2雷射玻璃切割製程之應力分析與有限元素模擬。” 發表於中華民國第二十九屆全國力學會議(2005年12月16-17日).
5.C.K.Chung, Y.C.Lin and G.R.Huang., “Bulge formation and improvement of the polymer in CO2 laser micromachining.” J. Micromech. Microeng. Vol. 15, pp. 1878–1884 (2005).
6.黃冠仁, “CO2雷射加工高分子及玻璃材料的缺陷改善探討。”國立成功大學機械工程學系碩士論文, 2006.
7.蔡明杰, “雷射切割產生金屬薄膜流之穩定性分析。”國立成功大學機械工程學系碩士論文, 1993.
8.A.R.Moss, and J.A.Sheward, “The Arc Plasma Cutting of Non-Metallic Materials.” IEE. Conf. On Electrical Methods of Machining, Forming and Coating, Mar. 1970, pp.41–47 (1970).
9.D.Rosenthal, “The Theory of Moving Sources of Heat and Its Application to Metal Treatment.” Trans. ASME, Vol. 68, pp. 849–866 (1946).
10.Y.Arata and I.Miyamoto, “Theoretical Analysis of Weld Pene- tration Due to High Energy Density Beam.” Trans. of J.W.R.I., Vol. 1, No. 1 (1972).
11.R.M.Lumley, “Controlled separation of brittle materials using a laser.” American Ceramic Society Bulletin, Vol. 48, pp. 850-854 (1969).
12.G.Allcock, P.E.Dyer, G.Elliner and H.V.Snelling, “Experimental observations and analysis of CO2 laser-induced microcracking of glass.” Journal of Applied Physics, Vol. 78, pp. 7295-7303 (1995).
13.J.Zhao, J.Sullivan and T.D.Bennett, “Wet etching study of silica glass after CW CO2 laser treatment.” Applied Surface Science, Vol. 225, pp. 250-255 (2004).
14.F.Weisbuch, V.N.Tokarev, S.Lazare and D.Debarre, “Viscosity of transient melt layer on polymer surface under conditions of KrF laser ablation.” Applied Surface Science, Vol. 186, pp. 95-99(2002).
15.B.C.Sim and W.S.Kim, “Melting and dynamic-surface deformation in laser surface heating.” International Journal of Heat and Mass Transfer, Vol. 48, pp. 1137-1144 (2005).
16.B.L.Sowers, R.D.Birkhoff and E.T.Arakawa, “Optical absorption of liquid water in the vacuum ultraviolet.” Journal of Chemical Physics, Vol. 57, pp. 583-584 (1972).
17.G.M.Hale and M.R.Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region.” Applied Optics, Vol. 12, pp. 555-563 (1973).

18.A.Kruusing, S.Leppavuori, A.Uusimaki, B.Petretis and O.Makarova, “Micromachining of magnetic materials.” Sensors and Actuators, Vol. 74, pp. 45-51 (1999).
19.H.S.Carslaw and J.C.Jaeger, Conduction of Heat in Solids, 2nd ed., Clarendon Press, Oxford (1959).
20.A.A.Wells, Welding J., Vol. 31, pp. 263s–266s (1952).
21.K.A.Bunting and G.Cornfield, “Toward a General Theory of Cutting: A Relation Between the Incident Power Density and the Cut Speed.” Trans. ASME, J. Heat Transfer, Febuary Issue, pp. 116–122 (1975).
22.Y.C,FUNG, A First Course in Continuum Mechanics, 2nd ed., Prentice-Hall, Inc.,(1977)
23.K.A.Bunting and G.Cornfield, “Supersonic Plasma Jets,” Electricity Council Research Centre Report M.395, July 1971.
24.J.F.Humphreys, and J.Lawton, “Arcs With Free Anode Roots in the Presence of Gas Flow and Magnetic Fields,” B. J. App. Phys, D., Vol. 5, pp. 701–709 (1971).
25.K.A.Bunting, “Metal Foil Cutting by Plasma,” Metal Construction and Brit. Welding Journal, Vol.4, No. 3, Mar. 1972.