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如果将利用连续功率分析光束在材料内的加热效应,并且认为材料的参量各向同性且忽略加热过程中的材料相变,那么可以得到如下方程:
$I(x, y, z) = \frac{{\alpha P}}{{\pi {r^2}}}\exp \left( { - \frac{{{x^2} + {y^2}}}{{{r^2}}}} \right)\exp ( - \alpha z) $
(1) $\rho c\frac{{\partial T}}{{\partial t}} = \frac{\partial }{{\partial x}}\left( {\kappa \frac{{\partial T}}{{\partial x}}} \right) + \frac{\partial }{{\partial y}}\left( {\kappa \frac{{\partial T}}{{\partial y}}} \right) + \frac{\partial }{{\partial z}}\left( {\kappa \frac{{\partial T}}{{\partial z}}} \right) + I $
(2) $\lambda \frac{{\partial T}}{{\partial n}} = - h\left( {t - {t_0}} \right) $
(3) $T{\left. {(x, y, z)} \right|_{t = 0}} = {T_0}\ $
(4) (1) 式描述了激光作为热源时在材料内部的产热分布, 式中, α为吸收系数,P为测量得到的连续功率, r为光束到达材料表面时的光斑半径。(2)式为材料空间温度变化与热扩散和产热的关系, 式中, ρ是密度,T是材料温度,t是时间, κ为导热系数, c为质量热容, I为热能。(3)式为空气对流下材料边界的换热效应, 式中,t0为初始时间,h为表面传热系数,n为折对率。(4)式表示材料内的初始温度, 式中,T0为环境温度(20℃)。由于上述关系在材料参量随温度改变的情况下没有解析解,所以模拟利用有限元模型计算方程描述的温度效应。图 3a为模型示意图,其中光斑在模拟过程中位于坐标轴中心。由于计算过程中温度变化关于光斑中心对称分布,因而将模型尺寸减半为5mm×10mm×1mm,模拟单元选用热学模拟单元solid70。同时光斑附近网格较密,远处网格较疏如图 3b所示。具体模拟参量见表 1[18]。
Table 1. Physical properties of float glass at different temperatures[18]
temperatureT/ ℃ density ρ/
(kg·m-3)thermal conductivity κ/
(W·m-1·K-1)specific heat capacity c/
(J·kg-1·K-1)25 2.43×103 1.06 8.28×102 200 — 1.23 1.01×103 400 — 1.38 1.16×103 500 — 实验过程中玻璃的温度变化范围低于浮法玻璃的转化温度(560℃),材料的导热系数可以当作线性函数近似处理[19]。由于材料对光的吸收率在此温度范围内变化较小,所以近似当作常数处理[20],取实际测量值10760m-1。环境温度为20℃,空气的对流换热系数为0.1W/(m2·K)。模拟和测量的材料温度均普遍小于熔化温度(1040℃), 材料相变导致的热量传递以及材料的辐射热量损失均不考虑。
6.45μm激光加热浮法玻璃后温度分布特性研究
Research of temperature distribution in float glass after heating by 6.45μm laser
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摘要: 为了提升激光可控断裂法切割玻璃的质量,研究了6.45μm激光照射浮法玻璃后材料的温度变化。利用激光输出的连续功率计算了6.45μm激光照射玻璃后的温度分布,并通过实验验证了该模型的正确性;模拟对比了相同激光参量下6.45μm激光和10.6μm激光加热玻璃后的温度场,通过实验获得了光滑、无表面裂纹的切割样品。结果表明,6.45μm激光产生的表面温度低于10.6μm激光;6.45μm激光可以利用热裂法获得高质量切割端面。该研究对中红外激光玻璃切割的模型建立和方案优化具有一定的帮助。Abstract: In order to improve the quality of glass cut by laser controlled fracture method, the temperature change of material after 6.45μm laser irradiation was studied. The temperature distribution of glass irradiated by 6.45μm laser was calculated by using the continuous laser output power, and the correctness of the model was verified by experiments. Temperature field of glass heated by 6.45μm laser and 10.6μm laser under the same laser parameters was simulated and compared. The smooth and crack-free cutting samples were obtained by experiment. The results show that, the surface temperature of 6.45μm laser is below than that of 10.6μm laser. 6.45μm laser can obtain high quality cutting face by hot cracking. The research is helpful for the modeling and the optimization of mid infrared laser glass cutting.
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Key words:
- laser technique /
- laser cutting /
- crack controlled method /
- 6.45μm laser /
- float glass
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Table 1. Physical properties of float glass at different temperatures[18]
temperatureT/ ℃ density ρ/
(kg·m-3)thermal conductivity κ/
(W·m-1·K-1)specific heat capacity c/
(J·kg-1·K-1)25 2.43×103 1.06 8.28×102 200 — 1.23 1.01×103 400 — 1.38 1.16×103 500 — -
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