CO2激光在加工玻璃的数值研究毕业论文外文翻译

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1、安徽工业大学毕业设计说明书（论文）英文原文Numerical investigation on machining glass with CO2 lasersJunke JIAO1,2, Xinbing WANG ()11 Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China2 Institute of Industry Technology, Guangzhou and Chinese Academy of Scienc

2、es, Guangzhou 511458, ChinaAbstract When a glass substrate was irradiated by three different temporal shapes of laser sources, namely, line-time-shape laser, triangle-time-shape laser, and parabola-time-shape laser, the mathematical models were proposed,and the temperature distribution and the resul

3、ting thermal stress were calculated by the finite-element-method (FEM) software ANSYS. With these three types of lasers having the same output laser energy, the resulting thermal stress induced in the glass substrate was analyzed. The results showed that, with the same output laser energy, the therm

4、al stress produced in glass heated by line-time-shape laser is higher than that produced in glass heated by the other two shapes of lasers.Keywords laser machining, soda-lime glass, finite-element-method (FEM), ANSYS1 IntroductionWith the development of laser technology, many studies have been carri

5、ed out on cutting glass with lasers 117. Li et al. 3 put forward a mathematical model to explain the heat transfer of glass heated by a laser beam. Wei et al. 4 and Tian et al. 5 investigated the thermal behavior of glass heated by a CO2-laser beam numerically, and concluded that the resulting tempe

6、rature distribution was strongly dependent on the speed and the parameters of the laser beam. Tsai et al. 6 studied the thermal stress of alumina ceramic substrates irradiated by a moving laser beam and some experiments were carried out to investigate how the crack propagation was influenced by lase

7、r power, cutting speed, and specimen geometry. Glass can be cut by continuous-wave lasers in two different ways. One is the controlled fracture method and the other is melting means. The former has attracted more attention and lots of research has been reported in literatures 716. In contrast, very

8、few studies have been made in detail to investigate cutting glass with the melting method except by Chui 17, due to the low thermal conductivity and the brittleness of the glass material. How to reduce the thermal stress in the glass manufacturing process is a challenging task. Thermal stress is alw

9、ays generated by rapid heating or cooling. If the glass is heated slowly and cools down smoothly, the thermal stress may be controlled below the critical value. In this study, three different temporal shapes of lasers were used to heat the glass substrate, and the thermal stress was calculated by us

10、ing finite-element-method (FEM) software ANSYS.2 Theoretical approachesAs shown in Fig. 1, the length L, width W, and thickness H of the glass substrate are 40 mm, 20 mm, and 2 mm, respectively. A stationary unfocused CO2-laser irradiates on the surface and the diameter of this laser beam is 6 mm. B

11、efore establishing mathematical models, some assumptions should be made as follows.1) The physical properties of the glass material are isotropic and symmetrical.2) There is no phase change in the machining process.3) On the surface of the glass, without laser heating, the superficial heat irradiati

12、on is negligible.4) The CO2-laser energy is fully absorbed by soda-lime glass ( = 1), and the emission coefficient is treated as 1.Fig. 1 Diagram of glass laser heating and grid structure of glass substrate2.1 Mathematical models for heat transfer and mechanismBased on the above-mentioned assumption

13、s, the mathematical heat transfer model can be established as follows:where k is the thermal conductivity; c and r are the heat capacity and the density, respectively; T0 denotes the initial temperature of glass which is the same as the environment temperature; Ts denotes the temperature of heated z

14、one and Tn denotes the temperature of the area without laser heating; h is the convection heat-transfer coefficient and B is the Stefan-Bolzmann constant; I (x, y, z, t) is the density of the laser power and n is the direction cosine of boundary. In this study, the stress and strain responses were a

15、ssumed to be quasi-static at each interval and the thermo-elastic model was used. The entire surfaces of the glass plate are free of stress, and the distribution of the thermal stress can be obtained by solving the heat-elasticity equation mentioned in Ref. 18. During the process of laser glass mach

16、ining, the thermal stress may be established as a result of thermal gradients in glass, frequently caused by rapid heating or cooling. Here, caused by a temperature difference T, the thermal stress therm is given as 19= (2)where is the Poissons ratio, and E and b are the Yangs modulus and the coeffi

17、cient of linear expansion, respectively. From Eq. (2), the sharp change in temperature will lead to a steep thermal gradient and a large thermal stress. Heating and cooling down the glass substrate smoothly may be a feasible means to reduce this thermal stress in the machining process.2.2 Model of l

18、aser beamLasers focusing on the top surface maintain a constant TEM00 mode. The density of the laser power can be described by Gaussian distribution aswhere P and r are the power and the radius of the CO2-laser beam, respectively. The absorption depth is less than 15 m, so the CO2-laser beam is trea

19、ted as a surface heating source, and an impulse function _(z) is applied in Eq. (3).In this study, three different temporal shapes of laser sources were used to heat the glass substrate, and the difference of the thermal behavior among them was studied to find a best temporal shape of laser to reduc

20、e the thermal stress. The output power for these three different laser sources isIn the current work, P0= 30W and t0= 10 s. The output power temporal histories for these three shapes of laser sources are shown in Fig. 2. For the line-time-shape laser, the output power keeps in a constant value (P =

21、30W) in the first 10 s, and there is no output laser in the next 10 s. For triangle-time-shape laser source and parabola-time-shape laser source, the power of the laser increases in the first 10 s, and decreases slowly in the following 10 s. It should be noted that the output laser energy is the sam

22、e for these three temporal shapes of laser sources during the analyzing time (020 s).Fig. 2 Time history of power for line-time-shape, triangle-time-shape, and parabola-time-shape lasers3 Numerical calculationsA coupled-field analysis was performed to determine the temperature distribution and the r

23、esulting thermal stress in the workpiece using the FEM software ANSYS. The coupling between the thermal and structural fields was accomplished by direct coupling. A three-dimensional coupled-field solid element in SOLID5 was used for the current work. The element had eight nodes with up to six degre

24、es of freedom at each node. The grid structure of the glass substrate is shown in Fig. 1. On the heated zone, the size of elements is optimized balancing the demand for simulating precision and computational efficiency, which turns out to be smaller than that in other regions. The size of elements o

25、n the heated zone is 0.5 mm, which is accurate enough for this study.The physical parameters of soda-lime glass are shown in Table 1 11. The initial temperature T0 was 20C and the convection heat-transfer coefficient h was 10.4 Results and discussionAccording to the above-mentioned mathematical mode

26、ls and the parameters of the soda-lime glass given in Table 1, the distribution of the temperature and the resulting thermal stress can be calculated by using the FEM software ANSYS, which is powerful in coupling thermal and structural fields.When the glass substrate is irradiated by these three tem

27、poral shapes of laser sources, the temperature history is given in Fig. 3. For line-time-shape laser, the workpiece is heated by high-density laser beam, and the temperature increases rapidly in the first 10 s. Then, the workpiece is cooled down sharply by the convection between the workpiece and th

28、e air surrounding in the following 10 s. This rapid heating and cooling will result a large thermal stress in the glass substrate. On the other hand, for triangle-time-shape and parabola-time-shape laser sources, the power increases with time slowly in the first 10 s and descends smoothly in the nex

29、t 10 s. When the workpiece is irradiated by these two temporal shapes of laser sources, the temperature varies smoothly, and the thermal gradient and the resulting thermal stress would be very small.With these three temporal shapes of lasers having the same output laser energy, the maximum value of

30、the temperature generated in the glass substrate is different. The maximum temperature for line-time-shape laser is much higher than the other two laser sources due to the low thermal conductivity of the glass material, and the heat energy is accumulated on the heating zone at a short time for line-

31、time-shape laser. Otherwise, the maximum temperature is a little higher for triangle-time-shape laser than that for parabola-time-shape laser. In the heating zone, because of the high temperature, a compressive thermal stress is generated (see Fig. 4). The resulting compressive thermal stress is hig

32、her for line-time-shape laser than that for the other two shapes of laser sources. The thermal stress changes most smoothly for parabola-time-shape laser and most sharply for line-time-shape laser.At the time step t = 10 s, which is the inflexion of the output laser, the temperature on the top surfa

33、ce is much higher for line-time-shape laser than those for triangle-time-shape and parabola-time-shape lasers (see Fig. 5). In the last 10 s, the tensile stress decreases with time for line-time-shape laser, and the minimum value is 140 MPa at the time step t = 20 s at the edge of the glass substrat

34、e (see Fig. 6). However, for triangle-time-shape and parabola-time-shape lasers, the tensile stress reaches to the maximum value at the time step t = 14 s and then decreases to 178 MPa (see Fig. 7) and 175 MPa (see Fig. 8) at the time step t = 20 s, respectively. When a laser beam is irradiating on

35、glass substrate, the maximum tensile stress occurs at the edge of the workpiece. This tensile stress is an important factor in glass laser machining. If this stress exceeds the critical value, a fracture will be produced. In glass laser cutting with the controlled fracture method, this fracture prop

36、agates in a predicted way to separate the glass substrate. However, in most glass manufacturing processes, this tensile stress is negative, such as cutting glass in the melting method and shaping glass materials. In these machining processes, the tensile stress is a negative factor that has to be re

37、duced.Fig. 3 Temperature history in laser heating zoneFig. 4 Thermal stress history in laser heating zoneFig. 5 Temperature distribution on heating surface at time stept = 10 sFig. 6 Thermal stress on heating surface at different time for line-time-shape laserFig. 7 Thermal stress on heating surface

38、 at different time for triangle-time-shape laserFig. 8 Thermal stress on heating surface at different time for parabola-time-shape laserFor line-time-shape laser, the maximum tensile stress occurs at the time step t = 10 s (see Fig. 6), which is the point of the laser stopping to irradiate the glass

39、. On the other hand, for triangle-time-shape and parabola-time-shape lasers, the maximum tensile stress occurs at the time step t = 14 s (see Figs. 7 and 8). This phenomenon is consistent with the temperature history for these two laser sources. On the other hand, the maximum tensile stress is much

40、larger for line-time-shape laser than that for triangle-time-shape and parabola-time-shape lasers with the same output laser energy.5 ConclusionThe mathematical models of glass irradiated by line-time-shape, triangle-time-shape, and parabola-time-shape lasers were put forward. The temperature distri

41、bution and the resulting thermal stress were calculated by ANSYS. For line-time-shape laser, the workpiece was heated to a high temperature in a short time and cooled down rapidly in the air surrounding. And, a higher thermal stress including the compressive stress in the heating zone and the tensil

42、e stress at the edge of glass substrate were generated. For triangle-time-shape and parabola-time-shape lasers, the workpiece was heated slowly in the first 10 s and cooled down smoothly in the following 10 s. And, the temperature varied more smoothly and a smaller thermal stress was generated in th

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53、 Bernstein J R, Li L, Stott F H. Dual laser beam modification of high alumina ceramics. Journal of Laser Applications, 2003, 15(1): 4954附录 2 译文CO2激光在加工玻璃的数值研究焦俊科 王新兵1 武汉 国家光电实验室 华中科技大学科学与技术实验室 武汉430074,中国2 工业技术研究院 广州中科院 广州511458,中国摘要 当三种不同时间的形状的激光源，即，线时间形状的激光，激光三角形状，和抛物线时间形状的激光照射玻璃基板时，用有限元法计算的应力（FEM

54、）ANSYS软件，提出数学模型，计算温度分布和产生的热。对这三个有相同的输出类型的激光，引起的玻璃基板产生的热应力进行了分析。结果表明，具有相同的输出能量的激光，在由线时间形激光加热玻璃产生的热应力高于其他两个形状在玻璃中产生的热应力。关键词 激光加工 钠钙玻璃 有限元法(FEM) ANSYS.1 简介 随着激光技术的发展，许多研究已经应用到用激光切割玻璃1-17 。Li等人3提出一个数学模型来解释通过激光束加热的玻璃的传热。Wei4以及Tian等人5考查了由二氧化碳激光束加热的玻璃的热行为数值，并且得出结论，由此产生的温度分布强烈地依赖于速度和激光束的参数。Tsai等人【6】研究了由移动的激

55、光束照射氧化铝陶瓷基片的产生的热应力和一些实验研究激光功率，切割速度，和试样的几何形状如何影响裂纹的扩展。玻璃可用两种不同的连续波激光器切割。一个是控制断裂的方法，另一种是熔融装置。前者已经吸引了更多的关注和大量的研究报道文献7-16。与此相反，除Chui的方法, 由于低导热性的玻璃材料的脆性,很少有研究进行详细调查玻璃切割熔化17 。如何降低在玻璃制造过程中的热应力是一项具有挑战性的任务。热应力总是由于快速加热或冷却所产生的。如果玻璃被慢慢加热，并顺利地冷却下来，产生的热应力可被控制到低于临界值。在这项研究中，使用了三个不同的时间形状的激光器对玻璃基板加热，通过使用有限元法（FEM）软件AN

56、SYS对热应力进行了计算。2 理论方法如图1所示,玻璃的长L,宽W,厚H分别为40mm,20mm,2mm。静止的未聚焦的CO2激光照射在表面上，该激光束的直径为6毫米。在建立数学模型前，应作如下假设。图1 激光加热以及电网结构玻璃基板图1） 玻璃材料的物理性能是各向同性的且对称的。2） 加工过程中没有相变。3） 未经激光加热的玻璃表面的热辐射忽略不计。4） 二氧化碳激光的能量由钠钙玻璃（= 1）充分吸收且发射系数被视为1。2.1 传热机制的数学模型根据上述的假设，数学传热模型的建立如下：其中k是传导率；c和分别是热容量和密度；表示玻璃的初始温度也是环境温度；表示加热区的温度；表示未经激光加热区

57、域的温度；h为对流换热系数；B是Stefan-Bolzmann常数；是激光功率密度；n为边界的方向余弦。 在这项研究中，应力和应变的响应被用来假定为在每个时间间隔和准静态热弹性模型。整个玻璃板表面的应力以及热力分布可以通过Ref18提到的热弹性方程解决。在激光加工玻璃的过程中，产生的热应力课设立作为玻璃中的热梯度，是频繁的快速加热或者冷却造成的结果。在这里，由温差引起的热应力给定为19 = (2)是泊松比，E是杨氏模量，是线性膨胀系数。从公式（2）中，温度的剧变会导致一个陡峭的热梯度和一个大的应力。缓和的加热或者冷却玻璃基板在加工过程中减少这种应力可能是一种可行的方法。2.2 激光束模型激光聚

58、焦的顶表面上保持恒定的TEM00模。激光的能量密度可以通过高斯分布描述为P是激光的功率，r是激光束半径。吸收深度小于15微米，因此激光束当作表面加热源，并且冲激函数应用到公式（3）中。在这项研究中，三种不同形状的激光源被用于加热玻璃基板，并对其中的热行为的差异进行了研究，找到了最佳的瞬时形状的激光，以减少热应力。这三种不同激光源的输出能量是在当前的工作，=30W，=10s 。这三种形状的激光光源的输出功率的时间的历程显示如图2所示。对于线激光前10s保持激光功率为P=30W并在接下来的10s中无激光输出。对于三角激光和抛物线激光在前10s激光功率在增加，接下来的10s激光功率缓慢减小。应该指出

59、的是在这分析时间（020s）内这三个激光源的输出能量是相同的。图2 线形、三角形、抛物线形激光时间功率图3 数值计算采用有限元软件ANSYS进行耦合场分析，以确定工件的温度分布和产生的热应力。热和结构直接的耦合是通过直接耦合的。在目前的工作中用的是一个三维的耦合场固体元素SOLID5，该元素有八个节点，每个节点有六个自由度。如图1所示，玻璃基本的网格结构。在加热区，对元素的大小进行了平衡模拟精度和计算效率的需求的优化，这原来是小于其他区域的。加热区域元素的尺寸是0.5毫米，在这个研究中是足够的。钠钙玻璃的物理参数如表111所示。初始温度是20，对流换热系数h是10。表1 钠钙玻璃的物理参数20

60、20040060080010002520-1.401.621.822.10-68095510751145119512200.1650.1730.1770.1820.1860.19472.975.077.278.880.081.04 结果和结论通过上述的数学模型以及表1给出的钠钙玻璃参数,可以通过在热结构耦合领域计算强大的有限元软件ANSYS计算出温度分布以及由此而产生的热应力。当三种形状的激光照射在玻璃基板上，温度时间如图3所示。线形激光时，工件被高密度激光束加热，并在前10s时间内温度迅速增加。然后，冷却工件，在接下来的10s内，通过工件和周围空气之间热对流急剧降温。这温升和冷却会导致玻璃基

61、板内部产生热应力。另一方面，三角形激光源和抛物线形激光源在前10s能量增加的很缓慢而且在接下来的10s能量减少的也是很缓慢，当基板被这两种激光源辐照时，温度变化很自如，热梯度以及热应力变化的很小。这三个时间的形状具有相同的输出的激光能量的激光，但是在玻璃基板上产生的温度的最高值是不同的。由于玻璃材料的低导热系数使得线形激光所产生的温度最大值要比另外两种激光产生的温度最大值要高出许多。并且线形激光在短时间内在加热区域积蓄了热能，否则，最高温度只比三角形激光和抛物线激光高一点。在加热区，由于高温，产生了压缩的热应力（图4）。由此而产生的热应力是线形激光源比另两种激光源要高，抛物线形激光源产生的热应

62、力改变是最顺畅的，而线形激光源产生的热应力改变幅度是最大的。图.3 激光加热区域的温度时间图图.4 加热区热应力时间图在第10s的时刻，也就是激光输出拐点的时刻，线形激光比三角形激光和抛物线形激光在顶表面的温度要高的多（参照图.5），在过去的10s，线形激光的拉伸应力随时间增加而增加，在20s的时间内，玻璃基板边缘应力（参照图6）的最小值为140兆帕。然而，在时间步长为20s是，对于三角形和抛物线形激光，拉伸应力在14s达到最大值，分别为178兆帕（参照图7）和175兆帕(参照图8)图.5 时间步长t=10s受热面温度分布图图.6 不同时间的线形激光在加热表面的热应力图.7 不同时间的三角形激

63、光在加热表面的热应力图.8 不同时间的抛物线形激光在加热表面的热应力当激光束照射在玻璃基板上，最大的拉应力产生在工件的边缘。这种拉伸应力在激光加工玻璃上是一个重要的因素。如果这种拉伸应力超过了临界值时，将会产生断裂。用控制断裂的方法激光切割玻璃，这种断裂传播预示着玻璃分离的方式。然而，在大多数玻璃制造过程中，拉伸应力为负，例如熔融发切割玻璃和玻璃材料的成形。在这些加工过程中，拉伸应力是一个不利因素，已被减少。对于线形激光，最大拉伸应力产生在时间步长t=10s（参照图6），这是激光停止照射玻璃的时间点。另一方面，对于三角形和抛物线形激光，最大拉伸应力发生在t=14s（参照图7和8,）这两种激光的

64、温度时间历程现象是一致的。另一方面，在相同的激光输出能量，线形激光的最大拉伸应力要比三角形和抛物线形激光大得多。5 结论线形、三角形、抛物线形激光照射玻璃的数学模型提出了，温度的分布和产生的热应力可以通过ANSYS计算，对于线形激光，工件可以在短时间升到很高的温度，也可以在周围环境中迅速冷却。此外，有较高的热应力的产生，包括加热区的压缩应力和玻璃基板边缘的拉伸应力。对于三角形和抛物线形激光，在前10s内加热缓慢，后10s冷却顺利，并且，温度变化顺利，工件加工过程中内部有较小应力产生。6 参考文献1. Kang H S, Hong S K, Oh S C, Choi J Y, Song M G.激光切割玻璃的研究。 SPIE ，2002，4426:367-3702. Hermanns C.激光切割玻璃。SPIE，2000，4102:219-2263. Li J F, Li L, Stott F H.对激光加热源对陶瓷材料熔化体积和表面的比较，国际传热传质杂志，2004，47（6-7）：1159-11744. Wei C Y, He H B, Deng Z, Shao J D, Fan Z X. 二氧化碳激光照射玻璃的热行为的研究。光学工程，2005，44（4）：044202-1044202-45. Tian W X, Chiu K S.