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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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