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1
УДК 621.382:539.3
OPTIMIZATION OF LASER SPLITTING PARAMETERS OF SILICATE GLASSES WITH ELLIPTICAL BEAMS IN THE PLANE OF PARALLEL SURFACE
Y. V. NIKITYUK, A. N. SERDYUKOV
Francisk Skorina Gomel State University, the Republic of Belarus
I. Y. AUSHEV
State Educational Institution "University of Civil Protection of the Ministry for Emergency Situations of the Republic of Belarus", Minsk
Regression and neural network models of the process of laser splitting of silicate glasses by elliptical beams in a plane parallel to the surface were obtained. To conduct a numerical experiment, a central compositional plan was used. The processing speed, laser beam power and its geometric parameters were selected as variable factors. As responses, the values of maximum temperatures and the values of maximum thermoelastic tensile stresses in the processing zone were determined, the calculation of which was performed using the APDL programming language. An effective architecture for an artificial neural network created using the TensorFlow program has been established. A comparative analysis of neural network and regression models was carried out. The influence of input parameters on responses was assessed. Using the MOGA algorithm of the ANSYS program, the optimal modes for the formation of laser-induced cracks by elliptical beams were determined, ensuring the effective implementation ofparallel laser splitting of silicate glass.
Keywords: laser chopping, artificial neural network, optimization, MOGA, ANSYS.
ОПТИМИЗАЦИЯ ПАРАМЕТРОВ ЛАЗЕРНОГО РАСКАЛЫВАНИЯ СИЛИКАТНЫХ СТЕКОЛ ЭЛЛИПТИЧЕСКИМИ ПУЧКАМИ В ПЛОСКОСТИ, ПАРАЛЛЕЛЬНОЙ ПОВЕРХНОСТИ
Ю. В. НИКИТЮК, А. Н. СЕРДЮКОВ
Учреждение образования «Гомельский государственный университет имени Франциска Скорины», Республика Беларусь
И. Ю. АУШЕВ
Государственное учреждение образования «Университет гражданской защиты Министерства по чрезвычайным ситуациям Республики Беларусь», г. Минск
Получены регрессионные и нейросетевые модели процесса лазерного раскалывания силикатных стекол эллиптическими пучками в плоскости, параллельной поверхности. Для проведения численного эксперимента был использован центральный композиционный план. В качестве варьируемых факторов выбраны скорость обработки, мощность лазерного пучка и его геометрические параметры. В качестве откликов определялись значения максимальных температур и значения максимальных термоупругих напряжений растяжения в зоне обработки, расчет которых был выполнен с применением языка программирования APDL. Установлена эффективная архитектура искусственной
нейронной сети, созданной с использованием программы TensorFlow. Проведен сравнительный анализ нейросетевых и регрессионных моделей. Выполнена оценка влияния входных параметров на отклики. С использованием алгоритма MOGA программы ANSYS определены оптимальные режимы формирования эллиптическими пучками лазерно-индуцированных трещин, обеспечивающие эффективную реализацию параллельного лазерного раскалывания силикатного стекла.
Ключевые слова: лазерное раскалывание, искусственная нейронная сеть, оптимизация, MOGA, ANSYS.
Introduction
Glass, with its unique combination of properties, is extensively employed in various industrial applications. Cutting is a fundamental procedure in glass manufacturing, serving to achieve the desired shape and dimensions of the final products. Of particular importance is the efficient production of thin glass plates. The conventional methods for manufacturing thin glass plates rely on mechanical cutting, a process that is associated with substantial material losses, limited efficiency, and diminished strength of the final glass products [1, 2].
Presently, laser cleaving techniques have gained significant prevalence in the industrial sector [1-10]. Brittle nonmetallic materials, such as silicate glasses, can be effectively processed with these tools. The parallel laser cleaving technique can be used in this instance to produce thin glass plates. The fundamental principle underlying this technique is the generation of a laser-induced crack parallel to the surface of the material being processed. This crack is formed as a consequence of the glass plate being heated with an elliptical laser beam. Previous research has been conducted on the parallel laser cleaving technique for cutting brittle nonmetallic materials, as documented in [1, 11-13].
The use of metamodels has proven to be effective in several scenarios for the purpose of optimizing laser processing parameters. Metamodels have the potential to ascertain the output parameters of laser processing without performing exhaustive calculations, through the application of regression or neural network models [14-16]. Furthermore, within the context of metamodeling, it is possible to determine the optimal laser processing parameters, which may involve the use of genetic algorithms [17-22].
There is a perceived necessity to conduct a more comprehensive examination of the parallel laser cleaving technique employed on silicate glasses. This investigation would involve the use of regression and neural network models to determine the optimal modes for generating laser-induced cracks that are parallel to the treated surface.
Determination of optimal parameters for glass cutting
APDL was used to compute the temperatures and thermoelastic stresses that arise in silicate glasses when subjected to an elliptical laser beam. This analysis was conducted within the context of the unbound thermoelasticity problem in the quasi-static problem statement [23, 24].
Figure 1 displays the schematic of spatial arrangement of the laser radiation impact zone. In Fig. 1, position 1 represents the laser beam with a wavelength of 10.6 microns, position 2 denotes the processed glass product, and position 3 represents the cross-section of the laser beam 1 in the cutting plane. The horizontal arrow indicates the direction of movement of the glass plate relative to the laser beam.
-
1 1
3
Bug A
л Y
Fig. 1. Schematic of spatial arrangement of the laser radiation impact zone
The following properties of silicate glasses were used for calculations: thermal conductivity X = 0.88 W/m • ^ specific heat capacity C = 860 J/kg • ^ density p = 450 kg/m3, thermal expansion coefficient aT = 89 -10~7 (1/К), Young's modulus E = 70 GPa, Poisson's ratio v = 0.22 [25]. Finite element calculations were performed for a plate with dimensions of 0.025 x 0.02 x 0.002 m. The corresponding finite element model consisted of 69000 Solid 70 and Solid 185 elements utilized for thermal and strength analysis, respectively. The calculations were performed using the following parameters: V was set to 0.03 m/s, the laser power P was set to 10 W, the minor semi-axis of the laser beam A was set to 1 • 10-3 m, and the major semi-axis B was set to 4 • 10-3 m. Fig. 2, 3 illustrate the computed distributions of temperature fields and thermoelastic stress fields for the specified parameters of laser-induced heating of the silicate glass surface.
1
Fig. 2. Computed distribution of the temperature field under the influence of an elliptical laser beam, К
Fig. 3. Computed distribution of stresses azz under the influence of an elliptical laser beam, MPa
The maximum calculated temperature does not exceed the glass transition temperature, which is equal to 789 K for silicate glass. This is a necessary condition for cutting glass via laser cleaving [25]. The presented distribution of stress fields a zz acting perpendicular to the treated surface reveals that a zone of compression stresses is formed in front of the elliptical beam center, and a zone of tensile stresses is formed in the depth of the glass, thus ensuring the generation of a laser-induced crack parallel to the surface of the glass plate. Here, the through-cut cleaving due to localization of stresses a in the sample (see Fig. 4) emerges as a noteworthy contender in
comparison to laser glass delamination. The consideration of this particular circumstance is imperative in the determination of effective modes for parallel laser cleaving.
Fig. 4. Computed distribution of stresses ayy under the influence of an elliptical laser beam, MPa
The numerical experiment was carried out using 25 combinations of the face-centered version of the central composite design for four factors (P1-P4): P1 was the processing speed V, P2 was the laser power P, P3 was the minor semi-axis of the laser beam A, and P4 was the major semi-axis of the beam B (see Table 1). The following responses were determined: maximum temperature T and maximum tensile stresses aand azz
in the treatment zone.
Table 1
Experimental design and calculation results
No. P1 V, m/s P2 P, W P3 А, m P4 В, m P5 Т, K P6 ovv, MPa P6 Gzz, MPa
1 0.015 15 0.0015 0.003 610 26.2 27.3
2 0.01 15 0.0015 0.003 687 31.7 26.7
3 0.02 15 0.0015 0.003 563 22.1 27.8
4 0.015 10 0.0015 0.003 504 17.4 18.2
5 0.015 20 0.0015 0.003 715 34.9 36.4
6 0.015 15 0.001 0.003 636 25.2 41.5
7 0.015 15 0.002 0.003 582 25.2 20.4
8 0.015 15 0.0015 0.002 768 38.8 41.5
9 0.015 15 0.0015 0.004 531 18.9 20.4
10 0.01 10 0.001 0.002 727 31.6 41.8
11 0.02 10 0.001 0.002 581 22.8 40.1
12 0.01 20 0.001 0.002 1160 63.3 83.7
13 0.02 20 0.001 0.002 868 45.6 80.3
14 0.01 10 0.002 0.002 647 29.0 20.2
15 0.02 10 0.002 0.002 540 21.6 20.8
16 0.01 20 0.002 0.002 1001 58 40.3
17 0.02 20 0.002 0.002 787 43.1 41.5
18 0.01 10 0.001 0.004 510 15.4 20.6
19 0.02 10 0.001 0.004 437 10.0 19.9
20 0.01 20 0.001 0.004 727 30.7 41.2
21 0.02 20 0.001 0.004 581 20.1 39.8
22 0.01 10 0.002 0.004 471 14.9 9.9
23 0.02 10 0.002 0.004 417 10.6 10.2
24 0.01 20 0.002 0.004 650 29.9 19.9
25 0.02 20 0.002 0.004 540 21.1 20.5
The corresponding regression equations that determine the relationship between the response functions (T, , azz) and the factors (V, P, A, B) are as follows:
YT = 7.10 - 4.75-10 •V + 8.7340-2 • P -1.5840-2 • A - 4.30 -102 • B + + 7.12-102 •V •V - 6.62-10-4 • P • P + 4.43-104 • B • B - 6.4110-1 •V • P + + 4.12 403 •V • A + 3.13 403 •V • B - 2.89 • P • A - 5.80 • P • B +1.56 404 • A • B;
rr< YT 1
T = e -1;
Ysy = 6.21102 - 8.83 •10-3 •V + 2.25 P -1.04405 B +
+1.24405 V V-2.2540-1 • P• P-1.33 107 • A^A + 9.10406 B^B--1.09402 V• P + 9.09405 V• A -1.15403 P^B + 7.12406^ AB;
а ^ ={rsy • 0.295 +1)( J-1;
Yz = 1.95 -10 +1.60 -10-1 • P -1.51-103 • A - 7.63 -102 • B -
- 2.83-10-3 • P • P + 2.47 -105 • A • A + 6.30-104 • B • B +
+ 7.32•Ю2 • V• A;
а zz = {YSZ • 0.005 +1)) 0.°05 ]-1.
The impact of factors on the response functions was evaluated (Fig. 5). All output parameters are considerably affected by the laser radiation power P and the length B of the major semi-axis of the elliptical beam during the implementation of parallel laser cleaving. Simultaneously, the maximum temperatures in the treatment zone T and the maximum tensile stresses o)y are significantly influenced by the processing speed V.
Additionally, the maximum tensile stresses azz are affected by the size A of the minor semi-axis of the laser elliptical beam.
Local Sensitivity
Vnsys
>
w с
Ф
W
"rö о о
LOO SD ВО 70 ВО 50 40 30 20 10 0 -10 -20 -30 -40 -50 -60 -70 -ВО -Э0 -100
Р4
Output Parameters
Fig. 5. Sensitivity diagram of optimized parameters:
PI - V; P2 - P; P3 - A; P4 - B; P5 - T; P6 - cyy; P7 - cz.
Figure 6 illustrates the dependences of the maximum temperatures T and the maximum tensile stresses (o^ and a zz ) on the input parameters within the treatment zone.
Fig. 6. Dependence of input parameters on output parameters
The study conducted a simulation of the laser cleaving process of silicate glasses through artificial neural networks, using the algorithm outlined in reference [17]. The results of finite element calculations performed in accordance with a numerical experiment design were used to prepare data for training and testing neural networks. In addition to the initial 25 combinations of the central compositional design, another 200 combinations were included.
The construction of neural networks containing two hidden layers (see Fig. 7) was performed using TensorFlow. The Adam optimizer, ReLU activation function, and MSE loss function were applied in the process of constructing the artificial neural network. The neural network underwent training for a total of 500 epochs. Consequently, 16 artificial neural networks were created with the number of neurons in two hidden layers ranging from 5 to 20, with an interval of 5.
Fig. 7. Artificial neural network architecture
The dataset presented in Table 2 was used to perform tests on regression and neural network models.
Table 2
Test dataset
No. P1 V, m/s P2 P, W P3 А, m P4 В, m P5 Т, K P6 Oyy, MPa P6 огг, MPa
1 0.011 12 0.002 0.003 564 23.1 16.1
2 0.013 12 0.001 0.004 517 15.9 25.0
3 0.015 10 0.001 0.003 522 16.8 27.6
4 0.017 16 0.002 0.003 581 25.4 21.8
5 0.019 20 0.001 0.003 689 29.1 53.6
6 0.015 15 0.002 0.003 582 25.2 20.4
7 0.018 18 0.002 0.003 607 27.8 24.6
8 0.011 19 0.002 0.003 723 36.6 25.5
9 0.011 16 0.002 0.003 655 30.8 21.5
10 0.017 19 0.002 0.002 805 44.7 39.3
The resulting models were evaluated using mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and determination coefficient R2 [17].
Figure 8 shows heat maps illustrating the distribution of the mean absolute percentage error while estimating the maximum values of temperature and tensile stresses in the treatment zone of silicate glasses using elliptical beams. The number of neurons in the first and second hidden layers of the artificial neural network are shown by the vertical and horizontal axes, respectively. The intensity of color coding represents the extent of error: the error increases from light to dark. The artificial neural network with the architecture [5-15-15-15-2] demonstrated the most favourable results.
а) b) c)
Fig. 8. Heatmap of mean absolute percentage error distribution: when determining T (d); when determining Cyy (b); when determining czz (c)
Table 3 displays the estimation outcomes of both the regression and neural network models.
Table 3
Evaluation results of regression and neural network models
Criterion Regression model Neural network model
T Ozz T CTw
RMSE 1.7 К 0.29 MPa 0.29 MPa 1.5 К 0.12 MPa 0.28 MPa
MAE 2.3 К 0.41 MPa 0.41 MPa 0.9 К 0.14 MPa 0.21 MPa
MAPE 0.3 % 1.1 % 0.9 % 0.2 % 0.5 % 0.8 %
R2 0.9993 0.9975 0.9984 0.9997 0.9996 0.9993
The evaluation findings of the generated models demonstrate a significant consistency with the outcomes obtained from finite element computations. The study revealed that the neural network model with the architecture [5-15-15-2] demonstrates superior efficacy in predicting the output parameters associated with the process of laser parallel splitting of silicate glasses.
The Ansys software module was used to optimize the parameters for parallel laser cleaving of silicate glass. The optimization procedures were conducted in accordance with the algorithm outlined in [20].
To optimize the parallel cleaving of silicate glass using the MOGA algorithm, the following criteria were chosen: V ^ max; a^ ^ min; azz ^ max; T < 789 K.
The optimization results are provided in Table 4 (parameter values derived using the finite element method are presented in brackets).
Table 4
Optimization results
P1 P2 P3 P4 P5 P6 P6
V, m/s P, W А, m В, m Т, К Cyy, MPa огг, MPa
0.02 19.7 0.001 0.0023 784 38.3 68.5
(786) (38.4) (68.4)
The application of the genetic algorithm provided a maximum relative error of less than 1 % when determining the maximum temperatures and maximum thermoelastic stresses generated in glass plates under the influence of elliptical laser beams on their surface.
Conclusion
This study presents the construction of regression models for parallel laser cleaving using the central composite design of numerical experimentation. An efficient artificial neural network architecture has been identified, which has superior prediction capabilities compared to regression models. The application of a genetic algorithm for optimization led to the determination of the laser cleaving modes of silicate glasses using elliptical beams in the plane parallel to the surface. These modes effectively facilitate the production of laser-induced cracks.
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Поступила 15.08.2023 г
