Mathematical Modeling of Energy Distribution in Entering a Beam into the Workpiece Material in the Course of Electron Beam Welding
Keywords:
electron beam welding, thermal processes, control automation, optimization of process parameters, electron beam entering/removal, mathematical modeling
Abstract
Modeling of electron beam welding processes is one of the most important parts of applied research, because full-scale experimental investigations are either expensive or highly labor intensive. The problem of modeling the temperature fields at the electron beam entering stage during welding is considered. The aim of the study is to simplify the adjustment of the electron beam welding process technological parameters and to elaborate and develop more efficient control algorithms through replacing full-scale experiments by model ones. The mathematical body of the proposed solutions is constructed using the theories of thermal and welding processes, based on which the energy distribution mathematical models are developed. For practically implementing the computations, an algorithmic support is presented that allows the mathematical models to be applied in modern modeling systems, such as Matlab, Comsol Multiphysics, and Ansys. Apart from supplementing the set of existing mathematical models of the electron beam welding process, the obtained models for calculating the temperature in the beam entering area widen their application for calculating and optimizing the welding process, taking into account the workpiece temperature in the electron beam entering area. By using the proposed solutions, several numerical experiments were carried out for a workpiece made of VT-14 titanium alloy and two pieces of different thickness made of AMg-6 aluminum alloy. The obtained temperature fields and the rms values of process parameters are almost identical with the results of previously conducted full-scale studies.
References
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2. Gierth P., Rebenklau L., Michaelis A. Evaluation of Soldering Processes for High Efficiency Solar Cells // Proc. XXXV Intern. Spring Seminar on Electronics Technol. 2012. Pp. 133—137.
3. Murygin A.V. e. a. Complex of Automated Equipment and Technologies for Waveguides Soldering Using Induction Heating // IOP Conf. Series: Materials Sci. and Eng. 2017. V. 173. No. 1. P. 012023.
4. Nishimura F. e. a. Development of a New Investment for High-Frequency Induction Soldering // Dental Materials J. 1992. V. 11. No. 1. Pp. 59—69.
5. Cai H. e. a. Study on Multiple-frequency IGBT High Frequency Power Supply for Induction Heating // Proc. CSEE. 2006. V. 26. Pp. 154—158.
6. Lanin V.L., Sergachev I.I. Induction Devices for Assembly Soldering in Electronics // Surface Eng. and Appl. Electrochem. 2012. V. 48. No. 4. Pp. 384—388.
7. Moghaddam M., Mojallali H. Neural Network Based Modeling and Predictive Position Control of Traveling Wave Ultrasonic Motor Using Chaotic Genetic Algorithm // Intern. Rev. Modelling and Simulations. 2013. V. 6. No. 2. Pp. 370—379.
8. Ghazanfarpour B., Radzi M., Mariun N. Adaptive Neural Network with Heuristic Learning Rule for series Active Power Filter // International Rev. Modelling and Simulations. 2013. V. 6. No. 6. Pp. 1753—1759.
9. Lin C.T. e. a. Neural-network-based Fuzzy Logic Control and Decision System // IEEE Trans. Computers. 1991. V. 40. No. 12. Pp. 1320—1336.
10. Peter S.E. e. a. Wavelet Based Spike Propagation Neural Network (WSPNN) for Wind Power Forecasting // Proc. Int Rev Model Simul. 2013. V. 6. No. 5. Pp. 1513—1522.
11. Farahat M.A. e. a. Short Term Load Forecasting Using BP Neural Network Optimized by Particle Swarm Optimization // Int. Rev. Model. Simulations. 2013. V. 6. No. 2. Pp. 450—454.
12. Ananthamoorthy N., Baskaran K. Modelling, Simulation and Analysis of Fuzzy Logic Controllers for Permanent Magnet Synchronous Motor Drive // Ibid. No. 1. Pp. 75—82.
13. Wei H. e. a. Angular Sensing System Based on Y-type Twin-core Fiber and Reflective Varied-line Spacing Grating Fabricated by Electron Beam Lithography // Results Physics. 2020. V. 18. P. 103193.
14. Sitnikov I.V., Belenkiy V.Y., Olshanskaya T.V. Study of the Effect of Focusing and Oscillation of Electron Beam on the Structure and Properties of Welded Seams // IOP Conf. Series: Materials Sci. and Eng. 2019. V. 611. No. 1. P. 012009.
15. Kasitsyn A.N. e. a. Control of Electron Beam Wielding Parameters Based on the Gap Scanning System Data During the Welding Process // IOP Conf. Series: Materials Sci. and Eng. 2020. V. 759. No. 1. P. 012013.
16. Рапопорт Э.Я., Плешивцева Ю.Э. Оптимальное управление температурными режимами индукционного нагрева. М.: Наука, 2012.
17. Серегин Ю.Н. и др. Экспериментальные исследования по оптимизации технологии электронно-лучевой сварки алюминиевых сплавов // Технологии и оборудование ЭЛС-2011: Материалы Междунар. науч.-техн. конф. СПб., 2011. С. 71—80.
18. Серегин Ю.Н., Курашкин С.О. Моделирование режима ЭЛС для прогнозирования параметров сварного шва // Электронно-лучевая сварка и смежные технологии. 2017. С. 26—36.
19. Tynchenko V. e. a. Application of Artificial Neural Networks for Identification of Non-normative Errors in Measuring Instruments for Controlling the Induction Soldering Process // Intern. Multidisciplinary Sci. Geo Conf. 2018. V. 18. No. 2. Pp. 117—124.
20. Milov A.V., Tynchenko V.S., Murygin A.V. Experimental Verification of Flux Effect on Process of Aluminium Waveguide Paths Induction Soldering // Proc. Intern. Russian Automation Conf. N.-Y.: Springer, 2019. Pp. 282—291.
21. Рапопорт Э.Я., Плешивцева Ю.Э. Алгоритмически точный метод параметрической оптимизации в краевых задачах оптимального управления системами с распределенными параметрами // Автометрия. 2009. Т. 45. №. 5. С. 103—112.
22. Seregin Y.N., Kurashkin S.O. Modeling the Thermal Process Using the Temperature Functional by Electron Beam Welding // IOP Conf. Series: Materials Sci. and Eng. 2020. V. 734. No. 1. P. 012003.
23. Пермяков Г.Л. и др. Численное моделирование процесса электронно-лучевой сварки с продольной осцилляцией луча на основе экспериментально определенной формы канала проплавления // Сибирский журнал науки и технологий. 2015. Т. 16. №. 4. С. 828—832.
24. Cho W.I. e. a. Numerical Simulation of Molten Pool Dynamics in High Power Disk Laser Welding // J. Materials Proc. Technol. 2012. V. 212. No. 1. Pp. 262—275.
25. Reich M. e. a. Real-time Beam Tracing for Control of the Deposition Location of Electron Cyclotron Waves // Fusion Eng. and Design. 2015. V. 100. Pp. 73—80.
26. Коновалов А.В. и др. Теория сварочных процессов. М.: Изд-во МГТУ им. Н.Э. Баумана, 2007.
---
Для цитирования: Курашкин С.О., Тынченко В.С., Мурыгин А.В. Математическое моделирование распределения энергии при вводе в материал изделия луча в процессе электронно-лучевой сварки // Вестник МЭИ. 2021. № 3. С. 88—95. DOI: 10.24160/1993-6982-2021-3-88-95
---
Работа выполнена при поддержке: РФФИ, Правительства Красноярского края и Краевого фонда науки (проект № 19-48-240007)
#
1. Lozinskiĭ M.G. Industrial Applications of Induction Heating. Oxford: Pergamon Press, 1969.
2. Gierth P., Rebenklau L., Michaelis A. Evaluation of Soldering Processes for High Efficiency Solar Cells. Proc. XXXV Intern. Spring Seminar on Electronics Technol. 2012:133—137.
3. Murygin A.V. e. a. Complex of Automated Equipment and Technologies for Waveguides Soldering Using Induction Heating. IOP Conf. Series: Materials Sci. and Eng. 2017;173;1:012023.
4. Nishimura F. e. a. Development of a New Investment for High-Frequency Induction Soldering. Dental Materials J. 1992;11;1:59—69.
5. Cai H. e. a. Study on Multiple-frequency IGBT High Frequency Power Supply for Induction Heating. Proc. CSEE. 2006;26:154—158.
6. Lanin V.L., Sergachev I.I. Induction Devices for Assembly Soldering in Electronics. Surface Eng. and Appl. Electrochem. 2012;48;4:384—388.
7. Moghaddam M., Mojallali H. Neural Network Based Modeling and Predictive Position Control of Traveling Wave Ultrasonic Motor Using Chaotic Genetic Algorithm. Intern. Rev. Modelling and Simulations. 2013;6;2:370—379.
8. Ghazanfarpour B., Radzi M., Mariun N. Adaptive Neural Network with Heuristic Learning Rule for series Active Power Filter. International Rev. Modelling and Simulations. 2013;6;6:1753—1759.
9. Lin C.T. e. a. Neural-network-based Fuzzy Logic Control and Decision System. IEEE Trans. Computers. 1991;40;12:1320—1336.
10. Peter S.E. e. a. Wavelet Based Spike Propagation Neural Network (WSPNN) for Wind Power Forecasting. Proc. Int Rev Model Simul. 2013;6;5:1513—1522.
11. Farahat M.A. e. a. Short Term Load Forecasting Using BP Neural Network Optimized by Particle Swarm Optimization. Int. Rev. Model. Simulations. 2013;6;2:450—454.
12. Ananthamoorthy N., Baskaran K. Modelling, Simulation and Analysis of Fuzzy Logic Controllers for Permanent Magnet Synchronous Motor Drive. Ibid;1:75—82.
13. Wei H. e. a. Angular Sensing System Based on Y-type Twin-core Fiber and Reflective Varied-line Spacing Grating Fabricated by Electron Beam Lithography. Results Physics. 2020;18:103193.
14. Sitnikov I.V., Belenkiy V.Y., Olshanskaya T.V. Study of the Effect of Focusing and Oscillation of Electron Beam on the Structure and Properties of Welded Seams. IOP Conf. Series: Materials Sci. and Eng. 2019;611;1:012009.
15. Kasitsyn A.N. e. a. Control of Electron Beam Wielding Parameters Based on the Gap Scanning System Data During the Welding Process. IOP Conf. Series: Materials Sci. and Eng. 2020;759;1:012013.
16. Rapoport E.Ya., Pleshivtseva Yu.E. Optimal'noe Upravlenie Temperaturnymi Rezhimami Induktsionnogo Nagreva. M.: Nauka, 2012. (in Russian).
17. Seregin Yu.N. i dr. Eksperimental'nye Issledovaniya po Optimizatsii Tekhnologii Elektronno-luchevoy Svarki Alyuminievykh Splavov. Tekhnologii i Oborudovanie ELS-2011: Materialy Mezhdunar. Nauch.-tekhn. Konf. SPb., 2011:71—80. (in Russian).
18. Seregin Yu.N., Kurashkin S.O. Modelirovanie Rezhima ELS dlya Prognozirovaniya Parametrov Svarnogo Shva. Elektronno-luchevaya Svarka i Smezhnye Tekhnologii. 2017:26—36. (in Russian).
19. Tynchenko V. e. a. Application of Artificial Neural Networks for Identification of Non-normative Errors in Measuring Instruments for Controlling the Induction Soldering Process. Intern. Multidisciplinary Sci. Geo Conf. 2018;18;2:117—124.
20. Milov A.V., Tynchenko V.S., Murygin A.V. Experimental Verification of Flux Effect on Process of Aluminium Waveguide Paths Induction Soldering. Proc. Intern. Russian Automation Conf. N.-Y.: Springer, 2019:282—291.
21. Rapoport E.Ya., Pleshivtseva Yu.E. Algoritmicheski Tochnyy Metod Parametricheskoy Optimizatsii v Kraevykh Zadachakh Optimal'nogo Upravleniya Sistemami s Raspredelennymi Parametrami. Avtometriya. 2009;45;5:103—112. (in Russian).
22. Seregin Y.N., Kurashkin S.O. Modeling the Thermal Process Using the Temperature Functional by Electron Beam Welding. IOP Conf. Series: Materials Sci. and Eng. 2020;734;1:012003.
23. Permyakov G.L. i dr. Chislennoe Modelirovanie Protsessa Elektronno-luchevoy Svarki s Prodol'noy Ostsillyatsiey Lucha na Osnove Eksperimental'no Opredelennoy Formy Kanala Proplavleniya. Sibirskiy Zhurnal Nauki i Tekhnologiy. 2015;16;4:828—832. (in Russian).
24. Cho W.I. e. a. Numerical Simulation of Molten Pool Dynamics in High Power Disk Laser Welding. J. Materials Proc. Technol. 2012;212;1:262—275.
25. Reich M. e. a. Real-time Beam Tracing for Control of the Deposition Location of Electron Cyclotron Waves. Fusion Eng. and Design. 2015;100:73—80.
26. Konovalov A.V. i dr. Teoriya Svarochnykh Protsessov. M.: Izd-vo MGTU im. N.E. Baumana, 2007. (in Russian).
---
For citation: Kurashkin S.O., Tynchenko V.S., Murygin A.V. Mathematical Modeling of Energy Distribution in Entering a Beam into the Workpiece Material in the Course of Electron Beam Welding. Bulletin of MPEI. 2021;3:88—95. (in Russian). DOI: 10.24160/1993-6982-2021-3-88-95
---
The work is executed at support: RFBR, Government of the Krasnoyarsk Territory and the Regional Science Foundation (Project No. 19-48-240007)
2. Gierth P., Rebenklau L., Michaelis A. Evaluation of Soldering Processes for High Efficiency Solar Cells // Proc. XXXV Intern. Spring Seminar on Electronics Technol. 2012. Pp. 133—137.
3. Murygin A.V. e. a. Complex of Automated Equipment and Technologies for Waveguides Soldering Using Induction Heating // IOP Conf. Series: Materials Sci. and Eng. 2017. V. 173. No. 1. P. 012023.
4. Nishimura F. e. a. Development of a New Investment for High-Frequency Induction Soldering // Dental Materials J. 1992. V. 11. No. 1. Pp. 59—69.
5. Cai H. e. a. Study on Multiple-frequency IGBT High Frequency Power Supply for Induction Heating // Proc. CSEE. 2006. V. 26. Pp. 154—158.
6. Lanin V.L., Sergachev I.I. Induction Devices for Assembly Soldering in Electronics // Surface Eng. and Appl. Electrochem. 2012. V. 48. No. 4. Pp. 384—388.
7. Moghaddam M., Mojallali H. Neural Network Based Modeling and Predictive Position Control of Traveling Wave Ultrasonic Motor Using Chaotic Genetic Algorithm // Intern. Rev. Modelling and Simulations. 2013. V. 6. No. 2. Pp. 370—379.
8. Ghazanfarpour B., Radzi M., Mariun N. Adaptive Neural Network with Heuristic Learning Rule for series Active Power Filter // International Rev. Modelling and Simulations. 2013. V. 6. No. 6. Pp. 1753—1759.
9. Lin C.T. e. a. Neural-network-based Fuzzy Logic Control and Decision System // IEEE Trans. Computers. 1991. V. 40. No. 12. Pp. 1320—1336.
10. Peter S.E. e. a. Wavelet Based Spike Propagation Neural Network (WSPNN) for Wind Power Forecasting // Proc. Int Rev Model Simul. 2013. V. 6. No. 5. Pp. 1513—1522.
11. Farahat M.A. e. a. Short Term Load Forecasting Using BP Neural Network Optimized by Particle Swarm Optimization // Int. Rev. Model. Simulations. 2013. V. 6. No. 2. Pp. 450—454.
12. Ananthamoorthy N., Baskaran K. Modelling, Simulation and Analysis of Fuzzy Logic Controllers for Permanent Magnet Synchronous Motor Drive // Ibid. No. 1. Pp. 75—82.
13. Wei H. e. a. Angular Sensing System Based on Y-type Twin-core Fiber and Reflective Varied-line Spacing Grating Fabricated by Electron Beam Lithography // Results Physics. 2020. V. 18. P. 103193.
14. Sitnikov I.V., Belenkiy V.Y., Olshanskaya T.V. Study of the Effect of Focusing and Oscillation of Electron Beam on the Structure and Properties of Welded Seams // IOP Conf. Series: Materials Sci. and Eng. 2019. V. 611. No. 1. P. 012009.
15. Kasitsyn A.N. e. a. Control of Electron Beam Wielding Parameters Based on the Gap Scanning System Data During the Welding Process // IOP Conf. Series: Materials Sci. and Eng. 2020. V. 759. No. 1. P. 012013.
16. Рапопорт Э.Я., Плешивцева Ю.Э. Оптимальное управление температурными режимами индукционного нагрева. М.: Наука, 2012.
17. Серегин Ю.Н. и др. Экспериментальные исследования по оптимизации технологии электронно-лучевой сварки алюминиевых сплавов // Технологии и оборудование ЭЛС-2011: Материалы Междунар. науч.-техн. конф. СПб., 2011. С. 71—80.
18. Серегин Ю.Н., Курашкин С.О. Моделирование режима ЭЛС для прогнозирования параметров сварного шва // Электронно-лучевая сварка и смежные технологии. 2017. С. 26—36.
19. Tynchenko V. e. a. Application of Artificial Neural Networks for Identification of Non-normative Errors in Measuring Instruments for Controlling the Induction Soldering Process // Intern. Multidisciplinary Sci. Geo Conf. 2018. V. 18. No. 2. Pp. 117—124.
20. Milov A.V., Tynchenko V.S., Murygin A.V. Experimental Verification of Flux Effect on Process of Aluminium Waveguide Paths Induction Soldering // Proc. Intern. Russian Automation Conf. N.-Y.: Springer, 2019. Pp. 282—291.
21. Рапопорт Э.Я., Плешивцева Ю.Э. Алгоритмически точный метод параметрической оптимизации в краевых задачах оптимального управления системами с распределенными параметрами // Автометрия. 2009. Т. 45. №. 5. С. 103—112.
22. Seregin Y.N., Kurashkin S.O. Modeling the Thermal Process Using the Temperature Functional by Electron Beam Welding // IOP Conf. Series: Materials Sci. and Eng. 2020. V. 734. No. 1. P. 012003.
23. Пермяков Г.Л. и др. Численное моделирование процесса электронно-лучевой сварки с продольной осцилляцией луча на основе экспериментально определенной формы канала проплавления // Сибирский журнал науки и технологий. 2015. Т. 16. №. 4. С. 828—832.
24. Cho W.I. e. a. Numerical Simulation of Molten Pool Dynamics in High Power Disk Laser Welding // J. Materials Proc. Technol. 2012. V. 212. No. 1. Pp. 262—275.
25. Reich M. e. a. Real-time Beam Tracing for Control of the Deposition Location of Electron Cyclotron Waves // Fusion Eng. and Design. 2015. V. 100. Pp. 73—80.
26. Коновалов А.В. и др. Теория сварочных процессов. М.: Изд-во МГТУ им. Н.Э. Баумана, 2007.
---
Для цитирования: Курашкин С.О., Тынченко В.С., Мурыгин А.В. Математическое моделирование распределения энергии при вводе в материал изделия луча в процессе электронно-лучевой сварки // Вестник МЭИ. 2021. № 3. С. 88—95. DOI: 10.24160/1993-6982-2021-3-88-95
---
Работа выполнена при поддержке: РФФИ, Правительства Красноярского края и Краевого фонда науки (проект № 19-48-240007)
#
1. Lozinskiĭ M.G. Industrial Applications of Induction Heating. Oxford: Pergamon Press, 1969.
2. Gierth P., Rebenklau L., Michaelis A. Evaluation of Soldering Processes for High Efficiency Solar Cells. Proc. XXXV Intern. Spring Seminar on Electronics Technol. 2012:133—137.
3. Murygin A.V. e. a. Complex of Automated Equipment and Technologies for Waveguides Soldering Using Induction Heating. IOP Conf. Series: Materials Sci. and Eng. 2017;173;1:012023.
4. Nishimura F. e. a. Development of a New Investment for High-Frequency Induction Soldering. Dental Materials J. 1992;11;1:59—69.
5. Cai H. e. a. Study on Multiple-frequency IGBT High Frequency Power Supply for Induction Heating. Proc. CSEE. 2006;26:154—158.
6. Lanin V.L., Sergachev I.I. Induction Devices for Assembly Soldering in Electronics. Surface Eng. and Appl. Electrochem. 2012;48;4:384—388.
7. Moghaddam M., Mojallali H. Neural Network Based Modeling and Predictive Position Control of Traveling Wave Ultrasonic Motor Using Chaotic Genetic Algorithm. Intern. Rev. Modelling and Simulations. 2013;6;2:370—379.
8. Ghazanfarpour B., Radzi M., Mariun N. Adaptive Neural Network with Heuristic Learning Rule for series Active Power Filter. International Rev. Modelling and Simulations. 2013;6;6:1753—1759.
9. Lin C.T. e. a. Neural-network-based Fuzzy Logic Control and Decision System. IEEE Trans. Computers. 1991;40;12:1320—1336.
10. Peter S.E. e. a. Wavelet Based Spike Propagation Neural Network (WSPNN) for Wind Power Forecasting. Proc. Int Rev Model Simul. 2013;6;5:1513—1522.
11. Farahat M.A. e. a. Short Term Load Forecasting Using BP Neural Network Optimized by Particle Swarm Optimization. Int. Rev. Model. Simulations. 2013;6;2:450—454.
12. Ananthamoorthy N., Baskaran K. Modelling, Simulation and Analysis of Fuzzy Logic Controllers for Permanent Magnet Synchronous Motor Drive. Ibid;1:75—82.
13. Wei H. e. a. Angular Sensing System Based on Y-type Twin-core Fiber and Reflective Varied-line Spacing Grating Fabricated by Electron Beam Lithography. Results Physics. 2020;18:103193.
14. Sitnikov I.V., Belenkiy V.Y., Olshanskaya T.V. Study of the Effect of Focusing and Oscillation of Electron Beam on the Structure and Properties of Welded Seams. IOP Conf. Series: Materials Sci. and Eng. 2019;611;1:012009.
15. Kasitsyn A.N. e. a. Control of Electron Beam Wielding Parameters Based on the Gap Scanning System Data During the Welding Process. IOP Conf. Series: Materials Sci. and Eng. 2020;759;1:012013.
16. Rapoport E.Ya., Pleshivtseva Yu.E. Optimal'noe Upravlenie Temperaturnymi Rezhimami Induktsionnogo Nagreva. M.: Nauka, 2012. (in Russian).
17. Seregin Yu.N. i dr. Eksperimental'nye Issledovaniya po Optimizatsii Tekhnologii Elektronno-luchevoy Svarki Alyuminievykh Splavov. Tekhnologii i Oborudovanie ELS-2011: Materialy Mezhdunar. Nauch.-tekhn. Konf. SPb., 2011:71—80. (in Russian).
18. Seregin Yu.N., Kurashkin S.O. Modelirovanie Rezhima ELS dlya Prognozirovaniya Parametrov Svarnogo Shva. Elektronno-luchevaya Svarka i Smezhnye Tekhnologii. 2017:26—36. (in Russian).
19. Tynchenko V. e. a. Application of Artificial Neural Networks for Identification of Non-normative Errors in Measuring Instruments for Controlling the Induction Soldering Process. Intern. Multidisciplinary Sci. Geo Conf. 2018;18;2:117—124.
20. Milov A.V., Tynchenko V.S., Murygin A.V. Experimental Verification of Flux Effect on Process of Aluminium Waveguide Paths Induction Soldering. Proc. Intern. Russian Automation Conf. N.-Y.: Springer, 2019:282—291.
21. Rapoport E.Ya., Pleshivtseva Yu.E. Algoritmicheski Tochnyy Metod Parametricheskoy Optimizatsii v Kraevykh Zadachakh Optimal'nogo Upravleniya Sistemami s Raspredelennymi Parametrami. Avtometriya. 2009;45;5:103—112. (in Russian).
22. Seregin Y.N., Kurashkin S.O. Modeling the Thermal Process Using the Temperature Functional by Electron Beam Welding. IOP Conf. Series: Materials Sci. and Eng. 2020;734;1:012003.
23. Permyakov G.L. i dr. Chislennoe Modelirovanie Protsessa Elektronno-luchevoy Svarki s Prodol'noy Ostsillyatsiey Lucha na Osnove Eksperimental'no Opredelennoy Formy Kanala Proplavleniya. Sibirskiy Zhurnal Nauki i Tekhnologiy. 2015;16;4:828—832. (in Russian).
24. Cho W.I. e. a. Numerical Simulation of Molten Pool Dynamics in High Power Disk Laser Welding. J. Materials Proc. Technol. 2012;212;1:262—275.
25. Reich M. e. a. Real-time Beam Tracing for Control of the Deposition Location of Electron Cyclotron Waves. Fusion Eng. and Design. 2015;100:73—80.
26. Konovalov A.V. i dr. Teoriya Svarochnykh Protsessov. M.: Izd-vo MGTU im. N.E. Baumana, 2007. (in Russian).
---
For citation: Kurashkin S.O., Tynchenko V.S., Murygin A.V. Mathematical Modeling of Energy Distribution in Entering a Beam into the Workpiece Material in the Course of Electron Beam Welding. Bulletin of MPEI. 2021;3:88—95. (in Russian). DOI: 10.24160/1993-6982-2021-3-88-95
---
The work is executed at support: RFBR, Government of the Krasnoyarsk Territory and the Regional Science Foundation (Project No. 19-48-240007)
Published
2020-09-03
Section
Automation and Control of Technological Processes and Production (05.13.06)
