Calculation method for dynamic target destruction by laser beam within the specified range

Аuthors

Marchukov E. Y.^1*, Kulalaev V. V.^2**, Vovk M. Y.^3***

1. ,
2. Lyulka Desing Bureau, 13, Kasatkina str., Moscow, 129301, Russia
3. Lyulka Experimental Design Bureau, branch of the United Engine Corporation – Ufa Engine Industrial Association, 13, Kasatkina str., Moscow, 129301, Russia

*e-mail: kaf205@mail.ru
**e-mail: kulalayev.viktor@gmail.com
***e-mail: mihail.vovk@okb.umpo.ru

Abstract

The near and far space exploration is impossible without creating modern technologies of constructional assembly welding employing laser radiation when the structural surface can be considered as a conditional target. At the same time, the calculation method development of laser beam thermal effect is one of prior scientific tasks, which solution is obtained in this paper based on the variation method [1-20]. The advantage of the variation method [1-3] consists in the possibility of solving nonlinear problems of the heat and mass transfer when the coefficient of thermal conductivity is a tensor quantity in non-isotropic mediums [3-8]. Such situation is implemented completely at impact of the powerful laser beam on physical environments of various targets while their destruction at a specified variable range. In these initial conditions of thermal impact of the powerful laser beam the thermal problem solution of target environment destruction using the variation method [4, 7] becomes significantly simpler. In this case the solution is reduced to searching some function, describing the formation of caverne mobile walls with some temperature gradient on the surface of liquid-alloy. The solution of the specified task herewith is performed for the benefit of the wide class of various industrial technological processes, including technologies of near and far space exploration.

The presented method is based on the solution of the non-stationary problem of the powerful laser beam installed on the mobile platform effect on the dynamic target firm surface – the structure for variable range. The thermal spot sizes are determined by the output aperture of the focusing laser optics. Under the impact of thermal gradients on the target surface depending on time of laser beam influence the mobile borders destruction of the target body occurs in the form of a melting cavern and material boiling. If the conditional target represents the sheet of metal with the specified thickness, the formed cavern can form through smelting rate of metal that is not admissible. The cavern borders movement is described in the paper as the corresponding mathematical model of an unknown quasi-stationary temperature field formation, which is formed by large concentration of heat energy on the limited area of the thermal spot at the set influence period. The application example of the cavern formation calculation method in industrial laser welding processes is given.

The results of this work can be employed for the benefit of creating and optimizing industrial technological processes of temperature processing, various materials cutting and welding by laser machines in different physical environments.

Keywords:

laser beam, heat and mass transfer, variation method, Lagrange's equation, target, focusing, cavern

References

1. Gel’fand I.M., Fomin S.V. Variatsionnoe ischislenie (Variational calculus), Moscow, Fizmatizdat, 1961, 288 p.

2. Rektoris K. Variatsionnye metody v matematicheskoi fizike i tekhnike (Variation methods in mathematical physics and engineering), Mir, 1985, 636 p.

3. Kulalaev V.V., Kornienko O.G., Fursov A.P. Matematicheskie metody analiza dinamicheskikh system, 1985, no. 1, pp. 215 – 224.

4. Bio M. Variatsionnye printsipy v teorii teploobmena (Variation principles in the heat exchange theory), Moscow, Energiya, 1975, 208 p.

5. Lardner T.J. Approximate solutions to phase – change problems, AIAA, 1967, vol. 5, pp. 2079 – 2080.

6. Osobennosti lazernoi svarki, available at: http://expertsvarki.ru/tehnologii/lazernaya-svarka.html

7. Muchnik G.F., Polyakov Yu.A. Teplofizika vysokikh temperatur, 1964, vol. 2, no. 3, pp. 424 – 428.

8. Shekhter R. Variatsionnyi metod v inzhenernykh raschetakh (Variation method in engineering calculations), Moscow, Mir, 1971, 291 p.

9. Volosevich P.P., Levanov E.I. Avtomodel’nye resheniya zadach gazovoi dinamiki i teploperenosa (Self-simulated solutions of gas dynamic problems and heat transfer), Moscow, Izd-vo MFTI, 1997, 245 p.

10. Kantorovich L.V., Krylov V.I. Priblizhennye metody vysshego analiza (Approximate methods of the highest analysis), Leningrad, Fizmatgiz, 1962, 708 p.

11. Arsenin V.Ya. Metody matematicheskoi fiziki i spetsial’nye funktsii (Methods of mathematical physics and higher transcendental functions), Moscow, Nauka, 1984, 304 p.

12. Tikhonov A.N., Samarskii A.A. Uravneniya matematicheskoi fiziki (Equations of mathematical physics), Moscow, Nauka, 1972, 736 p.

13. Kurant R., Gil’bert D. Metody matematicheskoi fiziki (Methods of mathematical physics), Moscow, Gostekhizdat, 1951, 340 p.

14. Berdichevskii V.L. Variatsionnye printsipy mekhaniki sploshnoi sredy (Variational principles of continuum mechanics), Moscow, Nauka, 1983, 448 p.

15. Kartashov E.M. Analiticheskie metody v teorii teploprovodnosti tverdykh tel (Analytical methods in the theory of heat conductivity of solid bodies), Moscow, Vysshaya shkola, 2001, 550 p.

16. Kogan M.G. Primenenie metodov Galerkina i Kantorovicha v teorii teploprovodnosti. V Kn.: Issledovanie nestatsionarnogo teplo- i massoobmena (Application of Galerkin and Kantorovich’s methods in the theory of heat conductivity. Research of non-stationary warm and mass exchange), Minsk, Nauka i tekhnika, 1966, pp. 42 – 51.

17. Korenev B.G. Vvedenie v teoriyu besselevykh funktsii (Introduction to Bessel functions theory), Moscow, Nauka, 1971, 287 p.

18. Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov (The reference book on mathematics for scientists and engineers), Moscow, Nauka, 1984, 831 p.

19. Dëch Gustav. Rukovodstvo k prakticheskomu primeneniyu preobrazovaniya Laplasa i Z – preobrazovaniya (Guidance to practical application of Laplace transformation and Z-transformation), Moscow, Nauka, 1971, 288 p.

20. Tyurekhodzhaev A.N., Karybaeva G.A. Trudy Mezhdunarodnoi nauchno-prakticheskoi konferentsii “Informatsionno-innovatsionnye tekhnologii: integratsiya nauki, obrazovaniya i biznesa”, Almaty, 2008, pp. 481 – 486.

21. Gidaspov V.Yu. Trudy MAI, 2016, no. 91, available at: http://trudymai.ru/eng/published.php?ID=75562

22. Nazyrova R.R. Trudy MAI, 2017, no. 92, available at: http://trudymai.ru/eng/published.php?ID=76946

Download