Journals →  Chernye Metally →  2019 →  #6 →  Back

55th anniversary of JSC “EVRAZ ZSMK”
ArticleName The loading model of the cylindrical sample’s end face with a short-term distributed density heat source
ArticleAuthor V. I. Bazaikin, O. L. Bazaikina, M. V. Temlyantsev, O. S. Babushkina
ArticleAuthorData

Siberian State Industrial University (Novokuznetsk, Russia):

V. I. Bazaikin, Dr. Eng., Prof., Chair of Applied Mathematics and Informatics, e-mail: bazaikin.vi@yandex.ru
O. L. Bazaikina, Cand. Eng., Associate Prof., Chair of Applied Mathematics and Informatics
M. V. Temlyantsev, Dr. Eng., Prof., Vice-Rector on Science and Innovations
O. S. Babushkina, Student

Abstract

A model of the temperature field in a cylindrical sample arising under the action of a short-term energy pulse on the cylinder end has been proposed. The temperature field for solving the task for a homogeneous heat equation and the temperature field for a particular solution of a inhomogeneous equation with a triangular pulse shape of a heat load have a common zero initial condition, which is a real description of the onset and propagation of a pulse. The method of solving a model task uses both the solution expansion in terms of the basis of the task eigenfunctions, and the Laplace transform of the task in the time coordinate. By changing the parameters of the thermal sources distribution density, it is possible to vary the resulting temperature field. The set of temperature versus time curves in different cross sections of the cylinder with two maxima simulates a spectrum of different heat treatments of the sample, some of which are hardening. A numerical example of loading a cylindrical tablet with a radius of 12 mm and a height of 10 mm from steel 40KhN with a triangular-shaped temperature pulse of 163 ms with a height having a maximum equal to the melting temperature of steel 40KhN is given. At selected values of the pulse parameters, the sample sections located at a distance from 0.5 mm to 1 mm from the loaded plane of the tablet fall into the temperature zone of the austenite-pearlitic transition between Ar3 = 700 °C and Ar1 = 660 °C. Changes in the pulse temperature in the cross section at a distance of 6 mm from the loaded plane correspond to heat treatment, which consists of quenching with a high cooling rate and subsequent high tempering. Heat treatment creates a martensitic structure (effect of long-range action hardening).

keywords Energy pulse, round cylinder, parabolic equation of heat conduction, boundary conditions of the third kind, Laplace transform, Heaviside function, temperature field, near-surface layer, hardening, heat treatment
References

1. Lange E. Steel innovations and development of up-to-date transporting infrastructure. Chernye Metally. 2016. No. 10. pp. 69–75.
2. Gushchin V. N. Ulyanov V. A., Kurilina Т. D., Gevorgyan G. А. Modifying, refining and degassing of cast iron melts through impulse action. Chernye Metally. 2018. No. 9. pp. 54–59.
3. Oskolkova T. N., Glezer A. M. Surface Hardening of Hard Tungsten-Carbide Alloys: A Review. Steel in Translation. 2017. Vol. 47. No. 12. pp. 788–796.
4. Yakushin V. L. Modification of carbon and low-alloyed steels by hightemperature pulse plasma streams. Metally. 2005. No. 2. pp. 12–24.
5. Ivanov Yu. F., Teresov A. D., Petrikova E. A., Raikov S. V., Goryushkin V. F., Budovskikh E. A. Surface layer of commercially pure VT1-0 titanium after electric-explosion alloying and subsequent treatment by a high-intensity pulsed electron beam. Steel in Translation. 2013. Vol. 43. No. 12. pp. 798–802.
6. Romanov D. A., Protopopov E. V. Effect of electron-beam treatment on wear-resistant coatings applied by electroexplosive sputtering. Steel in Translation. 2017. Vol. 47. No. 12. pp. 782–787.
7. Ivanov Yu. F., Kolubaeva Yu. А., Filimonov S. Yu., Vostretsova А. V., Budovskikh Е. А. Forming structure and properties of 45 grade steel during complex electric-detonation and electron beam treatment. Izvestiya vuzov. Chernaya metallurgiya. 2008. Vol. 51. No. 12. pp. 43–48.
8. Gromov V. Е., Ivanov Yu. F., Glezer А. М., Kormyshev V. Е., Konovalov S. V. Electron beam modification of build-up surface layer obtained on low-carbon steel by the electric arc method. Izvestiya RAN. Seriya fizicheskaya. 2017. Vol. 81. No. 11. pp. 1505–1512.

9. Yakushin V. L., Aung T. Ch., Dzhumaev P. S., Isaenkova М. G., Kalin B. А., Leontyeva-Smirnova М. V., Naumenko I. А., Perlovich Yu. А., Polsky V. I. Modification of the structure and phase state of ferritic and martensitic steels by action of impulse gas plasma streams. Perspektivnye materialy. 2013. № 5. С. 5–14.
10. Shinkin V. N. Preliminary straightening of thick steel sheet in a seven-roller machine. Steel in Translation. 2016. Vol. 46. No. 12. pp. 836–840.
11. Shinkin V. N. Asymmetric three-roller sheet-bending systems in steel-pipe production. Steel in Translation. 2017. Vol. 47. No. 4. pp. 235–240.
12. Kudinov V. А., Kartashov E. М., Kalashnikov V. V. Analytical solution of tasks of heat and mass transfer and thermoelasticity for multilayer structures. Moscow: Vysshaya shkola, 2005. 429 p.
13. Lord H. W., Shulman Y. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids. 1967. Vol. 15. No. 5. pp. 299–309.
14. Kaminski W. Hyperbolic heat conduction equation for materials with a non-homogeneous inner structure. ASME Journal of Heat Transfer. 1990. Vol. 112. pp. 555–560.
15. Shinkin V. N. Calculation of technological parameters of O-forming press for manufacture of large-diameter steel pipes. CIS Iron and Steel Review. 2017. Vol. 13. pp. 33–37.
16. Shinkin V. N. Springback coefficient of the main pipelines’ steel large-diameter pipes under elastoplastic bending. CIS Iron and Steel Review. 2017. Vol. 14. pp. 28–33.
17. Lykov А. V. Theory of thermal conductivity. Moscow: Vysshaya shkola, 1967. 600 p.
18. Koshlyakov N. S., Gliner E. B., Smirnov М. М. Partial derivative equations of mathematic physics. Moscow: Vysshaya shkola. 1970. 712 p.
19. Bazaikin V. I., Bazaikina О. L., Oskolkova Т. N., Temlyantsev М. V. Mathematic modeling of heat processes during treatment of the metal ware surface by high-density energy streams. Izvestiya vuzov. Chernaya metallurgiya. 2017. Vol. 60. No. 5. pp. 398–409.
20. Bazaikin V. I., Temlyantsev M. V., Bazaikina O. L. Influence of thermal stress on the formation of plastic-flow zones in the hot forging of cylindrical blanks. Steel in Translation. 2015. Vol. 45. No. 4. pp. 237–242.
21. Bazaikin V. I., Temlyantsev M. V., Bobrov B. Y. Initial stress in the hot forging of a cylindrical blank. Steel in Translation. 2015. Vol. 45. No. 2. pp. 105–110.
22. Simachev A. S., Temlyantsev M. V., Oskolkova T. N., Peretyatko V. N., Bazaikin V. I. High-temperature plasticity of the solidification zones of continuous-cast Э76Φ rail-steel billet. Steel in Translation. 2014. Vol. 44. No. 10. pp. 719–722.
23. Tylkin М. А. Handbook of a rebuild service heat-treater. Moscow: Metallurgiya, 1981. 648 p.
24. Dyakonov V. P. Maple 10/11/12/13/14 in mathematical calculations. Moscow: DMK Press, 2011. 800 p.

Language of full-text russian
Full content Buy
Back