Simulation of crystallization of cast products in the area of cylindrical holes
DOI:
https://doi.org/10.34185/1991-7848.2019.01.12Keywords:
casting of tracks, surface doping of castings, non-stationary temperature field, heat equation, finite difference method, crystallization rate, meltAbstract
One of the methods of intensive high-energy processing of metal products is their surface alloying. In the process of surface doping, the saturation of the surface layer of the metal by the necessary, for example, strengthening, components and thermal effects on the metal occurs. When surface doping of castings, firstly, high-temperature heat fluxes are formed, which provide high efficiency of doping, secondly, by using the energy of the melt, significant savings are achieved in the energy costs required for heat treatment.
Experiments on surface doping of track tracks in the area of their holes, which are widely used in agricultural and construction equipment, have shown the need to accurately determine the rate of movement of the crystallization front in the process of hardening the surface layer of castings. In connection with the technical difficulties of experimental research, there was a need for numerical-analytical modeling of this process. . The features of the model under study, first of all, are its axial symmetry, which leads to a significant deviation of the expected results in comparison with the classical flat models.
The dynamics of temperature distribution in the system “casting core - melt” was studied in the process of crystallization of tracks in the area of their holes. The problem of temperature distribution in the presence of a phase transition and the speed of movement of the interface between the phases within a crystallizing melt was solved by the finite difference method using an implicit scheme for drawing up a system of difference equations. The time dependence of the crystallization front displacement in graphical and analytical forms was obtained. The rate of crystallization of the surface layer of tracks in the area of their holes was calculated. The cooling rates of the surface layers of the castings during their crystallization are determined.
The calculated crystallization rate of the metal in the area of the tracks of the castings of tracks allows to determine the time of active dissolution of the alloying components in the surface layer of the castings and to predict the required dispersion of fractions of saturating components in the composition of the alloying coating of the cores.
References
Taran Yu. N. Kolichestvennoe issledovanie teksturyi rosta kristallov tsementita evtekticheskogo chuguna / Yu. N. Taran, G. M. Vorobev, O. A. Petrova // Izvestiya AN SSSR. Metallyi. # 1. − 1987. − S. 62-66.
A. s. 1766609 SSSR, MKI3 B 22 D 27/04. Ustroystvo dlya polucheniya chugunnyih otlivok s otbelennyim rabochim sloem / G. M. Vorobev, O. A. Petrova, V. I. Тsotsko (SSSR) . – opubl. v 1992. – Byul. # 37.
Tsotsko V. I. Application of casting surface alloying for hardening surface of track pin holes / V. I. Tsotsko, A. I. Burya, V. I. Shemavnev, G. M. Vorobyev // 2nd International Conference ”Research and Development in Mechanical Industry” (RaDMI 2002), 01-04 September 2002, Vrnjačka Banja, Yugoslavia. – V. 2. – S. 1100-1105.
A. s. 1540937 SSSR, MKI3 B 22 D 27/20. Sposob legirovaniya poverhnosti proushin v otlivkah trakov / G. M. Vorobev, V. I. Tsotsko (SSSR) . – opubl. v 1990. – Byul. # 5.
Tsotsko V. I. Lehuvannia poverkhnevoho sharu lyvarnoi zahotovky v protsesi lyttia / V. I. Tsotsko, B. H. Peleshenko, P. I. Melnyk. – Metaloznavstvo ta obrobka metaliv. – № 2. – 2009. – S. 27-30.
Melnyk P. I. Dyfuziini protsesy ta tverdofazni peretvorennia v metalakh i splavakh / P. I. Melnyk, B. K. Ostafiichuk, S. I. Sydorenko. – Ivano-Frankivsk: Plai, 1999. – 220 s.
Lepinskih B. M. Diffuziya elementov v zhidkih metallah gruppyi zheleza / B. M. Lepinskih, A. V. Kaybichev, Yu. A. Savelev. – M.: Nauka, 1974. – 192 s.
Bokshteyn B. S. Diffuziya v metallah / B. S. Bokshteyn. – M.: Metallurgiya, 1978. – 248 s.
Tihonov A. N. Uravneniya matematicheskoy fiziki / A. N. Tihonov, A. A. Samarskiy. – M.: Nauka, 1972. – 736 s.
Korn G. Spravochnik po matematike / G. Korn, T. Korn. – M.: Nauka, 1974. – 832 s.
Markovich E. S. Kurs vyisshey matematiki s elementami teorii veroyatnostey i matematicheskoy statistiki. M.: Vyisshaya shkola, 1972. – 480 s.
Tsotsko V. I. Simulation of crystallization of the surface layer of track castings in the region of holes / V. I. Tsotsko, B. G. Peleshenko // International Conference Differential Equations, Mathematical Physics and Applications, October 17-19, 2017, Cherkasy, Ukraine / Book of Abstracts. – Vinnitsa: Vasyl’ Stus Donetsk National University, 2017. – P. 144-145.
