Модель динаміки нагрівання металу в полуменевих печах камерного типу
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 1
Abstract
A MODEL OF DYNAMICS FOR HEAT OF METAL IN THE FLAMING FURNACES OF CHAMBER TYPE Revun M.P., Zinchenko V.Yu., Ivanov V.І., Mosejko Yu.V. Abstract The task of control by heat work for flaming furnaces of chamber type supports development and realization of optimal algorithm of treason in times of heat influence on an incalescent metal. Development of the simplified model for dynamics of heat in the system «the furnace gases – fettling of furnace – metal» without the significant departure from the dynamics of the real object. The system «the furnace gases – fettling of furnace – metal» from position of control is a nonlinear object with distributed in time and space parameters, which is described by differential equation with the partial derivatives. At the estimation of order for values constant of heat time are performed the calculations of the heat and temperature modes of flaming recyrculative furnace for heat treatment of massive blanks. According to the results of calculations the constant of heat time fold Tfet = 7.90 hours, Tmet = 0.20 hours, Tfur.gas = 0.001 hours, id est. there is possibility to reduce the degree of differential equation, when to equate Tfur.gas = 0. For furnaces which work with the stationary temperature of the furnace gases, it is possible elimination from the model of positive back action and aperiodic link, which is responsible for furnace laying. At the real conditions when laying of furnace is heated in a period loading of new party metal there is supervised only cooling of its superficial layer. After loading of metal at next fuel feed there is the rapid heating of fettling, id est. holdover properties do not appears. At cyclic work of furnace on heating and cooling together with a metal a model it follows to complement initial conditions – temperature of fettling for furnace and temperature of metal charge. Mathematical model of dynamics of heat in flaming chamber furnaces in the linear approaching presents the complex of three aperiodic lanocs of first-order, that it is overcame by a positive back action. For the decision of optimization task simplification of model is the possible elimination of constant of heat time for furnace gases or fettling of furnace, the choice of which it follows to carry out coming from design features of furnace, mode of its work, and also thermophysical parameters of metal. Reference [1] Butkovskij А.G. Review of some new aspects, ideas and results in the problem of control by the system with the distributed temperatures. Izvestiya AS USSR. Tekhnicheskaya cibernetika – Proceedings of the Academy Science USSR. Technical cybernetics, 1983, no. 2, pp. 112-122 (in USSR). [2] Butkovskij А.G, Goldfarb E.M., Geskin S. Application of concept maximum for optimization of furnace mode temperature. IzvestiyaVuzov Chornaya metallurgiya – Proceedings of institutes of higher education. Ferrous Metallurgy, 1967, no. 7, pp. 173-177 (in USSR). [3] Vyrk А.Kh. Control by heat massive body taking into account of limitation on thermal tensions Avtomatika i telemekhanika – Automation and telemechanics. 1972, no. 5. pp. 185-188 (in USSR). [4] Kapustin Е.А., Goldfarb E.M., Sidorin G.N., Polevoj G.A., Turovskij E.L. Programming of metal heat on fuel expense taking into account technological limitations IzvestiyaVuzov Chornaya metallurgiya – Proceedings of institutes of higher education. Ferrous Metallurgy, 1980, no. 7, pp. 114-118 (in USSR). [5] Goldfarb E.М., Ibryaev V.S. Metal heat optimal mode by criterion minimum of total cost fuel and loss of metal on oxidation IzvestiyaVuzov Chornaya metallurgiya – Proceedings of institutes of higher education. Ferrous Metallurgy, 1971, no. 12, pp. 144-148 (in USSR). [6] Minaev A.N., Grinberg V.Ya., Olshanskij V.M., Borbots Yu.S. To the question of heating thin bodies with the set exactness IzvestiyaVuzov Chornaya metallurgiya – Proceedings of institutes of higher education. Ferrous Metallurgy, 1975, no. 7, pp. 184-186 (in USSR). [7] Krylova L.S., Gorbunov V.A. [Calculation of heat exchange in a chamber heater furnace taking into account nonisotherming of gas volume] Trudy MetAU MetalurgicheskayaTeplotekhnika [Proc. of the MetAU «Metallurgical heating engineering»], Dnepropetrovsk. MetAU, 1989, ussue. 2, pp. 167-168 (in Ukraine). [8] Gubinskij V.I., Zhung-U. Lu. [Theory of flaming furnaces] Teoriya plamennykh pechej. Moscow. Engineering, 1995, 256 p (in Russian). [9] Feldbaum A.A. [Bases of theory of the optimal automatic systems] Osnovy teoriioptimalnykh avtomaticheskikh system. Moscow :Physical and mathematical state publishing house, 1963, 623 p (in USSR).
Authors and Affiliations
М. П. Ревун, В. Ю. Зінченко, В. І. Іванов, Ю. В. Мосейко
Keywords
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