ДО ОПТИМІЗАЦІЇ УПРАВЛІННЯ ТЕПЛОВОЮ РОБОТОЮ ПОЛУМЕНЕВИХ ТЕРМІЧНИХ ПЕЧЕЙ КАМЕРНОГО ТИПУ ПІД ЧАС НАГРІВАННЯ МАСИВНИХ ЗЛИВКІВ
Journal Title: Математичне моделювання - Year 2018, Vol 1, Issue 1
Abstract
TO OPTIMIZATION OF CONTROL BY HEAT WORK FOR FLAMING THERMAL FURNACES CHAMBER TYPE AT HEATING OF MASSIVE BARS Zinchenko V.Yu., Ivanov V.I., Cheprasov A.I., Kayukov Yu.M. Abstract The flaming thermal furnaces of chamber type got wide distribution in connection with universality of heat treatment by different in a form and mass of bars, but quite often are economic ineffective aggregates. In this connection a basic task is certain of development of control by the fields of temperature in furnaces, by motion of warming gases and also optimization of heat work in the whole. The analytical decision of nonlinear tasks of radiation-convective heat exchange at the non-stationary temperature of warming environment in the furnaces of this type has substantial complications. So, differential equation of heat conductivity from nonlinear dependence of thermophysical metal parameters on a temperature, become nonlinear and does not have an only decision. A task of this work is a making of simple mathematical model of heating of massive bars, allowing without the decision of differential equation to work out the algorithm of change of temperature of warming environment in time, which provides the given distribution of temperature on the section of the heated metal. Coming from that an optimal on a quick-action control is the piece-wise linear function of time and the temperature of warming environment changes from a maximum-possible size to the value, corresponding to the given temperature of metal surface, development of control algorithm is taken to determination of moments of switching of the thermal loading of furnace. As basic data at a modeling there are give the thermophysical parameters of metal charge, limitations on speed of its heating, temperature of furnace, initial and eventual distribution of temperature on the section of metal. On results calculations there is determine the temperature-time mode at which in a metal the given distribution of temperature during the minimum interval of time is provided. At the definition of the required distribution of temperature in a bar it is apple the method of lines, in accordance with which the heated thickness of metal is divided into separate areas, and a decision is executed by the method of progressive approximations. Adequacy of mathematical model there is define by comparison of optimal on a quick-action algorithms of control with the results of calculation on the models of other authors. Enough convergence of the got results is detected. References [1] Olshanskiy V.M. [Problem of energy-saving at the production of rolling on the metallurgical enterprises of Ukraine] Trudy GMAU «Metallurgicheskaya teplotekhnika» [Proc. Of the SMAU «Metallurgical heating engineering»]. 1999, vol. 2, pp. 63–66 (in Russian). [2] Panfilov V.I. Adaptivnye sistemy controlya kachestva nagreva metalla v pechakh [The adaptive system for control of metal heating quality in furnaces] «Izvestiya vuzov. Chernaya metallurgia» [News of Institutes of higher. Ferrous metallurgy]. 1974, no. 4, pp. 42–45 (in Russian). [3] Olshanskiy V.M., Shemet T.N. [Development of the optimal metal heating modes in chamber furnaces] Trudy GMAU «Metallurgicheskaya teplotekhnika» [Proc. of the SMAU «Metallurgical heating engineering»]. 1989, vol. 2, pp. 192–193 (in Russian). [4] Tajts N.Yu, Guzov L.A., Olshanskiy V.M., Borbots Yu.S. [Choice of the metal heating mode with the minimum expense of fuel] «Izvestiya vuzov. Chernaya metallurgia» [News of Institutes of higher. Ferrous metallurgy]. 1974, no. 4, pp. 164–167 (in Russian). [5] Reshetnik I.S., Litvin A.I., Reshetnik C.I. [A mathematical modeling of heating of metals in chamber furnaces] Trudy DGU «Matematicheckie metody teplomassoperenosa» [Mathematical methods of heat and mass transfer] 1983, pp. 39–43 (in Russian). [6] Bukhmirov V.V., Krupennikov S.A. Nosova S.V. [Mathematical modeling of heater furnace of batch operation] Trudy NMAU «Metallurgicheskaya teplotekhnika» [Proc. Of the NMAU «Metallurgical heating engineering»]. 2002, vol. 7, pp. 24–32 (in Russian). [7] Arutyunov V.A., Bukhmirov V.V., Krupennikov S.A. Matematicheskoe modelirovanie teplovoi raboty promyshlennykh pechei [Mathematical modeling of thermal work of industrial furnaces]. Moskow, 1990. 239 p. [8] Lisienko V.G., Volkov V.V., Goncharov A.L. Matematicheskoe modelirovanie teploobmena v pechakh i agregatakh [Mathematical modeling of heat exchange in furnaces and aggregates]. Kiev, 1984. 230 p. [9] Butkovskiy A.G. Teoriya optimalnogo upravleniya sistemami s raspredelennymi parametrami [Theory of optimal control by systems with distributed parameters]. Moskow, 1965. 476 p. [10] Belyaev N.M. Osnovy teploperedachi [Bases of heat transfer]. Kiev, 1989. 342 p. [11] Pevun M.P., Sokolov A.K. Adaptivnye sistemy upravleniya protsessami nagreva metalla [Adaptive systems of control by processes of heating metals]. Zaporozhe, 1998. 352 p. [12] Butkovskiy A.G. Metody upravleniya sistemami s paspredelennymi parametrami [Methods of control by the system with distributes parameters]. Moskow, 1975. 508 p.
Authors and Affiliations
В. Ю. Зінченко, В. І. Іванов, О. І. Чепрасов, Ю. М. Каюков
Keywords
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- EP ID EP294943
- DOI 10.31319/2519-8106.1(38)2018.129027
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