blackmetИзвестия высших учебных заведений. Черная МеталлургияIzvestiya. Ferrous Metallurgy0368-07972410-2091National University of Science and Technology "MISIS"10.17073/0368-0797-2024-5-616-624blackmet-2801Research ArticleИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ И АВТОМАТИЗАЦИЯ В ЧЕРНОЙ МЕТАЛЛУРГИИINFORMATION TECHNOLOGIES AND AUTOMATIC CONTROL IN FERROUS METALLURGYВид обобщенной математической модели для описания больших горячих деформацийType of generalized mathematical model for describing large hot deformationsБеломытцевМ. Ю.BelomyttsevM. Yu.

Михаил Юрьевич Беломытцев, д.т.н., профессор кафедры металловедения и физики прочности

Россия, 119049, Москва, Ленинский пр., 4

Mikhail Yu. Belomyttsev, Dr. Sci. (Eng.), Prof. of the Chair “Metallography and Physics of Strength”

4 Leninskii Ave., Moscow 119049, Russian Federation

myubelom@yandex.ruНациональный исследовательский технологический университет «МИСИС»РоссияNational University of Science and Technology “MISIS”Russian Federation202430102024675616624Copyright © Беломытцев М.Ю., 20242024Беломытцев М.Ю.Belomyttsev M.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://fermet.misis.ru/jour/article/view/2801

Взаимосвязь температурно-деформационно-силовых параметров в процессах горячей деформации имеет важное значение в практике обработки давлением. Из двух вариантов поиска и описания таких связей (основанных на физических закономер­ностях и математических приемах) в некоторых случаях оказывается более простым способ математического поиска искомой зависимости. Именно такой путь реализован в данной работе. Для этого из оцифрованных диаграмм деформации образцов жаропрочной 12 %-ной хромистой стали 1Cr12Ni3Mo2VNbN, продеформированных до истинной степени деформации ~1 при 1253 – 1453 К и скорости сжатия 0,01 – 10 с–1 в истинных координатах (φ и S) создавали матрицу исходных данных, в которой для каждой точки экспериментальной диаграммы деформации указывались напряжение S, степень деформации φ, скорость деформации φ′ и температура Т. Проведен поиск математической модели в мультипликативной форме, что позволило логарифмированием привести ее к линейному виду, а для поиска коэффициентов при сомножителях (а после логарифмирования – при слагаемых) использовать стандартные операторы программы Mathcad, использующие алгоритмы расчетов на основе метода наименьших квадратов. Качество модели оценивали количественно через расчет Q – суммы квадратов разностей между расчетными и экспериментальными значениями напряжений с нормировкой ее на среднее значение напряжения S от всего массива. Для найденной наилучшей формы связи S = f(φ, φ′, T) вида \(\log (S) = A + B\log (\varphi ) + C{[\log (\varphi )]^2} + D{[\log (\varphi )]^3} + E\log (\varphi ') + F\log (\varphi )\log (\varphi ') + G\frac{\varphi }{{\varphi '}} + \frac{{H + K\varphi  + M\log (\varphi ) + N\log (\varphi ') + P\log (\varphi )\log (\varphi ')}}{T}\) значение Q составило 6 % от Sср = 130 МПа. Установлено, что найденный вид математического описания горячей деформации применим к анализу процессов горячей деформации самых разнообразных металлических материалов, при этом точность прогнозных характеристик напряжения деформирования составляет 3 – 11 %.

The relationship between temperature-strain-force parameters in hot deformation processes is important in the forming practice. Of the two options for searching and describing such relationships (based on physical laws and mathematical techniques), in some cases the method of mathe­matical search for the desired dependence turns out to be simpler. This is exactly the path implemented in the abstracted message. For this propose, a matrix of initial data was created from digitized strain diagrams of the samples made of heat-resistant 1Cr12Ni3Mo2VNbN 12 % Cr steel deformed to a true deformation degree of ~1 at 1253 – 1453 K and a compression rate of 0.01 – 10 s–1 in true coordinates (φ and S). In this matrix, for each point of the experimental deformation diagram the stress S, the deformation degree φ, the deformation rate φ′, and the temperature T were indicated. The required mathematical model has a multiplicative form, which made it possible to bring it into a linear form by taking logarithms and to search for coefficients with the factors (and after logarithm, with terms in a polynomial) to use standard Mathcad operators with calculation algorithms based on the least squares method. The quality of the model was assessed quantitatively by calculating Q – the sum of squared differences between the calculated and experimental stress values ​​with its normalization to the average stress value S from the entire array. For the found best form of relationship S = f (φ, φ′, T) as \(\log (S) = A + B\log (\varphi ) + C{[\log (\varphi )]^2} + D{[\log (\varphi )]^3} + E\log (\varphi ') + F\log (\varphi )\log (\varphi ') + G\frac{\varphi }{{\varphi '}} + \frac{{H + K\varphi  + M\log (\varphi ) + N\log (\varphi ') + P\log (\varphi )\log (\varphi ')}}{T}\) the Q value was 6 % of Sav = 130 MPa. It was established that the found type of mathematical description of hot deformation is applicable to the analysis of hot deformation processes of a wide variety of metal materials, while the accuracy of the predictive characteristics of the deformation stress is 3 – 11 %.

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The authors declare that there are no conflicts of interest present.