Journal articles on the topic 'Steel castings Mathematical models'
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1
Selivyorstov, Vadim, Tatjana Selivyorstova, and Anton Guda. "SYSTEM ANALYSIS OF POROSITY FORMATION PROCESSES IN STEEL CASTINGS AND THEIR MATHEMATICAL MODELS." System technologies 6, no. 125 (December 27, 2019): 89–104. http://dx.doi.org/10.34185/1562-9945-6-125-2019-09.
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The analysis of scientific and technical information about the hardening features of steel castings, which lead to the formation of shrinkage defects is presented. The mechanisms of the relationship of the casting properties of alloys are shown. The analysis of factors that determine fluidity is carried out. The technological parameters of casting are determined, which lead to the formation of pores in steel castings. The mechanisms of porosity formation of endogenous and exogenous nature are considered. Siverts law is given, that describes the dependence of gas concentration on pressure. Graphs of changes in the concentration of nitrogen and hydrogen in the pressure range 1 - 4 atm are given for medium alloyed steel, open-hearth steel, cast iron. The mechanism of the influence of temperature and gas pressure on the process of gas evolution in the melt is analyzed. Technological methods for influencing the solubility of gases during the solidification of the casting are described. The microporosity model of Advanced Porosity Module, the Niyama criterion are analyzed. The need for further studies to develop a general model for the formation of shrinkage defects, which will take into account, inter alia, the dependence of the concentration of gases dissolved in the metal on pressure temperature, is noted.
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SELIVYORSTOVA, TETJANA, VADIM SELIVYORSTOV, and VITALIY KUZNECOV. "COMPLEX OF MATHEMATICAL MODELS AND METHODS TO CALCULATE PRESSURE EFFECT ON SULFIDE DISTRIBUTION IN STEEL." Computer systems and information technologies, no. 2 (October 4, 2021): 57–65. http://dx.doi.org/10.31891/csit-2021-4-7.
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Primary objective is to develop computational method to analyze digital pictures of sulfide prints, helping obtain qualitative image characteristics, and to formulate mathematical model of the distribution of sulphide inclusions to determine specific features of the pressure effect on the macrostructure formation of carbon steel castings flooded into the uncooled mold.
The research was carried out using images of sulfide prints of templates cut of steel cylindrical castings; L500 steel was applied. The castings result from industrial tests of a method of gas-dynamic effect on the fusion in the foundry forms under the conditions of a casthouse of Dnipropetrovsk aggregate plant PJSC. Digital pictures of sulfide prints, obtained in terms of the increased rate of gas pressure and maximum pressure, were binarized; defective fra gments were removed; and zoning took place. The developed computational method has been applied for fragments of images, representing different zones; data arrays have been received containing sizes and amounts of inclusions in the fragment.
The developed computational method to analyze digital images of sulfide prints has been implemented. ASImprints software support has helped obtain qualitative characteristics of images; namely, distribution of amount of the certain-size sulfide inclusions.
The computational method to analyze digital images of sulfide prints has made it possible to study the set of patterns of sulfide prints. The dependences have been obtained, describing specific features of sulfide inclusion distribution while varying gas-dynamic pressure method in terms of fusion in the casting form. It has been demonstrated that the distribution describes effectively the power-series distribution to compare with the exponential one. Mathematical model of the power-series distribution parameter dependence upon pressure has been developed. Deviation of the distribution parameters in terms of the experimental values and the model values has been evaluated.
The research demonstrates the ways to apply an algorithm of simple recursive casting for quantitative analysis of digital images of sulfide prints. Use of ASImprints, being software implementation of the computational method to analyze digital images of sulfide prints making it possible to obtain qualitative characteristics of images, has helped identify that the increased pressure within a casting-device for gas injection system results in the increased specific amount of inclusions and the decreased specific zone of sulfide inclusions respectively. It has been defined that exponential function describes reliably the nature of sulfide inclusion distribution in the digital image of sulfide print. The research has demonstrated that fragments of a sulfide print, belonging to one zone, are statistically homogeneous. Thus, it is possible to analyze quantitively digital image zone of a sulfide print on its fragment. Mathematical model of dependence of sulfide inclusion distribution in carbon-steel castings in terms of gas-dynamic effect on fusion solidifying in a mold has been developed. The model may be applied to predict sulfide inclusion distribution within the selected zones of cross section of the cylindrical castings solidifying in the uncooled mold in terms of the preset mode of gas-dynamic effect.
Keywords: gas-dynamic effect, pressure, solidification, casting, steel, 35 Л, mold, macrostructure, sulfides, inclusions, template, sulfide print, distribution, polynomial, parameters, prediction, software implementation, ASImprints
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Bondarenko, V. I., V. V. Bilousov, F. V. Nedopekin, and J. I. Shalapko. "The Mathematical Model of Hydrodynamics and Heat and Mass Transfer at Formation of Steel Ingots and Castings." Archives of Foundry Engineering 15, no. 1 (March 1, 2015): 13–16. http://dx.doi.org/10.1515/afe-2015-0003.
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Abstract The generic mathematical model and computational algorithm considering hydrodynamics, heat and mass transfer processes during casting and forming steel ingots and castings are offered. Usage domains for turbulent, convective and non-convective models are determined depending on ingot geometry and thermal overheating of the poured melt. The expert system is developed, enabling to choose a mathematical model depending on the physical statement of a problem.
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Kondratyuk, S. Ye, V. I. Veis, and Z. V. Parkhomchuk. "Structure formation and properties of overheated steel depending on thermokinetic parameters of crystallization." Journal of Achievements in Materials and Manufacturing Engineering 2, no. 97 (December 1, 2019): 49–56. http://dx.doi.org/10.5604/01.3001.0013.8537.
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Purpose: The aim of the proposed research is to investigate the mutual influence of the temperature of an overheated melt and its cooling rate during crystallization on the formation of the cast structure and mechanical properties of structural steels. Design/methodology/approach: Two structural medium-carbon steels were melted in induction furnace and poured from temperatures 1520-1670°C into casting moulds with different heat removal ability. This ensured the crystallization and structure formation of the studied steel castings at cooling rates (Vc) of 5°C/sec (sand-clay mould), 45°C/sec (steel mould), 350°C/sec (water cooled copper mould). It was studied a change of structure formation, mechanical characteristics depending on the temperature-kinetic conditions of the processing of the melt. Based on the processing of the array of obtained experimental data using linear regression analysis and a software package, interpolation models and their graphic images obtained allow a quantitative assessment of the established patterns of structural characteristics and mechanical properties of the studied steels depending on melt temperature (T, °C) and its cooling rate (Vc, °C/sec) during crystallization and structure formation. Findings: Among the technological factors that determine the formation of the cast structure and the mechanical properties of steels, the dominant role is played by the intensity of heat removal during the solidification of castings. The high cooling rate of the melt during crystallization determines an increase in the number of crystallization nuclei due to an increase in the degree of supercooling of the melt, eliminates the negative effect of the high overheating temperature of the metal before casting. Research limitations/implications: In the future, the results can be complemented by studies of the influence of the duration of isothermal exposure of the melt at different temperatures of superheating and cooling conditions. Practical implications: The obtained mathematical models (regression equations) that determine the mutual influence of the cooling rate and the temperature of the melt overheating on the structure and mechanical properties of the studied steels make it possible to obtain steel castings with predetermined properties at the level of properties of wrought steel of similar chemical composition. Originality/value: Interpolation models that allow a quantitative assessment of the established patterns of structural characteristics and mechanical properties of the studied steels depending on the melt temperature (T, °C) and its cooling rate (Vc, °C/sec) during crystallization and structure formation are obtained.
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Kondratyuk, S. Ye, V. I. Veis, Z. V. Parkhomchuk, and G. I. Shevchenko. "Gradient structure and properties of steel castings." Metaloznavstvo ta obrobka metalìv 99, no. 3 (September 30, 2021): 3–14. http://dx.doi.org/10.15407/mom2021.03.003.
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The influence of melt overheating in the range of 50-150 °C on the equilibrium liquidus and its cooling rate during crystallization of castings on the formation of macrostructural zones along their cross section, on the change of grain dispersion, dendritic structure characteristics and mechanical properties was investigated on the example of 25L steel. It is established that the macrostructure of castings in the direction of unilateral heat removal as it moves away from the cooled surface consists of four main structural zones - small coaxial crystals, columnar, branched and large coaxial crystals, the length and morphology of which naturally change depending on thermokinetic conditions of crystallization. The decisive role of the cooling rate at significant overheating of the melt to increase the number of crystallization nuclei, the formation of a more dispersed cast structure by increasing the degree of supercooling of the melt during crystallization is shown. The regularities of quantitative characteristics change of microstructure and dendritic structure depending on change of temperature-time parameters of crystallization in different structural zones of castings and their connection with characteristics of mechanical properties of steel are established. On the basis of mathematical processing of experimental data by linear regression analysis interpolation models and their graphical interpretations are obtained, which allow to quantify and predict the change of mechanical properties in different structural zones of gradient castings depending on melt overheating temperature and cooling modes within the investigated factor space. Keywords: gradient structure, structural zones, melt, mechanical properties.
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Grămescu, Traian, and Constantin Cărăușu. "Machinability by Milling of Gray Cast Iron." Applied Mechanics and Materials 657 (October 2014): 88–92. http://dx.doi.org/10.4028/www.scientific.net/amm.657.88.
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In the laboratory of cutting machining technologies from the “Gheorghe Asachi” Technical University of Iaşi, a series of investigations on the machinability of cast iron samples having various structures were designed and developed. The aim of the research was to know and to explain the way in which various constituents of some iron castings exert influence on the degree of wear of a milling tool made of high speed steel. Within this research, mathematical empirical models were determined, in order to calculate the cutting speed v60, considered as an indicator for the evaluation of machinability. The research allowed establishing the factors able to have a major influence on tool wear phenomenon and obtaining thus a more complete image concerning the machinability of grey iron used for castings.
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Arif Mammadov, Arif Mammadov, Nizami Ismayilov Nizami Ismayilov, Mukhtar Huseynov Mukhtar Huseynov, and Faiq Guliyev Faiq Guliyev. "SOME ASPECTS OF MATHEMATICAL MODELING OF ELECTRIC STEEL MELTING PROCESS." PAHTEI-Procedings of Azerbaijan High Technical Educational Institutions 14, no. 03 (March 21, 2022): 04–12. http://dx.doi.org/10.36962/pahtei14032022-04.
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The article discusses some aspects of mathematical modeling of the process of melting electric steel on the basis of innovative metallurgical technologies. It was noted that the production of electric steel mainly consists of three stages - preparation of the charge, melting and casting of liquid steel. The most important of these stages is the mathematical modeling of the melting process, especially the physicochemical processes that take place during melting. All physicochemical processes controlled in order to obtain the required chemical composition of electric steel for modeling are combined into two main groups, such as metal refining and alloying. Possibilities of mathematical modeling of electric steel melting processes have been identified: to successfully solve different types of problems without conducting pro¬duc¬tion experiments; to ensure optimal modes of melting in specific production conditions. The problems to be solved by mathematical modeling have been identified: con¬struc¬tion of a model for specific conditions that allow to achieve the required value of any parameter of the solution; possibility to purchase electric steel in specific conditions; minimum cost of material, time, labor and energy and required chemical composition, temperature and mass melting of steel; automatic control of all parameters of the solution. To solve these problems, the characteristics of static, dynamic and mixed mathematical models have been identified. It has been shown that a deterministic mathematical model can be applied to a system of equations expressing the functional relationships between the parameters of the solution and the factors affecting them. The mixed mathematical model includes equations expressing functional correlations. This model is actually a deterministic static model. Depending on the problem, the expediency of using appropriate models in the melting of electric steel is justified. In general, the creation of a mathematical model of melting processes of electric steel includes: dividing the melting into elementary physicochemical processes within the limits of each period, ie decomposing the melting process; to give a quantitative description of each elementary process, ie to describe the process mathematically; write a mathematical model of each cycle of melting by combining the quantitative characteristics of the parameters and elementary processes controlled on the basis of the equations of material and heat balances; to obtain a mathematical model of the solution as a whole by combining mathematical models of different periods. As an example of the application of mathematical modeling in electroplating processes, the amount of pores formed during the steel melting process in the main braided electric arc furnace was calculated using scrap metal. Keywords: electroplating steel, mathematical modeling, static model, dynamic model, deterministic model, mixed model, functional relationships.
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Siciliano, Fulvio. "Mathematical Modelling of Hot Rolling: A Practical Tool to Improve Rolling Schedules and Steel Properties." Materials Science Forum 762 (July 2013): 210–17. http://dx.doi.org/10.4028/www.scientific.net/msf.762.210.
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Most of the commercial metallic materials undergo at least one hot deformation stage during fabrication. Hot deformation processing leads to the production of plates, strips, rods, pipes and other shapes at lower overall cost when compared to the cold deformation/annealing route. Comprehensive study of the metallurgical phenomena during hot deformation has enormous potential application in the control of industrial rolling processes. Understanding of the microstructural and mean flow stress evolution lead to sound steel developments and innovative rolling schedules. The models predict parameters such as grain size, fractional softening (static and dynamic) and strain induced precipitation which are useful to improve rolling schedules. Effects such as incomplete softening and strain accumulation can be easily detected as well as their consequences on the final grain size and mechanical properties. In this regard, special attention must be given to steels, the most important metallic material in terms of history, present and future. In this paper, three hot rolling routes will be analyzed in order to produce high strength linepipe steels. Examples were selected on how the use of modelling during development stage can help to meet mechanical properties, mainly toughness and drop weight tear test. Firstly, it is presented a brief overview on mathematical models applied to hot rolling. Thin slab casting/direct rolling, hot strip mill and plate mill are exemplified in the present work. The development of new steel grades can greatly accelerated with the aid of modelling, which is an useful, low-cost technique.
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Miłkowska‐Piszczek, Katarzyna, and Jan Falkus. "Control and Design of the Steel Continuous Casting Process Based on Advanced Numerical Models." Metals 8, no. 8 (July 30, 2018): 591. http://dx.doi.org/10.3390/met8080591.
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The process of continuous casting of steel is a complex technological task, including issues related to heat transfer, the steel solidification process, liquid metal flow and phase transitions in the solid state. This involves considerable difficulty in creating the optimal process control system, which would include the influence of all the physico‐chemical phenomena which may occur. In parallel, there is an intensive development of new mathematical models and an increase in computer performance, therefore complex numerical simulations requiring substantial computing time can be conducted. This paper presents a review of currently applied numerical methods allowing the phenomena accompanying the process of continuous casting of steel to be accurately represented. Special attention was paid to the selection of appropriate methods to solve the technological problem selected. The possibilities of applying selected numerical models were analysed in order to modify and improve the existing process or to design a new one linked to the implementation of new steel grades in the current production. The description of the method of defining the boundary conditions, initial conditions and material parameters as vital components ensuring that numerical calculations based upon them in the finite element method, which is that most frequently applied, are correct is an important element of the paper. The possibility of reliably defining the values of boundary parameters on the basis of information on the intensity of cooling in individual zones of the continuous casting machine was analysed.
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Ramírez-López, Adán, Omar Dávila-Maldonado, Alfonso Nájera-Bastida, Rodolfo Dávila Morales, Carlos Rodrigo Muñiz-Valdés, and Jafeth Rodríguez-Ávila. "Computer Modeling of Grain Structure Formation during Quenching including Algorithms with Pre- and Post-Solidification." Metals 12, no. 4 (April 4, 2022): 623. http://dx.doi.org/10.3390/met12040623.
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Simulation of the grain growth process, as a function of steel heat transfer conditions, is helpful for predicting grain structures of continuous cast steel products. Many authors have developed models based on numerical methods to simulate grain growth during metal solidification. Nevertheless, the anisotropic nature of grain structures makes necessary the employment of new mathematical methods such as chaos theory, fractals, and probabilistic and stochastic theories of simulation. The problem is significant for steelmakers to avoid defects in products and to control the steel microstructure during the continuous casting process. This work discusses the influence of nodal solidification times and computer algorithms on the dynamic formation of the chill, columnar, and equiaxed zones including physical phenomena such as nucleation and grain growth. Moreover, the model incorporates pre-nucleation and pre-growth routines in the original algorithm. There is a description of the influence of the mathematical parameter criteria and probabilities over the grain morphology obtained after solidification. Finally, an analysis of these algorithms elucidates the differences between these structures and those obtained from models considering only the solidification.
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Kawalla, Rudolf, Wolfhart Müller, and Werner Jungnickel. "Physical Simulation at Hot Deformation." Materials Science Forum 638-642 (January 2010): 2591–97. http://dx.doi.org/10.4028/www.scientific.net/msf.638-642.2591.
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Today the numerical simulation of hot deformation processes is very advanced. But it requires mathematical models for metalphysical processes as for microstructure development, which take place during the deformation. Until now such models were developed for many steel grades and non-ferrous materials. For new steels as multi-phase steels laboratory investigations are required, in order to determine the optimal processing technologies of these materials. This applies also to the modelling. So far it is impossible, to calculate sole by mathematical solutions the manifold parameters of metalphysical processes and microstructure, for this reason laboratory trials and simulations are needed implicitly. Even for well known materials such procedures can be essential and useful. Using the multi-functional simulation system Gleeble HDS-V40 it is shown, which possibilities a physical simulation offers today. Starting with the annealing conditions, followed by microstructure development up to cooling, selected examples reflect the results of property development during hot deformation processes. The differences between conventional deformation after re-heating and deformation after direct-charging will be presented. The last-mentioned concept offers in its combination of near-netshape casting and direct charging special benefits, especially saving of energy.
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Vynnycky, Michael. "Applied Mathematical Modelling of Continuous Casting Processes: A Review." Metals 8, no. 11 (November 9, 2018): 928. http://dx.doi.org/10.3390/met8110928.
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With readily available and ever-increasing computational resources, the modelling of continuous casting processes—mainly for steel, but also for copper and aluminium alloys—has predominantly focused on large-scale numerical simulation. Whilst there is certainly a need for this type of modelling, this paper highlights an alternative approach more grounded in applied mathematics, which lies between overly simplified analytical models and multi-dimensional simulations. In this approach, the governing equations are nondimensionalized and systematically simplified to obtain a formulation which is numerically much cheaper to compute, yet does not sacrifice any of the physics that was present in the original problem; in addition, the results should agree also quantitatively with those of the original model. This approach is well-suited to the modelling of continuous casting processes, which often involve the interaction of complex multiphysics. Recent examples involving mould taper, oscillation-mark formation, solidification shrinkage-induced macrosegregation and electromagnetic stirring are considered, as are the possibilities for the modelling of exudation, columnar-to-equiaxed transition, V-segregation, centreline porosity and mechanical soft reduction.
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Jędrzejczyk, D., M. Hojny, and M. Głowacki. "Development of Software for the Simulation of Rolling Steel Under the Coexistence of Liquid and Solid State / Rozwój Oprogramowania Do Symulacji Walcowania Stali W Warunkach Współistnienia Fazy Ciekłej I Stałej." Archives of Metallurgy and Materials 60, no. 4 (December 1, 2015): 2783–90. http://dx.doi.org/10.1515/amm-2015-0447.
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The paper presents the results of the application simulating the rolling process of steel in terms of coexistence of liquid and solid phases. The created mathematical models can be the basis for creation of systems that simulate the final phase of the continuous casting process relying on using a roller burnishing machine for continuous casting of steel. For a complete description of the performance of the material during deformation in these conditions, the constructed mathematical model is a fully three-dimensional model and consists of three parts: thermal, mechanical, and density variation submodels. The thermal model allows the prediction of temperature changes during plastic deformation of solidifying material. The mechanical model determines the kinetics of plastic continuum flow in the solid and semi-solid states, and the resulting deformation field. The temperature of the process forces supplementing the description of the performance of the material with a density variation model that allows the prediction of changes in the density of the material during the final phase of solidification with simultaneous plastic deformation. For the purpose built model, experimental studies were performed using a physical simulator Gleeble 3800®. They allowed the determination of the necessary physical properties of the metal within the temperature of change state. In addition to presenting the developed models the work also includes the description of the author’s application that uses the above mathematical models. The application was written in the fully object-oriented language C++ and is based on the finite element method. The developed application beside the module data input, also consist of a module of three-dimensional visualization of the calculations results. Thanks to it, the analysis of the distribution of the particular rolling parameters in any cross-section of the rolled strip will be possible. The paper presents the results of the authors’ research in the area of the advanced computer simulation.
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Dobrovská, Jana, Hana Francová, Bedřich Smetana, Karel Stránský, Věra Dobrovská, and František Kavička. "Experimental Analysis on the Causes of the Breakout of Continuous Cast Steel Slab." Materials Science Forum 782 (April 2014): 67–72. http://dx.doi.org/10.4028/www.scientific.net/msf.782.67.
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The paper deals with investigation into segregation behavior of selected elements in longitudinal cut of continuous steel slab, in the breakout area. The breakout occurred after a flying change of tundish in order to begin casting of another steel grade. Altogether 11 samples were taken from the part of a solidified slab. Concentrations of selected elements (Al, Si, P, S, Cr, Mn, Ni and Mo) were measured in these samples using scanning electron microscope and energy dispersive spectroscopy. Using the original mathematical models the basic micro-segregation characteristics and the parameter of macro-heterogeneity were further determined for each analyzed element. Then a quantitative measurement of inclusions ("micro-purity") in the samples was performed using a metallographic microscope. Then method of differential thermal analysis was used for the measurements of temperatures of phase transformations. The following main results were found: - magnitude of micro-segregation of the analyzed elements in the measured sections of 1000 μm is approximately the same in all the analyzed samples, - chemical macro-heterogeneity is very high across the analyzed slab section, - very uneven mixing of melts of both steels was probably one of the main causes of formation of the breakout.
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Moro, L., J. Srnec Novak, D. Benasciutti, and F. de Bona. "Copper Mold for Continuous Casting of Steel: Modelling Strategies to Assess Thermal Distortion and Durability." Key Engineering Materials 754 (September 2017): 287–90. http://dx.doi.org/10.4028/www.scientific.net/kem.754.287.
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In this work the durability assessment and the permanent deformation of a copper mold for continuous casting of steel have been investigated using mathematical models based on the Finite Element method. The cyclic plasticity behavior of the material is represented by a combined kinematic-isotropic model experimentally validated. Results from thermo-mechanical analysis are in good agreement with measurements. In particular, creep effects included into the model permit the evolution of bulging near the meniscus area to be correctly predicted. A life estimation is performed considering strain-life and stress-rupture time curves according to a cumulative damage law.
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Anikeev, A. N., I. V. Chumanov, A. I. Alekseev, and V. V. Sedukhin. "Computer modeling of distribution of dispersed particles by the cross-section of cylindrical dispersion-strengthened metal materials." Izvestiya. Ferrous Metallurgy 63, no. 8 (October 8, 2020): 657–64. http://dx.doi.org/10.17073/0368-0797-2020-8-657-664.
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The article presents the process of creating a computer model for predicting the distribution of particles during centrifugal casting using the ANSYS FLUENT 16.0 software module. To predict the distribution of particles by volume in the world at the moment there are several mathematical models. Most of them are based on the steady state assumption: models describing the criteria for dropping particles by a growing crystallization front and models calculating critical particle absorption rates by growing dendritic crystals. Some models attempt to describe the dynamic state of the system or to determine the criterion for capturing non-metallic inclusions by the solidification front during centrifugal casting of metal. The process of creating the new model, its scheme and geometry are described. Its preprocessor takes into account such phenomena as two-phase flow, energy equation, lamellar flow, introduction of discrete phases (strengthening particles), melting/crystallization. The model considers account of interaction of two liquid phases: air and steel melt; interfacial interaction is described by the equation of surface tension. As the materials used, the authors used steel grade 12Kh18N10T as the base metal, carbides of tungsten, boron and yttrium oxide as input particles. During simulation, the physicochemical parameters of these substances were taken into account. The process of modeling the distribution of particles during centrifugal casting using the Skif-Ural computing cluster, included in the TOP-500 of the world’s most powerful computers, is presented. As a result of the simulation, in addition to graphical display, data arrays were obtained that describe the coordinates of each particle at each moment in time in increments of 0.00001 seconds, which allows us to predict the exact location of each particle at each moment of casting. The results of the work indicate that centrifugal casting technology with the introduction of dispersed particles during the casting process allows obtaining dispersion-strengthened metal materials with predicting the distribution of refractory particles.
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Chen, Yongli, Yuhua Li, Xuejiao Zhou, Yueyue Jiang, and Fei Tan. "Dynamic Recrystallization and Recovery Behaviors in Austenite of a Novel Fe-1.93Mn-0.07Ni-1.96Cr-0.35Mo Ultrahigh Strength Steel." Journal of Chemistry 2021 (July 14, 2021): 1–8. http://dx.doi.org/10.1155/2021/2809145.
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Due to the complex composition and high proportion of alloys in traditional ultrahigh strength steel, the dilemma caused by ultrahigh strength and low toughness in casting and forging processes requiring subsequent heat treatment can be mitigated with an efficient and economical rolling process. In this work, the effect of deformation parameters on dynamic recrystallization (DRX) and dynamic recovery (DRV) is discussed through stress-strain analysis, the DRV mathematical model is obtained, and then the dynamic recrystallization activation energy, Zener–Hollomon equation, and hot working equation are obtained. The critical strain of DRX detected by the P-J method is ε c / ε p = 0.631 , which indicates that dynamic recrystallization of this novel steel is relatively easy to achieve by the rolling process. These models and conclusions have potential to be generalized for the formulation of process specification and process configuration without requiring extensive material testing.
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Odinokov, V. I., E. A. Dmitriev, and A. I. Evstigneev. "MATHEMATICAL MODELING OF METAL FLOW IN CRYSTALLIZER AT ITS SUPPLY FROM SUBMERSIBLE NOZZLE WITH ECCENTRIC HOLES." Izvestiya Visshikh Uchebnykh Zavedenii. Chernaya Metallurgiya = Izvestiya. Ferrous Metallurgy 61, no. 8 (October 24, 2018): 606–12. http://dx.doi.org/10.17073/0368-0797-2018-8-606-612.
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Flow of liquid melt in the crystallizer is a little-studied process. Analytical solutions of melt flow in general case refer to complex mathematical problems, therefore numerical methods are used to model it. The purpose of this work is to use numerical method proposed by Professor V.I. Odinokov, based on finite-difference representation of the initial system of equations. This method has been successfully used in mechanics of continuous media, in foundry industry in mathematical modeling of strained deformed state of shell molds on investment models,as well as in other technological works, which indicates its universality. In the present study, the object of research is hydrodynamic flows of liquid metal during steel casting into a rectangular section mold when fed from a submerged nozzle with eccentric holes, and the result is a spatial mathematical model describing the flows of liquid metal in the crystallizer. To simulate the processes occurring in the crystallizer, the software complex “Odyssey” was used. The theoretical calculation is based on fundamental equations of hydrodynamics and approved numericalmethod. Solution of differential equations system formulatedin the work was carried out numerically. Investigated area was divided into elements of finite dimensions, for each element the resulting system of equations was written in the difference form. The result of the solution is velocity field of metal flow in crystallizer volume. To solve the system of algebraic equations obtained, a numerical scheme and a calculation algorithm were developed. Based on developed numerical scheme and algorithm, a computation program was compiled in Fortran-4. Mathematical model makes it possible to vary geometric dimensions of the crystallizer and cross-section of metal exit openings from the immersion nozzle, and it can also help to understand the flow pattern of the cast metal that affects heat dissipation of crystallizer walls and to find the optimal parameters for liquid metal outlet from the gravy glass at various casting modes. As an example it is given calculation of steel casting into a rectangular mold with a height of 100 cm and a section of 2000×40 (cm) in plan. Casting was carried out from immersion nozzle eccentrically in both sides in a horizontal plane. The calculation results are presented in graphical form. The movement of liquid metal flows is shown, their magnitudes and intensity are determined.
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Krasnikov, Kyrylo Serhiiovych. "MATHEMATICAL MODELING OF THE DISTRIBUTION OF ARGON IN A TUNDISH WITH A MOLTEN METAL DURING FILLING." Modern Problems of Metalurgy, no. 23 (March 27, 2020): 130–35. http://dx.doi.org/10.34185/1991-7848.2020.01.13.
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The article is devoted to the mathematical description of the process of filling an intermediate ladle (tundish) with argon, which is blown into the melt stream falling from the steel casting ladle, which is common at metallurgical plants. Metallurgical plants use an intermediate ladle to reliably supply a continuous casting machine for the melt. Also important for the tundish is the removal of non-metallic inclusions using argon. The good distribution of argon bubbles in the tundish significantly influences the removal of unwanted melt components such as hydrogen and nitrogen. Given the need for gas to escape, the melt speed in the intermediate ladle should be sufficiently low, especially near outflow holes, where melt needs to be homogeneous and slow for a high–quality casting. Conducting experiments during the operation of a metallurgical plant is undesirable, costly and is accompanied by difficulties associated with high temperature and opacity of the melt. Therefore, the experiments are often carried out in laboratories on the so-called cold models, where the melt is replaced by water, argon – by air, and the tundish – by the transparent container of the rectangular shape under the conditions of similarity. Despite the obvious advantages of such cold modeling, today most experiments are still conducted on mathematical models, which are a much cheaper and low-erroneous way of predicting the development of a given process under different conditions. Mathematical modeling of melt motion helps to select the optimal geometry of the tundish, as well as the required amount of argon and usefulness of barriers on a way of melt streams. The article proposes to use the convection-diffusion equation for the argon field and the Navier-Stokes equations – for the velocity field. The numerical solution using finite volume method is well tested and provides sufficient accuracy. In addition, this method is easily parallelized to speed up computing on modern multi-core processors. A graphical user interface software application allows you to display the status of the system on the screen for further review and adoption decisions.
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Ortiz-Domínguez, Martín, Oscar Armando Gómez-Vargas, Mariana Bárcenas-Castañeda, and Víctor Augusto Castellanos-Escamilla. "Comparison and Analysis of Diffusion Models: Growth Kinetics of Diiron Boride Layers on ASTM A283 Steel." Materials 15, no. 23 (November 26, 2022): 8420. http://dx.doi.org/10.3390/ma15238420.
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Hard-coated surfacing of a few micrometers is widely applied to increase the efficiency of tools, e.g., for cutting, forming, and casting applications. Therefore, the base thermodiffusion surface treatment is a practical solution to these issues by hardening surface layers with interstitial elements such as carbon, nitrogen, and boron. In particular, within this study, the growth kinetics of an iron boride layer on ASTM 283 steel were investigated with two diffusion models of the powder-pack boriding technique in the temperature range of 1123–1273 K with different treatment periods. The first model, called the steady-state diffusion model, used the modified version of the mass balance equations at the Fe2B/substrate growth interface, the parabolic growth law, and the solution of Fick’s second law without time dependence. At the same time, the second diffusion model was based on Goodman’s method, also called the integral heat balance method. Afterward, the diffusion coefficient of boron in the Fe2B phase was calculated by fitting the experimental data to the models. Nevertheless, the estimated value for the activation energy of ASTM A238 steel in both diffusion models was coincident (168.2 kJ∙mol−1). A mathematical analysis was implemented by means of a power series (Taylor series) to explain this similarity. The SEM examinations showed a solid tendency to saw-tooth morphology at the growth interface with the formation of the Fe2B layer, whose presence was verified by XRD analysis. The tribological characterizations, including the tests of Rockwell-C indentation, pin-on-disc, and Vickers hardness test method, were used to analyze the antiwear features of the Fe2B layers. Finally, this value of energy was compared to the literature for its experimental validation.
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Bielnicki, Marcin, and Jan Jowsa. "Physical and numerical modeling of liquid slag entrainment in mould during slabs casting." Metallurgical Research & Technology 117, no. 5 (2020): 509. http://dx.doi.org/10.1051/metal/2020055.
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The paper presents results of physical and numerical modeling of liquid slag entrainment during continuous casting of steel slabs process. The main aim of this work was to determine the critical casting speed and also to specify, which entrainment mechanism is most responsible for transport of slag droplets into steel volume. Physical modeling was based on water-oil model of mould, made on reduced linear scale of Sl = 0.4. In mathematical modeling, Realizable k-ε and LES WALE models were used to describe turbulent motion of water and oil, whereas Volume of Fluid model was used to take into account interactions between phases. It was found, that the main cause of slag entrainment is the formation of von Karman vortex in the vicinity of submerged entry nozzle. The results of laboratory experiments and numerical simulations were compared each other. Both method are a useful tools for modeling of slag entrainment. Great agreement was found between laboratory experiments and numerical simulation carried out using LES WALE model, regarding the shape of the oil and oil entrainment as a result of vortex structures formation. However, in the simulation case using Realizable k-ε model, the oil entrainment hasn’t been modeled for the conditions under consideration.
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Pieprzyca, J., and J. Jowsa. "Method for Determining the Time Constants Characterizing the Intensity of Steel Mixing in Continuous Casting Tundish." Archives of Metallurgy and Materials 60, no. 1 (April 1, 2015): 245–49. http://dx.doi.org/10.1515/amm-2015-0039.
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AbstractA common method used in identification of hydrodynamics phenomena occurring in Continuous Casting (CC) device's tundish is to determine the RTD curves of time. These curves allows to determine the way of the liquid steel flowing and mixing in the tundish. These can be identified either as the result of numerical simulation or by the experiments - as the result of researching the physical models. Special problem is to objectify it while conducting physical research. It is necessary to precisely determine the time constants which characterize researched phenomena basing on the data acquired in the measured change of the concentration of the tracer in model liquid's volume. The mathematical description of determined curves is based on the approximate differential equations formulated in the theory of fluid mechanics. Solving these equations to calculate the time constants requires a special software and it is very time-consuming. To improve the process a method was created to calculate the time constants with use of automation elements. It allows to solve problems using algebraic method, which improves interpretation of the research results of physical modeling.
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Shalomeev, V. A., and O. V. Liutova. "Economically alloyed steel for the needs of the mining industry." Metaloznavstvo ta obrobka metalìv 101, no. 1 (March 30, 2022): 44–52. http://dx.doi.org/10.15407/mom2022.01.044.
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It has been established that the downtime of ball mills due to the low durability of cast parts is 70...80 % of the total number of downtime, while material damage is estimated in hundreds of thousands of hryvnia. One of the weakest units of these mills are the discharge grids and scoops of the cochlear feeder, the durability of which reaches 5.5...6 months and 1.0...1.5 months, respectively, with the resource of operation of other parts of the mill 9...12 months. As a result of the analysis of the operating conditions of the gratings and scoops of the MSHR, it was found that the duration of operation and the mechanical properties of these parts depend mainly on the material from which they are made. Steel with a high level of plasticity and toughness (35GFL, 35HNL, 34HNML, etc.) had insufficient wear resistance due to low strength, hardness. Materials with a high level of hardness and strength (60Kh2SML) had a low impact toughness, which was the reason for emergency shutdowns of the mills as a result of breakdowns of parts. The analysis of the mechanical properties of ladles and gratings has established the required level of properties of these parts; σВ ≥ 850 MPa; НВ ≥ 2600 МPa; δ ≥ 8 %; Ψ ≥ 20 %, KCU ≥ 0,20 MJ/m2. The effect of changing the silicon concentration on the mechanical properties and wear resistance of steel containing 1.5% chromium and 0.40% manganese with different carbon contents has been studied. With an increase in the silicon content, the strength and hardness indicators increase. The effect of silicon on the plastic properties of steel, impact strength and wear resistance is nonlinear, with 0.9% manganese in this case, a monotonic decrease is observed not only in plastic properties and toughness, but also in wear resistance. This is explained by the fact that with an increase in the manganese content in steel, the segregation heterogeneity and stability of supercooled austenite increase, leading, after normalization, to the formation of a martensite-like structure. It is shown that in the production of castings operating under conditions of abrasive wear in combination with shock loads, it is advisable to observe the ratio of silicon to carbon 2.0...2.5. Mathematical planning of the experiment made it possible to obtain models that adequately describe the effect of the composition of steel on the level of its mechanical and operational properties. Based on the processing of the data obtained from the «STATISTICA» software package, a wear-resistant economically alloyed steel of the following composition was proposed: 0.45...0.50 % carbon; 1.7...2.0 % chromium; 0.5...0.7 % manganese; 1.2...1.5 % silicon. The use of such a composition of steel for the manufacture of unloading gratings and scoops of snail feeder allowed to increase their service life by 1.5 times by improving performance, and, consequently, reduce the maintenance cycle of ball mills, which increased economic efficiency. Keywords: ball grinding mill, alloy steel, mathematic modeling, structure, mechanical properties.
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Odinokov, V. I., A. I. Evstigneev, E. A. Dmitriev, D. V. Chernyshova, and A. A. Evstigneeva. "Influence of internal factor on crack resistance of shell mold by investment models." Izvestiya. Ferrous Metallurgy 65, no. 2 (March 17, 2022): 137–44. http://dx.doi.org/10.17073/0368-0797-2022-2-137-144.
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The process of evolution of the stress-strain state (SSS) of a multilayer shell mold (SM) is modeled at properties change between layers during cooling of poured steel casting. A mathematical model was constructed and a theoretical study of the stress state of the SM was carried out in absence of connection between the layers in a multilayer composite. The article describes a complex three-component system: liquid metal, solid metal, and ceramic SM. Solid metal and SM are considered to be isotropic. To solve this problem, the authors used the theory of small elastic-plastic deformations and equations of thermal conductivity, as well as proven numerical methods. Evolution of SSS in SM was traced by time steps. Thickness of the solidifying metal was determined through the equation of interphase transition. The article considers the process of heating an axisymmetric SM when pouring liquid metal into it. Stress state was estimated by stresses and displacements that occur in SM. At SM contact with support filler (SF), SM surface move away from the SF is possible during cooling of liquid metal. In this case, contact problem is solved. Taking into account the compiled algorithm for solving the problem, calculations were performed for the case of complete sliding of layers using developed numerical schemes and software complexes. Obtained results of numerical calculations are clearly displayed by graphic illustrations in form of plots and graphs. Detailed analysis of the obtained results is given. There is inconsistency of the previously expressed idea about the applicability of sliding between layers in a multilayer composite from the position of reducing its stress state. The research results can be useful in calculations of other functional multilayer shell systems.
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Haas, Tim, Christian Schubert, Moritz Eickhoff, and Herbert Pfeifer. "Numerical Modeling of the Ladle Flow by a LES-Based Eulerian–Lagrange Approach: A Systematic Survey." Metallurgical and Materials Transactions B 52, no. 2 (February 16, 2021): 903–21. http://dx.doi.org/10.1007/s11663-021-02064-2.
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AbstractTo account for increasing economic and ecological pressure, the steel industry is obligated to continuously optimize all processes. An important optimization approach is numerical modeling although its potential is limited by the accuracy of the mathematical models. In a previous work, a validation database was created and a validation score was derived from this data which allows a comprehensive qualitative accuracy assessment for those models. Here, this system is employed for a systematic optimization of the isothermal flow in the casting ladle. For that, different submodels, namely the turbulence models, subgrid turbulence models, bubble-induced turbulence and interfacial closure models as well as influencing factors, such as the grid resolution or the initial bubble size, are analyzed. It is shown that the large eddy turbulence model is more accurate than the Reynolds-average approach because it is able to reproduce the anisotropy of turbulence in the bubble region. In accordance with the literature, a grid dependency of the lift force is found which can be reduced using an averaged shear field as an additional variable. For the interfacial closure models, the combination of the Tomiyama drag model for fully contaminated systems and the Tomiyama lift correlation showed the best agreement with the experimental data. The results of the survey are summarized to a best-practice guideline with which the validation score can be increased from 38.7 with the Reynolds-average approach to 85.1 on a coarse grid respectively, and 87.8 on a fine grid. However, some upscaling problems of the numerical system from the water model to the real ladle are revealed. There is a need to find accurate yet efficient grid resolutions which make the large eddy turbulence model affordable with the current computational resources. Furthermore, alloying elements or non-metallic inclusions might alter the interfacial forces considerably. However, no studies on their effect have been published yet.
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Meshcheryakov, Viktor, Tatyana Sinyukova, Vladislav Gladyshev, Alexey Sinyukov, Lyudmila Solovieva, and Elena Gracheva. "Modeling and analysis of vector control systems for asynchronous motor." E3S Web of Conferences 220 (2020): 01075. http://dx.doi.org/10.1051/e3sconf/202022001075.
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At metallurgical enterprises, slab transfer devices are widely used, the principle of operation of which is to lift slabs in the steel casting area and transport them to the storage area. The article considers the existing control system of the slab transfer device. At the moment, the mechanism has a DC motor controlled by a thyristor Converter. This system is difficult to maintain and has a large size. As an upgrade, the installation of an asynchronous motor with a frequency Converter is proposed. In the Matlab environment, mathematical models of single-circuit and double-circuit DC motor control systems and a model of asynchronous motor with a short-circuited rotor have been developed. A vector control system is used as an AC motor control system. As a result of simulation performed analysis of the characteristics. As an optimization of the system with vector control, in order to reduce dynamic loads on the turntable, it is proposed to introduce an intensity setter into the system, the use of which provides the necessary restriction of accelerations and jerks, reduces shock loads on the mechanical components of the electric drive, including a reduction in the load on the turntable when lowering the slab.
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Jiang, Zhou Hua, Jia Yu, Fu Bin Liu, Xu Chen, and Xin Geng. "Application of Mathematical Models for Different Electroslag Remelting Processes." High Temperature Materials and Processes 36, no. 4 (April 1, 2017): 411–26. http://dx.doi.org/10.1515/htmp-2016-0146.
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AbstractThe electroslag remelting (ESR) process has been effectively applied to produce high grade special steels and super alloys based on the controllable solidification and chemical refining process. Due to the difficulties of precise measurements in a high temperature environment and the excessive expenses, mathematical models have been more and more attractive in terms of investigating the transport phenomena in ESR process. In this paper, the numerical models for different ESR processes made by our lab in last decade have been introduced. The first topic deals with traditional ESR process predicting the relationship between operating parameters and metallurgical parameters of interest. The second topic is concerning the new ESR technology process including ESR with current-conductive mould (CCM), ESR hollow ingot technology, electroslag casting with liquid metal(ESC LM), and so on. Finally, the numerical simulation of solidification microstructure with multi-scale model is presented, which reveals the formation mechanism of microstructure.
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Polyakov, S., O. Kuzyi, A. Korotschenko, V. Korovin, and J. Bast. "Computer-Aided Design of Steel Casting Taking into Account the Feeding Ability." Archives of Foundry Engineering 16, no. 1 (March 1, 2016): 49–54. http://dx.doi.org/10.1515/afe-2016-0002.
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Abstract A new Computer-Aided Design approach is introduced for design of steel castings taking into account the feeding ability in sand moulds. This approach uses the geometrical modeling by a CAD-program, in which the modul “Castdesigner” is implemented, which includes the feeding models of steel castings. Furthermore, the feeding ability is guaranteed immediately during the design by an interactive geometry change of the casting cross section, so that a directional feeding of the solidifying casting from the installed risers is assured.
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Mazur, Igor, and Tanya I. Cherkashina. "Mathematical and Physical Modeling of Soft Cobbing Process of Hot Rolling Steels." Materials Science Forum 704-705 (December 2011): 160–64. http://dx.doi.org/10.4028/www.scientific.net/msf.704-705.160.
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The soft cobbing, used in steel’s continuous casting, is widely applying in technologies of rolled metal manufacturing. It is important to know ingot’s stress-strain state and dynamics of ingot’s changes while cobbing, when there is a liquid metal in the centre of section. The complex questions of numerical modeling of soft cobbing process and experimental investigation on physics plasticine models are considered in presented work. The analysis of findings is presented in the article.
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Arapov, S. L., S. V. Belyaev, A. A. Kosovich, E. G. Partyko, N. A. Stepanenko, P. O. Yuriev, and Y. N. Mansurov. "APPLICATION OF MATHEMATICAL STATISTICS TO IMPROVE IMPACT HARDNESS OF CASTINGS FROM HADFIELD STEEL." Metallurg, no. 9 (2022): 55–61. http://dx.doi.org/10.52351/00260827_2022_09_55.
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Скрябин, М. Л. "Effect of the chemical composition of 35HGSL steel on shrinkage, casting defects and microstructure." Informacionno-technologicheskij vestnik, no. 1(23) (March 11, 2020): 171–79. http://dx.doi.org/10.21499/2409-1650-2020-23-1-171-179.
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Стальные отливки на сегодняшний день стали неотъемлемой частью современного литейного производства. В процессе получения отливок неизбежно появляются какие-либо дефекты. В данной работе рассмотрены причины образования дефектов при изготовлении отливок из стали 35ХГСЛ при литье по выплавляемым моделям. Также рассмотрены особенности отвода теплоты от отливки при первичной и вторичной кристаллизации. Приведена классификация зон отливок по ориентации кристаллов в отливках. Выявлена закономерность влияния интенсивности охлаждения на характер усадки. Today, steel castings have become an integral part of modern foundry production. In the process of obtaining castings, any defects inevitably appear. In this paper, we consider the production reasons for the formation of defects in the manufacture of castings made of 35XGSL steel when casting on investment models. The features of heat removal from the casting during primary and secondary crystallization are also considered. The classification of casting zones by the orientation of crystals in castings is given. The regularity of the influence of the cooling intensity on the shrinkage character is revealed.
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Rostislav, Liutyi. "Analytical method of calculation of thermal fields of cast parts during crystallization." Theory and practice of metallurgy 1,2021, no. 1,2021(126) (February 22, 2021): 5–13. http://dx.doi.org/10.34185/tpm.1.2021.01.
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The aim of the work is to create a mathematical method that allows to calculate the distribution of thermal fields in cast parts during crystallization using a system of analytical formulas. During the calculations, a combination of known analytical formulas GF was used. Balandin, AY Weinik, S. Schwartz with their own original mathematical solutions created on the basis of the analysis of thermophysical processes in castings in the process of their crystallization. Computer simulation of thermal fields using the LVMFlow program was used to compare the results. According to the created mathematical method, examples of calculation of thermal fields for two castings made of steel 25L of hollow cylindrical shape, the wall thickness of which is 100 mm and 4 mm, respectively, are given. Calculations were performed for the conditions of crystallization of castings in a single sand form. The comparison of results of calculations by the developed method and with use of the existing software is presented. For the first time, based on our own mathematical and thermophysical developments, a comprehensive calculation method for determining the thermal field of the casting during crystallization and cooling was developed. casting. The technique is expressed in a number of analytical formulas, each of which describes a specific thermal process that occurs in the casting. This takes into account the features of the casting configuration. The created complex method of calculation of thermal fields of cast parts is a mathematical basis for determining the thermal fields of molds and rods, which allows to predict their properties and select the optimal molding materials. The created technique can also be offered as a mathematical basis for refining applied computer programs for foundry production. CASTING, TEMPERATURE, THERMAL FIELD, COOLING DYNAMICS, COOLING DURATION, MATHEMATICAL LAW, COLORING FRONT, CALCULATION
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Grebnev, Yu V., V. F. Zharkova, D. Yu Grebnev, E. E. Davydov, and D. R. Muratov. "CEMENTING OF THE SURFACE OF STEEL CASTINGS DURING CASTING ACCORDING TO CAST MODELS." Izvestia Volgograd State Technical University, no. 2 (2022): 82–86. http://dx.doi.org/10.35211/1990-5297-2022-2-261-82-86.
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Vdovin, K. N., N. A. Feoktistov, D. A. Gorlenko, O. A. Nikitenko, and D. D. Khamidulina. "INOCULATION OF HIGH MANGANESE STEEL CASTINGS USING TITANIUM CARBONITRIDE." Izvestiya. Ferrous Metallurgy 62, no. 3 (June 20, 2019): 188–94. http://dx.doi.org/10.17073/0368-0797-2019-3-188-194.
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The article is devoted to study of the process of mold inoculation of high manganese steel castings using titanium carbonitride. Introduction considers basic principles, alloying and inoculation of casting alloys. Review of the papers on this topic made by native and foreign researchers was given. Conclusions were made on the materials presented in the studied papers, goals and tasks for studies were formed. Besides, in this part of the article relevance of the conducted researches was substantiated as well as practical significance for casters. The second part of the article describes routine of experiments. Materials involved when conducting experimental works were considered in details: charge materials, treatment agent, materials for foundry molds. Besides, there are also described the way to receive experimental cast products, methodology to determine thermal conditions for forming experimental models in foundry mold and regimen of thermal treatment. Herewith, methodology for conducting metallographical test was considered. The third part of the article mentions the results received during carrying out experimental works on mold inoculation using fine titanium carbonitride powder of high manganese steel castings. Influence of inoculation on the level of performance properties expressed via coefficients of abrasive wear and wear striking resistance was considered as well as change of the indicated peculiarities in relation to not inoculated alloy was evaluated. Besides, results of metallographical tests were given which allowed to substantiate change of the performance properties level of high manganese steel. Influence of thermal conditions of forming cast products was also evaluated, in particular speed of alloy cooling in foundry mold on the level of performance properties of inoculated high manganese steel. In final part of the article conclusions on the results of conducted researches were made as well as manufacturing recommendations were given for practical implementation of the work results to increase the level of performance properties of high manganese steel. Besides, recommendations on the most reasonable expenditure of titanium carbonitride powder ensuring receipt of the necessary characteristics of microstructure and as a consequence, increase of the level of performance properties were given.
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Khan, Muhammad Azhar Ali, Anwar Khalil Sheikh, Zuhair Mattoug Gasem, and Muhammad Asad. "Fatigue Life and Reliability of Steel Castings through Integrated Simulations and Experiments." Metals 12, no. 2 (February 15, 2022): 339. http://dx.doi.org/10.3390/met12020339.
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The quality and performance of steel castings is always a concern due to porosities formed during solidification of the melt. Nowadays, computational tools are playing a pivotal role in analyzing such defects, followed by their minimization through mold design optimization. Even if the castings are produced with defects in a permissible range, it is important to examine their service life and performance with those defects in a virtual domain using simulation software. This paper aims to develop a methodology with a similar idea of simulation-based optimization of mold design and predictions of life and reliability of components manufactured with minimized casting defects, especially porosities. The cast parts are standard fatigue specimens which are produced through an optimized multi-cavity mold. X-ray imaging is done to determine the soundness of cast parts. Experimental work includes load-controlled fatigue testing under fully reversed condition. The fatigue life of specimens is also simulated and compared with the experimental results. The classical strength-stress model is used to determine the reliability of cast parts through which a safe-load induced stress of steel castings is determined. Finally, probability distributions are fit to the reliability results to develop the reliability models. It is found that porosities can be minimized significantly in the mold design phase using casting simulations. Nevertheless, some porosities are bound to exist, which must be included in realistic estimation of fatigue life and reliability of cast parts.
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Duda, J., A. Stawowy, and R. Basiura. "Mathematical Programming for Lot Sizing and Production Scheduling in Foundries." Archives of Foundry Engineering 14, no. 3 (August 8, 2014): 17–20. http://dx.doi.org/10.2478/afe-2014-0053.
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Abstract The problem considered in the paper is motivated by production planning in a foundry equipped with the furnace and casting line, which provides a variety of castings in various grades of cast iron/steel for a large number of customers. The quantity of molten metal does not exceed the capacity of the furnace, the load is a particular type of metal from which the products are made. The goal is to create the order of the melted metal loads to prevent delays in delivery of goods to customers. This problem is generally considered as a lot-sizing and scheduling problem. The paper describes a mathematical programming model that formally defines the optimization problem and its relaxed version that is based on the conception of rolling-horizon planning.
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Prikhod’ko, O. G., V. B. Deev, E. S. Prusov, and A. I. Kutsenko. "Influence of thermophysical characteristics of alloy and mold material on castings solidification rate." Izvestiya. Ferrous Metallurgy 63, no. 5 (July 1, 2020): 327–34. http://dx.doi.org/10.17073/0368-0797-2020-5-327-334.
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Obtaining castings of given quality is the main task of foundry production. One of the stages of casting technology is solidification of melt in the mold. When studying the process of castings solidification, it is necessary to fully take into account all the features of heat transfer between casting and mold. Influence of various thermophysical parameters of alloy and mold material on casting formation is considered. In the analysis, original mathematical models were used to calculate the coefficient and time of complete solidification of castings in sand-clay and metal forms. These models take into account geometric parameters of casting, main thermophysical parameters of casting metal and mold material, heat transfer conditions at crystallization front, on casting-mold boundary and on the mold surface. Analysis of dependence of time and rate of castings solidification on thermophysical parameters (heat capacity, density, heat conductivity of casting material and mold, specific heat of metal crystallization) was carried out. Storage capacity and process of heat storage are quite fully characterized by the value of heat storage coefficient. This coefficient practically determines the rate of heat loss by the casting which plays a decisive role in its properties forming. Therefore, this parameter is selected for a comprehensive analysis of thermal processes occurring in casting and mold. The influence of thickness and thermal conductivity of chill paint layer on solidification of castings in metal molds is considered. The basic calculation formulas and initial data are presented. Calculations were carried out for castings of the following types: endless plate, endless cylinder, ball. The results of simulation of solidification process parameters are presented in graphic form. Using various alloys as an example, it has been shown by calculation that when changing composition and properties of mold material, it is possible to change time and speed of alloys solidification in a wide range. In this case, processes of forming the structure and properties of castings are controlled.
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Vapalahti, Sami, Seppo Louhenkilpi, and Tuomo Räisänen. "The Effect of Fluid Flow on Heat Transfer and Shell Growth in Continuous Casting of Copper." Materials Science Forum 508 (March 2006): 503–8. http://dx.doi.org/10.4028/www.scientific.net/msf.508.503.
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Molten metal is cooled in a continuous casting mould forming initially a thin shell that grows thicker. The main phenomena in the mould are: fluid flow, heat transfer and solidification. A lot of mathematical models have been developed to simulate these phenomenons in continuous casting machines but most of the models developed are not calculating the fluid flow at all. In these models, it is assumed that the strand (solid and liquid) is withdrawn through the machine with a constant velocity field (= casting speed) and the convective heat transfer generated by the fluid flow is taken into account by using an effective thermal conductivity method. Also at the Helsinki University of Technology, these kinds of heat transfer models have been developed (TEMPSIMU for steels and CTEMP3D for coppers). The flow in the mould is three-dimensional and turbulent. Coupled models calculate the fluid flow, heat transfer and solidification simultaneously. The fluid flow is affected by many things: inlet flow rate, design of the inlet nozzle (SEN), immersion depth of the SEN, movement of the solid shell, natural convection, solidification shrinkage, etc. and the fully coupled, turbulent fluid flow and heat transfer models are generally subjected to convergence difficulties and they need a lot of computing time. Due to these reasons, these kinds of models are not so much used in industry so far. In the present study, a commercial FLOW-3D package is used to make coupled simulations of heat transfer, turbulent fluid flow and solidification in a copper continuous casting machine. The effect of thermophysical material data are also studied and presented. The material data are calculated by a model developed at the Helsinki University of Technology, called CASBOA.
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VISINTIN, A. "Mathematical Models of Solid-Solid Phase Transitions in Steel." IMA Journal of Applied Mathematics 39, no. 2 (1987): 143–57. http://dx.doi.org/10.1093/imamat/39.2.143.
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Pommersheim, James M., Tinh Nguyen, Zhuohong Zhang, and Joseph B. Hubbard. "Degradation of organic coatings on steel: Mathematical models and predictions." Progress in Organic Coatings 25, no. 1 (October 1994): 23–41. http://dx.doi.org/10.1016/0300-9440(94)00501-x.
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Gonzalez-Trejo, Jesus, Cesar Augusto Real-Ramirez, Ignacio Carvajal-Mariscal, Florencio Sanchez-Silva, Francisco Cervantes-De-La-Torre, Raul Miranda-Tello, and Ruslan Gabbasov. "Hydrodynamic Analysis of the Flow inside the Submerged Entry Nozzle." Mathematical Problems in Engineering 2020 (October 20, 2020): 1–14. http://dx.doi.org/10.1155/2020/6267472.
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The quality of steel produced by continuous casting depends mainly on the characteristics of the liquid steel flow pattern within the mold. This pattern depends on the flow dynamics of the nozzle that is immersed in liquid steel. This work characterizes the fluid dynamics within two separate submerged entry nozzle models with a square cross section bore. The Froude similarity criterion and water as working fluid have been used. The models consist of a square-shaped tube with one inlet and two lateral squared exits at the bottom. To enhance the flow visualization, the models do not have exit ports. Moreover, one of the models has a “pool,” a volume at the bottom, and the other prescinds of it. The geometrical parameters and operational conditions of physical experiments were reproduced in the numerical simulations. The turbulence model used in this work is large eddy simulation (LES) with dynamic k-equation filtering. It was found that transient numerical simulations reproduce the dynamic nature of the internal flow pattern seen in physical experiments. The results show that the flow pattern within the pool nozzle is defined by only one large vortex; on the other hand, in the nozzle, without the pool, the flow pattern achieves a complex behavior characterized by two small vortexes. This study will allow to build nozzles that produce a symmetric, regular fluid flow pattern inside the mold, which leads to improvements on the process such as low energy consumption and finally in cost reductions.
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Prysiazhnyi, Andrii H., Volodymyr V. Kukhar, Vadym Hornostai, Ekaterina Kudinova, Maryna Korenko, and Oleksandr S. Anishchenko. "Mathematical Models for Forecasting of 10Mn2VNb Steel Heavy Plates Mechanical Properties." Materials Science Forum 1045 (September 6, 2021): 237–45. http://dx.doi.org/10.4028/www.scientific.net/msf.1045.237.
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The problem urgency for determining the optimal rolling and heat treatment schedules for providing the required indices of heavy plates physical and mechanical properties is shown. The use of statistical mathematical models for solving this problem is substantiated and the methodology for their design is described. Statistical mathematical models were designed using the mathematical statistics methods and Data Mining tools to determine the yield strength, ultimate tensile strength and percent elongation for 10Mn2VNb steel plates rolled under 3600 heavy plate mill conditions. Software for the numerical implementation of these statistical mathematical models has been developed. Applied software has been developed for the numerical implementation of the statistical mathematical models for predicting the heavy plate’s mechanical properties, and high calculation accuracy has been confirmed with the ones help: 95.82% for the yield strength, 96.78% for the ultimate tensile strength, and 91.48% for the percent elongation. The regularities of the influence for finish rolling factual temperature in the finishing stand of 3600 heavy plate mill and the plate thickness on 10Mn2VNb pipe steel physical and mechanical properties were identified by processing the database and using the designed software.
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Pană, Gabriela Monica, and Laura Diana Grigorie. "The Issue of Car Body Manufacture in Unibody Aluminum Alloy Design." Applied Mechanics and Materials 880 (March 2018): 183–88. http://dx.doi.org/10.4028/www.scientific.net/amm.880.183.
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Weight reduction is the present and future issue in the automotive industry. The use of aluminum for bodywork is a growing solution due to the specific properties and the recyclability it offers. The unibody design concept with high productivity is developed for steel sheet metal car bodies. They can also be made with aluminum sheets with different product shapes (sheets, extrusions, castings etc.). The aluminum offers a wide variety of design options. The most important difference between aluminum and steel models is the predominant joining technique. In order to obtain optimal solutions from a technical and economical point of view, it is necessary to apply aluminum design concepts and correspondingly adapted manufacturing technologies.
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SHINOKURA, Tsuneki, and Koichi TAKAI. "Mathematical Models of Roll Force and Torque in Steel Bar Rolling." Tetsu-to-Hagane 72, no. 14 (1986): 1870–76. http://dx.doi.org/10.2355/tetsutohagane1955.72.14_1870.
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Colson, A., and M. Boulabiza. "On the identification of mathematical models for steel strees-strain curves." Materials and Structures 25, no. 5 (June 1992): 313–16. http://dx.doi.org/10.1007/bf02472672.
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RATH, S., P. P. SENGUPTA, A. P. SINGH, A. K. MARIK, and P. TALUKDAR. "MATHEMATICAL-ARTIFICIAL NEURAL NETWORK HYBRID MODEL TO PREDICT ROLL FORCE DURING HOT ROLLING OF STEEL." International Journal of Computational Materials Science and Engineering 02, no. 01 (March 2013): 1350004. http://dx.doi.org/10.1142/s2047684113500048.
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Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.
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Ding, Hui, Yan Jin, Hui Yu, Hong Bin Huang, Jun Wang, Fan Ai, and Kang Yang. "Mathematical Simulation the Influence of Tundish with a Retaining Wall." Advanced Materials Research 774-776 (September 2013): 375–78. http://dx.doi.org/10.4028/www.scientific.net/amr.774-776.375.
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Placement in the middle retaining wall package, aimed at controlling the flow of liquid steel forms, so that movement of a reasonable level remained stable, while reducing interference from turbulence and dead zones, molten steel in order to extend the average stay of removal in favor of inclusion to improve the cleanliness of molten steel.In this paper, with the tundish wall flow field of research is the use of mathematical simulation methods, three dimensional mathematical models are currently being used successfully to simulate liquid steel flow and temperature distribution, the large-scale universal Finite Element analyses software ANSYS CFX is used and many models based on different tundishes are built
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Kumar, Rajesh, Rupinder Singh, and Inderpreet Singh Ahuja. "Modeling of Dimensional Accuracy in Three Dimensional Printing for Light Alloy Casting." Materials Science Forum 808 (December 2014): 65–78. http://dx.doi.org/10.4028/www.scientific.net/msf.808.65.
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The purpose of this paper is to develop mathematical model to investigate the influence of shell casting parameters. Three input parameters such as shell wall thickness (SWT), Pouring temperature (PT) and weight density (WD) were selected to give output in the form of average outer diameter (AOD) as dimensional accuracy. After identification of component, technological prototypes were produced. In this work three dimensional printing (3DP) has been used as rapid shell casting to make shell mould by using Zcast 501 powder with different shell wall thickness for six different light alloy materials. Measurements on a coordinate-measuring machine helped in calculating the dimensional tolerances of the castings produced. For obtaining tight casting tolerances the dimensional accuracy of component is the most important element. The thickness, curing time and orientation of the shell molds, play an important role in providing a high quality of the cast part in time. The dimensional accuracy was found to be more in the case of maximum layer thickness and horizontal position of the component. The investigation has led to conclusions as the Quadratic models were developed for the response. The F - value is 23.93, which implies that the model as well as lack of fit is significant. The value of Prob > F is less then the standard value 0.05, which indicates model terms are significant. With the help of Post curing, shell Mold temperature was not found to affect the dimensional accuracy of the castings, significantly. It was observed that high pouring temperatures also produced castings with better dimensional accuracy. This study will provide main effect of the inputs on average outer diameter as dimensional accuracy in three dimensional printing of light alloys castings. Statistically in this case B, C, A2, B2, C2, AB, BC is the model terms which contributes significantly to the model developed for dimensional accuracy.
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Rakhmonov, I., N. Niyozov, and K. Li. "DEVELOPMENT OF CORRELATION AND REGRESSION MODELS OF ELECTRIC ENERGY INDICATORS OF THE EQUIPMENT WITH CONTINUOUS NATURE OF PRODUCTION." Technical science and innovation 2019, no. 4 (December 12, 2019): 203–8. http://dx.doi.org/10.51346/tstu-01.19.4.-77-0039.
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The article presents an analysis of the use of correlation-regression analysis, which is based on the methods of mathematical statistics and probability theory in the study of the power consumption of enterprises with equipment of continuous production. On the basis of the annual power consumption schedule of the electric steel-smelting shop in a monthly time section, mathematical models have been developed for the power consumption parameters. And also, on the basis of statistical data with the use of a mathematical method, mathematical expressions were obtained for the electric power consumption and the specific consumption for the main equipment of the electric steel-smelting shop. In order to assess the adequacy of the developed mathematical models, mathematical models of the total and specific consumption of their power consumption are compared with actual data. The comparison results show high reliability of the power consumption modes of the main equipment of the facility in question. The analysis of the values of forecast errors with low error rates determines the adequacy of the developed mathematical models of the parameters of power consumption in terms of power consumption and specific consumption for the main equipment of the electric steel-smelting shop. In this regard, they can be used to determine the predicted values of the parameters of power consumption in electric steelmaking equipment.
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Barglik, Jerzy. "Mathematical modeling of induction surface hardening." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 35, no. 4 (July 4, 2016): 1403–17. http://dx.doi.org/10.1108/compel-09-2015-0323.
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Purpose – As far as the author knows the modeling of induction surface hardening is still a challenge. The purpose of this paper is to present both mathematical models of continuous and simultaneous hardening processes and exemplary results of computations and measurements. The upper critical temperature Ac3 is determined from the Time Temperature Austenization diagram for investigated steel. Design/methodology/approach – Computation of coupled electromagnetic, thermal and hardness fields is based on the finite element methods, while the hardness distribution is determined by means of experimental dependence derived from the continuous cooling temperature diagram for investigated steel. Findings – The presented results may be used as a theoretical background for design of inductor-sprayer systems in continual and simultaneous arrangements and a proper selection of their electromagnetic and thermal parameters. Research limitations/implications – The both models reached a quite good accuracy validated by the experiments. Next work in the field should be aimed at further improvement of numerical models in order to shorten the computation time. Practical implications – The results may be used for designing induction hardening systems and proper selection of field current and cooling parameters. Originality/value – Complete mathematical and numerical models for continuous and simultaneous surface induction hardening including dual frequency induction heating of gear wheels. Experimental validation of achieved results. Taking into account dependence of the upper critical temperature Ac3 on speed of heating.