Jaime A. Spim

Mathematical modeling and optimization strategies (genetic algorithm and knowledge base) applied to the continuous casting of steel

Abstract The control of quality in continuous casting products cannot be achieved without a knowledge base which incorporates parameters and variables of influence such as: equipment characteristics, steel, each component of the system and operational conditions. This work presents the development of a computational algorithm (software) applied to maximize the quality of steel billets produced by continuous casting. A mathematical model of solidification works integrated with a genetic search algorithm and a knowledge base of operational parameters. The optimization strategy selects a set of cooling conditions (mold and secondary cooling) and metallurgical criteria in order to attain highest product quality, which is related to a homogeneous thermal behavior during solidification. The results of simulations performed using the mathematical model are validated against both experimental and literature results and a good agreement is observed. Using the numerical model linked to a search method and the knowledge base, results can be produced for determining optimum settings of casting conditions, which are conducive to the best strand surface temperature profile and metallurgical length.

Evaluation of heat transfer coefficients along the secondary cooling zones in the continuous casting of steel billets

In the present work, heat transfer coefficients (h) along different cooling zones of a continuous caster billet machine were determined during casting of low and medium carbon steels. The effects of casting parameters, such as machine characteristics, the ingot dimension, mold, sprays zones, radiant cooling, melt composition, and casting temperature were investigated and correlated with heat transfer coefficients. By using industrial measured billet surface temperatures, linked with a numerical solution of the solidification problem, ingot/cooling zones heat transfer coefficients were quantified based on the solution of the inverse heat conduction problem (IHCP). The experimental temperatures were compared with simulations furnished by an explicit finite difference numerical model, and an automatic search has selected the best theoretical–experimental fit from a range of values of h. The computer software algorithm has been developed to simulate temperature profiles, solid shell growth, phase transformations, and the point of complete solidification in continuous casting of steel billets and blooms. Industrial experiments were monitored with an optical infrared pyrometer to analyze the evolution of surface temperatures during solidification along the machine. The results permitted the establishment of expressions of h as a function of position along the caster, for different steel compositions, casting parameters and melt superheats.

Application of a Solidification Mathematical Model and a Genetic Algorithm in the Optimization of Strand Thermal Profile Along the Continuous Casting of Steel

ABSTRACT This work presents an optimization method based on a genetic algorithm applied to continuous casting process. A simple genetic algorithm was developed, which works linked to a mathematical model permitting the determination of optimum values for the water flow rates in the secondary cooling zones. First, experimental data (industrial) were compared with simulated results obtained by the solidification mathematical model, to determine the metal/cooling heat transfer coefficients along the machine by the inverse heat conduction problem method. The industrial data concerning surface strand temperature were obtained by using infrared pyrometers along a continuous caster machine during casting of both SAE 1007 and 1025 steels. In a second step, these results were used by a numerical code based on a genetic algorithm for determining optimum settings of water flow rates in the different sprays zones, which are conducive to the best quality of the solidified strand. The simulations were carried out by analyzing the solidification process during continuous casting to attain metallurgical restrictions concerning the reheating of strand surface temperature and metallurgical length.

Metal–mold heat transfer coefficients during horizontal and vertical Unsteady-State solidification of Al–Cu and Sn–Pb Alloys

In this work, metal–mold heat transfer coefficients (h) are determined during unidirectional solidification of Al–Cu and Sn–Pb alloys. The effects of casting assembly (horizontal and vertical), alloy composition, material and thickness of the mold and melt superheat are investigated. By using measured temperatures in both casting and metal, together with numerical solutions of the solidification problem, metal–mold heat transfer coefficients are quantified based on solution of the inverse heat conduction problem. Experimental temperatures are compared with simulations furnished by an explicit finite difference numerical model, and an automatic search selects the best theoretical–experimental fitting from a range of values of metal–mold heat transfer coefficients. Experiments were conducted to analyze the evolution of h during solidification of Al–2, 4.5, 5, 8, 10, 15, 33 wt% Cu alloys and Sn–5, 10, 15, 20, 30, 39 wt% Pb in horizontal and vertical steel chills. The results permitted the establishment of expressions as a power function of time, for different alloy compositions, casting assembly material and thickness of the mold and melt superheat.

A solidification heat transfer model and a neural network based algorithm applied to the continuous casting of steel billets and blooms

This work presents the development of a computational algorithm applied to improve the thermal behaviour in the secondary cooling zone of steel billets and blooms produced by continuous casting. A mathematical solidification heat transfer model works integrated with a neural network based algorithm (NNBA) connected to a knowledge base of boundary conditions of operational parameters and metallurgical constraints. The improved strategy selects a set of cooling conditions (in the secondary cooling zone) and metallurgical criteria established to attain high product quality, which are related to a more homogeneous thermal behaviour during solidification. Initially, the results of simulations performed by using the mathematical model are validated against experimental industrial data, and good agreement is observed, in any case examined, permitting the determination of nominal heat transfer conditions by the inverse heat conduction method. By using the numerical model linked to a NNBA results have been produced determining a set of casting conditions, which has permitted better strand surface temperature profile and metallurgical length to be attained during the continuous casting of SAE 1007 billets and SAE 1025 blooms.

Analysis of metal mould heat transfer coefficients during continuous casting of steel

Abstract Heat transfer coefficients in the mould were determined by the inverse method and they are related to both process conditions and carbon equivalents of steels. Experimental data were obtained from an industrial plant by temperatures measured in moulds of the continuous casting machine by thermocouples placed in the mould wall in known positions. The temperatures are compared to profiles of simulations by the numerical model of both solidification and heat transfer processes previously examined. As a result, the numerical model calculates the heat transfer coefficients in the metal/mould interface for heats cast with different process parameters. The results make possible the determination of expressions for the calculation of the interfacial metal/mould heat transfer coefficients that include the effects of steels grades, mould faces, casting speed, mould taper, mould section and pouring temperatures for a range of process parameters.

The Interrelation between Casting Size, Steel Grade, and Temperature Evolution Along the Mold Length and at the Strand Surface during Continuous Casting of Steel

The present work focuses on the investigation of thermal profiles in copper molds and at the strand surface during continuous casting of different steel grades in an industrial plant. Thermocouples embedded in the mold walls were used to measure temperatures along the mold length. Noncontact pyrometers positioned at different locations along the machine monitored the strand surface temperatures. The experimental results permitted an interrelation between steel grade, mold section (240 × 240 mm, 180 × 180 mm, and 150 × 150 mm), and mold wall, and strand surface temperatures to be established as a function of casting operating conditions. It is shown that the mold outer face (external curved wall) has the highest temperature distribution from the meniscus to the bottom of the mold followed by the inner and side faces, respectively. The deepest meniscus is shown to occur for the 150-mold, and the 180-mold is shown to have the highest temperature profiles along the mold length in all faces examined. Low carbon steels present the highest strand surface temperatures along the machine when compared with those of medium and high carbon steels. When the steel composition is parameterized, it is shown that the 150-mold has the smaller strand surface temperature close to the mold exit when compared with the 180 and 240 molds, and it is shown that this behavior changes after the unbending point.

Microstructural Analysis of the Special Steels Produced by Continuous Casting Process

The objective of the present work is to obtain empirical equations allowing the correlation between secondary dendrite arm spacing (SDAS) (λ2) and cooling rates ( ) of the special steels, produced by continuous casting process. For that, samples were extracted from ingots with three different sections, i.e., 150 × 150 mm, 180 × 180 mm, and 240 × 240 mm, choosing steels with nine different chemical compositions (equivalent carbon contents). Metallographic techniques to reveal the structures, acquisition data system, and image analysis were employed to determine the SDAS in function of its position from surface to center of the ingots. Computer simulations generated by the continuous casting process software (InALC + Artificial Intelligence in the Continuous Casting), developed by the research group, were performed to obtain the relations between the solidification conditions and the cooling rates in operational conditions (chemical composition, ingot section, casting speed, and casting temperature). In the obtained equations for λ2 in function of the position, it was observed in the steels with similar chemical composition that the 150 mm section samples presented lower values when compared with 180 mm and 240 mm sections samples. In the comparison among the steels with similar equivalent carbon contents, the values of λ2 presented an increment in function of the increasing of the sections. In the comparison of steels with same section and different chemical compositions, the equations for λ2 in function of the simulated cooling rates presented an increasing of the λ2 with the increasing of the equivalent carbon contents.

MONITORAMENTO DOS DEFEITOS EM FERRO FUNDIDO USANDO RESÍDUOS DE MODELOS AUTOREGRESSIVOS

The purpose of this study is to monitor the index of general waste irons forecasting nodular and gray using the residues originated from the methodology Box & Jenkins by means of X-bar and R control charts. Search is to find a general class of model ARIMA (p, d, q) but as data have autocorrelation is found to the number of residues which allowed the application of charts. The found model was the model SARIMA (0,1,1)(0,1,1 12 ) . In step of checking the stability of the model