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

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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.

Introduction

The continuous casting process is responsible for most of the steel production in the world, and has largely replaced conventional ingot casting/rolling for the production of semi-finished steel shape products. Fig. 1 shows a schematic representation of a continuous caster and the different cooling zones along the machine. The casters have been implemented with modern equipments for billets, slabs or blooms, multiple casting and process control.

The quality control of continuous casting is fundamental for reducing production costs, processing time, and to assure reproducibility of the casting operation and increase of production. This cannot be achieved without a greater knowledge about the process, incorporating both operational parameters, such as components of the machine, steel composition, casting temperature, and casting metallurgical constraints, such as thickness of solidified shell at mold exit and strand surface temperature profile along the different cooling zones. The use of optimization strategies, such as genetic algorithm, heuristic search, knowledge base, working connected to mathematical models of solidification, can be seen as a useful tool in the search of operational parameters that maximize or minimize any aspect of the dynamic process. The idea of using simulation to optimize a continuous caster is not just a theoretical concept and its practicality has already been demonstrated (Larreq and Birat, 1982; Lally et al., 1991a; Lally et al., 1991b; Kumar et al., 1993; Samarasekera et al., 1994; Spim et al., 1997; Filipic and Saler, 1998; Brimacombe, 1999; Cheung and Garcia, 2001). An expert system for billet-casting problems has been developed to guide caster operators in analyzing quality-related problems and to provide them with a ready source of fundamental knowledge related to caster operation (Kumar et al., 1993). J.K. Brimacombe, I.V. Samarasekera, S. Kumar and J.A Meech projected this expert system. Filipic and Saler proposed and implemented a computational approach to the continuous casting of steel, which consists of a numerical simulator of the casting process and a genetic algorithm for real parameter optimization (Filipic and Saler, 1998). Cheung, Santos, Spim and Garcia have used a heuristic search technique for the optimization of the quality of carbon steel billets (Cheung and Garcia, 2001; Santos et al., 2002).

The present paper describes a software, which was developed and is based on the interaction between a finite difference heat transfer solidification model and a genetic algorithm and a knowledge base. The heat transfer model is validated against experimental results concerning both static casting of Al–Cu and Sn–Pb alloys and continuous casting of a low carbon steel slab and a high carbon steel billet. The software has been used to explore the space parameter settings in order to find optimized cooling conditions, which result in best strand surface temperature profile and minimum metallurgical length.

Section snippets

Mathematical model

The mathematical formulation of heat transfer to predict the temperature distribution and the solid shell profile during solidification is based on the General Equation of Heat Conduction in Unsteady State, which is given for three-dimensional heat flux byρcTt=(kT)+q,where ρ is the material density (kg/m3); c is specific heat (J/kgK); k is thermal conductivity (W/mK); ∂T/∂t is the cooling rate (K/s), T is temperature (K), t is the time (s) and q represents the term associated to internal

Optimization strategies

In this work, an algorithm is developed which incorporates optimization strategies to determine best operational parameters to the continuous caster. The algorithm employs search techniques for finding these operational parameters, including the type and characteristics of mold, mold taper, mold and sprays cooling systems, etc., which are incorporated in a knowledge base. The search includes finding the casting objective of maximum production rate as a function of casting metallurgical

Experimental procedure

To validate the proposed solidification mathematical model and the use of the different fS formulations, the results of the calculations are compared with experimental data obtained in an experimental setup monitored by thermocouples located both in the mold and in the metal. The casting assembly used in static solidification experiments is shown in Fig. 6. The main design criterion was to ensure a dominant unidirectional heat flow during solidification.

Both copper and steel molds were used,

Results and discussion

The temperature files containing the experimentally monitored temperatures during solidification in static molds were compared to the proposed mathematical model with the transient metal/mold heat transfer coefficient, hm/s, described in previous articles (Santos et al., 2001; Quaresma et al., 2000). Fig. 7 shows typical examples of temperature data collected in metal and chill during the course of solidification of Sn–10wt%Pb alloy (Fig. 7A) and Al–4.5wt%Cu alloy (Fig. 7B). These experimental

Conclusions

A mathematical model of solidification working integrated with a genetic search algorithm and a knowledge base of operational parameters has permitted the optimization of cooling conditions (mold and secondary cooling) for the continuous casting of steel billets and slabs. The search method supported by the knowledge base based on metallurgical criteria permits a more homogenous strand surface temperature profile to be attained and with lower thermal gradients between adjacent sprays zones. The

Acknowledgements

The authors acknowledge the financial support provided by FAPESP (The Scientific Research Foundation of the State of São Paulo, Brazil) and CNPq (The Brazilian Research Council). Marco Olı́vio Sotelo is also acknowledged for helping with the computer programming.

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