A run-out-table (ROT) in hot strip rolling has a cooling system residing between the last finishing stand and the down coiler. The quality of the final product, such as the metallurgical and mechanical properties and the flatness of the strip, may vary significantly depending upon how the strip is cooled when it passes through ROT. Consequently, many mill engineers and researchers were keenly interested in precise prediction and control of the thermo-mechanical and metallurgical behavior occurring on ROT.Modeling for the precise prediction of such behaviors, however, is a difficult task, due to strong interaction among the thermal, mechanical, and metallurgical behavior, and also due to the three dimensional nature of the problem. As a result, most of the modeling efforts were concentrated either on revealing the local heat transfer characteristics associated with laminar cooling, [1][2][3][4][5] or on approximately assessing the phase evolution. 6,7) Recently, researchers began to recognize the importance of a rigorous treatment of the interaction between the heat transfer and phase evolution, but related works [8][9][10][11] were mostly limited to one dimensional analysis.Described in this paper is an Eulerian finite element (FE) model for the analysis of steady-state heat transfer. Also described are the models for the analysis of thermodynamics and phase transformation kinetics. Then, it is shown that, on the basis of these models, an integrated process model may be developed for the full 3-D, coupled analysis of the thermal and metallurgical behavior of the strip on ROT. Validity of the proposed model is examined through comparison with measurements. Then, a series of process simulation is conducted to demonstrate the model's capability of reflecting the effect of diverse process parameters.
Metallurgical Models
Thermodynamic ModelThe phase diagram, the heat capacity of each phase and the heat evolution due to phase transformation were obtained from the thermodynamic analysis of the Fe-C-Mn system 12,13) using a two-sublattice model, (Fe, Mn)(C, V a ) c/a , where V a denotes the vacancy, and the subscript, c/a, defines the site ratio of the substitutional sublattice to the interstitial one. 12) The phases considered in this study were austenite (g), ferrite (a), and cementite (cm). The heat evolved from the ferrite formation (DH F ) was the heat of reaction, g®a, divided by mole fraction of ferrite formed. The heat evolved from the pearlite formation (DH P ) was the heat of reaction, g®aϩcm. For the formation of bainite, the additional shear energy of 600 J/mol 14) was considered to be required to achieve the phase equilibrium. Thus, the heat evolved from the bainite formation (DH B ) was DH F Ϫ 600 J/mol.The temperature dependent nature of heat capacity for a Fe-C-Mn system, which was considered as the strip material, is illustrated in Fig. 1. Note that the heat capacity of each phase-ferrite, pearlite and bainite, was larger than that of austenite, and showed the maximum value at Curie temperature, due to...
