An integrated finite element-based model is presented for the prediction of the steady-state thermomechanical behavior of the roll-strip system and of roll life in hot strip rolling. The model is comprised of basic finite-element models, which are incorporated into an iterative-solution procedure to deal with the interdependence between the thermomechanical behavior of the strip and that of the work roll, which arises from roll-strip contact, as well as with the interdependence between the thermal and mechanical behavior. Comparison is made between the predictions and the measurements to assess solution accuracy. Then, the effect of various process parameters on the detailed aspects of thermomechanical behavior of the work roll and on roll life is investigated via a series of process simulations.

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...

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An, FE-based, off-line model is presented for the precise prediction of roll thermal profile. The validity of the model is demonstrated through comparison with measurements. Also demonstrated is its capability of reflecting the effect of diverse process variables.KEY WORDS: finite element method; off-line model; roll thermal profile.roll) and strip (JS-SS400) and other process variables selected for process simulation were shown in Table 1. The thermal and mechanical boundary conditions and the FE meshes were illustrated in Fig. 2 and in Fig. 3, respectively. Surface Temperatures of the Roll and StripInvestigated was the transient thermal behavior of the roll-strip system during a very short period of time after initiation of rolling of the first strip. The roll initial temperature, as well as the initial temperature of the strip in the bite region before initiation of rolling, was assumed to be 20°C. It was found that in 0.4 sec after initiation of rolling, the strip surface temperatures at the roll-strip interface as well as the core temperatures of the strip in the bite region almost reached the steady-state temperatures, as shown in Fig. 4. Considering that normally the rolling time would be much longer than 0.4 sec, the present result indicated that ISIJ International, Vol. 40 (2000), No. 8 795© 2000 ISIJ the transient strip temperature distributions may be approximated by the steady-state temperature distributions. It was seen from Fig. 5(a) that the same conclusion may be drawn for the surface temperatures of the roll at the roll-strip interface. However, except at the roll-strip interface, the transient roll surface temperatures were far from reaching the steady-state, as shown in Fig. 5(b). Roll Main Body TemperaturesIllustrated in Fig. 6 was the gradual increase of the roll main body temperatures as rolling proceeded. The temperature distributions in the roll was remarkably axi-symmetric, except in a thin, circular layer encompassing the roll main body where the temperature gradient in the radial direction was very large, especially at the roll-strip interface. The thickness of the thin layer was found to be less than 5 mm or 1.2 % of the roll radius, indicating that its effect on overall roll thermal expansion could be neglected. Also revealed was that the roll main body temperatures, predicted at the completion of rolling of the fifth strip, were only a fraction of the steady-state roll main body temperatures (which were about 65°C), which may be attributed to periodic roll idling. An Off-line Model for the Prediction of RollThermal Profile Prediction of Roll Main Body TemperaturesOn the basis of the characteristics of the transient thermal behavior revealed by process simulation with the integrated FE process model, a simplified approach was developed for the prediction of roll main body temperatures, ISIJ International, Vol. 40 (2000), No. 8 which was described in the following:At any moment during rolling, net heat flux coming into the roll through the entire roll arc at a given plane perpendicu...

Investigated via a series of finite element (FE) process simulation is the effect of diverse process variables on some selected non-dimensional parameters characterising the thermomechanical behaviour of the roll and strip in hot strip rolling. Then, on the basis of these parameters, online models are derived for precise prediction of the temperature changes occurring in the bite zone as well as in the interstand zone in a finishing mill. The prediction accuracy of the proposed models is examined through comparison with predictions from a FE process model.

A finite element-based approach is presented for the prediction of the thermal behavior of the strip occurring in the finishing mill during hot strip rolling. The approach, which is fully coupled and three dimensional, is described in detail. The validity of the proposed approach is examined through comparison with measurements. Then the capability of the approach to predict the detailed aspects of the thermal behavior is demonstrated through an application to revealing the effect of an edge heater.KEY WORDS: hot strip rolling; finite element method; thermal behavior; three-dimensional; edge heater.

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A finite element-based, integrated process model is presented for a transient, coupled analysis of the thermal and mechanical behavior of type 304 stainless steel during hot plate rolling process. The validity of the proposed model is examined through comparison with measurements. The model's capability of revealing the effect of diverse process parameters is demonstrated through a series of process simulation. Discussions are made on the effect of various rolling conditions on the generation of edge seam defect.KEY WORDS: finite element method; hot plate rolling; thermo-mechanical behavior; transient; edge seam defect. Fig. 1. Typical edge seam defect during plate rolling.