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Note: (1) Models discussed here contains only those developed between 1995 and 1999. They are in Process Industry. They do not include another sets of the models, also over 100 sets in Discrete industries. Neither do they contain models in advanced materials (e.g. about 50 sets on 5G materials). (2) This portion of the model demonstrates importance of model in describing Engineering Know-how.

Rolling - Mechanical and Metallurgical Aspects

Mechanical aspect. (We may image the steel inside two calendar rolls) With a reduction in height during rolling, metal moves towards direction of width (spread) and length (elongation, forward slip and backward slip). The metal flow and force and power requirement depend on height reduction, roll diameter, shape of deformation zone, speed, temperature, steel grade, interstand tension, etc. Due to forward slip, stock exit speed is higher than roll circumference speed. In grooved rolling, average roll diameter should be used instead of collar diameter.

Metallurgical aspect. Both softening and hardening phenomena exist in a rolling process. During rolling there exists dynamic recrystallization in the stock. In the interpass time, static and metadymical recrystallization and grain growth may happen. In order to achieve good mechanical property of a rolled product, grain growth and phase transformation should be controlled. Desired microstructure could be achieved by both controlled rolling and controlled cooling.

Interaction. It often happens that recrystallization is only partially completed in modern rolling process (normally in lower temperature than earlier). In this case, a given pass should inherit a portion of the strain from former passes. For example, when a pass strain is 0.3, the effective strain, which should be used on for force and torque calculation, could even be 0.5 or more. Besides, initial grain size has effect on forming resistance. On another hand, strain and strain rate affect microstructure change; possible non-homogeneity in local reduction may result in different local temperatures and thus different local microstructures. In general, the interaction during low temperature rolling plays more important role than in high temperature rolling.

Mathematical models. Today, technological development has made it possible to take into account major factors of rolling process, even though many of them (e.g. effective strain) were neglected years ago. Also, advance in computer technique has made it affordable to acquire more detailed information of the process. For example, 5 years ago (Note: the article was written in 1999) it was still expensive to determine local metal flow during rolling for I-beam, angle, U-section, etc., especially with finite element simulation. Today, the computational cost has become much lower. So a combination of empirical procedures and Finite element method may provide a good solution in the area. For a product with relative simple cross-section, empirical models might be sufficient to simulate the production processes. In this case, finite difference method could be used to determine temperature.

The Aim of the Work

The aim of the work is to develop a whole series of mathematical models to simulate every production stage (casting, rolling, controlled cooling, for both mechanical and metallurgical processes). The model should consist of empirical models, finite element model and finite different model. They may cover production processes of the major products (strip, rod, bar, I-beam, angle steel, U-section, railroad rail, etc.).

The mathematical models can be used, either to upgrade an existing mill-management system to expand functions and to increase prediction accuracy, or to build a new mill-management system. In addition, since most of the empirical models are from evaluation of experiment results and site data, they can also help to build a data base. The mill-management system based on the models could be employed to simulate, plan, control and optimize various production process. As example, a system based on the models may be applied to:

  • Optimize thermomechanical rolling of an existing mill. During rolling in low temperature with high reduction, a high prediction accuracy for load and power requirements can make an adequate utilization of equipment capacity and ensure that the capacity limit is not exceeded.
  • Optimize temperature control system (controlled water cooling or controlled air cooling) for desired temperature profile in every stage of production process.
  • Tolerance improvement and new production process design for the products with complicated cross-section form. Due to a complicated deformation, high quality model, especially FEM model is required.
  • Optimize local metal flow during thermomechanical rolling of sections, e.g., to achieve a most possibly homogeneous deformation in web, flange and the transition area during I-beam rolling.

Example of Mathematical Models

1. Empirical Models

(1) Metal flow

  • spread during rolling (evaluation and improvement of approx. 10 different methods)
  • forward slip during rolling (evaluation and improvement of 5-10 different procedures)
  • average roll diameter, work diameter and rolling speed
  • tension correction for spread and forward slip
  • steel grade or material correction for spread and forward slip
  • free side contour of the stock after rolling
  • homogeneity of local metal flow (especially for rolling of complicated sections)

(2) Force, torque and power requirement

  • mean flow stress
  • roll separating force (evaluation and improvement of approx. 10 different methods)
  • contact area (evaluation and improvement of approx. 5 prediction procedures)
  • shape factor in function of roll gap geometry (for some procedures of force prediction)
  • lever arm ratio in function of roll gap geometry and rolling process parameters
  • rolling torque, power requirement
  • effective strain, especially during low temperature, multi-pass rolling
  • force, torque and power during high speed rolling (strain rate up to over 3000/s)
  • tension correction for force and power requirements

(3) Roll deformation, strength and mill vibration

  • elastic deformation of rolls and stand
  • stress concentration in the roll neck
  • roll strength and stand capacity
  • roll material
  • vibration of stock, roll and stand, especially in high speed rolling

(4) Heat transfer and temperature

  • heat transfer and heat balance during casting
  • heat loss and temperature process during transportation on roll table
  • temperature and heat balance during reheating
  • energy balance and temperature process during rolling
  • interactive relationship between temperature and power requirement during rolling
  • heat transfer during controlled air cooling
  • heat transfer during controlled water cooling and emission cooling

(5) Microstructure formation

  • phase transformation during casting
  • austenite grain size change during casting
  • grain growth during billet transportation
  • grain growth during reheating
  • dynamic recrystallization during rolling
  • static and metadynamic recrystallization in the interpass time
  • grain growth in the interpass time
  • phase transformation during controlled water cooling and controlled air cooling
  • mechanical properties after rolling and controlled cooling

(6) Data base

  • flow stress in function of strain, strain rate, temperature and initial grain size
  • heat transfer coefficient during rolling, depending on scale formation, roll cooling, pressure
  • heat transfer coefficient during controlled water cooling, in function of water flow (GPM), flow speed (FPM), water temperature and water pressure
  • heat transfer coefficient during controlled air cooling, in function of air flow (GPM), flow speed (FPM), air temperature and air pressure
  • Friction during various rolling processes, in dependence on scale formation, stock and roll material, relative speed stock/roll, rolling temperature, roll pressure and gap geometry, etc.
  • Specific heat in function of temperature
  • E-modulus and poisson ratio in various temperatures
  • Other thermal and mechanical data such as thermal conductivity or temperature conductivity, density

2. Finite Element Model and Finite Difference Model

Finite difference model could be employed to determine temperature distribution and average temperature during casting, reheating, interpass cooling, rolling and controlled cooling, if the empirical models are used to simulate a production process.

Finite Element Method can be used in two main areas: to analyze very complicated production process (such as rolling of complicated sections), and to determine local metal flow, local temperature and local microstructure. The main disadvantages of the FEM application exist in the relatively high computational cost and various technical difficulties. To solve such problems, a special FEM code could be developed. The code should be capable of automatic simulation with low cost and high accuracy. Following FEM models could be used for the FEM code:

  • Model for automatic simulation of rolling process. The user only needs to fed in the necessary rolling process parameters (such as groove and roll dimensions, roll gap, speed, temperature, billet form and billet material) to perform a high quality FEM simulation. This is possible because all the long-product rolling processes are actually similar to each other. The only difference between them exists in the cross-section form of grooves and billets. The meshing process could be done automatically or according to simple instructions of the user. It might be also possible to model settings for time step and convergence errors, as function of mesh data and forming parameters.
  • Deformation adapted meshing and remeshing model. With a finer mesh being used in the deformation zone, coarser mesh should be automatically employed for the part(s) of stock outside the deformation zone. With it an analysis might require only 30-50% CPU time of that with a normal model.
  • A simplified FEM model for local parameter determination at an extremely low computational cost. With slab method to determine parameters in the length direction, and FEM method to predict parameters over the cross-section, the calculation time could be tremendously reduced. If cross-sectional reduction, forward and backward slip, etc. can be provided by a roll pass design program, then the determination of local metal flow, temperature and microstructure, etc. in roll gap could take only approx. 0.5% time of those with a normal model.
  • Multi-pass rolling model: With a reduced interstand distance and adapted heat transfer and microstructure models, time for multi-pass hot rolling could be heavily reduced while all the mechanical and metallurgical features could be maintained. Special attention should be paid to keep the same microstructure as with real interstand distance.
  • Models for liquid-solid two phase rolling can also be generated to describe mechanical, thermal and metallurgical features for a combined casting and rolling process. The model are particularly attractive to mini-mill developers and operators.

The Finished Work

A whole series of empirical models for rod and bar rolling and controlled cooling have been established. They enable the prediction for metal flow (spread, forward slip), speed, force, torque, power, temperature and microstructure to be with high or sufficient accuracy. Till now there is already no problem to predict both mechanical and metallurgical parameters for heating, rolling, controlled cooling and interpass air cooling, and for some steel grades, mechanical properties of finish product. Following published and unpublished research results were employed to develop the process models:

  • Results from my former institute in Germany. The institute built a four-stand rod mill for research in early 80s, in which all major parameters can be measured and controlled. After that, the institute spent over 15 years to study the metal flow, force and power requirements and microstructure formation during rod rolling.
  • Morgan lab mill data, from a five-year rolling test performed in Round-Oval and Ova-Round pass sequence.
  • Various site data collected from rolling mills, such as measurement made in ASW, USS-Kobel, etc.
  • Published research reports collected earlier from Germany, such as StahlEisen report series, publication from Aachen, etc., together with some Japanese and Finnish publications.

A complete FEM model with high prediction accuracy and low computational cost has been established. Application of the FEM model in simulation of angle steel rolling, I-beam rolling, strip castrolling with liquid core, and wire rod rolling has demonstrated the high quality of the model. A specially simplified FEM model with sufficient accuracy and extremely low computational cost (approx. 0.5% of those with normal model) was also built up. This simplified model could be incorporated into a roll pass design program to perform microstructure simulation.

A great number of material data were collected from various measurements, and modeled as function of forming parameters. Flow stress for a wide range of steel grades was modeled as function of strain, strain rate, temperature and initial grain size. Some measurements for E-modulus were done. Heat transfer coefficients during rolling, water-cooling and air-cooling, as well as thermal conductivity were measured with various experiments. Data for specific heat, coefficient of thermal expansion, Poisson ratio were also collected in various rolling temperatures.

A great number of mathematical models, process data and material properties have been published in various research reports, technical papers and other sources. After verification and improvement with rolling mill site data and certain new experiment results, the published models and data could also be used. Of course, in evaluation of published data and mathematical models, a very strong technical background and excellent understanding of the production process are necessary. In addition, several major languages such as English, German, Japanese and Chinese are also very important, since China, Japan, USA and Germany are the top 4 of the steel production and do most research and development in the world.



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Bingji (Benjamin) Li 2009. All rights reserved.