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Mill Level 2 Model Basics

Automation System. Steel rolling mills are operated with sophisticated automation systems that greatly increase the production efficiency and product quality, and reduce the energy cost. The automation system generally consists of three levels of interactive functions: (1) Level 1 basic process automation, particularly in the level of Programmable Logic Controller (PLC). (2) Level 2 production supervisory and execution system, which provides set point for the Level 1 system and consists of two primary functions, the production management and the process modeling; and (3) Level 3 scheduling and business system. Level 2 collects data from PLC and user input as well as from Level 3 system. It uses the collected data and the data read from its own database to predict rolling process parameters and to execute the production. Finally, Level 2 sends data to the Database Management System (DBMS) such as SQL Server or Oracle (except the old-version Level 2 systems that still store data in flat files).

Level 2 Model. Rolling mill Level 2 model is a substantial portion of the rolling mill Level 2 system. The Level 2 model is, in traditional sense, an expanded roll pass design program, which creates pass schedule (draft distribution and stage plan) based on a long list of influence parameters. One of the primary parameters the Level 2 model takes into account in creating draft schedule is the roll separating force. For a given mill, the roll separating force is the one to determine whether the limits of the mill are reached (force and torque, etc.). On the one hand, a higher draft is preferred to reduce number of passes and to achieve better mechanical properties (in view of controlled rolling); on the other hand, a lower draft is helpful for better shape, especially in the finish passes. The draft schedule should compromise those two conflicting factors. Further factors that have to be considered for the good flatness of the rolled steel include roll crown (thermal, mechanical, and wearing), roll deflection, roll flattening, roll bending and stand deformation, and so on. In particular, any variation in temperature, composition, entry slab size, etc. should be compensated. The high complexity of the problem is far beyond the reach of human experience; a computer system (Level 2 model) has to be used.

One of the most critical areas for the Level 2 model is the Level 2 force prediction. Therefore, in the following sections, particular attention is paid on the force model.

Force and Flow Stress. The roll separating force is the multiplication of the mean flow stress, the projective contact area and the shape factor (Q-factor) [1]. Steel rolling in a pass starts at strain 0 (at the entrance) and ends at the maximum strain (pass strain, at the exit), so the mean flow stress rather than the instant flow stress should be used. The projective contact area increases with roll flattening. The shape factor (Q-factor) accounts for both deformation zone geometry and friction.

Among the factors affecting the roll separating force, the flow stress is the one that bear the effect of material, strain, strain rate and temperature. The strain is usually used as pass strain in the hot rolling, but it should be accumulated strain in the cold rolling. Many rolling passes in the hot mills could be cold rolling as long as the recrystallization cannot be completed (and so, the strain from previous passes cannot be fully removed). Some people term it as "warm rolling" to avoid confusion. If there is phase transformation during the rolling, a different material is involved and so the flow stress formula would fail.

Depending on the rolling practice, flow stress prediction may be based on various empirical formulas. In many Level 2 systems, the following equation is used:


The four parameters C1, C2, C3 and C4 represent the coefficients of material (grade or phase), temperature (T in K), strain (e ) and strain rate (u), respectively. A good feature for this simple formula is that the flow stress and the mean flow stress enjoy the same form and share the same value of C3. The potential problem of it is a very narrow valid range for the strain; the wider the strain range, the poorer the result. In particular, it is not valid for the strain below 0.1 (draft below 10%). In view of the strain rate, this formula applies to most flat rolling practices but is not valid for the high-speed rolling with strain rate over 100/s (e.g., finish passes of wire-rod rolling).

Force Learning. To increase accuracy of the rolling force prediction, the flow stress model maintains separate sets of flow stress coefficients for each model grade. A model grade is created based on the steel grade (chemical composition), the product (type and dimension) and the production practice (e.g., with or without hold). For each model grade, there are three sets of coefficients that are automatically adjusted by the long-term learning function to cover the three ranges (either thickness or temperature) expected during rolling. A Level 2 model should pursue not only high accuracy but also good robustness (accuracy over a wide range of operating conditions).

Many Level 2 models use adaptive learning. The learning includes the short-term learning to shift the values upwards or downwards based on the error in the previous pass, and the long term learning to recalculate and adjust all parameter coefficients (such as flow stress coefficients and heat transfer coefficient) after a qualified piece is rolled. The long-term learning of the Level 2 may use four fitting mechanisms, as showed in the Table 1. If a coefficient is not used for learning (e.g., C4 in FIT3A), it should be set to a medium value rather than zero.

Table 1: Four fitting mechanisms for flow stress learning


Learning Coefficient

Fixed Coefficient


C1, C2

C3, C4


C1, C2, C3



C1, C2, C4



C1, C2, C3, C4


Significance of an accurate Level 2 model. Accurate Level 2 automation system that is with metallurgical principle, modern information technologies for controlling data, methods, and uninterrupted learning historical data to adapt the control for continuous improvement in accuracy, is in demand. Accurate prediction of roll separating force is vital to the good shape of rolled flat products. Draft distribution is usually tied to the force distribution, since certain pattern of force distribution over passes leads to good shape of rolled plate/coil and good equipment utilization. Sometimes, temperature from pass to pass is calculated based on the measured force, so force prediction error also causes temperature error. In addition, a rolling schedule based on inaccurate force prediction may have either more or less passes than needed. More passes than needed leads to lower productivity and higher costs (energy, equipment, labor, etc.), and less pass would cause product shape problem and even equipment damage.

In particular, inaccurate automation system causes tremendous problems and waste in the production scheduling. For a product order applied to a steel mill, the required properties (often, mechanical properties) of steel are specified. The steel mill usually designates a certain steel grade plus certain rolling/cooling procedure to produce the required steel. If the system is sufficiently accurate, the finish product should satisfy all the requirements. However, the automation system may have significant error, so the roll separating force, temperature and draft, etc. may be different from what were expected, and as the result, the product quality may be below what was planned. To guarantee the satisfaction of the property requirements, the steel producer has to plan higher quality of the product than that required by the customer. This causes unnecessary costs for the steel plant. Some plants conduct mill trial-and-error to search the proper rolling procedure for a new product; the cost is tremendous.

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