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, particular 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, various formulas for flow stress prediction should be used. In many Level 2 systems, the following formula is used:
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(1) |
The four parameters C1, C2, C3 and C4 represent the coefficients of material, 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
