The trials in March 2007, though demonstrated the significant improvement of the Level 2 model, revealed several new sources of error. After the tests, further improvements could be achieved by optimizing temperature ranges for each temperature region. The temperature range for the third region (lower-temperature region) was narrowed, so that there would not be too many passes in this region. The temperatures with metallurgical meaning, such as the hot/cold forming boundaries, were used as reference in determining the dividing points for temperature regions. By technical definition, the hot forming is the forming conducted over the recrystallization temperature range, while the cold forming is the one below the recrystallization temperature. The flow stress modeling in the hot forming is different from that in the cold forming. Traditional rolling in the hot mills was conducted in the hot forming temperature range. However, today the rolling in hot mills may be carried out below the recrystallization temperature, especially for finishing passes and those passes in the second stage of controlled rolling. Technically, it is cold rolling (it is often referred to as warm rolling to avoid confusion).

The philosophy behind the EOS Level 2 models, which was installed over a dozens of years ago, was primarily for the hot rolling. Due to the invalidity of the flow stress model in the passes below the hot forming range, usually in the finishing passes when this occurs, improvements can be made using a narrowed range in the third temperature region. In this aspect, the Guided Two-Parameter Learning (FIT2G) fits well a narrowed temperature range because it only has two learning parameters (degrees of freedom) instead of three or four, and thus necessitates fewer passes to perform a regression.

The flow stress model was improved for passes with drafts 10% and lower, and for drafts 30% and higher. Those passes were often identified to be with high force errors. Technically, the flow stress formula described in Equation (1) is not valid for the strain below 0.1 [6]. The strain value 0.1 corresponds to a draft of 10%. Unfortunately, many finishing passes were rolled with a draft at or below 10%, and the resultant force error more easily caused shape problems in the finishing passes than other passes because the thickness is smaller. In addition, this same formula is with a relatively narrow valid range of strain, so for a relatively high draft, it introduces errors, too.

In order not to make significant change to the Level 2 source code, the improvement of the flow stress valid range problem was tackled by scaling up the strain for the passes where the strain was below 0.15, and scaling down the strain for the passes where strain was over 0.35. The improvement in this way only required a modification to the function that defines the strain.

The controlled rolling technique is applied at EOS when rolling X-grade and some HSLA grade products. The rolling process is divided into two or three stages by one or two delays. A delay (or hold) begins when the piece reaches a PDI defined intermediate thickness. During a delay, the piece is held until its surface temperature drops to a specified value. A hold involves complicated metallurgical evolution processes. The Level 2 models in EOS, like most others, ignores the metallurgical effects during a hold. This frequently caused errors 10% to 30% in the resume passes (the passes after holds). Some passes often had errors of -10% to 40%. Fig. 4 shows the flow stress errors in the resume passes.

The modification was done with the results of error pattern analysis with empirical formula, so the flow stress for the resume pass was scaled down (or up) by multiplying a factor:

S = a * T + b                                 (3)

In which T is the entry temperature of the resume pass, S is the scale factor, and a and b are constants for a given grade. Constants a and b were calculated from historical data for each model grade with holds. The value of a and b could be stored in the grade file; it may be recommended that a database (file or table) be created to store the constants a and b for all those model grades with a hold.

Fig. 4: Resume Pass Flow Stress Error

Entering into the austenite/ferrite two-phase region was not intended; rather, it was due to inaccurate scheduling. Primarily the metallurgist, through Level 3 production scheduling system, should perform improvement for the problem. Because this problem, as long as it occurs, would cause significant error as showed in the Fig. 2, a quick fix was proposed for the Level 2. First, the system could be set up to allow the temperature coefficient C₂ to be negative, and secondly, narrowing the range of the lower-temperature region. The Guided Two-Parameter Learning is recommended in this case since it requires a very narrow temperature range (or number of passes). For a complete solution of this Two-Phase Region problem, metallurgical modeling for the flow stress should be performed, during which the volume fraction of each phase should be predicted and the flow stress for each material (phase) should be determined.

<To Be Continued>

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