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3.    draft scheduling for improving plate shape (1)

Aa mentioned earlier, a high-quality draft schedule depends on two inseparateable factors: high accuracy of parameter prediction such as that for force and temperature, and superior logics for draft schedule determination. This section assumes that model prediction accuracy for the roll separating force and temperature, etc. has been sufficiently high, so the focus is on the draft scheduling logics.

Poor logic may lead to inappropriate draft schedule that causes plate shape and production problems such as

1. Center buckle, edge wave
2. Kinks, knuckles, etc.
3. Other types of bad finish shape (e.g. head-end turnup/turndown, poor flatness)
4. Too few passes (with the risk for equipment damage and product shape defect)
5. Too many passes (with low efficiency and poor temperature profile)

Level 2 model creates pass schedule for the purpose of satisfying various requirements such as shape, property and productivity. In the followings, the common issues and approaches related to the shape and some aspects of the productivity are discussed.

Flat rolling draft scheduling is primarily based on force induced roll deformation, etc. During the rolling, due to the existence of the roll separating force, there must be roll deformations such as roll deflection and roll flattening. Due to the high requirement for the flatness of the rolled steel, the roll crown (thermal crown and mechanical crown), roll wear and roll deflection, etc. have to be accurately determined. Failure to achieve so would cause e.g. center buckle (if the draft in the width middle is too high) or edge wave (while the drafts in the two edges are too high).

Level 2 model combines roll ground crown, roll wear, roll thermal crown, roll deflection, mill stretch and roll flattening, etc., to form an environment that the draft across the stock width is equal. This is very critical in the finishing passes when the plate is thin.

One of the key functions for the Level 2 model is to select the right roll deflection for a given roll crown. If the Level 2 model cannot accurately determine those roll deformations and the roll crowns, for whatever reason (force inaccuracy, poor deformation model or poor crown model, etc.), the deformation over the plate width may not be equal. If the difference is over a certain limit, defects would be caused.

Prediction of the roll crown also faces various design issues. For example, how to determine the thermal crown while the temperature is different over the roll diameter and across the roll width.

Roll deflection is determined based on the rolling force. A preferred way to predict the roll deflection is the use of elastic finite-element method, which is a practice in e.g. Tippins Level 2. Often, the mill deflection is also considered and integrated into this factor.

One of the key functions for the Level 2 model is to select the needed roll deflection for a given roll crown. Theoretically there is only one optimal roll deflection pattern that can be compensated exactly by the given roll crown. This means that there is only one roll force and thus, only one percentage reduction for a given material, temperature and rolling speed, that fits the roll crown perfectly for creating a perfectly flat roll gap over the width. In the real mill operation, due to interaction of mill equipment (such as roll bending system) and rolling process (such as temperature, speed, etc.), usually a range of the forces (and thus percentage reductions) are accepted. The Level 2 model pursues not only accuracy, but also robustness.

Handling temperature variation should be one of the primary features in a high-quality Level 2 package. Throughout the plate length, there are many variations. Even short plates has changes in temperatures and in flow stress, etc. along the length, particularly for X grades. Even when rolling steel from coil furnaces, the temperature differences can still be over 100˚C. Near the edges of the steel, the temperatures are often about 100˚C colder during rolling and quenching. Current Level 2 models usually do not track this difference or the effects of the temperature on the flow stress and the percentage of plastic deformation near the edge. Draft scheduling should take those variations into consideration.

Because the temperatures in the head end and tail end are usually much lower, the higher roll force leads to larger deformation for the roll and stand (mill stretch) and consequently, a smaller initial roll gap is needed for the head end and tail end, in order to achieve equal draft among the head end, tail end and body. Inappropriate handling to such issues may cause various shape defects (kinks, knuckles, etc.).

<To Be Continued>

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