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FIELD OF APPLICATION
The present invention relates to a method for the prediction of coiling temperature over the length of hot rolled coil at run-out table.
In particular, the invention relates to an adaptation technique applied to level-II Automation for microstructural prediction for hot rolling. The developed method minimizes the heat transfer coefficient error such that the actual coiling temperature is close to the predicted temperature from the mathematical model. The resultant close variation of coiling temperature in turn provides better prediction of mechanical properties over the length of the coil.
BACKGROUND OF THE INVENTION
Typically run-out table of a hot strip mill is equipped with a coiling system consisting of eleven numbers of water banks between the last finishing stand and the down coiler. The run-out table has 2*34 cooling nozzles from eleven water banks, comprising of 10 banks of macro cooling and one bank of micro cooling.

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The use of mathematical model enables one to get the details of the temperature profile and the cooling rate over the length of the coil. To obtain the temperature profile of run-out table, a numerical model has been developed to obtain the through-thickness coiling temperature of the strip.
Due to the complex nature of heat transfer mechanism in run-out table, reported numerical models in literature are either very plant specific or totally theoretical. No general consensus has been established so far about the particular method to determine the temperature profile. Previous numerical studies (reported) have found the heat transfer coefficient in a round about way or from experimental method by measuring the water jet diameter and coolant flow.
Although, Guo [1] has not used any adaptive technique, but the power law expression for heat transfer coefficient has been able to represent the predicted temperature of the strip over the length of the coil very closely with the measured values. Literature indicates the use of adaptive technique but in a different way for the control of the coiling temperature. Kato et al. [2] has developed a different new cooling method for low temperature cooling- With the development of new cooling nozzles in their study, the uniform cooling abjlity is maintained even with the changes in heat transfer coefficient and thus the possibility of nucleate boiling is avoided. A heat transfer coefficient correlation, which is a power law of water flow density, strip velocity, and strip temperature, has been developed in the same study. After incorporation of the same heat

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transfer coefficient correlation, the mathematical equation has been modified with an adaptation technique. The adaptive control employed compensates the water-cooling effect and compensates also the modelling error. The adaptive control uses the performance index to be minimized the difference between estimated and actual coiling temperature. By this method, the standard deviation between actual temperature and predicted temperature has been found to be ± 13° C.
Auzinger et al. [3] have developed a run-out table cooling model, which is a part of model for microstructural evolution during rolling. To meet the target values of coiling temperature, it is mentioned that the cooling model has taken help of an adaptation technique without any discussion of it. All process data of importance, including finishing temperature, cooling pattern (on / off), strip speed, coiling temperature, etc., are collected for different sections of the strip and a correction has been made on heat transfer coefficient at strip-coolant interface to minimize the difference between prediction and measurement. The result of long-term adaptation is used for the next strip of the same class. Shimoda and Wakamiya [4] have used a control system whereby the heat flux coefficient for water cooling is adjusted by recursive processing of past history data. Van ditzhuijzen et al. [5] have applied a control system for the calculation of required number of sprays in run-out table bed for getting the measured temperature close to the model prediction and determined the adaptation coefficients of the five no-linear models from the on-line data of the plant. However, the details of the function / models are not described in their work.

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The details of the adaptation technique for close prediction of coiling temperature in comparison to the measured temperature has not been found in open literature.
A need therefore, existed for developing a technique for prediction of coiling temperature over the length of hot rolled coil at run-out table.
SUMMARY OF THE INVENTION
The main object of this invention is to achieve the predicted coiling temperature from a Level-II on-line model as close as possible to the measured coiling temperature (actual) by the use of an adaptation technique.
This and other objects of the invention are achieved by developing an adaptation technique and applying it in the numerical simulation to predict the coiling temperature. The invention is an adjustment made on the mathematical method and the method of its implementation in Level-II model. The invention relates to capturing of online data, process them to obtain the heat transfer coefficient for a particular thickness after use of the adaptation technique and then delivering the prediction of temperature profile of the strip over the length of the coil, with the variation of coiling temperature as small as possible in relation to the measured temperature from the level-2 automation.

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As the work for the present invention started with the main focus on on-line prediction of the temperature over the length of the run-out table, the emphasis was more on the quick response of the prediction of the coiling temperature with the change of the valve opening or closing for the water banks. The numerical code has been developed with total base on the level-2 automation to record the opening / closing of the valves. With a view to match the measured temperature profile over the length of the coil, an adaptation technique has been evolved to modify the mathematical model so as to obtain a predicted value of temperature close to the predicted one.
Thus the present invention provides a method for the prediction of coiling
temperature over the length of hot rolled coil at a run-out table, comprising the
steps of: developing an on-line mathematical model for coiling temperature
prediction in run-out table of hot strip mill using transient heat conduction
equation: *,wherefrc Wfcare density, specific heat and
thermal conductivity respectively; developing heat transfer coefficient equations
for different thickness of the strip; developing an adaptation technique for
adjustment of the heat transfer coefficient for the next sequence using the
equation h N +1 = h N + [ (Ts)Pred - (Ts)Actual] [ T-> h] where
hN+1 ; Heat transfer coefficient for the next sequence.
hN : Heat transfer coefficient for the present sequence.
(Ts)pred : Predicted value of strip temperature at the present sequence.
(Ts)Actual : Measured coiling temperature at the next sequence.
T -> h : The increase in value of h for 1-degree rise in T,
strip surface temperature; and coupling said adaptation model with said online model for reducing discrepancy between measured value and predicted value of coiling temperature.

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BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
The invention can now be described in detail with the help of the figures of the accompanying drawings in which:
Figure 1 shows schematic diagram of run-out table in hot strip mill.
figure 2 shows the temperature profile over the length of the coil without adaptation technique.
Figure3 shows the temperature profile over the length of the coil with adaptation technique.
DETAILED DESCRIPTION
In the on-line model, a one dimensional parabolic heat conduction equation was solved with initial condition and the boundary conditions, which are in general heat transfer coefficient. The area of the strip under the water-cooling is a complex phenomenon of conduction to the strip and the convection mechanism by the water.


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The equation used in the numerical model is:
whereP, c and K are density, specific heat and thermal conductivity respectively. The last term in the right hand side, heat generation term during phase transformation during run-out table cooling, plays an important role. The whole length of the run-out table is subdivided into number of zories. Finish rolling temperature after the last deformation in hot strip mill is the initial condition and the heat transfer coefficient has been used in different zones.
For the use of heat transfer coefficient at water-strip surface a correlation has been developed in terms of the strip surface temperature, the details, which are described in other patent submitted. The corresponding correlation for the heat transfer coefficient of different grades of steel have been found to follow the correlation: H= h (Ts) and the form of equation is polynomial. The constants of the polynomial were obtained through statistical regression model. An on-line model needs simplification and tuning for the length of the coil. The following adaptation technique provides the necessary tuning of the on-line model.
The coiling temperature is measured by the pyrometer near the down coiler. The data acquisition frequency is 1 sec. Once the value of the temperature predicted by the above model is compared with the measured temperature (by pyrometer) for the whole length of the coil, it has been observed to have a better agreement at the tail end of the coil. This is because the initial approximate heat transfer coefficient was developed from tail end of coil data. Hence it offers a coiling temperature close to the measured coiling temperature, the matching is better a the tail end.

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Error or deviation from the measured value of temperature arises from modelling error similar to the above or arising from other approximation. To obviate them, we need to match with the measured coiling temperature from pyrometer. To overcome this problem, an adaptation technique has been put into use. A correction has been introduced in the heat transfer coefficient term, so the heat transfer coefficient in the next sequence or next point over the length of the coil is adjusted. To have a better match for the whole length of the coil or to reduce the deviation of the predicted temperature with the measured values of the coiling temperature, the following equation is used in the adjustment of heat transfer coefficient for the next sequence:
hN+l= hN + [(Ts)pred - (Ts)Actual][T -> h], (2)
rlN+i : Heat transfer coefficient for the next sequence.
hN : Heat transfer coefficient for the present sequence.
: Predicted value of strip temperature at the present sequence.
(Ts)Actual : Measured coiling temperature at the next sequence.
T^h : The increase in value of h for 1-degree rise in T,
strip surface temperature.

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The calculated coiling temperature is compared with the measured coiling temperature. The result from this numerical study is found to be reasonable.
By using the adaptation technique, a close agreement has been observed for the predicted temperature profile over the length of the coil with the measured temperature profile over the length.
The computer screen of the plot of the temperature profile before the use of adaptation has been presented for a coil in Figure 2. The above adaptation technique has been applied in the run-out table cooling model and the simulated temperature profile follows the measured temperature profile very closely. The predicted temperature from the above model has been found to have ± 15P C variation when compared with the measured temperature. The corrected model has been applied in hot strip mill of Tata Steel, India for a wide range of grades steel with thickness ranging from 1.6 to 6 mm. The reliability has been found to be 80 %. The on-line model with the adaptation technique has been running for more than 3 months successfully with more than thousand of coils. Figure 3 displays the representative use of adaptation technique for a rolled strip of 2.5mm. Our result for the temperature profile over the length of the coil for one grade of steel, following the use of the above mentioned adaptation technique, has been depicted in Figure 3, which has + 15° C variation from the measured temperature. The yellow colour represents the predicted value by adaptation technique from the model, while the green colour displays the actual (measured) temperature from the pyrometer.

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WE CLAIM
1. A method for prediction of coiling temperature over the length of hot rolled coil at run-out table, comprising the steps of:
- developing an on-line mathematical model for prediction of coiling temperature in run-out table of hot strip mill using a transient heat conduction eauation

where P , C and K are density, specific heat and thermal conductivity respectively;
- developing heat transfer coefficient equation for different
thickness;
- developing an adaptation technique for adjustment of the heat
transfer coefficient for the next sequence using the equation

where
hN+1 : Heat transfer coefficient for the next sequence.
hN : Heat transfer coefficient for the present sequence.
(Ts)pred : Predicted value of strip temperature at the present
sequence.

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(Ts)Actual : Measured coiling temperature at the next sequence.
T -? h : Trie increase in value of h for 1-degree rise in T,
strip surface temperature; and
coupling said adaptation model with said on-line model for reducing
discrepancy between measured value and predicted value of coiling
temperature.
2. The method as claimed in claim 1, wherein said adaptive model is
integrated with said on-line model.
3. The method as claimed in claim 1, wherein said adaptation technique is
tested for steel strip of various grades and thicknesses like grades D, DD
and EDD, CRM-CQ steel and for the strip of thickness ranging from 1.6. to
6mm.
4. The method for prediction of coiling temperature over the length of hot
rolled coil at run-out table, substantially as herein described and
illustrated in the accompanying drawings.

The main object of this invention is to achieve the predicted coiling temperature from a Level-II on-line model as close as possible to the measured coiling temperature (actual) by the use of an adaptation technique.
This and other objects of the invention are achieved by developing an adaptation technique and applying it in the numerical simulation to predict the coiling temperature. The invention is an adjustment made on the mathematical method and the method of its implementation in Level-II model. The invention relates to capturing of online data, process them to obtain the heat transfer coefficient for a particular thickness after use of the adaptation technique and then delivering the prediction of temperature profile of the strip over the length of the coil, with the variation of coiling temperature as small as possible in relation to the measured temperature from the level-2 automation.

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As the work for the present invention started with the main focus on on-line prediction of the temperature over the length of the run-out table, the emphasis was more on the quick response of the prediction of the coiling temperature with the change of the valve opening or closing for the water banks. The numerical code has been developed with total base on the level-2 automation to record the opening / closing of the valves. With a view to match the measured temperature profile over the length of the coil, an adaptation technique has been evolved to modify the mathematical model so as to obtain a predicted value of temperature close to the predicted one.

hN+1 ; Heat transfer coefficient for the next sequence.
hN : Heat transfer coefficient for the present sequence.
(Ts)pred : Predicted value of strip temperature at the present sequence.
(Ts)Actual : Measured coiling temperature at the next sequence.
T -> h : The increase in value of h for 1-degree rise in T,
strip surface temperature; and coupling said adaptation model with said online
model for reducing discrepancy between measured value and predicted value of
coiling temperature.