A MATHEMATICAL & STOCHASTIC MODELLING OF THE CONCASTING OF STEEL SLABS

Transcription

1 A MATHEMATICAL & STOCHASTIC MODELLING OF THE CONCASTING OF STEEL SLABS Tomas Mauder a Josef Stetina a Frantisek Kavicka a Zdenek Franek b Milos Masarik c a VUT FSI v Brně, Technická 2, Brno, ČR, ymaude006@stud.fme.vutbr.cz b SU OPF Karviná, Univerzitní náměstí 3, Karviná, ČR, franek@opf.slu.cz c EVRAZ VITKOVICE STEEL, Ostrava, ČR, milos.masarik@cz.evraz.com Abstract Optimization and control of production of steel slabs on real casters, with the aim of achieving the maximum possible savings and product quality, is unthinkable without perfect knowledge of the course of solidification and cooling, which must be known with the aid of an on-line model of the transient temperature field of the concasting in real time. The functioning of the on-line model is conditioned by the availability of real-time data (as are the pouring temperature, the dimensions of the slab, the chemical composition of the poured steel, the casting speed, the position of the level within the mould, the temperatures of the cooling water within the walls of the mould on the input and output, the flow of water through each mould plate, the settings of the flow of water and the pressure of the air through the secondary-cooling zone, the temperature from the pyrometers within the secondary-cooling zone), which is passed on to the model via the latest information standards. A data warehouse is created from which the data will be processed statistically. Recommended limit values of the deciding parameters are established. Modern mathematical & statistical methods and artificial intelligence methods, based on knowledge acquisition from data, are used to predict defects.. THE ON-LINE MODEL OF THE TEMPERATURE FIELD The on-line model of the temperature field is based on the off-line version that has been described in detail, together with application results, in a number of publications [2, 3]. The development of the software is based on multi-tier architecture. The online model receives data from the first and second level of control of the caster via a communication tier. The correct data is transferred to the tier of the temperature model that carries out the calculation of the temperature field. The calculated temperature field is passed on to the visualisation tier and on to the output communication tier, which sends the data to the storage server and to the quality monitoring system LITIOS. The individual parts of the on-line temperature model are described below. Since the control hardware and software of the caster are significantly heterogeneous and, furthermore, the casting process is continuous, it is necessary to ensure reliability of the communication tier. The communication tier enters data into its own temperature model using the XML/RPC standard over the standard TCP/IP protocol. It can easily be adapted to various hardware and software on the first and second levels of caster control currently, there exist drivers for Siemens and ABB PLCs and for ORACLE and MS SQL databases. Synchronous data (recurring at

2 regular intervals) is recorded every 0 seconds. Other asynchronous information, such as the melt number, chemical analyses, positioning of the tundish and the opening of the tundish are read only when a new event occurs. The communication tier checks the validity of the data collected in this way, i.e. it verifies whether it lies within acceptable limits, or whether or not it has Fig.. The screen of the on-line model in the control room arrived. Erroneous data is replaced by previous correct data or so-called standard values, and then this complete and verified data is passed on to the dynamic on-line model. There are approx. 250 such quantities. The tier of the numerical model carries out the calculation of the temperature field and other aggregated quantities that it sends back to the information system of the steel works. The temperature model calculates the values of approx. 250 aggregated quantities, so there are approx. 500 values every 0 seconds. Fig. 2. The casting technology control system 2

3 The visualising tier enables the operator to monitor the calculated temperature field graphically (Fig. ). This visualising tier is simultaneously a web server. It is therefore possible for technologists and other computer network users to be able to observe all data from the on-line temperature model using a standard Internet browser. The results of the calculated temperature field of the blank of each melt are saved on the storage server for a period of six months. All filtered input data and their corresponding aggregated quantities from the temperature field are stored in the database of the application server where they are recalculated for a specific slab and merged with information on the actual quality of the slab and the sheet-steel produced from this slab. The data from the application server is sent to the prediction system. Another objective of the on-line model is to raise the quality and precision of the data, its mutual interconnections and the qualitative parameters, including the setting of the limit values that should facilitate the decision-making process of the operators and technologists. It is therefore a system that very quickly and accurately displays the real temperature field of the blank during the course of the casting process, including all necessary technological data from the caster. Fig. 2 illustrates the integration of the on-line model into the technology control system of the caster used by EVRAZ VÍTKOVICE STEEL. The control room is equipped with a high performance quad-core computer permanently running the on-line model. Users (i.e. technologists) can load real-time data from the on-line model into their off-line model of the temperature field, perform changes in the input parameters (e.g. alter the secondary cooling, the casting speed). After simulation using the offline model, it is possible to predict the formation of the temperature field. Another objective of the off-line version of the model is to establish causes of defects in the slabs or successively produced sheet steel. The user can load previously recorded temperature field data from the storage server, analyse it using the off-line model, find possible causes of defects and establish corrective action in order for the defects not to recur in future. 2. TRENDS Most quantities from the control system of the caster, including the pyrometermeasured surface temperatures, enter the temperature field software where a number of calculated quantities are added and they are all stored in the application server database. The temperature model operator can select any from the measured and calculated quantities and plot them in the form of trends. Since there are a number of quantities, only the main ones were selected so as to include more effects. For this purpose, a graph containing the casting speed, metallurgical length, length of liquid pool and surface temperatures (calculated by the model and measured using the pyrometers in the same points) was established. The surface temperatures are measured by two pyrometers positioned on the small radius in the centre of the blank approx. in the centres of segments 7 and (Fig. ). Fig. 3 shows an example of real data from the dynamic model of a mm slab upon the intervention of the breakout system. This intervention brought about a drop in the casting speed from.22 to 0.5 m/min and an increase back to the original value. It is interesting to observe the course of the measured temperatures in the unbending point and at the end of the cage where the drop in the casting speed is visible. It is quite obvious that the calculated temperature history will facilitate any decision-making by the operator regarding the control of the caster. 3

4 Casting speed Metallurgical length Length of liquid pool Measured temperature of segment 7 Calculated temperature of segment 7 Measured temperature of segment Calculated temperature of segment Temperature [ C] Metallurgical length [m] Cast length [m] Fig. 3. A drop in the casting speed upon the intervention of the breakout system 3. STATISTICAL PROCESSING OF DATA FROM THE ON-LINE MODEL For each melt, the following statistical quantities are calculated for all measured and calculated values: the arithmetic mean, the minimal value, the maximal value and the standard deviation. The basic statistical quantities are evaluated only from so-called clean data the statistics does not include the transition sections of the first and last melts in the sequence and also the data from any unexpected interruptions in casting. It is advisable to evaluate such situations from trend graphs (see chapter 2 above). In the evaluation of the statistical data, it is necessary to compare the data for the same slab profile and also for the same class or group of steel. This paper presents the graphs of the statistical quantities for three basic slab profiles and only one class of carbon steel (with an average carbon content of 0.6 %) within a period of 2 months of operation of the caster at EVRAZ VITKOVICE STEEL. Figs 4 to 9 illustrate the dependences for a mm slab. Fig. 4 shows the average casting speed (blue) together with the interval of the minimal and maximal casting speed and also the linear trend of the average casting speed throughout the year. Fig. 5 compares the average values of the measured surface temperatures in two points with the average calculated temperatures in the same points. The graphs indicate that the measured and calculated values are practically identical in terms of their trends. Comparing the absolute values, it is possible to see that there are long intervals where the deviation is significant and, on the other hand, there are intervals where the values are identical. Furthermore, there are sequences of melts where one pyrometer is out of operation. The conclusion here is that the calculated values of the temperatures are much more reliable and give values that are much more suitable for the prediction system or the secondary-cooling regulation. Another reason why there can be a difference between the measured and calculated temperatures is the state of the secondary cooling. 4

5 x250 C=0,6 % x250 C=0.6 % Pyrometer Pyrometer 2 Pyrometer mean Pyrometer mean 2 Calculated temp. Calculated temp. 2 Casting seed [m/min] 0.7 Temperature [ C] Meltage sequence Fig. 4. The casting speed of individual melts for a mm slab x250 C=0.6 % Meltage sequence Fig. 5. The measured and calculated temperatures of a mm slab x250 C=0,6 % Metallurgical length [m] Fig. 6. Metallurgical length in 530x250 C=0.6 % Superheat temperature [ C] Fig. 7. Superheat temperature in 530x250 C=0.6 % Pressure [MPa] Fig. 8. Water flow in dependence on casting speed Fig. 9. Water pressure in dependence on water flow 5

6 .4 530x80 C=0.6 % x80 C=0.6 % Pyrometer Pyrometer 2 Pyrometer mean Pyrometer mean 2 Calculated temp. Calculated temp. 2.2 Temperature [ C] Melt sequence Fig. 0. Casting speed of individual mm profile melts x80 C=0.6 % Melt sequence Fig.. The measured and calculated temperatures for mm slab.3 530x80 C=0.6 % 9 Metallurgical length [m] Fig. 2. Metallurgical length in 530x80 C = 0.6 % Superheat temperature [ C] Fig. 3. Superheat temperature in 530x80 C = 0.6 % Pressure [MPa] Fig. 4. Water flow in dependence on casting speed Fig. 5. Water pressure in dependence on water flow 6

7 Pyrometer Pyrometer 2 Pyrometer mean Pyrometer mean 2 Calculated temp. Calculated temp. 2.2 Temperature [ C] Melt sequence Fig. 6. Casting speed of individual mm profile melts Melt sequence Fig. 7. The measured and calculated temperatures for mm slab.4 5 Metallurgical length [m] Fig. 8. Metallurgical length in Superheat temperature [ C] Fig. 9. Superheat temperature in Pressure [MPa] Fig. 20. Water flow in dependence on casting speed Fig. 2. Water pressure in dependence on water flow 7

8 In Figs 6 and 7, the monitored quantity is shown in dependence on the casting speed where each melt is indicated by a blue bubble whose radius corresponds to one standard deviation of the relevant quantity. Fig. 6 shows that there is an almost linear dependence between the metallurgical length and the casting speed corresponding to the solidification constant K = 25.5 mm 2 /min. Fig. 7 presents the dependence of the superheat temperature on the casting speed. The caster has a total of 3 cooling circuits here the graph shows the data from the secondary cooling circuit 5, which works approximately in the centre of the arc on the small and large radius. The graph in Fig. 8 shows the classic dependence of the cooling water on the casting speed, where the course of this dependence should correspond to the set cooling curve. The characteristic of the cooling circuit is the dependence of the pressure on the flow of the cooling water (Fig. 9). Here, there occur changes in this curve throughout the year due to changes of and manipulation with the cooling nozzles. The graphs in Figs 0-5 show the same dependences that had been presented for the slabs, now for a mm profile. The graphs indicate a similar dependence. The solidification constant for this dimension is K=23.5 mm 2 /min. The graphs in Figs 6-2 show the same dependences that had been presented for the and 80 mm slabs, now for a mm profile. The graphs indicate a similar dependence. The solidification constant for this dimension is K=23.3 mm 2 /min. 4. CONCLUSIONS This paper introduces three basic ways of utilizing the results of the dynamic online model of the temperature field in a real caster operation. The operator or user of the computer network of the steelworks can monitor the current temperature field, including the information on the current metallurgical length and surface temperatures. Another possibility is to monitor the quantities in the form of trends, always after the melt has finished or in the case of an irregular situation. The last online possibility is to monitor the statistical quantities from individual melts []. In the case of trend graphs, it is suitable for the trends to be supported by graphic output of limits/intervals, within which the quantity regarding the specific dimension of the slab and class of steel should be. With statistical graphs, it is useful to display the longer histories of the values from previous melts. REFERENCES [] BRIMACOMBE, J. K. The Challenge of Quality in Continuous Casting Process, Metallurgical and Materials Trans, B, Volume 30B, 999, pp [2] STETINA, J., Optimization of casting parameters of billets using a temperature field model. Thesis, Technical University of Ostrava, Czech Republic [3] STETINA, J.; KAVICKA, F.; DOBROVSKA, J.; CAMEK, L.; MASARIK, M. Optimization of a concasting technology via a dynamic solidification model of a slab caster. Materials Science Forum (5). p ISSN ACKNOWLEDGMENTS This analysis was conducted using a program devised within the framework of the GA CR Projects No. 06/09/0940, 06/08/