Combination of inverse problem and neural network for thermal behaviour calculation of mould process based on temperature measurements in plant trial

Abstract

Heat transfer between mould and strand has a critical influence on billet quality, caster productivity and operating safety. It is very important to obtain the correct distributions of temperature and heat flux, and many studies are made on the calculation methods of heat transfer between strand and mould, aiming to reduce the computation time and improve the calculation accuracy. In the present paper, based on measured data of temperature and heat flux during round billet continuous casting, the calculation method which combines the online measurement data and numerical simulation was investigated. Through identifying the local thermal resistance and its distribution between the mould and the strand by an inverse heat transfer model, the heat flux and shell thickness profiles were calculated. To avoid the iterative solution by inverse model, a faster alternative model using an artificial neural network was developed to predict the thermal resistance from the measured temperature. After training, there is an exact correspondence between the observed temperature values and the thermal resistance. The calculation results obtained by the combination of neural network and numerical simulation can correctly reflect the characteristics of non-uniform heat transfer around the mould circumference, which provides a worthwhile and applicable method for online calculation and visual technology of heat transfer and solidification in continuous casting mould.     

Continuous casting mould powder evaluation

Abstract

A continuous casting mould powder must satisfy various requirements including thermal insulation, chemical insulation, inclusion absorption, lubrication, and promotion of uniform heat transfer from the solidifying steel strand to the copper mould. The relative importance of these properties varies according to the type of steel cast, the prevailing casting conditions, and the end steel requirements. Development of mould powders at Corus UK Ltd involves plant based trials of different powders whose properties influence the above characteristics of which heat transfer is a major consideration. Particular use is made of mould thermal monitoring which, although primarily designed for sticker breakout detection, is now finding increasing use as an investigative tool in mould slag assessment. Both static and dynamic plant data are now available relating mould slag heat transfer performance to casting conditions and this paper describes some recent investigative work carried out by the Aluminium & Steel Casting Department of Teesside Technology Centre, Corus UK Ltd. The study shows that using a combination of plant based observation and laboratory analysis, a greater depth in understanding of mould powder performance can be realised, yielding important information for future powder development.     

Mould heat transfer and continuously cast billet quality with mould flux lubrication Part 1 Mould heat transfer

Abstract

With the drive to cast higher quality, many minimills are adopting mould powder as a lubricant for the continous casting of steel billets. Over the past three decades considerable experience has been accumulated on the relationship between mould behaviour and billet quality for oil lubrication, but comparatively few studies have been conducted for mould powder lubrication. This study, conducted at a Canadian minimill, involved instrumenting four faces of a copper mould with thermocouples and monitoring mould temperatures during casting of 208 × 208 mm billets with mould flux lubrication. Billet samples were also taken to coincide with periods of measurements. Mould temperatures were monitored for two different mould powder compositions, for different mould oscillation frequencies, two mould cooling water velocities, and a range of steel compositions. An inverse heat conduction model was developed to calculate mould heat transfer from the measured temperatures. In this paper, which is the first part of a two part series, details of the inverse heat conduction model and mould heat transfer data are presented. The results obtained for mould flux lubrication have been compared with those for mould heat transfer for oil lubrication. For peritectic steels, with carbon content in the range 0·12–0·14%, it was found that lubricant type has little influence on the measured mould heat flux distribution at the centreline of a face. The peak mould heat flux was found to be approximately 2500 kW m^-2 . In contrast, for medium carbon steels, mould heat transfer with mould powder was significantly lower than when oil was employed as a lubricant. For instance, at the meniscus, the peak heat flux with mould powder was approximately 2500 kW m^-2 , which was half that recorded with oil as a lubricant. The influence of oscillation frequency, mould cooling water velocity, and mould powder type on mould heat flux has also been presented.     

Analysis of variability and non-uniformity of mould heat extraction for round billet continuous casting in plant trials

Abstract

Maintaining a stable and uniform heat transfer from steel shell to mould is important to produce high quality casting billet. In the present paper, a large amount of measured data of heat flux and temperature for round billet continuous casting mould from a plant trial has been analysed to shed light on the variability and non-uniformity of mould heat transfer around the perimeter. The results show that the variability and non-uniformity of heat extraction from the steel through the mould is affected slightly by operational parameters, such as pouring temperature, casting speed, meniscus, electromagnetic stirring current, but strongly by the steel carbon content and mould powder type. The installation of the mould in caster machine determines the magnitude of non-uniformity of heat transfer to a great extent. The relative root mean square (rRMS) of mould heat flux, presenting the variability and non-uniformity of mould heat transfer around the perimeter in transverse section, has wider range of variation and higher mean value compared with that of temperature. When the abnormality of heat transfer happens, such as deposit, the non-uniformity of mould heat transfer is also studied.     

Abnormal transient phenomena in the continuous casting process: Part 2

Abstract

This paper is the second of a series of two describing abnormal transient phenomena observed during online monitoring of a billet continuous casting machine. Special attention is paid in Part 2 to in mould solidification. A mould heat flux drift phenomenon (HFD) has been detected, but only for mould powder basicities larger than 0·8. The HFD is related to a decrease of the heat flux in the lower part of the mould and an increase in both the billet-mould friction force and mould thermocouple variability. Results of tests changing the mould powder grade during casting have provided help in explaining the HFD. The probable reason for the HFD is crystallisation of the glassy slag layer. The heat flux ratio parameter (HFR), defined as the ratio between the heat flux in the lower part of the mould and the heat flux in the upper part of the mould, has proved to be a good tool for judging the casting performance of a mould powder.     

宽厚板连铸黏结漏钢的工艺因素

以钢厂宽厚板连铸黏结漏钢的实测样本为基础,重点考察了断面、拉速、液位等主要工艺因素对铸坯黏结的影响,统计和分析了黏结发生时的结晶器热流及其变化规律,对可能诱发黏结的浇铸参数和结晶器热流等进行了分析和探讨.      

Dynamic pressure in mould flux channel during mould non-sinusoidal oscillation

Abstract

Based on the lubrication theory of mould flux, a mathematical model of dynamic pressure in mould flux channel was developed, and the distribution of dynamic pressure and its variation during non-sinusoidal oscillation were investigated. The effects of casting speed and non-sinusoidal oscillation parameters, including the degree of non-sinusoidal operation (non-sinusoidal factor), amplitude and frequency of oscillation on the dynamic pressure in the mould flux channel, were studied. The results indicate that the maximum negative pressure is decreased, and the maximum positive pressure is increased with increasing non-sinusoidal factor. The optimum value of non-sinusoidal factor is ～0·2. With increasing amplitude and frequency of oscillation, both the negative and positive pressure are increased; moreover, the increment of positive pressure is obviously greater than that of negative pressure; especially when the oscillation frequency is increased, the increment of negative pressure is very little. When the casting speed is enhanced, the negative pressure is increased, but the positive pressure is decreased. Therefore, if the casting speed is increased, the oscillation amplitude needs to be increased, as well as the oscillation frequency needs to be decreased properly. With these adjustments, the positive pressure in mould flux channel is nearly unchanged. The actions of strand demoulding and cracks welding are kept effective. Moreover, the negative pressure in mould flux channel is increased properly, which causes the flux consumption to increase, so the mould lubrication is improved. Finally, the strand surface quality is improved greatly, and breakout can be avoided. The applicability of the optimised non-sinusoidal oscillation parameters for the two kinds of casting speed has been proven by industrial practice.     

Challenge to control mould heat transfer during thin slab casting

Abstract

At the thin slab caster of Tata Steel, IJmuiden, mild cooling mould powders were introduced with the aim to control the mould heat transfer during casting. These mild cooling mould powders are characterised by specific values of basicity, solidification point and chemical composition. Application of these mould powders resulted in a redistribution of mould heat transfer during casting, i.e. a reduced and more stable mould heat transfer in the critical upper part of the mould and an increased mould heat transfer in the lower part of the mould. The average mould heat transfer and hence the shell thickness at mould exit are comparable to the standard powder. The application of mild cooling mould powders also resulted in improved solidification behaviour of the steel shell. A thinner chill zone with smaller thickness variations was observed. Furthermore, it was found that the mould taper required optimisation to match the changes in shrinkage behaviour to ensure uniform solidification. The use of mild cooling powders was observed to give an increase in mould friction. Mould thermal monitoring indicated that the solid slag films fractured (sheeting) in the upper part of the mould. However, no operational problems were reported, which indicate that the first 200 mm under the steel meniscus is essential for initial solidification and for the formation of a homogeneous steel shell. All these findings can be understood by considering the crystallisation properties of the mould slag, which include the cooling rate. Mild cooling has been shown to provide uniform heat transfer and adequate lubrication for high speed thin slab casting.     

Mould lubrication and friction behaviour with hydraulic oscillators in slab continuous casting

Abstract

It is very important to obtain reliable lubrication from casting powder both at the meniscus and in the gap between strand and mould as it affects slab surface quality and caster productivity. With knowledge of mould friction, a quantitative insight into the behaviour of powder during caster operation is possible. In the present research, the friction was studied based on a slab continuous caster equipped with hydraulic oscillators. The effects of mould oscillation and the abrupt change of casting speed on mould friction force were evaluated, and the characteristics of lubrication behaviour in a casting sequence were investigated. In particular, a comparison between the mould friction force between sinusoidal oscillation mode and non-sinusoidal oscillation mode was made. Finally, the characteristics of friction before a breakout are discussed. The experimental and analytical results may contribute to the development of mould friction online measurement and more clearly learn the lubrication behaviour in different conditions.     

Simulation of heat transfer and strain behaviour in bloom casting mould

Abstract

An optimum casting model was developed to simulate the effect of mould flux on bloom heat transfer and strain behaviour based on a 3D MiLE method, and the influence of casting speed and superheat on bloom heat transfer and lubrication were also investigated. The simulation results showed that solidified shell thickness growth conforms to a Square Root Law, and that the model predicted results are basically in agreement with previous data in the literature, and provide confidence in model. The bloom temperature distribution range in the corner area is smaller than that in the mid-face, and the corner regions form a high cracking risk zone. The hot tearing indicator and effective stress in the corner area are significantly greater than that in the mid-face, so the corner area is the dangerous zone of cracking; The mould flux lubrication in the bloom mid-face is better than for the bloom corner region, due to a higher shell temperature and a fluid slag; The increasing of casting speed can delay air gap formation of the bloom corner area, improving the lubrication conditions, but when the casting speed is changed, it is also necessary for the mould flux viscosity and crystallization temperature be changed also. Increasing the superheat has little influence on the completely solidified distance of liquid flux in the bloom corner area.     

Three-dimensional analysis and design of petal-like mould for continuous casting of steels

Abstract

Understanding the shrinkage behaviour of a steel billet is very important for designing the continuous casting mould, and conversely, a well designed mould is beneficial when matching the shrinkage behaviour of the billet. The shrinkage behaviour of a billet is hard to measure in situ during continuous casting but can be calculated by numerical simulation. A three-dimensional finite element model has been built to simulate the thermal and stress fields of the billet in the mould. The dynamic thermal boundary condition, the effect of ferrostatic pressure and the temperature dependent thermophysical parameters have been considered in the model. The shrinkage of billet when considering ferrostatic pressure is on average 0·08 mm smaller than when not considering ferrostatic pressure. The temperature and stress distributions are analysed in the present paper, and based on this analysis, a novel petal-like mould was designed and its taper determined. The designed mould has been tested in industrial practice showing better lifetime and billet quality.     

Effect of solidus temperature and crystalline phase of mould flux on heat transfer in continuous casting mould

Abstract

Pieces of mould flux film obtained from a commercial continuous casting machine and measurements of the mould temperature have been used in an investigation to explain the mechanism of heat transfer in the mould. Comparison with the results of numerical calculations, indicates that the main factor responsible for the reduction of heat transfer with a high basicity flux is the contact resistance at the interface of the mould wall and solid flux film. The results show that a relatively high contact resistance is introduced when using a crystalline, high solidus mould flux because of the stability of the contact resistance.     

Modelling of steel shrinkage and optimisation of mould taper for high speed continuous casting

Abstract

In high speed continuous casting, optimisation of mould taper is key for intensifying heat transfer and for improving the quality of the cast products. Mathematical modelling has been carried out by combining heat transfer, steel shrinkage and parabolic continuous taper model in order to optimise the mould taper profile. These models have been assembled to a set of software, the inputs of which include the steel grade, casting speed, casting temperature, length and the cross-section of mould tube, while the outputs consist of surface temperature of the strand, thickness of solidified shell, thermal linear expansion coefficient, steel shrinkage, distortion of the mould tube wall, the actual air gap, total taper and the continuous taper profile. Optimum mould taper has a parabolic profile which is tapered inwards that changes continuously along the length of the strand in order to achieve reduction in air gap while avoiding distortion of the mould tube.     

Mould heat transfer and continuously cast billet quality with mould flux lubrication Part 2 Quality issues

Abstract

With many billet producers adopting mould powder lubrication, there is a need to clarify the gains in quality that can be achieved with this practice. Over the past three decades considerable research has been conducted to establish the relationship between mould behaviour and defect formation for billets continuously cast with oil lubrication, but little has been done to compare oil cast billets with powder cast billets. In this study, conducted at a Canadian minimill, four faces of a copper mould were instrumented with thermocouples and mould temperatures and billet quality were monitored with mould powder lubrication during casting of 208 × 208 mm billets. In the first part of this two part series (in Ironmaking & Steelmaking No. 1 2000), the results of the mould heat transfer analysis and the influence of variables were presented, together with a comparison between oil and powder lubrication. In the present paper, Part 2, billet quality is examined in detail. The difference in turbulence at the meniscus between oil and powder lubrication is established, and the need to tune mould level sensors when switching to mould powders is demonstrated. Previous work has shown that mould level fluctuations have a strong influence on defects such as offsquareness and transverse depressions, both of which are markedly reduced when casting with mould powders. The inherent stability of the meniscus is improved when employing mould powder lubrication and a submerged entry nozzle. Furthermore, the significant reduction in mould heat transfer at the meniscus, when mould powders are employed, particularly for medium carbon steels has been shown to correlate well with the observed reduction in offsquareness. The paper also elucidates the reasons for the reduction, and in most cases, elimination of transverse depressions in B–Ti grades when casting with mould powders. The mechanism of longitudinal depression formation and subsurface cracking observed in many of the powder cast, medium carbon billets has also been established.     

Tools and techniques for use in development of mould powders

Abstract

The tools and techniques used within Corus UK to improve mould powder performance and product quality are reviewed. Mould thermal monitoring, which allows real time assessment of heat transfer, is a critical tool in the development of mould powders. Thermal analysis, viscosity measurements, flux–mould plate interactions, steel velocity profiles in the mould and slag film properties also play a part in continuing studies. Case studies of improvements in process performance achieved using these methods are presented.     

Numerical simulation of fluid flow and solidification in continuous slab casting mould based on inverse heat transfer calculation

Abstract

A mathematical model based on an inverse heat transfer calculation was built to determine the heat flux between the mould and slab based on the measured mould temperatures. With K–? turbulence model, a mathematical model of three-dimensional heat transfer and solidification of molten steel in continuous slab casting mould is developed. Solidification has been taken into consideration, and flow in the mushy zone is modelled according to Darcy’s law as is the case of flow in the porous media. The heat flux prescribed on the boundaries is obtained in the inverse heat conduction calculation; thus, the effect of heat transfer in the mould has been taken into consideration. Results show that the calculated values of mould temperature coincide with the measured ones. Results also reveal that the temperature distribution and shell thickness are affected by the fluid flow and heat transfer of slab which is governed by the heat flux on the mould/slab interface.     

Design of mould fluxes for continuous casting of special steels

The melting behaviour of mould powder during continuous casting is an important consideration with respect to caster performance, production rate and steel quality. Two important factors, powder composition and carbon addition, are critical to control the properties and melting behaviour of the mould flux. In this study, the effect of different carbonaceous materials on the melting characteristics of mould powders was evaluated. Correlations were established between the structural factors and chemical reactivity of carbon and melting behaviour of mould flux. In addition, two examples are given of the effect of flux composition on casting performance for specific steels. A flux with reasonable basicity and additives was designed for the casting of heat-resistant steel (Incoloy 800) to reduce surface cracks. Another flux was designed for the casting of non-magnetic steel containing high aluminium by partially replacing SiO₂ with Al₂O₃ to limit aluminium oxidation by SiO₂.     

Break temperatures of mould fluxes and their relevance to continuous casting

Abstract

The break temperatures of mould fluxes are important since they help to control the horizontal heat transfer and lubrication between the steel shell and the mould, and consequently affect occurrences of longitudinal cracking and sticker breakout in continuous casting. Break temperatures T _br have been determined for both steady state and dynamic measurement of the viscosity, and equations relating T _br to chemical composition have been obtained for both cases. It has been found that T _br can be affected by (i) cooling rates and (ii) fluorine losses during the measurements.     

Analysis of basic network structure of continuous casting mould powder in electromagnetic field

ABSTRACT

In the continuous casting process, the mould powder plays the role of insulator and heat insulator in the crystallizer, prevents molten steel from oxidizing, absorbs non-metallic inclusions, and controls lubrication and heat transfer between the casting billet and the mould. It is an important functional material that promotes the quality of a billet and ensures that the continuous casting process proceeds smoothly. Here in we analyse the changes in the microstructure of the protective flux from the aspect of the infrastructure of the flux slag. Additionally, using the classical molecular dynamics simulation method, the structure of the CaO–SiO₂–Al₂O₃–MgO slag system was simulated in the presence of magnetic fields of various strengths. The magnetic field was found to have the following effects on the slag structure. The participation of the basic elements Si, Al, O, etc. in bond formation is independent of magnetic field strength. The magnetic field causes changes in the peaks, coordination numbers, and peak widths of the radial distribution functions of bonds such as Si–O, Al–O, and Mg–O. The greater the magnetic field strength, the more disordered the ionic clusters are, and the greater is the decrease in slag viscosity. Although the effect of the magnetic field influences the structure of the slag, there is not much change in the way the molecules and atoms are stacked in the slag.     

Real Heat Flux Analysis of Continuously Casting Round Billet

The distributions of heat flux along the height and the circumferential direction of round billet mould were measured continuously.The influence of casting speed,carbon content,powder,and pouring temperature on the average longitudinal and circumferential heat flux in the ＂high heat flux region＂ was discussed.The experimental and analytical results provide a basis for an intelligent mould with online detection of defects,adjustment of operational parameters,optimization of the monitoring system,and even prediction of abnormal heat transfer.