Mold Oscillation Research Articles

Initial Solidification Behavior of Spring Steel Billet Near the Mold Corner During Continuous Casting Process

Strand surface defects originate from the initial solidification of molten steel in continuous casting mold. This article investigates the initial solidification behavior during the continuous casting of 55SiCr spring steel billet using a novel mold simulator. First, the high‐frequency responding temperatures and high‐frequency heat fluxes across the mold corner and hot face are calculated by the 2D‐inverse heat conduction program mathematical model and the fast Fourier transformation, and the results indicate that the temperature variations and heat flux fluctuations around mold corner are stronger than those at mold hot face. Then, the characteristic heat fluxes around the meniscus at mold corner and hot face are analyzed, and their four corresponding signals are discussed with the help of power spectral density analysis. The average solidification factor K for shell corner is greater than shell face, which indicates that the cooling intensity of shell at corner is stronger due to the two‐dimensional heat transfer near mold corner, as demonstrated by heat transfer and dendrite structure analysis. Finally, the interrelations between the shell profile, mold oscillation, heat flux change rate, high‐frequency heat flux, temperature change rate, and high‐frequency temperature for the two cases are discussed.

Study on the Consumption Mechanism and Lubrication of Mold Powder Based on Non-Sinusoidal Oscillation Mode

A two-dimensional mold model coupled multiphase flow, heat transfer, solidification and mold oscillation was established based on the casting parameters of the mold of plant. The accuracy of the model was verified by comparing the measured by plant and calculated mold powder consumption under the same casting conditions. The mechanism of mold powder consumption and lubrication was analyzed based on the non-sinusoidal oscillation mode, and the effect of non-sinusoidal oscillation parameters on mold powder consumption was discussed. Mold powder consumption was determined by the downward flow velocity of liquid mold powder and the thickness of liquid mold powder film, the liquid mold powder consumption decreased with the decrease of those. When the mold moved downward, the mold powder thickness and downward flow velocity decreased, the minimum mold powder consumption reached at the middle of the negative strip time, and the variation was to opposite when the mold moved upward, the maximum mold powder consumption appeared during the positive strip time. With the decrease of casting speed and modification ratio, and increase of oscillation frequency and oscillation amplitude, the mold powder consumption had the tendency to increase. The nonlinear regression equation was fitted by the Levenberg–Marquardt method combined with the universal global optimization method to evaluate mold powder consumption.

Numerical Simulation of Oscillation Mark Formation and Slag Consumption in Meniscus Region During a Mold Oscillation Cycle

Numerical Simulation of Oscillation Mark Formation and Slag Consumption in Meniscus Region During a Mold Oscillation Cycle

Dynamic Characteristics Analysis of Mold Oscillation Mechanism Generating Non-Sinusoidal Waves

In this study, to understand the vibration characteristics of the mold vibrator, the vertical vibration, including the rotational transmission of a four-bar mechanism generating non-sinusoidal waves, was numerically implemented. Physical characteristics were compared through behavior comparison with a mechanism that vibrates in a sinusoidal wave due to gear transmission, and the impact that the system receives was discussed by introducing the jerk, a first-time derivative of acceleration. Based on this basic modeling, an optimization problem with the change in the length of the crank and connecting rod constituting the four-bar linkage as a variable was finally established, and the process of deriving the solution was performed. The equation of motion was derived using the Newmark, direct integration, and the transient response obtained by applying a constant rotational force was compared. Unlike the transmission of rotation by gears, the deviation of the behavior of the four-bar mechanism follower increases, and the non-sinusoidal vibration changes according to the length ratio of the crank and connecting rod, so the effect on the playing process was analyzed.

Investigation on Initial Shell Solidification and the Effect of Negative Strip Time on Oscillation Marks during Continuous Casting

The initial solidification of the shell and the effect of the negative strip on oscillation marks were studied during the oscillation of the mold. A two-dimensional model was established concerning mold oscillation, which was coupled with fluid flow, heat transfer, and solidification, and the validity of the model was verified. The results show that oscillation marks were formed at the negative strip stage and that the quality of the slabs can be improved by reducing the duration of the negative strip stage. During the negative strip stage, the shell was affected by the strong backflow of liquid slag and the pressure on the surface sharply increased, resulting in the formation of a depression oscillation mark on the shell. The effects of the negative strip stage on the initial solidified shell during each cycle were compared. As the depth of the oscillation mark decreased, the upward shear stress on the shell’s surface increased, without the occurrence of a negative strip stage during one cycle. The results provided a new method for reducing oscillation marks and are of great significance for improving casting slabs’ quality.

Effect of mold corner structures on the fluid flow, heat transfer and inclusion motion in slab continuous casting molds

Mold corner structures will influence the multiphase flow, heat transfer and inclusion motion behaviors in the mold, which have significant impacts on the quality of strands. Herein, a three-dimensional fluid flow and heat transfer mold model was employed to investigate the effect of four different corner structures (right-angle, big-chamfered, multi-chamfered and fillet) on the multiphase flow, heat transfer and inclusion motion behaviors in the mold. The Volume of Fluid model was used to describe the molten steel and slag, while the Discrete Phase Model was employed to track the motion of non-metallic inclusions. The dynamic mesh was applied to simulate the mold oscillation. Results show that the chamfered structures can obviously increase the flow velocity around the strand corner, especially for the big-chamfered mold. The chamfered molds can remarkably improve the corner temperature of strands at the mold exit, and the fillet mold is the most effective. The temperature on the narrow and chamfered faces of the copper plate in the chamfered molds is lower than that in the right-angle mold. The maximum amplitude of temperature fluctuation of the meniscus reaches 4.6 K. The shell thickness around the strand corner in the chamfered molds is obviously thinner than that in the right-angle mold. In addition, the chamfered structures will increase the number of inclusion particles around the strand corner.

Characterization and Assessment of Mold Flux for Continuous Casting of Liquid Steel Using an Inverse Mold Simulator

This investigation discusses the experimental methods to characterize and evaluate the mold flux performance during continuous casting of liquid steel. The mold fluxes are initially characterized by the conventional techniques for particle size, phase identification, phase transformation during the heating process, viscosity, break temperature, and other high‐temperature properties. Subsequently, the initial solidification behavior of the peritectic and interstitial free (IF) steel in the presence of respective molten mold flux has been simulated using an in‐house designed and developed inverse mold simulator. This simulator takes into account the physical, thermal, and fluid properties of mold flux, liquid steel to be cast, and casting parameters (casting speed, mold oscillation frequency, and stroke length), to assess the performance of liquid steel casting in the continuous caster. A suitable mathematical model has also been developed to predict the transient heat flux and hot face surface temperature of mold at the meniscus level. The current study successfully concludes the importance of a mold simulator along with the conventional characterization techniques to completely evaluate the performance of any mold flux.

3D Coupled Model on Dynamic Initial Solidification and Slag Infiltration at the Corner of Slab Continuous Casting Mold

Herein, a 3D mathematical model is established to elucidate the dynamic initial solidification and slag infiltration at the corner of the mold. The three‐phase fluid flow, heat transfer, the solidification of the steel, and the mold oscillation are considered. The slag movement and the variation of the meniscus solidification are revealed with the mold oscillation, and explained by the variation of the pressure in the gap and the heat flux at the meniscus. The direction of the liquid slag near the corner flowing into and out of the gap changes during the positive and negative strip stage, respectively. The liquid slag near the corner and that far from the corner can be supplied reciprocally along the gap. The speed of the liquid slag film at the corner has positive correlation with the pressure difference at the mouth of the gap and in the gap. The meniscus solidification near the corner varies with the mold oscillation, and is the smallest approximately 1.0 mm at the start of the negative strip stage. Therefore, the meniscus solidification and slag lubrication can be improved through the optimization of the mold oscillation.

HSMA-PS: a novel memetic approach for numerical and engineering design challenges

Recent work trend is to hybridize two and more variants in order to recognize better quality of functional and remedies to the global challenges of optimisation. The newly formed Slime Mould Algorithm (SMA) is premised upon naturally occurring slime mould oscillation feature. There is an effort to build a more effective way to accomplish exploration through process of exploitation. In a comprehensive collection of tests, the proposed hybrid Slime Mould Algorithm (SMA) – Pattern Search Algorithm (PS) (hSMA-PS) has been evaluated by comparing against accurate and reliable meta-heuristics for accuracy testing. In addition, nine classical engineering based optimization problems with design are used to guesstimate the algorithm’s efficacy in engineering based optimization challenges. The experiments demonstrate that the suggested algorithm enjoys efficiency, sometimes amazing result on sophisticated search landscapes.

Initial Solidification and Heat Transfer at Different Locations of Slab Continuous Casting Mold through 3D Coupled Model

Herein, a 3D mathematical model is established to investigate the initial solidification and heat transfer at different locations of the mold through considering the steel–slag–air three‐phase fluid flow, the heat transfer, the solidification, and the mold oscillation. The meniscus solidification on different sections is revealed, and the heat flux on hot face of the mold is compared. Through the simulation, the meniscus solidification on longitudinal sections parallel to narrow face is the largest at the center and the edge of wide face, and is the lowest at a quarter of wide face. The thickness of the total slag on the cross section is larger at the corner than that far from the corner. In the current simulation, the largest heat flux along the vertical direction is 2.6–3.5 MW m−2 at approximately 14 mm below initial meniscus. With the increase in thickness of the slag rim on different longitudinal sections, the thickness of the slag increases, resulting in the decrease in the heat flux on the hot face. Therefore, the initial solidification and heat transfer are significantly affected by the thickness of the slag as well as the heat supplement from the upper backflow.

A Modified Slime Mould Algorithm for Global Optimization.

Slime mould algorithm (SMA) is a population-based metaheuristic algorithm inspired by the phenomenon of slime mould oscillation. The SMA is competitive compared to other algorithms but still suffers from the disadvantages of unbalanced exploitation and exploration and is easy to fall into local optima. To address these shortcomings, an improved variant of SMA named MSMA is proposed in this paper. Firstly, a chaotic opposition-based learning strategy is used to enhance population diversity. Secondly, two adaptive parameter control strategies are proposed to balance exploitation and exploration. Finally, a spiral search strategy is used to help SMA get rid of local optimum. The superiority of MSMA is verified in 13 multidimensional test functions and 10 fixed-dimensional test functions. In addition, two engineering optimization problems are used to verify the potential of MSMA to solve real-world optimization problems. The simulation results show that the proposed MSMA outperforms other comparative algorithms in terms of convergence accuracy, convergence speed, and stability.

A 1D Analytical Model for Slag Infiltration during Continuous Casting of Steel under Non-Sinusoidal Mold Oscillation

A 1D analytical model for slag infiltration during continuous casting of steel is developed to investigate the slag behavior in the mold–strand gap. The superposition principle and Fourier expansion are applied to obtain the analytical solution for transient slag flow under arbitrary mold oscillation including non-sinusoidal oscillation mode. The validated model using literature data partially explains several controversies such as slope of slag film channel, mechanism of non-sinusoidal mold oscillation, and timing of slag infiltration. The model shows that a converging slag film into the casting direction is required to open the mold–strand gap if compression is applied in between. Also, model calculations imply that higher slag consumption is achievable from non-sinusoidal mold oscillation by means of the increase of film thickness through longer positive pressure with higher peak pressure. The model demonstrates a time difference between slag flow and pressure near the meniscus and the discrepancy in timing of infiltration between previous works is attributed to the mismatch. The model provides a concise but reliable tool to understand slag infiltration behavior and design mold oscillation settings.

Effects of Variation of Heat Flux Released from the Meniscus on the Surface Shape of the Solidified Shell During Continuous Casting

Mold oscillations, widely used in continuous casting for infiltrating the mold flux between the mold and the solidified shell, change periodically the heat flux from the meniscus to mold. These variations of the heat flux affect the solidification behavior near an initial solidification position. Because the surface shape of the solidified shell is influenced by the initial solidification behavior, it is important to understand the relation between the mold oscillation, the heat flux and initial solidification behavior. In the present study, we developed a numerical model that simulates the flow and thermal behavior of the mold flux near the meniscus. Using this model, we analyze the effects of the variations of the heat flux from the meniscus on the initial solidification position and suggest the formation mechanism of the oscillation marks (OMs) and the hooks. Also, we will present quantitative results about the depth of the OMs and the length of the hooks at the conditions used in the present study. The factors that influence the hooks’ types and the causes of the irregularity of the shell surface are also discussed.

Investigation on Mold Flux Melting and Consumption During Continuous Casting of Liquid Steel

Mold powders play an integral role in maintaining the stability and efficiency of the continuous casting process as they (1) provide lubrication, (2) control heat transfer, (3) absorb nonmetallic inclusions, and (4) prevent reoxidation of liquid steel during continuous casting of liquid steels. Much of the previous investigations are focused on the characterization of mold powders to understand the physicochemical aspects of the continuous casting process. However, limited attention has been given to analyzing the melting behavior of mold powder, which is necessitated for the proper functioning of the caster. An experimental technique akin to the industrial practice has been adopted in this investigation to study the melting behavior of the mold powder. A realistic nondimensional correlation is proposed considering the various casting parameters (casting speed, mold oscillation frequency, and stroke, negative strip time, and cross-sectional area of mold), the mold powder melting, and the consumption rate based on the adopted experimental and theoretical methods for real-time application.

Dynamic Investigation of Non-linear Behavior of Hydraulic Cylinder in Mold Oscillator using PID Control Process

To learn the dynamic characteristics of a mold oscillator, we establish a model that describes the relationship between force equilibrium of a hydraulic cylinder and mold under various oscillation conditions. The non-linearity caused by the servo-value and the operating fluid is considered as excitation, and is calculated as control error between an input signal and mold oscillation in real-time by a PID control process. Based on the non-linear property, we determine that the dynamic behavior is caused by mold oscillation displacement and hydraulic cylinder pressure. We define excitation frequency and harmonic terms, and determine that the sources of the harmonic peak frequency and high peak frequency; (50n ± exciting frequency ωexc) are friction between the piston and hydraulic cylinder, and variable stiffness of the operating fluid. Finally, a mathematical model of the hydraulic chamber that can represent the unknown non-linear phenomenon is derived.

An Approach for Modelling Slag Infiltration and Heat Transfer in Continuous Casting Mold for High Mn–High Al Steel

To clarify the characteristics of slag infiltration and heat transfer behaviors in the meniscus region during the casting of high Mn–high Al steel, a mathematical model of a continuous casting mold that couples fluid flow with heat transfer, and solidification is developed. The model is based on the change in slag composition and properties caused by the steel/slag reaction. The formation and evolution of the meniscus profile and slag films for different mold fluxes during mold oscillation are described. The results show that the rapid growth of the slag rim with a high Al2O3 content approaches and deforms the meniscus so that a series of casting problems such as slag infiltration blocking, large fluctuations in heat flux, and even meniscus breaking occur in the continuous casting process. Predictions are in good agreement with plant measurements. These findings provide an improved understanding of the complex phenomena occurring in the meniscus region and give new insights into the evaluation and optimization of mold flux properties for high Mn–high Al steel casting.

Neural Network Modelling to Characterize Steel Continuous Casting Process Parameters and Prediction of Casting Defects

The current work outlines application of a data-driven multilayer perceptron-based artificial neural network (ANN) model to characterize the influence of melt compositions, tundish temperature, tundish superheat, casting speed and mould oscillation frequency on the important processing parameters such as mould powder consumption rate, oscillation mark depth and metallurgical length during continuous casting process. A two-layer feedforward back-propagation neural network model has been developed for predicting the probability of occurrence of defect in the cast product. The network training architecture has been optimized using a gradient-based algorithm, namely the back-propagation algorithm. The neural network predictions are found to be in good agreement with regard to oscillation mark depth, mould powder consumption rate, metallurgical length and probability of occurrence of defect using data obtained from an operating Indian steel plant (Rashtriya Ispat Nigam Limited, Visakhapatnam). The ANN model prediction has been validated successfully with multiple linear regression analysis carried out on each data set.

Mold Nonsinusoidal Oscillation Mode and Its Effect on Slag Infiltration for Lubrication and Initial Shell Growth during Steel Continuous Casting

The effect of nonsinusoidal oscillation at different modification ratios (α) on slag lubrication was investigated during mold oscillation. A validated and reliable multiphase model was employed, which involved flow and solidification of the molten steel and mold slag. The main results revealed that a large amount of liquid slag at the entrance of the mold–strand channel reflowed into the slag pool at the middle of the negative strip period. The phenomenon was more distinct, with an increase in the modification ratio. The modification ratio had no obvious effect on the average thickness of the liquid film at different depths below the meniscus. A modification ratio of 0.5 caused less fluctuation of the transient liquid film. Quantitative prediction of slag consumption indicated that as the modification ratio increased from 0.2 to 0.5 to 0.8, the average values were 0.278, 0.286, and 0.279 kg/m2, respectively. Shell solidification and growth near the meniscus mainly occurred when the mold was descending, which not only depended on the heat flux, but also on the liquid slag flow, the pressure driven by slag rim, and the mold oscillation. Optimization of the modification ratio of nonsinusoidal oscillation could be an alternative to delay growth of the initial shell towards the molten steel. A modification ratio of 0.5 had the least robust shell tip at the meniscus, thereby reducing entrapment of inclusions and bubbles by the shell tip.

Characteristics of Slag Infiltration in High-Mn Steel Castings

To determine the composition difference between the solid and liquid films in plant practice for high-Mn steel castings, a reaction experiment was carried out to investigate the composition profile of MnO and SiO2 in the slag layer. Based on the experimental results, a mathematical model of the mold slag for high-Mn steel was developed to describe the nonuniform infiltration behavior of mold slag during oscillation cycles. Moreover, the effects of uneven slag films on slab lubrication and heat transfer in the mold are discussed. The results show that the concentrations of MnO and SiO2 over the flux layer have an opposite stair-step distribution, which consists of a reaction layer and nonreaction layer. When the reaction layer thickness is 5 mm, a thicker liquid film is formed between the slab and the mold. The inhomogeneity of the composition in the solid film causes large fluctuations in the heat flux in the mold, resulting in irregular depressions on the shell surface. With a reacting thickness of 10 mm, the reacting slag fills in the gap to generate a thinner solid film, which increases the overall heat flux in the mold. Since mold oscillation combined with slag rim enhances the pressure flow in the vicinity of the meniscus, the liquid slag within 80 mm of the mold wall is mixed and consumed quickly. In contrast, the liquid slag beyond 80 mm from the mold wall with a low velocity stays longer in the liquid pool. The model predictions illuminate the characteristics of slag infiltration during high-Mn steel casting, showing good agreement with plant measurements.

Study of Non-Newtonian Behavior of CaO-SiO2-Based Mold Slag and Its Effect on Lubrication in Continuous Casting of Steel

To understand the effect of the non-Newtonian behavior of mold slag on lubrication during continuous casting of steel, the current study investigated the rheology of CaO-SiO2-based mold slag using a rotational viscometer with variable rotating speed. The constitutive equations at different temperatures were determined. Subsequently, the obtained viscosity as a function of temperature and shear rate was incorporated into a validated mathematical model. The main results demonstrated that slag viscosity decreased dramatically with increased shear rate as the experimental temperature approached the break temperature of mold slag, meaning that the mold slag had a property of shear thinning. The predicted evolution of slag viscosity during mold oscillation was consistent with the shear thinning as the shear rate exerted on the slag channel varied. The calculated slag consumption was higher than that for slag treated as a Newtonian fluid, which agreed well with measurements using a miniature continuous caster. This study finds that the consideration of the non-Newtonian behavior of mold slag is significant to understand the lubrication mechanism and optimize related parameters via simulation.