Mold Taper Research Articles

Study on solidification and heat transfer of billet shell in a new-structure high-speed continuous casting mold

In this work, a three-dimensional finite element model of a newly structured high-speed continuous casting mold was established to study the heat transfer and solidification process of the billet shell. A complete billet shell, from the meniscus to the secondary cooling zone, was obtained through flame cutting. Using both simulations and test verification, detailed analyses were conducted on the temperature field distribution, thickness variation law, and cooling rate law of the billet shell within the mold, revealing its solidification behavior. Additionally, the effects of casting speed, molten steel superheat, and mold taper on the solidification behavior of the billet shell were discussed. Results showed that the simulation data were basically consistent with the test verification results. Within 200 mm from the meniscus, the heat dissipation accounted for three-quarters of the mold's total heat dissipation. The cooling rate at the corners of the billet shell was slightly higher than that at the sides. Between 200 mm and 400 mm from the meniscus, air gaps caused the temperature at the corners of the billet shell to rise. Afterwards, the whole billet shell eventually reached a similar the heat dissipation rates. The thickness of the billet shell increased exponentially within 110 mm from the curved meniscus, and from 110 mm to the exit of the mold, the thickness increased linearly but slowly. The effect of molten steel superheat within a range of 10 °C on billet shell solidification was relatively minor. Increasing the casting speed reduced the billet shell thickness and raised the billet shell surface temperature. However, increasing the taper of the mold had the opposite effect. Both adjustments shifted the gap formation position backward.

Influence of Mold Design on Shrinkage Porosity of Ti-6Al-4V Alloy Ingots

Mold design is one of the important ways to control shrinkage porosity. In this study, four mold forms with different tapers were first designed, the corresponding three-dimensional finite element models were built using the ProCAST software, and the influence of mold design on the filling and solidification processes of Ti-6Al-4V alloy was investigated. The results showed that the titanium alloy ingots exhibit typical characteristics of layer-by-layer solidification, and that the removal of the riser results in: (a) shortening the time it takes for molten metal to reach the bottom of the mold and the time needed to complete mold filling; (b) decreasing the maximum flow velocity and improving the filling stability; and (c) moving the shrinkage cavities up along the central axis of the ingot and decreasing the cavity volume. Meanwhile, it was also found that the shrinkage cavity volume decreases significantly with increasing mold taper, meaning a significant increase in ingot utilization rate. The shrinkage cavity formation mechanism was revealed through macrostructure analysis. During solidification, a grain frame is formed as a large number of equiaxed crystals intersect, thus creating an isolated liquid phase zone. When the liquid in this zone solidifies, the last zone to do so, its volume shrinkage cannot be compensated, thus leading to the formation of a shrinkage cavity.

Influence of heat flux different between wide and narrow face in continuous casting mould on unevenness of hypo-peritectic steel solidification at off-corner

ABSTRACT The effects of the difference of the heat flux between the wide face and narrow face of the mould, the mould taper, casting speed and cooling rate on unevenness of hypo-peritectic steel at the off-corner in the mould, which leads to longitudinal cracking, bleeding and breakout during continuous casting, were evaluated by a finite element model (FEM) simulation and a plant test with a commercial continuous caster. The simulation results show that an increase in the difference in the heat flux between the wide and narrow face increases the off-corner unevenness of solidification because the solidified shell on the low heat flux side is pulled toward the high heat flux side. The analysis results were in good agreement with the plant test results. These results revealed the importance of optimizing the heat flux ratio between the wide face and narrow face mould even under a high casting speed condition.

Thickness Distributions of Mold Flux Film and Air Gap in Billet Ultra-High Speed Continuous Casting Mold Through Multiphysics Modeling

The thicknesses of mold flux film and air gap are significant factors that affect the high-efficiency heat transfer, the strand lubrication and mold taper design of billet ultra-high speed continuous casting mold. Therefore, this paper established the three-dimensional fluid flow, heat transfer and solidification model, interfacial heat transfer model and two-dimensional stress-strain model to conduct multiphysics modeling. Thereby the thickness distributions of liquid slag, solid slag and air gap in the ultra-high speed billet continuous casting mold were obtained, and analyzing the effects of melting temperature of mold flux and mold taper. The results indicate that the thicknesses of liquid slag and solid slag increase and decrease respectively along the casting direction, and air gap mainly concentrates near the mold corner. The maximum thicknesses of liquid slag, air gap, and solid slag at the mold outlet are respectively 0.18 mm at the center of the strand surface (x = 0 mm), 0.28 mm at the strand corner (x = 80 mm) and 0.67 mm at x = 74 mm. The lower melting temperature of mold flux, the greater the liquid slag thicknesses and ascend from 0.14 to 0.18 mm, and conversely the maximum air gap thicknesses descend from 0.31 to 0.28 mm and existing ranges also get smaller, which is more favorable for the strand lubrication. To eliminate the air gap, the appropriate linear mold taper is 0.45% m−1 at the 6.5 m/min in casting speed.

Numerical Investigation on Solidification Shrinkage Behavior of P900 Hollow Ingot during Electroslag Remelting Process

A numerical model coupled with a multiphysical field based on a simple density‐based shrinkage model is established. After validation by comparing the experimental and simulation results, it is utilized to clarify solidification shrinkage behavior of electroslag remelting hollow ingot (ESR‐HI) process and investigate the effect of the inner mould taper angle and ingot withdrawing rate on air gap width and interfacial heat transfer coefficient (HTC). The interface between the hollow ingot and the inner mold can be divided into three regions, according to the change in heat transfer mechanisms. In region I, the inner wall and the inner mould are in complete contact, and effective HTC is maximum. In region II and region III, effective HTC decreases with increment in the air gap width. With increasing the inner mould taper angle and ingot withdrawing rate, solidification shrinkage at a given height of hollow ingot decreases. Moreover, it is reasonable that the inner mould taper angle is set to 1.5°, the distance from the slag‐metal interface to the bottom of the cylindrical section (Hcyl) is set to 20 mm, and the withdrawing rate is set to 5 mm min−1 for P900 during ESR‐HI process with a cross‐sectional size of Φ300 mm/Φ100 mm.

A validated asymptotic thermomechanical model for air-gap formation in tapered moulds in the continuous casting of steel

Abstract A recent asymptotics-based thermomechanical model is adapted and applied to the mould region in the continuous casting of round steel billets, with a view to describing the complex interplay between air-gap formation, mould taper, cooling channel width and cooling water velocity. Although the situation is steady state, the analysis leads to what is mathematically a dual moving-boundary problem for the solid–melt and solid–air interfaces, where the distance from the top of the mould region is the time-like variable in the problem. Moreover, the two interfaces are initiated at different locations. In addition, the thermal and mechanical problems are found to decouple and it is possible to solve the first ahead of the second. The model equations are solved numerically using a finite-difference method, and the approach is subsequently successfully validated against a previous finite-element model and experimental data from temperature measurements taken within the mould.

Effects of mold pattern characteristics on nanoimprinted aluminum investigated using quasi-continuum simulations

The effects of mold pattern characteristics on the mechanical deformation and mechanics of nanoimprinted aluminum are studied using quasi-continuum simulations in terms of atomic trajectories, strain distribution, and the imprinting stress-mold displacement curve. The simulation results show that a mold whose pattern has a larger period (S value) produces a larger imprinting stress on the substrate for deformation. The effect of mold taper angle on imprinting stress depends on the S value. The required imprinting stress for substrate deformation decreases when mold wear occurs, resulting in the appearance of more non-local atoms in the substrate because of a nonuniform stress distribution. The nucleation and propagation of dislocations in the substrate are significantly confined when the S value is very small (e.g., 150 Å).

Combined Study on Mold Taper and Corner Radius in Bloom Continuous Casting by FEM Simulation and Trial Experiment

A plane stress model was developed to study the coupled effect of mold taper and corner radius on the thermal–mechanical behavior of a 250 mm × 280 mm continuously cast bloom for a given special steel. Good agreement was obtained in both shell thickness and the off-corner cracking location from modeling and trial experiment. The results show that increasing mold taper results in the obvious decrease of surface temperature near the corner, while enlarging mold corner radius makes the shell surface temperature at the corner region more even with the mold taper between 0 and 1.5% m−1. It is also found that both the mold corner radius and taper are the key factors influencing the shell crack sensitivity but with different mechanism. For the internal crack, the mold taper takes more dominant effect for its corner radius between 0–10 mm, as the hoop strain at the solidification front decreases with increasing mold taper. For the surface crack, more sensitivity is noticed to the mold corner radius. Increasing mold corner radius leads to the increase of the surface hoop strain in the corner region, almost regardless of mold taper. The proper mold taper and corner radius for the present bloom casting should be 1.0–1.5% m−1 and 15–25 mm respectively.

Mold taper optimization for continuous casting of H-beam blanks

The objective of this study is to optimize the mold taper for continuous casting of H-beam blanks. A thermo-mechanical coupled mathematical model was established to analyze the heat transfer, solidification, and shrinkage of the strand in the mold based on the multiple load step method. Based on the simulation results of the air gap distribution in the mold, the mold taper was optimized at selected points on the surface of H-beam blank mold by minimizing the air gap thickness and the best taper scheme was proposed. The results show that the original mold tapers are relatively larger and the optimum mold tapers are as follows: (1) taper at the flange surface: 0.81%/m; (2) taper at the narrow face: 0.68%/m; (3) taper at the fillet: −1.44%/m. The optimum mold size obtained from taper optimization was used in the actual continuous casting process and based on the results, it can be concluded that the optimum mold taper scheme proposed in this study reduced the formation of surface cracks in H-beam blanks.

Applied Mathematical Modelling of Continuous Casting Processes: A Review

With readily available and ever-increasing computational resources, the modelling of continuous casting processes—mainly for steel, but also for copper and aluminium alloys—has predominantly focused on large-scale numerical simulation. Whilst there is certainly a need for this type of modelling, this paper highlights an alternative approach more grounded in applied mathematics, which lies between overly simplified analytical models and multi-dimensional simulations. In this approach, the governing equations are nondimensionalized and systematically simplified to obtain a formulation which is numerically much cheaper to compute, yet does not sacrifice any of the physics that was present in the original problem; in addition, the results should agree also quantitatively with those of the original model. This approach is well-suited to the modelling of continuous casting processes, which often involve the interaction of complex multiphysics. Recent examples involving mould taper, oscillation-mark formation, solidification shrinkage-induced macrosegregation and electromagnetic stirring are considered, as are the possibilities for the modelling of exudation, columnar-to-equiaxed transition, V-segregation, centreline porosity and mechanical soft reduction.

Optimization of machine parameters to improve the quality of continuously cast slab

Industries in general target to produce high quality tonnage steel at a lowest possible cost. On this count the technology of continuous casting (con-cast) is very promising. However, one of the serious quality problems that may arise in the con-cast slabs is the formation of cracks, on the surface and/or in the interior of the slabs. The cracks appearing on the surface get oxidized in air and therefore cannot be re-welded during rolling of the slab resulting into defective rolled plates. In this work, carried out at Bhilai Steel plant Bhilai (MP), machine parameters responsible for the formation of longitudinal surface cracks are studied. The objective of doing this exercise is to optimize these parameters to reduce the frequency of crack formation. Mould taper, age of the mould, pinch roll conditions and rigidity in fixing the pinch rolls are some of the parameters studied. The study concludes that, the existing level of 1.3% of mould taper is excessive and the optimum value is found to be 1.13%. From this study, the history of the machine after maintenance is optimized to 140 heats and the rigidity maintenance period for pinch rolls to 80 heats. It is proposed that the roll gap of the pinch rolls should be checked and rectified for every 65 heats.

Effect of Grade on Thermal–Mechanical Behavior of Steel During Initial Solidification

Thermal–mechanical analysis of solidification is important to understand crack formation, shape problems, and other aspects of casting processes. This work investigates the effect of grade on thermal–mechanical behavior during initial solidification of steels during continuous casting of a wide strand. The employed finite element model includes non-linear temperature-, phase-, and carbon content-dependent elastic–viscoplastic constitutive equations. The model is verified using an analytical solution, and a mesh convergence study is performed. Four steel grades are simulated for 30 seconds of casting without friction: ultra-low-carbon, low-carbon, peritectic, and high-carbon steel. All grades show the same general behavior. Initially, rapid cooling causes tensile stress and inelastic strain near the surface of the shell, with slight complementary compression beneath the surface, especially with lower carbon content. As the cooling rate decreases with time, the surface quickly reverses into compression, with a tensile region developing toward the solidification front. Higher stress and inelastic strain are generated in the high-carbon steel, because it contains more high-strength austenite. Stress in the δ-ferrite phase near the solidification front is always very small, owing to the low strength of this phase. This modeling methodology is a step toward designing better mold taper profiles for continuous casting of different steels.

On the interactive effects of mould taper and superheat on air gaps in continuous casting

The formation of an air gap in continuous casting systems is detrimental to the process efficiency as it acts to thermally insulate the cast from the water-cooled mould. By tapering the mould wall, ...

Formation of shrinkage porosity during solidification of steel: Numerical simulation and experimental validation

The phase transformations in solidification of steel are accompanied by shrinkage and sudden changes in the solubility of alloying elements, resulting in negative side effects as micro- and macrosegregation and the formation of gas and shrinkage porosities. This paper deals with the numerical and experimental simulation of the formation of shrinkage porosity during the solidification of steel.First the physical basics for the mechanism of shrinkage pore formation will be discussed. The main reason for this type of porosity is the restraint of fluid flow in the mushy zone which leads to a pressure drop. The pressure decreases from the dendrite tip to the root. When the pressure falls below a critical value, a pore can form.The second part of the paper deals with different approaches for the prediction of the formation of shrinkage porosity. The most common one according to these models is the usage of a simple criterion function, like the Niyama criterion. For the computation of the porosity criterion the thermal gradient, cooling rate and solidification rate must be known, easily to determine from numerical simulation. More complex simulation tools like ProCAST include higher sophisticated models, which allow further calculations of the shrinkage cavity.Finally, the different approaches will be applied to a benchmark laboratory experiment. The presented results deal with an ingot casting experiment under variation of taper. The dominant influence of mould taper on the formation of shrinkage porosities can both be demonstrated by the lab experiment as well as numerical simulations. These results serve for the optimization of all ingot layouts for lab castings at the Chair of Ferrous Metallurgy.

USAGE OF UNEVEN ESTIMATED NETS FOR MATHEMATICAL MODELING OF THE PROCESSES OF CONTINUOUS CAST BILLET FORMATION IN A CCM CRYSTALLIZER

The discrete analog of diff erential equation of heat conduction allowing applying irregular computational net for the mathematical modeling of continuous casting was proposed. This method of meshing allows taking into account the distribution of temperature gradients in the model. It improves accuracy of the approximation and adequacy of the computation results. The mathematical model of crystallization and shrinkage of slab in CCM mold was developed. Application of irre gular computational net allowed using the elements of size of 1 – 2 mm in modeling. The researches of slab cross-section profi le distortion under the influence of the mold were conducted on the basis of this model. Calculation of the geometrical profi le allows to specify the conditions of the thermal and mechanical interaction of the solidified shell with the mold walls and to solve the task of determination of optimal mold taper of CCM, ensuring reduction in number of slabs aff ected by surface and subsurface cracks.

In-depth study of mold heat transfer for the high speed continuous casting process

Mold heat transfer during the commercial high speed continuous casting up to 7 m/min was investigated in order to clarify the influence of various operating conditions such as casting speed, mold flux, mold thickness, thickness and height of mold coated layer and so on. A simple, but practical formula of heat flux has been derived in terms of those operating conditions by analyzing the heat flux data obtained in CEM® (Compact Endless Casting and Rolling Mill) caster based on simplified one dimensional heat transfer model. Especially, impact of mold parameters such as mold thickness, mold coated layer thickness and its height on the heat flux can be linearly expressed in the empirical formula derived. Heat flux ratio (HR), the ratio of the narrow face heat flux to the wide face one, is one of the important indicators to evaluate whether the solidified shell is evenly robust or not. Averaged HR in CEM® caster is around 0.87, which varies according to the caster specifications and operating conditions. It is suggested that the mold taper should be adjusted to maintain the HR as close to 0.87 as possible.

Simulation of slab formation in a continuous-casting machine

A discrete analog of the differential heat-conduction equation permits the use of nonuniform calculation grids in the simulation of continuous casting. That allows the distribution of the temperature gradients in the model to be taken into account, with corresponding increase in the accuracy of the approximation and the results. A mathematical model is developed for the solidification and shrinkage of continuous-cast slab in the mold. The adoption of a nonuniform grid permits the use of elements measuring 1–2 mm in the simulation. This model is used to study the distortion of the slab cross section at the mold walls. Calculation of the geometric profile permits refinement of the thermal and mechanical interaction of the solidifying shell and the mold walls and determination of the optimal mold taper so as to reduce the risk of surface and subsurface cracking in the slabs.

Mould-taper asymptotics and air gap formation in continuous casting

We develop a coupled thermomechanical model, that includes mould taper, for the formation of air gaps in the vertical continuous casting of round billets. The system is very sensitive to the small width of the air gap. Mould tapers are used to mitigate the contraction of the solidified shell during cooling. We apply numerical and perturbation methods to show that a small mould taper significantly reduces the insulating effect of the air gap. The analysis is presented in a more transparent and less computationally expensive way than earlier, fully numerical models. We also consider a theoretical ideal taper, which eliminates the air gap altogether. The air gap is found to be quite robust; increasing the size of the taper does not constitute an equal reduction in the air gap size. Sample computations are carried out using parameters for the continuous casting of a pure metal (copper), although the framework can easily be extended to the continuous casting of alloys.

Measures for Reducing the Rate of Breakout of Slab Casters

In order to reduce the rate of breakout of slab caster, improve the operating rate and ensure the stability of the caster, measures including the tundish casting auto-start, the mold level automatic control system optimization, the SEN one-button automatic quick-change technology, the mold breakout forecast system optimization, the mold oscillation parameters optimization, the mold taper measurement optimization and the mold powder management have been adopted by a steel plant of WISCO. As a result, the breakout rate of slab caster was significantly reduced to be zero level in the first 3 years, which is a new record for all steelmaking plant in China.

Thermo-mechanical Modeling in Continuous Slab Casting Mould and Its Application

In order to understand the thermal and mechanical behavior during solidification of the strand in the slab casting mould, a two-dimensional coupled thermo-mechanical finite element model was built and the corresponding FEM program was developed. The model simulates a quarter of the transverse section of the strand as it moves down in the mould at the casting speed. The heat transfer in the mould and the strand is analyzed with the steady model and the transient model, respectively. A thermo-elastoplastic plane stress model is used for analyzing the strand deformation. The heat transfer and the deformation are coupled through the interfacial thermal resistance between the strand and the mould. The model was used to investigate the effects of mould corner configuration and mould taper on the crack formation tendency of strand. The results show that employing a chamfered mould with proper corner size could modify the 2D heat transfer conditions at slab corners, hence reducing the risk of transverse corner cracks. Likewise, employing an optimized parabolic mould taper could remarkably achieve better uniformity of the strand temperature and stress, and simultaneously reduce the peak value of the stress, thus resulting in less crack occurrence, which favorably coincides with the theoretical expectation. The successful application of the coupled thermo-mechanical model demonstrates its tremendous potentialities for further understanding of the internal crack formation and for the optimization of operation parameters and the mould configuration.