Round Billet Research Articles

Analytical modeling of the extrusion process using the electrostatics concept

Analytical and numerical modeling of metal forming processes has been studied by many researchers during the past decades. So far, several methods have been introduced to model material behavior during forming processes. In this research, the analogy between the classical plasticity theorem and electrostatic field line formation has been investigated for the first time. It is shown that the velocity potential function of movement in the plasticity and the charge-free electrostatic field are both in the form of Laplace’s relation. The aim of the current research is to model the metal forming processes using the equations governing the electrostatic fields. To demonstrate the effectiveness of the proposed method, the extrusion process is used as the benchmark. A three-dimensional CAD model of the deformation region is constructed and two different voltages are applied to the entry and exit sections based on the geometrical and extrusion parameters. Then, the Laplace’s relation is solved numerically and the relative extrusion pressure, particle flow path in the deforming region, and maximum plastic strain are calculated.To verify the proposed method, different sections are modeled and the results are compared with those in the literature. Finally, some experimental tests are conducted for the extrusion process of the round billets to complex sections. Significant agreement has been observed between the experimental results and the analytical ones. It is shown that the extrusion process could be modeled easily and accurately using the mathematical formalism of the electrostatics.

Effects of an even secondary cooling mode on the temperature and stress fields of round billet continuous casting steel

An unequal interval arrangement of nozzles (UIAN) in the casting direction of the secondary cooling process for round billet continuous casting has been presented. The cooling coefficient, spray width in the casting direction and water flow density distribution around the round billet circumference of the nozzles have been accurately determined. The effects of transverse nozzle arrangement, inter-zone distance, number of segments, and length of cooling zone on the temperature and stress fields of round billets were analyzed with a thermal-mechanical finite-element model. Alternating the maximum and minimum water flux by rotating 22.5° between the odd and even rows nozzles can prevent the cooling intensity from being too strong at the same position along the casting direction of a round billet, and enhance the quality of the strand. Decreasing the inter-zone distance can help to even out the surface temperature and stress distribution of a round billet. Careful design of the number of segments number and length of the cooling zone can avoid sharp fluctuations in temperature at the spray cooling end position. An optimized secondary cooling system for achieving even secondary cooling has been designed and applied to an actual round billet casting machine, and the surface temperature of the round billets was very even, with mid-way cracks being completely eliminated.

DIE ENTRANCE BELL MATERIAL FIBERS DEFORMATION INHOMOGENEITY

The calculation of the absolute and relative increase in length of the fiber material, their true strain in the central and peripheral layers of the wire piece, depending on the draw ratio solid round billets. When driving in the hearth of plastic deformation fibers can only be shortened or lengthened or shortened at first, and then lengthen. Calculations have shown that for certain values of the degree of deformation of the wire may be a maximum of inhomogeneous deformation of fibers in cross-section and in the amount of plastic deformation.

Numerical Simulation of Distribution Characteristics of Electromagnetic Field for Round Billet with Mold Electromagnetic Stirring

A three-dimensional mathematical model of mold electromagnetic stirring (M-EMS) for round billet was established. Based on Maxwell’s equations, the distribution of electromagnetic field was solved by ANSYS software. Different process parameters’ influence on magnetic flux density and electromagnetic force (EMF) was studied. The results show that the magnetic flux density reaches the maximum at the stirrer center in the axis direction and increases with the increasing distance from the circle center on the cross section of the stirrer center. The tangential EMF is symmetric about the circle center and reaches the maximum at the edge of round billet. Both the magnetic flux density and the tangential EMF increase with the increasing current intensity. With the increasing current frequency, the magnetic flux density decreases, while the tangential EMF increases in the applied range of current frequency for M-EMS.

Use of a Round Continuous-Cast Billet for the Production of Rolled Sections

Different methods of making rolled sections are analyzed along with the advantages and disadvantages of rolling sections from round and square continuous-cast billets. A literature search is made to find studies concerning the use of round continuous-cast semifinished products for making sections.

Optimization of secondary cooling in continuous casting of round billet

Secondary cooling has significant effect on the quality of billet and the solidification law is also important to the practical production. A 2D mathematical model of solidification and heat transfer for round billet was established to study these based on surface temperature measurement and nail shooting test. Then water rate of every zone was redistributed and surface temperature recovery reduced 35.5 °C and 68.9 °C respectively when blank just entered secondary cooling zone and air cooling zone. The optimized water rate was applied in plant for two months, and the macroscopic samples were in good quality.

A Hybrid Numerical Method for Modeling the Extrusion Process

Analytical and numerical modelling of the metal forming processes has been studied by many researchers during the past decades. So far, several methods have been introduced to model the material behaviour during the forming processes. In this research, the analogy between the metal forming process and the electrostatics is investigated. It is shown that the governing relations in the plasticity theory of upper bound are analogous to the electrostatic equations. The forward extrusions of round billets to complex sections from the published papers were analyzed using the electrostatic method and the calculated results were compared to the simulated and experimental data in the literature. Finally, some experiments were performed for the extrusion of a round billet to a complex section. It was shown that the extrusion process could be modelled easily and accurately using the electrostatics mathematical formulation.

Effect of Groove Shape on Closure of Center Defects in Symmetric Rolling of Round Billets

Effect of Groove Shape on Closure of Center Defects in Symmetric Rolling of Round Billets

Characteristic and Formation Mechanism of Inclusions in 2205 Duplex Stainless Steel Containing Rare Earth Elements

RE2O3, RE2O2S, Cr2O3-RE2O3 and (Ca,Mg,Cr,RE)xOy inclusions are mainly identified in 2205 duplex stainless steel containing 0.041wt% rare earth elements. According to thermodynamic analysis, rare earth inclusions could be produced by rare earth elements combining with oxygen, sulfur, pre-existing Cr2O3 or (Ca,Mg,Cr)xOy. Most spherical or spindle rare earth inclusions may be deformed slightly during the rolling process. Large rare earth inclusions are distributed mainly at the edge and at a quarter of the diameter of the 2205 duplex stainless steel round billet. Prolonging soft blowing time after adding rare earth elements, increasing inclusions floating time and controlling sulfur content to suppress segregation may contribute to reduce the quantity of large rare earth inclusions.

Continuous round billet for bar production

Bar-production process systems are analyzed. The benefits of rolling bar from continuous-cast round and square billet are considered. The literature on bar production from continuous-cast round billet is reviewed.

Coupled numerical simulation on electromagnetic field and flow field in the round billet mould with electromagnetic stirring

In order to improve the quality of steel strands, mould electromagnetic stirrers (M-EMS) have become a widely used technique to control the molten steel flow in the mould. In this paper, a coupled three-dimensional numerical simulation of the electromagnetic field and flow field in the mould with M-EMS for round billet continuous casting was carried out based on the finite element method. The effects of the current, frequency and the nozzle insertion depth on the flow field are discussed. According to the calculations and analysis, the optimum combination of the current and frequency is 150–250 A and 4–6 Hz, and the corresponding depth of nozzle 100–120 mm. Industrial application shows that with these optimum parameters, the round billet quality was improved effectively and the simulation can serve for actual production.

Comparison of Uniform and Non-uniform Water Flux Density Approaches Applied on a Mathematical Model of Heat Transfer and Solidification for a Continuous Casting of Round Billets

Luiz F.P. Pereira’s name appeared incorrectly on the original publication of this article. It has been corrected here.

Load Prediction for the Extrusion from Circular Billet to Symmetric and Asymmetric Polygons Using Linearly Converging Die Profiles

The deformation load is the most important parameter in the press design as it affects the structure and the general integrity of the final product. Therefore, every other parameter such as die shape, friction, type of process (hot or cold), and speed considered in modeling is optimized to cut back on the metal forming load. The flow of metal is largely influenced by the geometry of the die and hence the geometric shape of the tools is the main factor by which an optimum load can be evaluated. In extrusion process the strain distribution, resulting from deformation load, and other important variables that influence material structure, such as a hydrostatic stress, are strongly dependent on the geometry of the die. In the present investigation using linearly converging die profiles, the extrusion of symmetric and asymmetric polygons such as circular, square, triangular, hexagonal, heptagonal, octagonal, and L-, T-and H-, respectively sections from round billet have been numerically simulated. Mathematical equations describing the die profiles were derived, and then using MATLAB R2009b the co-ordinate of the die profiles was evaluated. A solid CAD model for the linearly converging die profile was made using Autodesk Inventor 2013 software and numerical analysis using DEFORM software for extrusion of the above sections from round billet was then performed to predict, for dry and lubricated condition, the extrusion load during deformation. It is found that the predictive loads for asymmetric shapes are found to be higher than that of the symmetric shapes. While there is no marked difference between the predictive loads for symmetric shapes that of the asymmetric shapes is significant where L-section has the highest extrusion load, followed by T-section and the H-section given the least pressure.

Simulation of Low Frequency Electromagnetic DC Casting

A comprehensive multiphysics model has been developed to describe the effect of the low frequency electromagnetic field (LFEM) [1, on solidification in the hot-top Direct-Chill (DC) casting [ of round aluminium alloy billets. The volume averaged equations and the rigid solid phase assumption are assumed for fluid flow and heat transfer [. The electromagnetic induction equation for the field imposed by the coil is solved using the diffuse approximate method (DAM), structured in axial symmetry with Gaussian weight function, 6 polynomial basis and 9 nodded domains. The heat, mass, and momentum transfer equations are solved in primitive variables by meshless [ method using 5 nodded domains of influence and 5 scaled multiquadrics radial basis functions, using collocation. Explicit time stepping is used. Pressure-velocity coupling is performed by the fractional step method. The effects of intensity and frequency of the LFEM [ on the velocity and temperature fields is investigated. A comparison of the calculated results with different LFEM field process variables with that of the conventional hot-top DC casting process indicates that the velocity patterns, the temperature profiles, and the shape of the sump could be modified remarkably.

Improvement in secondary cooling of continuous casting of round billets through analysis of heat flux distribution

A mathematical model of heat transfer and solidification for a continuous casting of round billets was developed. The water flux density of the secondary cooling zone was experimentally measured, using an apparatus in industrial scale with two types of nozzles, flat jet and full cone jet. The profiles of water distribution were applied on the mathematical model. The results showed that the water distribution is not uniform in both longitudinal and angular directions owing to the unevenness of the spray and to the curvature effect of the round billet. This non-uniformity causes important variation of the heat transfer coefficients and superficial temperature of the billet, especially in the first cooling zones, where the temperature is higher. The mathematical model was used to simulate a change of nozzle type in the first cooling zone. The results showed that the heat flux and superficial temperature variations were reduced with a full cone jet nozzle in comparison with the flat jet nozzles.

Simulation on Effect of Divergent Angle of Submerged Entry Nozzle on Flow and Temperature Fields in Round Billet Mold in Electromagnetic Swirling Continuous Casting Process

A new process for swirling flow generation in the submerged entry nozzle (SEN) in continuous casting process of steel was proposed. A rotating electromagnetic field was set up around the SEN to induce swirling flow by Lorentz force. The flow and temperature fields in the SEN and round billet mold with electromagnetic swirling were numerically simulated and then verified by the electromagnetic swirling model experiment of low melting point alloy. The effects of divergent angle of the SEN on the flow and temperature fields in mold with electromagnetic swirling were investigated. The electromagnetic swirling flow generator (EMSFG) could effectively induce swirling flow of molten steel in the SEN, which consequently improved greatly the flow and temperature fields in the mold. Below the nozzle outlet in mold, with the increase of divergent angle, the stream of bulk flow diverged more widely, the high temperature zone shifted up, and the temperature field became more uniform. Above the nozzle outlet in mold, with 350 A electromagnetic swirling, when the divergent angle of the SEN increased, the upward flow velocity and the meniscus temperature first increased and then decreased. With a divergent angle of 60°, the upward flow velocity and meniscus temperature reaced the largest value.

Effect of Stress Field on Closure of Center Defects in Symmetric Rolling and Asymmetric Rolling of Round Billets

Although the closure of defects at the center of billets on rolling such billets is an important subject, a method of quantity evaluation for such closure has not yet been clarified. Therefore, to establish a method for such quantity evaluation, we study such defects using experiments and finite element analysis including asymmetric rolling, especially with respect to the integration of the hydrostatic stress Gm. The results showed that stress was widely distributed, as determined in the experiment and in the FEM analysis of rolling at the edge around an artificial central hole in which defects were simulated. Therefore, it was suggested that, to evaluate the behavior of defect closure, the size of defects and the shape of the grooved roll used should be taken into account. [doi:10.2320/matertrans.P-M2014837]

NON-UNIFORM WATER FLUX DENSITY APPROACH APPLIED ON A MATHEMATICAL MODEL OF HEAT TRANSFER AND SOLIDIFICATION FOR A CONTINUOUS CASTING OF ROUND BILLETS

In the present work, the water flux densities of nozzles with flat jet and full cone jet were experimentally measured using an apparatus in industrial scale that reproduces the secondary cooling of the continuous casting of round billets of Vallourec Tubos do Brasil. A mathematical model for heat transfer and solidification for the continuous casting of round billets was developed applying the experimental water flux density profile, establishing a non-uniform water distribution approach. The mathematical model was validated by experimental measurements of the billet superficial temperature, performed at the industrial plant. The results of the mathematical model using both uniform and non-uniform water flux density approaches were compared. The non-uniform water distribution approach enabled to identify important variations of the heat transfer coefficients and the billet temperatures, especially in the first cooling zone, and to assess more accurately the local effects of the water distribution on the thermal behavior of the strand. The non-uniform water flux density approach applied to the mathematical model was a useful and more accurate tool to improve the comprehension of the thermal behavior of the steel along the secondary cooling

An analytical formulation as an alternative to FEM software giving strain and stress distributions for the three-dimensional solution of extrusion problems

A new improved analytical method based on the upper bound theorem is presented for the solution of extrusion problems. This method has been formulated in such a way as to eliminate the deficiencies in the previous works in order to enable it as a powerful analytical tool as an alternative to finite element software. The proposed formulation is a general method of solution, which could be used for the analysis of many bulk forming processes. However, in this paper, the forward extrusion of a square section from a round billet has been presented as an example. Kinematically admissible velocity fields were computed which gave a more physically realistic material flow patterns as compared to previous works. The distribution of strain and stress as well as the results for the effect of process parameters on the extrusion load and die geometry was also given. These results were compared with FEM data to observe the accuracy and effectiveness of the present method. For the extrusion of square sections from round billets, detailed analysis of strain distribution on the exit section was carried out using the components of the power due to internal deformation, interface friction, and velocity discontinuities at the entry and exit surfaces. Comparison with experimental data was made, and verification of the theoretical results was carried out. The improvement of the results computed using the present method was shown by comparison with the previous works.

Adaptable dies to minimize distortion in non-axisymmetric extrusions

An upper bound model for the extrusion of a round billet into a round-corner rectangular product has been developed for use with the adaptable die design method. The analysis shows the use of the adaptable die design method for minimizing distortion in the extrusion product. The flow fields are a modification of previous axisymmetric models, but are extended to permit rotational movement to occur during deformation. The extrusion die is analyzed in two segments. A streamlined segment imposes the deformation, and a bearing length segment is attached at the end. The power terms associated with the deformation process are derived. Similar to the axisymmetric analysis, the use of a streamlined die shape at the entrance and exit regions for the deformation zone produces no internal shear power losses along the two internal surfaces, which separate the initial and final rigid body material from the deformation region. The extrusion die shapes are determined by the adaptable die design method, where adjustable coefficients for characterizing the streamlined die are found by minimizing the volumetric effective strain rate deviation. The adaptable extrusion die shapes, based on minimizing the volumetric effective strain rate deviation in the deformation zone, produce minimum distortion in the extrusion product and are equivalent to a controlled strain rate die shape. Confirmation is obtained by analyzing the results from three-dimensional finite element models for extrusion through the adaptable die shapes. The analysis presented can also be modified to analyze other non-reentrant extrusion product shapes.