JPH09103856A - Continuous casting system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a continuous casting system for steel by which good-quality steel free from central segregation and central porosity is easily obtained at all times even if steel kinds, sectional shapes and sizes, continuous casting machine profiles and operating conditions (casting speeds, temps., cooling methods, etc.) change. SOLUTION: The conditions to arise internal defects and the positions where such defects arise are calculated by taking notice of the solidification condition over the entire area from a meniscus (the surface position in the upper part of the molten metal layer) to a crater end and the liquid phase pressure drop occurring in the intra-dendrite liquid phase flow (Darcy flow) induced by the shrinkage by solidification in the casting direction in the solid-liquid co-existence phase in accordance with the kinds (profiles) of the continuous casting machines and the steel kinds, sectional shapes and sizes and the operation conditions (casting speeds, temps., cooling methods, etc.). This system includes an electromagnet booster for impressing electromagnet body force (Lorentz force: remote force) in the casting direction near the position where the internal defects arise.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a continuous casting system, and more particularly to a continuous casting system suitable for obtaining a high quality steel free from segregation and porosity.

[0002]

2. Description of the Related Art In continuous casting of so-called steel such as carbon steel, low alloy steel and special steel, it has been said that it has been technically established for more than 20 years since the current bending type continuous casting machine started to operate. On the other hand, quality requirements are becoming stricter year by year, and at the same time, the pressure for cost reduction is increasing. Apart from problems such as breakouts that often became a problem in the early stage of operation, as an important quality problem,
(1) Center segregation and (2) Center microporosity remain.

The center segregation is a V-shaped segregation which is generated with periodicity in the final solidified portion with the thickness center, and is often called V segregation.

The central microporosity is also a minute void generated between dendrites in the final solidified portion at the center of thickness.

In the present specification, these defects will be collectively referred to as central defects hereinafter.

Next, the influence of the central defect on the quality of the product will be briefly described.

(1) In case of thick plate:

Hydrogen coagulates and precipitates in the central defects, and cracks called hydrogen-induced cracking occur during use. In addition, when welding is performed, weld cracking occurs from the center defect.

(2) In the case of bar wire:

At the time of wire drawing, microporosity becomes a starting point and breaks.

(3) In case of thin plate:

Band-like defects are generated during press forming or cold rolling. This is caused by unevenness of hardness due to the mixture of hard and soft parts due to segregation.

These are defects that occur during the solidification process in continuous casting and are defective products.

The segregation generated in the solidification process remains in the final product and cannot be eliminated in the intermediate process. For the time being, there is a method of diffusing and eliminating macrosegregation by heat treatment, but this requires long-time treatment at a high temperature, which is not preferable in terms of heat economy and technology.

Although microporosity can be crushed by hot rolling, whether it can be completely eliminated depends on the amount of porosity. Furthermore, it should be noted that microporosity is often accompanied by segregation.

As described above, the central defect is a problem related to the essence of the solidification phenomenon, but at present it is difficult to solve it by accumulating know-how or by means of trial and error improving.

These central defects are, to varying degrees, old and new problems existing from the beginning of continuous casting common to all steel grades of slab, bloom and billet.

Next, important techniques will be described with respect to the countermeasures that have been taken so far to improve the internal defects.

(1) Prevention of bulging

It is said that in a slab having a wide plate width, when the solidified shell between the support roll pitches, that is, the solid portion of the slab swells by the molten steel pressure, center segregation occurs. This is caused by the flow of the high-concentration liquid phase in the solid-liquid coexisting phase due to the deformation of the solidification shell, but the detailed mechanism has not been sufficiently clarified. Therefore, in order to reduce the bulging as much as possible, the support roll interval should be shortened or 1
A split roll system is adopted in which the length of a book support roll is split in the longitudinal direction. In addition, it is said that uneven rolls cause the liquid phase between dendrites to flow and cause segregation. However, in reality, center segregation occurs in blooms and billets where bulging hardly poses a problem, and therefore internal defects cannot be eliminated even if these mechanical disturbances are eliminated.

(2) Enhancement of secondary cooling (Reference (1),
(2))

Near the final solidification part (near the crater end)
It is a method of reducing the amount of porosity in the central part by strongly cooling and compressing it by heat stress so as to correspond to the solidification shrinkage in the solid-liquid coexisting phase.

On the other hand, the current mainstream method is to reduce internal defects by pressing down the solidified shell in the vicinity of the final solidified portion and compressively deforming the solid-liquid coexisting phase in the central portion to suppress liquid phase flow between dendrites. According to the difference in the amount of reduction, it is divided into a light reduction method and a strong reduction method.

(3) End-coagulation light reduction method (Reference (3),
(4))

Although solidification shrinkage occurs continuously with the progress of solidification, this method is intended to improve the center segregation by compressively deforming the solid-liquid coexisting phase so as to compensate the shrinkage amount commensurate with this.

Since the rolling reduction needs to correspond to the amount of solidification shrinkage that occurs continuously as closely as possible, it is necessary to make a gradient in the rolling reduction amount. For example, Document (3) shows that center segregation is improved by an actual machine test of a carbon steel bloom using a crown roll having a rounding down roll. Further, in Reference (4), high carbon steel (C content 0.7 to 1 m
%), a theoretical calculation example of the necessary reduction gradient in the case of a bloom having a cross section of 300 × 500 mm is shown, and it is estimated that a reduction gradient of 0.2 to 0.5 mm / m is required. ing.

However, in order to implement this method on an actual machine, the following problems must be overcome.

[0028] Usually, the reduction is performed within a range of several meters near the final solidification portion, but in the case of the bloom of the above-mentioned document (4),
In this range, it is about 0.3 mm / m. That is, it is necessary to roll down the solidified shell with an inclination of 0.3 mm per 1 m, but this requires controlling the rolling down amount with a very high precision by a multi-stage roll rolling down device or the like. Therefore, the reduction device is inevitably expensive.

[0029] If the amount of reduction is insufficient, the effect cannot be expected, and if it is too large, the liquid phase will flow back to the upstream side and the channel will change.
There is a difficulty in causing l-segregation (reverse V segregation).

[0030] The required reduction amount and gradient differ depending on the operating conditions such as steel type, sectional size and continuous casting speed, and cooling conditions. Therefore, a great deal of labor and cost are required for trial and error to find an appropriate condition even when the number of applicable product types is small.

[0031] Since the light reduction method often causes a new problem of internal cracking (Reference (5)), the conditions for preventing this must also be taken into consideration.

As described above, it is very difficult to exert the effect by this method.

(4) Continuous forging method (see references (7) and (8))

Next, the strong reduction method will be described. This method is a method of mechanically applying large downward deformation in the vicinity of the final stage of solidification and squeezing out the liquid phase having a high solute concentration in the solid-liquid coexisting phase to the upstream side to prevent center segregation (V segregation). There are a method of reducing with a caliber roll (reference (6)) and a continuous forging method of reducing with an Anvil (die) (references (7) and (8)). Since both belong to the same category ideologically, only the latter will be described.

As shown in FIG. 42, Anvil is pressed down while moving in the casting direction to crush the vicinity of the final solidified portion. It is reported that by repeating this periodically, the liquid phase having a high solute concentration in the solid-liquid coexisting phase can be squeezed out to the low solid fraction region on the upstream side to eliminate the center segregation and the center porosity. It also says that internal cracks can be eliminated by setting appropriate forging pressure conditions. In this method, Degree) can be controlled to Ke <1.

The most important point in the segregation control by this method is the elucidation of the flow phenomenon of the solid-liquid coexisting phase at the time of forging. Offer (7)).

In their model, the flow of the liquid phase in the solid-liquid coexisting phase is not treated explicitly, and therefore it is not clarified how the flow of the concentrated liquid phase on the dendrite scale affects the segregation.

Therefore, the average macrosegregation in the macroscopic inspection region in the solid-liquid coexisting phase can be controlled, but no information can be obtained about the segregation in the smaller inspection region (dendritic scale) called semi-macrosegregation. . Semi-macro segregation remains to some extent.

Therefore, elucidation of the phenomenon that the semi-macro segregation remains is a future subject, and for that purpose, it is necessary to clarify the flow phenomenon of the discharged liquid phase.

In connection with this, at the time of forging, V
It is quite possible that segregation has formed, and in this case what effect does the effluent phase flow have? Problems such as whether it remains as semi-macro segregation are raised.

In these documents, a bloom having a cross-sectional shape close to a square is dealt with, and the shape of the solid-liquid coexisting phase can be approximated to a cylindrical shape. When the solid-liquid coexisting phase is compressed roughly concentrically, the discharge flow pattern is relatively simple. However, whether or not a wide slab has a simple upstream flow pattern is an issue.

In any case, when the solid-liquid coexisting phase is mechanically largely deformed, it is not easy to predict the flow of the concentrated liquid phase and evaluate its influence.

(5) Electromagnetic stirring (references (9), (10))

A method of agitating the solid-liquid coexisting phase near the final solidification position by electromagnetic force to disperse the central segregation, and specifically, a method of swirling and flowing in the cross section of the solidification shell (Reference (9)) ).

Another method is a method of changing columnar crystals into equiaxed crystals by performing electromagnetic stirring in a secondary cooling zone (cooling zone other than the casting mold part) or in the casting mold (Reference (1
0)).

The latter method is based on the premise that equiaxed crystals have less center segregation than columnar crystals, but the theoretical basis for this is not clear.

These are not essential solutions and have not become current mainstream.

(6) Method by a combination of the above (1) to (5)

The bulging prevention measure has been consistently emphasized as a basic technique until now, and the following combinations are carried out based on this.

For example, in Document (10), 0.08 to 0.1
8wt% carbon steel slab with short roll pitch and split rolls (preventing bulging) and taper alignment method (corresponding to shrinkage of slab (solidification shrinkage + shrinkage due to temperature drop) corresponding to the gap between the rolls in the downstream direction. The technology to gradually narrow down is described.

However, it is difficult to realize with high accuracy.

Further, Document (11) states that central porosity is reduced when carbon steel bloom and round billet in which equiaxed crystals are hard to develop are combined with low temperature casting and electromagnetic stirring to develop equiaxed crystals. Furthermore, it is reported that the center segregation and the center porosity can be reduced by electromagnetic stirring in the mold to form equiaxed crystals and to optimize the final solidification reduction amount.

(7) Cast in thin slab continuous casting
Rolling method

The so-called mini mill, which is a compact integrated steel making process, is more effective in utilizing raw materials (recycling), energy saving, than the heavy and long process using a conventional blast furnace.
It has advantages such as low construction cost and environmental friendliness, and is steadily gaining momentum. 200m which is conventional in the mini mill
Near-net-shape-cas as close as possible to the final product shape rather than a large cross section of m, 300 mm
Continuous casting of thin slabs with a thickness of 50 mm and 60 mm, which is called tinging, is performed.

Here, as an example, Casting Ro
The lling method (reference (12)) will be described. This method is a technique in which a region containing a solid-liquid coexisting phase and a liquid phase is gradually compressed by a roll (reduction rate: 10 to 30%) to be thinned. The original purpose is considered to be born from the idea that there is a limit to reducing the wall thickness at the casting port, and it should be thinned during solidification, but it is reported that this has the following effects. . . Mechanical destruction of dendrites gives rise to granular fine crystals. . As a result, macro segregation is also considerably reduced.

However, when the solid-liquid coexisting phase is strongly worked, the behavior of the liquid phase having a high solute concentration induced is difficult to predict, and it is very difficult to control it so as not to cause harmful results such as inverse V segregation. .

In the above, the important points for the important technique for improving the internal quality have been explained from a large amount of literature on continuous casting of steel.

Historically, it was traced back to the taper alignment method aimed at suppressing the bulging that causes segregation, and the roll pitch was shortened and the split roll system was adopted.
Progressed to strong cooling of secondary cooling zone and electromagnetic stirring, and now is light /
The mainstream is high pressure or a combination of electromagnetic stirring and light pressure.

However, as the demand for product quality becomes stricter, this old and new problem is always re-evaporated, and these measures have been repeatedly implemented in a certain sense.

In the meantime, although the technical level has improved, the solution to the essential problem has not been reached.

[0061]

However, all of the conventional improvement techniques are trial and error improvement measures based on empirical and qualitative insights on the solidification phenomenon.
When the cross-sectional shape and dimensions, continuous casting machine profile, and operating conditions (casting speed, temperature, cooling method, etc.) differed, enormous amount of time and labor was required to find new appropriate conditions.
Moreover, there were many cases in which it was not always possible to find optimal conditions.

In other words, each of the measures has succeeded in temporarily reducing the segregation to some extent, but since the behavior of the solidification is not accurately grasped based on the solidification theory, its effect cannot be evaluated correctly, and it is optimum. There was an inconvenience that the condition could not be found.

[0063]

OBJECTS OF THE INVENTION It is an object of the present invention to improve the disadvantages of the prior art, particularly in a continuous steel casting system,
Even if the steel type, cross-sectional shape and dimensions, continuous casting machine profile, and operating conditions (casting speed, temperature, cooling method, etc.) change, it is always possible to easily obtain high-quality steel without center segregation and center porosity. To provide a casting system.

[0064]

Therefore, according to the present invention, the meniscus (molten metal) is determined based on the type (profile) of the continuous casting machine, the steel type, the sectional shape and dimensions, and the operating conditions (casting speed, temperature, cooling conditions). Focusing on the liquid state pressure drop caused by the liquid phase flow (Darcy flow) between dendrites induced by solidification contraction in the casting direction in the solid-liquid coexisting phase, and the internal defects The continuous casting system is equipped with an electromagnetic booster that calculates the conditions and the position where the internal defect is generated, and applies an electromagnetic volume force (Lorentz force: remote force) in the casting direction in the vicinity of the internal defect generation position. . This aims to achieve the above-mentioned object.

[0065]

In order to accurately know the generation position, generation form and shape of internal defects, it is necessary to clarify the generation mechanism of internal defects by conducting a numerical analysis of the solidification phenomenon based on the solidification theory. The theory of numerical analysis by the calculating means in the present invention will be described in detail.

A. Numerical analysis of solidification phenomenon

A-1. Calculation formula required for numerical analysis of solidification phenomenon

The calculation formula required for the numerical analysis of the solidification phenomenon devised by the inventor based on the solidification theory will be described.

(1). Energy conservation formula

The energy conservation equation for the heat balance of a certain volume element in the solid-liquid coexisting phase is given by equation (1).

As shown in FIG. 7, the volume element is sufficiently larger than the spacing between the branches of the dendrite crystal (dendritic arm spacing), the temperature T of the object, and the solid fraction g.
_It should be sufficiently small so that changes in physical quantities such as _S can be investigated.

[0072]

Details of each symbol are shown in Table 1.

[0074]

[Table 1]

Here, the first term on the left side of the equation (1) is the change in the amount of heat per unit volume / unit time, and the second term is the divergence due to the flow of the liquid phase in the coexistence of solid and liquid and the deformation of the solid phase (unit time / unit. (Outflowing heat amount per volume), the first term on the right side is the divergence due to heat conduction, and S is the heat generating term.

As shown in the following equation (2), S is composed of the sum of the heat generation term due to the latent heat of solidification, the influence term due to the solid phase deformation, and the Joule heat due to the current.

[0077]

[0078] It is given by the following equation (3) using g _S and liquid phase volume ratio (hereinafter, simply referred to as liquid phase ratio) g _L.

[0079]

Here, when g _V is the volume ratio of porosity, there is a relation of equation (4).

[0081]

The specific heat C, the density ρ, and the thermal conductivity λ take into consideration the temperature dependence for each of the liquid phase and the solid phase.

The expressions (1) and (2) can be applied not only to the solid-liquid coexisting phase but also to the liquid phase, the solid phase and the phase containing porosity.

(2). Solute redistribution formula

Solute atoms are dissolved in the solid phase and the liquid phase, but their distribution state is determined by the equilibrium diagram and the diffusion rate of atoms in each phase. For example, carbon atoms diffuse rapidly not only in the liquid phase but also in the solid phase. On the other hand, the diffusion of silicon atoms in the solid phase is very slow.

Therefore, in the present invention, all alloy elements are completely diffused in the liquid phase between dendrites, but only carbon is completely diffused in the solid phase, and other elements are not diffused. That is, carbon is an equilibrium solidification type alloy element as shown in FIG. 3B, and other elements are non-equilibrium solidification type alloy elements as shown in FIG. 3C.

As shown in FIG. 4, the liquidus and solidus lines in the equilibrium diagram are bent. Equation (15).

[0088]

[0089]

[0090]

^{M L} and m ^S are the slopes of the liquidus and solidus lines, respectively, and other symbols are shown in FIG.

To derive the conservation law for solutes in the liquid and solid phases, it is necessary to consider the flow of the concentrated liquid phase and the deformation of the solid phase. The solute conservation law considering these is expressed by the following equation.

[0093]

Here, the first term on the left side of the equation (8) is the change in the average dissolved mass of the alloying element n in the solid-liquid coexisting phase, the second term is the divergence due to the liquid phase flow between dendrites and the solid phase deformation, and the right side is the liquid. This is the diffusion term in the phase. A detailed explanation of the symbols is given in Table 1.

The law of conservation of mass, that is, the continuity condition is given by the following equation.

[0096]

[0097] By combining (9) to (9), the following series of equations are derived for equilibrium solidification type alloy elements and non-equilibrium solidification type alloy elements.

[0098]

[0099]

Here, the coefficient for the equilibrium solidification type (j type) alloy element is obtained by the equations (12) to (15).

[0101]

[0102]

[0103]

[0104]

The coefficient for the non-equilibrium solidification type (i type) alloy element is determined by the equations (16) to (19).

[0106]

[0107]

[0108]

[0109]

It should be noted that β is obtained by the equation (20).

[0111]

(3). Relation between temperature and solid fraction

[0113]

[0114]

Here, the liquidus temperature during solidification of the multi-component alloy is determined by the superposition of temperature drops in the binary equilibrium diagram of the mother metal and each alloy element (Reference (15)). That is, the relationship of the expression (21) can be expressed as the expressions (22) and (23).

[0116]

[0117]

Details of each symbol are shown in Table 1. N represents the number of alloying elements.

Next, the equation (22) is differentiated with respect to time,
Substituting the equation (10), the temperature as in the equation (24)
The solid phase relation is obtained.

[0120]

Here, S is given by (25).

[0122]

Further, A _n , B _n , C in the equation (25)
_n and D _n are given by the equations (12) to (20).

(4). Darcy's formula

The flow of liquid phase between dendrites is (26)
It is known that it is described by Darcy's formula as shown by the formula (p.234 of document (14)). The detailed meanings of the symbols are shown in Table 1.

[0126]

[0127] The volume force (Lorentz force) is included.

K is a constant determined by the geometric structure of dendrite, and is given by the following equation when the Kozney-Carman equation (Reference (17)) is applied.

[0129]

Here, Sb is the surface area (specific surface area) per unit volume of the dendrite crystal, and it is known that the dimensionless constant f has a value of 5 by the flow experiment in the porous medium. K is a tensor amount that originally has anisotropy,
It was determined by the following two methods.

.. Method 1: Dendrite solidification model

In order to obtain Sb in the K equation, it is necessary to consider the specific dendrite shape and solute diffusion in the solid and liquid phases. Kubo and Fukusako modeled dendrites as shown in Fig. 5, consisting of cylindrical branches and trunks and hemispherical tips, and derived a conservation equation for the solute balance at the solid-liquid interface. Phenomenon in which supercooling occurs at the spherical interface due to the curvature effect (p.152, 26 of Ref. (14))
6) was used to derive the formula for Sb, and it was shown that K calculated using this was in good agreement with the measured value (Reference (18)). The shaded area in FIG. 5 represents the portion where the solute concentration discharged from the interface is high. Further, d is the diameter of the dendrite cell, and r is the radius of the tip of the hemispherical dendrite.

Therefore, their method was applied to a nonlinear multi-component alloy to obtain the following equation.

[0134]

Here, α is a correction coefficient introduced for correcting errors in various physical property values.

[0136] Then, Sb and K at time t + Δt can be calculated.

It is known that the relationship between Sb and the diameter d of the dendrite cell is given by the following equation from Stereology.

[0138]

Here, φ is the shape factor, and φ =
1 and φ = 2/3 in a cylinder (application of powder theory, Maruzen (1961), p.87, p.132). g _S is about 0.
When the value becomes 7, adjacent dendrite cells collide with each other. Therefore, the value of d when g _S = 0.7 was calculated from the equation (29) and used as the size of the dendrite cell at the end of solidification.

.. Method 2: Experimental method

Substituting equation (29) into equation (27), f = 5
Then, the equation (30) is obtained.

[0142]

If the dendrite has a stubby shape, φ = 1 may be set (reference: Determined and given by the following empirical formula (Reference (14)
P. 146).

[0143]

[0144] The diameter d of the dendrite cell can be calculated.

The formula (30) is a simple formula, but since it has a drawback that the accelerated solidification phenomenon in the central portion cannot be expressed, it is necessary to properly use the method 1 and the method 2.

(5). Equation of motion

The flow of the liquid phase in the completely liquid phase region is New
The second law of ton, that is, (mass) × (acceleration) =
It is described by (force acting on the object). This is (3
As shown in the equation (2), it can be rephrased to the law of conservation of momentum that "the temporal change of momentum (= mass x velocity) is equal to the force acting on the object".

[0148]

The right side of the equation (32) is the total sum of pressure, viscous force, volume force and the like.

Therefore, the equation of motion regarding the liquid phase flow in the solidification process can be expressed by equation (33). Details of the meanings of the symbols are shown in Table 1.

[0151]

The expression (33) is solved so as to satisfy the continuous condition expression of the expression (9).

The subscript i of the equation (33) represents each component in the given coordinate system (for example, in the (x, y, z) Cartesian coordinate system, v ₁ = v _X , v ₂ = v _y , v ₃ = v _Z ).

[0154] Introduced for your convenience.

The first term on the right side is the viscous force term, the second term is the pressure term,
The third term is the sum of various volume forces, and the fourth term is the Darcy flow resistance term.

Therefore, the equation (33) does not distinguish the liquid phase region, the solid-liquid coexistence region, and the solid phase region. Then, the equation of motion becomes normal, and Dar in the solid-liquid coexisting phase
Cy resistance is dominant (inertial force and viscous force are small and can be ignored), and in the solid phase, μ is set to a large number

(6). Treatment of perlite metamorphosis

When the surface of the solidified shell is strongly cooled, pearlite transformation may occur due to the temperature drop of the surface layer.

[0159] 4).

[0160]

Here, Vex is the expanded volume of pearlite particles, t is time, T is temperature, and the function f (T) is obtained from the isothermal transformation diagram (TTT diagram) (Reference (21)).

[0162] It is added to the heat generation term of energy equation (2).

A-2. Discretization of equations

The above equations that describe the solidification phenomenon facilitate the transformation and manipulation of the equations, are simple, and are scalar and vector gradients (▽ () or g) so that they can be used in all coordinate systems.
rad () and divergence (▽ ・ () or di
It is formulated using symbols such as v ().

Therefore, in order to perform high-speed calculation by a computer, these expressions are concretely expressed for each coordinate system such as Cartesian coordinates and cylindrical coordinates, and as shown in FIG. It is necessary to carry out and make it concrete. This is called the discretization of the equation.

In the present invention, the discretization is performed based on the method by Patankar (reference (20)).

Generally, when a scalar or vector physical quantity is represented by φ, the conservation law regarding φ can be represented by the equation (35).

[0168]

[0169] It is the source term.

Further, the velocity must satisfy the continuous condition given by the following equation (36).

[0171]

Since the expressions (35) and (36) are displayed in the differential form, the three-dimensional Cartesian coordinate system (x, y) When t is executed and t is rearranged, the following series of equations (37) to (46) are obtained (reference (2)
0) p. 101). In FIG. 8, the shaded area is cont
Representing a roll volume, points marked with a circle are gri
Called d point. Fe, Fw, Fn, Fs,
Ft and Fb are each surface e of the control volume,
w, n, s, t, b (t and b are planes parallel to the paper surface)
Shows the entry and exit of the physical quantity φ in.

[0173]

Here, the subscript P indicates the defining position (not necessarily the center of gravity) of the physical quantity φ in the volume element. nb refers to six adjacent defining points (E, W, N, S, T, B).
these It is represented by (38).

[0175]

[0176]

[0177]

[0178]

The side term (source) on the right side of the equation (37)
e term) b is given by the following equation (41).

[0180]

The superscript “old” indicates the time t to the time t +.
Calculation step in time change to Δt A term relating to diffusion of the physical quantity φ on each surface (e, w, n, s, t, b) of the element (diffusion term)
And is given by the following equation (42).

[0182]

[0183] Is a term (flow term) related to
Given in 3).

[0184]

The sign in the equation (58) is defined as + when it flows into the volume element and-when it flows out.

[0186] It means adopting one. This allows, for example,
When φ means the temperature T, Fw is effective because it is an inflow on the surface w, and Tp is affected by the temperature Tw on the upstream side, while −Fe is ineffective and Tp is a downstream because it is an outflow on the surface e. The physical rationality of not being affected by the temperature T _E of the side is taken into consideration (however,

P _nb is a Peclet number representing the relative degree of influence of flow and diffusion, and is defined by the following equation (44).

[0188]

[0189]

[0190]

Source term S
Considering that is generally a function of φ, the following equation (46)
Can be linearized as shown in.

[0192]

Here, S _c and S _p are constants determined in association with concrete equations.

The result of discretizing each equation described in A-1 above is described at the end of this specification.

Regarding the coordinate system, in consideration of the fact that the continuous cast slab is elongated and curved in the middle, as shown in FIG. 9, a curved coordinate system having orthogonality so as to fit the slab profile. It was adopted. Each discretization formula is written in the coordinate system.

Further, since the right cylinder and the orthogonal three-dimensional coordinates are included as a simple case of the orthogonal curve coordinate system, they can be applied with a minimum modification such as deleting an unnecessary part from the discretization formula. That is, each discretization formula is applicable to various slab profiles and cross-sectional shapes.

A-3. Internal defect analysis

(1). Macro segregation

The average solute concentration of the solid-liquid coexisting phase is, as shown in FIG. 3 (b), the equilibrium solidification type (j type).

[0200]

As shown in FIG. 3C, the nonequilibrium solidified (i-type) alloy element is represented by the formula (48).

[0202]

[0203]

(2). Effect of solid solution gas in molten steel

It is widely known that the gas solid-solved in the molten steel is concentrated in the liquid phase between the dendrite crystals as the solidification proceeds to form gas-based microporosity.

Here, the analysis method will be described according to the treatment of Kubo et al. (Reference (19)).

CO is the main cause of gas porosity in cast steel.
Since it is a gas, CO gas is assumed to be the only gas source. This CO gas is produced by the reaction of the following equation.

[0207]

That is, the equilibrium pressure of CO gas is given by equation (50).

[0209]

Here, CL is the carbon concentration in the liquid phase, OL is the oxygen concentration in the liquid phase, and Pco is the equilibrium atmospheric pressure (at
m) and Kco are equilibrium constants.

Further, O is S which is usually added as a deoxidizing element.
It is assumed to combine with i to generate SiO ₂ (solid) (ignoring the effect of Mn).

Accordingly, the mass conservation law concerning C and O is given by the following equations (51) and (52).

[0213]

[0214]

[0215]

The solid solution amount of carbon and oxygen in the solid phase is expressed by the following equation (53) using the equilibrium partition coefficient.

[0219]

[0218]

Similarly for the reaction between Si and O

[0220]

[0221]

[0222]

[0223]

By solving the simultaneous equations composed of the above equations (50) and (52) to (58), Pco and

(3). Effective void radius and growth law of porosity

As shown in FIG. 6, the place where the microporosity is generated is considered to be the place where the local free energy is minimized, that is, the root part of the dendrite (Reference (19)). The effective radius r of the void is modeled as follows.

Now, between the pair of dendrite arms, 1
Assuming that there exists a liquid phase space of x, consider a situation in which these minute spaces are three-dimensionally distributed, as shown in FIG. 6 (b).

The three-dimensional average value of the dendrite interval is D,
Liquid phase ratio, where n is the number of liquid space

[0229]

Further, as shown in FIG. 6C, r, D
And the relationship between the dendrite cell size d and Eq. (60).

[0231]

Then, the following equation (61) regarding r is obtained from the equations (59) and (60).

[0233]

However, in an actual dendrite structure having a complicated morphology, r is corrected. .

[0235] It can be seen that and d become smaller, and r becomes smaller.

If the solid solution gas is not taken into consideration, the gas equilibrium pressure becomes zero. Even in such a case, when the hydraulic pressure becomes lower than the critical pressure, porosity due to contraction is generated. In such a case, the equation relating to the growth of the internal porosity once generated is given by the continuous condition equation (9) as follows (however, the influence of solid phase deformation is ignored).

[0237]

The first term on the right side is the contribution from the solidification contraction, and the second term is
The term represents the contribution from the divergence of the liquid phase.

A-4. Numerical analysis method

In the above energy formula, the temperature can be calculated from the solid fraction, the volume fraction of porosity, the density of the liquid phase, and the flow velocity vector of the liquid phase.

In the solute redistribution formula, the solute concentration in the liquid phase can be calculated from the solid fraction, the volume ratio of porosity, the density of the liquid phase, and the flow velocity vector of the liquid phase.

In the above temperature-solid fraction equation, the liquid phase temperature in the solid-liquid coexisting phase can be calculated from the solid fraction, the volume fraction of porosity, the solute concentration of the liquid phase, and the flow velocity vector of the liquid phase.

In the above equation of motion, the flow velocity vector of the liquid phase can be calculated from the density of the liquid phase, the density of the solid phase, the pressure of the liquid phase, and the transmittance.

In the above pressure equation, the pressure of the liquid phase can be calculated from the density and solid fraction of the liquid phase and the flow velocity vector of the liquid phase.

However, since the variables in the above equations are linked (linked) to each other, iterative calculation is required until a coupled solution is obtained.

Here, as the solid phase velocity, a theoretical value or an actually measured value by stress analysis or the like is used.

Next, the analysis method will be specifically described with reference to the flowchart of FIG.

.. Boundary conditions and initial conditions are set as variables (step S1 in FIG. 10A).

.. The flow velocity distribution of the liquid phase and the pressure distribution of the liquid phase are obtained based on the region shapes and the transmittances of the solid phase, the liquid phase, and the solid-liquid coexisting phase, and the density distribution of the liquid phase (step S in FIG.
2).

Here, the flow velocity distribution of the liquid phase is calculated using the equation of motion or the Darcy formula, and the result is used to calculate the pressure distribution of the liquid phase from the pressure formula.

.. From the calculated pressure distribution of the liquid phase, it is determined whether or not the microporosity generation condition is satisfied (Fig. 10).
If it is satisfied in step S3 of (a), the volume ratio and size of porosity are calculated (step S4 of FIG. 10A).

.. Based on the calculated flow velocity distribution of the liquid phase and the volume fraction of porosity and the heat removal rate from the surface of the slab,
Obtain the temperature, solid fraction, and solute concentration in the liquid phase (Fig. 10 (a))
Step S5).

Here, a coupled solution of the energy equation, the solute redistribution equation, and the temperature-solid fraction equation is calculated.

.. The specific surface area Sb and the diameter d of the dendrite cell are calculated by applying the dendrite solidification model based on the calculated temperature, solid phase ratio, and solute concentration in the liquid phase (FIG. 1).
0 (a) step S6).

.. The transmittance K is calculated based on the calculation result of the specific surface area Sb and the diameter d of the dendrite cell (FIG. 10).
(A) Step S7).

.. Calculate temperature and density of liquid phase (Fig. 10)
(A) Step S8).

.. It is determined whether the pressure of the liquid phase has converged (step S9 in FIG. 10A), and if it has converged, macrosegregation is calculated from the equations (34) and (35) (see FIG. 10 ( In step S10) of a), if not converged, the subsequent arithmetic processing is repeated. The reason for repeating the arithmetic processing here is that the solution of the simultaneous equations cannot be uniquely determined because the number of equations and the number of unknown variables are the same.

That is, since the transmittance calculated in step 1 and the density of the liquid phase calculated in step 1 influence the flow velocity distribution of the liquid phase, it is necessary to perform the calculation again using these values. .

Here, the details of the method for obtaining the flow velocity distribution of the liquid phase and the pressure distribution of the liquid phase using the equation of motion will be described.

.. As an initial setting, the speed at time t is set to an initial value (step S in FIG. 10B).
1).

.. Coefficients ap, aN, a of the velocity discretization formula
S, aT, aB, aW, aE, b are calculated, and v1, v
2 and v3 are calculated (step S2 in FIG. 10B).

.. The coefficient of the pressure discretization formula (E.86) is calculated (step S3 in FIG. 10B).

.. A boundary condition for pressure is introduced (step S4 in FIG. 10B).

.. The pressure distribution of the liquid phase is calculated from the pressure discretization formula (step S5 in FIG. 10B).

.. Based on the calculated liquid phase pressure distribution,
The velocity field is calculated from the velocity discretization formula (step S6 in FIG. 10B).

.. It is determined whether or not the calculated velocity field satisfies the continuous condition (step S7 in FIG. 10B), and if not, the pressure distribution is corrected from the pressure correction equation (E.118), and the corrected pressure is corrected. The velocity field is corrected using the distribution (step S8 in FIG. 10B). Then, the process returns to.

As described above, the solution method using the equation of motion when obtaining the flow velocity distribution of the liquid phase and the pressure distribution of the liquid phase is one of the solution methods of the thermal / fluid analysis unique to the present inventor. Various modifications and extensions are made based on the SIMPLER method. That is, in the sense that the solid-liquid coexisting phase is extended, the present analysis method is extended by the SIMPLER method (Exte
named SIMPLER method).

In the last-mentioned numerical solution of various discretization formulas, T suitable for iterative convergence calculation by a computer is used.
DMA method (Tridiagonal-matrix a
lgolithm, p. 52) is used.

The numerical analysis can be applied to various slab cross-sectional shapes and slab profiles (vertical type, vertical bending type, bending type, etc.), and the analysis function can be selected. That is, from the simplest level of only temperature and solid fraction to the highest level including all the above equations, considering the deformation of the slab and the influence of the electromagnetic volume force (Lorentz force) application. be able to. Therefore, the calculation level may be specified according to the purpose, and the calculation at the highest level is not always necessary.

The levels of the numerical analysis function defined in this specification are as follows.

Level 1: The governing equation is the energy equation and D
arcy expression. The function performs porosity analysis. The relational expression between the solid fraction and the temperature obtained experimentally or theoretically is used.

Level 2: The governing equations are energy equation, solid fraction-temperature relational equation, solute redistribution equation and Darc.
y expression. The function calculates macro segregation. However, the porosity is not calculated. Uses multi-source alloy model.

Level 3: Added porosity analysis to Level 2.

Level 4: The governing equations are an energy equation, a solid fraction-temperature relational equation, a solute redistribution equation and a kinetic equation. The function calculates macro segregation. However, the porosity is not calculated. Uses multi-source alloy model. Darcy flow resistance is included in the equation of motion.

Level 5: Added porosity analysis to Level 4.

Further, the continuous casting process has a function of dealing with electromagnetic force and deformation of the slab. In addition, the effect of Joule heat due to pearlite transformation and energization is taken into consideration in the temperature calculation (energy formula). The output information includes metallurgical information on a microscale such as macrosegregation and microporosity, in addition to macroscopic phenomena such as temperature, solid fraction, pressure and flow velocity of liquid phase.

The calculation in the above-mentioned numerical analysis is dummy ba
An unsteady solution method is adopted, which is carried out throughout the entire process from the initial stage of injecting molten steel into the r box to the end of pouring and the completion of solidification. This makes it possible to analyze unsteady processes from the start of pouring until the steady state is reached, and from the stop of pouring to the end of solidification. In addition, it is possible to analyze the influence of changes over time such as casting speed and cooling conditions during this period. Judgment as to whether or not the steady state is reached is made by fixed point observation such as temperature change.

Conventionally, for this kind of problem, a stationary solution method using a spatial coordinate system (that is, a method in which an equation is described using a coordinate system fixed in space and a stationary solution is obtained by repeated calculation, and the computational domain is a space) However, these methods have the drawback that the unsteady part, which is an important part of continuous casting, cannot be analyzed. On the other hand, the non-stationary solution method has an advantage that it can accurately respond to changes in various physical phenomena.

In the vertical-bending type continuous casting or the like, the slab is subjected to bending deformation. Therefore, as shown in FIG. 9B, the topology (distance, area, volume, etc.) of the analysis object and FIG.
As shown in (a), the direction of gravity viewed from the inset coordinates fixed to the slab changes. Therefore, it is necessary to recalculate these values at each time step.

The boundary condition of the surface of the slab should be given by either the method of giving the heat transfer coefficient h on the surface (hereinafter referred to as h method) or the method of giving the surface temperature Tb itself (hereinafter referred to as Tb method). did. In the h method, the response of Tb is obtained, and in the Tb method, the response of h is obtained. For example, if you want to set the surface temperature to a certain distribution depending on the purpose,
It suffices to find h using the b method and determine the specific cooling condition from the relationship between h and the cooling condition (spray amount, etc.).

In the region where the liquid pressure drop of the solid-liquid coexisting phase occurs, the liquid phase flow can be regarded as a one-dimensional flow in the casting direction. Therefore, from the Darcy equation (26), the volume force X in the Z direction can be approximated as being one-dimensional only in the Z direction (casting direction).
_{By solving} for _z , equation (63) is obtained.

[0282]

Therefore, after the pressure and velocity fields are obtained (calculated assuming that porosity does not occur), the P distribution necessary to prevent porosity is arbitrarily given (for example, P is ) From the equation, X _z (= Z direction component of gravity + Lorentz
Force), and then the required electromagnetic volume force (Lorentz
Force) distribution can be obtained.

A large amount of input data is added as an external function. For example, normal operating conditions (casting temperature, speed, surface cooling capacity, etc.) are given as a function of time, position, etc.

The merit of the nonlinear multi-component alloy model adopted in the present invention is that the numerical analysis can be applied to practical metallic materials regardless of ferrous, non-ferrous, stainless steel by fitting the non-linearity in the actual alloy phase diagram. Can be greatly expanded, and it can be applied to many important industrial metal materials. For example, for carbon steel containing peritectic reaction (C = 0.1 to 0.51%), the peritectic reaction is ignored and the δ solid line and the γ solid line are smoothly linearly approximated. The relationship between temperature and solid fraction can be determined. Application to low carbon steel with C <0.1% is of course possible.

A-5. Numerical analysis calculation example

As shown in FIG. 11A, the diameter is 1
Numerical analysis was carried out on the solidification process of molten steel injected into a m-shaped and 3 m-high mold.

[0288] In particular, steel types (0.72% C-0.57% Si-0.70% Mn) in which the tendency of the liquid phase density to decrease with solidification of the liquid solute between dendrites during solidification appears remarkably.
-0.02% P-0.01% S-remaining Fe (wt%)) was selected.

The initial temperature was 1475 ° C. and the degree of superheat from the solidification start temperature was 13 ° C. Moreover, as the various physical property values used in the calculation, the values of 0.55 wt% carbon steel shown in Tables 2 and 3 were adopted.

[0290]

[Table 2]

[Table 3]

Calculation was started with the state where the molten steel filled the mold as the initial state. After the start of the calculation, the liquid phase flow basically has a downward flow pattern on the side surface and an upward flow pattern at the central part until about 10 minutes before the solidification from the mold wall begins, but it is turbulent. That is, the flow velocity is about 10 cm /
The temperature in the liquid phase region is rapidly equalized (temperature difference is 2 ° C or less) due to turbulent flow such as s, where a temperature inversion layer in which the temperature of the central part is lower than the side surface is generated, etc. Loses superheat.

Thereafter, such a situation continues until about 2 hours after the liquid phase region disappears and the entire region becomes the solid-liquid coexisting phase. During this time, the flow velocity gradually decreases.

The solidification starts from the bottom, continues to the sides, and finally ends slightly above the center of the center of the ingot (solidification time is 20.9 hr).

As shown in FIG. 11B, 11.5
In the temperature distribution chart after the elapse of time, the isothermal lines are greatly curved, which is in good agreement with the actual case. In addition, C is a contraction part, M is a solid-liquid coexistence part, and S is a solid phase part.

Further, as shown in FIG. 11 (c), 1
In the solid fraction distribution map after 1.5 hours, the isosolid percentage curve is largely curved, which is also in good agreement with the actual case.

As shown in FIGS. 11D and 11E,
In the liquid phase flow between the dendrites, the liquid solute concentration between the dendrites is lower than the outside even though the temperature of the center is higher than that of the outside, so the balance between the two causes the liquid phase in the center to be relatively heavy. , Descending at the center and rising at the outside. This liquid-phase flow pattern continues until the latter half of solidification, and as revealed by the solidification theory of Flemings et al. (Reference (14), p. 244-25.
2), a positive segregation part is generated by the liquid phase flow from the low temperature part, that is, the high liquid phase concentration part to the high temperature part, that is, the low liquid phase concentration part, A negative segregation portion is generated by the flow to the.

FIG. 11 (f) shows the segregation state of C.
The segregation state of P is shown in (g), which is in good agreement with the actual case. The other alloying elements (Si, Mn, S) also produce the same segregation pattern, which is in good agreement with the actual case.

Regarding the calculation error, the difference between the amount of heat Qout removed from the ingot and the amount of heat lost Qlot of the ingot, | (Qout-Qlost) / Qoutx100
It was evaluated by |%, but in the case of only temperature calculation, the total error until completion of solidification was 0.1% or less.

B. Internal defect generation mechanism

Much literature has been published on internal defects in steel castings.

FIG. 43 schematically shows the central defects occurring in the rod-shaped long steel casting. Areas A and C in the figure
Is a sound area where there is no defect due to liquid phase replenishment between dendrites, area B cannot be replenished with liquid phase, and microporosity between dendrites is generated near the center of the wall thickness. It is known that these microporosities usually have a V pattern facing the liquid phase replenishing direction as shown in FIG. 43, and are often accompanied by V-shaped macrosegregation (so-called V segregation) (for example, V segregation). Reference (34)).

In many past documents, there are few that clearly describe V-shaped microporosity and segregation. For example, Pellini (Reference (35)) does not distinguish them and calls them centerline shrinkage. The central defects occurring in the continuous cast product of steel are essentially the same as those of the above-mentioned steel casting, and as described above, in the present specification, V-shaped porosity and segregation are summarized (regardless of the presence or absence of segregation or the degree thereof). ) Called central defects.

The central defect is generated when the liquid phase supply between dendrites is insufficient, and therefore it can be said that the flow of the liquid phase in the solid-liquid coexisting phase plays a decisive role in the generation of internal defects. The following factors can be considered as the driving force that causes the liquid phase flow.

(1) Solidification contraction flow induced by the difference in density between solid and liquid during solidification.

(2) Flow (natural convection) caused by difference in density of liquid phase. The liquid phase density ρ _L depends not only on the temperature but also on the solute concentration in the liquid phase as shown in the following equation (64).

[0306]

(3) Forced flow caused by external mechanical deformation. There are deformations such as bulging, bending back, and rolling. This is easy to understand by recalling that the water inside flows when the water-containing sponge is squeezed or bent. It is also within this category to subject the slab to strong cooling to cause heat shrinkage.

The inventor conducted a series of preliminary numerical analyzes in order to investigate the influence of the factors (1) and (2) on the central defect. The results are summarized below.

.. In the case of a large steel ingot, macrosegregation appears remarkably because the liquid phase flow between dendrites is generated over a wide area for a long period of time. When the size of the ingot is reduced with respect to the same alloy, the width of the solid-liquid coexisting phase is narrowed, but the flow patterns show the same tendency as in FIGS. 11 (d) and 11 (e). However, since the solidification time is short, the flow is limited to a very small range, and segregation does not substantially occur. This is in agreement with empirical facts.

That is, as the solidification rate increases, natural convection type segregation due to the difference in liquid phase density is less likely to occur.

.. In continuous casting, the flow pattern was a simple solidification contraction flow in the casting direction, without a natural convection type flow due to the difference in liquid phase densities, as seen in the analysis example described later.

In the slab, the cooling ability is often nonuniform in the width direction, but even in such a case, macrosegregation (not V segregation) caused by the flow in the plate surface is generated unless "normal solidification", that is, a central defect is generated. The degree is small and is not a problem in practical use. This is also due to the high solidification rate. The Darcy flow pattern in normal coagulation is in the form of spreading slightly outward as shown in FIG. 12 (a) (somewhat oversized to emphasize spreading in the figure). Further, the flow velocity in the casting direction is overwhelmingly higher than that in the thickness direction near the center where the central defect occurs, and the flow velocity in the thickness direction is so small that it can be ignored.

In the above numerical analysis, the level 3 function was used for the entire cast piece including the meniscus to the final solidification position. From the viewpoint of the overall Darcy flow, the influence of the molten steel discharge flow from the nozzle is small.

From the above, it can be said that the main internal defect occurring in the continuous cast product is the V-shaped defect generated in the final solidification portion of the cross section, and the solidification contraction flow is deeply involved as a factor thereof.

Next, the mechanism by which V-shaped defects occur will be described.

Since the main flow of the liquid phase of the solid-liquid coexisting phase extending in the casting direction occurs in the casting direction, the pressure drop of the liquid phase caused by the Darcy flow occurs almost in the casting direction, especially in the wall thickness center and its vicinity. Largest pressure drop.

Then, when the pressure P of the liquid phase reaches the critical condition given by the following equation (65), porosity occurs (p.239 of document (14)).

[0318]

Here, Pgas is the equilibrium gas partial pressure in the porosity in equilibrium with the gas dissolved in the liquid phase, σ _LG is the surface tension at the interface between the liquid phase and the porosity, and r is the radius of curvature of the porosity. , (61) is given.

The porosities are arranged in a V shape as shown in FIG.

When V segregation develops, the formation of porosity triggers Darc toward the casting direction.
It is considered that the y-flow changes from the normal pattern as shown in FIG. 12 (a) to the flow as shown in FIG. 12 (b). That is, the liquid phase flows from the low temperature side (high solute concentration side) to the high temperature side (low solute concentration side) of the wall thickness center along the V-shaped void, and a local positive segregation band higher than the average concentration, that is, V Form segregation.

It is considered that such a flow of the liquid phase is triggered by the formation of porosity and occurs simultaneously with the formation of porosity.

Here, if the flow velocity from the low temperature side to the high temperature side increases and the condition given by the following equation (66) is met, the solid phase in that portion is locally redissolved. Occurs (p. 249 of document (14)).

[0324]

When such remelting occurs locally, the resistance to the Darcy flow in that part becomes smaller than that in the surroundings, the flow becomes larger and the remelting increases.
As a result, V segregation appears more severely. The degree of segregation depends on the degree of this channel phenomenon ((6
6) The value of the second term on the left side of the equation is involved).

To verify the above discussion of central defect formation, carbon steel was high frequency atmospherically melted and cast into a tapered mold of diameter 32 mm to 30 mm x length 350 mm as shown in FIG. Further, as a means for increasing the liquid phase replenishing ability between the dendrites, a dry mold was installed in the pressure vessel as shown in FIG. 44, and after pouring the molten metal into the dry mold, it was pressurized with argon gas.

The chemical composition of the cast sample is shown in Table 4. Casting temperature is 1560 to 1580 ° C, pouring time is about 1 for all
It was 0 seconds. The analytical values of oxygen and nitrogen are 50 to 1
It was in the range of 20 ppm. Sample No. For the air cast material of No. 1 (without pressurization with argon gas), thermocouples were inserted at three locations in the center of the sample as shown in FIG. 44, and the temperature change during solidification was measured. The measurement data is shown in FIG.

In addition to these experiments, numerical analysis according to the present invention from the start of pouring to the end of solidification was conducted.
The formation process of internal defects was traced and compared with the experiment. The values of physical properties of steel used in the numerical analysis are shown in Tables 2 and 3. As the chemical component values, the values shown in Table 4 were used. The thermal conductivity of the dry type is 0.0036 cal / cmS ° C., and the specific heat is 0.
The density was 257 cal / g ° C. and the density was 1.5 g / cm ³ .
The thermal conductivity of the riser insulation is 0.000.
3 cal / cmS ° C., specific heat 0.26 cal / g ° C., and density 0.35 g / cm ³ .

[0329]

[Table 4]

Sample No. The calculated value of the temperature history at each temperature measurement position 1 is in good agreement with the actual measured value as indicated by the broken line in FIG.

Sample No. FIG. 46 shows a macrostructure in which the central cross section of No. 1 was polished and etched with a 4% nital solution. FIG. 46 (a) schematically shows the state of the V pattern obtained by visual observation, and FIG.
Shows a part of it. It is darkly corroded by etching, and V-shaped central defects are conspicuous. The macrostructure consists of columnar crystals and fine granular crystals in the surface layer. FIG. 46 (c) shows the sampling position of the microscopic structure and the Vickers hardness measurement position.

Further, FIG. 47 shows the microstructure, and FIG. 48 shows the Vickers hardness measurement results. In FIG. 47, the needle-shaped white portion is ferrite, and the darkly etched base material is pearlite. The dark color part (a part of V band) flowing from the upper left to the lower right of FIG. 47 has less ferrite, and therefore has a higher carbon content than the peripheral part. FIG.
As shown in (c), when the Vickers hardness was measured so as to cross this flow, as shown in FIG. 48, the hardness was higher in the V band portion in which pearlite occupies the majority than in the peripheral portion. Further, as shown in FIG.
It is considered that the hardness once decreases near the band and then increases to the right because the liquid phase with high solute concentration around (in this case, from the left side) flows along the V band when the V band is formed. To be

Further, a flaw detection color check inspection of the central cross section was conducted to examine the microporosity distribution, and it was confirmed that the microporosity was distributed along the V pattern. The volume of the riser shrinkage holes (Fig. 46 (a)) occupying the entire casting is about 1%, which is smaller than the solidification shrinkage 4% of the casting, and most of the defects exist as microporosity in the V pattern. ing.

From the above, it was confirmed that the V-shaped central defects consist of V-shaped microporosity and V segregation (positive segregation) bands.

[0335] FIG. Numerical analysis of the level of Sample 1 was conducted and the results of examining the formation process of microporosity are shown. As shown in FIG. 49 (b), the porosity distribution state after completion of solidification is in good agreement with the actual V pattern (FIG. 46 (a)).

From the results of the numerical analysis, the time at which internal porosity begins to occur is 55 seconds after the start of pouring, and the solid fraction distribution at this time is shown in FIG. 49 (a). In addition, the position where porosity occurs is indicated by the diagonal line in the figure. When calculated assuming that porosity does not occur (level), 63 seconds after the start of pouring, the pressure drop due to the Darcy flow becomes maximum at a position 75 mm from the bottom surface, and the negative pressure at that time is -20.
It was 5 atm. Refer to this and set the atmospheric pressure to 10 atm.
As a result of calculation by changing in the range from 25 to 25 atm, the critical pressure for generating porosity was found to be 20 atm. That is, it is considered that the volume fraction of porosity decreases as the pressing force increases, and the porosity completely disappears at 20 atm or more.

Then, referring to the above examination results, casting 2
Pressing was started after 0 seconds (when the solid fraction of the central portion was about 0.3), and the pressure was maintained at 10 atm from 30 seconds after casting until the end of solidification. The macrostructure of No. 2 is shown in FIG. Sample No. Compared with No. 1, the porosity volume ratio was reduced, but V defects were noticeable.

22 atm Pressed No. As shown in FIG. 51, in the macrostructure of No. 3, the sound part without V segregation and porosity is expanded from 30 mm to 130 mm, which shows that the pressurization worked effectively. These sample No. 2 and No. 3 numerical analysis of Level 3 (chemical composition is shown in Table 4
According to the above), 10 atm as shown in FIG.
Then the porosity decreases slightly and disappears at 20 atm. Sample No. A defect was generated in the portion below the feeder in Fig. 3 (Fig. 51) because the amount of feeder was small and the sink was deep. On the other hand, the numerical analysis does not strictly deal with the formation of shrinkage holes in the feeder (in order to handle this precisely, it is necessary to make the element division of the feeder part fairly fine, but there is a problem in displaying the results. not going).

From the above, it is clear that the central defect can be eliminated by the pressurization, which reconfirms the experimental results published in the past. However, in these conventional experiments, the pressurizing effect was not treated theoretically and quantitatively and was insufficient. For example, in Reference (34), a negative view is put on the practical effect of pressurization, such that center segregation appears conspicuously when the feeder part is pressurized. In this document, the specific casting size (3 inch square cross section, length 24 inches), chemical composition value, casting temperature, pressurizing condition, temperature measurement data during solidification and internal defect observation result are given, Comparison with numerical analysis is possible.

Therefore, when the present inventor conducted a numerical analysis on the steel casting, as shown in FIG. 53, the effect was small at the pressure of 4.2 atm of the document, and the pressure of at least 20 atm was required to eliminate the central defect. I found it necessary. In connection with this, FIG. 54 schematically illustrates the relationship between the liquid phase pressure drop and the porosity generation in the porosity generation critical condition expression (69). In the figure, porosity is generated in a region where the solid phase ratio is equal to or more than the critical solid phase ratio gs ^* . From the above, the fact that the center segregation appears conspicuously is the result of the inflow of a liquid phase having a high solute concentration around the porosity triggered by the occurrence of V porosity when the effect of pressurization by pressurization is insufficient. it is conceivable that. In any case, apart from the detailed consideration on the dendrite scale, it can be said that the central defect does not occur if the feeder effect is sufficient.

From the above, the region where the liquid pressure in the solid-liquid coexistence region is below the critical pressure in the solidification process is the region where internal defects occur, and the critical pressure of defect generation is determined by numerical analysis according to the present invention based on the solidification theory. Can be calculated.

Furthermore, it can be said that "if the microporosity is eliminated, the segregation is eliminated at the same time". That is, rather than completely eliminating microporosity, it is more important not to give an opportunity of occurrence to be precise. For this purpose, Da in the casting direction near the center of the wall thickness (final solidified portion) is important.
The hydraulic pressure drop associated with the rcy flow may be minimized and maintained at or above the critical pressure given by equation (65).

C. Calculation of applied electromagnetic force

Various methods are conceivable for applying the electromagnetic volume force (Lorentz force). For example, there are a method of applying a DC magnetic field and a DC current, a method of using a linear motor type remote thrust, etc., which is appropriate considering the cross-sectional shape of the slab, the position to be applied, the magnitude of the required force, the equipment cost, etc. You can choose any method.

Here, the calculation method for the former will be described. As shown in Figure 2, casting method

[0346]

[0347]

[0348]

[0349] The distribution φ is given by the following equation (69) (reference (2
2) p. 8, it is assumed that there is no electric charge in the object in the equation (2.13)).

[0350]

Φ can be obtained by solving the equation (69) using the potential applied to the electrode as a boundary condition. Iron is non-magnetic above the Curie point (about 770 ° C.) and can be approximately regarded as the same as air.

Therefore, it is relatively easy to apply a uniform static magnetic field to the solid-liquid coexisting phase.

[0353] You can do it easily. .

[0354] Have been.

[0355]

[0356]

Embodiments of the present invention will be described below.

A. For vertical continuous casting of round billet material:

In the first embodiment, as shown in FIG. 13, a water-cooled copper mold 5 for solidifying the molten steel surface in a predetermined shape to obtain a solidified shell, and a ladle outlet 2 for inflowing the molten steel are provided. , The tundish 3 for supplying molten steel from the ladle outlet 2 to the water-cooled copper mold 5 at a constant rate through the nozzle 4, and the electromagnetic volume force on the solid-liquid coexisting portion inside the cast piece 6 that has passed through the water-cooled copper mold 5. Electromagnetic booster 1 for applying
It is composed of Here, the electromagnetic booster 1
As shown in FIG. 23, the device is a device that includes a superconducting coil or an electromagnet for generating a DC magnetic field and an electrode for passing a DC current, and generates an electromagnetic volume force in the casting direction.

Since the bearing is subjected to repeated load under high speed, the bearing material is required to have excellent fatigue strength and abrasion resistance. That is, bearing steel is one of the steels that require particularly strict quality among special steels such as cleanliness of material and uniformity of structure.

1% C-1% Cr bearing steel has a wide solidification temperature range and is likely to cause center segregation. This causes generation of huge carbides, which causes deterioration of quality such as reduction of service life.

Therefore, in this embodiment, 1% C-1% Cr
A case where a round billet material of bearing steel is cast by a vertical continuous casting machine will be described. In addition, 1% C-1% C here
For r bearing steel, 0.2% Si, 0.5% Mn, 0.1%
It contains Ni, 0.01% P, and 0.01% S. The physical property values are shown in Table 2.

A-1. Numerical analysis of solidification process

In the Fe-C binary phase diagram, as shown in FIG. 14, the solidus line and the liquidus line at 1100 ° C. to 1500 ° C. are linearized.

As shown in FIG. 15 (a), the relationship between the temperature T and the solid fraction gS was determined by a non-linear multi-component alloy model in order to consider the influence of each alloy element. However, non-linear multi-component alloy Follow. In order to avoid this calculation inconvenience, g _S = 0.95
It was considered that the coagulation was completed (Reference (16)).

In view of the fact that the solid-liquid coexisting phase extends long in the casting direction, the latent heat is generated uniformly.
That is, the latent heat value of 65 (cal / g) is changed to g _S (0.9
A value of 68.4 (cal / g) divided by 5) was used as an apparent latent heat value.

Next, the manner in which the solid solution oxygen in the liquid phase is concentrated in the liquid phase between the dendrites as the solidification progresses and the equilibrium CO gas pressure (equilibrium pressure when CO gas bubbles do not exist) changes ( Numerical analysis was performed using equations 36) to (45). Table 3 shows the physical property values used for the calculation. FIG.
As shown in (a), the equilibrium CO gas pressure Pco decreases as the oxygen content decreases. Further, when the amount of Si is increased, the concentration of O in the liquid phase is reduced due to the generation of SiO ₂ , and the equilibrium CO gas pressure Pco is relaxed.

As shown in FIG. 13, the elemental division of the area to be subjected to the numerical analysis is divided into 10 equal parts in the radial direction (the radial direction division length is Δr = 1.75 cm), and the casting direction division length is Δz =.
It was 5 cm. Here, prior to the numerical solution, the number of divisions in the radial direction where the temperature change is large was examined. As a result, when the number of divisions was 8 or more, no substantial difference was found in the calculation results, so the element division was set to 10. The casting direction was also determined in the same way as above. A level 3 cylindrical coordinate system two-dimensional analysis was performed.

Regarding the correction coefficient α for the dendrite specific surface area Sb in the equation (28) for obtaining the transmittance controlling the liquid phase flow between dendrites, the solidification temperature range (1453-1327 = 126 ° C.) obtained from the calculation is used. Using the average cooling rate (° C / min), 1C-1.5Cr in which the alloy components are close to each other as shown in the equation (71).
Α was set to 1.2 so as to agree with the measured value of the dendrite arm spacing (das) of steel (Reference (23)).

[0369]

Since the molten steel at a constant temperature was continuously poured from the tundish, heat dissipation from the surface of the meniscus was ignored.

Usually, the flow of the liquid phase in the upper molten steel pool is affected by the discharge flow from the nozzle, the convection due to the temperature difference in the molten steel pool, etc., and a complicated flow pattern is generated.
However, the flow is turbulent, and the temperature difference in the molten steel pool is also small. Further, the influence of the flow in the liquid phase pool on the behavior of the liquid pressure drop in the solid-liquid coexisting phase elongated in the casting direction is negligibly small. Therefore, focusing on the problem of internal defects, which is the object of the present invention, it is not always necessary to analyze the flow in the molten steel pool in detail. From the above points, in the molten steel pool, the solution method by the Darcy equation was used without using the equation of motion that requires a long calculation time.

However, with the solution by the Darcy equation, the flow in the molten steel pool is extremely small, and the temperature diffusion due to convection is small. Therefore, in order to correct this, the thermal conductivity was apparently set to 5 times the thermal conductivity of the liquid in the liquid-phase region and the solid-liquid coexistence range in which the solid-phase percentage is less than 0.05. This method is often used when calculating the temperature of continuous casting (Reference (24)).

As shown in FIG. 17, the solidification coexisting phase becomes longer due to the effect of the higher temperature Darcy flow from the upstream side, because the solidification start point in the central part is accelerated by considering the Darcy flow. I understand. this is,
This is in agreement with the actual solidification phenomenon, and it is clear that Darcy flow analysis is necessary even on a macroscopic scale.

The boundary conditions for the numerical analysis are shown in FIG.
As shown in (b), the heat transfer coefficient h of the mold part was set to 0.
It was set so as to prevent a breakout by changing stepwise from 02 to 0.01.

Further, in the secondary cooling zone where water spray (mist) is performed, the surface temperature of the solidified shell was set to 1125 ° C. so as to be as uniform as possible. At this time, h can be obtained as a response.

Further, as shown in FIGS. 18B and 18D, the boundary condition is switched from the mist cooling to the natural radiation cooling at a position where the cooling capacity by radiation exceeds the mist cooling capacity.

As shown in FIG. 18 (a), the hydraulic pressure P increases almost linearly (that is, static pressure distribution) at a low solid fraction of Gs of 0.2 or less. This is because when the solid fraction is low, the pressure drop of the liquid phase is extremely small, and even if the starting point of the solid-liquid coexisting phase on the upstream side changes to some extent, it affects the pressure drop of the liquid phase on the high solid fraction side. It means that it does not reach.

From this, it is understood that it is not necessary to perform a strict flow analysis by the equation of motion in the molten steel pool.

The Darcy flow is a downflow of -2.8 mm / s at the maximum, and the velocity decreases as the width of the flow widens toward the upstream (similar to the flow of the river).

[0380] The upward flow is observed in the upper molten steel pool due to the natural convection caused by the temperature of the central portion being higher than that of the side surface.
_.

FIG. 1 shows changes in the volume force (self-weight due to gravity) X.
8 (c). The self-weight is small on the crater end side because the effect of concentration of solute elements (all elements other than Ni) lighter than Fe in the liquid phase is larger than the effect of temperature drop, and the liquid phase density ρ _L is small. This is because

In the continuous casting, the driving force that causes the Darcy flow is contraction accompanying solidification, and as shown in FIG. 12 (a), the driving force is directed substantially uniformly in the downstream direction.

As shown in FIG. 21, the flow path becomes narrower as it approaches the crater end, and the flow velocity in the radial direction becomes gradually smaller than the velocity in the casting direction.

The segregation of each alloy element is within the calculation error (several percent), and it can be considered that there is substantially no segregation.

The permeability K for the Darcy flow is one of the important factors in evaluating the hydraulic pressure drop ((2
7) or (30)). Regarding the dendrite cell diameter d in the K formula, the present invention has shown two formulas given by the formulas (29) and (31). FIG. 22 shows the dendrite arm spacing obtained from these equations. (2
In (a) of FIG. 22 using the equations 8) and (29), the value is smallest on the surface and increases toward the inner side, but reversely decreases at the central portion. This is because solidification is accelerated at the final stage of solidification, as can be seen from the fact that the shell thickness rapidly increases when approaching the crater end (see FIG. 18 (b)). This means that when there is no segregation from the equations (28) and (29), d is g _S Therefore, it can be seen that d of the central element is finally reduced.
On the other hand, in (b) of FIG. 22 using the equation (31), the local coagulation time t _f becomes maximum at the center portion, and therefore dendrite arm spacing also becomes maximum at the center.

Accelerated solidification from the latter half to the final stage of solidification appears more clearly in a large steel ingot, but continuous casting of steel (Refer to (2
This is a general phenomenon also observed in 5)). Regarding the distribution of dendrite arm spacing in the wall thickness direction, a diameter of 203 mm and a casting speed of 0.11 m / min were 6
It has been reported that the dendrite arm spacing at the center is also small in the continuous casting of 063 aluminum alloy (Reference (26)).

A-2. Area where internal defects occur

As shown in FIG. 16 (a), the gas pressure Pco increases up to 0.9 atm with an increase in the solid fraction. On the other hand, in the case of the present embodiment, “−2σ _LG / r” in the expression (69) increases to about −1.2 atm (negative value). Therefore, the hydraulic pressure on the high solid fraction side where the pressure drop is large is P (absolute pressure) = 0.9-1.2 = -0.3 atm
Porosity does not occur unless:

Liquid pressure P and gas pressure Pco after porosity generation
And the volume ratio of porosity g _V are adjusted so as to satisfy the equation (69) and the series of equations (36) to (45). Also, even in the presence of porosity, Da
Considering the rcy flow.

In this way, it can be predicted that a porosity of 5 to 10% by volume is produced over the range of about 6 cm in the center (20% of the diameter).

From the above, a value of 1 atm estimated on the safe side can be obtained as the critical pressure for judging the occurrence of internal defects. Considering the relative value with the meniscus surface as 0, the liquid phase pressure in the solid-liquid coexistence region is 0 atm.
If it is above, it can be predicted that no internal defect will occur. That is, as shown in FIG. 19, it can be expected that porosity will occur when the distance from the meniscus is around 20 m.

A-3. Calculation of applied electromagnetic volume force

A schematic view of an electromagnetic booster in vertical round billet continuous casting is shown in FIG.

The electromagnetic volume force (Lorentz force) is (5
From the equation (1), the product of the uniform DC magnetic flux density B _{x in the} X direction and the DC current density Jy in the y direction passing through the solid-liquid coexisting phase at the center is given by the equation (72).

[0395]

Referring to the P distribution in FIG. 18A and the calculated value of the required electromagnetic volume force (Lorentz force) (equation (67)), from the vicinity of the upstream side of the position where P becomes 0, the crater end, that is, Electromagnetic volume force (Lorentz force) of 8 times the force) was applied.

As a result of numerical analysis, the length of the solid-liquid coexistence region is 1
6.05 m, Zmax is 21.0 m, Pmax is -0.
It was 03 atm.

That is, as shown in FIG. 24, the hydraulic pressure drop near the crater end is relaxed and maintained at a positive pressure (absolute pressure of about 1 atm), and porosity does not occur.

From this, a continuous cast product without internal defects can be manufactured by applying an electromagnetic volume force (Lorentz force) of the above value or more.

When the electric resistance ρ is constant in the cross section, the current density becomes maximum in the shortest distance between the electrodes, that is, in the vicinity of the center line connecting both electrodes. However, since the electric resistance ρ is a function of temperature, it is optimal to use the mechanism as shown in FIG. 2C for the electrode.

In continuous casting of vertical billets or blooms, a large number of supporting rolls required for wide slab continuous casting are not generally used. However, by giving a slight reduction gradient to the slab, the hydraulic pressure drop is mitigated, and the required electromagnetic volume force (Lorentz force)
2D, it is also effective to dispose a roll between the round billet and the rigid frame 1 to give a slight pressure gradient, as shown in FIG. 2 (d).

B. For vertical bending continuous casting of thick plate slab:

The second embodiment, as shown in FIG.
A water-cooled copper mold 5 for solidifying the molten steel surface in a predetermined shape to obtain a solidified shell, a ladle outlet 2 for inflowing the molten steel, and molten steel from the ladle outlet 2 into a water-cooled copper mold 5 via a nozzle 4. A tundish 3 for supplying at a constant speed, a plurality of bending rolls 7 for bending the slab 6 that has passed through the water-cooled copper mold 5, and a middle stitch 6 that has passed through the bending roll 7.
It is composed of a plurality of straightening rolls 8 for horizontally leveling, and an electromagnetic booster 1 for applying an electromagnetic volume force to the solid-liquid coexisting portion inside the slab 6 that has passed through the straightening rolls 8.
In addition, the electromagnetic booster 1 is based on operation data etc.
The calculation means is provided for calculating the magnitude and position of the applied electromagnetic volume force. Further, this computing means corrects the numerical analysis data in the computing means based on the operation data which changes in real time, and at the same time the solidification process of the continuous cast product is displayed in real time on the display means 12 installed in the operator room. Compensation means for displaying is provided. That is, the detection unit 9 is a device for capturing an input signal of an operation parameter, and the computer system 10 performs a numerical calculation process of a solidification process based on the operation data from the detection unit, and a continuous casting machine main body to be controlled via the operation unit 11. It has a function to feed back the operation amount. Further, the display device 12 can monitor the coagulation situation at any time.

In FIG. 2A, the vector B indicates the magnetic flux density (Tesla) of the DC magnetic field, the vector J indicates the DC current density (A / m ² ), and the vector f indicates the electromagnetic volume force (Lorentz force) ( N / m ³ ) is shown.

FIGS. 2B and 2C show an example of an electrode and an electrode mechanism when a DC magnetic field and a DC current are used. The DC rotating electrode 1c is lightly attached to the side surface of the slab 1b by a spring. It is pressed and rotates according to the drawing speed. Alternatively, a method of fixing the electrode with a spring and sliding it with respect to the cast piece may be used.

Further, FIG. 2 (d) shows a mechanism for applying an electromagnetic volume force (Lorentz force) by a DC magnetic field and a DC current, and at the same time giving a light reduction gradient by lightly reducing it around the fixed shaft 1e. .

Further, as shown in FIG.
It is also possible to set the device shown in (d) as one unit and arrange a plurality of the units.

Since the central defect of high-grade heavy steel such as steel for offshore structures becomes a starting point of cracking and causes quality deterioration, it has been energetically studied as an important problem affecting quality.

The center segregation appears more markedly in a steel having a large solidification temperature range and a high carbon content. Therefore, in this embodiment, JIS S55c (AISI) having a carbon concentration of 0.55 (wt%) is used.
1055) was selected. This steel also contains 0.2% Si,
It contains 0.75% Mn, 0.02% P, and 0.01% S.

B-1. Numerical analysis of solidification process

FIG. 15 shows the relationship between the temperature and the solid fraction determined by the nonlinear multi-component alloy model based on the binary equilibrium diagram.
(B).

Physical properties are shown in Tables 2 and 3. 0.55%
Specific heat of carbon steel C (ca1 / g ° C) and thermal conductivity λ (cal
/ Cms ° C) is shown in FIG.

The deoxidizing agent was Si. Further, as shown in Table 3, the oxygen content was 0.003 wt%.

[0414] Fig. 2 shows the specifications and operating conditions of the vertical bending type continuous casting machine.
As shown in 6 (b), the length of the mold is 1.2 m, the length of the vertical part including the mold is 3 m, the bending radius is 8 m, the slab dimension is 220 mm in width, 1500 mm in width, and casting speed is 1 m / mi.
n) The degree of superheat of molten steel during casting was set to 15 ° C.

The dimensions and operating conditions of the continuous casting machine are not significantly different from each other in the world, and the set values and operating conditions in this specification are typical values.

The slab undergoes bending deformation when passing through the bending roll portion and the straightening roll portion, but since the radius of curvature is sufficiently larger than the slab thickness, it can be regarded as simple bending deformation. That is, the position of the neutral axis can be regarded as invariable, epsilon _z in maximum surface of the casting direction of strain epsilon _z
= 110/8000 = 1.375%.

Therefore, in the bending roll section, as shown in FIG.
As shown in (b), it is gradually bent over 5 steps, and the total is 1.375% (that is, about 0.275% /
The radius of curvature was set so that the strain would be 1 step). The same applies to bending back in the straightening roll portion.

In the numerical analysis area, as shown in FIG. 26C, the total wall thickness was divided into 19 equal parts (division width Δx = 22 cm / 19) in consideration of the asymmetry due to bending. The element division length in the casting direction was Δz = 10 cm. Two-dimensional orthogonal curve coordinate analysis of Levels 2 and 3 was performed.

The correction coefficient α for the dendrite specific surface area Sb in the equation (28) is 1, that is, no correction is made.

Surface heat transfer coefficient H (cal / cm ² s ° C.)
27b, as shown in FIG. Was set to 0.015 and Z ≧ 3 m was set to 0.010.

The change in shell thickness is shown in FIG.
The slab surface temperature is shown in (d).

When the solid phase ratio g _S is 0.2, a hydraulic pressure drop has already occurred, and when it becomes 0.6 or more, the hydraulic pressure drop sharply increases to a negative pressure of -4.7 atm at the crater end. ing. This is because the transmittance K rapidly decreases as shown in FIG. The casting direction component X of gravity also becomes 0 when Z is 16 m or more, and there is no feeder effect due to its own weight (Fig. 27 (c)).

B-2. Area where internal defects occur

As shown in FIG. 28, Zmax is 1
When it is 8.4 m, the length of the solid-liquid coexistence region is 8.5 m, and Pmax is -0.3 atm. Here, 8v over the range of about 11 mm in the center (5.2% of the wall thickness)
It produces a porosity of 1%. The size of porosity is 50 μm. Segregation with porosity occurs at this center.

B-3. Calculation of applied electromagnetic volume force

Based on the pressure and velocity field calculated assuming that porosity does not occur, a pressure distribution for preventing porosity is arbitrarily given, and Xz (Z direction component of gravity + Lorentz force) is calculated from equation (67). , And the electromagnetic volume force (Lorentz force) distribution was determined.

Based on the electromagnetic volume force (Lorentz force) distribution, the following setting was made within a range of a distance Z from the meniscus at which the pressure drop suddenly increases to 18 m or more.

Between Z = 18.0 and 18.6 m, the DC magnetic flux density in the slab thickness direction was B = 0.7 (T), and the DC current density in the slab width direction was J = 1.47 × 10.
⁶ (A / m ² ) and f = JxB = 1.02 in the casting direction.
An electromagnetic volume force (Lorentz force) of 9 × 10 ⁶ (N / m ³ ) (15 G, 15 times gravity) is applied.

The slab analysis necessary for this purpose, the potential difference between both ends in the width direction (0.01 m) is obtained from the following equation.

E = Jx0.01 / σ = 1.47 × 10 ⁶
x0.01 / 7.0x10 ⁵ = 0.021 (V)

The electric conductivity σ is an average value in the solid-liquid coexisting phase. Normally, as shown in FIG. 32, σ changes with temperature, but the change is small in the central solid-liquid coexisting phase where the temperature difference is small.

As shown in FIG. 26 (a), the electromagnetic booster is installed in the horizontal portion behind the straightening roll.

[0433] Further, the electromagnetic volume force (Lorentz force) is increased by increasing the application range of the electromagnetic volume force (Lorentz force).
May be reduced.

Numerical analysis was performed for the case where the electromagnetic volume force (Lorentz force) was applied.

As shown in FIG. 29 (a), the hydraulic pressure at the crater end is -0.11 atm (0.89 in absolute value).
atm), and porosity does not occur. The center segregation is also a level of calculation error of several% and can be regarded as substantially nonexistent.

The overall coagulation profile and Darcy flow distribution near the crater end are shown in FIG. As shown in FIG. 30, the flow pattern is normal even in the region to which the electromagnetic force is applied and the straightening / bending region.

Usually, in the straightening zone, the free side (inside of the curvature) pulls on the boundary of the wall thickness center, and the fixed side (outside of the curvature) causes compressive deformation. On the free side, the liquid phase is squeezed out due to the decrease in wall thickness. As a result (vice versa on the fixed side), the liquid phase flows from the free side to the fixed side.

However, in this example, such a disturbance due to bending back was not observed. This is because the amount of bending strain is as small as 1.4% (ε _z max on the surface), and it is further smaller at the central portion.

From the above, it can be said that if the deformation in the straightening roll portion is close to that of simple bending, there is no effect on segregation.

As shown in FIG. 29C, generation of Joule heat is slightly observed in the electromagnetic volume force (Lorentz force) application zone. Crater end length Zmax is 1
This is why it is 40 cm longer from 8.6 m to 19.0 m.

When the product of the current density J and the magnetic flux density B (exactly the outer product of both vectors) is constant, the electromagnetic volume force (Loren)
The tz force) f also becomes constant. However, if the current density J is too large, the vicinity of the slab center is redissolved by Joule heat, so it is desirable to increase the magnetic flux density B and minimize the current density J in operation. On the other hand, in order to increase the magnetic flux density B, the number of turns N of the coil and the coil current I
The product NI (magnetomotive force) must be increased. The current density J and the magnetic flux density B may be determined in consideration of these influences. In the case of a normal electromagnet, B = 1 Tesla is the limit, so if it is larger than this, it is preferable to use a superconducting magnet.

Then, the magnetic flux density B was reduced to 0.5 (T), the current density J was increased to 1.029 × 10 ⁶ (A / m ² ) to make the electromagnetic volume forces equal, and the effect of Joule heat was examined.

As a result of the numerical calculation, the length of the solid-liquid coexistence region is 9.
4m, Zmax 19.3m, Pmax 0.78at
m.

As shown in FIG. 31, the influence of Joule heat is further increased as compared with the case where the magnetic flux density B is 0.7 (T), and Zmax is changed from 18.6 m to 19.3 m.
cm longer. At the crater end, 0.7
It is held at a positive pressure of 8 atm and no defects have occurred,
It can be seen that there is no problem in generating Joule heat to this extent. However, in an extreme case where the current density J is further increased and the central part is redissolved, it takes time to solidify again, and the solid-liquid coexisting phase also becomes long, so a pressure drop occurs again and electromagnetic force is generated. There is no point in applying.

From the above, it is preferable to increase the magnetic flux density and lower the current density. Then, it can be said that using a superconducting magnet capable of generating a high magnetic flux density is advantageous from the viewpoints of space saving and economical efficiency.

In this embodiment, the direct current is applied to the entire cross section in the wall thickness direction on the side surface of the slab. However, in actuality, the electromagnetic volume force (Lorentz force) may be applied only in the vicinity of the center portion of the wall thickness. . This makes it possible to reduce the total current and the generation of Joule heat.

As described above, the internal defect can be eliminated even for the thick plate slab. Further, the calculation means and the correction means are
The solidification state of the continuous cast product is calculated based on operation data from various sensors and measuring devices installed in the continuous caster, and a graphic display is performed on the display means in real time. This allows the operator to visually and accurately grasp the operating state.

C. For vertical bending type continuous high speed casting of thick plate slab:

Generally, monthly production (ton) per continuous casting machine
The productivity of the continuous casting machine represented by is determined by the non-operation time, the casting preparation time, the cross-sectional dimension, the casting speed, and the like. Of these, in order to improve productivity, the cross-sectional dimension and the casting speed, which are closely related to the quality of the continuous cast product, are important items.

Since increasing the cross-sectional dimension is problematic from a metallurgical point of view and cannot be said to be a good idea, great efforts have been made to increase the casting speed.

Therefore, a case where the present invention is applied to continuous casting of slabs, which has recently been aimed at higher speed, will be described.

C-1. Numerical analysis of solidification process

The specifications and operating conditions of the continuous casting machine are the same as those of the second embodiment except that the cooling conditions are changed corresponding to the casting speed of 2 m / min.

As a result of numerical analysis, the length of the solid-liquid coexistence region was 12.6 m, Zmax was 31.2 m, and Pmax was −.
It was 1.15 atm.

C-2. Area where internal defects occur

As shown in FIG. 34, the central portion 35 mm
In the range (16% of wall thickness), porosity of about 5 to 15 vol% is generated. The porosity is about 60 to 65 μm.

C-3. Calculation of applied electromagnetic volume force

From the results of the numerical analysis, it was found that an electromagnetic volume force (Lorentz force) equivalent to an average of 22 G is required in the range of Z = 30.2 to 33.1 m to eliminate porosity.

Then, in the negative pressure region, the electromagnetic volume force (Lorentz force) was applied in two zones as follows.

(1) First zone:

Distance from meniscus Z = 30.2 to 3
Electromagnetic volume force (Lorent) equivalent to 15 G within 1.7 m
z force) is applied. Therefore, the DC magnetic flux density B is 1.3
3 (T), DC current density J is 7.775 × 10 ⁵ (A /
m ² ), slab analysis width direction potential difference E is Jx0.01 / σ
= 0.0111 (V).

(2) Second zone:

An electromagnetic volume force (Lorentz force) equivalent to 34 G is applied between Z = 31.7 to 33.1 m. Therefore, the DC magnetic flux density B was set to 3.0 (T), the DC current density J was set to 7.775 × 10 ⁵ (A / m ² ), and the slab analysis width direction potential difference E was set to 0.0111 (V).

As a result of the numerical analysis, as shown in FIG. 35, the solid-liquid coexistence region has a length of 14.8 m and Zmax of 33.
4 m, Pmax was -0.16 atm.

Liquid pressure P = -0.16 at crater end
(Atm) (Absolute pressure 0.84 atm) The positive pressure is maintained and porosity does not occur.

The crater end length is 33.1 m to 33.
The reason why the length is increased from 4 m to 30 cm is that the solidification is slightly delayed due to the effect of Joule heat.

In the present embodiment, the electromagnetic volume force (Lorentz force) of 22 G on average was required over the range of 2.8 m in the casting direction, but from the viewpoint of equipment or economics, the applicable range and the required electromagnetic volume force (Lorentz force). It is desirable to reduce the force).

Then, as a logical means that can be considered next, as shown in FIG. 7 (d), the hydraulic pressure drop is mitigated by supplementarily using a light pressure reduction utilizing a magnetic attractive force, and the required electromagnetic volume force ( Lorentz force) was attempted.

As a preparation, a numerical analysis was conducted to examine the effect of light pressure reduction.

(1) Calculation of rolling reduction distribution δ

At the time of obtaining the reduction amount distribution δ required for completely compensating the solidification shrinkage, the solid phase ratio gs of the thickness center element is 0.1 (in this case, Z = 25).
Based on m) (δ = 0), the solidification shrinkage volume in the solid-liquid coexisting phase was determined, and was determined as being equal to the rolling reduction δ in the slab thickness direction. That is, the reduction amount increase Δδ between Δt can be obtained by the equation (73).

[0472]

[0473] This is the volume of the element, and the subscript i indicates the solid-liquid coexisting element in the thickness direction of a certain cross section.

As shown in FIG. 36 (a), Z = 25
Based on the position of m, δ = 1.06 mm at the position of 33.1 m from the meniscus.

(2) Calculation of pressure drop

Next, the actual reduction gradient was determined with reference to the reduction amount distribution.

That is, as shown in FIG. 36 (b), the reduction amount at the position 31 m from the meniscus is 0, and the reduction amount at the crater end is 0. Numerical analyzes were performed for a case where a light reduction of 1 mm was applied and a case where a reduction of 32 mm from the meniscus was 0 and a reduction of 0.06 mm at the crater end was applied.

As shown in FIG. 36 (c), the pressure drop in the vicinity of the crater end is alleviated by applying the light pressure reduction.

(3) Effect of light reduction on electromagnetic volume force

The reduction amount at the position of 30.8 m from the meniscus is 0, and the reduction amount at the crater end is 0. Numerical analysis was performed for a case where an electromagnetic volume force (Lorentz force) equivalent to 8 G was applied to the range while applying a light reduction of 1 mm.

As shown in FIG. 37, the length of the solid-liquid coexistence region was 14.6 m, Zmax was 33.2 m, and Pmax was 5.1 atm. The condition that no defects occur is satisfied.

As compared with the case where only the electromagnetic volume force (Lorentz force) is applied, the applicable range (casting direction) is shortened by 50 cm, and the required electromagnetic volume force (Lorentz force) is also reduced to about 1/3. It can be seen that the effect is great simply by applying a reduction gradient to the slab very lightly.

[0483] Since the reduction gradient by the conventional light reduction method is aimed at completely compensating the solidification shrinkage, when the strain in the solid-liquid coexisting phase exceeds a certain limit, the dendrite crystals are mechanically destroyed and the high solute concentration is increased. It has been pointed out that the liquid phase may be sucked and cause internal cracking (Reference (27)).

On the other hand, in the present invention, the amount of reduction is small (thus, it is less than the above-mentioned limit strain), and it is used only as an auxiliary means for alleviating the pressure drop, and the electromagnetic volume force (Lorentz force) is applied. Since liquid phase replenishment between dendrites plays a major role, there is no concern about internal cracking.

The large-diameter transport pipe (line pipe) used for transporting petroleum and natural gas is used in harsh environments such as underground, seabed, and cold regions, and is therefore excellent not only in strength but also in toughness and various fracture characteristics. High performance is required.

[0486] When it penetrates and is trapped by the central defects (remaining in the final product) formed during continuous casting, so-called HIC (hydrogen-induced cracking) occurs.

[0487] The accident caused by HIC of the submarine transportation pipe has been given special attention (Reference (28)).

An example of countermeasures currently taken against HIC is to accept center segregation and porosity that occur in continuous cast products as an unavoidable reality and try to eliminate HIC by adjusting alloy components. . For example, reference (2
In 9), C, Mn,
Focusing on P, the components are adjusted so that the HIC sensitivity parameter P _HIC given by the following equation (74) becomes 0.6 or less.

[0489]

[0490] And SM represents the segregation degree (> 1) of the alloy element M.

[0491]

According to this criterion, for example, API
(American Petroleum Institute) Standard X65 class (65 is a proof strength 650
As a means for satisfying the strength requirement of 0.00 psi (448 MPa or more), C = 0.03, P = 0.
004 (wt%) and keep it very low and Cu, N
Strictly controlling the composition of other elements such as i, we have also made special efforts in thermo-mechanical processing technology. The HIC acceptability parameter at this time is P _HIC

Incidentally, in the case of the 0.55% carbon steel used in Examples 2 and 3, P _HIC = 0.715, assuming that there is no segregation according to the present invention. When only the amount of C is 0.20%, P _HIC decreases to 0.365. (However, for these evaluations, Cu, Ni, Cr, M
o Trace elements of V and V are not included). This means that if segregation is eliminated, the strict control of components as described above becomes unnecessary, and the degree of freedom that can be taken regarding the balance of alloy components is greatly expanded.

With respect to the steel pipe for transportation, the demand for strength exceeding the X70 class (proof strength 70000 PSI or 482 MPa or higher) and the X80 class (proof strength 80000 PSI or 551 MPa or higher) is increased, and at the same time not only HIC resistance but also SSC resistance (sulfide resistance). Considering the situation in which the requirements for material stress cracking) and weldability are becoming stricter year by year, it is significant that the degree of freedom for the component balance is expanded. Judging from the current technological level in which high-strength materials are being developed one after another, it can be said that it is easy to meet the above-mentioned quality requirements.

That is, by applying the present invention and completely eliminating the central defect, it is possible to sufficiently meet such a severe requirement.

[0496] It was determined as follows from the temperature transformation diagram (TTT diagram).

[0497]

As shown in FIG. 38, the TTT diagram obtained by using the equations (50) and (76) substantially agrees with the measured values. In the case of the present embodiment, the surface temperature has dropped to 540 ° C., and the distance from the meniscus Z = 18.7 to 2
10 for surface elements (thickness 11.6 mm) between 2.5 m
0% pearlite transformation occurred. As shown in FIG. 33D, the re-rise of the surface temperature T _s is due to the latent heat of pearlite transformation.

When the pearlite transformation occurs, the surface layer of the cast slab becomes magnetized, and is therefore magnetized by the static magnetic field. Therefore, when designing a superconducting magnet or the like, it is necessary to take into consideration various interactions due to this, for example, the influence on the magnetic flux density at the center of the slab.

Now, the result of studying the attractive force acting between the coils when an air-core type superconducting magnet is used will be described.

As shown in FIG. 39 (a), it is assumed that the coils are circular and the total current I (= coil current × number of turns) flowing through each coil is one point current (actually, the finite cross-sectional area is Have). Although the slab exists between both coils, it was regarded as the same as air for simplicity. At this time, Z of the central axis
The magnetic flux density B _Z in the Z direction at the position of = b / 2 is given by the following equation (77).

[0502]

Where μ _o is the magnetic permeability of vacuum and is 4πx
It has a value of 10 ⁻⁷ (H / m). On the other hand, the force in the Z direction that the current of the coil 2 receives by the magnetic field generated by the coil 1 is given by the following equation (78).

[0504]

Here, Br is the r-direction component of the magnetic flux density on the coil 2, and is given by the following equation using the vector potential A _θ (θ-direction component).

[0506]

(For A _θ , see, for example, Naohei Yamada et al. 2
Name: Exercise on electromagnetics (1970), P. 159 [Corona]. )

As shown in FIG. 39 (b), the inter-coil pressure P (the value obtained by dividing F _Z by the coil cross-sectional area) decreases as the inter-coil distance increases, but decreases markedly as Bz increases. . However, here, a = 0.8 m is fixed for calculation.

In the above calculation, the parameters assuming actual operation are used, and it is possible to control the pressure applied to the slab in a wide range by controlling the magnetic flux density, that is, the coil current and the distance between the coils. It is shown.

Considering that the strength of the dendrite skeleton in the solid-liquid coexisting phase is about several Kg / cm ² to about 50 Kg / cm ² (p.72 of Reference (27)), the attractive force between the coils is used. It is understood that it is possible to give a very small rolling down gradient. For example, in the case of the present embodiment, the solid fraction g _S of the central portion is 0.65 or more in the light reduction range Z = 30.8 to 33.1 m, and the inter-coil distance is 0.6 m as judged from the dendrite skeleton strength. It is possible to apply a predetermined light pressure reduction gradient at B = 1 to 2 (tesla).

Further, in actual application, as shown in FIG. 40, in an actual machine equipped with an electromagnetic booster, the relationship between the magnetic attractive force and the reduction gradient was previously obtained experimentally, and the magnetic attraction force with respect to the required reduction gradient was obtained. Just give it. Since the light pressure reduction is used as an auxiliary means for reducing the hydraulic pressure drop, it is not necessary to strictly control it.
The magnetic force may be controlled so that it falls within a certain range.

From the above description, in the present invention, all the continuous casting methods other than the vertical round bloom and the vertical bending slab continuous casting mentioned in the examples, that is, the vertical bending bloom and the billet, and the bending slab, the bloom and the In addition to conventional continuous casting such as billets, thin slab continuous casting having a wall thickness of about 50 mm or 60 mm, which has recently been attracting attention, and so-called near-ne having an H-shaped profile cross-section.
It can also be applied to the t-shape continuous casting method, a different steel type composite continuous casting method and the like.

The reason is that the liquid phase pressure drop between the dendrites in the casting direction in the solid-liquid coexisting phase in the final solidified portion in the cross section of the slab is focused and the liquid pressure is maintained above the critical pressure for porosity generation. This is because the principle of the present invention that defects (segregation and microporosity) can be completely eliminated is universal to all these continuous casting processes.

Since the liquid phase flow between the dendrites in the casting direction of the center portion induced by solidification shrinkage is a physical phenomenon common to all alloys, the present invention is applicable to all steel types regardless of the type of steel, that is, carbon. It can be applied to steel, low alloy steel, stainless steel, etc. The same applies to continuous casting of non-ferrous alloys such as aluminum and copper.

The present invention is based on the electromagnetic volume force (Lorentz).
Force alone, and electromagnetic volume force (Lor
entz force) and light reduction using magnetic attraction are combined, but in any case, the effect cannot be expected if the timing of coagulation, that is, the position to be applied (distance from meniscus) is incorrect. .

For example, even if the electromagnetic volume force (Lorentz force) is applied on the downstream side (the position away from the meniscus) from the position where the porosity generation critical pressure is reached, the V-shaped porosity has already occurred, and FIG. ), It further promotes the flow that forms V segregation (flow from the surrounding low temperature part to the central high temperature part), and therefore, depending on the degree of the electromagnetic volume force (Lorentz force), more V It may produce segregation or no effect at all.

On the contrary, if it is too upstream of the critical pressure position, the liquid pressure in the portion that does not need to be increased is unnecessarily increased, and the effect to the vicinity of the crater end, which requires the most liquid phase replenishment, becomes small, which is not preferable. .

Even if the position is appropriate, if the electromagnetic volume force (Lorentz force) is too small and the pressure becomes lower than the critical pressure, the generation of defects may be promoted.

Therefore, it is extremely important to know the critical pressure position and the necessary electromagnetic volume force (Lorentz force) quantitatively and accurately. However, it is not possible to directly know the critical position by physical measurement, and it is impossible to know the required electromagnetic volume force (Lorentz force) distribution by experimental means. This is the reason why the numerical analysis developed by the present inventor is required as an element constituting the invention.

As a method of applying an electromagnetic volume force (Lorentz force), there are a method using a DC magnetic field and a DC current and a method using a linear motor type electromagnetic propulsive force, as described in the embodiments of the present specification. Which method to use is
As shown in FIGS. 7 and 23, the cross-sectional shape of the slab (slab, bloom, billet or irregular cross section), continuous casting machine profile, required electromagnetic volume force (Loren)
The most suitable method may be adopted in consideration of the magnitude of (tz force).

Also, the electromagnetic volume force (Lorentz force) generated by the electromagnetic booster can be used as the pulling force of the slab. Usually, in continuous casting of a bending die or a vertical bending die, the pulling resistance is received by the pulling resistance due to the straight bending of the cast piece, the frictional resistance between the cast piece and the mold wall, and the like. For example, in reference (31), 190 mm x 1490 m
In the continuous casting of slab with m and casting speed of 1.5 m / min, the pulling resistance of about 60 ton is actually measured. In order to obtain a sufficient pulling force against such a large pulling resistance force, it is necessary to effectively apply a driving torque by the roll to the slab, and a multi-drive system is generally adopted.

However, in the method in which the frictional force due to pressing is applied to the slab, it is considered that the quality is affected in some way. For example, if the pressing force of the roll is large, the solidified shell is deformed, which is one of the causes of internal cracks and segregation (Reference (31)).

On the other hand, the capacity of the electromagnetic booster used in this embodiment was calculated as the maximum value F _max of the pulling force (Lore).
application volume × density × G ratio) result in ntz force, in the second embodiment _F max = _20.88ton, a third embodiment when the electromagnetic body force only in _{F m} ax = _154ton of (2z
One), and F _max = 5 ton in the case of combining the light pressure reduction of the third embodiment, which is substantially comparable to the required pulling force.

Therefore, the electromagnetic volume force (Lorentz) is adjusted by adjusting the current cross-sectional area or increasing the magnetic flux density.
Force) can be adjusted to obtain a pulling force comparable to the pulling resistance force.

The electromagnetic volume force (Lorentz force) quietly acts on the slab, which eliminates the need for a driving roll in the quality-critical range from the meniscus to the crater end. Since the rolls used during this period are purely used to support the slab, many drive roll devices can be greatly reduced to the minimum number required, which contributes to the reduction of equipment cost and adversely affects the quality. It produces the effect of reducing the factors.

The operation method when the present invention is applied to actual continuous casting is as follows.

(1) Matching between solidification simulation by the numerical analysis and actual continuous casting machine test (matchin)
g). As a matter of course, the numerical analysis result shown in the present embodiment involves an error.

The first cause of the error is the accuracy relating to the heat transfer coefficient on the surface of the slab used in the calculation and various physical property value data. The physical property value data used in this example are appropriate values with reference to various documents, but it is difficult to ensure accuracy for many data.

The second is the modeling of the morphology of dendrite crystals and the accuracy of the transmittance K determined by the modeling. Although the validity of modeling of complicated dendrite morphology has been verified in Ref. (18), the transmissivity of the dendrite crystal in the direction parallel to the growth direction (K _p ) and in the vertical direction (K _V ) is different. Is known (reference (32)). K _p and K _V appear to be cooling rate dependent. However there no reliable data about the magnitude of K _p and K _V practical steel is reality.

Therefore, when matching the numerical analysis and the actual machine test, only the above two points need to be considered.

By measuring the temperature change of the surface (or inside) of the solidified shell (for example, Document (33)), the error due to the first cause can be corrected. At present, considerable data have been accumulated regarding the relationship between cooling conditions such as water spray and surface heat transfer coefficient. Further, since the solidified shell thickness and the crater end can be measured, accurate correction can be performed. As an example, the correction is made by the temperature diffusivity λ / cp.

Regarding the error due to the second cause, the dendrite specific surface area Sb ((28) in the transmittance K equation (27) is
In addition to the correction coefficient α introduced in (equation), a parameter α _K that corrects the influence of the anisotropy of the columnar dendrites is introduced in the K expression, and these correction coefficients are set so that the porosity generation critical position matches the calculated value. Just decide. That is, the critical position may be narrowed down while observing the state of internal defects (generation range, porosity size, etc.) after completion of solidification and making a comparative study with the results of numerical analysis.

When various correction factors are determined, the optimum conditions for eliminating internal defects by numerical analysis (that is, the position, range, size of the electromagnetic volume force (Lorentz force) to be applied, and magnetic attraction force as necessary) are selected. Conditions such as light reduction)
You can find out.

Since the optimum condition determined in this way is corrected, it is sufficiently reliable, and it goes without saying that the set value is set on the safe side in the actual operation.

The solution to the internal defect problem of the continuous cast product has been described above. However, the internal defect is not limited to the examples given here, but to almost all steel grades to some extent. Given the problems that arise, the present invention applies to a very wide range of steel grades for all continuous casting processes.

Finally, the effects of the present invention will be briefly summarized as follows.

(1) Internal defects (center segregation and porosity) can be completely eliminated.

(2) High speed casting is possible.

(3) The degree of freedom in chemical component balance is expanded.

(4) The type of continuous cast steel can be expanded.

(5) Labor of the drawing device can be saved.

In particular, with regard to the above item (2), the number of continuous casting plants can be reduced by half by increasing the casting speed by 2 times or 3 times, and the economical effect thereof is extremely large. From the viewpoint of construction cost and space saving, a superconducting magnet is more preferable than a normal electromagnet as a magnetic field generator. Also,
For the bloom, a shape suitable for the shape of the slab, such as a racetrack type coil, may be used. Furthermore, it is convenient to be able to move the position of the booster in response to changes in operating conditions.

From the above, it can be said that the continuous casting process according to the present invention is a novel process excellent not only in quality but also in productivity and economy.

The present inventor is not limited to macroscopic physical phenomena such as heat and flow, and couples these macroscopic phenomena with microscopic solidification phenomena such as dendrite growth and solute redistribution in a multi-component alloy system. By developing a computer program that introduced the effects of electromagnetic force, mechanical deformation, and pearlite transformation, it was possible (for the present inventor's knowledge) to understand the whole picture of the solidification phenomenon in continuous casting for the first time. [Discretization of governing equation] A: Discretization of energy equation The discretization equation for temperature is as follows. Subscripts 1, 2 and 3 are grid point P
From the perspective, the velocity components in the N, T, and W directions are expressed,
Faces n, s, ... of the element (control volume)
..Defined in Harmonic mean of both elements
n) is taken. That is, B: Discretization of solute redistribution formula It represents the latest value in the return convergence calculation, and uses the average with the old value before Δt (Crank-Nicholson
(scheme). There are as many discretization expressions as there are prime numbers. C: Discretization of temperature-solid fraction equation The discretization equation of the temperature T with respect to the solid fraction g _S is as follows. D: Darcy-Discretization of pressure equation The velocity calculation formula based on the Darcy law (formula (26) of the text) is as follows: And X ₃ direction components. That is, Becomes The subscripts 1, ... Of K consider the anisotropy of columnar dendrites: For example, in the case of continuous slab casting, K ₁ = K _p
(Parallel to the columnar dendrite growth direction) and K ₂ = K ₃ =
K _V (perpendicular to the growth direction). K ₁ = for equiaxed crystals
K ₂ = K ₃ . Also, the harmonic mean in the element plane is used.
Next, the pressure equation is a continuous condition (equation (9) in the text and the above (D.
1), etc. Join and guide. First, when the equation (9) is discretized, It should be emphasized again that the P field is determined so as to satisfy the continuous condition including the influence of the Lorentz force in addition to the force. E: Discretization of equation of motion For the equation of motion, staggered grid is used (see Reference (20)). X ₁ (r) direction stag
Using the gered grid (see FIG. 41 (a)),
The v ₁ discretization formula is as follows (subscript 1 is omitted for simplicity). R-direction staggered gr in curvilinear coordinate system (Fig. 9)
For id: All common except S _{c, n and S n} are given by: For μ, the harmonic mean is used. Z direction staggered g
Using rid (see FIG. 41 (b)), the v ₂ discretization formula is as follows (subscript 2 is omitted for simplicity). Z direction staggered gr in Cartesian and cylindrical coordinate system
For id: Z-direction staggered gr in curvilinear coordinate system (Fig. 9)
For id: All common except S _{c, t} and S _t are given by: X ₃ (Y) direction staggered grid (FIG. 41)
(See (c)), the v ₃ discretization equation is as follows (subscript 3 is omitted for simplicity). Y-direction stag in curvilinear coordinate system (Fig. 9) and Cartesian coordinate system
for ered grid; Pressure discretization formula: The discretization formula regarding the pressure in the equations of motion (E.1), (E.30) and (E.58) is Darcy.
Similar to the case of analysis, these equations of motion and continuous condition expressions (formula (9) in the text) are combined and derived. First, the equation of motion is transformed as follows. When P is rearranged, the discretization formula for P is obtained.
As is clear from the equation (E.92), P is stagger
It is defined in the original grid, not in the ed grid (see FIGS. 8 and 9). Note the issue). Pressure correction formula and velocity correction formula: When the velocity field converges in the repeated calculation, the pressure equation is solved to obtain the correct pressure field at once. Therefore, the v field is modified, but first, the P field is modified. This is the iterative convergent solution method using the SIMPLER algorithm. The method is as follows: Now, P (correct answer) = P ^* (latest value) + P '(correction amount) (E.107) v (correct answer) = v ^* (latest value) + v' (correction amount) (E. 108). The equations of motion for P and P ^* are

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[Brief description of the drawings]

FIG. 1 is a configuration diagram showing a first embodiment of the present invention.

FIG. 2 is a detailed explanatory diagram for explaining the details of the electromagnetic booster in FIG.

FIG. 3 is an explanatory diagram for explaining redistribution of solute elements. FIG. 3A shows an equilibrium diagram of Fe and an alloy element, FIG. 3B shows a solute concentration distribution in the case of an equilibrium solidification type alloy element, and FIG. 3C shows a non-equilibrium solidification type alloy. The solute concentration distribution in the case of an element is shown.

FIG. 4 is an explanatory diagram for explaining piecewise linear modeling of a nonlinear binary state diagram.

FIG. 5 is an explanatory diagram for explaining a dendrite solidification model.

FIG. 6 is an explanatory diagram for explaining a generation site of microporosity and a size of a liquid phase space between dendrites.
FIG. 6A shows the place where the porosity occurs. FIG. 6 (b)
And (c) are models for calculating the size of the liquid phase space.

FIG. 7 is an explanatory diagram for explaining a volume element used in numerical analysis. Dendrites have been greatly expanded. V _L represents a liquid phase flow velocity vector between dendrites, and V _S represents a deformation velocity vector of the dendrite crystal.

FIG. 8 is a p. 97
It is the explanatory view quoted more. The shaded area is control
Representing a volume, the points marked with a circle are grid po
called int. Fe, Fw, Fn, and Fs on the surfaces e, w, n, and s of the control volume represent the physical quantity φ.

FIG. 9 shows the coordinate system used in the numerical analysis, and FIG. 9 (b) shows the topology related to discretization. FIG. 9B
The meanings of the symbols in are the same as in FIG.

FIG. 10A is a schematic flowchart of a main program showing a flow of calculation in numerical analysis.

FIG. 10 (b) is a schematic flowchart of a solution method using a motion equation in numerical analysis.

FIG. 11 is an explanatory diagram for explaining the analysis result of a large steel ingot (diameter 1 m × height 3 m) selected as an example for verifying the validity of the numerical analysis result. FIG. 11A shows a casting method. FIG. 11B shows an example of isothermal lines during solidification (after 11.5 hours). Reference symbol S is a solid, M is a solid-liquid coexisting phase (Mushy zone), and C is a contraction hole (c).
avity), and the dashed line represents the boundary of these phases. FIG. 11C is an isosolid rate line at the same time as FIG. The numbers in the figure indicate the solid phase ratio (0 to 1). FIG.
(D) shows a liquid phase flow pattern after 4.28 hours when the whole area became a solid-liquid coexisting state (M). The part where the streamline density is high (central part) shows that the flow velocity is high. It is about 3.5 mm / s at the center of the center where the flow velocity is fast. Similarly, FIG. 11 (e) is a liquid phase flow pattern between dendrites after 11.5 hours. The flow velocity at the central central portion is about 0.1 mm / s. 11 (f) and 11 (g) show the completion of solidification As described above, about 5% of positive segregation occurs near the outer periphery (portion where A segregation appears). The negative segregation is greatest near the center of the lower part, and becomes smaller toward the outside and the upper part (about -10).
%). FIG. 11 (g) shows the case of phosphorus, which shows the same tendency as that of carbon, but positive and negative segregation appears more strongly.

FIG. 12 shows a solidification shrinkage flow pattern between dendrites confirmed by numerical analysis in FIG. 12 (a), and a schematic view of V defects in FIG. 12 (b). In FIG. 12A, the central portion having a high streamline density indicates that the flow velocity is high. The flow in the lateral direction is extremely small compared to the flow in the casting direction. FIG.
(B) is local along the V-shape (dendritic scale)
Shows a V-shaped defect with a strong positive segregation (+) at the same time with microporosity. The arrow indicates the liquid phase flow between dendrites flowing along the V defect.

FIG. 13 is a schematic view of a typical current vertical billet continuous casting machine. L represents a liquid phase region, M represents a solid-liquid coexisting phase, and S represents a solid part.

FIG. 14 is an explanatory diagram for explaining the linearized data of the Fe—C state diagram.

FIG. 15 is an explanatory diagram showing a relationship between temperature and solid fraction calculated using a nonlinear multi-component alloy model. FIG. 15 (a) shows the case of IC-1Cr bearing steel (see Table 2 for composition),
FIG. 15B shows the case of 0.55% carbon steel (see Table 6 for composition).

FIG. 16 is an explanatory diagram for explaining the influence of the oxygen content on the equilibrium CO gas pressure in the liquid phase between dendrites.
However, there is no CO gas bubble ((4
9)-(58) type formula). Figure 16 (a) shows IC-1Cr
The case of bearing steel (see Table 2 for composition) is shown in Fig. 16 (b).
Is for 0.55% carbon steel (AISI 1055, composition see Table 6).

17 (a) shows the distribution of the temperature T and the solid fraction g _S of the central element in the first embodiment, and FIG.
(B) shows a solidified shell wall thickness distribution (all are in a steady state). (A) in the figure is a case of simple temperature calculation,
(B) shows a case where the liquid phase thermal conductivity is apparently increased to 5 times in consideration of the Darcy flow.

FIG. 18 (a) shows the temperature T of the central portion, the solid fraction g _S , the liquid pressure P, and the Darcy flow velocity V in the first embodiment.
18 (b) shows the surface heat transfer coefficient H and the solidified shell thickness, and FIG. 18 (c) shows the transmittance K and the volume force (self-weight or Lorentz force) X of the central portion.
(D) shows the surface temperature T _S.

FIG. 19 is an explanatory diagram for explaining a result of numerical analysis in the first example.

FIG. 20 is an explanatory diagram for explaining a phase distribution in the first embodiment. L indicates a molten steel pool, M indicates a solid-liquid coexisting phase, and S indicates a solid phase. The solid phase rate of 1% or more was defined as M.

FIG. 21 is an explanatory diagram for explaining a liquid phase flow between dendrites near a crater end of vertical type continuous casting in the first example.

FIG. 22 is an explanatory diagram for explaining the dendrite arm spacing of vertical continuous casting in the first example. FIG. 22 (a) shows the case where the theoretical formulas based on the formulas (28) and (29) are used, and FIG. 22 (b) shows the case where the empirical formula based on the formula (71) is used. Make sure that the surface elements are the same (28)
The correction coefficient α in the equation is 1.2.

FIG. 23 is an explanatory diagram illustrating an electromagnetic booster according to the first embodiment. FIG. 23A is a conceptual configuration diagram, and FIG. 23B is a horizontal sectional configuration diagram. Electromagnetic volume force (Lorentz force) is applied vertically downward.

FIG. 24 is a graph showing electromagnetic volume force (Lore) in the first embodiment.
It is an explanatory view for explaining the effect of (ntz force).

FIG. 25: Specific heat C of 0.55% carbon steel C (cal / g ° C.)
FIG. 6 is an explanatory diagram for explaining data regarding thermal conductivity λ (cal / cms ° C.).

FIG. 26 is a diagram showing an outline of a typical vertical bending continuous casting machine used in a second embodiment of the present invention. The supporting rolls other than the bending roll and the straightening roll are not shown.

FIG. 27 (a) shows the temperature T, the solid phase fraction g _S , the liquid pressure P, and the Darcy flow velocity V of the thickness center element in the second embodiment, and FIG. 27 (b) shows the surface heat transfer coefficient. H and the solidified shell thickness are shown, and FIG. 27C shows the transmittance K of the thickness center element.
And the casting direction component X of its own weight or electromagnetic volume force,
FIG. 27D shows the surface temperature T _S.

FIG. 28 is an explanatory diagram for explaining the result of numerical analysis in the second example.

FIG. 29 is a graph showing the electromagnetic volume force (Lore) in the second embodiment.
It is an explanatory view for explaining the effect of (ntz force).

30A and 30B show a coagulation profile and a Darcy flow distribution near the crater end in the second example. The symbol L indicates a liquid phase, M indicates a solid-liquid coexisting phase, and S indicates a solid phase. The distance from the meniscus is a value along the slab thickness central axis. The slab is actually curved but shown as a long rectangle for ease of display. The position of the roll in the straightening zone is indicated by a circle.

FIG. 31 is a diagram showing an electromagnetic volume force (Lore) in the second embodiment.
It is an explanatory view for explaining the effect of (ntz force).

FIG. 32 is an explanatory diagram for showing the electrical conductivity σ (1 / Ωm) of carbon steel (edited by Japan Iron and Steel Institute: Iron and Steel Handbook 3rd edition, p.
311).

FIG. 33 is an explanatory diagram for explaining a numerical analysis result in the third example.

FIG. 34 is an explanatory diagram for explaining a numerical analysis result in the third example.

FIG. 35 is a graph showing the electromagnetic volume force (Lore) in the third embodiment.
It is an explanatory view for explaining the effect of (ntz force).

FIG. 36 is an explanatory diagram for explaining a preliminary calculation result performed for studying the light rolling-down effect in the third embodiment. FIG. 36 (a) shows a reduction amount distribution (calculated from the position (25 m) where the solid fraction of the central portion is 0.1 to the downstream side) necessary for compensating the net coagulation contraction, and FIG. FIG. 36B shows linear reduction gradients near the crater end, and FIG. 36C shows calculation results showing relaxation of the hydraulic pressure drop with respect to these reduction gradients.

FIG. 37 is a graph showing the electromagnetic volume force (Lore) in the third embodiment.
It is an explanatory view for explaining the effect of (ntz force) and light reduction.

FIG. 38 shows an isothermal transformation diagram of 0.55% carbon steel. Reference numeral A in the drawing indicates austenite, and P indicates pearlite.
The solid line is the experimental data (reference (30)), and the broken line is the calculated value by the equations (34) and (76) in the present specification (see reference (21)). Since ferrite, pearlite, and bainite are produced by diffusion of C, they are all regarded as C diffusion type pearlite transformation. The volume ratio of P was g _P = 0.01 at the start of transformation and g _P = 0.99 at the end.

FIG. 39 is an explanatory diagram for explaining an attractive force acting between both coils when a superconducting air-core coil is used as the DC static magnetic field generation device. FIG. 39A shows a cylindrical coordinate system (r,
θ, z), and FIG. 39 (b) shows the magnetic flux density Bz at the center z = b / 2 between the coils, 1, 2 and 3 (T
Shows the calculation result when set to (esla) (however, a
= Fixed at 0.8 m). I is the coil current, pressure P (K
gf / cm ² ) is a value obtained by dividing the attractive force between the coils by the coil cross-sectional area.

FIG. 40 is an explanatory diagram for explaining the relationship between the magnetic force (attractive force) and the reduction gradient (mm / m) in the third embodiment. Deformation is concentrated on the dendrite skeleton in the central solid-liquid coexisting phase, which is extremely weaker than the solid, and the relationship between force and gradient (ie displacement) is slightly non-linear.

FIG. 41 is an explanatory diagram for explaining staggered grid used for discretization of a motion equation (see Appendix E). 41 (a) is in the X ₁ (r) direction.
41B is in the X ₂ (Z) direction, and FIG. 41C is X ₃ (Y).
The staggered grid of directions is shown.

FIG. 42 is a schematic view of a continuous forging method according to the related art.
It shows how the liquid phase in the solid-liquid coexisting phase is discharged to the upstream side under the pressure of Anvil. δ is the amount of reduction.

FIG. 43 is an explanatory diagram for explaining formation of a central shrinkage cavity of cast steel (p242 of Document 14).

FIG. 44 is an explanatory diagram for explaining a pressure casting experimental device.

FIG. 45 is an explanatory diagram showing measured and calculated temperature histories in atmospheric casting.

FIG. 46 is an explanatory diagram for explaining a macrostructure of an atmospherically cast product.

FIG. 47 is a microscopic observation structure of a V pattern in an atmospherically cast product.

FIG. 48 is an explanatory diagram for explaining a change in Vickers hardness in the vicinity of a V pattern in an atmospherically cast product.

FIG. 49 is an explanatory diagram for explaining a generation process of porosity by numerical analysis in atmospheric casting. FIG.
(A) is a solid fraction distribution 55 seconds after the start of pouring, which starts to generate internal porosity, and FIG. 49 (b) shows a porosity distribution after completion of solidification.

FIG. 50 is an explanatory diagram for explaining a macrostructure of a pressure cast product of 10 atm.

FIG. 51 is an explanatory diagram for explaining a macrostructure of a pressure cast product of 22 atm.

FIG. 52 is an explanatory diagram showing a result of predicting the effect of pressure casting by numerical analysis. 52 (a) is atmospheric casting (no pressurization), FIG. 52 (b) is 10 atm pressurization and FIG.
(C) shows the volume ratio of the internal defect at the time of 20 atm pressure casting.

FIG. 53 is an explanatory diagram showing the results of numerically predicting the effect of pressure casting on the steel casting of Document (34).
53 (a) is not pressurized, and FIG. 53 (b) is 4.2.
The porosity volume ratio at the time of pressurizing atm is shown.

FIG. 54 is an explanatory diagram for explaining a mechanism of causing an internal defect.

[Explanation of symbols]

 1 Electromagnetic Booster 1a High Rigidity Frame 1b Cast Piece 1c DC Rotating Electrode 1d Spring 1e Fixed Axis 1f Non-Magnetic Roll 2 Ladle 3 Tundish 4 Nozzle 5 Water Cooled Mold 6 Cast Piece 7 Bending Roll 8 Straightening Roll 9 Display Means

Claims (14)

[Claims] 1. A continuous casting system comprising an electromagnetic booster for applying an electromagnetic volume force (Lorentz force) in the casting direction of a continuous cast product in continuous casting. 2. The electromagnetic booster applies an electromagnetic force in the casting direction to the solid-liquid coexisting phase of the continuous cast product.
Z continuous force is applied, The continuous casting system of Claim 1 characterized by the above-mentioned. 3. The electromagnetic booster applies an electromagnetic volume force (Lorentz force) in the casting direction to the solid-liquid coexisting phase near the final solidification portion of the continuous cast product. Continuous casting system. 4. The electromagnetic booster has an electromagnetic volume of a size required to maintain a liquid phase pressure between dendrites in a solid-liquid coexisting phase near a final solidification portion of the continuous cast product at a pressure equal to or higher than a porosity generation critical pressure. The continuous casting system according to claim 1, wherein a force (Lorentz force) is applied. 5. The electromagnetic booster comprises an alloy component of the continuous cast product, a solid solution gas amount in a liquid phase, a cross-sectional shape / dimension of the continuous cast product, a casting temperature, a casting speed, a continuous cast slab (solidified shell). And a calculation means for calculating the magnitude of the electromagnetic volume force (Lorentz force) and the application area based on the cooling conditions on the surface and the operating parameters such as the deformation rate of the slab by bending, straightening, and rolling. The continuous casting system according to claim 1, which is characterized in that. 6. The calculation means calculates the internal defect occurrence position by paying attention to the pressure drop of the liquid phase caused by the flow of the liquid phase generated between the dendrites in the solid-liquid coexisting phase of the continuous cast product. The continuous casting system according to claim 5, characterized in that The continuous casting system according to claim 5, further comprising display means for displaying in real time. 7. The calculation means comprises a correction means for correcting the magnitude of the electromagnetic volume force (Lorentz force) and the applied area based on an actual measurement value. Continuous casting system. 8. The continuous casting system according to claim 7, wherein the correction means performs arithmetic processing based on experimentally measured data. 9. The correction means has a function of performing feedback control in real time with respect to the magnitude and application region of the electromagnetic force and the operation parameter based on the actual measurement data of the operation parameter.
The continuous casting system described. 10. The continuous casting system according to claim 5, wherein the arithmetic means includes a display means for displaying the solidification process of the continuous cast product in real time based on an actually measured value. 11. The continuous casting system according to claim 1, wherein a reduction means for imparting a reduction gradient to the continuous cast product is provided together with the electromagnetic booster. 12. The continuous casting system according to claim 11, wherein the reduction means applies a reduction gradient not more than a solidification shrinkage gradient near the final solidification portion of the continuous cast product through the slab surface. . 13. The continuous casting system according to claim 11, wherein the rolling-down means includes a facing roll. 14. The continuous casting system according to claim 11, wherein the reduction means comprises a magnetic field generator.