Continuous Casting Method and Continuous Casting Machine for Steel

This is the U.S. National Phase application of PCT/JP2023/018120, filed May 15, 2023, which claims priority to Japanese Patent Application No. 2022-086206, filed May 26, 2022, the disclosures of these applications being incorporated herein by reference in their entireties for all purposes.

The present invention relates to a continuous casting method for steel and a continuous casting machine for steel.

In a steel solidification process, solute elements, such as carbon (C), phosphorus (P), sulfur(S), and manganese (Mn), are concentrated to an unsolidified liquid phase side due to redistribution in solidification. The concentrated solute elements result in microsegregation formed between dendrite trees. In a steel continuous casting process in a continuous casting machine, solidification shrinkage or thermal shrinkage of a cast piece, bulging of a solidified shell generated between rolls in the continuous casting machine, or the like causes the formation of cavities or the generation of a negative pressure in a thickness center part of the cast piece, so that molten steel is absorbed into this portion. However, a sufficient amount of molten steel is not present in an unsolidified layer at the end of the solidification, and therefore the molten steel concentrated by the microsegregation flows, and accumulates and solidifies in a center part of the cast piece. In a segregation spot thus formed, the concentration of the solute elements is much higher than the initial concentration of the molten steel. This is generally referred to as macrosegregation, and is also referred to as center segregation due to a site where the macrosegregation is present.

The center segregation deteriorates the quality of line pipe materials for transporting crude oil, natural gas, and the like. When manganese sulfides or niobium carbides are formed in a center segregation part, hydrogen entering steel by a corrosion reaction diffuses and accumulates around the manganese sulfides or the niobium carbides in the steel, and the internal pressure of the hydrogen causes cracking. Further, the center segregation part is hardened, and therefore the cracking propagates. This cracking is referred to as hydrogen-induced cracking (also referred to as “HIC”) and is the primary cause of deteriorating the quality of the line pipe materials used in sour gas environments.

To address the above, a number of measures for reducing the center segregation in the cast piece or making the center segregation harmless from a continuous casting step to a rolling step have been proposed.

For example, PTL 1 and PTL 2 have proposed methods of casting a cast piece at the end of solidification having an unsolidified layer while the cast piece is being gradually rolling-reduced with cast piece supporting rolls with a rolling reduction amount to an extent equivalent to the sum of a solidification shrinkage amount and a thermal shrinkage amount in a continuous casting machine.

The technologies of gradually rolling-reducing the cast piece during casting with the rolling reduction amount to an extent equivalent to the sum of the solidification shrinkage amount and the thermal shrinkage amount in the continuous casting machine as in PTL 1 and PTL 2 are referred to as “soft reduction” or “soft reduction methods”. The soft reduction technology gradually reduces the volume of the unsolidified layer by gradually rolling-reducing the cast piece using a plurality of pairs of rolls aligned in the casting direction with a rolling reduction amount corresponding to the sum of the solidification shrinkage amount and the thermal shrinkage amount. This prevents the formation of the cavities or a negative pressure part in the center part of the cast piece and simultaneously prevents the flow of the concentrated molten steel formed between dendrite trees, which reduces the center segregation in the cast piece.

As recent continuous casting machines, segment type continuous casting machines containing segments each including a plurality of pairs of rolls have been mainly used. In the case of the segment type continuous casting machines, a rolling reduction roll group carrying out soft reduction (also referred to as “soft reduction zone”) also contains a plurality of segments. The soft reduction zone containing the segments is configured such that a predetermined rolling reduction amount is applied to a cast piece on the inlet side and the outlet side of each segment by adjusting the opening degrees between the rolls facing each other in the thickness direction of the cast piece to be larger on the inlet side than on the outlet side.

It is known that the shape in the cast piece width direction at a solidification completion position of the cast piece and the center segregation are closely related to each other. For example, PTL 3 has proposed a method for detecting the solidification completion position in the cast piece width direction and adjusting the molten steel flow in a mold or adjusting the width cut amount of secondary cooling such that a difference between the shortest part and the longest part at the detected solidification completion position is within the standard. When the solidification completion position varies in the cast piece width direction, the rolling reduction amount in the soft reduction zone varies in positions in the cast piece width direction, and therefore, at a position where the solidification completion position extends to the casting direction downstream side, the rolling reduction amount decreases, so that a sufficient center segregation improvement effect cannot be obtained. However, according to the method in PTL 3, the center segregation improvement effect can be obtained even when the solidification completion position varies in the cast piece width direction.

It is also known that bulging between the rolls of the cast piece also affects the center segregation. For example, PTL 4 has proposed a continuous casting method including calculating inter-roll bulging of a cast piece in the soft reduction zone using an unsteady heat transfer solidification calculation and changing the rolling reduction rate to be applied to the cast piece corresponding to the calculated inter-roll bulging.

As described above, to improve the center segregation of the cast piece, measures have been individually taken for the rolling reduction rate in the soft reduction, the shape at the solidification completion position in the cast piece width direction, and inter-roll bulging. However, the closest quality requirement level for the continuously cast cast-piece has further increased, and a variation in the segregation degree in the cast piece width direction has also become problematic. In particular, steel materials strict about segregation, such as line pipe materials, are difficult to be used as line pipe materials when even one portion in the width direction has a large segregation at a cast piece stage.

Even when the above-described conventional technologies are applied, problems sometimes arise for the center segregation, such as a deterioration of the overall segregation level in the cast piece width direction or an increase in a variation in the segregation degree in the cast piece width direction of the center segregation, and therefore a technology of stably reducing the center segregation has been demanded.

Thus, aspects of the present invention have been made in view of the above-described circumstances, and aim to provide a continuous casting method for steel and a continuous casting machine for steel capable of reducing the overall segregation level in the cast piece width direction and reducing the variation in the cast piece width direction in the segregation degree of the center segregation.

(1) One aspect of the present invention provides a continuous casting method for steel for continuously casting steel with a continuous casting machine of a curved type continuous casting machine or a vertical bending type continuous casting machine, including: applying rolling reduction to a cast piece to be continuously cast at a rolling reduction rate of 0.3 mm/min or more and 2.0 mm/min or less in a range where a solid phase ratio in a thickness center of the cast piece is at least 0.2 or more and less than 1.0, in which a segment deflection t being a deflection in the thickness direction of a segment frame of a segment where the rolling reduction is applied to the cast piece satisfies Equation (1).

In Equation (1),

(2) In the continuous casting method for steel described in (1) above, for a segment frame equivalent to the final solidification position, a deflection deviation σ is set to 0.2 mm or less and a lateral displacement difference t of the segment frame is constantly set to 0.2 mm or less.

(3) In the continuous casting method for steel described in (1) or (2) above, the long side surfaces of the cast piece are bulged with a total bulging amount of 3 mm or more and 20 mm or less by stepwise increasing the roll opening degree of a plurality of pairs of cast piece supporting rolls toward the casting direction downstream side in an intentional bulging zone of the continuous casting machine, and the rolling reduction is applied to the cast piece by stepwise reducing the roll opening degree of the plurality of pairs of cast piece supporting rolls toward the casting direction downstream side in the soft reduction zone on the casting direction downstream side relative to the intentional bulging zone.

(4) One aspect of the present invention provides a continuous casting machine for steel of a curved type continuous casting machine or a vertical bending type continuous casting machine for continuously casting steel, including: a soft reduction zone where a cast piece to be continuously cast is rolling-reduced in the thickness direction, in which, in the soft reduction zone, the rolling reduction is applied to the cast piece at a rolling reduction rate of 0.3 mm/min or more and 2.0 mm/min or less in a range where a center solid phase ratio being a solid phase ratio in a thickness center of the cast piece is at least 0.2 or more and less than 1.0, and a segment deflection t being a deflection in the thickness direction of a segment frame of a segment where the rolling reduction is applied to the cast piece in the soft reduction zone satisfies Equation (1).

One aspect of the present invention provides the continuous casting method for steel and the continuous casting machine for steel capable of reducing the overall segregation level in the cast piece width direction and reducing the variation in the cast piece width direction in the segregation degree of the center segregation.

The following detailed description gives a description of embodiments of the present invention with reference to the drawings. The drawings are schematic and are sometimes different from the actual ones. The embodiments described below exemplify devices and methods for embodying the technical idea according to aspects of the present invention. The technical idea according to aspects of the present invention does not specify materials, structures, arrangement, and the like of constituent components to the materials, structures, arrangement, and the like described below. The technical idea according to aspects of the present invention can be variously altered within the technical range defined by Claims.

In one embodiment of the present invention, a continuous casting machineis a device for producing a slab by continuously casting steel, the slab being a cast piece having a rectangular transverse cross-sectional shape that is the shape of a cross section orthogonal to the longitudinal direction, and is a curved type continuous casting machine or a vertical bending type continuous casting machine. The continuous casting machineaccording to this embodiment can be applied to either type of the curved type continuous casting machine or the vertical bending type continuous casting machine because the machines are common in principle. The following description of this embodiment is given using the vertical bending type continuous casting machine as the continuous casting machineas one example.

illustrates a schematic side view of the continuous casting machinethat is a vertical bending type slab continuous casting machine used when aspects of the present invention are implemented. In this embodiment, the longitudinal direction of a cast pieceand the movement direction of the cast pieceand a solidified shellin the continuous casting machineare referred to as a casting direction. The lateral direction (direction orthogonal to the casting direction in a cross section of the cast piecein) of the rectangle in the transverse cross-section (cross section orthogonal to the longitudinal direction) of the cast pieceis referred to as a thickness direction. The longitudinal direction (front-back direction in) of the rectangle in the transverse cross-section of the cast pieceis referred to as a width direction. The length in the thickness direction of the cast pieceis referred to as a thickness and the length in the width direction is referred to as a width. In the transverse cross-section of the cast piece, the sides facing each other in the thickness direction are longer than the sides facing each other in the width direction. The sides facing each other in the thickness direction are referred to as long sides and the sides facing each other in the width direction are referred to as short sides.

As illustrated in, a moldinto which molten steelis poured and which solidifies the molten steelby cooling and forms the outer shell shape of the cast piecehaving the rectangular transverse cross-section is placed in the slab continuous casting machine. At a predetermined position above the mold, a tundishthat is an intermediate vessel for relay-supplying the molten steelto be supplied from a ladle (not illustrated) to the moldis placed. At a bottom part of the tundish, a sliding nozzlefor adjusting the flow rate of the molten steelis placed. On the lower surface of the sliding nozzle, an immersion nozzleis placed.

Below the mold, a plurality of pairs of cast piece supporting rollscontaining supporting rolls, guide rolls, and pinch rolls are arranged. In gaps between the cast piece supporting rollsadjacent to each other in the casting direction, spray nozzles (not illustrated), such as water spray nozzles or air mist spray nozzles, are arranged. A secondary cooling zone is configured in a range from the cast piece supporting rollsimmediately below the mold to the cast piece supporting rollsat the machine end. The cast pieceis cooled by secondary cooling water sprayed from the spray nozzles in the secondary cooling zone while being drawn out.

The plurality of pairs of cast piece supporting rollsis arranged on the casting direction downstream side from a position distant from the outlet of the moldby about 1 m to 4 m in the casting direction and configures an upper straightening zonein which a support and guide direction of the cast pieceis changed from the vertical direction to a curved direction. More specifically, the cast piecein a flat sheet shape drawn out in the vertical direction from the moldis gradually bent into a circular arc shape and straightened into a curved part having a constant radius in the upper straightening zone. In the upper straightening zone, a tensile stress acts on the lower surface side of the cast pieceand a compressive stress acts on the upper surface side. Thus, in the upper straightening zone, surface cracking is likely to occur on the lower surface side of the cast piece, and generally no surface cracking occurs on the upper surface side. In this case, the inside and the outside in the radial direction of a curved part are defined as the upper surface side and the lower surface side, respectively, with the center position in the thickness direction of the cast pieceas the boundary. For the surfaces on the long sides (long side surfaces) of the cast piece, the surface on the inside in the radial direction of the curved part is referred to as an upper surface and the surface on the outside in the radial direction of the curved part is referred to as a lower surface.

Similarly, the plurality of pairs of cast piece supporting rollsarranged in the vicinity of the position where the casting direction of the curved part is parallel to the horizontal direction configures a lower straightening zonewhere the support and guide direction of the cast pieceis changed from the curved direction to the horizontal direction. More specifically, the cast piecein the circular arc shape is gradually bent back to the flat sheet shape and straightened into a horizontal part in the lower straightening zone. In the lower straightening zone, a tensile stress acts on the upper surface side of the cast pieceand a compressive stress acts on the lower surface side. Thus, in the lower straightening zone, surface cracking is likely to occur on the upper surface side of the cast piece, and generally no surface cracking occurs on the lower surface side.

On the casting direction downstream side relative to cast piece supporting rollsthat are cast piece supporting rollson the most casting direction downstream side, a plurality of conveying rollsfor conveying the cast cast-pieceis placed. Above the conveying rolls, a cast piece cutting machinefor cutting a cast piecehaving a predetermined length from the cast pieceto be cast is arranged.

On the casting direction upstream side and downstream side with a solidification completion positionof the cast pieceinterposed therebetween, a soft reduction zoneis placed. The soft reduction zonecontains a group of the plurality of cast piece supporting rolls in which the interval (referred to as “roll opening degree”) between the two cast piece supporting rollsfacing each other in the thickness direction with the cast pieceinterposed therebetween and forming a pair is set to be sequentially narrowed toward the casting direction downstream side, i.e., a rolling reduction gradient is applied. In the soft reduction zone, the soft reduction can be applied to the cast piecethroughout the entire region or in a partially selected region. The soft reduction is a technology of gradually rolling-reducing the cast piece during casting with the rolling reduction amount to an extent equivalent to the sum of the solidification shrinkage amount and the thermal shrinkage amount in the continuous casting machineas described above. Between the cast piece supporting rollsadjacent to each other in the casting direction in the soft reduction zone, a spray nozzle for cooling the cast pieceis arranged. The cast piece supporting rollsarranged in the soft reduction zoneare also referred to as rolling reduction rolls

In the continuous casting machineillustrated in, the soft reduction zonecontains three segments, each containing three pairs of rolling reduction rollsas one set, connected in the casting direction. In, the soft reduction zonecontains the three segments, but the number of the segmentsis not particularly limited and may be one, two, or four or more. In, the three pairs of rolling reduction rollsare arranged in one segment, but the number is not limited to the three pairs. The rolling reduction rollsarranged in one segment may be a plurality of pairs of rolling reduction rolls, and any number of rolling reduction rollsmay be arranged insofar as two or more pairs of rolling reduction rollsare arranged. Further, although not illustrated, the cast piece supporting rollsother than those in the soft reduction zonealso have the segment structure in the continuous casting machine, and particularly the segmentsin the soft reduction zoneare also referred to as soft reduction segments

As illustrated in, the soft reduction segmenthas an upper surface side frame, a lower surface side frame, and support posts. The upper surface side framesupports the plurality (three in this embodiment) of cast piece supporting rollson the upper surface side. The lower surface side framesupports the plurality (three in this embodiment) of cast piece supporting rollson the lower surface side. The upper surface side frame, the lower surface side frame, and the support postsare also collectively referred to as a segment frame. The support postsare posts that connect and support the upper surface side frameand the lower surface side frame. The support postsare provided on both width direction ends. When one pair of support postsarranged in the width direction is set as one set, a plurality of sets of support postsis provided in the casting direction. In this embodiment, one pair of support postsis provided in two places of an inlet side end part and an outlet side end part in the casting direction as illustrated in. The support postshave a mechanism of adjusting the roll opening degree by adjusting the interval in the thickness direction between the upper surface side frameand the lower surface side frameusing a hydraulic pressure or the like.

In usual, the rolling reduction gradient in the soft reduction zoneis expressed by the roll opening degree reduction amount per meter in the casting direction, i.e., “mm/m” unit. Thus, the rolling reduction rate (mm/min) of the cast piecesin the soft reduction zoneis obtained by multiplying the rolling reduction gradient (mm/m) by the cast drawing rate (m/min).

The cast piece supporting rollsarranged between the lower end of the moldand a liquidus crater end position of the cast piecepreferably configure an intentional bulging zone. The liquidus crater end position is a position in the casting direction in the machine of the continuous casting machinewhere the center temperature of the cast pieceis the liquidus temperature of steel to be cast and is determined by a heat transfer solidification calculation (e.g., calculation method described in PTL 4) corresponding to the molten steel temperature or the cooling capacity of the continuous casting machine. In the intentional bulging zone, the cast piece supporting rollsare set such that the roll opening degrees are sequentially widened for each roll pair or for a plurality of roll pairs toward the casting direction downstream side until the increase amount of the roll opening degrees reaches a predetermined value. In the cast piece supporting rollsplaced on the casting direction downstream side relative to the intentional bulging zoneand on the casting direction upstream side relative to the soft reduction zone, the roll opening degrees are set to a constant value or reduced to the extent corresponding to a shrinkage amount with the temperature drop of the cast piece.

Herein, the bulging in this embodiment refers to intentional bulging (“intentional bulging”), and hereinafter is also simply referred to as “bulging”. The intentional bulging preferably starts at the stage when a solid phase ratio of a center part is 0 and ends when the total bulging amount of the long side surfaces of the cast piece (total of the bulging amounts of the upper surface and the lower surface) reaches 3 mm or more and 20 mm or less. When the total bulging amount of the intentional bulging is less than 3 mm, there is a risk that the short sides of the cast pieceand the cast piece supporting rollscome into contact with each other, posing a risk that a sufficient soft reduction cannot be applied. When bulging is intentionally performed, the total bulging amount is preferably 15 mm or less and more preferably 10 mm or less from the viewpoint of suppressing internal cracking.

illustrates one example of a profile of the roll opening degrees of the cast piece supporting rollsin this embodiment. In the profile of the roll opening degrees illustrated in, the cast piece long side surfaces are intentionally bulged by a molten steel static pressure, and the thicknesses of the center parts of the cast piece long side surfaces are increased in the intentional bulging zone(area b). In the profile of the roll opening degrees illustrated in, the roll opening degrees are set to a constant value or reduced to the extent corresponding to a shrinkage amount with the temperature drop of the cast pieceon the downstream side after passing through the intentional bulging zone(region c). Therefore, in the profile of the roll opening degrees illustrated in, the cast piece long side surfaces are rolling-reduced in the soft reduction zone(area d). a and e inare regions where the roll opening degrees are reduced to the extent corresponding to the shrinkage amount with the temperature drop of the cast piece. a′ in the figure is an example of the roll opening degrees according to a conventional method including reducing the roll opening degrees to the extent corresponding to the shrinkage amount with the temperature drop of the cast piece.

In the intentional bulging zone, the roll opening degrees of the cast piece supporting rollsare sequentially increased toward the casting direction downstream side, so that the long side surfaces excluding the vicinities of the short sides of the cast pieceare intentionally bulged following the cast piece supporting rollsby a molten steel static pressure by an unsolidified layer. The long side surfaces in the vicinities of the short sides of the cast pieceare made to adhere to and restrained to the short side surfaces of the cast pieceafter the solidification has completed, and therefore maintains the thickness at the time when the intentional bulging is started. Accordingly, the cast piececomes into contact with the cast piece supporting rollsonly in bulged portions of the long side surfaces by the intentional bulging. In the soft reduction zone, the total rolling reduction amount is set to be equal to or less than the total bulging amount, so that only the bulged portions of the long side surfaces of the cast pieceare rolling-reduced, enabling efficient soft reduction. The total rolling reduction amount is a rolling reduction amount of the cast piecefrom the start of the rolling reduction to the end of the rolling reduction in the soft reduction zone. The total bulging amount is the bulging amount from the start of the intentional bulging to the end of the intentional bulging in the intentional bulging zone. The bulging amount is the maximum amount of the bulging of the thickness in the width direction of the cast piece, and is the length (mm) calculated as a difference between the maximum thickness value in the transverse cross-section of the cast piece(basically, thickness in the width direction center) and the thickness on the short sides.

When the cast pieceis intentionally bulged, the intentional bulging zoneis preferably arranged between the lower end of the moldand the liquidus crater end position of the cast piece. The reason for this is that a cast piece thickness center part entirely contains an unsolidified layer(liquid phase) on the casting direction upstream side relative to the liquidus crater end position of the cast piece, and the solidified shellof the cast piecehas a high temperature and low deformation resistance, and can be easily bulged. When the cast pieceis intentionally bulged, the bulging when the unsolidified layerpresent inside the cast pieceis insufficient rather deteriorates the center segregation. However, when the bulging is performed on the casting direction upstream side relative to the liquidus crater end position of the cast piece, the molten steel having an initial concentration in which the solute elements are not concentrated is abundantly present inside the cast piece at this point, and the molten steel easily flows. Even when the molten steel flows, no segregation occurs, and thus the bulging at this point does not cause the center segregation.

The liquidus of the cast pieceis the solidification starting temperature determined by the chemical composition of the cast piece, and can be determined from Equation (2) below, for example.

In Equation (2), Tis the liquidus temperature (° C.), [% C] is the carbon concentration of the molten steel (% by mass), [% Si] is the silicon concentration of the molten steel (% by mass), [% Mn] is the manganese concentration of the molten steel (% by mass), [% P] is the phosphorus concentration of the molten steel (% by mass), [% S] is the sulfur concentration of the molten steel (% by mass), [% Cu] is the copper concentration of the molten steel (% by mass), [% Ni] is the nickel concentration of the molten steel (% by mass), [% Cr] is the chromium concentration of the molten steel (% by mass), and [% Al] is the aluminum concentration of the molten steel (% by mass). In the study of this embodiment, low-carbon aluminum killed steel was used which contains C: 0.03% by mass or more and 0.2% by mass or less, Si: 0.05% by mass or more and 0.5% by mass or less, Mn: 0.8% by mass or more and 1.8% by mass or less, P: less than 0.02% by mass, and S: less than 0.005% by mass. However, the application range of the present invention is not limited to the component range above.

The intentional bulging zonedoes not require any special mechanism and is configured simply by adjusting the roll opening degrees, and therefore it can be placed in any position insofar as it is in the range from the lower end of the moldto the liquidus crater end position of the cast piece.

In the slab continuous casting machineof this configuration, the molten steelpoured from the tundishinto the moldthrough the immersion nozzleis cooled in the moldto form the solidified shell. The cast piecehaving the solidified shellas the outer shell and having the unsolidified layerinside is continuously drawn out to the downward of the moldwhile being supported by the cast piece supporting rollsprovided below the mold. The cast pieceis cooled by secondary cooling water in the secondary cooling zone while passing through the cast piece supporting rolls, and increases the thickness of the solidified shell. Then, the cast pieceincreases the thicknesses of portions excluding short side end parts of the long side surfaces in the intentional bulging zoneand completes the solidification up to the inside at the solidification completion positionwhile being subjected to soft reduction in the soft reduction zone. The cast pieceafter the completion of the solidification is cut by the cast piece cutting machineto be the cast piece. To the inside of the mold, mold powder (not illustrated) functioning as a heat insulator, a lubricant, an antioxidant, and the like is added.

In this embodiment, continuous casting is performed under the casting conditions in the soft reduction zonedescribed below. In the soft reduction zone, the cast pieceis roll-reduced (soft reduction) at a rolling reduction rate of 0.3 mm/min or more and 2.0 mm/min or less in a range where a center solid phase ratio that is the solid phase ratio in the thickness center of the cast pieceis at least 0.2 or more and less than 1.0. The thickness center of the cast piecein this embodiment means the center in the thickness direction in the width direction position where the solid phase ratio in the thickness center part is the lowest in the transverse cross-section of the cast piece. In a case where the rolling reduction rate of the soft reduction when the center solid phase ratio is in the range above is less than 0.3 mm/min, a possibility of the occurrence of V-segregation increases. On the other hand, in a case where the rolling reduction rate of the soft reduction when the center solid phase ratio is in the range above exceeds 2.0 mm/min, a possibility of the occurrence of inverse V-segregation increases.

In this embodiment, in the soft reduction zone where the center solid phase ratio is in the range of at least 0.2 or more and less than 1.0, a deflection t of the soft reduction segmentsthat are the segmentsconfiguring the soft reduction zone satisfies Equation (1) below.

In Equation (1),

In Equation (1), the segment deflection t is the deflection in the thickness direction in the width direction center of the segment frame and is determined from the heights in the thickness direction of both width direction end parts and a width direction center part of the segment frame. Specifically, the deflection t is expressed as the sum of deflections τ, τ(τ=τ+τ) in both the upper surface side frameand the lower surface side frameas indicated by the alternate long and short dash line in. The deflection τ is preferably the maximum value among the deflections in a plurality of places in the casting direction of the segment frame. For example, the deflection τ may be a value of the largest deflection of the deflections at least in two places on the outlet side and the inlet side in the casting direction of the segment frame. In this case, the segment deflection τ may be determined by measuring each of the deflections at casting direction positions of the two places where the support postsare provided as illustrated in. The deflection τ of the soft reduction segmentmay be a value measured when the cast pieceis actually continuously cast or may be a value measured when steel of a similar steel grade is continuously cast with the continuous casting machine.

The actually measured bulging amount δ is a bulging amount after the point in time when the center solid phase ratio of the cast piecechanges to more than 0.0. The actually measured bulging amount δ is the bulging amount of either the upper surface or the lower surface, and is preferably an actually measured value of the bulging amount of the upper surface for ease of measurement. The bulging amounts are usually the same in the upper surface and the lower surface, and therefore the bulging amount can be determined by measuring the bulging amount of the long side surface of either one of the upper surface and the lower surface and doubling the measured bulging amount. In Equation (1), the actually measured value of the total bulging amount is expressed by multiplying the actually measure bulging amount δ by 2 as a coefficient.

The set rolling reduction of soft reduction amount A is such an amount (set amount) that the cast pieceis rolling-reduced until the cast pieceis completely solidified from the center solid phase ratio of 0.2 or more. The set rolling reduction amount of the soft reduction is the rolling reduction amount in setting determined only by the roll profile, i.e., set roll gap.