JPH08276208A - Mandrel mill - Google Patents

Abstract

PURPOSE: To make it possible to suppress the occurrence of a hole defect, and to enlarge a thin wall limit by specifying the caliber shape of a roll, and specifying the caliber ellipticity of at least a second stand. CONSTITUTION: The roll caliber of a grooved roll composing a mandrel mill is equipped with a grooved bottom shape with the radius R1 of curvature with an offset quantity S to a caliber center O. As a whole, it is about elliptic in shape with minor diameter 2B and major diameter 2A. And, it is formed so that the ratio R/S of the radius R1 of curvature and an offset quantity S becomes 30 or over. Also, the shape of the roll caliber of at least a second stand is formed so that its ellipticity A/B becomes 1.20 or below in addition to the condition. Consequently, since a thickness distribution in the peripheral direction of a pipe material is made uniform as much as possible, a uniaxial tension state at a flange part is reduced, and a necking phenomenon occurring in this part is suppressed. As a result, even when performing the rolling of high working, the occurrence of a punching defect can be reduced or eliminated.

Description

Detailed Description of the Invention

[0001]

The present invention relates to a mandrel mill.

[0002]

As a rolling mill for producing hot seamless steel pipes,
A plurality of (usually 5 to 8) hole type roll stands are continuously arranged so that the roll hole type groove bottom directions of the front and rear stands are in phase with each other by 90 °, and are formed by the plurality of hole type roll stands. There is a mandrel mill in which a mandrel bar is arranged in a roll hole type array and a tube is continuously stretch-rolled.

In the above mandrel mill rolling, when a thin-walled tube having a small wall thickness / outer diameter ratio or a high alloy steel having poor hot workability such as 13% Cr steel or austenitic stainless steel is stretch-rolled, roll holes are formed. A necking phenomenon occurs in which the wall thickness of the pipe material portion corresponding to the portion called the flange portion of the die is periodically thinned in the axial direction of the pipe. When this necking phenomenon is remarkable, as shown in FIG. 6, a so-called perforation defect A, which is a flaw in which a hole penetrates through the wall thickness of the pipe material, may occur.

In the mandrel mill rolling, as shown in FIG. 7, the pipe material P is processed by the hole-type roll 1 and the mandrel bar 2, and the wall thickness M is reduced in the groove bottom portion M. At the flange portion F, the material is stretched in the axial direction by being stretched by the plastic deformation of the material in the axial direction due to the thinning of the groove bottom portion M. That is, in the flange portion F, since the inner surface of the pipe material is not in contact with the hole type roll 1 and the mandrel bar 2, the inner surface pressure is not received,
Since it receives almost no external pressure, it is in a state close to uniaxial tension, in which it is stretched by receiving only the tensile force in the axial direction. Therefore, a so-called necking phenomenon in which the wall thickness due to thinning is partially reduced is likely to occur in the pipe material portion corresponding to the flange portion F, and when this necking phenomenon is remarkable, the material breaks and a perforation defect A occurs. It will be. Therefore, in the mandrel mill rolling, the size of the thin-walled pipe that can be rolled and the material of the high-alloy steel are limited depending on the occurrence and extent of the necking phenomenon and the occurrence of the perforation defect.

As a technique for preventing the above-mentioned necking phenomenon and generation of perforated defects, "Plasticity and Machining, No. 34
Vol. 390, 800-805, July 1993 "
There is a method disclosed in. As shown in FIG. 8, the method disclosed in “Plasticity and Machining” includes a mandrel mill having a hole-type roll determined by the following eight independent variables. The ratio of the target finishing outer diameter Ds to the pipe outer peripheral length “π × Ds” is defined as the hole type peripheral length ratio αi expressed by the following formula (A), while the groove bottom radius of the upper and lower rolls having the following groove bottom curvature radius R1i is defined. The ratio of the interval Gi to half is defined as the groove bottom curvature radius ratio βi expressed by the following equation (B).

[0006] Usually, the hole-type peripheral length ratios α1, α2 and α3 of the first to third hole-type roll stands to which a large workability (area reduction rate) is given are increased and the groove bottom curvature radius is increased. By reducing the ratios β1, β2 and β3, a gap can be formed between the inner surface of the pipe rear end portion after the mandrel mill rolling and the outer surface of the bar. As a result,
Bar stripping error occurs in the burst ripping device which is provided outside the mandrel mill's pass line and pulls out the mandrel bar from the pipe material after stretch rolling by fixing and restraining the rolled end of the pipe with a U-shaped stopper member. It is said that it is possible to solve the problem and to reduce the occurrence of perforation defects.

R1i: radius of curvature of groove bottom, R2i: radius of curvature of side wall, R3i: radius of curvature of corner, θ1i: R1i area angle, θ2i:
R2i area angle, θ3i: R3i area angle, Hi: Hole depth and Gi: Distance between groove bottoms of upper and lower rolls, i: Stand number (1
~ N).

Αi = Li / (π · Ds) ······· (A) βi = 2 · R1i / Gi ······ (B) Further, in addition to reducing the groove bottom curvature radius ratio βi of the first to third hole type roll stands, the following (C) in the second hole type roll stand having the largest working degree is used. It is said that the occurrence of perforation defects can be completely eliminated by reducing the elongation strain φl2 defined by the formula in the axial direction of the pipe material.

Φl 2 = ln (S 1 −S 2) ... (C) where S 1 is the cross-sectional area of the pipe material on the outlet side of the first stand S 2 is the Cross-sectional area of the pipe material on the outlet side of the two stands The above Li is a value obtained by the following equation (D).

Li = 4 (R1i.theta.1i + R2i.theta.2i + R4i.theta.4i) (D) where R4i is an arc having a center on the hole center line of the upper and lower rolls in contact with the contact points of R2i and R3i. Is a value represented by the following equation (E). Further, θ4i is a value represented by the following formula (F).

R4i = (0.5Gi−H + R3i) / cos θ3i−R3i ... (E) θ4i = π / 2−θ3i ... ... (F) More specifically, the hole type circumference ratio α of the first to third stands
Under the following conditions where i does not cause bar stripping mistakes, the groove bottom curvature radius ratio β of the first to third stands is
When i is set to the following condition, the occurrence rate of perforated defects is 100% for SUS304, 60% for 13% Cr steel,
It is 8% for ordinary steel.

On the other hand, when the groove bottom curvature radius ratio βi is reduced to the following condition, the rate of occurrence of perforated defects becomes
It is reduced to 60% for SUS304, 30% for 13% Cr steel, and 1% for ordinary steel. However, even if the groove bottom curvature radius ratio βi is made smaller under the following conditions, the effect is not changed.

Α1 = 1.140, α2 = 1.070, α3 = 1.030 ··· β1 = 1.146, β2 = 1.066, β3 = 1.034 ··· β1 = 1.060, β2 = 1.042, β3 = 1.011 ··· β1 = 1.036, β2 = 1.019, β3 = 1.010 ··· The gap between the groove bottoms of the upper and lower rolls of the largest second hole roll stand is opened so that the groove bottom curvature radius ratio βi is set to the following condition, while the elongation in the axial direction of the pipe material in the second hole roll stand is performed. Distortion φl2 becomes "0.4
When it is reduced from "88" to "0.418" or "0.354", it is said that the rate of occurrence of perforation defects becomes "zero" for any of the steel types.

Β1 = 1.060, β2 ≦ 1.030, β3 = 1.011 By the way, in the case of drawing and rolling with a mandrel mill, when further thin-wall rolling is performed with a mandrel mill with a predetermined number of stands. Or, when trying to obtain a relatively high degree of processing with a mandrel mill with a smaller number of stands,
Naturally, the degree of processing per stand is large. Therefore, in such a case, it is impossible to prevent the necking phenomenon from occurring and prevent the perforation defect from occurring.

As a countermeasure against this, a method of using a thin-walled material pipe and reducing the total thickness working degree in a mandrel mill can be considered. However, in this method, the mandrel mill is used as a virtual thick finish rolling mill, and since a stretch reducer or sizer used as a post-finish rolling mill cannot perform thick-wall processing, it is used as a front-stage rolling mill. There is no choice but to obtain a thin-walled raw tube by increasing the degree of processing with the piercer. However, piercing and rolling with a high degree of workability with a piercer causes surface defects in the raw pipe and increases in uneven thickness, and the material temperature drops significantly, so it is difficult to employ.

However, the technology for preventing perforation defects, which is disclosed in the above "Plasticity and Machining", is based on the premise of preventing the occurrence of stripping mistakes in the bar, and originally has the largest machinability (area reduction rate). Since it is a method of reducing the elongation strain φl2 in the axial direction of the pipe at the second stand to be reduced, in other words, the workability is reduced, the workability cannot be increased and the efficient stretching rolling cannot be performed. Therefore, according to this conventional technique, the stretching and rolling with a high workability using a mandrel mill with the fewest number of stands, particularly the workability per stand in the first to third stands, can be achieved by extending in the axial direction of the pipe material. Distortion φli is 0.41
It has a drawback that it cannot be applied when stretch rolling is performed with a high workability of more than 8.

[0017]

SUMMARY OF THE INVENTION The object of the present invention was made in view of the above-mentioned circumstances, and more specifically, in the case of carrying out stretch rolling of a relatively high workability with a small number of stands, more specifically, a large workability is required. The degree of workability per stand in the 1st to 3rd stands to be added is 0 in terms of elongation strain φli in the axial direction of the pipe material.
An object of the present invention is to provide a mandrel mill capable of suppressing the occurrence of a necking phenomenon and reliably reducing the occurrence of perforation defects even when performing stretching rolling with a high workability set to exceed 418. .

[0018]

The gist of the present invention resides in the mandrel mill described in the following (a) and (b).

(A) A mandrel mill in which a plurality of hole type roll stands are arranged in series, a mandrel bar is arranged in a roll hole type array formed by these hole type roll stands, and the tube is continuously stretch-rolled. In the roll hole type of each stand, the ratio R1 / S of the groove bottom curvature radius R1 and the deviation offset amount S between the groove bottom curvature center and the mill center is 30 or more, and at least the second A mandrel mill characterized in that the ellipticity of the stand is 1.20 or less.

(B) A pipe material represented by the following formula (2) of a roll hole type after the third stand in which the elongation strain φli in the axial direction of the pipe material represented by the following formula (1) becomes 0.30 or more. The mandrel mill according to (1) above, wherein the circumferential reduction ratio rci in the circumferential direction is 2.0% or more.

Φli = ln (Ai-1 / Ai) (1) where Ai: disconnection of the pipe material on the outlet side of the i stand Area Ai-1: (i-1) Cross-sectional area of pipe material on stand-out side rci = {(Li-1 −Li) / Li-1} × 100 (2) where Li: i-stand roll hole type circumferential length Li-1: (i-1) stand roll hole type circumferential length Note that the above Li can be obtained in the same manner as in the prior art (see FIG. 8 and formula (D)). Needless to say.

The inventor of the present invention has determined that the workability of the preceding stage stand, which requires a large workability, specifically, the first to third stands, is 0.4 in terms of the elongation strain φli in the axial direction of the pipe material.
Even when a thin pipe having a wall thickness / outer diameter ratio of 3.5% or less is stretch-rolled by imparting a large workability of more than 18, the occurrence rate of the above-mentioned perforation defects is as high as possible. We conducted various experimental studies on methods that can be reduced to
The following findings were obtained and the present invention was completed.

In the above-mentioned prior art, firstly, on the premise that the stripping mistake of the bar in the burst ripper device provided outside the pass line of the mandrel mill is eliminated, the roll hole type in the first to third stands is used. By increasing the circumference ratio αi of the pipe, the elongation strain lφ2 in the axial direction of the pipe material in the second stand to which the greatest workability should be added is reduced, in other words, the wall thickness workability in the second stand is reduced. There is. But eliminating the stripping mistakes on the bar
Peripheral length ratio αi of the roll hole type of 1st to 3rd stand
And it is not necessary to increase the elongation strain lφ2 in the axial direction of the pipe material at the second stand, and it can be solved by the following methods.

That is, in the first method, a bar drawing rolling machine including one or more hole type roll stands for reducing the outer diameter of the pipe material after the mandrel mill rolling is provided in the rear stage of the mandrel mill. This is a method using a so-called extract rolling method, in which a pipe material is pulled out from a mandrel bar whose rear end is supported by a bar holding device provided on the mill entrance side during drawing and rolling.

In the second method, a burst ripping device similar to the prior art, which has a U-shaped stopper member in place of the above bar pulling rolling mill, is arranged in the rear stage of the final stand of the mandrel mill, and stretch rolling is performed. After completion, the rolling rear end of the pipe material is fixedly restrained by the burst ripping device, and in this state the mandrel bar is pulled back to the mandrel mill inlet side by the mandrel bar holding device to pull out the mandrel bar from the pipe material, a method using a so-called retract rolling method, In this case, since the time from the end of rolling to the start of burst ripping is short and the temperature of the pipe material hardly drops, stripping mistakes of the bar hardly occur.

The third method is to reduce the stripping force even when using a burst ripping device similar to the prior art, which has the U-shaped stopper member provided outside the pass line of the mandrel mill. This is a method of applying a lubricant having a small friction coefficient and excellent in lubricity to the mandrel bar, or shortening the transportation time from the end of rolling to the burst ripping device to reduce the temperature drop of the pipe material.

By doing so, when rolling is performed with a high degree of processing on the first to third stands without fear of burst ripping mistakes, the occurrence of the above-mentioned necking phenomenon can be suppressed and perforated defects can be prevented. To prevent the occurrence of the above, set the roll hole shape of each stand to the above (1).
Or do something like (2).

The present invention will be described in detail below with reference to the drawings.

FIG. 1 is a view for explaining the shape of the roll hole type of each hole type roll stand constituting the mandrel mill according to the first aspect of the present invention, and only one hole type roll is shown.

As shown in FIG. 1, the roll type of the type roll forming the mandrel mill of the first invention has a center O of the hole type.
In contrast, it has a groove bottom shape with a radius of curvature R1 with an offset amount S, and is a substantially elliptical shape with a minor axis of 2B and a major axis of 2A as a whole, and the ratio R1 / of the radius of curvature R1 and the offset amount S is R1 /. It is formed so that S is 30 or more.

Further, at least the roll-hole type shape of the second stand is formed so that its ellipticity A / B is 1.20 or less in addition to the above conditions.

As described above, when the roll hole type of each stand is formed, the wall thickness distribution in the circumferential direction of the pipe material is made as uniform as possible, so that the uniaxial tension state at the flange portion is reduced. Therefore, the necking phenomenon occurring in this portion is effectively suppressed. As a result, it is possible to reduce or eliminate the occurrence of perforation defects even when rolling with high workability is performed.

2 and 3 show the above R1 in a stand provided with a hole-shaped roll having the same radius of curvature R1, short diameter 2B and long diameter 2A, in other words, a stand having the same cross-section reduction rate.
The case where / S is made small and the case where it is made large are shown, and it is clear from the comparison between these two figures.

FIG. 2 shows a case where the offset amount S is increased and R1 / S is decreased. In this case, the thickness reduction amount at the central portion Mc of the groove bottom portion M in the stand is large, but the flange portion is large. The amount of wall thickness reduction at the groove bottom end portion Hf close to F is small. Therefore, the amount of wall thickness reduction at the groove bottom portion M in the next-stage stand becomes extremely larger than the amount of wall thickness reduction at the flange portion F, and the uniaxial tension state at the flange portion F becomes remarkable. Perforated defects are likely to occur.

On the other hand, FIG. 3 shows the case where the offset amount S is reduced and R1 / S is increased. In this case, the groove bottom M near the central portion Mc of the groove bottom M and the groove bottom F in the stand in question. The thickness reduction amount at the end portion Hf and the flange portion F is made uniform as much as possible. For this reason, the phenomenon of thinning at the groove bottom portion M in the next-stage stand is alleviated and the uniaxial tension state at the flange portion F is suppressed, so that necking phenomenon and perforation defects are less likely to occur. But,
Since the effect is not remarkable when R1 / S is less than 30, R1 / S is set to 30 or more in the present invention.

In the present invention, R1 / S is set to 30
The above means (B) in the above-mentioned related art.
Substituting for βi represented by the formula “βi = 2 · R1i / Gi” gives “Gi = 2 (R1-S)”, and therefore the following formula (G) is obtained. By substituting “/ S ≧ 30”, the following formula (H) is obtained.

Βi = R1 / (R1-S) = 1 / (1-S / R1) ... (G) βi = 1 / (1-1 / 30) ≦ 1.0345 (H) Therefore, in the above-mentioned conventional technique, in the case of the roll hole shape in which the above condition, in other words, the R1 / S of the first and second stands is less than 30, is set, The present invention can reduce or eliminate the occurrence of perforating defects even under the condition that the effect of reducing perforating defects can be obtained, but even if R1 / S is 30 or more, the effect cannot be obtained. It means that.

On the other hand, in the rolling by the mandrel mill, from the viewpoint of improving the productivity, the thick-walled raw pipe is stretch-rolled into the thin-walled pipe material as much as possible. Therefore, in general, the flange portion F is supported after the third stand. Since the material thickness of the portion to be processed is thinned by processing at the groove bottom portion M of the front stand, the necking phenomenon and perforation defects are more likely to occur at this flange portion F, so a large degree of processing should be provided. For that reason, the roll hole shape of each stand is determined so that the wall thickness reduction amount in the second stand is maximized.

Therefore, rolling in the second stand is different from that in the first stand in which a thick tube having a uniform wall thickness distribution in the circumferential direction is rolled, and thus the roll hole type groove bottom portion M of the first stand is rolled. The thickness of the corresponding portion is mainly reduced to be thin, and a material (tube material) having a large thickness of the portion corresponding to the flange portion F is rolled. As a result, in the second stand, the wall thickness machining of the portion corresponding to the roll hole type groove bottom portion M becomes extremely large, and large uniaxial tension is applied to the material portion thinned in the first stand corresponding to the flange portion F. Since stress acts, a necking phenomenon or a perforated defect is likely to occur in the flange portion F.

This shows a case where the ellipticity (A / B) is increased or decreased in the second stand provided with the hole type roll having the same radius of curvature R1, minor axis 2B and R1 / S. This is clear from the comparison between FIG.

In FIG. 4, the ellipticity (A
/ B) is increased, and in this case, the material of the portion corresponding to the flange portion F of the stand is not restrained on the outer surface by the hole roll. Therefore, since the flange portion F of the second stand is not subjected to wall thickness reduction,
A large amount of uniaxial tensile stress acts on the material corresponding to this portion, and necking phenomenon and perforation defects are likely to occur.

On the other hand, FIG. 5 shows a case where the major axis 2A is reduced to reduce the ellipticity (A / B). In this case, the material of the portion corresponding to the flange portion F of the second stand is a hole. The outer surface is restrained by the die roll. For this reason, since the flange portion F of the second stand is also subjected to wall thickness reduction, the uniaxial tensile stress acting on the material corresponding to this portion is suppressed, so that the necking phenomenon and the perforation defect are less likely to occur. However, the effect is not remarkable when the ellipticity (A / B) exceeds 1.20,
In the present invention, the roll hole type ellipticity of the second stand (A /
B) was defined as 1.20 or less.

The above-mentioned definition of the ellipticity (A / B) may be applied to all the stands to which the thickness reduction is applied after the first stand and the third stand. However, as described above, since the thickness reduction amount of these stands is smaller than that of the second stand, it is sufficient to set R1 / S to 30 or more. Therefore, in the present invention, at least the ellipticity of the second stand is set to 1.20 or less.

Next, the second invention will be described.

In the second aspect of the invention, in order to perform rolling with higher efficiency, the workability of each stand, specifically, the third stand and thereafter, that is, the elongation in the axial direction of the pipe material represented by the above formula (1), is obtained. Even in the case of rolling with a working degree that the strain φli becomes 0.30 or more, the occurrence of necking phenomenon and perforation defects can be reduced or eliminated.

As in the first aspect of the invention, the roll hole shape of each stand has a groove bottom shape with R1 / S of 30 or more, and at least the ellipticity of the roll hole type of the second stand is 1.20. Even in the following cases, the elongation strain φli in the axial direction of the pipe material after the third stand is 0.30.
The above causes the following problems.

After the third stand, unlike the first and second stands, the thickness of the material to be rolled is the first
Since it is as thin as possible in comparison with that of the second stand, the strength against deformation is small, and the necking phenomenon and the perforated defect in the flange portion are easily generated. Therefore, if the extension strain φli in the axial direction of the pipe material becomes excessive in the third and subsequent stands, the uniaxial tensile stress exceeding the above-mentioned strength acts on the material corresponding to the flange portion, and the wall thickness decreases, resulting in necking. Phenomena and perforated defects occur.

However, when appropriate peripheral length working is applied to the rolled pipe material in the third and subsequent stands, the wall thickness of the material corresponding to the flange portion increases, and the wall thickness reduction due to the uniaxial tensile stress occurs. It is possible to prevent the necking phenomenon and the perforation defect from occurring in the flange portion due to the cancellation. However, if the circumference working ratio is less than 2.0% in the circumference reduction ratio rci obtained by the above formula, the effect cannot be obtained. Therefore, in the present invention, the circumference reduction ratio rci is set to 2.0% or more.

[0049]

According to the present invention, the roll hole shape of each hole roll stand is such that R1 / S is 30 or more and the ellipticity (A / B) of at least the second stand is 1.20 or less, Furthermore, it is preferable to use a special shape with a circumferential reduction rc of 2.0% or more after the third stand with elongation strain φl of 0.30 or more. Even in the case of rolling, it is possible to effectively reduce or eliminate the occurrence of perforation defects. Further, since the degree of processing per stand can be increased, the mill can be constructed with a small number of stands.

[0050]

EXAMPLES Experimental conditions are shown in Tables 1 to 6, and experimental results are shown in Table 7.

The experimental conditions in Tables 1 and 2 are the above-mentioned conventional examples, the experimental conditions in Tables 3 to 5 are the examples of the present invention, Tables 3 and 4 are the first inventive examples, and Table 5 is the 2 is an example of invention,
The experimental conditions in Table 6 are comparative examples of the second invention of the present invention.

Tables 1 to 6 also show the management specification values αi and βi defined in the above-mentioned conventional technique.

[0053]

[Table 1]

[0054]

[Table 2]

[0055]

[Table 3]

[0056]

[Table 4]

[0057]

[Table 5]

[0058]

[Table 6]

[0059]

[Table 7]

As is clear from the results shown in Table 7, according to the present invention, the effect of improving the perforated defects is greater than that of the prior art, and in particular, the greater effect is obtained when the degree of processing per stand is large. I understand. Further, it can be seen that the occurrence of perforation defects is reduced even when rolled into a thinner tube (see Tables 5 and 6).

[0061]

As described above, according to the present invention, 13% Cr
Even in the case of thin-wall rolling a pipe material made of a difficult-to-work material such as steel or austenitic stainless steel, the occurrence of necking phenomenon and perforation defect can be effectively reduced or eliminated. As a result, a material having poor hot workability can be manufactured to a thinner range. Further, the mill can be configured with a small number of stands, and the facility cost can be reduced.

[Brief description of drawings]

FIG. 1 is a diagram illustrating a roll hole type shape that constitutes a mandrel mill of the present invention.

FIG. 2 is a diagram for explaining a problem at the time of tube rolling by a roll hole type having a small R1 / S.

FIG. 3 is a diagram for explaining an effect at the time of tube rolling with a roll hole type having a large R1 / S.

FIG. 4 is a diagram for explaining a problem at the time of tube rolling with a roll hole type having a large ellipticity (A / B).

FIG. 5 is a diagram for explaining the effect of tube rolling with a roll hole type having a small ellipticity (A / B).

FIG. 6 is a schematic diagram showing perforated defects that occur during mandrel mill rolling.

FIG. 7 is a diagram illustrating the concept of tube rolling in a mandrel mill and the machinism in which perforated defects are generated.

FIG. 8 is a diagram illustrating a roll hole type shape that constitutes a conventional mandrel mill.

[Explanation of symbols]

1: Porous roll, 2: Mandrel bar, P: Tube material, M: Groove bottom, F: Flange

Claims (2)

[Claims] 1. A mandrel mill in which a plurality of hole type roll stands are connected in series, a mandrel bar is arranged in a roll hole type array formed by these hole type roll stands, and a tube is continuously stretch-rolled. Therefore, the roll hole type of each stand has a ratio R1 / S of the groove bottom curvature radius R1 and the deviation offset amount S between the groove bottom curvature center and the mill center is 30.
That is, at least the ellipticity of the second stand is 1.2.
A mandrel mill characterized by being set to 0 or less. 2. A pipe material circle represented by the following formula (2) of a roll hole type after the third stand in which the elongation strain φli represented by the following formula (1) in the axial direction of the pipe material is 0.30 or more. The mandrel mill according to claim 1, wherein the circumferential reduction ratio rci in the circumferential direction is 2.0% or more. φli = ln (Ai-1 / Ai) (1) where Ai is the cross-sectional area of the pipe on the outlet side of the i stand Ai- 1: (i-1) Cross-sectional area of pipe material on the stand outlet side rci = {(Li-1 -Li) / Li-1} × 100 (2) where Li: i stand Roll hole type circumference Li-1: (i-1) Roll hole type circumference of stand