DOUBLE-SIDED FRICTION-STIFFNESS WELDING METHOD, METHODS FOR PRODUCING A COLD-ROLLED STEEL STRIP AND A COATED STEEL STRIP, DOUBLE-SIDED FRICTION-STIFFNESS WELDING APPARATUS AND INSTALLATIONS FOR PRODUCING A COLD-ROLLED STEEL STRIP AND A COATED STEEL STRIP

Abstract

A double-sided friction-stir welding method is provided, methods for producing a cold-rolled steel strip and a coated steel strip, a double-sided friction-stir welding apparatus, and facilities for producing a cold-rolled steel strip and a coated steel strip.The double-sided friction-stirring welding method according to the present invention comprises pressing two rotating tools, arranged on a first and a second surface of a butt or overlap portion of the steel strips, against the butt or overlap portion of the steel strips and displacing the rotating tools in the welding direction while rotating in opposite directions to each other, so that an unwelded portion of the steel strips is softened by the frictional heat generated between the rotating tools and the unwelded portion of the steel strips, and the softened portion is stirred by the rotating tools to generate a plastic flow for the purpose of welding the steel strips together. Each of the two rotating tools has a terminal portion formed to have a flat circular shape.Each of the terminal portions is made of a material harder than the steel strips.

Description

Patent Literature 1 discloses a technique for welding a pair of workpieces, such as steel strips, by rotating both strips or one of the steel strips to generate frictional heat that softens the steel strips and by agitating the softened portion to generate a plastic flow. However, the technique described in Patent Literature 1 requires the rotation of the workpieces, such as steel strips, and therefore limits the shape and dimensions of the workpieces, such as steel strips. A friction welding method other than that of Patent Literature 1 is disclosed, for example, in Patent Literature 2. In Patent Literature 2, a rotating tool (hereinafter referred to simply as the tool) having a probe (hereinafter referred to simply as the pin) made of a material substantially harder than the workpieces, such as a steel strip, is inserted into an unwelded portion of the steel strips, and the rotating tool is moved while rotating. In this method, the heat and plastic flow generated between the rotating tool and the steel strips are used to continuously weld the steel strips longitudinally. In the present description, a portion in which the steel strips are butted or overlapped and which has not yet been welded shall hereinafter be referred to as the unwelded portion, and a portion which has been welded and integrated shall hereinafter be referred to as the welded portion.As described above, the friction welding method described in Patent Literature 1 involves rotating steel strips and welding them together using frictional heat. The friction-stir welding method described in Patent Literature 2 involves welding steel strips together by rotating and moving rotating tools with the steel strips fixed in place. The friction-stir welding method has the advantage that, even when welding pieces of substantially infinite length, the pieces can be continuously subjected to solid-state welding in the longitudinal direction.Since friction stir welding is a solid-state welding method that utilizes the plastic flow of the metal caused by the frictional heat generated between the rotating tool and the steel strips, welding can be performed without melting the unwelded portion. Furthermore, friction stir welding offers many advantages, such as less deformation after welding due to the lower heating temperature, fewer defects in the welded portion as a result of not melting the steel strips, and no need for filler material. The friction stir welding method has a wide range of applications in the aerospace, naval, rail vehicle, and automotive industries, as well as in other fields, as a method for welding low-melting-point metallic materials such as aluminum and magnesium alloys. This is because such low-melting-point metallic materials are unlikely to produce a weld with satisfactory properties using arc welding techniques, but they can yield a high-quality weld (joint) with high productivity using the friction stir welding method. The use of friction stir welding for structural steel, primarily used in building materials such as buildings, ships, heavy equipment, pipelines, and automobiles, can avoid the brittleness resulting from impurity segregation during melting and solidification, as well as the brittleness caused by hydrogen intrusion, which have proven problematic in fusion welding. Simultaneously, the microstructures of the steel are less susceptible to alteration, leading to improved joint performance. Furthermore, stirring the weld interface with a rotating tool creates clean surfaces, which can then be brought into contact with each other. This offers the additional advantage of eliminating the need for a pretreatment step, unlike diffusion welding.As described earlier, the friction stir welding method for structural steel has many anticipated advantages. However, its use in structural steel still presents challenges regarding weld feasibility, such as joint defects appearing during the welding process and slow welding speeds. Therefore, the friction stir welding method has been less popular for structural steel than for low-melting-point metals. Among the joint defects mentioned are form defects and weld defects on the joint surfaces or within the joints themselves, particularly immediately after welding. Among the main factors influencing the occurrence of defects in the friction-stirring welding method described in Patent Literature 2 are the variations in temperature and plastic flow that occur along the thickness of the workpieces. Specifically, if the rotating tool is positioned only on the first surfaces of the workpieces, sufficient plastic flow can be achieved to obtain a metallurgically favorable weld condition on the first surface side. However, plastic flow on the second surface side is often insufficient because the temperature rise and shear stress load are insufficient in the unwelded portion during the welding process. When the friction-stirring welding method described in Patent Literature 2 is used for structural steel, in many cases sufficient plastic flow cannot be achieved in the unwelded portion with low heat input and high welding speed because structural steel, being a workpiece, has high resistance to high temperatures. Therefore, it is difficult to increase the welding speed while simultaneously suppressing the occurrence of defects during the welding process. As a means of solving such problems, for example, a double-sided friction-stir welding method is disclosed in Patent Literature 3 through Patent Literature 5. In this method, two opposing rotating tools are pressed against a first and a second surface of a weldable portion of metal plates (workpieces) to generate sufficient and uniform plastic flow in the thickness direction of the workpieces. As a result, the welding speed can be increased, and the occurrence of joint defects during the welding process is suppressed. Incidentally, the steel strip production process requires a continuous supply of steel strips to improve productivity and throughput. To supply the steel strips continuously, a preceding coil and a subsequent coil must be welded together. In other words, a rear end of a preceding material (previous steel strip) is welded to a front end of a subsequent material (subsequent steel strip), and the welded steel strips are continuously fed to the pickling, cold rolling, continuous annealing, and continuous coating lines in a single process. This process allows the steel strips to be wound along their entire length under tension and enables precise control of the thickness and shape of the steel strips, even at their front and rear ends. With high-alloy cold-rolled steel strips and advanced laser welders, laser welding is becoming the primary method for joining material to material, replacing butt welding and other related techniques. However, laser welding is a fusion welding process and can be susceptible to brittleness issues arising from impurity segregation during melting and solidification, as well as hydrogen embrittlement. To address these problems, friction stir welding, a solid-state welding method, is considered effective.However, as described above, it is difficult to increase the welding speed while simultaneously suppressing defects in common friction-stir welding, and therefore, common friction-stir welding cannot meet the required productivity in the process of producing steel strips. As a means to solve such problems, for example, Patent Literature 4 discloses a cold rolling mill that utilizes double-sided friction-stir welding. Furthermore, the use of a friction-stir welding method for welding cold-rolled steel strips requires a highly durable and long-lasting rotary tool. This is because the rotary tool needs to be repaired due to damage and wear. However, if welding defects are expected to occur frequently for this reason, it becomes practically impossible to use a friction-stir welding method for welding cold-rolled steel strips together, despite the aforementioned advantages. A typical friction stir welding method uses a rotating tool with a probe protruding from its end and centered on its axis of rotation, along with a flatter support portion surrounding the probe. The process involves inserting the probe into an unwelded portion and rotating and translating the probe to weld the workpieces together. Consequently, the probe is subjected to a high load during welding and is therefore particularly susceptible to breakage and wear between the rotating tool components. Some examples of techniques to avoid breakage or other damage to probes include friction-stir welding using a rotary tool having a flat, probe-less terminal portion, as described in Patent Literature 6 to Patent Literature 11. APPOINTMENT LIST Patent Literature Patent Literature 1: Publication of Unexamined Japanese Patent Application No. 62183979. Patent Literature 2: Publication of Unexamined Japanese Patent Application (Translation of PCT Application) No. 07-505090. Patent Literature 3: Japanese Patent No. 3261433 Patent Literature 4: Japanese Patent No. 4838385 Patent Literature 5: Japanese Patent No. 4838388 Patent Literature 6: Japanese Patent No. 5185103 Patent Literature 7: Publication of Unexamined Japanese Patent Application No. 2015-127063. n Lfrenn / zznz / E / Yii Patent Literature 8: Publication of Unexamined Japanese Patent Application No. 2003-181655. Patent Literature 9: Publication of Unexamined Japanese Patent Application No. 2003-290936. Patent Literature 10: Publication of Unexamined Japanese Patent Application No. 2004-195480. Patent Literature 11: Publication of Unexamined Japanese Patent Application No. 2011-115846. BRIEF DESCRIPTION OF THE INVENTION Technical problem However, the techniques disclosed in Patent Literature 6 and 7 are intended to reinforce a welded portion or harden a metal surface, and do not consider any application to welding steel strips. Patent Literature 6 and Patent Literature 7 each describe the end portion of a rotary tool having a flat or level surface, but do not describe the end portion of a rotary tool having a concave or convex curved shape for the purpose of improving plastic flow. Nor do Patent Literature 6 and 7 describe rotary tools of the related art having a spirally stepped portion extending in a direction opposite to the direction of rotation.Therefore, the use of the rotary tools of the related technique mentioned to weld steel strips together can produce insufficient plastic flow in the thickness direction, causing a weld defect. The techniques disclosed in Patent Literature 8 through Patent Literature 11 pertain to the welding of metal plates using a friction stir welding method and do not consider any application to a double-sided friction stir welding method. In other words, Patent Literature 8 through Patent Literature 11 does not disclose a suitable relationship between the diameter of a rotary tool end portion and the thickness of the metal plates being welded together in the double-sided friction stir welding method. Therefore, the techniques disclosed in Patent Literature 8 through Patent Literature 11 may not produce a defect-free weld portion. The present invention has been developed in view of the above problems, and an objective of the present invention is to provide: a double-sided friction-stir welding method, methods for producing a cold-rolled steel strip and a coated steel strip, a double-sided friction-stir welding apparatus, as well as installations for producing a cold-rolled steel strip and a coated steel strip, wherein the welding speed with a rotary tool n Lfrenn / zznz / E / Yii can be increased and it is possible to improve the durability of the rotary tool, as well as at the same time suppressing the occurrence of defects in a welded portion. Solution to the problem The essence of the present invention is described below. [1] A double-sided friction-stirring welding method, comprising: Butt welding or lap welding between a rear end of a preceding steel strip and a front end of a subsequent steel strip, pressing two rotating tools, which are arranged on a first and a second surface of a butt or overlap portion of the steel strips, against the butt or overlap portion of the steel strips and displacing the rotating tools in a welding direction while the rotating tools rotate in opposite directions to each other, so that an unwelded portion of the steel strips is softened by the frictional heat generated between the rotating tools and the unwelded portion of the steel strips, and the softened portion is agitated with the rotating tools to generate a plastic flow in order to weld the steel strips together, wherein: Both rotary tools have a terminal portion configured to have one of the following shapes: a flat circular surface, a convex curved circular surface, and a concave curved circular surface; and the terminal portions are made of a material harder than steel strips. [2] In the double-sided friction-stir welding method in accordance with section [1], each of the terminal portions has a spirally stepped portion that extends in a direction opposite to a direction of rotation. [3] In the double-sided friction-stirring welding method in accordance with section [1] or [2], an inclination angle a (°) at which the rotation axes of the two rotary tools are tilted backward in the welding direction with respect to a normal to a surface of the unwelded portion of the steel strips, a diameter D (mm) of each end portion and a distance G (mm) between the end portions of the two rotary tools obey the following formula (1) and formula (2): 0 <a<3 (1) 0.25 xt - 0.2 x D x sin cc < G < 0.8 xt - 0.2 x D x sin a (2) where t represents the thickness (mm) of each steel strip for butt welding of steel strips or the total thickness (mm) of the overlapping steel strips for lap welding of steel strips. n Lfrenn / zznz / E / Yii [4] In the double-sided friction-stir welding method in accordance with any of subsections [1] to [3], the diameter D (mm) of each terminal portion obeys formula (3): xt < D < 20 xt (3) where t represents the thickness (mm) of each steel strip for butt welding of steel strips or the total thickness (mm) of the overlapping steel strips for lap welding of steel strips. [5] In the double-sided friction-stir welding method in accordance with any of subsections [1] to [4], where the height of the convex curved surface of each end portion is denoted as dv (mm), the diameter D (mm) of each end portion and the height dv of the convex curved surface obey formula (4): dv / D < 0.06 (4). [6] In the double-sided friction-stir welding method in accordance with any of subsections [1] to [4], where the depth of the concave curved surface of each terminal portion is denoted as de (mm), the diameter D (mm) of each terminal portion and the depth of the concave curved surface obey formula (5): dc / D < 0.03 (5). [7] A method for producing a cold-rolled steel strip, comprising: after the welding process between a rear end of a preceding steel strip and a front end of a subsequent steel strip by using the double-sided friction-stir welding method in accordance with any of subparagraphs [1] to [6], carrying out cold rolling or performing cold rolling after pickling. [8] The method for producing a cold-rolled steel strip in accordance with paragraph [7], which further includes carrying out an annealing process after cold rolling. [9] A method for producing a coated steel strip, comprising: after the welding process between a rear end of a preceding steel strip and a front end of a subsequent steel strip by using the double-sided friction-stir welding method in accordance with any of subparagraphs [1] to [6], carrying out cold rolling or carrying out cold rolling after pickling and then carrying out an annealing and coating process.

[10] A double-sided friction-stirring welding apparatus comprising two opposing rotating tools across an unwelded portion of two steel strips, and a control device controlling the operation of the two rotating tools, wherein: n Lfrenn / zznz / E / Yii the double-sided friction-stirring welding apparatus welds the steel strips together when the two rotating tools move in one welding direction while pressing the unwelded portion of the steel strips butt-to-butt or overlapping and rotating in opposite directions to each other; Each of the two rotary tools has a terminal portion configured to have one of the following shapes: a flat circular surface, a convex curved circular surface, and a concave curved circular surface; and the terminal portions are made of a material harder than the steel strips.

[11] In the double-sided friction-stirring welding apparatus according to section

[10] , each of the terminal portions has a spirally stepped portion that extends in a direction opposite to a direction of rotation.

[12] In the double-sided friction-stirring welding apparatus according to section

[10] or

[11] , the control device carries out the control such that a tilt angle a (°) at which the rotation axes of the two rotating tools are tilted backward in the welding direction with respect to a normal to a surface of the unwelded portion of the steel strips, a diameter D (mm) of each end portion, and a distance G (mm) between the end portions of the two rotating tools obey the following formula (1) and formula (2): 0 <a<3 (1) 0.25 xt - 0.2 x D x sin cc < G < 0.8 xt - 0.2 x D x sin a (2) where t represents the thickness (mm) of each steel strip for butt welding of steel strips or the total thickness (mm) of the overlapping steel strips for lap welding of steel strips.

[13] In the double-sided friction-stirring welding apparatus in accordance with any of subsections

[10] to

[12] , the diameter D (mm) of each terminal portion obeys formula (3): xt < D < 20 xt Formula (3) where t represents the thickness (mm) of each steel strip for butt welding of steel strips or the total thickness (mm) of the overlapping steel strips for lap welding of steel strips.

[14] In the double-sided friction-stirring welding apparatus in accordance with any of subsections

[10] to

[13] , where the height of the convex curved surface of each terminal portion is denoted as dv (mm), the diameter D (mm) of each terminal portion and the height dv of the convex curved surface obey formula (4): dv / D < 0.06 (4). n Lfrenn / zznz / E / Yii

[15] In the double-sided friction-stirring welding apparatus in accordance with any of subsections

[10] to

[13] , where the depth of the concave curved surface of each terminal portion is denoted as d (mm), the diameter D (mm) of each terminal portion and the depth of the concave curved surface obey formula (5): dc / D <0.03 ·· (5).

[16] An installation for producing a cold-rolled steel strip comprising: in addition to the double-sided friction-stir welding apparatus in accordance with any of subparagraphs

[10] to

[15] , a cold rolling unit that cold-rolls the welded steel strips, or a cold rolling unit that cold-rolls the welded steel strips after the pickling process in a pickling unit.

[17] The installation for producing a cold-rolled steel strip in accordance with paragraph

[16] , which further includes an annealing unit that allows the cold-rolled steel strips to be annealed.

[18] An installation for producing a coated steel strip comprising: in addition to the double-sided friction-stir welding apparatus in accordance with any of subparagraphs

[10] to

[15] , a cold rolling unit that cold rolls the welded steel strips, or a cold rolling unit that cold rolls the welded steel strips after pickling in a pickling unit; an annealing unit that allows the cold-rolled steel strips to be annealed; and a coating unit that coats the annealed steel strips. Favorable Effects of the Invention In accordance with the present invention, it is possible to avoid the brittle condition resulting from the segregation of impurities during melting and solidification, as well as the fragility resulting from hydrogen intrusion, which have been problems present in fusion welding of the related technique, and it is also possible to increase the welding speed and simultaneously suppress the occurrence of defects. According to the present invention, the uniform plastic flow favored in the thickness direction of the steel strips suppresses the occurrence of defects even in double-sided friction-stir welding at a high welding speed to provide a welded portion that has sufficient strength. In accordance with the present invention, it is possible to eliminate a probe that breaks and wears out preferentially as a result of receiving a stress greater than the stress in a portion of n Lfrenn / zznz / E / Yii support in a rotary tool of the related art, thereby improving the durability of rotary tools for double-sided friction-stir welding. BRIEF DESCRIPTION OF THE FIGURES Figure 1 is a schematic diagram illustrating a double-sided friction stir welding method according to the present invention, which is an example of butt welding. Figure 2 is a schematic diagram illustrating a double-sided friction stir welding method according to the present invention, which is an example of lap welding. Figure 3(a) and Figure 3(b) are diagrams illustrating a friction-agitation region using rotating tools, where Figure 3(a) and Figure 3(b) correspond, respectively, to a plan view and a cross-sectional view captured along line AA' of Figure 3(a). Figure 4(a) and Figure 4(b) illustrate the shape of a rotary tool of the related technique and each includes a side view at the top and a plan view at the bottom. Figures 5(a) to 5(c) illustrate the shape of a rotary tool according to a first embodiment of the present invention, and each includes a side view at the top and a plan view at the bottom. Figure 6(a) and Figure 6(b) illustrate the shape of a rotary tool according to a second embodiment of the present invention and each includes a side view at the top and a plan view at the bottom. Figure 7(a) and Figure 7(b) illustrate the shape of a rotary tool according to a third embodiment of the present invention and each includes a side view at the top and a plan view at the bottom. Figures 8(a) to 8(c) illustrate the shapes of the stepped portions of the rotary tool according to the present invention, wherein Figure 8(a) is a plan view and Figures 8(b) and 8(c) are cutaway views taken along line BB' of Figure 8(a). Figure 9 includes diagrams (1) to (4) illustrating an example of how to plot spirals that form the stepped portions in accordance with the present invention. Figure 10 includes diagrams (1) to (4) that illustrate an example of how to plot spirals that form the stepped portions in accordance with the present invention. Figure 11 includes diagrams (1) to (4) that illustrate an example of how to plot spirals that form the stepped portions in accordance with the present invention. n Lfrenn / zznz / E / Yii Figure 12 includes diagrams (1) to (4) that illustrate an example of how to plot spirals that form the stepped portions in accordance with the present invention. Figure 13 includes diagrams (1) to (4) that illustrate an example of how to plot spirals that form the stepped portions in accordance with the present invention. Figure 14 is a schematic diagram illustrating a method for welding steel strips (a preceding steel strip and a subsequent steel strip) together by using a double-sided friction-stirring welding apparatus in accordance with the present invention, which is an example of butt welding. DESCRIPTION OF THE MODALITIES The present invention will now be described with reference to the figures. The present invention is not limited to the following embodiments. First, a double-sided friction stir welding method and a double-sided friction stir welding apparatus according to the present invention will be described. Figure 1 illustrates an example of a butt weld using a double-sided friction stir welding method. Figure 2 illustrates an example of a lap weld using a double-sided friction stir welding method. A double-sided friction-stirring welding method according to the present invention includes, in butt welding or lap welding between the rear end of a preceding steel strip and the front end of a subsequent steel strip, pressing two rotating tools, which are arranged on a first surface and a second surface of a butt or overlap portion of the steel strips, against the butt or overlap portion of the steel strips and displacing the rotating tools in the welding direction while the rotating tools rotate in opposite directions to each other.Next, an unwelded portion of the steel strips is softened by the frictional heat generated between the rotating tools and the unwelded portion of the steel strips, and the softened portion is agitated with the rotating tools to generate a plastic flow, by means of which the steel strips are welded together. As illustrated in Figure 1 and Figure 2, the double-sided friction-stir welding method according to the present invention uses a double-sided friction-stir welding apparatus comprising two rotating tools (1) and (8), a clamping device (not illustrated), and a control device (not illustrated) that controls the operation of the rotating tools (1) and (8). In the examples illustrated in Figure 1 and Figure 2, one of the two steel strips (4) is the preceding steel strip located at the front in the direction of travel (not illustrated), and the other steel strip (4) is the subsequent steel strip located at the rear in the direction of travel. n Lfrenn / zznz / E / Yii The control device controls, for example, the tilt angle a of each of the rotary tools (1) and (8), the distance G between a terminal portion of the rotary tool (1) and a terminal portion of the rotary tool (8), the welding speed, the rotation speed and the direction of rotation of each of the rotary tools (1) and (8), as described below. The rotary tools (1) and (8) (the rotary tool arranged on the front surfaces of the steel strips may hereafter be referred to as the front-side rotary tool (1), and the rotary tool arranged on the rear surfaces of the steel strips may hereafter be referred to as the rear-side rotary tool (8)) are arranged, respectively, on the first surfaces (front surfaces) and the second surfaces (rear surfaces) of the steel strips (4) (workpieces or pieces to be welded). The two steel strips (4) are arranged parallel to a centerline of a joint (7) illustrated in Figure 1 and Figure 2, and each is held by a clamping device (not illustrated).In an unwelded portion of the two steel strips (4) located on the centerline of the joint (7), the rotating tools (1) and (8) are moved in the welding direction (the direction indicated by the arrow in the figures) while rotating and pressing the steel strips (4). The steel strips (4) are thus softened by the frictional heat generated between the rotating tools (1) and (8) and the steel strips (4), while the softened portion is agitated by the rotating tools (1) and (8) to generate a plastic flow, through which the steel strips (4) are welded together. In the following description, a portion where the welding is complete will be referred to as the welded portion (5). As illustrated in Figure 1 and Figure 2, the rotating tool (1) on the front surface and the rotating tool (8) on the rear surface, which oppose each other, rotate in opposite directions when viewed from the front (or rear) surface of the steel strips (4). This allows a rotational torque applied by the rotating tool (1) to the steel strips (4) and a rotational torque applied by the rotating tool (8) to the steel strips (4) to cancel each other out. As a result, the structure of a jig that constrains the parts to be welded can be further simplified compared to a friction-stir welding method of the related technique in which an unwelded portion is pressed and welded using only a rotating tool arranged on a surface.In the examples illustrated in Figure 1 and Figure 2, the direction of rotation of the rotary tool on the front surface side (1) is indicated by arrow Ts, and the direction of rotation of the rotary tool on the rear surface side (8) is indicated by arrow Tb. If the rotating tool (1) on the front surface and the rotating tool (8) on the rear surface, which are opposite each other, rotate in the same direction, the speed of one of the rotating tools relative to the other approaches zero. As a result, as the plastic flow of the steel strips (4) becomes more uniform, plastic deformation decreases, and the plastic deformation of the material generates less heat, making it more difficult to achieve a favorable welding state.In order to provide a uniform temperature increase and a uniform shear stress in the thickness direction of the steel strips that is sufficient to obtain a favorable welding state, it is effective to fix the rotation directions of the rotary tool (1) on the front surface (first surface) and the rotary tool (8) on the rear surface (second surface) so that they are opposite to each other. The welding methods for steel strips will be described below. Preferred examples of welding methods for steel strips include butt welding and lap welding. As illustrated in Figure 1, butt welding refers to the welding of steel strips by pressing the rotating tools (1) and (8) against a butt portion that includes the end surfaces (adjacent surfaces) of two opposing steel strips (4) placed end-to-end without overlap, and moving the rotating tools (1) and (8) in the welding direction while the tools are rotating.As illustrated in Figure 2, lap welding refers to the welding of steel strips that involves pressing the rotating tools (1) and (8) against an overlapping portion of two steel strips (4) with the end portions of the steel strips (4) at least partially overlapping each other, and displacing the rotating tools (1) and (8) in the welding direction while the rotating tools (1) and (8) are rotating. Since Figure 1 and Figure 2 differ only in terms of the type of weld and are identical in terms of the device configurations, etc., the following will primarily describe an example of a butt weld illustrated in Figure 1. The rotary tools used in the double-sided friction-stir welding of the present invention are described below. Figure 4(a) and Figure 4(b) are diagrams illustrating a rotary tool (20) of the related art, which includes a probe. Figures 5(a) to 8(c) are diagrams illustrating the rotary tools (1) and (8) of the present invention. Figures 5(a) to 5(c) illustrate a rotary tool according to a first embodiment of the present invention. Figure 6(a) and Figure 6(b) illustrate a rotary tool according to a second embodiment of the present invention. Figure 7(a) and Figure 7(b) illustrate a rotary tool according to a third embodiment of the present invention. Figures 8(a) to 8(c) illustrate an example of the rotary tool according to the second modality, which has stepped portions in its terminal portion.Figures 4(a) to 7(b) include a side view at the top and a plan view at the bottom. Since the front surface side rotary tool (1) and the rear surface side rotary tool (8) have the same shape, only the front surface side rotary tool (1) is illustrated in Figures 4(a) to 8(c). The rotary tool (20) including a probe (pin) 21, which is an example of the related art, is described below with reference to Figure 4(a) and Figure 4(b). Figure 4(a) and Figure 4(b) illustrate an example of the rotary tool (20) including the probe (21) in a support portion (22). For example, in the rotary tool (20) illustrated in Figure 4(a), the rotary tool (20) has the following shape: the diameter of the support portion (22) (support diameter) is 12 mm, the diameter of the probe (21) (pin diameter) is 4 mm, the length of the probe (21) (pin length) is 0.5 mm, and the depth of a concave surface is 0.3 mm. In the example of the rotary tool (20) illustrated in Figure 4(b), the rotary tool (20) has the following shape: the support diameter is 20 mm, the pin diameter is 6.7 mm, the pin length is 0.7 mm and the depth of a concave surface is 0.3 mm. As illustrated in Figure 4(a) and Figure 4(b), a terminal portion of the rotary tool (20) of the related art, i.e., a portion of the rotary tool (20) that comes into contact with a softened portion of the steel strips during welding, includes the support portion (22) (the area indicated by the support diameter in Figure 4(a) and Figure 4(b)) and the probe (21) (the area indicated by the pin diameter in Figure 4(a) and Figure 4(b)). The support portion (22) has a flat shape formed by a substantially flat surface or a slightly curved surface. The probe (21) is discontinuous with the support portion (22) and projects substantially vertically into the (unillustrated) steel strips. The probe (21) is designed to improve stirring performance near the central portions of the steel strips in the thickness direction as the softened portion of the strips enters and advances toward the center during welding. However, a problem arises: the portion of the probe (21) positioned closer to its end in the thickness direction (closer to the center of the thickness) experiences greater stress than the supporting portion (22). Consequently, the rotating tool requires repair due to damage and wear, as previously described. The inventors of the present invention have carried out intensive studies. As a result, they have discovered a double-sided friction-stir welding method that uses rotating tools for double-sided friction-stir welding that are capable of suppressing the occurrence of defects in a welded portion and increasing the welding speed without a probe that breaks and wears out particularly easily due to the increased stress applied to it. As illustrated in Figures 5(a) to 7(c), one end of each of the rotary tools (the opposing rotary tools (1) and (8)) for double-sided friction-stir welding of the present invention is formed simply from a terminal portion (11). Unlike the rotary tool configuration of the related art, illustrated in Figure 4(a) and Figure 4(b), the terminal portion (11) of each of the rotary tools of the present invention does not include the probe (21). The end portion (11) of each of the rotary tools (1) and (8) has a flat shape (11a) (see Figures 5(a) to 5(c)), a convex curved shape (11b) (see Figure 6(a) and Figure 6(b)), and a concave curved shape (11c) (see Figure 7(a) and Figure 7(b)). Each of the end portions (11) has a circular cross section in plan view. The end portions (11) of the rotary tools (1) and (8) (a terminal portion (2) of the front-surface rotary tool and a terminal portion (9) of the rear-surface rotary tool, illustrated in Figure 1 and other figures) are the portions that come into contact with the steel strips (4) and the flux-cored portion (softened portion) of the steel strips (4) during welding. Therefore, the end portions (11) of the rotary tools (1) and (8) are made of a material harder than the steel strips (4) in the high-temperature environment to which the end portions (11) are exposed during welding. Thus, the rotary tools (1) and (8) can deform the steel strips (4) during the welding process while preserving the shapes of the end portions (11).As a result, high stirring performance can be achieved continuously and proper welding can be performed. To compare hardness, test methods for measuring Vickers hardness at elevated temperatures can be used. The rotary tools (1) and (8) can be formed so that only their end portions have the hardness mentioned above, or so that all of the rotary tools (1) and (8) have the hardness mentioned above. In addition to the configuration described above, the terminal portion (11) of each of the rotary tools (1) and (8) preferably has spiral (helical) stepped portions (12) in the present invention. The spirals (helixes) forming the stepped portion (12) of the rotary tool (1) are preferably oriented in a direction opposite to the direction of rotation of the rotary tool (1), and the spirals (helixes) forming the stepped portion (12) of the rotary tool (8) are preferably oriented in a direction opposite to the direction of rotation of the rotary tool (8). The number of spirals forming the stepped portions (12) is preferably one or more. In the case of one or more spirals, curves (radial curves) are formed so that they extend radially from the center of the terminal portion (11) or from the circumference of an empty circular region at the center to the outer circumference of the terminal portion (11). If the number of spirals forming the stepped portions (12) is greater than 6, the material flow improvement effect is reduced, and the end portions (11) of the rotating tools (1) and (8) can break easily due to their complex shape. Therefore, the number of spirals forming the stepped portions (12) is preferably 6 or fewer. In the examples illustrated in Figure 5(b), Figure 6(b), and Figure 7(b), as well as the example illustrated in Figure 8(a), the number of spirals is 4. To avoid breaking the end portions (11) of the rotary tools (1) and (8) and simultaneously improve material flow, the number of spirals forming the stepped portions (12) can be adjusted based on the diameter of each end portion (11). Specifically, the number of spirals preferably increases as the diameter of each end portion (11) increases, and the number of spirals preferably decreases as the diameter of each end portion (11) decreases. n Lfrenn / zznz / E / Yii Specifically, the number of spirals is preferably 2 or less when the diameter of the terminal portion is less than 6 mm, and the number of spirals is preferably 3 to 6 when the diameter of the terminal portion is 6 mm or more. The process of drawing the spirals will be described using the examples illustrated in Figures 9 through 13. Figures 9 through 13 correspond to the top views of the terminal portion, and each illustrates the process for drawing the spirals in the terminal portion. In Figure 9, the number of spirals is 2, and Figure 9 illustrates an example of how to draw two spirals at regular intervals. As illustrated in Figure 9, first, two semicircles (first semicircles) with a radius equal to the length of line AB are drawn from the starting points at point A and point B (see (1)). Next, each of the semicircles (second semicircles) with centers at point A and point B, each with a radius equal to twice the length of line AB, is drawn outside the first semicircles (see (2)). Subsequently, each of the semicircles (third semicircles) with centers at point A and point B, each with a radius equal to three times the length of line AB, is drawn outside the second semicircles (see (3)). Similarly, semicircles (fourth semicircles), each with a radius equal to four times the length of line AB, are drawn (see (4)). By repeating this process, two spirals can be drawn at regular intervals in the terminal portion. Figures 10 to 13 illustrate an example of how to plot spirals at regular intervals, where the number n of spirals is selected from 3 < n < 6. As illustrated in Figures 10 to 13, regular n-sided polygons are first drawn. A regular triangle is drawn in the example illustrated in Figure 10, a square in the example illustrated in Figure 11, a regular pentagon in the example illustrated in Figure 12, and a regular hexagon in the example illustrated in Figure 13. Arcs (first arcs) centered at the vertices of each regular n-sided polygon, each with a radius equal to the length of one side of the regular n-sided polygon, are drawn to the points of intersection with the lines extending from the sides of the regular n-sided polygon (see (1)).Next, outside the first arcs, arcs (second arcs) centered at the vertices of the regular n-sided polygon, each with a radius equal to twice the length of a side of the regular n-sided polygon, are drawn to the points of intersection with the lines extending from the sides of the regular n-sided polygon (see (2)). Subsequently, outside the second arcs, arcs (third arcs) centered at the vertices of the regular n-sided polygon, each with a radius equal to three times the length of a side of the regular n-sided polygon, are drawn to the points of intersection with the lines extending from the sides of the regular n-sided polygon (see (3)). Similarly, arcs (fourth arcs) are drawn, each with a radius equal to four times the length of a side of the regular n-sided polygon (see (4)).By repeating this process, n (3 < n < 6) spirals can be drawn at regular intervals in the terminal portion. n Lfrenn / zznz / E / Yii In a case where the number of spirals is 1, the spiral can be drawn using any of the methods illustrated in Figures 9 to 13. In a case where the number of spirals is 2 and two spirals are drawn at regular intervals, the spirals can also be drawn using the method illustrated in Figure 11 or 13, in addition to the method illustrated in Figure 9. In a case where the number of spirals is 3 and three spirals are drawn at regular intervals, the spirals can also be drawn using the method illustrated in Figure 13, in addition to the method illustrated in Figure 10. In these cases, the number of spirals (the number of lines) is adjusted by appropriately selecting the starting points illustrated in Figure 9 or the vertices of the regular n-sided polygons illustrated in Figures 10 to 13, depending on the number of spirals. Each of the stepped portions (12) is recessed from the other surface (flat or curved) of the corresponding end portion. These recessed stepped portions (12) cause the metallic material softened by frictional heat to flow from the outside to the inside of the rotating tools (1) and (8) when the rotating tools (1) and (8) press and agitate the steel strips (4). Consequently, the rotating tools (1) and (8) can prevent the metallic material from flowing out of the pressed portion. This can promote plastic flow of the pressed portion and can also prevent a welded portion from being thinner than the base material, resulting in a smooth, burr-free weld surface.The aforementioned favorable effects of the stepped portions are obtained by forming the stepped portions in a spiral (12), such that the stepped portions (12) extend in the opposite direction to the direction of rotation of the rotary tools (1) and (8). The rotary tools according to the present invention preferably do not have a spiral stepped portion in the center of their end portion, or preferably do not have a spiral stepped portion in the center of their end portion that extends in the opposite direction to the direction of rotation. Favorable effects similar to those described above can be obtained by providing one or more spirally stepped portions (12) that extend in the opposite direction to the rotational direction of the corresponding rotating tool. The stepped portions (12) will now be described more specifically, with reference to Figures 8(a) to 8(c). Figure 8(a) is a plan view of the rotary tool (1) (rotary tool on the front surface side) including the terminal portion (11) having a convex curved shape (11b), and Figures 8(b) and 8(c) are cutaway views taken along line BB' of Figure 8(a). As illustrated in Figure 8(a), the stepped portions (12) extend in the opposite direction to the direction of rotation in the plan view. In other words, the direction of the curve of each of the stepped portions (12) extending from the circumference of the circle toward the center of the circle is opposite to the direction of rotation of the rotary tool. n Lfrenn / zznz / E / Yii As shown in Figure 8(a), each of the stepped spiral portions (12) forms a curve extending from a starting point near the center of the circle to the circumference of the circle in the plan view. The length of each spiral is preferably 0.5 turns or more and 2 turns or less when the length of the outer circumference of the terminal portion (11) is one turn. The length of each spiral can also be adjusted according to the diameter of the terminal portion (11). Preferably, the length of each spiral increases as the diameter of the terminal portion (11) increases. Preferably, the length of each spiral decreases as the diameter of the terminal portion (11) decreases. Specific examples of the stepped portions (12) include the stepped portions (12b) illustrated in Figure 8(b) and the slotted portions (12c) illustrated in Figure 8(c). In the example illustrated in Figure 8(b), the stepped portions (12b) form substantially horizontal steps, such that the step heights gradually increase from the circumference of the circle toward the center of the circle, as on the convex curved surface of the end portion (11) of the rotary tool (1). To obtain the favorable effects described above, one or more spiral steps can be formed in the present invention. In the example illustrated in Figure 8(b), each of the formed stepped portions (12) has a spiral shape in plan view, as illustrated in Figure 8(a). Although not illustrated, when the rotary tool having a terminal portion with a concave curved shape includes the stepped portions (12b) on the concave curved surface, the steps can be formed so that their heights gradually decrease from the circumference of the circle towards the center of the circle depending on the concave curved surface. In the example illustrated in Figure 8(c), each of the grooved portions (12c) on the curved surface (convex curved surface) of the end portion (11) of the rotary tool 1 has a groove with a substantially U-shaped cross-section for embedding from the other surface. To obtain the favorable effects described above, one or more grooved portions (12c) can be formed in the present invention. In the example illustrated in Figure 8(c), each of the grooved portions (12c) has a long, narrow shape that extends in a spiral in the plan view, as illustrated in Figure 8(a). The favorable effects described above are obtained, for example, with a V-shape or a checkmark shape instead of the U-shape. Although not illustrated, when the rotary tool (1) with the terminal portion (11) in a concave curved shape (11c) or in a flat shape (11a) includes the portions with grooves (12c) on the concave curved surface or the flat surface, grooves with a substantially U-shaped cross section can be similarly formed. n Lfrenn / zznz / E / Yii In addition to the configuration described above, the diameter D (mm) of the terminal portion (11) of each of the rotary tools (1) and (8) preferably complies with the relationship represented by the following formula (3) in the present invention: xt < D < 20 xt Formula (3) where t represents the thickness (mm) of each steel strip for butt welding of steel strips, or the total thickness (mm) of the steel strips for lap welding of steel strips. With the diameter of each end portion (11) controlled, the rotary tools (1) and (8) can provide a uniform and effective temperature increase and shear stress in the thickness direction of the steel strips (4). The diameter D of the end portion (11) of the rotary tool (1) is preferably controlled according to the thickness of each of the steel strips (4) (the total thickness t of the steel strips (4) for the lap weld). In other words, it is effective to set the diameter D (mm) of the end portion (11) of each of the rotary tools (1) and (8) according to formula (3): 4 x t < D < 20 x t. If the diameter D (mm) is less than 4 xt (mm), a uniform plastic flow in the thickness direction cannot be effectively achieved. If the diameter D (mm) is greater than 20 xt (mm), a plastic flow region is unnecessarily widened, and an excessive load is placed on the apparatus, which is undesirable. The diameter D is preferably 5.5 xt (mm) or greater, and optimally 14 xt (mm) or less. As described above, the shape of the rotary tool according to the present invention can be simplified by eliminating a probe required for a rotary tool of the related art. The rotary tool can have greater durability. The rotary tool can be produced in fewer steps and at lower costs. In accordance with the double-sided friction-stir welding method of the present invention, which utilizes rotary tools, it is possible to uniformly provide a sufficient temperature rise and sufficient shear stress during the welding process in the thickness direction. In other words, a uniform temperature rise in the thickness direction can be achieved more effectively by promoting plastic flow using a welding method that employs the rotary tools of the present invention in the configuration described above, compared to a uniform temperature rise that can be obtained by double-sided friction-stir welding of the related art.Therefore, part of the welded portion is not exposed to an excessive increase in temperature to complete the welding of the steel strips, thus avoiding liquefaction embrittlement caused by liquefaction of the segregation zone due to exposure to high temperatures, as well as hydrogen embrittlement caused by increased hydrogen intrusion into the steel due to high temperature. n Lfrenn / zznz / E / Yii The rotary tools according to embodiments 1 to 3 of the present invention will now be described in detail. It should be noted that, in Figures 5(a) to 7(b), only the rotary tool is illustrated from the front surface side (1). First Modality As illustrated in Figure 5(a) and Figure 5(c), the rotary tools (1) and (8) according to the first embodiment of the present invention have a circular end formed by the flat end portion (11) (11a). Each of the flat end portions (11) has a terminal surface that contacts the steel strips and is formed by a single flat surface perpendicular to the axis of rotation of the corresponding rotary tools (1) and (8). Unlike a rotary tool of the related art, the terminal surface does not have a probe projecting into the steel strips. As illustrated in Figure 5(b), the terminal portion (11) of each of the rotary tools (1) and (8) may have one or more spirally stepped (helical) portions (12) extending in the opposite direction to the direction of rotation, as described above.The stepped portions (12) have either the stepped portions (12b) or the slotted portions (12c), as described above. The top view of Figure 5(c) is a cross-sectional view taken along line BB' at the bottom of Figure 5(c). The stepped portions (12b) are formed, for example, by angling substantially horizontal faces, as illustrated in Figure 5(c). In other words, checkmark-shaped or tick-shaped slot portions are formed. The spirals of the stepped portions (12b) in Figure 5(c) can be drawn, for example, using the method in Figure 10 described above. Second Modality As illustrated in Figure 6(a) and Figure 6(b), each of the rotary tools (1) and (8) according to the second embodiment has a circular end formed by the convex curved end portion (11b), and the end of each rotary tool is convex. Although a rotary tool of the related art includes a probe projecting into the steel strips and discontinuous with a support portion, each of the convex curved end portions (11) is continuous without a probe and forms an approximately uniform inclined surface.In other words, each of the convex curved end portions (11) has a terminal surface that contacts the steel strips and is formed by a single curved surface (a parabolic, prolate, or spherical surface) projecting toward the center. This terminal surface forms a curve with an approximately uniform radius of curvature in a cross-section that includes the axis of rotation perpendicular to the steel strips. As illustrated in Figure 6(b), the terminal portion (11) of each of the rotary tools (1) and (8) may have one or more spirally stepped (helical) portions (12) extending in the opposite direction to the direction of rotation, as described above. The stepped portions (12) are either stepped portions (12b) or grooved portions (12c), as described above. In a case where the end of each of the rotary tools (1) and (8) is formed by the convex curved terminal portion (11b), the rotary tools preferably comply with the relationship represented by the following formula (4), where dv represents the height (mm) of the convex curved surface (convex surface) and D represents the diameter (mm) of the terminal portion of the rotary tool: dv / D < 0.06 Formula (4) When the terminal portions come into contact with the steel strips in a way that satisfies formula (4) (i.e., with a dv / D value of 0.06 or less), pressure can be effectively applied to the flow portion. As a result, the rotation of the rotary tools can generate sufficient plastic flow for welding. If the dv / D ratio exceeds the range of formula (4) (i.e., the dv / D value is greater than 0.06), the front and back surfaces of the weld portion become noticeably embedded or inset, and the thickness of the weld portion becomes significantly less than the thickness of each of the steel strips. Therefore, ensuring joint strength can be difficult, which is undesirable. To effectively apply pressure to the flow portion, the lower limit of the dv / D value is preferably 0.01 or greater. Third Modality As illustrated in Figure 7(a) and Figure 7(b), each of the rotary tools (1) and (8) according to the third embodiment has a circular end formed by the concave curved end portion (11) (11c), and the end of each rotary tool is concave. Although a rotary tool of the related art includes a probe projecting into the steel strips and discontinuous with a support portion, each of the concave curved end portions (11) is continuous without a probe and forms an approximately uniform inclined surface.In other words, each of the concave curved end portions (11) has a terminal surface that contacts the steel strips and is formed by a single curved surface (a parabolic, prolate, or spherical surface) recessed toward the center. This terminal surface forms a curve with an approximately uniform radius of curvature in a cross-section that includes the axis of rotation perpendicular to the steel strips. As illustrated in Figure 7(b), the end portion (11) of each of the rotary tools (1) and (8) may have one or more spirally stepped (helical) portions (12) extending in the opposite direction to the direction of rotation, as described above. The stepped portions (12) are either stepped portions (12b) or grooved portions (12c), as described above. In a case where the terminal portion of the rotary tool is formed by the concave curved terminal portion (11), the rotary tool preferably complies with the relationship represented by the following formula (5), where de represents the depth (mm) of the concave curved surface (concave surface) and D represents the diameter (mm) of the terminal portion of the rotary tool: dc / D < 0.03 Formula (5) When the end portions come into contact with the steel strips, such that formula (5) is satisfied (i.e., when the dc / D value is 0.03 or less), the concave curved surfaces of the end portions are surrounded by the softened metal, applying uniform pressure to the flux portion. As a result, the rotation of the rotary tools can generate sufficient plastic flow for welding. If the dc / D ratio exceeds the range of formula (5) (i.e., if the dc / D value is greater than 0.03), it becomes difficult to apply uniform pressure to the flux portion described above, and ensuring sufficient plastic flow for welding may be challenging, which is undesirable. To apply uniform pressure to the flux portion, the lower limit of the dc / D value is preferably 0.01 or greater. The shapes of the base portions of the rotary tools (1) and (8), which are portions opposite to the terminal portions of the rotary tools (1) and (8), are not particularly restricted, as long as the base portions can be attached to a double-sided friction-stir welding apparatus described in the related art. A preferred example of a double-sided friction stir welding method using rotary tools (1) and (8) according to the present invention will now be described. In the double-sided friction-stirring welding method, more favorable effects can be obtained related to improving the durability of rotary tools, suppressing the occurrence of defects in joints, and increasing the welding speed by optimizing the conditions of the following parameters. In the present invention, the inclination angle a (°) towards which the rotation axes of the two rotary tools (1) and (8) are inclined in the welding direction with respect to the normal to the surface of the unwelded portion of the steel strips, the diameter D (mm) of the terminal portions (11) of the rotary tools (1) and (8), as well as the distance G (mm) between the terminal portions of the two rotary tools (1) and (8) are preferably controlled so as to comply with the following formula (1) and formula (2). (1) Tilt angle a (°) of the rotating tools: 0 < a < 3 Formula (1) Figure 3(a) and Figure 3(b) are diagrams illustrating a friction-agitation region with the rotating tools according to the present invention. Figure 3(a) is a diagram illustrating the movement of the rotating tools (1) and (8), which are arranged on the front and rear surfaces of the steel strips (4) as illustrated in Figure 1, in the welding direction in a plan view from the front surfaces of the steel strips (4). Figure 3(b) illustrates a cutaway view taken along line AA' in Figure 3(a). As illustrated in Fig. 3(b), the rotation axes of the rotary tools (1) and (8) (a rotation axis (3) of the front-surface rotary tool and a rotation axis (10) of the rear-surface rotary tool) are preferably inclined backward in the welding direction at an angle α° with respect to a vertical (normal) line (6), which extends in the direction perpendicular to the steel strips (4) during welding. In other words, the rotary tools (1) and (8) are preferably inclined such that the proximal ends of the rotary tools (1) and (8) are positioned further forward than the distal ends of the rotary tools (1) and (8) in the welding direction.As a result, a load that would otherwise be applied to the rotating tools (1) and (8) in the horizontal direction (bending direction) during welding, can be dispersed as force components that cause compression in the axial directions. The rotating tools (1) and (8) must be made of a material harder than the steel strips (4) and can be made, for example, of a material with low toughness, such as a ceramic material. In this case, applying a force to the rotating tools (1) and (8) in the bending direction can locally concentrate the stress and result in the breakage of the rotating tools (1) and (8). To avoid this situation, the axes of rotation (3) and (10) of the rotating tools (1) and (8) are inclined at a predetermined angle (a°), as described above, so that the load applied to the rotating tools (1) and (8) can be received as force components that cause compression in the axial direction, thus reducing the force in the bending direction. As a result, the durability of each of the rotating tools (1) and (8) can be further improved. The favorable effects mentioned above are obtained at an inclination angle α of 0 degrees or more. If the inclination angle α is greater than 3°, the front and rear surfaces of the welded portion may become recessed, which can negatively affect the joint's strength. The inclination angle of the rotation axis of each of the rotary tools (1) and (8) is preferably 0 < α < 3°. n Lfrenn / zznz / E / Yii The angle of inclination a is preferably 100 more, and optimally 200 less. (2) Distance G (mm) between the terminal portions of two rotary tools (1) and (8): 0.25 xt - 0.2 x D x sin a < G < 0.8 xt - 0.2 x D x sin a Formula (2) where t is: the thickness (mm) of the unwelded portion of the steel strip (4), D: is the diameter (mm) of the terminal portions of the rotary tools (1) and (8), ya: is the inclination angle (°) of the rotary tools (1) and (8). In this case, t represents the thickness (mm) of each steel strip for butt welding of the steel strips or the total thickness (mm) of the overlapping steel strips for lap welding of the steel strips. In double-sided friction stir welding, it is important to control the distance G between the end portions of the opposing rotating tools (1) and (8) to provide sufficient temperature rise and sufficient shear stress uniformly in the thickness direction during welding. Specifically, the distance G between the end portions of the rotating tools (1) and (8) is preferably controlled (adjusted) within the range of formula (2) by using the thickness t of the unwelded portion of the steel strips (4), the diameter D of the end portion of each of the rotating tools (1) and (8), and the tilt angle α of each of the rotating tools (1) and (8). For the butt weld illustrated in Figure 1, the thickness t of the unwelded portion of the steel strips (4) refers to the thickness of one steel strip (4). For the lap weld illustrated in Figure 2, the thickness t of the unwelded portion of the steel strips (4) refers to the total thickness of the overlapping steel strips (4). The tilt angle α of each of the two rotating tools (1) and (8) may be the same angle. The diameter D of the end portion of each of the rotating tools (1) and (8) refers to the end diameter (pin diameter) of the end portion (11) in a cross section that includes the corresponding axis of rotation in the direction perpendicular to the steel strips, wherein the end portion (11) has the flat or curved shape (concave or convex curve) illustrated in Figures 5(a) to 7(b). In the event that the rotary tools (1) and (8) are not inclined (i.e., the inclination angle a of each of the rotary tools (1) and (8) is 0o), the lower limit and the upper limit of the distance G between the terminal portions (reference signs 2 and 9 in Figure 3(b)) of the rotary tools (1) and (8) are fixed, respectively, at 0.25 xty 0.8 x t. In the event that the rotary tools (1) and (8) are inclined (i.e., the inclination angle a of each of the rotary tools (1) and (8) is 0 < a < 3), or in a case where the diameter D of the end portion of each of the rotary tools (1) and (8) is increased in order to increase the contact area between the end portion of the rotary tool (1) and the front surfaces of the steel strips (4), as well as the contact area between the end portion of the rotary tool (8) and the rear surfaces of the steel strips (4), the distance G between the rotary tools (1) and (8) must be set to a smaller value. In this case, as expressed in formula (2), the lower limit of G can be obtained by subtracting 0.2 x D x sin a from 0.25 xt, and the upper limit of G can be obtained by subtracting 0.2 x D x sin a from 0.8 x t. As described above, when the distance G between the end portions of the rotating tools (1) and (8) is controlled within the range of formula (2), the end portions of the opposing rotating tools (1) and (8) are pressed against the front and rear surfaces of the steel strips (4) with sufficient load, adequately promoting both heat generation and plastic flow in the welded portion. As a result, plastic flow is uniformly favored in the thickness direction, and a joint (welded portion) in a favorable state can be obtained. If the value of the distance G exceeds the upper limit in formula (2), the end portions of the rotating tools (1) and (8) cannot press the front and rear surfaces of the steel strips (4) (workpieces) with sufficient load, and the aforementioned favorable effects may not be achieved.If the value of the distance G is below the lower limit in formula (2), the front and rear surfaces of the welded portion may be embedded, which can negatively affect the strength of the joint. The value of the distance G is preferably 0.4 xt - 0.2 x D x sina or more and, optimally, 0.7 xt - 0.2 x D x sina or less. As illustrated in Figure 3(b), the distance G corresponds to the shortest length in the vertical direction between the end surface of the rotary tool (rotary tool on the front surface side) (1) and the end surface of the rotary tool (rotary tool on the back surface side) (8), opposite each other. The other welding conditions can be set conventionally. For example, the rotational speed of each of the rotating tools (1) and (8) is preferably from 100 to 5000 rpm and, optimally, from 500 to 3000 rpm in the double-sided friction-stir welding apparatus and by the double-sided friction-stir welding method according to the present invention. At a rotational speed in these ranges, the deterioration of mechanical properties due to excessive heat input can be suppressed while maintaining a favorable surface profile. The welding speed is preferably 1000 mm / min or more and is increased in its optimum range to 2000 mm / min or more. For welding steel strips in process, the welding method of the present invention can preferably be used to weld common structural steels and carbon steels, such as rolled steels for welded structures according to Japanese Industrial Standards (JIS) G 3106 and carbon steels for structural use in machinery according to JIS G 4051. The welding method of the present invention can be favorably used for high-strength structural steels having a tensile strength of 800 MPa or more. Even in this case, the strength of the welded portion is 85% or more, preferably 90% or more, and optimally 95% or more, with respect to the tensile strength of a steel sheet (base material). The welded portion of steel strips undergoes bending or compressive deformation during the production process. The Erichsen test is used to determine if the welded portion is properly welded and resistant to this deformation. In the Erichsen test, the welded portion is held in a die, and a hemispherical punch is pressed into it. The Erichsen test measures the depth of indentation until cracking occurs, and this indentation depth is used to evaluate the performance of the welded portion. The double-sided friction-stir welding for steel strips utilizes a double-sided friction-stir welding apparatus comprising two rotary tools (1) and (8) of the present invention, a clamping device (13) (described in Figure 14), and a control device (not illustrated) that controls the rotary tools, as illustrated in Figure 1 and other figures. The control device allows control of, for example, the tilt angle of each of the rotary tools (1) and (8), the distance between the end portions of the rotary tools, the welding speed, and the rotational speed of the rotary tools to satisfy welding conditions (1) and (2).In Figure 14, the right side of the figure corresponds to the front side in the direction of travel (direction of the steel strip), and the left side of the figure corresponds to the rear side in the direction of travel. The clamping device (13) holds the front and rear surfaces of the preceding steel strip (4a) and the subsequent steel strip (4b) together to secure both strips. As the rotating tools (1) and (8) operate in a portion (butt portion) where the steel strips oppose each other to travel in the direction of the width of the steel strips (the direction from rear to front in the figure), the steel strips are welded together. In accordance with the rotary tools (1) and (8) of the present invention, it is possible to improve the durability of each of the rotary tools (1) and (8), as described above. When each of the end portions of the rotary tools has the shape mentioned above, and the opposing rotary tools (1) and (8) rotate in opposite directions, the steel strips experience a sufficient temperature increase and sufficient shear stress during the welding process. As a result, the occurrence of defects in the welded portion can be suppressed, and the welding speed can be increased. The methods and installations for producing a cold-rolled steel strip and a coated steel strip according to the present invention will now be described. The double-sided friction-stir welding apparatus (double-sided friction-stir welding method) according to the present invention and described above can be used in an installation for producing a cold-rolled steel strip (a method for producing a cold-rolled steel strip) and an installation for producing a coated steel strip (a method for producing a coated steel strip). In a method for producing a cold-rolled steel strip using the related technique, a spirally welded portion can break on the production lines. This has become more noticeable recently and poses a problem that needs to be solved in the field of high-strength cold-rolled steel sheet production. Applying the double-sided friction-stir welding technique described above to the production of cold-rolled steel strips and other similar techniques can prevent the breakage and brittleness of the welded portions of the resulting cold-rolled steel strips, or similar products, thereby improving the material properties and resolving the problem described above. The installation for producing a cold-rolled steel strip according to the present invention includes at least the double-sided friction-stir welding apparatus described above and, as required, a pickling unit, a cold-rolling unit, and an annealing unit. The installation for producing a coated steel strip according to the present invention further includes a coating unit in addition to these units. The method for producing a cold-rolled steel strip according to the present invention involves welding the rear end of a preceding steel strip to the front end of a subsequent steel strip using the double-sided friction-stir welding described above, and then cold-rolling the welded steel strips using the cold-rolling unit (cold-rolling process) to produce cold-rolled steel strips. Cold rolling may be preceded by pickling, using the pickling unit as required. After cold rolling, the cold-rolled steel strips may be annealed (annealing process) using the annealing unit as required. In the method for producing a coated steel strip according to the present invention, the cold-rolled steel strips obtained after the cold rolling process and the annealing process are subjected to a coating process using a coating unit to produce coated steel strips. The use of the double-sided friction-stir welding apparatus (and the double-sided friction-stir welding method) according to the present invention for the production of cold-rolled steel strips and coated steel strips can reduce defects in the welded portion of the obtained cold-rolled steel strips and the produced coated steel strips and can ensure sufficient joint strength. n Lfrenn / zznz / E / Yii EXAMPLES The functions and effects of the present invention will be described below by means of Examples. The present invention is not limited to the following Examples. The double-sided friction stir welding was carried out using steel sheets having the thickness, chemical composition, tensile strength, and Vickers hardness described in Table 1. In the Examples, a lap weld was performed on some of the steel sheets, and a butt weld was performed on the remaining steel sheets. For butt welding, two steel sheets of the same type were placed side by side to form butt joint surfaces without a groove angle, commonly called a square groove, and which have a surface condition similar to that of a milled surface. Rotating tools were pressed against the butt portion of both a first surface (front surface) and a second surface (back surface) and moved in the welding direction, thereby welding the steel sheets together. For lap welding, two steel sheets of the same type were positioned overlapping each other, and rotary tools were pressed against the overlapping portion of the steel sheets on both a first surface (front surface) and a second surface (back surface), thereby welding the steel sheets together. The weld length for one process was 0.5 m. For both butt and lap welding, two rotary tools were rotated in opposite directions during welding. In other words, the rotary tools rotate in the same direction when the tool tips are viewed from the front. The welding conditions for friction stir welding are described in Table 2-1 and Table 2-2. Eight types of rotary tools were used in the welding process, with the cross-sectional dimensions and shapes illustrated in Figures 4(a) through 7(b). The shape column in Table 2-1 and Table 2-2 features one of the tools shown in Figures 4(a) through 7(b). These rotary tools were made of tungsten carbide (WC) with a Vickers hardness of 1090. Rotary tools without a probe or a spiral stepped portion, as illustrated in Figures 5(a), 6(a) and 7(a), were used in the Examples of the Invention. Since the spirals are directed clockwise in the probeless rotary tools having stepped spiral portions, as illustrated in Figures 5(b), 6(b) and 7(b), the rotation of the rotary tools was counterclockwise in the Examples of the invention, and the rotation of the rotary tools was clockwise in the Comparative Examples. The rotary tools corresponding to stepped in the column condition of the stepped portions in Table 2-1 and Table 2-2 are those illustrated in Figure 8(b), and the rotary tools corresponding to slotted are those illustrated in Figure 8(c). The rotary tools having a probe, as illustrated in Figure 4(a) and Figure 4(b), were used in the Comparative Examples. n Lfrenn / zznz / E / Yii n Lfrenn / zznz / E / YiA TABLE 1 Thickness Number (mm) Chemical composition (% by mass) Tensile strength (MPa) Vickers hardness C? Si Mn PS i te 03 021 0.69 0.012 0.003 1010 337 2 2.4 0.16 007 0.69 0.016 0.009 425 142 3 1.2 0.3 0.21 0.69 0.012 0.003 1012 339 TABLE 2-1 n Lfrenn / zznz / E / YiA Z' <x es X X'' o <·.< í § <ϊ><·* & fe> «> <·> í íS & & 11 § § 1 § f S g | |1 & s 11 δ II I i — .íx- § -¾ i 1 8 & «> $ 8 <:> í — — — — — — ----------J £ <* o ·» W '>> 11 «í ·» <u jx •fe i u» j 1 ' § íl>ΊΓ <» <:> íí> <:> <:> <:> <:> <:> $ Z» ¡fe fe’ <·> <:> <fe g> V' <:> x''· X'' i <$ ·<< •>x & í»J &' o? 1 ί·Λ' 5 >x? S & « i ·* i « s «> »’K < s v<; <* v:« «.· ''' - - - <v 4 < / -X 11 Uí .<$ -4 ·$ ΐ »1 Sí. t' <5 t b S·' " ü? ·- Esssisífes ''Má&Sú #1 .fe. £ ÍXl ''' Λ .χ>, fe ΐ a'p « $ 4> Ui" - zy> 1 H LU '«· « $ íS fe .y< «· %¥ Kí X.. Si >?: S8 ¿xj fe & sí & r V $ fe >ϊ: «i 1 <v M· i »; fe. •s. o X» ..· s <> i i S (fe' 1? i .o^ fe :$ <x? !A-· i£ fe? I s> :x «J & <> Ά· fe .8 í? £ íS £ $ <8 $? i s <j>«» <? A? S* £: A^. «> "^ JS t i Λ». jé ,»Λ <6 > ce -fe λι Sí fe ¿3 J>x >ΰ o> $ fe s fe i. $ $$ >'·· <? t fe t & § fe fe ?> fe fe fe • X fe B >x fe fe •Λ*. *· •s •>A x> x> •Sí χ·> $ '35 Λ 3 v> § Afe «tí % K? fe fe? 8 <É ·<> o i x> § Si fe TV ,| fe fe B i i ís s. I fe ,g í s & Si & § Jv £ <Q s & fe $ & i i f ·» x¥ ¿f fe· fe § fe § <S' | fe· <j5>I fe' fe fe' & Le. y- ife % JS fe XX fe fe <: fe Si & $ fe s «X Άχ >- rtj & $ XS X. fe ií' .¾ <5 <> $ x> $ .w i •fe *V '2? fe & fe í> o> fe «1 i ?v Ft fe iV y* $ ¿X s O já .fe n Lfrenn / zznz / E / YiAi n Lfrenn / zznz / E / YiA TABLA 2-2 <> >xi § fe <0 <:> fe i fe S ΔΟ «: | f :§ & $ § 11 s .§ i s s fe : § $ : » S® í§ fe o <.> : »·· : ::> •λ» <:< g g <δ úi i > <x><?>Yes y> : <> '5> cy· or : — »> <·> — '> ' í<; '-S 2> & i ?s fe § w : X-.' •V·' te; •ν' x->' S' s ^?- >F á? : f * ti • w ! v< <s : o.í •n «>te wT te to §Í $ cb $ S :>7 § F $ • £$ íi^ i i. < $ izT i Λί n Lfrenn / zznz / E / YiAi The following evaluation was carried out using the weld joint obtained. (I) Presence or absence of surface defects in the observation of the joint's appearance The observation was performed using portions of the resulting weld joints that were welded at the welding speeds indicated in Table 2-1 and Table 2-2. The presence or absence of surface defects was determined visually based on whether a groove-like portion was observed in the unwelded state due to insufficient plastic flow, or whether a recessed welded portion was observed due to the distance G between the welding tool holders being too narrow. If the groove-like portion in the unwelded state or the recessed welded portion was observed as a surface defect, the depth Dd (mm) of the surface defect was measured with a laser displacement gauge and evaluated based on the following criteria. Criteria No: None of the surface defects described above were observed. Acceptable: One of the surface defects described above was observed, but the ratio (Dd / t) between the depth Dd (mm) and the thickness t (mm) of the steel sheets was 0.1 or less. Yes: One of the surface defects described above was observed, and the ratio (Dd / t) between the depth Dd (mm) and the thickness t (mm) of the steel sheets was greater than 0.1. Alternatively, the groove-shaped portion in the unwelded state extended from the front surface to the back surface. If the groove-shaped portion in the unwelded state extended from the front surface to the back surface, the weld was considered defective, and neither internal defects nor joint strength were evaluated. (II) Presence or absence of internal defects in the observation of cross-sections of the joints The observation was performed using portions of the welded joints obtained at the welding speeds indicated in Table 2-1 and Table 2-2. Cross-sections were prepared by cutting the portions at a position 20 mm from the weld start end, at a position 20 mm from the weld end, and at an intermediate position between the ends to prepare the test specimens. The presence or absence of internal defects was determined based on whether or not an unwelded state formed in the welded portion due to insufficient plastic flow was observed, using an optical microscope (magnification: 10x), and was evaluated based on the following criteria: n Lfrenn / zznz / E / Yii Criteria No: The unwelded tunnel-shaped state was not observed in any of the three positions mentioned above. Acceptable: The unwelded state formed in the welded portion was observed in one of the three positions mentioned above. Yes: The unwelded state formed in the welded portion was observed in two or more of the three positions mentioned above. Table 3 shows the results of determining (I) the presence or absence of surface defects by observing the appearance of the joint when the weld was performed once with a weld length of 0.5 m, as well as the results of determining (II) the presence or absence of internal defects by observing the cross-sections of the joint. Table 3 also shows the tensile strength and indentation depth. Tensile strength was measured in a tensile test (JIS Z 3121) using tensile test specimens, each taken from the welded joints and with the dimensions of a No. 1 test specimen defined by JIS Z 3121. The indentation depth at plastic deformation to cracking in the welded portion was measured using an Erichsen gauge. Table 3 indicates that, in the butt joints of Examples of the Invention 1 to 24 and in the lap joints of Examples of the Invention 25 to 27, a defect-free weld condition was obtained even at high welding speeds of 1.0 m / min or higher, and no surface defects were detected by observing the appearance of the joint, nor any internal defects by observing the cross-sections of each joint. The joint strength was found to be equal to or greater than 95% of the tensile strength of the steel sheets used as the base material, and the depth of indentation to cracking in the welded portion was equal to or greater than 5 mm in the Erichsen test. In the butt joints of Comparative Examples 1 to 3, welding was performed using rotary tools, each without a probe and with spirally stepped portions extending clockwise, while the rotation direction of each tool was also clockwise. Surface and internal defects were observed in the resulting joints, and a defect-free weld condition was not achieved. The joint strength was found to be 70% or less of the tensile strength of the steel sheets used as the base material, and the depth of indentation to cracking in the welded portion was 4 mm or less in the Erichsen test. In the butt joint of Comparative Examples 1 to 4, welding was performed using rotary tools, each without a probe and with spirally stepped portions extending clockwise, while the rotation direction of each rotary tool was set to clockwise. Surface and internal defects were observed in the resulting joint, and a defect-free weld condition was not achieved. The strength of the joint was found to be 70% or less of the tensile strength of the steel sheets used as the base material, and the depth of indentation to cracking in the welded portion was 4 mm or less in the Erichsen test. In the butt joints of Comparative Examples 5 to 9, rotary tools (each with a pin) were used under conditions where D (the diameter (mm) of the terminal portion of each rotary tool), a (the tilt angle (°) of each rotary tool) and G (the distance (mm) between the terminal portions of the two rotary tools) obey formulas (1), (2) and (3). In the butt joints of Comparative Examples 5 to 9, a defect-free weld condition was achieved even at high welding speeds of 1.0 m / min or higher, with no surface defects found by visual inspection of the joint and no internal defects detected by examining the cross-sections of each joint. The joint strength and the Erichsen test were confirmed to have favorable results. However, it was also confirmed that the rotary tools exhibited poor durability. In the butt joint of Comparative Example 10, a defect-free weld condition was achieved even at high welding speeds of 1.0 m / min or higher, with no surface defects found by visual inspection of the joint or any internal defects detected by examining the joint's cross-sections. The joint strength and the Erichsen test were confirmed to have favorable results. However, it was also confirmed that the rotating tools exhibited poor durability. n Lfrenn / zznz / E / Yii TABLE 3 n Lfrenn / zznz / E / Yii Presence of defects: observe the appearance of the joint. Presence of straight edges: observe the joints. s te tension Í^B) EHchsen test: probability of te rnctót-actó liaste the cracking in the welded portion (mm) Example of te tevención 1 No No 8.3 Example of tetendón 2 No No 1012 8.4 Example of Ib Invention 3 No No W 8.2 Example of the invention 4 No No 10S5 8.2 Examples of the Invention 5 No No 1&3S 8.3 Tension of the welt 6 No No 1®1 8.1 Example of te welt 7 No No 430 8.8 Example of te tevenctón 8 No No 433 9.0 Example of te tevenctón 8 No No 432 9.0 Example of te Invention 15 No No 1SÜ5 8.1 Example of the Invention 11 No No 1092 8.2 Example of the Inventions 12 No No 1®í 8.0 Example of the Inventions 13 No No 8.3 Example of the Inventions 14 No No 1015 8.3 Example of the Inventions 15 No No 1007 8.1 Example of the Invention 15 No No 43G 8.8 Example of the Invention 17 No No 433 8.9 Example of the Invention 13 No No 432 8.8 Example of Invention 1S Not Accepted 7.8 Example of Invention 25 Accepted Acceptable 7.8 Example of Invention 21 Accepted Not SS5 7.9 Example of Invention 22 Not Acceptable S3G 7.5 Example of Invention 23 Accepted Accepted S87 7.7 Example of Invention 24 Accepted Not 333 7.6 Example of Invention 25 No No imi 5.5 Example of Invention 25 No No 100b 5.2 Example of Invention 27 Accepted Not w 5.2 Comparative Example 1 (portion without solid) Yes 587 3.3 Comparative Example 2 Yes {portion without solid} 31 274 25 Example Qompatów» 3 Yes {portion without welding) Yes W 2.8 Comparative Example 4 Yes {portion without welding) Yes 657 2.1 Comparative Example 5 No No 1001 7.9 Comparative Example s No No 1003 85 Comparative Example 7 No No 987 78 Comparative Example 8 No No 424 §7 Comparative Example No No 422 8.7 Comparative Example 18 No No í*5 4.2. Table 4 shows the number of repeated welding operations with a weld length of 0.5 m, based on the cumulative number of welds, in which a defect-free joint was obtained with a probability of 90% or higher, while no internal defects were found by observing the joint's cross-sections. As shown in Table 4, in the butt joints of Examples of the Invention 1 to 24 and in the lap joints of Examples of the Invention 25 to 27, the number of welding operations in which a defect-free joint was obtained with a probability of 90% or higher was 13 or more. In the butt joints of Comparative Examples 1 through 3, welding was performed using rotary tools, each probeless and with spirally stepped portions extending clockwise, while the rotation direction of each rotary tool was set to clockwise. In Comparative Examples 1 through 3, the number of welding operations in which a defect-free joint was obtained with a probability of 90% or greater was 0. In the lap joint of Comparative Example 4, welding was performed using rotary tools, each probeless and with stepped, slotted portions extending clockwise, while the rotation direction of each rotary tool was set to clockwise. In Comparative Example 4, the number of welding operations in which a defect-free joint was obtained with a probability of 90% or greater was 0. In the butt joints of Comparative Examples 5 through 9, welding was performed using rotary tools, each with a pin. The number of welding operations in which a defect-free joint was obtained with a probability of 90% or more was 10 or fewer. In the lap joints of Comparative Example 10, welding was performed using rotary tools, each with a pin. The number of welding operations in which a defect-free joint was obtained with a probability of 90% or more was 10 or fewer. As previously described, the use of probeless rotary tools with spiral stepped portions resulted in joint defects or joint strength problems in welds where the spirals of the stepped portions were oriented in the same direction as the rotary tool's rotation. Rotary tools with a pin were found to exhibit poor durability. Table 3 shows that the use of rotary tools having spirally stepped portions increased the weld strength of the joints, based on the results of experiments under the same conditions, except for the presence or absence of the spirally stepped portions, which correspond to pairs of Examples of the Invention, i.e., Examples of the Invention 1 and Lfrenn / zznz / E / Yii 4, Examples of Invention 2 and 5, Examples of Invention 3 and 6, Examples of Invention 19 and 22, Examples of Invention 20 and 23, and Examples of Invention 21 and 24. The results of Examples of the Invention 19 and 22, in which experiments were conducted under conditions not conforming to formula (5), indicate that conditions above the range of formula (5) can affect the attainment of sufficient plastic flow for welding and can result in the appearance of internal defects, even if surface defects are evaluated under the criterion of no. In other words, when each of the rotating tools with a concave surface additionally complies with the conditions of formula (5), the occurrence of both surface and internal defects can be more effectively suppressed to provide a joint with sufficient strength. dc / D < 0.03 Formula (5) The results of Examples of the Invention 20 and 23, in which experiments were conducted under conditions below the lower limit of the range of formula (3), indicate that conditions below the lower limit of the range of formula (3) can affect the achievement of uniform plastic flow in the thickness direction and can result in the appearance of surface or internal defects, although these surface and internal defects are considered acceptable. In other words, when each of the rotary tools with a flat surface additionally meets the conditions of formula (3), the occurrence of surface and internal defects can be more effectively suppressed to provide a joint with sufficient strength. xt < D < 20 xt Formula (3) The results of Examples of the Invention 21 and 24, in which experiments were conducted under conditions that did not comply with formula (4), indicate that conditions above the range of formula (4) can affect the surface shape of the welded portion and can lead to the appearance of surface defects, although both surface and internal defects are considered acceptable. In other words, when each of the rotating tools with a convex surface also complies with the conditions of formula (4), the occurrence of surface and internal defects can be more effectively suppressed to provide a joint with sufficient strength.< / s> < / x> < / j>

Claims

1. A double-sided friction-stirring welding method comprising: butt welding or lap welding between a rear end of a preceding steel strip and a front end of a subsequent steel strip; pressing two rotating tools, arranged on a first and a second surface of a butt or overlap portion of the steel strips, against the butt or overlap portion of the steel strips; and displacing the rotating tools in a welding direction while rotating in opposite directions to each other, such that an unwelded portion of the steel strips is softened by the frictional heat generated between the rotating tools and the unwelded portion of the steel strips, and the softened portion is stirred with the rotating tools to generate a plastic flow for the purpose of welding the steel strips together.Where: each of the two rotating tools has a terminal portion configured to have one of the following shapes: a flat circular surface, a convex curved circular surface, and a concave curved circular surface; and the terminal portions are made of a material harder than steel strips.

2. The double-sided friction-stirring welding method according to claim 1, wherein each of the terminal portions has a spirally stepped portion extending in a direction opposite to a direction of rotation.

3. The double-sided friction-stir welding method according to claim 1 or 2, wherein an inclination angle a (°) in which the rotation axes of the two rotating tools are tilted backward in the welding direction with respect to a normal to a surface of the unwelded portion of the steel strips, a diameter D (mm) of each end portion, and a distance G (mm) between the end portions of the two rotating tools obey the following formula (1) and formula (2): 0 <a<3 (1) 0.25 x t - 0.2 x D x sin a < G < 0.8 x t - 0.2 x D x sin a (2) en donde t representa el espesor (mm) de cada tira de acero para la soldadura a tope de las tiras de acero o el espesor total (mm) de las tiras de acero superpuestas para la soldadura de traslape de las tiras de acero.

4. The double-sided friction-stirring welding method according to any of claims 1 to 3, wherein the diameter D (mm) of each terminal portion obeys the formula (3): 4 xt < D < 20 xt (3) n Lfrenn / zznz / E / Yii wherein t represents the thickness (mm) of each steel strip for butt welding of the steel strips or the total thickness (mm) of the overlapping steel strips for lap welding of the steel strips.

5. The double-sided friction-stirring welding method according to any of claims 1 to 4, wherein, when the height of the convex curved surface of each terminal portion is denoted as dv (mm), the diameter D (mm) of each terminal portion and the height dv of the convex curved surface obey formula (4): dv / D < 0.06 (4).

6. The double-sided friction-stirring welding method according to any of claims 1 to 4, wherein, when the depth of the concave curved surface of each terminal portion is denoted as d (mm), the diameter D (mm) of each terminal portion and the depth of the concave curved surface obey formula (5): dc / D < 0.03 (5).

7. A method for producing a cold-rolled steel strip, wherein said method includes: after the welding process between a rear end of a preceding steel strip and a front end of a subsequent steel strip by using the double-sided friction-stir welding method according to any of claims 1 to 6, carrying out cold rolling or performing cold rolling after pickling.

8. The method for producing a cold-rolled steel strip according to claim 7, further comprising carrying out an annealing process after cold rolling.

9. A method for producing a coated steel strip, wherein said method includes: after the welding process between a rear end of a preceding steel strip and a front end of a subsequent steel strip by using the double-sided friction-stirring welding method according to any of claims 1 to 6, carrying out cold rolling or performing cold rolling after pickling and then carrying out an annealing and coating process.

10. A double-sided friction-stirring welding apparatus comprising: two rotating tools opposed to each other across an unwelded portion of two steel strips; and a control device controlling the operation of the two rotating tools, wherein: the double-sided friction-stirring welding apparatus welds the steel strips together when the two rotating tools are moved in a welding direction while pressing the unwelded portion of the butted or overlapping steel strips and rotating in opposite directions to each other; each of the two rotating tools has a terminal portion configured to have one of the following shapes: a flat circular surface, a convex curved circular surface, and a concave curved circular surface; and the terminal portions are made of a material harder than the steel strips.

11. The double-sided friction-stirring welding apparatus according to claim 10, wherein each of the terminal portions has a spirally stepped portion extending in a direction opposite to a direction of rotation.

12. The double-sided friction-stirring welding apparatus according to claim 10 or 11, wherein the control device carries out the control such that an inclination angle a (°) in which the rotation axes of the two rotating tools are tilted backward in the welding direction with respect to a normal to a surface of the unwelded portion of the steel strips, a diameter D (mm) of each end portion and a distance G (mm) between the end portions of the two rotating tools obey the following formula (1) and formula (2): 0 <a<3 (1) 0.25 x t - 0.2 x D x sin oc < G < 0.8 x t - 0.2 x D x sin a (2) en donde t representa el espesor (mm) de cada tira de acero para la soldadura a tope de las tiras de acero o el espesor total (mm) de las tiras de acero superpuestas para la soldadura de traslape de las tiras de acero.

13. The double-sided friction-stirring welding apparatus according to any of claims 10 to 12, wherein the diameter D (mm) of each terminal portion obeys formula (3): 4 xt < D < 20 xt Formula (3) wherein t represents the thickness (mm) of each steel strip for butt welding of the steel strips or the total thickness (mm) of the overlapping steel strips for lap welding of the steel strips.

14. The double-sided friction-stirring welding apparatus according to any of claims 10 to 13, wherein, when the height of the convex curved surface of each terminal portion is denoted as dv (mm), the diameter D (mm) of each terminal portion and the height dv of the convex curved surface obey formula (4): dv / D < 0.06 (4).

15. The double-sided friction-stirring welding apparatus according to any of claims 10 to 13, wherein, when the depth of the concave curved surface of each terminal portion is denoted as d (mm), the diameter D (mm) of each terminal portion and the depth of the concave curved surface obey formula (5): dc / D < 0.03 (5).

16. An installation for producing a cold-rolled steel strip, wherein said installation comprises: in addition to the double-sided friction-stirring welding apparatus according to any of claims 10 to 15, a cold rolling unit that cold rolls the welded steel strips, or a cold rolling unit that cold rolls the welded steel strips after the pickling process in a pickling unit.

17. The installation for producing a cold-rolled steel strip according to claim 16, further including an annealing unit that allows the cold-rolled steel strips to be annealed.

18. An installation for producing a coated steel strip, wherein said installation comprises: in addition to the double-sided friction-stir welding apparatus according to any of claims 10 to 15, a cold rolling unit that cold rolls the welded steel strips, or a cold rolling unit that cold rolls the welded steel strips after pickling in a pickling unit; an annealing unit that allows the cold-rolled steel strips to be annealed; and a coating unit that coats the annealed steel strips.

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