[0001](Cross-reference to related application) This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2019-054469, filed in Japan on March 22, 2019, the entire contents of which are incorporated herein by reference. [0002] The present invention relates to a manufacturing apparatus and a 10 manufacturing method of a coil by winding a hot-rolled steel sheet with a mandrel in a hot-rolling process. [Background Art] [0003] The hot-rolled steel sheet after finish rolling in the hot-rolling process is cooled to a predetermined temperature by a cooling device while 15 being conveyed by a run-out table from a finishing mill to a coiler and then wound up in the coiler (mandrel) to be manufactured as a coil (hot-rolled coil). [0004] The coils manufactured as described above are once wound at a predetermined winding temperature and then conveyed to a coil yard, where 20 they are cooled to room temperature and then shipped to users or conveyed to a next process. At this time, flatness of the hot-rolled steel sheet may be poor when the coil to be shipped or conveyed to the next process is unwound for processing. In such a case, it is necessary to correct a shape of the hot-rolled steel sheet because it meanders due to poor sheet-passing ability, 25 and problems such as squeezing occur during processing and rolling. However, since the shape (flatness) of the hot-rolled steel sheet is not known 2 in a state of the coil, coils with a flatness specification that cannot be shipped with poor flatness are conveyed to a precise process for correction, regardless of whether the shape is good or bad, which is costly. Therefore, the flatness of the hot-rolled steel sheet in the wound state as a coil is required to be 5 within a standard value in advance to convey only the hot-rolled steel sheet with a bad shape to the precise process. It is important to develop a technology to reduce the sheet passages to correct the shape in the precise process, especially in conventional mills, mini-mills, and thin-slab processes that are targeted for hot finalization. 10 [0005] For example, Patent Document 1 discloses a method for predicting a shape of a hot-rolled steel sheet by separating residual stress in the hot-rolled steel sheet (metal sheet) into a stress component that is converted into a waveform during buckling and a stress component that remains in the hot-rolled steel sheet after buckling and using the stress 15 component that is converted into the waveform. In this shape prediction method, the waveform of the hot-rolled steel sheet generated after finish-rolling is corrected by, for example, tension acting on the hot-rolled steel sheet when it is wound on the coiler so that the residual stress is ultimately generated by temperature distribution in a width direction of the 20 hot-rolled steel sheet at the time of winding. Furthermore, based on the predicted shape, the flatness of the hot-rolled steel sheet is improved by controlling the temperature distribution in the width direction using, for example, an edge heater or edge mask. [Prior Art Document] 25 [Patent Document] [0006] [Patent Document 1] Japanese Patent No. 4262142 3 [Disclosure of the Invention] [Problems to Be Solved by the Invention] [0007] However, when the inventors investigated the shape of the steel sheet after the hot-rolling process in detail, they found that there was 5 deterioration in flatness that could not be clarified simply by predicting the shape using the residual stress (elongation-strain difference) caused by the temperature distribution of the hot-rolled steel sheet, as disclosed in Patent Document 1. It was also found that the flatness of the hot-rolled steel sheet could not be sufficiently improved simply by controlling the temperature 10 distribution in the width direction based on the shape prediction result. Therefore, there is room for improvement in improving the flatness of the hot-rolled steel sheet. [0008] The present invention has been made because of the above problems, and an object thereof is to improve flatness of a hot-rolled steel 15 sheet in a coil when the coil is manufactured by winding the hot-rolled steel sheet with a mandrel in a hot-rolling process. [Means for Solving the Problems] [0009] To solve the above-mentioned problems, the inventors made keen investigations and clarified a mechanism of the flatness deterioration of the 20 hot-rolled steel sheet after the hot-rolling process, and found that the flatness deterioration was concretely caused by a combination of two factors: a temperature factor and a tight winding factor. The first temperature factor is thermal strain caused by non-uniform temperature distribution in the width direction of the hot-rolled steel sheet just before it is wound on the coiler 25 (mandrel), and this thermal strain becomes the elongation-strain difference (residual strain). The second tight winding factor is that the tension acting 4 on the hot-rolled steel sheet when it is wound on the coiler (mandrel) is distributed non-uniformly in the width direction due to a crown generated in the hot-rolled steel sheet after finishing rolling, for example, and the tight winding under the non-uniform tension distribution causes plastic 5 deformation of an inner peripheral portion of the coil, resulting in plastic strain, and this plastic strain becomes the elongation-strain difference (residual strain). [0010] Of the two factors, the first factor, the temperature factor, has been considered as the factor for deteriorating flatness in the past, and 10 countermeasures have been taken such as, for example, the shape prediction method disclosed in Patent Document 1 above. On the other hand, the second factor, the tight winding factor, was newly discovered by the inventors, who found that deformation caused by tight winding in a cold-rolling process also occurs in the hot-rolling process. 15 [0011] As a result of keen investigation regarding the flatness deterioration due to the tight winding factor, the inventors found that compressive stress acting on the mandrel of the coiler was also distributed non-uniformly in the width direction due to the non-uniform tension distribution acting on the hot-rolled steel sheet at an inner peripheral portion 20 of the coil, and a diameter reduction amount of the mandrel became non-uniform in the width direction. Concretely, the diameter reduction amount at a center portion of the mandrel in the width direction is large and becomes small at an end portion in the width direction. Then, the hot-rolled steel sheet wound on the deformed mandrel has a peripheral length difference 25 in the width direction, and the flatness of the hot-rolled steel sheet deteriorates. 5 [0012] The present invention is made based on such knowledge and is an apparatus for winding a hot-rolled steel sheet with a mandrel in a hot-rolling process to produce a coil, wherein the mandrel has a protruding shape with a center portion in an axial direction protruding from both end portions when 5 seen from a lateral side in the axial direction. [0013] When the hot-rolled steel sheet is wound on the mandrel as described above, even if a diameter reduction amount of the mandrel becomes non-uniform in a width direction, the mandrel can be made uniform in diameter in the width direction after the tight winding because the mandrel is 10 made to protrude in the present invention in advance in anticipation of this non-uniform diameter reduction amount. Therefore, it is possible to improve the flatness of the hot-rolled steel sheet by suppressing a peripheral length difference in the width direction in the hot-rolled steel sheet wound on the mandrel. 15 [0014] In the manufacturing apparatus of the hot-rolled coil, regarding a peripheral length difference, which is a difference between a peripheral length of the center portion and a peripheral length at a predetermined distance from the center portion, the ratio of the peripheral length difference to the peripheral length of the center portion may be 0.0002 to 0.012. The ratio of 20 the peripheral length difference to the peripheral length of the center portion may be 0.002 to 0.008. [0015] In the manufacturing apparatus of the hot-rolled coil, the protruding shape may be a trapezoidal shape or a polynomial function shape. [0016] Furthermore, the present invention according to another aspect is 25 a manufacturing method of a hot-rolled coil using the above-mentioned manufacturing apparatus, characterized in that a hot-rolled steel sheet that is 6 non-transformed or undergoing transformation, or after completion of transformation and is at a temperature of 700°C or higher is wound with the above-mentioned mandrel to manufacture the coil. [Effect of the Invention] 5 [0017] According to the present invention, since the mandrel is made to protrude in advance in anticipation of the non-uniform diameter reduction amount in the width direction of the mandrel due to the tight winding factor, the mandrel after tight winding can be made uniform in diameter in the width direction. Therefore, it is possible to suppress the peripheral length 10 difference in the width direction in the hot-rolled steel sheet wound on the mandrel and improve the flatness of the hot-rolled steel sheet. [Brief Description of the Drawings] [0018] [FIG. 1] is an explanatory diagram illustrating an outline of a configuration of a finishing mill and beyond in a hot-rolling facility. 15 [FIG. 2] is an explanatory diagram illustrating an outline of a configuration of a coiler. [FIG. 3] is an explanatory diagram illustrating an outline of a configuration of a mandrel when seen from a cross-section in an axial direction. 20 [FIG. 4] is an explanatory diagram illustrating the outline of the configuration of the mandrel when seen from a cross-section in a direction orthogonal to an axis. [FIG. 5] is an explanatory diagram illustrating a definition of steepness representing a degree of an ear wave. 25 [FIG. 6] is a conceptual diagram explaining a mechanism of flatness deterioration due to a tight winding factor. 7 [FIG. 7] is a conceptual diagram explaining the mechanism of the flatness deterioration due to the tight winding factor, where (a) illustrates compressive stress (zero) acting on an end portion in a width direction of the mandrel, (b) illustrates compressive stress (arrows in the drawing) acting 5 between the end portion and a center portion in the width direction, and (c) illustrates compressive stress (arrows in the drawing) acting on the center portion in the width direction [FIG. 8] is an explanatory diagram illustrating deformation of a mandrel segment due to the compressive stress. 10 [FIG. 9] is an explanatory diagram illustrating the deformation of the mandrel due to the compressive stress. [FIG. 10] is an explanatory diagram illustrating an outline of a configuration of the mandrel according to the embodiment. [FIG. 11] is an explanatory diagram illustrating a protruding shape of 15 the mandrel according to the embodiment. [FIG. 12] is a graphic chart illustrating steepness of a medium wave of a hot-rolled steel sheet against a peripheral length difference ratio. [FIG. 13] is a graphic chart illustrating steepness of an ear wave of the hot-rolled steel sheet against the peripheral length difference ratio. 20 [Embodiments for Carrying out the Invention] [0019] Embodiments of the present invention will be described below with reference to the drawings. In this specification and the drawings, duplicate explanations are omitted by appending the same code to elements that have substantially the same functional configuration. 25 [0020] First, a configuration of a hot-rolling facility according to the present 8 invention will be explained. FIG. 1 is an explanatory diagram illustrating an outline of a configuration of a finishing mill 2 and beyond in a hot-rolling facility 1. [0021] In the hot-rolling facility 1, the finishing mill 2 which 5 continuously rolls a steel sheet H discharged from a heating furnace (not illustrated) and rolled by a roughing mill (not illustrated) to a predetermined thickness, a cooling device 3 which cools the steel sheet H after finish rolling (hereinafter, referred to as a hot-rolled steel sheet H) to a predetermined temperature, and a coiler 4 which winds up the cooled hot-rolled steel sheet H 10 are provided in this order in a conveyance direction of the hot-rolled steel sheet H. A run-out table 5 is provided between the finishing mill 2 and the coiler 4 to convey the hot-rolled steel sheet H. The hot-rolled steel sheet H rolled by the finishing mill 2 is cooled by the cooling device 3 while being conveyed on the run-out table 5, and then wound by the coiler 4 to be 15 manufactured as a coil C. [0022] Between the finishing mill 2 and the cooling device 3 of the hot-rolling facility 1, a sheet-thickness gauge 6 is provided to measure a sheet thickness of the hot-rolled steel sheet H rolled by the finishing mill 2. The sheet-thickness gauge 6 can measure sheet thickness distribution in a width 20 direction of the hot-rolled steel sheet H and measure a crown of the hot-rolled steel sheet H. [0023] FIG. 2 is an explanatory diagram illustrating an outline of a configuration of the coiler 4. An example in FIG. 2 illustrates a state of start of winding operation at the coiler 4. The coiler 4 has a pinch roll 10, a chute 25 11, a mandrel 12, and wrapper rolls 13. [0024] In the coiler 4, the hot-rolled steel sheet H is bent by the pinch roll 9 10 in a direction of the mandrel 12 and passes through the chute 11. Here, the wrapper rolls 13 are closed (in contact with the mandrel 12) and stand by while rotating at a speed several percent faster than a steel sheet speed of each other before a tip of the hot-rolled steel sheet H reaches the mandrel 12. 5 When the hot-rolled steel sheet H reaches the mandrel 12 and the wrapper rolls 13, the mandrel 12 and the wrapper rolls 13 sandwich and wind the hot-rolled steel sheet H. The mandrel 12 can expand and contract its diameter by a cylinder portion 24 as described below and starts expanding when the hot-rolled steel sheet H is wound on the coil C by the predetermined 10 number of windings and stops expanding its diameter when a force of expansion is balanced with a force of tightening the coil C, and the wrapper rolls 13 open and move away from coil C. [0025] FIG. 3 and FIG. 4 are each an explanatory diagram illustrating an outline of a configuration of the mandrel 12. As illustrated in FIG. 3, the 15 mandrel 12 is of a segment type and has mandrel segments 20, wedges 21, a slide rod 22, and a wedge shaft 23. Of these components, the slide rod 22 and the wedge shaft 23 constitute the cylinder portion 24. By sliding the wedges 21 by the cylinder portion 24, the mandrel segment 20 slides in a radial direction in expanding or contracting direction along a gradient on the 20 wedge shaft 23. [0026] As illustrated in FIG. 4, the mandrel 12 has a gap A between a segment flange portion 25 and a wedge jaw portion 26 and has a mechanism that the mandrel 12 expands due to the gap A eliminated by a centrifugal force when the mandrel 12 rotates. A segment-wedge portion 27 has a set of 25 mandrel segment 20 and wedge 21, and the mandrel 12 is constituted by four sets of segment-wedge portions 27. 10 [0027] The above is the mechanism of the flatness deterioration of the hot-rolled steel sheet, and the inventors found that the flatness deterioration is caused by the combination of the temperature factor and the tight winding factor. As described above, the flatness deterioration due to the temperature 15 factor has been known in the past, and countermeasures have been taken. Concretely, it is possible to improve the flatness of the hot-rolled steel sheet by controlling the temperature distribution in the width direction to be uniform using, for example, an edge heater installed prior to the finishing mill or an edge mask installed in the cooling device. Therefore, the present 20 invention improves the flatness of the hot-rolled steel sheet, which is worsened by the tight winding factor. [0039] As mentioned above, the peripheral length difference in the width direction is generated at the mandrel due to the tight winding factor. Therefore, the inventors decided to reduce the peripheral length difference 25 caused by the tight winding factor by giving the mandrel a protruding profile in advance. By reducing the peripheral length difference of the mandrel in 16 this way, the flatness of the hot-rolled steel sheet can be improved at the inner peripheral portion of the coil wound on the mandrel. Concretely, by making the mandrel protrude, a medium wave is intentionally generated at the center portion in the width direction of the hot-rolled steel sheet, thereby improving 5 an ear wave and increasing the flatness of the hot-rolled steel sheet. The inner peripheral portion of the coil is a range of 200 m from a tip of the hot-rolled steel sheet, where the flatness of the hot-rolled steel sheet has deteriorated in the past. In actual operation, experience has shown that the shape of the hot-rolled steel sheet wound on the coil becomes flat in the range 10 of 200 m or further from the tip. This is probably because tension is generated at the hot-rolled steel sheet when the tip of the hot-rolled steel sheet reaches the mandrel, and the shape is corrected. [0040] FIG. 10 is an explanatory diagram illustrating an outline of a configuration of the mandrel of this embodiment. The mandrel has a 15 protruding shape with the center portion in the width direction protruding than both end portions when seen from a lateral side in an axial direction. FIG. 10 also illustrates parameters: a reference radius rc; an evaluation radius re; and a radius difference Δr, which determine a profile of this protruding shape. The reference radius rc is the radius at the center portion in the width direction 20 (reference position). The evaluation radius re is the radius at a position 500 mm from the center portion (evaluation position). The radius difference Δr is the difference between the reference radius rc and the evaluation radius re (Δr = rc - re). In an example illustrated in FIG. 10, the protruding shape is a trapezoidal shape, and when seen from the lateral side, a surface is flat up to 25 250 mm from the center portion, and the diameter contracts from the 250 mm position to the end portion. In the present invention, a position at a 17 predetermined distance from the center portion, that is the evaluation position, is 500 mm from the center portion. [0041] As illustrated in FIG. 11, the protruding shape is not limited to the trapezoidal shape but can be, for example, a quadratic function shape, a cubic 5 function shape, or a quartic function shape. A horizontal axis in FIG. 11 represents a position from the center portion in the width direction. A vertical axis represents a ratio of a difference (r - re) between a radius r and the evaluation radius re at a predetermined position from the center portion in the width direction to the radius difference Δr. Concretely, it is a 10 dimensionless radius difference calculated by (r - re)/Δr. [0042] In determining the concrete profile of this protruding shape, the inventors conducted an experiment. In this experiment, a flat hot-rolled steel sheet with a sheet thickness of 3 mm and a sheet width of 1200 mm without a crown was wound in a coiled state by a mandrel. The tension at the time of 15 winding was set at 20 MP and the number of windings was set at 100. The protruding shape of the mandrel was set to a trapezoidal shape, and steepness of the hot-rolled steel sheet at a representative point was measured by varying the peripheral length difference ratio, Δr/rc, within a range of 0.0002 < Δr/rc < 0.08. The mandrel peripheral length difference ratio is calculated by 20 dividing the difference between the peripheral length at the reference position (center portion in the width direction) and the peripheral length at the evaluation position (500 mm position) by the peripheral length at the reference position; concretely, it is calculated by Δr/rc because the peripheral length and radius are proportional. The mandrel peripheral length difference 25 ratio can also be said to be a ratio of the elongation-strain difference of the hot-rolled steel sheet. 18 [0043] FIG. 12 is a graphic chart illustrating steepness of a medium wave of the hot-rolled steel sheet against the peripheral length difference ratio. A horizontal axis in FIG. 12 represents the peripheral length difference ratio. A vertical axis represents the steepness of the medium wave generated in the 5 hot-rolled steel sheet at an innermost periphery of the coil. It can be seen that as the peripheral length difference ratio changes from 0.0002 to 0.08, the steepness of the medium wave increases from 0.8% to 16%. Therefore, increasing the peripheral length difference ratio of the mandrel can increase the medium wave generated in the hot-rolled steel sheet, and as a result, the 10 ear wave can be improved and the flatness of the hot-rolled steel sheet can be improved. [0044] FIG. 13 is a graphic chart illustrating steepness of the ear wave of hot-rolled steel sheet against the peripheral length difference ratio. A horizontal axis in FIG. 13 represents the peripheral length difference ratio. A 15 vertical axis represents the steepness of the ear wave generated in the hot-rolled steel sheet at the innermost periphery of the coil. When the peripheral length difference ratio is 0 (zero), as in the conventional case, the steepness of the ear wave generated in the hot-rolled steel sheet is 3%, based on past results. FIG. 13 also indicates that the steepness of the ear wave is 20 3% when the peripheral length difference ratio is 0 (zero). On the other hand, the steepness at which the hot-rolled steel sheet can be said to be sufficiently flattened as a product is 2% or less. Therefore, a peripheral length ratio difference Δr/rc should be 0.0002 < Δr/rc < 0.012 (shaded area in the drawing), according to the graphic chart in FIG. 13 to keep the steepness 25 in a range of -2% to 2%. The peripheral length difference ratio of 0.0002 corresponds to 2% ear wave steepness, and the peripheral length difference 19 ratio of 0.012 corresponds to -2% ear wave steepness. [0045] Besides, for example, the peripheral length ratio difference Δr/rc may be 0.001 < Δr/rc < 0.010 to make the steepness in the range of -1.8% to 1.8% from the graphic chart in FIG. 13, from the viewpoint that the hot-rolled 5 steel sheet should be flatter as a product. More preferably, Δr/rc may be 0.002 < Δr/rc < 0.008 to make the steepness in the range of -1.5% to 1.5%. [0046] Furthermore, the inventors have verified that the protruding shape is not limited to the trapezoidal shape as in this experiment, but other quadratic function shapes, cubic function shapes, and even quartic function 10 shapes can enjoy the same effect as above if the peripheral length ratio difference Δr/rc is set to 0.0002 < Δr/rc < 0.012. [0047] As mentioned above, in addition to the tight winding factor, there is also the temperature factor that contributes to the flatness deterioration. In this experiment, it is assumed that the flatness deterioration due to this 15 temperature factor has been improved by using, for example, the edge heater or edge mask. [0048] As described above, if the mandrel has the protruding shape, the flatness of the hot-rolled steel sheet can be improved, and if the peripheral length ratio difference Δr/rc is set to 0.0002 < Δr/rc < 0.012, the flatness of the 20 hot-rolled steel sheet can be further improved within the range of -2% to 2%. The flatness can be improved to a level where the coil does not need to be conveyed to a precise process for shape correction. As a result, a manufacturing cost can be lowered, and a manufacturing period can be stably shortened. Besides, defects that occur on a surface of the hot-rolled steel 25 sheet in the precise process can be suppressed, and an yield of the product can be improved. 20 [0049] The flatness improvement method according to the present invention described above is particularly useful when the hot-rolled steel sheet to be wound with the mandrel is non-transformed or undergoing transformation. 5 For example, if the hot-rolled steel sheet is wound after the transformation is completed, the shape of the hot-rolled steel sheet does not deteriorate more than when it is wound. On the other hand, if the hot-rolled steel sheet to be wound on the mandrel is non-transformed or undergoing transformation, the hot-rolled steel sheet may be further deformed. In this respect, if the 10 mandrel is made to protrude in advance as in the present invention, the flatness of the hot-rolled steel sheet can be improved even if the hot-rolled steel sheet is non-transformed or undergoing transformation. [0050] For example, when the hot-rolled steel sheet is wound at a high temperature of 700°C or higher after the transformation is completed, the 15 hot-rolled steel sheet may be deformed due to a creep phenomenon. Therefore, the flatness improvement method of the present invention is also useful in cases where the creep phenomenon occurs during such high-temperature winding. [0051] Dimensions of the hot-rolled steel sheet to which the flatness 20 improvement method of the present invention is applied are not particularly limited, but it is useful, for example, for the hot-rolled steel sheet with a sheet thickness of 1.4 mm to 6.0 mm and a sheet width of 600 mm to 1800 mm. [0052] The embodiments of the present invention have been described above, but the present invention is not limited to such examples. It should 25 be understood that various changes and modifications are readily apparent to those skilled in the art to which the present invention belongs within the scope 21 of the technical idea as set forth in claims, and those should also be covered by the technical scope of the present invention. [Industrial Applicability] [0053] The present invention is useful when a hot-rolled steel sheet is 5 wound by a mandrel in a hot-rolling process to manufacture a coil. [Explanation of Codes] [0054] 1 ... hot-rolling facility 2 ... finishing mill 3 ... cooling device 10 4 ... coiler 5 ... run-out table 6 ... sheet-thickness gauge 10 ... pinch roll 11 ... chute 15 12 ... mandrel 13 ... wrapper roll 20 ... mandrel segment 21 ... wedge 22 ... slide rod 20 23 ... wedge shaft 24 ... cylinder portion 25 ... segment flange portion 26 ... wedge jaw portion 27 ... segment-wedge portion 25 C ... coil H ... hot-rolled steel sheet WE CLAIMS A manufacturing apparatus of a hot-rolled coil which manufactures a coil by winding a hot-rolled steel sheet with a mandrel in a hot-rolling process, wherein 5 the mandrel has a protruding shape with a center portion in an axial direction protruding from both end portions when seen from a lateral side in the axial direction. [Claim 2] The manufacturing apparatus of the hot-rolled coil according to claim 1, wherein 10 regarding a peripheral length difference, which is a difference between a peripheral length of the center portion and a peripheral length at a predetermined distance from the center portion, the ratio of the peripheral length difference to the peripheral length of the center portion is 0.0002 to 0.012. 15 [Claim 3] The manufacturing apparatus of the hot-rolled coil according to claim 2, wherein the ratio of the peripheral length difference to the peripheral length of the center portion is 0.002 to 0.008. [Claim 4] The manufacturing apparatus of the hot-rolled coil according 20 to any one of claims 1 to 3, wherein the protruding shape is a trapezoidal shape or a polynomial function shape. [Claim 5] A manufacturing method of a hot-rolled coil, which uses the manufacturing apparatus according to any one of claims 1 to 4, comprising: 25 winding a hot-rolled steel sheet, which is non-transformed or undergoing transformation, or after the completion of transformation and is at 23 a temperature of 700°C or higher, with a mandrel to manufacture a coil.