Patent Publication Number: US-2022212240-A1

Title: Mandrel, Bent Tube, and Method and Apparatus for Producing Bent Tube

Description:
RELATED APPLICATIONS 
     This application is a divisional of U.S. patent application Ser. No. 16/484,531, filed Aug. 8, 2019, which is a National Stage Application under 35 U.S.C. 371 of expired PCT application PCT/JP2018/005920 designating the United States and filed Feb. 20, 2018; which claims the benefit of JP application number 2017-029804 and filed Feb. 21, 2017, each of which are hereby incorporated by reference in their entireties. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a mandrel and a bent tube, and also to a production method and a production apparatus for producing the bent tube. 
     BACKGROUND ART 
     Several methods for producing a bent tube by bending an original tube that is a straight tube made of a metal such as steel, aluminum or aluminum alloy are already known. Among these, rotary draw bending is widely used as a bending process for efficiently producing a bent tube for its fast machining speed, even though large local distortions arise in the bent tube. 
       FIG. 5( a )  and  FIG. 5( b )  are explanatory drawings that schematically and chronologically illustrate the circumstances when producing a bent tube  6  by rotary draw bending. Note that, in the description hereinafter, a case in which the tube is a steel tube is taken as an example. 
     As illustrated in  FIG. 5( a )  and  FIG. 5( b ) , rotary draw bending is performed using a bending die  2 , a cramping die  3 , a wiper  4  and a pressure die  5 . In the rotary draw bending, an axial end portion of an original tube  1  is gripped by the bending die  2  and the cramping die  3 , and the original tube  1  is pressed against the rotating bending die  2  for bending the shell  1  while applying a tensile load in the axial direction of the original tube  1 . 
     The bending die  2  has a groove  2   a  that guides a portion corresponding to inside of bend  1   a  of the original tube  1 . The bending die  2  is disposed so as to be freely rotatable two-dimensionally about a central axis of rotation  2   b.  The cramping die  3  presses an end portion at inside of bend  1   c  of the original tube  1  against the bending die  2  by pressing an end portion at outside of bend lb of the original tube  1 . 
     The cramping die  3  is disposed so as to be freely rotatable two-dimensionally about the central axis of rotation  2   b  together with the bending die  2 . The wiper  4  supports the portion corresponding to inside of bend  1   a  of the original tube  1 . In addition, the pressure die  5  presses the portion corresponding to inside of bend  1   a  of the original tube  1  against the wiper  4  by pressing a portion corresponding to outside of bend  1   d  of the original tube  1 . 
     At the time of machining, tensile strain arises in the original tube  1  mainly in the axial direction. The tensile strain amount of the portion corresponding to outside of bend  1   d  is greater than the tensile strain amount of the portion corresponding to inside of bend  1   a.  Therefore, if the bending conditions such as the bending speed and tensile force are not appropriate, the tensile strain amount of the portion corresponding to outside of bend  1   d  will exceed the rupture limit of the original tube  1 , and consequently the original tube  1  will rupture. When performing rotary draw bending, it is important to reduce the tensile strain amount of the portion corresponding to outside of bend  1   d  as much as possible by appropriately selecting the bending conditions. 
     As means for reducing the tensile strain amount of the portion corresponding to outside of bend  1   d  of the original tube  1 , it has been known to apply a compressive force in the axial direction of the original tube  1  by: 
     (a) pushing the original tube  1  in the axial direction by means of a back booster  7 ; or 
     (b) moving the pressure die  5  in the feeding direction of original tube at a higher speed than the rotational speed of the bending die  2 . 
     For example, post-processing such as tube hydroforming may in some cases be performed on the bent tube  6  that was produced by rotary draw bending. A comparatively large load is continuously applied to the bent tube  6  by tube hydroforming. 
     Even if the original tube  1  does not rupture during the rotary draw bending, the bent tube  6  will rupture if the total amount of the tensile strain amount that is already present in the bent tube  6  due to rotary draw bending and the strain amount that is newly generated by tube hydroforming exceeds the rupture limit. This total amount is not the simple total amount of strain, but rather is a total amount that is based on plasto-mechanical principles. To prevent rupturing of the bent tube  6 , it is effective to reduce the tensile strain amount that is produced in the original tube  1  by the rotary draw bending. 
     Heretofore, there have been many cases in which the bent tube  6  has been produced as an end product by rotary draw bending, or in which a strain amount that is applied to the bent tube  6  by tube hydroforming after rotary draw bending has not been large. 
     Consequently, heretofore, when producing the bent tube  6  by rotary draw bending, attention has been paid to inhibiting as much as possible the flattening of a bending portion  9  under conditions such that the portion corresponding to outside of bend  1   d  of the original tube  1  does not rupture. A mandrel (also referred to as a “core bar” or a “core”)  8  has been used as an effective tool for that purpose. 
     The mandrel  8  includes a shank (handle)  8   a,  a connection mechanism  8   b  such as, for example, a spherical bearing, and a mandrel ball  8   c  supported in a two-dimensionally or three-dimensionally displaceable manner with respect to the shank  8   a  by the connection mechanism  8   b.    
     The mandrel  8  is disposed inside the original tube  1  in a manner such that a gap exists between the mandrel  8  and the original tube  1 . The mandrel  8  shown in  FIG. 5( a )  and  FIG. 5( b )  has two connection mechanisms  8   b  and two mandrel balls  8   c.  The two mandrel balls  8   c  that each have a circular cross section which are disposed at the front end of the shank  8   a  inhibit flattening of the bending portion  9 . 
     Patent Documents 1 to 3 disclose mandrels that are used in rotary draw bending. 
     LIST OF PRIOR ART DOCUMENTS 
     Patent Document 
     Patent Document 1: JP7-290156A 
     Patent Document 2: JP2001-232421A 
     Patent Document 3: JP2006-187785A 
     SUMMARY OF INVENTION 
     Technical Problem 
     In recent years, there is a demand for enhancing the strength and reduce the thickness of the wall of the bent tube  6  to thereby achieve a further reduction in the weight of industrial products that adopt the bent tube  6  as a starting material. In addition, there is a demand for achieving a smaller radius of curvature as well as wall thinning of the wall of the bending portion  9  of the bent tube  6  to thereby achieve a reduction in the size of such industrial products. 
     The present inventors conducted studies and investigations regarding producing the bent tube  6  having the bending portion  9  which has high strength, a small radius of curvature and a thin wall by rotary draw bending. As a result, the present inventors newly discovered that not only does rupturing occur due to a localized thickness reduction at an outside of bend  9   b  of the bending portion  9  as is conventionally known, but also that winkles or buckling also occurs at an inside of bend  9   a. Naturally a ruptured bent tube  6  cannot be used as the starting material of an end product, and the bent tube  6  in which winkles or buckling has occurred can also not be used as the starting material. 
     An objective of the present invention is to produce, by rotary draw bending, a bent tube having a bending portion that has high strength or that has a small radius of curvature with a thin wall in a manner in which ruptures do not occur at an outside of bend of a bending portion and in which winkles and buckling at an inside of bend are each within an allowable range. 
     Solution to Problem 
     The present inventors conducted intensive studies to solve the above problem, and as a result obtained findings A to C described hereunder, and then conducted further studies to thereby complete the present invention. 
     (A) When producing the bent tube  6  by performing rotary draw bending on the original tube  1  using a conventional mandrel ball having a circular cross section, there is a trade-off relation between thickness reduction and flattening of the bending portion  9 . 
     For example, when the arrangement position of the mandrel  8  is advanced toward the bending portion  9  side (the rightward direction in  FIG. 5( a ) ) from a reference position to increase the action of the mandrel  8 , although flattening of the bending portion  9  can be inhibited, rupturing is liable to occur at the outside of bend  9   b  of the bending portion  9 . 
     In contrast, when the arrangement position of the mandrel  8  is drawn back in the leftward direction in  FIG. 5( b )  from the reference position to weaken the action of the mandrel  8 , although the occurrence of rupturing at the outside of bend  9   b  of the bending portion  9  can be inhibited, flattening of the bending portion  9  is noticeable. 
     (B) If a mandrel ball (hereinafter, also referred to as an “asymmetrical mandrel ball”) having a shape in which, in a cross-section orthogonal to the axial direction of the mandrel ball at a central position in the axial direction of the mandrel ball, a dimension from the mandrel ball center to a first position of the mandrel ball located facing a portion corresponding to outermost of bend of a straight tube is smaller by a predetermined amount than a dimension from the mandrel ball center to a second position of the mandrel ball located facing a portion corresponding to innermost of bend of the straight tube is used in place of the conventional mandrel ball  8   c  shown in  FIG. 5( a )  and  FIG. 5( b ) , when performing rotary draw bending, a gap between the mandrel ball and the portion corresponding to outside of bend of the original tube can be made larger than when using the conventional mandrel ball. 
     By this means, flattening of the bending portion and winkles or buckling that occurs on the inside of bend can be inhibited to an allowable level while preventing the occurrence of rupturing on the outside of bend of the bending portion. 
     (C) A bent tube produced using the asymmetrical mandrel ball has high strength and also has both an appropriate flattening ratio and a thickness reduction ratio of a satisfactory level. Therefore, the bent tube can be used as the starting material for a product as it is without being performed a secondary operation such as tube hydroforming, or can be subjected to a secondary operation to thereby produce an end product. 
     The present invention is as enumerated hereunder. 
     (1) A mandrel including: a shank, a connection mechanism being in a spherical contact with the shank so as to be rotatable in an arbitrary direction, and a mandrel ball supported in a two-dimensionally or three-dimensionally displaceable manner with respect to the shank by the connection mechanism; wherein: 
     the mandrel has only one set of a combination of the connection mechanism and the mandrel ball; and 
     in a cross-section orthogonal to an axial direction of the mandrel ball at a central position in the axial direction of the mandrel ball, 
     the mandrel ball has a first position and a second position at which a first straight line that passes through a mandrel ball center meets an outer periphery of the mandrel ball, and 
     a ratio (L 1 /L 2 ) between a dimension L 1  from the mandrel ball center to the first position and a dimension L 2  from the mandrel ball center to the second position is in a range of 0.915 or more to 0.976 or less. 
     (2) The mandrel according to item (1) above, wherein, in the cross-section orthogonal to the axial direction of the mandrel ball at a central position in the axial direction of the mandrel ball, the mandrel ball has a first region surrounded by a second straight line orthogonal to the first straight line and an outer periphery of the mandrel ball which includes the first position, and a second region surrounded by the second straight line and an outer periphery of the mandrel ball which includes the second position. 
     (3) The mandrel according to item (1) or (2) above, wherein, in the cross-section orthogonal to the axial direction of the mandrel ball at a central position in the axial direction of the mandrel ball, the outer periphery of the mandrel ball in the first region and the outer periphery of the mandrel ball in the second region are continuously connected. 
     (4) The mandrel according to item (2) or (3) above, wherein, in the cross-section orthogonal to the axial direction of the mandrel ball at a central position in the axial direction of the mandrel ball, a shape of the outer periphery of the mandrel ball in the second region is semicircular. 
     (5) A method for producing a bent tube having a bending portion that is two-dimensionally bent by performing rotary draw bending on an original tube using: 
     a two-dimensionally rotatable bending die having a groove for guiding a portion corresponding to inside of bend of the original tube that is a straight tube; 
     a cramping die that presses an end portion at outside of bend of the original tube to thereby press an end portion at inside of bend of the original tube against the bending die, the cramping die being two-dimensionally rotatable together with the bending die; 
     a wiper that supports the portion corresponding to inside of bend of the original tube; and 
     a pressure die that presses a portion corresponding to outside of bend of the original tube to thereby press the portion corresponding to inside of bend of the original tube against the wiper; 
     wherein the rotary draw bending is performed by disposing a mandrel according to any one of items (1) to (4) above inside the original tube in a manner such that the first position of the mandrel ball is located facing a portion corresponding to outermost of bend of the original tube and the second position of the mandrel ball is located facing a portion corresponding to innermost of bend of the original tube. 
     (6) The method for producing a bent tube according to item (5) above, wherein the rotary draw bending is performed while applying a compressive force in an axial direction to the original tube. 
     (7) An apparatus for producing a bent tube having a bending portion that is two-dimensionally bent by performing rotary draw bending on an original tube, including: 
     a two-dimensionally rotatable bending die having a groove for guiding a portion corresponding to inside of bend of the original tube that is a straight tube; 
     a cramping die that presses an end portion at outside of bend of the original tube to thereby press an end portion at inside of bend of the original tube against the bending die, the cramping die being two-dimensionally rotatable together with the bending die; 
     a wiper that supports the portion corresponding to inside of bend of the original tube; and 
     a pressure die that presses a portion corresponding to outside of bend of the original tube to thereby press the portion corresponding to inside of bend of the original tube against the wiper; 
     the apparatus further including a mandrel according to any one of items (1) to (4) above that is to be disposed inside the original tube, 
     wherein the mandrel is disposed in a manner such that the first position of the mandrel ball is located facing a portion corresponding to outermost of bend of the straight tube, and the second position of the mandrel ball is located facing a portion corresponding to innermost of bend of the straight tube. 
     (8) The apparatus for producing a bent tube according to item (7) above, including means for applying a compressive force in an axial direction to the original tube on which the rotary draw bending is being performed. 
     (9) A bent tube made of steel that includes a bending portion that is two-dimensionally bent and a straight tube portion, wherein: 
     when a wall thickness of the bending portion is represented by t 1  (mm), a wall thickness of the straight tube portion is represented by t 2  (mm), an outside diameter of the straight tube portion is represented by D 1  (mm), a bending radius of the bending portion is represented by R (mm), and a bending angle of the bending portion is represented by θ (°), 
     t 2 /D 1 : 0.005 to 0.3, 
     t 2 : 0.5 to 30, 
     D 1 : 15 to 700, 
     R: 1D 1  to 6D 1 , 
     θ: 0 to 180, 
     a maximum thickness reduction ratio: 14.5% or less, 
     a maximum flattening ratio: 8.0% or less, and 
     a hardness ratio between straight tube portion and bending portion: 8 to 50%; 
     where, 
     the maximum thickness reduction ratio: a maximum value of {(t 2 -t 1 }×100(%), 
     the maximum flattening ratio: a maximum value of {(maximum value of outside diameter−minimum value of outside diameter)/D 1 } of the bending portion×100(%), and 
     the hardness ratio between straight tube portion and bending portion: {(average value of values obtained by measuring an L cross-section of a center portion of an outside of bend of the bending portion at 5 points under conditions of a 1 mm pitch in a longitudinal direction of the tube with Hv (10 kg))—(average value of values obtained by measuring an L cross-section of the straight tube portion at 5 points under conditions of a 1 mm pitch in the longitudinal direction of the tube with Hv (10 kg))}/(average value of values obtained by measuring the L cross-section of the straight tube portion at 5 points under conditions of a 1 mm pitch in the longitudinal direction of the tube with Hv (10 kg)). 
     Advantageous Effects of Invention 
     According to the present invention, a thin-walled bent tube having a bending portion with high strength or with a small radius of curvature can be produced by cold working by means of rotary draw bending, in which flattening of a cross-section of a bending portion is inhibited to an allowable level and the occurrence of winkles and buckling on an inside of bend are each also inhibited to an allowable level while preventing the occurrence of rupturing on an outside of bend of the bending portion. 
     The bent tube according to the present invention has high strength and also has both an appropriate flattening ratio and a thickness reduction ratio of a satisfactory level. Therefore, the bent tube according to the present invention can thereafter be used as the starting material of a product as it is without being performed a secondary operation such as tube hydroforming, or can be made into an end product by further performing a secondary operation. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1( a )  is a side view illustrating a mandrel according to the present invention, and  FIG. 1( b )  is a cross-sectional view along a line A-A in  FIG. 1( a ) . 
         FIG. 2  is an explanatory drawing illustrating a state at the start of rotary draw bending. 
         FIG. 3  is an explanatory drawing illustrating a state at the end of rotary draw bending. 
         FIG. 4  is a graph showing results relating to thickness reduction ratios. 
         FIG. 5( a )  and  FIG. 5( b )  are explanatory drawings that schematically and chronologically illustrate the circumstances when producing a bent tube by rotary draw bending. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The present invention will now be described. In the following description, a case in which an original tube is a high tensile strength steel tube of 980 MPa-grade, in other words, a tube having a tensile strength in the range of 980 to 1179 MPa, is taken as an example. The present invention is not limited to a high tensile strength steel tube. The present invention is equally applicable to a case where an original tube is a steel tube having a tensile strength of less than 980 MPa, a stainless steel tube, a pure aluminum tube for industrial use, an aluminum alloy tube, a pure titanium tube for industrial use or a titanium alloy tube. 
     1. Mandrel  10  According to the Present Invention 
       FIG. 1( a )  is a side view illustrating a mandrel  10 , and  FIG. 1( b )  is a cross-sectional view along a line A-A in  FIG. 1( a )  that shows a cross-section at a central position in the axial direction of a mandrel ball  16 .  FIG. 2  is an explanatory drawing illustrating a state at the start of rotary draw bending.  FIG. 3  is an explanatory drawing illustrating a state at the end of rotary draw bending. 
     As illustrated in  FIG. 1( a ) , the mandrel  10  includes a shank  14 , a connection mechanism  15  and the mandrel ball  16 . The connection mechanism  15  is provided in the shank  14 . The connection mechanism  15  is rotatably disposed in an arbitrary direction by spherical contact with the shank  14 . 
     The mandrel ball  16  is supported by the connection mechanism  15 . The mandrel ball  16  is disposed in a manner in which the mandrel ball  16  is freely rotatable in two-dimensional or three-dimensional direction with respect to the shank  14  by the connection mechanism  15 . The maximum value of a displacement angle of the mandrel ball  16  with respect to the shank  14  is 40°. The mandrel  10  is disposed inside an original tube  11 , illustrated in  FIG. 2 , in a manner such that a gap exists between the mandrel  10  and the original tube  11 . 
     It suffices that the material of the shank  14 , the connection mechanism  15  and the mandrel ball  16  is a material that is commonly used for a mandrel of this kind, and for example, an alloy tool steel is used. 
     As illustrated in  FIGS. 2 and 3 , when producing a bent tube  13  having a bending portion  12 - 1  by performing rotary draw bending on the original tube  11 , the mandrel  10  is disposed inside the original tube  11  and used for inhibiting flattening of the cross-section of the bending portion  12 - 1 . 
     As illustrated in  FIG. 1( b ) , in a cross-section orthogonal to the axial direction of the mandrel ball  16  at a central position in the axial direction of the mandrel ball  16 , the mandrel ball  16  has a first position  19  and a second position  20  at which a first straight line m that passes through a mandrel ball center  17  which matches a shank center  14  a meets an outer periphery  21  of the mandrel ball. 
     A ratio (L 1 /L 2 ) between a dimension L 1  from the mandrel ball center  17  to the first position  19  and a dimension L 2  from the mandrel ball center  17  to the second position  20  is within a range of 0.915 to 0.976, and preferably is within a range of 0.915 to 0.953. In other words, the dimension L 1  is smaller than the dimension L 2  by an amount equivalent to a percentage within the range of 2.4 to 8.5%, and preferably a percentage within the range of 4.7 to 8.5%. Thus, the mandrel ball  16  is an asymmetrical mandrel ball. 
     Because the mandrel ball  16  is an asymmetrical mandrel ball, a gap between the mandrel ball  16  and a portion corresponding to outside of bend  11   d  of the original tube  11  can be enlarged in comparison to the conventional configuration. By this means, while preventing the occurrence of rupturing of an outside of bend  12   b  of the bending portion  12 - 1  of the bent tube  13 , flattening of the cross-section of the bending portion  12 - 1  as well as the occurrence of winkles or buckling at an inside of bend  12   a  can each be inhibited to an allowable level. 
     As illustrated in  FIG. 1( b ) , in a cross-section orthogonal to the axial direction of the mandrel ball  16  at a central position in the axial direction of the mandrel ball  16 , the mandrel ball  16  has a first region  22  surrounded by a second straight line n that is orthogonal to the first straight line m, and the outer periphery  21  of the mandrel ball which includes the first position  19 . In addition, the mandrel ball  16  has a second region  23  surrounded by the second straight line n and the outer periphery  21  of the mandrel ball which includes the second position  20 . In  FIG. 1( b ) , the first region  22  is denoted by hatching that slopes in the right-upward direction, and the second region  23  is denoted by hatching that slopes in the right-downward direction. 
     As illustrated in  FIG. 1( b ) , it is preferable that the outer periphery  21  of the mandrel ball in the first region  22  and the outer periphery  21  of the mandrel ball in the second region  23  are smoothly connected continuously in order to inhibit deformation of the bent tube  13 . However, the present invention is not limited thereto. 
     It suffices that the shape of the outer periphery  21  of the mandrel ball in the first region  22  is a shape that can make a gap between the mandrel ball  16  and the portion corresponding to outside of bend  11   d  of the original tube  11  larger than a gap between the mandrel ball  16  and a portion corresponding to inside of bend  11   a  of the original tube  11 . Therefore, for example, it is also acceptable for a step height or a concave to exist at a meeting position between the outer periphery  21  of the mandrel ball in the first region  22  and the outer periphery  21  of the mandrel ball in the second region  23 . 
     Further, in the cross-section orthogonal to the axial direction of the mandrel ball  16  at a central position in the axial direction of the mandrel ball  16 , it is not necessary for the outer periphery  21  of the mandrel ball in the first region  22  to be a curve having a constant curvature. 
     It is preferable that, when the outside diameter of the original tube  11  is represented by D 1  (mm), if within the range of a small diameter tube (025.4 to 0114.3), a dimension L 3  in the axial direction of the mandrel ball  16  is within the range of 0.3 D 1  to 0.5 D 1 . 
     Further, if within the range of a small diameter tube (025.4 to 0114.3), it is preferable that a distance L 4  in the mandrel axial direction from the position of the most frontward end portion of the mandrel ball  16  to a reference position that is described later is in the range of 0.5 D 1  to 0.7 D 1  in order to inhibit flattening of the cross-section of the bending portion  12 - 1  as well as the occurrence of winkles or buckling on the inside of bend  12   a  to an allowable level, respectively, while preventing the occurrence of ruptures in the outside of bend  12   b  of the bending portion  12 - 1 . 
     As illustrated in  FIG. 1( b ) , it is preferable that, in a cross-section orthogonal to the axial direction of the mandrel ball  16  at a central position in the axial direction of the mandrel ball  16 , the shape of the outer periphery  21  of the mandrel ball of the second region  23  is for example, semicircular, since the shape follows the inner surface shape of the inside of bend  12   a  of the bent tube  13 . 
     In  FIG. 2 , the mandrel  10  is disposed so that the first position  19  of the mandrel ball  16  is located facing a portion corresponding to outermost of bend  11   e  of the original tube  11 , and the second position  20  of the mandrel ball  16  is located facing a portion corresponding to innermost of bend  11   f  of the straight tube  11 . However, the present invention is not limited to this configuration. 
     Specifically, in the case of the cross-section illustrated in  FIG. 1( b ) , that is, in a case where the size of a central angle of the mandrel ball center  17  in a cross-section orthogonal to the axial direction of the mandrel ball  16  at a central position in the axial direction of the mandrel ball  16  is taken as 0°, the effect of the present invention is obtained even if the mandrel  10  is disposed in a manner in which the aforementioned central angle is shifted within a range of ±30°, preferably a range of ±15°, relative to the straight tube  11 . 
     The structure of the mandrel  10  other than the structure described above may be the same as a structure that is commonly used in a mandrel of this kind, and because such a structure is well-known to persons having ordinary skill in the art, a description thereof is omitted herein. 
     2. Production Apparatus  30  According to the Present Invention 
     As illustrated in  FIGS. 2 and 3 , a production apparatus  30  is an apparatus that subjects the original tube  11  to rotary draw bending to produce the bent tube  13  having the bending portion  12 - 1  that is two-dimensionally bent. 
     When the tensile strength of the original tube  11  is 980 MPa or more, the effect of the present invention appears more markedly. The reason is that, when the tensile strength of the original tube  11  is 980 MPa or more, flattening of the cross-section of the bending portion  12 - 1 , rupturing in the outside of bend  12   b  of the bending portion  12 - 1 , and the occurrence of winkles or buckling in the inside of bend  12   a  during bending are marked. 
     Similarly to the conventional production apparatus illustrated in  FIG. 5( a )  and  FIG. 5( b ) , the production apparatus  30  includes a bending die  31 , a cramping die  32 , a wiper  33  and a pressure die  34 . The bending die  31  has a groove  31   a.  The groove  31   a  guides a portion corresponding to inside of bend  11   a  of the original tube  11 . The bending die  31  is disposed so as to be two-dimensionally rotatable about a central axis of rotation  31   b.    
     The cramping die  32  presses an end portion at outside of bend  11   b  of the original tube  11  to thereby press an end portion at inside of bend  11   c  of the original tube  11  against the bending die  31 . The cramping die  32  is disposed so as to be two-dimensionally rotatable about the central axis of rotation  31   b  together with the bending die  31 . 
     The wiper  33  supports the portion corresponding to inside of bend  11   a  of the original tube  11 . Further, the pressure die  34  presses the portion corresponding to outside of bend  11   d  of the original tube  11  to thereby press the portion corresponding to inside of bend  11   a  of the original tube  11  against the wiper  33 . 
     The production apparatus  30  further includes the mandrel  10 . The mandrel  10  is disposed inside the original tube  11  in a manner such that a gap exists between the mandrel  10  and the original tube  11 . 
     The mandrel  10  is disposed at a reference position inside the original tube  11  in a manner such that the first position  19  of the mandrel ball  16  is located facing the portion corresponding to outermost of bend  11   e  of the original tube  11 , and the second position  20  of the mandrel ball  16  is located facing the portion corresponding to innermost of bend  11   f  of the original tube  11 . 
     Here, the term “reference position” refers to a position at which, in a rotary plane of the bending die  31  at the start of rotary draw bending illustrated in  FIG. 2 , in relation to the feeding direction of the original tube  11 , a rounded end at which a straight-line portion and a front-end rounded portion of the shank  14  meet matches the central axis of rotation  31   b  of the bending die  31 . 
     The production apparatus  30  may be configured to apply a compressive force in the axial direction of the original tube  11  during bending by being equipped with a back booster  35  that pushes the original tube  11  in the axial direction, or by moving the pressure die  34  in the feeding direction of original tube at a higher speed than the rotational speed of the bending die  31 . 
     3. Production Method According to the Present Invention 
     The production method according to the present invention is performed using the production apparatus  30 . According to the production method of the present invention, the bent tube  13  having the bending portion  12 - 1  that is two-dimensionally bent is produced by performing rotary draw bending on the straight tube  11  using the bending die  31 , the cramping die  32 , the wiper  33 , the pressure die  34  and the mandrel  10  that are described above. 
     At the start of production of the bent tube  13  illustrated in  FIG. 2 , the mandrel  10  is disposed at the reference position inside the original tube  11  in a manner such that the first position  19  of the mandrel ball  16  is located facing the portion corresponding to outermost of bend  11   e  of the original tube  11 , and the second position  20  of the mandrel ball  16  is located facing the portion corresponding to innermost of bend  11   f  of the original tube  11 . 
     Therefore, during bending, a gap between the mandrel ball  16  and the portion corresponding to outermost of bend  11   e  of the original tube  11  can be enlarged in comparison to the conventional configuration. By this means, while preventing the occurrence of rupturing of the outside of bend  12   b  of the bending portion  12 - 1  of the bent tube  13 , flattening of the cross-section of the bending portion  12 - 1  as well as the occurrence of winkles or buckling at the inside of bend  12   a  can each be inhibited to within an allowable range. 
     The dimension L 3  in the axial direction of the mandrel ball  16  is preferably within the range of L 3 =0.3 D 1  to 0.5 D 1 , and the distance L 4  in the mandrel ball axial direction between the most frontward end portion of the mandrel ball  16  and the reference position is preferably within the range of L 4 =0.5 D 1  to 0.7 D 1 . 
     In addition, during bending, a compressive force may be applied in the axial direction to the original tube  11  by pressing the original tube  11  in the axial direction by means of the back booster  35 , or by moving the pressure die  34  in the feeding direction of original tube at a higher speed than the rotational speed of the bending die  31 . 
     4. Bent Tube According to the Present Invention 
     The bent tube  13  that is produced by means of the aforementioned production method and production apparatus according to the present invention has at least one bending portion  12 - 1  that is two-dimensionally bent. The tensile strength in the longitudinal direction of the tube at a straight tube portion is preferably 980 MPa or more, and further preferably is within a range of 980 to 1179 MPa. 
     When a wall thickness of the bending portion  12 - 1  of the bent tube  13  is represented by t 1  (mm), a wall thickness of the straight tube portion  12 - 2  that is other than the bending portion  12 - 1  is represented by t 2  (mm), the outside diameter is represented by D 1  (mm), a bending radius of the bending portion  12 - 1  is represented by R (mm), and a bending angle of the bending portion  12 - 1  is represented by θ(°), the bent tube  13  also has the characteristics enumerated hereunder.
     (4-1) t 2 /D 1 : 0.005 to 0.3   (4-2) t 2 : 0.5 to 30   (4-3) D 1 : 15 to 700   (4-4) R: 1 D 1  to 6 D 1      (4-5) θ: 0° to 180°   (4-6) Maximum thickness reduction ratio: 14.5% or less   

     The maximum thickness reduction ratio is determined as the maximum value of {(t 2 −t 1 )/t 2 }×100 (%).
     (4-7) Maximum flattening ratio: 8.0% or less   

     The maximum flattening ratio is determined as the maximum value of {(maximum value of outside diameter−minimum value of outside diameter)/D 1 }×100 (%) of the bending portion  12 - 1 .
     (4-8) Hardness ratio between straight tube portion and bending portion: 8 to 50%   

     The hardness ratio between straight tube portion and bending portion is determined as {(average value of values obtained by measuring an L cross-section of a center portion of an outside of bend  12   b  of a bending portion  12 - 1  at 5 points under conditions of a 1 mm pitch in a longitudinal direction of the tube with Hv (10 kg))—(average value of values obtained by measuring an L cross-section of a straight tube portion  12 - 2  at 5 points under conditions of a 1 mm pitch in a longitudinal direction of the tube with Hv (10 kg))}/(average value of values obtained by measuring an L cross-section of a straight tube portion  12 - 2  at 5 points under conditions of a 1 mm pitch in a longitudinal direction of the tube with Hv (10 kg)). 
     Thus, the bent tube  13  has a combination of these characteristics, and in particular has a combination of high strength, and an appropriate flattening ratio and a thickness reduction ratio of a satisfactory level. Therefore, the bent tube  13  can be used as the starting material for a product as it is without being performed a secondary operation such as tube hydroforming, or can be subjected to a secondary operation to thereby produce an end product. 
     EXAMPLES 
     A rotary draw bending apparatus in which a conventional mandrel  8  illustrated in  FIG. 5( a )  and  FIG. 5( b )  was disposed at the reference position (conventional example 1), a rotary draw bending apparatus in which a conventional ball-type mandrel  8  illustrated in  FIG. 5( a )  and  FIG. 5( b )  was disposed at a position that was drawn back from the reference position (conventional example 2), and a rotary draw bending apparatus that used the mandrel  10  according to the present invention illustrated in  FIGS. 1 to 3  (example embodiments 1 to 3 of the present invention) were used, respectively, to produce bent tubes  13  and  6  illustrated in  FIGS. 3 and 5 ( b ) under the following conditions with regard to the original tubes  1  and  11 . That is, the conditions were: tensile strength of the original tubes  1  and  11 : 980 MPa; wall thickness t 2  of straight tube portion  12 - 2 : 1.0 mm; outside diameter D 1  of straight tube portion  12 - 2 : 38.1 mm; bending radius R of bending portions  12 - 1  and  9 : 76.2 mm; and bending angle of bending portions  12 - 1  and  9 : 90°. The thus produced bent tubes  13  and  6  were analyzed by FE simulation, and the maximum flattening ratio, maximum thickness reduction ratio and hardness ratio between straight tube portion and bending portion of the bending portions  12 - 1  and  9  were determined by the aforementioned method. 
     In Table 1, a case where the maximum flattening ratio is 8.0% or less and the maximum thickness reduction ratio is 14.5% or less is evaluated as “satisfactory”. 
     The results regarding the thickness reduction ratio are shown in a graph in  FIG. 4 , and the results regarding the maximum flattening ratio and the maximum thickness reduction ratio are shown in Table 1. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                 Straight 
                 Straight 
                   
                   
                   
                   
                   
                 Hardness Ratio 
                   
               
               
                   
                 Bending 
                 Tube 
                 Tube 
                 Bending 
                 Bending 
                   
                   
                   
                 Between 
               
               
                   
                 Portion 
                 Portion 
                 Portion 
                 Portion 
                 Portion 
                   
                   
                 Maximum 
                 Straight 
               
               
                   
                 Wall 
                 Wall 
                 Outside 
                 Bending 
                 Bending 
                   
                 Maximum 
                 Thickness 
                 Tube Portion 
               
               
                   
                 Thickness 
                 Thickness 
                 Diameter 
                 Radius 
                 Angle θ 
                 Ratio 
                 Flattening 
                 Reduction 
                 And Bending 
               
               
                 Classification 
                 t 1  (mm) 
                 t 2  (mm) 
                 D 1  (mm) 
                 R (mm) 
                 (°) 
                 (L 1 /L 2 ) 
                 Ratio (%) 
                 Ratio (%) 
                 Portion 
                 Evaluation 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Conventional 
                 0.833 
                 1.0 
                 38.1 
                 76.2 
                 90 
                 1.0 
                 8.9 
                 16.7 
                 17% 
                 Maximum 
               
               
                 Example 1 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Thickness 
               
               
                 (Reference 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Reduction 
               
               
                 Position) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Ratio 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Excessive 
               
               
                 Conventional 
                 0.862 
                 1.0 
                 38.1 
                 76.2 
                 90 
                 1.0 
                 14.8 
                 13.8 
                 14% 
                 Maximum 
               
               
                 Example 2 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Flattening 
               
               
                 (Mandrel at a 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Ratio 
               
               
                 Drawn-back 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Excessive 
               
               
                 Position) 
               
               
                 Example 
                 0.861 
                 1.0 
                 38.1 
                 76.2 
                 90 
                 0.953 
                 7.5 
                 13.9 
                 14% 
                 Satisfactory 
               
               
                 Embodiment 1 of 
               
               
                 Present Invention 
               
               
                 Example 
                 0.863 
                 1.0 
                 38.1 
                 76.2 
                 90 
                 0.918 
                 7.9 
                 13.7 
                 13% 
                 Satisfactory 
               
               
                 Embodiment 2 of 
               
               
                 Present Invention 
               
               
                 Example 
                 0.857 
                 1.0 
                 38.1 
                 76.2 
                 90 
                 0.976 
                 7.7 
                 14.3 
                 14% 
                 Satisfactory 
               
               
                 Embodiment 3 of 
               
               
                 Present Invention 
               
               
                   
               
            
           
         
       
     
     In the conventional example 1, because the maximum thickness reduction ratio during rotary draw bending is large, even if cracks do not occur during rotary draw bending, for example, if a secondary operation such as tube hydroforming is performed after rotary draw bending, there is a risk that cracks will occur in the bent tube. 
     The conventional example 2 is a known method that reduces the maximum thickness reduction ratio in rotary draw bending. Although the conventional example 2 is certainly capable of reducing the maximum thickness reduction ratio, the maximum flattening ratio worsens and the obtained bent tube cannot be used as a product unless a secondary operation such as hydroforming is performed on the obtained bent tube. 
     In contrast, in example embodiments 1 to 3 of the present invention, the maximum flattening ratio was 7.5 to 7.9% and the maximum thickness reduction ratio was 13.7 to 14.3%, and prevention of an increase in the maximum thickness reduction and prevention of a deterioration in the maximum flattening ratio could both be achieved at a high level in a compatible manner. 
     The bent tube  13  of each of the example embodiments 1 to 3 of the present invention had a high strength, an appropriate flattening ratio and a thickness reduction ratio of a satisfactory level. Therefore, the bent tube  13  can be used as the starting material for a product as it is without being performed a secondary operation such as tube hydroforming, or can be further subjected to a secondary operation to be made into an end product. 
     REFERENCE SIGNS LIST 
     
         
           1  Original Tube 
           1   a  Portion corresponding to inside of bend 
           1   b  End portion at outside of bend 
           1   c  End portion at inside of bend 
           1   d  Portion corresponding to outside of bend 
           2  Bending Die 
           2   a  Groove 
           2   b  Central Axis Of Rotation 
           3  Cramping Die 
           4  Wiper 
           5  Pressure Die 
           6  Bent tube 
           7  Back Booster 
           8  Mandrel 
           8   a  Shank 
           8   b  Connection Mechanism 
           8   c  Mandrel Ball 
           9  Bending portion 
           9   a  Inside of bend 
           9   b  Outside of bend 
           10  Mandrel According To Present Invention 
           11  Original Tube 
           11   a  Portion corresponding to inside of bend 
           11   b  End portion at outside of bend 
           11   c  End portion at inside of bend 
           11   d  Portion corresponding to outside of bend 
           11   e  Portion corresponding to outermost of bend 
           11   f  Portion corresponding to innermost of bend 
           12   a  Inside of bend 
           12   b  Outside of bend 
           13  Bent tube 
           14  Shank 
           14   a  Shank Center 
           15  Connection Mechanism _p 0   16  Mandrel Ball 
           17  Mandrel Ball Center 
           19  First Position 
           20  Second Position 
           21  Outer Periphery Of Mandrel Ball 
           22  First Region 
           23  Second Region 
           30  Production Apparatus 
           31  Bending Die 
           31   a  Groove 
           31   b  Central Axis Of Rotation 
           32  Cramping Die 
           33  Wiper 
           34  Pressure Die 
           35  Back Booster 
         m First Straight Line 
         n Second Straight Line