Patent Publication Number: US-7213437-B2

Title: Bent-forming method

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a bent-forming method for forming a formed member such as a car part, and the like by bending a metal plate, and in particular, to prevention of shape defectives from occurring to the formed member, caused by elastic recovery after removal of the formed member from forming dies. 
   2. Description of the Related Art 
   In recent years, reinforcement as well as reduction in weight of a car body and its parts have been promoted in an attempt to attain objects of mileage improvement, environmental conservation, safety improvement, and so forth, and progress has been made in use of a lighter material, such as a steel sheet of high-tension, an aluminum alloy sheet, and so forth, for press-formed members of a metal sheet, accounting for the majority of constituent parts of the car body, as one of means for achieving the objects. 
   For example,  FIG. 1A  shows a Z-shaped member as a press-formed member, comprising an horizontal flat portion  1 , a inclined flat portion  3  continuing from one end of the horizontal flat portion  1  via a first bend  2 , and having one end thereof, extended downward, and a flange portion  5  coupled to the other end of the inclined flat portion  3  via a second bend  4 , so as to be parallel with the horizontal flat portion  1 , and  FIG. 1B  shows a hat-channel shaped member formed by disposing the Z-shaped members in bilateral symmetry. 
   A problem with press-forming of a metal sheet such as a high-tension steel sheet, and the like is that large elastic recovery (springback) occurs upon removing the metal sheet from a forming die, resulting in deterioration in dimensional accuracy of a formed member. This is shown in  FIG. 2  by taking an example of the hat-channel shaped member. In the figure, a member shape (target shape) of the hat-channel shaped member before removal from the forming die is indicated by dash and double dashed lines while a member shape thereof after removal from the forming die is indicated by solid lines. An angle change defect Δθp (an angle formed between a tangent to a bend-stop face of the first bend, on a side thereof, adjacent to the inclined flat portion, and the inclined flat portion in a target formed shape) occurs to the first bend  2 , and warpage curved outward (a maximum parting distance between the warpage and a line segment interconnecting bend-stop points at respective ends of the inclined flat portion is denoted by δ) occurs to the inclined flat portion  3  subjected to bending by bending-back. The bending by the bending-back refers to a phenomenon where after a sheet has once been formed by bending, a bent portion of the sheet is subjected to forming by bending, in a direction opposite to a direction of an initial forming by bending at the outset (bending-back), and a bent-back portion undergoes springback in the direction of the initial bending at the outset to be thereby deformed. Due to the angle change defect and warpage as described, an opening with an opening distance ΔD (a horizontal distance between the lower end of the inclined flat portion in the formed shape of the hat-channel shaped member after removal from the forming die, and that of the inclined flat portion in the target formed shape) occurs to the respective lower ends of the inclined flat portions  3  of the hat-channel shaped member. In this connection, the respective lower ends of the inclined flat portions of the hat-channel shaped member (the same applied to the Z-shaped member) refer to respective portions thereof, corresponding to an intersection of the inner face of the inclined flat portion, and an extension of the underside face of the flange portion. 
   As methods for preventing shape change defects from occurring to the formed member, there have been proposed, for example, a method of forming a reverse bending radius portion, oriented in a direction opposite from a bending direction for forming, along the ridge of a bend, and a method of providing compression stress in the direction of a sheet thickness at a bend, thereby reducing residual stress. Those methods, however, have problems of providing an originally unavailing shape, requiring special equipment, and so forth. Meanwhile, a forming method for improving shape defects without the problems described have been proposed in U.S. Pat. No. 6,748,788, and the 53rd Plastic Working Joint Conference Proceedings, pp. 251 to 252. As shown in  FIG. 3 , with this method, when a metal sheet P is formed by bending with a bending blade  52  descending toward a forming punch  51 , the metal sheet P is bent in an arch-like shape along a bend forming portion  55  of the forming punch  51 , and as the bending blade  52  further descends, portions of the surface of the metal sheet P, on a protruded side, are butted against an inclined flat forming portion  58  of the bending blade  52 , and an inclined flat forming portion  56  of the forming punch  51 , respectively, whereupon the metal sheet P is formed so as to undergo deformation such that arched parts A 1 , A 2 , having respective protuberances oriented in directions opposite from each other, are formed so as to be coupled with each other, thereby checking the angle change defect Δθp at the first bend  2 , and the warp δ of the inclined flat portion  3  as described with reference to the Z-shaped member, and the hat-channel shaped member. Incidentally, a deformation behavior where the two arched parts A 1 , A 2 , having the respective protuberances oriented in directions opposite from each other, are formed so as to be coupled with each other is referred to as “dancing”. 
   With adoption of the forming method utilizing the dancing described, it has become possible to suppress the angle change defect Δθp occurring to the first bend  2 , and the warpage δ occurring to the inclined flat portion  3  with reference to the Z-shaped member, and the hat-channel shaped member. However, in order to suppress such deformations as described, it has been necessary to form an bent angle θp of the bend forming portion  55  of the forming punch  51  so as to be an obtuse angle, posing therefore a problem that a formed shape is inevitably a particular shape in which the inclined flat portion  3  is inclined to the horizontal flat portion  1 . Furthermore, there has arisen another problem that with reference to an angle θd formed between the inclined flat portion  3 , and the flange portion  5 , an angle change defect Δθd comes to be observed larger as the angle θd becomes closer to a right angle. 
   SUMMARY OF THE INVENTION 
   In view of the problems described as above, the invention has been developed, and it is an object of the invention to provide a bent-forming method enabling bent-forming to be implemented with ease without causing angle change defects and warpage even in the case where an angle formed between the horizontal flat portion, and the inclined flat portion as well as the angle formed between the inclined flat portion, and the flange portion is a right angle when forming the Z-shaped member, and the hat-channel shaped member, having the flange portion, and another object of the invention is to provide forming dies for use in carrying out the bent-forming method. 
   The inventor, et al. have obtained knowledge that it is difficult to form a metal plate into a target shape in one stage when forming the Z-shaped member, and the hat-channel shaped member, however, if a provisional inclined flat portion, which is provisionally formed, and a flange portion coupled to the provisional inclined flat portion are first formed in a first forming step by taking advantage of “dancing” occurring when the provisional inclined flat portion is formed, this enables forming to be implemented, causing neither warpage occurring to the provisional inclined flat portion, nor an angle change defect occurring to an angle θd formed between the provisional inclined flat portion, and the flange portion. Further, it has been found out that when forming a provisional horizontal flat portion coupled to one end of the provisional inclined flat portion in a second forming step, if a provisional bend is formed between the provisional horizontal flat portion, and the provisional inclined flat portion so as to undergo bending back, a member in the target shape can be formed without causing an angle change defect occurring to an angle θp formed between the horizontal flat portion, and the inclined flat portion after forming operation. The invention is developed on the basis of the knowledge described as above. 
   More specifically, a bent-forming method according to the invention is a bent-forming method for bent-forming a metal plate into a Z-shaped member, or a hat-channel shaped member, having a horizontal flat portion, an inclined flat portion with one end thereof, coupled to one end of the horizontal flat portion via a first bend, and a flange portion coupled to the other end of the inclined flat portion, via a second bend comprising a first forming step for bent-forming the metal plate into a provisional formed member having a provisional inclined flat portion with one end thereof, coupled to one end of a provisional horizontal flat portion via a provisional bend, the other end of the provisional inclined flat portion, being coupled to a flange portion via the second bend, and a second forming step for forming the horizontal flat portion, first bend, and inclined flat portion, so as to be continuously coupled with each other, out of the provisional horizontal flat portion, provisional bend, and provisional inclined flat portion of the provisional formed member, respectively. The first forming step forms the provisional inclined flat portion by causing the same to undergo deformation so as to form two arch parts thereof, having respective protuberances oriented in directions opposite from each other between respective provisional inclined flat forming portions of forming die parts in pairs for forming the provisional inclined flat portion when forming the provisional inclined flat portion, and the second forming step bent-forms the provisional horizontal flat portion of the provisional formed member while forming the provisional bend by bending back. 
   The bent-forming method described can be executed with ease preferably by use of the following two forming dies. First, there are prepared a first forming die comprising a first forming die part having a provisional horizontal flat forming portion coupled to a provisional inclined flat forming portion via a provisional bend forming portion, and a flange forming portion coupled to the provisional inclined flat forming portion, and a second forming die part having a provisional inclined flat forming portion for bent-forming the metal sheet in conjunction with the provisional inclined flat forming portion, and the flange forming portion of the first forming die part, respectively, and a flange forming portion, and a second forming die comprising a first forming die part having a horizontal flat forming portion coupled to a inclined flat forming portion via a bend forming portion, and a second forming die part having an inclined flat forming portion for bent-forming the provisional horizontal flat portion of the provisional formed member along the bend forming portion in conjunction with the inclined flat forming portion of the first forming die part. By causing the second forming die part of the first forming die to make relative displacement against the first forming die part of the first forming die in the first forming step, the metal sheet placed on, and held by the provisional horizontal flat forming portion of the first forming die part is bent into an arch-like shape along the provisional bend forming portion of the first forming die part to be formed in such a way as to undergo deformation such that a first arch part, and a second arch part of the metal sheet, having respective protuberances oriented in directions opposite from each other, with protuberance surfaces being butted against the provisional inclined flat forming portion of the second forming die part, and the provisional inclined flat forming portion of the first forming die part, respectively, are coupled with each other, thereby forming the provisional formed member having the provisional inclined flat portion with the one end thereof, coupled to the one end of the provisional horizontal flat portion via the provisional bend, the other end of the provisional inclined flat portion, being coupled to the flange portion via the second bend. 
   Further, in the second forming step, the provisional horizontal flat portion of the provisional formed member is bent-formed by causing the second forming die part of the second forming die to make relative displacement against the first forming die part of the second forming die, and the provisional bend is formed by bending back. 
   An angle θp 1  formed between the provisional horizontal flat forming portion, and the provisional inclined flat forming portion of the first forming die part of the first forming die is preferably rendered to be an obtuse angle, more preferably an angle in a range of about 105 to 150°, thereby enabling dancing to occur to the provisional inclined flat forming portion with ease when forming the provisional inclined flat forming portion. Still further, forming by bending back is preferably executed such that a part of the provisional bend of the provisional formed member overlaps the bend forming portion of the first forming die part of the second forming die by placing the provisional horizontal flat portion of the provisional formed member on the horizontal flat forming portion of the first forming die part of the second forming die after a bend-stop point of the provisional bend of the provisional formed member, on a side thereof, adjacent to the provisional horizontal flat portion is slid outward from a bend-stop point of the bend forming portion of the first forming die part of the second forming die, on a side thereof, adjacent to the horizontal flat forming portion in the second forming step, thereby enabling a target angle to be formed by effectively preventing an angle change defect from occurring at the first bend. 
   Further, in the second forming step, if L is expressed by the following expression (1):
 
 L=ΔW+π×rp   1 ×(180−θ p   1 )/180−π rp   2 /2   (1)
 
where rp 1  is a curvature radius of the provisional bend forming portion of the first forming die part of the first forming die, rp 2  a curvature radius of the bend forming portion of the first forming die part of the second forming die, and ΔW a slippage of the provisional formed member, ΔW is preferably provided so as to satisfy the following expression (2):
 
 L   0 −Δ L≦L≦L   0 +Δ L   (2)
 
where L 0 =π×rp 1 ×(180−θp 1 )/180+0.0435θp 1 −6.253, and ΔL=−9.96×10 −5 ×e k +2.66, k=0.163×(θp 1 −90)
 
   Furthermore, forming dies according to the invention, comprises the first forming die, and the second forming die, suitable for use in carrying out the bent-forming method according to the invention. 
   With the bent-forming method according to the invention, it is possible to concurrently form the provisional inclined flat portion having no warpage occurring thereto by taking advantage of the dancing, and the flange portion forming the target angle with the provisional inclined flat portion, in the first forming step, and it is possible to bent-form the Z-shaped member, and the hat-channel shaped member, as the target, in the second forming step, by preventing an angle change defect from occurring to the angle formed between the horizontal flat portion, and the inclined flat portion. Further, with the use of the forming dies according to the invention, the bent-forming method can be easily executed by use of an ordinary pressing apparatus, resulting therefore in excellent productivity. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic diagram showing a Z-shaped member, and a hat-channel shaped member, in section. 
       FIG. 2  is a schematic diagram illustrating shape change defects occurring to the hat-channel shaped member. 
       FIG. 3  is a schematic diagram illustrating a deformation behavior (dancing) generating a spring-go component. 
       FIG. 4  is a schematic diagram showing a provisional formed member in section, formed in a first forming step. 
       FIG. 5  is a schematic sectional view illustrating a first forming die used in the first forming step. 
       FIG. 6  is a schematic view illustrating a forming state where the dancing has occurred to a provisional inclined flat portion in the first forming step. 
       FIG. 7  is a schematic sectional view illustrating a second forming die used in a second forming step. 
       FIG. 8  is a schematic sectional view illustrating a state where a bending moment has occurred to the Z-shaped member restrained by the second forming die in the second forming step. 
       FIG. 9  is a schematic sectional view showing a principal part of a Z-shaped member, upon completion of forming in the second forming step. 
       FIG. 10  is a graph showing a relationship between θp 1  and curvature ρ of warpage in the cases of steel sheets with various tensile strengths, in the first forming step according to a second embodiment. 
       FIG. 11  is a graph showing a relationship between θp 1  and Δθd in the cases of the steel sheets with various tensile strengths, in the first forming step according to the second embodiment. 
       FIG. 12  is a graph showing a relationship between L and Δθp/Δθ max in the case of rp 2 =5 mm, and θp 1  at 105° in the second forming step according to the second embodiment. 
       FIG. 13  is a graph showing a relationship between L and Δθp/Δθ max in the case of rp 2 =5 mm, and θp 1  at 120° in the second forming step according to the second embodiment. 
       FIG. 14  is a graph showing a relationship between L and Δθp/Δθ max in the case of rp 2 =5 mm, and θp 1  at 135° in the second forming step according to the second embodiment. 
       FIG. 15  is a graph showing a relationship between L and Δθp/Δθ max in the case of rp 2 =5 mm, and θp 1  at 150° in the second forming step according to the second embodiment. 
       FIG. 16  is a graph showing a relationship between L and Δθp/Δθ max in the case of rp 2 =3 mm, and θp 1  at 135° in the second forming step according to the second embodiment. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   A bent-forming method according to the invention is described in detail hereinafter with reference to the accompanying drawings. With a present embodiment of the invention, there will be described bent-forming of a Z-shaped member (refer to  FIG. 1A ) with bent angles θp, θd at a first bend  2 , and a second bend  4 , respectively, being a right angle, in which an angle change defect, and warpage of an inclined flat portion are prone to occur. Since a hat-channel shaped member is formed by coupling the Z-shaped members disposed in bilateral symmetry with each other, the hat-channel shaped member can be regarded as a member similar to the Z-shaped member. 
   When forming the Z-shaped member, a provisional formed member  7  comprising a provisional inclined flat portion  3 A without any warpage, formed continuously from a provisional horizontal flat portion  1 A via a provisional bend  2 A, and a flange portion  5  formed continuously from the provisional inclined flat portion  3 A via a second bend  4  so as to form a bent angle θd as a target is first bent-formed in a first forming step, as shown in  FIG. 4 . Next, in a second forming step, the Z-shaped member (refer to  FIG. 1 ) in the target shape is formed out of the provisional formed member  7 . In  FIG. 4 , an angle formed between the provisional horizontal flat portion  1 A, and the provisional inclined flat portion  3 A of the provisional formed member  7  is shown as θp 1  {an angle (a target angle for forming) formed between a provisional horizontal flat forming part of a first forming die described later on, and a provisional inclined flat forming part of the same}, however, the angle formed therebetween actually becomes an angle θp 1  plus an angle change Δ θp 1 . 
   Now, the first forming die used in the first forming step is described hereinafter. As shown in  FIG. 5 , the first forming die has a first forming die part (forming punch)  17  comprising a provisional horizontal flat forming portion  11  formed continuously from a provisional inclined flat forming portion  13  via a provisional bend forming portion  12 , and a flange forming portion  15  formed continuously from the provisional inclined flat forming portion  13 , and a second forming die part (bending blade)  18  comprising a provisional inclined flat forming portion  13 A for bent-forming a metal sheet P in conjunction with the provisional inclined flat forming portion  13 , and the flange forming portion  15  of the first forming die part  17 , respectively, and a flange forming portion  15 A formed continuously from the provisional inclined flat forming portion  13 A via a bend forming portion  14 A. Further, there is provided a presser member  19  for clamping the metal sheet P placed on the provisional horizontal flat forming portion  11  between the provisional horizontal flat forming portion  11 , and the presser member  19 . In the case of forming the hat-channel shaped member, there is no need for fully securing the metal sheet P to the provisional horizontal flat forming portion  11 , so that the presser member  19  can be omitted. The same applies to a second forming die to be described later on. 
   In the figure, θp 1  denotes a bent angle of the provisional bend forming portion  12  (an angle formed between the provisional horizontal flat forming portion  11 , and the provisional inclined flat forming portion  13 ), rp 1  a curvature radius of the provisional bend forming portion  12 , Hp a height from an intersection part between the provisional inclined flat forming portion  13 , and the flange forming portion  15  to the upper face (sheet-pressing face) of the provisional horizontal flat forming portion  11 , Hf a height from the intersection part to the upper face of the flange forming portion  15 , and rd 1  a curvature radius of the bend forming portion  14 A of the second forming die part  18 . The θp 1  is formed so as to become an obtuse angle preferably in a range of 105 to 150° so as to cause occurrence of “dancing” when forming the provisional inclined flat portion  3 A. 
   Meanwhile, as shown in  FIG. 7 , the second forming die used in the second first forming step has a first forming die part (forming punch)  25  comprising an horizontal flat forming portion  21  formed continuously from an inclined flat forming portion  23  via a bend forming portion  22 , and a second forming die part (bending blade)  26  comprising an inclined flat forming portion  23 A for forming the provisional horizontal flat portion  1 A of the provisional formed member  7  by bending the same along the bend forming portion  22  toward the inclined flat forming portion  23  in conjunction with the inclined flat forming portion  23  of the first forming die part  25 . Further, there is provided a presser member  27  for clamping the provisional horizontal flat portion  1 A of the provisional formed member  7  placed on the horizontal flat forming portion  21  between the horizontal flat forming portion  21 , and the presser member  27 . 
   In the figure, θp 2  denotes a bent angle of the bend forming portion  22  (an angle formed between the horizontal flat forming portion  21 , and the inclined flat forming portion  23 , and in this example, θp 2 =θp=90°), rp 2  a curvature radius of the bend forming portion  22 , ΔW an interval between a bending extremity (bend-stop point) of the provisional bend  2 A of the provisional formed member  7 , on a side thereof, adjacent to the provisional horizontal flat portion  1 A, and a bending extremity (bend-stop point) of the bend forming portion  22  of the first forming die part  25 , on a side thereof, adjacent to the horizontal flat forming portion  21 , in other words, a slippage of the provisional formed member  7 . 
   The first forming step is described hereinafter with reference to  FIG. 5 . First, a metal sheet P, such as a high-tension steel sheet, and so forth, is placed on, and held by the provisional horizontal flat forming portion  11  of the first forming die part  17  of the first forming die, and the second forming die part  18  is caused to descend from the inner dead center, thereby forming the metal sheet P into an arch-like shape by bending the same in a slanting and downward direction along the provisional bend forming portion  12 . At this point in time, a protuberance of an arch part of the metal sheet P is butted against a forming face of the provisional inclined flat forming portion  13 A of the second forming die part  18 . Upon the second forming die part  18  being further lowered, there are formed a first arch part A 1 , and a second arch part A 2  of the metal sheet P, having respective protuberances oriented in directions opposite from each other, with protuberance surfaces being butted against the provisional inclined flat forming portion  13 A of the second forming die part  18 , and the provisional inclined flat forming portion  13  of the first forming die part  17 , respectively, as shown in  FIG. 6 . That is, bent-forming is implemented in such a way as to cause “dancing”. In this case, a form of the dancing can be controlled by properly setting θp 1  (provided θp 1 &gt;90°), Hp, Hf, rp 1 , of the first forming die part  17 , and rd 1  of the second forming die part  18 , so that forming can be implemented so as to have the target angle θd (=90°) without causing warpage occurring to the provisional inclined flat portion  3 A of the provisional formed member  7 , and furthermore, without causing an angle change defect Δθd occurring to the angle θd formed between the provisional inclined flat portion  3 A, and the flange portion  5 . In the figure, symbol Lf denotes a flange length, representing a length from the inner face of the inclined flat portion  3  (or the provisional inclined flat portion  3 A) to the extremity of the flange portion  5 . 
   In  FIG. 6 , reference numerals M 1  to M 5  each denote a bending moment occurring to a formed member when the formed member is restrained with respective forming faces of the first forming die part and the second forming die part by causing the second forming die part  18  to descend down to the bottom dead center, in a state where the dancing is caused to occur. The bending moment M 2  acting in a direction for canceling out the warpage δ occurring to the inclined flat portion of the Z-shaped member occurs to a site opposite to the first arch part A 1 . Meanwhile, M 3 , M 5  occur to sites opposite to the second arch part A 2 , and the flange potion, respectively, and those bending moments are oriented in directions opposite from the orientation of M 4  (a springback component causing the angle change defect Δθd to occur to the second bend) occurring to a site of the Z-shaped member, opposite to the second bend, acting therefore as a spring-go component for canceling out spring-back occurring to the second bend. Accordingly, when the second forming die part  18  is caused to rise to be released, it is possible to obtain the provisional formed member  7  with the second bend  4  formed so as to have the bent angle θd as predetermined without causing the warpage δ to occur to the provisional inclined flat portion  3 A, as shown in  FIG. 4 . 
   Subsequently, in the second forming step, the provisional formed member  7  is formed into the target shape. As shown in  FIG. 7 , the provisional horizontal flat portion  1 A of the provisional formed member  7  is placed on, and held by the horizontal flat forming portion  21  of the first forming die part  25  of the second forming die. At this point in time, the provisional horizontal flat portion  1 A is placed by preferably shifting the same by ΔW such that a part of the provisional bend  2 A overlaps the bend forming portion  22 . Then, upon descending of the second forming die part  26 , the provisional bend  2 A of the provisional formed member  7  is bent back along the inclined flat forming portion  23 A of the second forming die part  26  to be thereby extended. A bending moment (M 2 : a spring-go component) causing elastic recovery to occur toward the first forming die part  25  in a state where the second forming die part  26  is released, as shown in  FIG. 8  (showing a restrained state), occurs to a site subjected to such a bending-back force. In this case, by properly setting rp 2 , and ΔW according to rp 1  of the first forming die part  17  of the first forming die, deformation due to elastic recovery occurring upon release, based on the bending moment (M 1 : the springback component) having occurred to the first bend  2  at the time of restraint cancels out deformation due to elastic recovery occurring upon release, based on the above-described M 2 , so that the angle change defect can be prevented from occurring to the bent angle θp at the first bend  2 . Consequently, it is possible to obtain the Z-shaped member with the respective bent angles θp, θd of the first bend  2 , and the second bend  4 , being 90°, and having no warpage occurring to the inclined flat portion  3 . 
   Herein, referring to  FIG. 9 , there is described ΔW (the slippage of the provisional formed member  7 ) for causing the part of the provisional bend  2 A to overlap the bend forming portion  22 .  FIG. 9  shows a principal part of the Z-shaped member, upon completion of the forming in the second forming step. In the figure, reference numerals P 21 , P 22  denote positions corresponding to the respective bend-stop points of the bend forming portion  22  of the first forming die part  25  of the second forming die, on the sides thereof, adjacent to the horizontal flat forming portion  21 , and the inclined flat forming portion  23 , respectively, while P 11 , P 12  denote positions corresponding to the respective bend-stop points of the provisional bend forming portion  12  of the first forming die part  17  of the first forming die, on the sides thereof, adjacent to the provisional horizontal flat forming portion  11 , and the provisional inclined flat forming portion  13 , respectively. Further, L 1  denotes a length of a portion bent-formed along the provisional bend forming portion  12 , upon completion of the forming in the first forming step (length from P 11  to P 12 ), and L 2  a length of a portion bent-formed along the bend forming portion  22 , upon completion of the forming in the second forming step (length from P 21  to P 22 ). Further, L denotes a length extending from P 22  to P 12 , and is represented by the following expression (1) (θp 1  in units of degree, and rp 1 , rp 2  in units of mm). As is evident from the figure, a precondition under which the part of the provisional bend  2 A is caused to overlap the bend forming portion  22  is ΔW≦L 2 , however, for part of the provisional bend to undergo deformation by bending back, it is necessary to render L&gt;0. After all, in order to control Δθp, the provisional bend  2 A in whole may be subjected to deformation by bending back, so that it is sufficient to set ΔW such that L&gt;0.
 
 L=ΔW+L   1 − L   2 
 
 L   1 =π× rp   1 ×(180−θ p   1 )/180,  L   2 =π× rp   2 /2
 
Therefore
 
 L=ΔW+π×rp   1 ×(180−θ p   1 )/180−π× rp   2 /2  (1)
 
   Further, for forming the Z-shaped member with a small Δθp, it need only be sufficient to set ΔW so as to satisfy the following expression (2). L 0  in expression (3) is an L value obtained by finding values of Δθp when steel sheets of various tensile strengths in a range of 340 to 1470 MPa with ΔW being variously changed against θp 1  in a range of 105 to 150° are bent-formed as described later, and examining a ratio of Δθp to Δθ max (Δθp/Δθ max) where the max. value of Δθp is defined as Δθ max, whereupon the ratio is found at the min. value. Meanwhile, ΔL in expression (4) is in a range of L/2 where Δθp/Δθ max is on the order of 0.5 or less, that is, Δθp is on the order of Δθ max× 1/2  or less. Any of respective coefficients in those expressions is found by regression analysis on the basis of results of bent-forming according to Embodiment 2 of the invention, described later on. Further, as is evident from Embodiment 2, Δθ max has occurred in a range (L&lt;0) where the provisional bend  2 A is not subject to deformation by bending back with any of the steel sheets.
 
 L   0 −Δ L≦L≦L   0 +Δ L   (2)
 
where
 
 L   0 =π× rp   1 ×(180−θ p   1 )/180+0.0435θ p   1 −6.253  (3)
 
Δ L=− 9.96×10 −5   ×e   k +2.66,  k= 0.163×(θ p   1 −90)  (4)
 
   Having described the method for bent-forming the Z-shaped member, according to the invention, as above, it is to be pointed out that the same can be applied to a hat-channel shaped member that is formed by disposing the Z-shaped members in bilateral symmetry. Further, the metal sheet to which the method for bent-forming, according to the invention, is applicable is not limited to the steel sheet, and the method for bent-forming, according to the invention, may be applied to an aluminum alloy sheet as well. Further, a pressing apparatus for use in carrying out the invention is not limited to specific type pressing apparatus, and use can be made of an oil hydraulic press, a mechanical press, an opposed hydraulic press, and so forth. 
   The invention will be described more specifically hereinafter with reference to preferred embodiments of the invention, however, it is our intention that the invention is not to be construed as being limited thereto. 
   [Embodiment 1] 
   There are shown specific examples where Z-shaped members each with respective bent angles θp, θd of bends, at 90°, were bent-formed with the use of high-tension cold-rolled steel sheets (40 mm in width) made of 780 MPa class, and 1180 MPa class materials, 1.2 mm in thickness, respectively, by bent-forming respective parts of the respective steel sheets, in the longitudinal direction. 
   When the first forming step was applied thereto with the use of a first forming die on a dimensional condition of θp 1 =135°, Hp=37 mm, Hf=37 mm, rp 1 =5 mm, and rd 1 =5 mm, dimensional changes having occurred to a provisional formed member  7  were found that Δθp 1  at a provisional bend  2 A was 2.2°, δ at a provisional inclined flat portion  3 A was −0.1 mm, and Δθd at a second bend  4  was 0.5°, in the case of the 780 MPa class material while Δθp 1  was 7°, δ was 0.0 mm, and Δθd was 1.0°, in the case of the 1180 MPa class material. It was confirmed from the above that a steep change occurring to Δθp 1  at the provisional bend  2 A, according to an increase in strength, was observed, however, the provisional formed member  7  was not dependent on a material strength, so that warpage δ at the provisional inclined flat portion  3 A as well as Δθd at the second bend  4  was nearly negligible in magnitude. 
   Next, when the second forming step was applied thereto on a condition of ΔW=4 mm with the use of a second forming die on a dimensional condition of rp 2 =2 mm, it was found that Δθp=−0.5 in the case of the 780 MPa class material, and Δθp=0.6° in the case of the 1180 MPa class material, indicating that Δθp was not dependent on a material strength, and was nearly negligible in magnitude. Further, with the Z-shaped member obtained by the second forming step, it was confirmed that warpage of an inclined flat portion  3 , and Δθd of a second bend  4  were nearly negligible in magnitude similarly to those prior to the application of the second forming step, proving that the second forming step has no effect thereon. 
   [Embodiment 2] 
   Two different Z-shaped members with respective bent angles θp, θd of bends, at 90°, an inclined flat portion 50 mm in length, and a flange length Lf in 16 and 26 mm, respectively, were bent-formed with the use of high-tension cold-rolled steel sheets (40 mm in width) at seven different tensile strength levels, made of 340 MPa, 440 MPa, 590 MPa, 780 Mpa, 980 MPa, 1180 MPa, and 1470 MPa class materials, 1.2 mm in thickness, respectively, by bent-forming respective parts of the respective steel sheets, in the longitudinal direction. 
   The first forming step was applied thereto with the use of a first forming die on a dimensional condition of θp 1  at 5 different degrees of 90°, 105°, 120°, 135°, 150°, Hp=37 mm, Hf=37 mm, rp 1 =5 mm, and rd 1 =5 mm.  FIGS. 10 and 11  show the results of application of the first forming step by way of example. In the figures, the first number in each of data series indicates the tensile strength level (MPa), and the second number the flange portion length Lf (mm). For example, “340−16” indicates the 340 MPa class materials with Lf 16 mm. Further, in  FIG. 10 , the vertical axis represents curvature ρ(ρ=1/R where a radius of curvature is R) of warpage of a provisional inclined flat portion of a provisional formed member, thereby showing magnitude of the warpage. The radius R of the curvature was found by the following procedure. By placing a measurement terminal of a dial gauge at the center in the widthwise direction of the steel sheet, corresponding to a center position between bend-stop points at respective ends of the provisional inclined flat portion  3 A of the provisional formed member, and taking a measurement span (23 mm) in the longitudinal direction of the provisional inclined flat portion, the maximum deflection ΔR within the measurement span was measured, and R was found by the following expression (three square theorem).
 
 R   2 =( R−ΔR ) 2 +(measurement span/2) 2  
 
   Based on those figures, there are observed effects of suppressing the curvature ρ of the warpage, and Δθd when θp 1  was caused to fall in the range of 105 to 150°, equivalent to, or greater than those when use was made of a normal forming die with θp 1  at 90°. Further, it was confirmed that the higher the strength of a high-tension steel sheet of not lower than 590 Mpa class, the more pronounced such effects became. 
   Next, the second forming step using a second forming die on a dimensional condition of rp 2 =5 mm with ΔW being variously set was applied to the provisional formed member obtained by the first forming step described as above.  FIGS. 12 to 15  show examples (Lf=26 mm) of the results of the second forming step. Further,  FIG. 16  shows an example (Lf=26 mm) of the results of the second forming step using a second forming die with rp 2 =3 mm with ΔW being variously set. In the respective figures, the horizontal axis represents L (mm) defined by the above-described expression (1), and respective scopes of intervals in a dotted line indicate scopes of L 0 −ΔL≦L≦L 0 +ΔL shown by the above-described expression (2). Further, the vertical axis represents the ratio Δθp/Δθ max. 
   It is evident from those figures that if ΔW is set such that L falls in a range of L 0 ±ΔL, this will cause Δθp to be reduced by about 50% in comparison with Δθ max, indicating that significant effect of reducing Δθp can be gained.