Abstract:
For forming a tubular work into a shaped hollow product by using hydroforming process, a method and a device are described. In the method, female and male dies are prepared. The female die has a longitudinally extending cavity which has a polygonal cross section when receiving the male die. The tubular work is placed into the cavity of the female die. The interior of the tubular work is then fed with a hydraulic fluid, and the pressure of the fluid is increased to a given level. The given level is smaller than a critical level that causes a bulging of the tubular work. The male die is then pressed against the tubular work to deform the same while keeping the hydraulic fluid at the given level, thereby forming a shaped hollow product that has a polygonal cross section that conforms to that of the cavity. The pressing work is continued until a circumferential length of the shaped hollow product becomes shorter than that of the tubular work.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates in general to tubular hydroforming and more particularly to method and device for forming a tubular work into a shaped hollow product by using hydroforming process. More specifically, the present invention relates to method and device for producing an automotive hollow part, such as front pillar, center pillar, roof rail or the like, by using tubular hydroforming process. 
     2. Description of the Prior Art 
     Tubular hydroforming process is a novel process that has recently gained much attention due to its cost-effective application particularly in the automotive industry. As is known, the tubular hydroforming is of a process that includes major steps wherein ends of a tubular work in a net shape die unit are sealed and a hydraulic fluid is pumped in the tubular work and pressurized to deform cross-sections of the work to conform to a cross section of the net shape die. Usually, before the major steps, a pre-forming is made wherein for obtaining a pre-defined shape of the tube that closely resembles the final component (viz., hollow product), a die closing is gradually carried out while receiving a relatively low hydraulic fluid in the work. While, in a so-called bulging process in the tubular hydroforming, axial feed is provided along the longitudinal axis of the tubular work in the net shape die while receiving the hydraulic fluid in the work. When employing this bulging process, a tube wall thinning during the hydroforming process can be reduced. 
     However, due to the nature of deformation of the material of the tubular work during the hydroforming process, it has been difficult to provide a hydroformed hollow product that gives users satisfaction. In fact, in the pre-forming step, even when aluminum and/or high strength steel tube is used as the tubular work, a crack tends to appear at a portion that has been subjected to a wall thinning during the expansion of the work. Furthermore, in the pre-forming step, a corner portion remote from the center of the work is particularly attacked by such wall thinning. In the bulging process, wall thickening throughout the length of the tubular work is readily made, however wall thickening at a specified or needed portion, such as a corner portion or the like, is not readily made, and thus, reduction in weight of the hydroformed hollow product has not been satisfactorily achieved particularly in the field of automotive industry. 
     SUMMARY OF THE INVENTION 
     It is therefore an object of the present invention to provide a method for forming a tubular work into a shaped hollow product by using hydroforming process, which method is free of the above-mentioned drawbacks. 
     It is further an object of the present invention to provide a hydroforming device which is suitable for practically carrying out the method of the present invention. 
     It is further an object of the present invention to provide a hydroforming method by which a specified or needed portion of a shaped hollow product can be exclusively thickened. 
     According to the present invention, there is provided a method for forming a tubular work into a shaped hollow product by using hydroforming process. In the method, female and male dies are prepared. The female die has a longitudinally extending cavity which has a polygonal cross section when receiving the male die. The tubular work is placed into the cavity of the female die. The interior of the tubular work is then fed with a hydraulic fluid, and the pressure of the fluid is increased to a given level. The given level is smaller than a critical level that causes a bulging of the tubular work. The male die is then pressed against the tubular work to deform the same while keeping the hydraulic fluid at the given level, thereby forming a shaped hollow product that has a polygonal cross section that conforms to that of the cavity. The pressing work is continued until a circumferential length of the shaped hollow product becomes shorter than that of the tubular work. 
     According to the present invention, there is further provided a hydroforming device for forming a tubular work into a shaped hollow product by using a hydroforming process. The device comprises a fixed female die having a longitudinally extending cavity, the cavity being sized to receive therein the tubular work; a male die having a work surface, the male die being movably received in the female die in such a manner that the work surface of the male die faces the cavity to cause the cavity to be enclosed and have a polygonal cross section; at least one projection formed on a lateral end of the work surface, the projection having a sloped surface angled relative to the work surface and an actuator which actuates the male die to press against the tubular work. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a longitudinally sectional view of a hydroforming device used for practically carrying out a method of a first embodiment of the present invention; 
     FIG. 2 is a view similar to FIG. 1, but showing a different or pressing condition of the device; 
     FIG. 3 is a perspective view of the hydroforming device for carrying out the method of the first embodiment; 
     FIG. 4 is a schematically illustrated laterally sectional view of the hydroforming device of FIG. 3; 
     FIG. 5 is a sectional view of a shaped hollow product provided by the method of the first embodiment; 
     FIG. 6 is a schematic illustration showing a test for examining a mechanical strength of the shaped hollow product; 
     FIG. 7 is a graph showing the results of the test; 
     FIG. 8 is a graph showing results of other test; 
     FIG. 9 is a schematically illustrated female die used in a hydroforming device which is used for carrying out a method of a second embodiment of the present invention; 
     FIG. 10 is a partial sectional view of a female die used in a hydroforming device which is used for carrying out a method of a third embodiment of the present invention; 
     FIG. 11 is a graph showing results of a test for finding a desired angle of an extra slanted wall possessed by the female die of FIG. 10; 
     FIG. 12 is a longitudinally sectional view of a hydroforming device used for carrying out a method of a fourth embodiment of the present invention; 
     FIG. 13 is a view similar to FIG. 12, but showing a different or pressing condition of the device; 
     FIG. 14 is a sectional view of a shaped hollow produced provided by the method of the fourth embodiment; 
     FIG. 15 is a laterally sectional view of a hydroforming device used for carrying out a method of a fifth embodiment of the present invention; 
     FIG. 16 is a graph showing results of a test for examining the thickness increasing rate relative to male die pressing stroke; 
     FIG. 17 is a laterally sectional view of a hydroforming device used for carrying out a method of a sixth embodiment of the present invention; 
     FIG. 18 is a laterally sectional view of a hydroforming device used for carrying out a method of a seventh embodiment of the present invention; 
     FIG. 19 is a laterally sectional view of a hydroforming device used for carrying out a method of an eighth embodiment of the present invention; 
     FIG. 20 is a laterally sectional view of a hydroforming device used for carrying out a method of a ninth embodiment of the present invention; 
     FIG. 21 is a sectional view of a shaped hollow product provided by the method of the ninth embodiment; 
     FIG. 22 is a laterally sectional view of a hydroforming device used for carrying out a method of a tenth embodiment of the present invention; 
     FIG. 23 is a sectional view of a shaped hollow product provided by the method of the tenth embodiment; 
     FIG. 24 is a laterally sectional view of a reference hydroforming device which was used for proving improvement achieved by the tenth embodiment of the invention; 
     FIG. 25 is a sectional view of a shaped hollow product provided by the device of FIG. 24; 
     FIG. 26 is a laterally sectional view of a hydroforming device used for carrying out a method of an eleventh embodiment of the present invention; 
     FIG. 27 is a sectional view of a shaped hollow product provided by the method of the eleventh embodiment; 
     FIG. 28 is an enlarged sectional view of one of four corner portions of the shaped hollow product shown in FIG. 27; 
     FIG. 29 is a graph showing results of a measurement for measuring the thickness of various positions of the corner portion; 
     FIG. 30 is a laterally sectional view of a hydroforming device used for carrying out a method of a twelfth embodiment of the present invention; 
     FIG. 31 is an enlarged view of a part of the device of FIG. 30, showing a pressing condition of the device; 
     FIG. 32 is a sectional view of a shaped hollow product provided by the method of the twelfth embodiment; 
     FIG. 33 is an enlarged sectional view of one of four projected round corner portions of the product of FIG. 32; 
     FIG. 34 is a laterally sectional view of a reference hydroforming device which was used for proving improvement achieved by the method of the twelfth embodiment; 
     FIG. 35 is an enlarged view of a part of the device of FIG. 34, showing a pressing condition of the device; 
     FIG. 36 is a graph showing results of a measurement for measuring the thickness of various portions of the projected round corner portion of the product of FIG. 32; and 
     FIG. 37 is a perspective view of an automotive body and frame construction having front pillars, center pillars, side roof rails and the like which can be provided by tubular hydroforming process. 
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     In the following, the present invention will be described in detail with reference to the drawings. 
     For ease of understanding, directional terms, such as upper, lower, right, left, vertical, horizontal, upward, downward, and the like are used in the description. However, it is to be noted that such terms are to be understood with respect to only a drawing or drawings on which the corresponding parts or structures are illustrated. 
     Referring to FIGS. 1 to  8 , particularly FIGS. 1 to  4 , there is shown a hydroforming device  1  with which a method of a first embodiment of the present invention is practically carried out. 
     As will become apparent as the description proceeds, the explanation will be made with respect to a process for producing an automotive side roof rail S (see FIG. 37) as an example of the final component or a shaped hollow product. 
     As is seen from FIGS. 1 to  4 , the hydroforming device  1  comprises generally a female die  2  which has a cavity  2   a  formed therein, two sealing tools  3  which seal both open ends of a tubular work W, two supporting members  4  which stably support both end portions of the tubular work W while having a major portion of the tubular work W put in the cavity  2   a  of the female die  2 , two feeding tubes  5  which feed and draw a hydraulic fluid into and from an interior Wa of the tubular work W whose ends are sealed by the sealing tools  3  and a male die  6  which presses the tubular work W in the cavity  2   a  of the female die  2 . During pressing of the tubular work W by the male die  6 , the interior Wa of the work W is kept filled with the hydraulic fluid of pressure P. For pressing the male die  6  against the work W, a ram R extending from a hydraulic actuator is connected to the male die  6 . 
     As is seen from FIG. 4, the cavity  2   a  of the female die  2  is defined by two mutually facing vertical walls  2   b , a bottom wall  2   c  and two slanted walls  2   d  each extending between the bottom wall  2   c  and the vertical wall  2   b . The male die  6  is arranged to move upward and downward in the cavity  2   a  of the female die  2 . The male die  6  comprises a work pressing main surface  6   a  and two projected side surfaces  6   b  which are located at lateral ends of the main surface  6   a . As shown, each projected side surface  6   b  is generally perpendicular to the vertical wall  2   b  of the female die  2 . 
     For producing the automotive side roof rail S from the tubular work W by using the above-mentioned hydroforming device  1 , the following steps were carried out. 
     First, the tubular work W was set in the cavity  2   a  of the female die  2  and held stably by the supporting members  4 . The tubular work W had a wall thickness of about 2.2 mm. More specifically, the work W was made of a steel of 370 MPa type, that is, a carbon steel tube of STKM11A specified by JIS (Japanese Industrial Standard) G 3445. Then, the sealing tools  3  were put into the open ends of the tubular work W to seal the same. Then, a hydraulic fluid was led into the interior Wa of the work W through the feeding tubes  5  and the interior of the work W was kept at a given pressure P that was 50 MPa. The pressure P was kept lower than a value that would induce expansion of the work W. 
     Then, as is seen from FIGS. 1 and 2 with the interior pressure P kept at 50 MPa, the male die  6  was lowered into the cavity  2   a  of the female die  2  to press the tubular work W at the work pressing main surface  6   a . With these steps, the automotive side roof rail S was produced, which had a depressed hexagonal cross section as is understood from FIG.  5 . 
     As is seen from FIG. 5, the depressed hexagonal cross section of the side roof rail S thus produced had a circumferential length that was smaller than that of the tubular work W. While, the thickness of the produced side roof rail S became greater than that of a corresponding portion of the tubular work W except a bottom wall Sc of the rail S and its neighboring portion. That is, as is seen from FIG. 5, by applying the hydroforming process of the invention to the work W, the thickness of each vertical wall Sb of the rail S increased by about 9%, the thickness of each corner portion Se defined between the vertical wall Sb and a horizontal upper wall Sa increased by over 25% and even each rounded portion Sf defined between the vertical wall Sb and the slanted wall Sd showed a little increase in thickness. 
     In addition to the above, by using the above-mentioned hydroforming device  1 , substantially identical hydroforming process was applied to a tubular work which was made of a steel of 590 MPa type and had a wall thickness of about 2.0 mm. Also, in this case, each rounded portion Sf defined between the vertical wall Sb and the slanted wall Sd showed a certain increase in thickness. This fact has revealed that even a tube of less malleable steel can be used as the work for the hydroforming process of the present invention. 
     For examining a mechanical strength of the side roof rail S thus produced, a test was carried out. That is, as is seen from FIG. 6, an elongate test piece S′ was cut from the rail S, and two I-type steel blocks  7  were welded to respective ends of the test piece S′ to provide an elongate test piece unit. The elongate test piece unit was put on two holders  8  which were spaced by 500 mm. Then, a center of the test piece unit was pressed down by a rounded pusher  9  of R 50 . That is, a load applied to the center of the test piece unit was gradually increased by the rounded head of the pusher  9 . 
     FIG. 7 is a graph showing the results of the test in terms of a relation between the load applied by the rounded pusher  9  and a stroke of the pusher  9 . For comparison, similar test was applied to a reference test piece which showed no increase in thickness. As is seen from this graph, the test piece S′ produced in accordance with the present invention exhibited the maximum flexural rigidity (viz., about 4200 Kgf) that is greater than that (viz., about 2600 Kgf) of the reference test piece by about 64%. Other tests revealed that as is seen from the graph of FIG. 8, when the thickness of the vertical walls Sb increased by over 3%, the mechanical strength showed a satisfied value. 
     Referring to FIG. 9, there is schematically shown a female die  22  employed in a hydroforming device  21  with which a method of a second embodiment of the present invention is carried out. 
     As is seen from the drawing, the female die  22  is formed with an axially extending stepped portion  22   g  between each vertical wall  22   b  and the adjacent slanted wall  22   d . Preferably, the size of the stepped portion  22   g  is smaller than the thickness of the tubular work W and greater than one tenth (viz., {fraction (1/10)}) of the thickness of the work W. Denoted by numeral  22   a  is a cavity defined by the female die  22 . Several tests have revealed that the presence of such stepped portions  22   g  lessens the possibility of producing undesired buckling of the tubular work W during the forming process. Furthermore, the tests have revealed that the presence of the stepped portions  22   g  assuredly reduces the stroke length of the male die. 
     Referring to FIGS. 10 and 11, particularly FIG. 10, there is shown but partially and in a sectional manner a female die  32  employed in a hydroforming device  31  with which a method of a third embodiment of the present invention is carried out. 
     As is seen from FIG. 10, in this female die  32 , there is formed, between each vertical wall  32   b  and the corresponding slanted wall  32   d , with an extra slanted wall  32   g  that defines an angle “θ” relative to the vertical wall  32   b . Preferably, the angle “θ” is within a range from 0 to 45°. Denoted by numeral  32   a  is a cavity defined by the female die  32 . Tests have revealed that due to presence of such extra slanted walls  32   g , the friction inevitably produced between the wall of the female die  32  and the male die  6  can be reduced and the pressing load applied by the male die  6  is evenly transmitted to the entire construction of the work W. 
     For finding a desired value of the angle “θ” in case wherein the hydroforming process reduces the circumferential length of the tubular work W by 3%, a test was carried out. In this test, many tubular works were subjected to the hydroforming process by using many female dies  32  that had different values of the angle “θ”, and the rate of increase in thickness of the vertical wall Sb of each product (viz., side rail roof S) was measured. 
     The result of this test is depicted in FIG.  11 . As is see from this graph, when the angle “θ” exceeded about 50°, the rate of increase in thickness of the vertical wall Sb of the product S became lower than 3%. 
     Referring to FIGS. 12 and 13, there is schematically shown a hydroforming device  41  with which a method of a fourth embodiment of the present invention is carried out. This forming device  41  is designed to make a hydroformed product SA having a rectangular cross section, as shown in FIG.  14 . 
     In this fourth embodiment, two male dies  46  are employed, which are arranged to move toward and away from each other in a cavity  42   a  formed in a female die  42 . Two sealing tools  3 , two supporting members  4  and two feeding tubes  5  are arranged in substantially the same manner as in the case of the above-mentioned first embodiment  1  of FIGS. 1 and 2. 
     For producing the product SA, a tubular work W was prepared. The tubular work W was the same as the work W used in the above-mentioned first embodiment. The tubular work W was set in the cavity  42   a  and held stably by the supporting members  4 . Then, the sealing tools  3  were put into the open ends of the tubular work W to seal the same. Then, a hydraulic fluid was led into the interior Wa of the work W through the feeding tubes  5  and the interior of the work W was kept at a given pressure that was 50 MPa. 
     Then, as is seen from FIG. 13, with the interior pressure kept constant, the two male dies  46  were moved toward each other to press the tubular work W from both sides. With these steps, the product SA as shown in FIG. 14 was provided, which had a rectangular cross section. 
     As is seen from FIG. 14, the product SA had a circumferential length that was smaller than that of the tubular work W. While, the thickness of each vertical wall SAb became greater than that of a corresponding portion of the tubular work W. In fact, the thickness of each vertical wall SAb was much greater than that of the vertical wall Sb of the product S produced in the above-mentioned first embodiment. That is, the thickness of each vertical wall SAb increased by about 20%. Furthermore, no reduction in thickness at the four corners SAe was found. That is, the thickness of each corner SAe increased by about 30%. 
     In addition to the above, substantially identical hydroforming process was applied to a tubular work which was made of a steel of 590 MPa type and had a wall thickness of about 2.0 mm. Also in this case, sufficient increase in thickness of the product was found. This fact has revealed that even a tube of less malleable steel can be used as the work for the hydroforming process of the present invention. 
     Referring to FIG. 15, there is schematically shown a hydroforming device  51  with which a method of a fifth embodiment of the present invention is carried out. 
     Similar to the device  1  for the above-mentioned first embodiment, the hydroforming device  51  for this fifth embodiment comprises generally a female die  53  and a male die  52 . The female die  53  has a generally U-shaped cross section and has a cavity  53   a  formed therein. The male die  52  is connected to a ram R (see FIG. 3) of a hydraulic actuator, so that the male die  52  can move up and down in the cavity  53   a  of the female die  53 . 
     As shown in the drawing, the male die  52  is formed at lateral ends of its major work surface  52   a  with respective projections  52   b  that project into the cavity  53   a . Each projection  52   b  has a triangular cross section and has a sloped work surface  52   c  that faces the cavity  53   a . Furthermore, each projection  52   b  has a leading edge that is rounded. Preferably, the radius of curvature of the rounded edge is about a half of the thickness of a tubular work W. In the illustrated embodiment, the radius of curvature is about 1 mm. 
     For finding a desired shape of the male die  52  to produce a satisfied hollow product M 1  from the tubular work W, four male dies  52  were prepared. These male dies  52  were different in shape of the projections  52   b . That is, the length “L” of the sloped work surface  52   c  and the angle “α” defined by the sloped work surface  52   c  relative to a vertical wall  53   b  of the female die  53  were different in the four male dies  52 . 
     By taking the following steps, four products M 1  were provided from respective tubular works W through the hydroforming process using the four male dies  52 . 
     First, each tubular work W was set in the cavity  53   a  of the female die  53  and stably held. Each tubular work W was made of a steel of 370 MPa type and was 101.6 mm in diameter and 2.0 mm in thickness. Then, the interior of the tubular work W was filled a hydraulic fluid and kept at 20 MPa. Then, the male die  52  was lowered into the cavity  53   a  to press the tubular work W. With these steps, the four products M 1  were provided, each product M 1  having a depressed octagonal cross section as is seen from the drawing. In these four products M 1 , the thickness of two sloped upper portions M 1   a  was measured for investigating a thickness change of the portions M 1   a  due to the hydroforming process. These two sloped upper portions M 1   a  were mainly shaped by the projections  52   b  of the male die  52 . 
     The result of the investigating is shown in TABLE-1. As is seen from the table, when using the first male die  52  (viz., α=141°, D=5.0), the thickness of each sloped upper portion M 1   a  increased by 30%, and when using the second male die  52  (viz., α=153°, D=5.6), the thickness of the portion M 1   a  increased by 15% and when using the third male die  52  (viz., α=153°, D=6.7), the thickness of the portion M 1   a  increased by 10%. In case of the first, second and third male dies  52 , it was further found that with increase of the pressing stroke of the male die  52 , the circumferential length of the product M 1  decreased and the thickness of each sloped upper portion M 1   a  increased. While, when using the fourth male die  52  (viz., α=124°, D=9.0), the sloped upper portions M 1   a  of the product M 1  showed creases. That is, in case of this fourth male die  52 , with increase of the pressing stroke of the male die  52 , creases gradually appeared at the two sloped upper portions M 1   a  of the product M 1 . 
     FIG. 16 is a graph showing the result in case of using the second male die  52  (viz., α=153°, D=5.6). That is, the graph plots the thickness increasing rate of the sloped upper portions M 1   a  relative the pressing stroke of the second male die  52 . As is seen from this graph, with increase of the pressing stroke of the second male die  52 , the thickness of the two sloped upper portions M 1   a  increased and at the same time, the thickness of two vertical wall portions M 1   b  (see FIG. 15) of the product M 1  increased. The two vertical wall portions M 1   b  were mainly shaped by the vertical walls  53   b  of the female die  53 . As is seen, once the pressing stroke of the male die  52  exceeded 20 mm, the thickness increasing rate of the sloped upper portions M 1   a  sharply increased as compared with that of the vertical wall portions M 1   b . That is, the thickness of the wall portions M 1   a  that were mainly shaped by the projections  52   b  of the male die  52  increased exclusively. 
     Referring to FIG. 17, there is schematically shown a hydroforming device  61  with which a method of a sixth embodiment of the present invention is carried out. 
     As shown, the device  61  of this embodiment comprises generally a female die  64  and two male dies  62  and  63  which are arranged to move toward and away from each other in a cavity  64   a  of the female die  64 . Although not shown in the drawing, the two male dies  62  and  63  are powered by a hydraulic actuator. 
     The male die  62  is formed at lateral ends of its major work surface  62   a  with respective projections  62   b  that project into the cavity  64   a . Each projection  62   b  has a triangular cross section and has a sloped work surface  62   c  that faces the cavity  64   a . The length “L1” of the sloped work surface  62   c  is 11.2 mm and the angle “α1” defined by the sloped work surface  62   c  relative to a vertical wall  64   b  of the female die  64  is 153°. 
     The other male die  63  is formed at lateral ends of its major work surface  63   a  with respective projections  63   b  that project into the cavity  64   a . Each projection  63   b  has a triangular cross section and has a sloped work surface  63   c . The length “L2” of the sloped work surface  63   c  is 11.2 mm and the angle “α2” defined by the sloped work surface  63   c  relative to the vertical wall  64   b  of the female die  64  is 117°. 
     By using the hydroforming device  61 , a tubular work W was subjected to a hydroforming process. The work W was the same as that used in the above-mentioned fifth embodiment. The tubular work W was set in the cavity  64   a  of the female die  64  and stably held. Then, the interior of the work W was filled with a hydraulic fluid and kept at a certain pressure that did induce a free bulging of the work W. The certain pressure was lower than a critical level that is calculated from the following equation: 
     
       
           CL=t   0 × Sy ×1.6  (1) 
       
     
     Wherein: 
     CL: critical level (MPa) 
     t 0 : thickness of tubular work (mm) 
     Sy: yield strength (MPa) 
     Then, the two male dies  62  and  63  are moved toward each other to press the tubular work W. 
     With these steps, a hollow product M 2  was provided that had a depressed octagonal cross section as is seen from the drawing. 
     The thickness of two sloped upper portions M 2   a  and that of two sloped lower portions M 2   b  of the product M 2  were measured for investigating the thickness change of those portions M 2   a  and M 2   b  due to the hydroforming process. 
     The result of the investigating is shown in TABLE-2. As is seen from this table, due to the hydroforming process using the hydroforming device  61  of the sixth embodiment, the thickness of the upper sloped portions M 2   a  and that of the lower sloped portions M 2   b  increased by 10% and 20% respectively. More specifically, the thickness of the portions M 2   a  and M 2   b  that were mainly shaped by the projections  62   b  and  63   b  of the upper and lower male dies  62  increased exclusively. In addition to this, it was further found that due to the hydroforming process by the device  61 , the thickness of vertical walls M 2   c  of the product M 2  increased also. 
     Because the increase in thickness of the specified portions induces a work-hardening of the same, the mechanical strength of the product M 2  is remarkably increased due to combination of the thickness increase and work-hardening. 
     If the product M 2  thus provided is put into the hydroforming device  61  and set in the cavity  64   a  with the two walls M 2   c  thereof facing the upper and lower male dies  62  and  63 , pressing of the product M 2  by the two male dies  62  and  63  can provide the product M 2  with a generally square cross section. Furthermore, with this process, the neighboring walls of the product M 2  can have different thickness. 
     Referring to FIG. 18, there is schematically shown a hydroforming device  71  with which a method of a seventh embodiment of the present invention is carried out. 
     The device  71  of this seventh embodiment is substantially the same as the device  51  of the above-mentioned fifth embodiment of FIG. 15 except that in the seventh embodiment the male die  72  is formed with only one projection  72   b . That is, the projection  72   b  is provided at one lateral end of the major work surface  72   a  of the male die  72 . The projection  72   b  has a triangular cross section and has a sloped work surface  72   c . The male die  72  moves in a cavity  73   a  of the female die  73 . The length “L” of the sloped work surface  72   c  is 11.2 mm and the angle “α” defined by the sloped work surface  72   c  relative to a vertical wall  73   b  of the female die  73  is 153°. 
     By using the hydroforming device  71 , a tubular work W was subjected to a hydroforming process. The work W was the same as that used in the above-mentioned fifth embodiment. The work W was set in the cavity  73   a  of the female die  73  and stably held. Then, the interior of the work W was filled with a hydraulic fluid and kept at a pressure that did make a substantial promotion of a free bulging of the work W. Then, the male die  72  was lowered to press the work W. With these steps, a product M 3  was provided that had a depressed heptagonal cross section as is seen from the drawing. 
     The thickness of a sloped upper portion M 3   a  of the product M 3  was measured for investigating the thickness change of that portion M 3   a  due to the hydroforming process. 
     The result of the investigating is shown in TABLE-3. As is seen from this table, due to the hydroforming process using the hydroforming device  71  of the seventh embodiment, the thickness of the sloped supper portion M 3   a  increased by 10%. In addition, it was found that due to the hydroforming process by the device  71 , the thickness of vertical walls M 3   b  of the product M 3  increased also. 
     Referring to FIG. 19, there is schematically shown a hydroforming device  81  with which a method of an eighth embodiment of the present invention is carried out. 
     The device  81  of this eighth embodiment is substantially the same as the device  61  of the above-mentioned sixth embodiment of FIG. 17 except that in the eighth embodiment each of the upper and lower male dies  82  and  83  is formed with only one projection  82   b  or  83   b . As shown, the projections  82   b  and  83   b  are positioned at opposite sides with respect to a center axis of the device  81  and each projection  82   b  or  83   b  is provided at one lateral end of the major work surface  82   a  or  83   a  of the male die  82  or  83 . The projection  82   b  or  83   b  has a triangular cross section and has a sloped work surface  82   c  or  83   c . The upper and lower male dies  82  and  83  move toward and away from each other in a cavity  84   a  of the female die  84 . The length “L1” of the sloped work surface  82   c  of the upper male die  82  is 11.2 mm and the angle “α1” defined by the sloped work surface  82   c  relative to a vertical wall  84   b  of the female die  84  is 153°. While, the length “L2” of the sloped work surface  83   c  of the lower male die  83  is 11.2 mm and the angle “α2” defined by the sloped work surface  83   c  relative to a vertical wall  84   b  of the female die  84  is 117°. 
     By using the hydroforming device  81 , a tubular work W was subjected to a hydroforming process. That is, the work W was set in the cavity  84   a  of the female die  84  and held stably. Then, the interior of the work W was filled with a hydraulic fluid and kept at a certain pressure that did not make a substantial promotion to a free bulging of the work W. Then, the two male dies  82  and  83  are moved toward each other to press the tubular work W. With these steps, a product M 4  was provided that had a depressed hexagonal cross section as is seen from the drawing. 
     The thickness of a sloped upper portion M 4   a  and that of a sloped lower portion M 4   b  of the product M 4  were measured for investigating the thickness change of these portions M 4   a  and M 4   b  due to the hydroforming process. 
     The result of this investigation is shown in TABLE-4. As is seen from this table, due to the hydroforming process using the hydroforming device  81 , the thickness of the upper and lower sloped portions M 4   a  and M 4   b  increased by 10% and 20% respectively. More specifically, the thickness of the portions M 4   a  and M 4   b  that were mainly shaped by the projections  82   b  and  83   b  of the male dies  82  and  83  increased exclusively. In addition to this, it was further found that due to the hydroforming process by the device  81 , the thickness of vertical walls M 4   c  of the product M 4  increased also. 
     Referring to FIG. 20, there is schematically shown a hydroforming device  91  with which a method of a ninth embodiment of the present invention is carried out. 
     The device  91  used in this ninth embodiment is substantially the same as the device  61  of the above-mentioned sixth embodiment of FIG. 17 except that in the ninth embodiment the projections  93   b  of the lower male die  93  are different from those  63   b  of the lower male die  63  of the sixth embodiment. That is, in the ninth embodiment, the length “L2” of each sloped work surface  93   c  is 11.2 mm, but the angle “α2” defined by the sloped work surface  93   c  relative to the vertical wall  94   b  of the female die  94  is 153° which is the same as the sloped work surface  92   c  of each projection  92   b  of the upper male die  92 . 
     By using the hydroforming device  91 , a tubular work W was subjected to a hydroforming process. The work W used in this embodiment was substantially the same as that used in the fifth embodiment except that in this ninth embodiment the work W was made of a steel of 590 MPa type. The tubular work W was set in the cavity  94   a  of the female die  94  and stably held. Then, the interior of the work W was filled with a hydraulic fluid and kept at about 20 MPa. Then, the two male dies  92  and  93  are moved toward each other to press the tubular work W. During this pressing, the hydraulic pressure in the work W increased. However, by using a leak-off valve (not shown), rapid increase of the pressure was suppressed. For this pressing, the maximum pressing stroke of each male die  92  or  93  was so determined as to cause a product M 5  (see FIG. 21) to have a circumferential length smaller than that of the non-pressed tubular work W. At the maximum pressing stroke of each male die  92  or  93 , the pressure of the fluid in the work W showed a level above 30 MPa. 
     With these steps, the product M 5  was provided that had a depressed octagonal cross section as is seen FIG.  21 . 
     The thickness of two sloped upper portions M 5   a , the thickness of two sloped lower portions M 5   b  and the thickness of two vertical portions M 5   c  of the product M 5  were measured, which were 2.30 mm, 2.30 mm and 2.20 mm respectively. That is, the sloped upper portions M 5   a  increased by 15%, the sloped lower portions M 5   b  increased 15% and the vertical portions M 5 C increased by 10% in thickness. It was further found that portions (viz., upper and lower horizontal wall portions) other than the above-mentioned portions M 5   a , M 5   b  and M 5   c  showed no change in thickness. 
     Referring to FIG. 22, there is schematically shown a hydroforming device  101  with which a method of a tenth embodiment of the present invention is carried out. 
     The device  101  used in this tenth embodiment is substantially the same ad the device  81  of the above-mentioned eighth embodiment of FIG. 19 except that in the tenth embodiment the projection  103   b  of the lower male die  103  is different from that  83   b  of the lower male die  83  of the eighth embodiment. That is, in the tenth embodiment, the length “L2” of the sloped work surface  103   c  is 11.2 mm, but the angle “α2” defined by the sloped work surface  103   c  relative to the vertical wall  104   b  of the female die  104  is 153° which is the same as the sloped work surface  102   c  of the projection  102   b  of the upper male die  102 . 
     By using the hydroforming device  101 , a tubular work W was subjected to a hydroforming process. The work W used in this embodiment was the same as that used in the above-mentioned ninth embodiment. The tubular work W was set in the cavity  104   a  of the female die  104  and stably held. The interior of the work W was filled with a hydraulic fluid and kept at about 20 MPa. Then, the two male dies  102  and  103  are moved toward each other to press the tubular work W. For this pressing, the maximum pressing stroke of each male die  102  or  103  was so determined as to cause a product M 6  (see FIG. 23) to have a circumferential length smaller than that of the non-pressed tubular work W. At the maximum pressing stroke of each male die  102  or  103 , the pressure of the fluid in the work W showed a value above 30 MPa. 
     With these steps, the product M 6  was provided that had a depressed hexagonal cross section, as is seen from FIG.  23 . 
     The thickness of a sloped upper portion M 6   a , that of a sloped lower portion M 6   b  and that of two vertical portions M 6   c  and M 6   d  of the product M 6  were measured, which were 2.24 mm, 2.24 mm, 2.16 mm and 2.20 mm respectively. That is, the sloped upper portion M 6   a  increased by 12%, the sloped lower portion M 6   b  increased by 12%, the vertical portion M 6   c  increased by 8% and the other vertical portion M 6   d  increased by 10% in thickness. It was further found that portions (viz., upper and lower horizontal wall portions) other than the above-mentioned portions M 6   a , M 6   b , M 6   c  and M 6   d  showed no change in thickness. 
     Referring to FIG. 24, there is shown a reference hydroforming device  111 , which was provided for proving the improvement achieved by the present invention. 
     The device  111  is substantially the same as the device  51  used in the above-mentioned fifth embodiment of FIG. 15 except that in this reference device  111   a  cavity  113   a  of the female die  113  has an entirely flat bottom  113   c , as shown. The length “L” of the sloped work surface  112   c  of each projection  112   b  is 11.2 mm and the angle “α” defined by the sloped work surface  112   c  relative to the vertical wall  113   b  of the female die  113  is 153°. 
     By using the reference device  111 , a tubular work was subjected to a hydroforming process. The work W was the same as the work W used in the above-mentioned ninth and tenth embodiments. Steps of the hydroforming process were substantially the same as those of the ninth and tenth embodiments. 
     With these steps, a product M 7  was provided, that had a depressed hexagonal cross section, as is seen from FIG.  25 . 
     The thickness of a right side sloped upper portion M 7   a  and that of a left side vertical wall M 7   c  of the product M 7  were measured, which were 2.30 mm and 2.20 mm respectively. That is, these portions M 7   a  and M 7   c  increased by 15% and 10% in thickness respectively. However, it was found that portions other than those portions M 7   a  and M 7   b  showed no change in thickness. That is, in case of this reference device  111 , the product M 7  failed to have continuous vertical and sloped portions that were both increased in thickness. 
     For the above, it has been revealed that if the sloped surface  92   c ,  93   c ,  102   c  or  103   c  of each projection  92   b ,  93   b ,  102   b  or  103   b  of the male die  92 ,  93 ,  102  or  103  is constructed to satisfy the following equations, a desired result is expected for producing the shaped hollow product M 5  or M 6 . 
     
       
         4≦ L/t   0 ≦7.5  (2) 
       
     
     
       
         α≧10×( L/t   0 )+68  (3) 
       
     
     wherein: 
     L: length of the sloped surface 
     t 0 : initial thickness of the tubular work 
     α: angle between the sloped surface and the vertical wall. 
     Referring to FIG. 26, there is schematically shown a hydroforming device  121  with which a method of an eleventh embodiment of the present invention is carried out. As will be described in detail hereinafter, the device  121  of this embodiment is constructed to shape a tubular work W into a hollow square product M 8  (see FIG. 27) with four rounded corners M 8   a.    
     As is seen from FIG. 26, the device  121  used in this eleventh embodiment comprises generally fixed lower and upper dies  122  and  123  which are mounted on each other to define therebetween a longitudinally extending cavity  121   a . Each fixed die  122  or  123  is formed at laterally spaced internal portions with longitudinally extending concave surfaces  122   a  or  123   a . These concave surfaces  122   a  and  123   a  are used for shaping the four rounded corners M 8   a  of the product M 8 . 
     The two fixed dies  122  and  123  are respectively formed with vertical slots  122   b  and  123   b  in which lower and upper male dies  124  and  125  are movably received. The two fixed dies  122  and  123  are vertically spaced from each other to define therebetween horizontal slots  126   a  and  126   b  in which left and right male dies  127  and  128  are movably received. These four male dies  124 ,  125 ,  127  and  128  are used for shaping the four flat wall portions M 8   b  of the product M 8 . 
     As is seen from FIG. 26, each slot  122   b ,  123   b ,  126   a  or  126   b  is exposed to the cavity  121   a  at longitudinally extending ridges P 1  that constitute circumferentially terminal ends of the corresponding concave surfaces  122   a  and  123   a . That is, each ridge P 1  constitutes an inside edge of the corresponding slot  122   b ,  123   b ,  126   a  or  126   b.    
     It is now to be noted that in this eleventh embodiment  121 , the ridges P 1  are shaped and sized to satisfy the following geometrical conditions. 
     That is, an imaginary straight line “T1” that passes through neighboring two ridges P 1  and P 1  of each slot extends outside of the cavity  121   a  defined by the lower and upper female dies  122  and  123 . In other words, the imaginary straight line “T1” does not pass any area of the cavity  121   a . When the male dies  124 ,  125 ,  127  and  128  are brought to their frontmost work positions, the flat work surface (no numeral) of each male die  124 ,  125 ,  127  or  128  becomes coincident with the corresponding imaginary straight line “T1”. In this condition, the work surface of each male die  124 ,  125 ,  127  or  128  is smoothly mated with the ridges P 1 , that is, the circumferentially terminal ends of the concave surfaces  122   a  and  123   a.    
     By using the hydroforming device  121 , a tubular work W was subjected to a hydroforming process. The work W was made of a steel of 370 MPa type and was 123 mm in diameter and 2 mm in thickness. That is, the work W was set in the cavity  121   a  of the fixed dies  122  and  123 , and the male dies  124 ,  125 ,  127  and  128  were moved to their rest position and then, the work W was stably held in the cavity  121   a . Then, the interior of the work W was filled with a hydraulic fluid and the pressure in the work W was increased to and kept at 10.1 MPa. Then, the male dies  124 ,  125 ,  127  and  128  were moved to their work or press positions to press the work W. During this pressing, the pressure in the work W gradually increased, and at the maximum pressing stroke of each male die, the pressure in the work W was increased to a level of 24.8 MPa. 
     With these steps, a hollow square product M 8  was provided that had a square cross section with four rounded corners, as is seen from FIG.  27 . The radius of curvature of each corner M 8   a  was 8 mm, the height was 100 mm and the width was 100 mm. 
     The thickness of various portions “a to j” of one rounded corner M 8   a  and its neighboring flat wall portion M 8   b  of the product M 8  was measured, as is seen from FIG.  28 . 
     FIG. 29 is a graph showing the result of the thickness measuring, that plots the thickness of such portions “a to j”. For comparison, the result provided by a conventional hydroforming device having no moving dies is also plotted. As is seen from this graph, in the conventional one, the thickness of the rounded corner M 8   a  reduced by 20% at most, while in case of the product M 8  of the invention, the thickness of such corner M 8   a  increased by 20% at most. That is, by using the hydroforming device  121  of the eleventh embodiment, undesired thickness reduction in the corner was suppressed. 
     Referring to FIG. 30, there is schematically shown a hydroforming device  131  with which is a method of a twelfth embodiment of the present invention is carried out. As will be described in detail hereinafter, the device  131  of this embodiment is constructed to shape a tubular work W into a hollow square product M 9  (see FIG. 32) with four projected round corners M 9   a.    
     As is seen from FIG. 30, the device  131  used in this twelfth embodiment comprises generally fixed lower and upper dies  133  and  134  which are mounted on each other to define therebetween a longitudinally extending cavity  131   a.    
     Each fixed die  133  or  134  is formed at laterally spaced internal portions with longitudinally extending concave surfaces  133   a  or  134   a.    
     The two fixed dies  133  and  134  are respectively formed with vertical slots  133   b  and  134   b  in which lower and upper male dies  135  and  136  are movably received. The two fixed dies  133  and  134  are vertically spaced from each other to define therebetween horizontal slots  137   a  and  137   b  in which left and right male dies  138  and  139  are movably received. 
     As shown, each male die  135 ,  136 ,  138  or  139  is formed at lateral ends of the work surface  135   a ,  136   a ,  138   a  or  139   a  with respective concave recesses  135   b ,  136   b ,  138   b  or  139   b . As is understood from FIG. 31, one concave surface  134   a  or  133   a  of the fixed female die  134  or  133  and neighboring two concave recesses  136   b  and  138   b ,  136   b  and  139   b ,  138   b  and  135   b  or  135   b  and  139   b  of the corresponding male dies  136 ,  138 ,  139  and  135  are used for shaping one projected round corner M 9   a  of the product M 9 . 
     As is seen from FIG. 30, each slot  133   b ,  134   b ,  137   a  or  137   b  is exposed to the cavity  131   a  at longitudinally extending ridges P 2  that constitute circumferentially terminal ends of the corresponding concave surfaces  133   a  and  134   a . That is, each ridge P 2  constitutes an inside edge of the corresponding slot  133   b ,  134   b ,  137   a  or  137   b.    
     It is now to be noted that in this twelfth embodiment  131 , the ridges P 2  are so shaped and sized as to satisfy the following geometrical conditions. 
     That is, as is seen from FIG. 30, an imaginary straight line “T2” that passes through neighboring two ridges P 2  and P 2  of each slot extends outside of the cavity  131   a  defined by the lower and upper fixed female dies  133  and  134 . In other words, the imaginary straight line “T2” does not pass any area of the cavity  131   a . As is seen from FIG. 31, when the male dies  136 ,  138 ,  135  and  139  are brought to their frontmost work positions, the outside edge of each concave recess  136   b ,  138   b ,  135   b  or  139   b  becomes coincident with the corresponding imaginary straight line “T2”. In this condition, the outside edge of each concave recess  136   b ,  138   b ,  135   b  or  139   b  is smoothly mated with the ridges P 2 , that is, the circumferentially terminal ends of the concave surfaces  134   a  and  133   a.    
     By using the hydroforming device  131 , a tubular work W was subjected to a hydroforming process. The work W was made of a steel of 370 MPa type and was 140 mm in diameter and 2 mm in thickness. That is, the work W was set in the cavity  131   a  of the fixed dies  133  and  134 , and the male dies  135 ,  136 ,  138  and  139  were moved to their rest positions and then, the work W was stably held in the cavity  131   a . Then, the interior of the work W was filled with a hydraulic fluid and the pressure in the work W was increased to and kept at 10.1 MPa. Then, the male dies  135 ,  136 ,  138  and  139  were moved toward their work or press positions to press the work W while keeping the internal pressure of the work W at 20.2 MPa. At the maximum pressing stroke of each male die, the pressure in the work W was increased to a level of 24.8 MPa. 
     With these steps, a hollow square product M 9  was provided, that had a generally square cross section with four projected round corners, as is seen from FIG.  32 . The radius of curvature of each corner M 9   a  was 10 mm, the height was 100 mm and the width was 100 mm. 
     The thickness of various portions “a to j” of one projected round corner M 9   a  and its neighboring flat wall portion M 9   b  of the product M 9  was measured, as is seen from FIG.  33 . 
     FIG. 36 is a graph showing the result of the thickness measuring, that plots the thickness of such portions “a to j”. 
     For proving the improvement achieved by the method of the twelfth embodiment, a reference method was carried out by using a hydroforming device  141  shown in FIG.  34 . 
     As is shown in the drawing, the device  141  comprises fixed lower and upper dies  143  and  144 , lower and upper male dies  145  and  146  and left and right male dies  148  and  149  which are arranged in substantially the same manner as those of the above-mentioned device  131  of the twelfth embodiment of FIG.  30 . 
     Each fixed die  143  or  144  is formed at laterally spaced internal portions with longitudinally extending concave surfaces  143   a  or  144   a.    
     Each male die  145 ,  146 ,  148  or  149  is formed with a flat work surface  145   a ,  146   a ,  148   a  or  149   a.    
     As is seen from FIGS. 34 and 35, each slot  143   b    144   b ,  147   a  or  147   b  is exposed to the cavity  141   a  at longitudinally extending ridges P 3  that constitute circumferentially terminal ends of the corresponding concave surfaces  143   a  and  144   a . That is, each ridge P 3  constitutes an inside edge of the corresponding slot  143   b ,  144   b ,  147   a  or  147   b.    
     In this reference device  141 , the ridges P 3  are so shaped and sized as to satisfy the following geometrical conditions. 
     That is, as is seen from FIG. 34, an imaginary straight line “T3” that passes through neighboring two ridges P 3  and P 3  of each slot extends inside (not outside) of the cavity  141   a  defined by the lower and upper fixed female dies  144  and  144 . In other words, the imaginary straight line “T3” passes through the projected part of the cavity  121   a , which is defined by the concave surface  144   a  or  143   a  of the female die  144  or  143 . When the male dies  145 ,  146 ,  148  and  149  are brought to their frontmost work positions, the flat work surface  145   a ,  146   a ,  148   a  or  149   a  of each male die becomes coincident with the corresponding imaginary straight line “T3”. In this condition, the work surface  145   a ,  146   a ,  148   a  or  149   a  of each male die is mated with the ridges P 3 , as is seen from FIG.  35 . 
     By using the reference device  141 , a tubular work W was subjected to a hydroforming process. The work W and the hydroforming steps were the same as those used in the above-mentioned twelfth embodiment. With this, a hollow square product MR was provided, that was similar in construction to the product M 9  provided according to the twelfth embodiment. The thickness of various portions “a to j” of the product MR was measured. The result of the thickness measurement is plotted in the graph of FIG.  36 . 
     As is seen from this graph, in the product M 9  according to the twelfth embodiment, the thickness of the projected round corner M 9   a  increased by about 15%, while in the product MR according to the reference device  141 , thickness increase was now found and a crack was produced at the portion “g”. 
     The entire contents of Japanese Patent Applications 11-083658 (filed Mar. 26, 1999), 11-183920 (filed Jun. 29, 1999), 11-366894 (filed Dec. 24, 1999) and 2000-49476 (filed Feb. 25, 2000), are incorporated herein by reference. 
     Although the invention has been described above with reference to the embodiments, the invention is not limited to such embodiments as described hereinabove. Various modifications and variations of such embodiments may be carried out by those skilled in the art, in light of the above description. 
     
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                 Length 
                   
                   
                   
                   
               
               
                   
                   
                 of 
               
               
                   
                 Angle 
                 sloped 
                   
                   
                   
                 Increasing 
               
               
                 Hydraulic 
                 of pro- 
                 work 
                 Initial 
                 Ratio 
                   
                 rate of 
               
               
                 forming 
                 jection 
                 surface 
                 thickness 
                 (D) 
                   
                 thickness 
               
               
                 device 
                 α(°) 
                 L (mm) 
                 t 0  (mm) 
                 (L/t 0 ) 
                 10D ÷ 68 
                 (%) 
               
               
                   
               
             
             
               
                 FIG. 15 
                 141 
                 10.0 
                 2.0 
                 5.0 
                 118 
                  3 
               
               
                   
                 153 
                 11.2 
                 2.0 
                 5.6 
                 124 
                 15 
               
               
                   
                 153 
                 13.4 
                 2.0 
                 6.7 
                 135 
                 10 
               
               
                   
                 124 
                 18.0 
                 2.0 
                 9.0 
                 158 
                 (Creases 
               
               
                   
                   
                   
                   
                   
                   
                 appeared) 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                 Length 
                   
                   
                   
                 In- 
               
               
                   
                   
                 of 
                   
                   
                   
                 creasing 
               
               
                   
                 Angle 
                 sloped 
                   
                   
                   
                 rate of 
               
               
                 Hydraulic 
                 of pro- 
                 work 
                 Initial 
                 Ratio 
                   
                 thick- 
               
               
                 forming 
                 jection 
                 surface 
                 thickness 
                 (D) 
                   
                 ness 
               
               
                 device 
                 α(°) 
                 L (mm) 
                 t 0  (mm) 
                 (L/t 0 ) 
                 10D ÷ 68 
                 (%) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 FIG. 
                 62b 
                 α1:153 
                 L1:11.2 
                 2.0 
                 5.6 
                 124 
                 10 
               
               
                 17 
                 63b 
                 α2:117 
                 L2:11.2 
                 2.0 
                 5.6 
                 124 
                  2 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                 Length 
                   
                   
                   
                   
               
               
                   
                   
                 of 
               
               
                   
                 Angle 
                 sloped 
                   
                   
                   
                 Increasing 
               
               
                 Hydraulic 
                 of pro- 
                 work 
                 Initial 
                 Ratio 
                   
                 rate of 
               
               
                 forming 
                 jection 
                 surface 
                 thickness 
                 (D) 
                   
                 thickness 
               
               
                 device 
                 α(°) 
                 L (mm) 
                 t 0  (mm) 
                 (L/t 0 ) 
                 10D ÷ 68 
                 (%) 
               
               
                   
               
             
             
               
                 FIG. 18 
                 153 
                 11.2 
                 2.0 
                 5.6 
                 124 
                 10 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                   
                   
                 Length 
                   
                   
                   
                 In- 
               
               
                   
                   
                 of 
                   
                   
                   
                 creasing 
               
               
                   
                 Angle 
                 sloped 
                   
                   
                   
                 rate of 
               
               
                 Hydraulic 
                 of pro- 
                 work 
                 Initial 
                 Ratio 
                   
                 thick- 
               
               
                 forming 
                 jection 
                 surface 
                 thickness 
                 (D) 
                   
                 ness 
               
               
                 device 
                 α(°) 
                 L (mm) 
                 t 0  (mm) 
                 (L/t 0 ) 
                 10D ÷ 68 
                 (%) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 FIG. 
                 82b 
                 α1:153 
                 L1:11.2 
                 2.0 
                 5.6 
                 124 
                 10 
               
               
                 19 
                 83b 
                 α2:117 
                 L2:11.2 
                 2.0 
                 5.6 
                 124 
                  2