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Effect of Bending Method on Tube Hydroforming+1
Masaaki Mizumura+2,+3 and Yukihisa Kuriyama+4
Steel Research Laboratories, Nippon Steel Corporation, Futtsu 293-8511, Japan
We studied the effect of the bending method on the hydroforming of a tube in a subsequent process, using experiments and the finiteelement method. Two bending methods, rotary draw bending and intrusion bending, were investigated. A tube was bent into an S-shape by eachbending method, and a hydroforming test was carried out with the same hydroforming die. The wall thickness distribution was measured afterthe hydroforming. The wall thickness of the tube is smallest on the compression side when it is bent by the rotary draw bending method and onthe tension side or the intermediate side when it is bent by the intrusion bending method. In both bending cases, burst occurs on the intermediateside during axial feeding. In rotary draw bending, a burst occurs on the compression side or at the R stop nearby, however, in intrusion bending,burst does not occur on the compression side but occurs on the R stop nearby during the final increase of internal pressure. Intrusion bendingleaves a larger hydroforming allowance than rotary draw bending. This is because the wall thickness after intrusion bending is greater than thatafter rotary draw bending. [doi:10.2320/matertrans.P-M2019866]
(Received September 11, 2019; Accepted November 11, 2019; Published January 20, 2020)
Keywords: tube forming, bending, forming property, bulge forming, deformation behavior, finite element method, tube hydroforming, processdesign
1. Introduction
The tube forming method with both internal pressure andaxial feeding has been used for bicycle parts1) and tubefittings.2) This method has been known as bulge formingsince long ago. However, the shapes formed are T-shapes andother simple forms. Recently, this forming method has beenapplied to a wide range of purposes, from integration ofparts to weight reduction in automobiles.3,4) The name waschanged to hydroforming and more complex shapes wereable to be formed.5,6) Hydroformed parts made of straighttube as well as bent tube are increasing, as shown in Fig. 1.
Deformation behaviors in hydroforming processes afterbending have been the subject of past research. Lei, et al.7)
researched deformation of actual parts and Sato, et al.8) andIshigaki, et al.9) investigated fundamental shape. In addition,the authors investigated strain behavior during hydroformingat bent portions and found suitable forming conditionswithout fractures or wrinkles,10) even with an expanding ratioof 30% or larger.
There are many kinds of tube bending methods employedprocesses before hydroforming, but investigation into theeffect of the bending method on hydroforming behavior hasnot been conducted thus far. In this paper, we explored twobending methods, rotary draw bending,11) which is the mostcommon method performed, and intrusion bending,12) whichenables the forming of various shapes. We investigated theeffect of the bending method on deformation behavior in thehydroforming process after each bending process throughexperiments and the finite element method (FEM).
2. Procedures for Experiment and Analysis
2.1 SpecimensFor specimens, we used tubes made from interstitial free
steel plates13) for deep drawing that were laser welded afterbeing pressed several times into a round shape. Table 1shows their sizes and representative mechanical properties.The mechanical properties in this table are the values inlongitudinal direction obtained by tensile tests with arc shapespecimens.
2.2 Final forming shape and processesThe final shape after forming is an S-shape with 2 bent
portions, as shown in Fig. 2. In this paper, the portion thatwas bent first is called Bend No. 1 and the second is calledBend No. 2. This forming shape was selected for thefollowing two reasons. The first, as previously reported,10)
is that the shape of the hydroforming die is simpler than thesingle bend shape in previous papers because both axialfeeding directions are parallel to each other. The secondreason is that deforming state can be observed both near thetube ends where axial feeding is readily effective andbetween the two bending portions where there it is moredifficulty in effectiveness. In the two bent portions, the radiusof the bend in the neutral axis was 152mm, the angle was 42
Tube
Bending
Die closing
Upper die
Lower die Flattening
Hydroforming
Piercing
Internal pressure
Internal pressure
Axial feeding
Axial feeding
Water filling
Fig. 1 General hydroforming processes.
+1This Paper was Originally Published in Japanese in J. JSTP 60 (2019)175181.
+2Corresponding author, E-mail: [email protected]
+3Present address: Futtsu Unit, Nippon Steel Technology, Futtsu 293-0011,Japan
+4Present address: Department of Systems Innovation, The University ofTokyo, Tokyo 113-8656, Japan
Materials Transactions, Vol. 61, No. 3 (2020) pp. 515 to 521©2020 The Japan Society for Technology of Plasticity
degrees and the length between the two bent portions was247mm. The cross sections at and between the bent portionswere rectangular with a 37% expanding ratio. In this paper,the expanding ratio is defined as the ratio of the elongationlength after expanding to the original length in a circum-ferential direction.
2.3 Bending procedureWe used two bending methods, rotary draw bending and
intrusion bending. An outline of each of these methods isshown in Fig. 3.
In rotary draw bending, a tube end is held with a clampingdie and bent by rotating the bending die to obtain a bent tubewith the same radius as the bending die. There are other toolsused for restraint, such as pressure dies, wipers, mandrels and
balls. These restrain the inside and outside of tubes to preventthe formation of defects such as wrinkles and ensure anaccurate forming shape. Because of this, this bending methodis most commonly used in industrial production. However,flexibility of the shape is limited because it is determined bythe die shape.
In intrusion bending, a tube is bent through the movementand rotation of a gyro set in front while pushing the tube fromthe back. Gyro movement enables several kinds of shapes tobe produced, so this method boasts more flexibility in shapethan rotary draw bending. However, forming defects such aswrinkles occur more readily and the process is less repeatablebecause of lack of restraint. Intrusion bending methods aredivided into two types by control method and tool conditions.One method was developed by Murata, et al.14) In this type,gyro movement is controlled to advance only the length oftube, and the gyro, set by spherical support according tomovement, is rotated automatically. The mandrel is notinserted into the tube. Another method was researched byNaoi, et al.12) In this type, both the movement and the angleof the gyro are controlled, and the mandrel is inserted intotube. The wall thickness of the tubes used in this paper wasthin, which causes flatness and wrinkles to occur morereadily, so the latter type (using a mandrel) was selected.
Now, we will discuss the general differences in shape afterapplication of the two bending methods. In rotary drawbending, a constant bending radius is obtained. However, inintrusion bending, the bending radius shape inevitablychanges at the beginning and end of gyro movement. Anexample of intrusion bending conditions and bending shapeis shown in Fig. 4. The parallel translation and rotation of thegyro occur simultaneously, but a constant radius cannot beobtained at the beginning and ending of gyro movement.Therefore, it is necessary to determine gyro movementconditions in consideration of transient areas in order toobtain the target bent shape.
The distribution of thickness also differs between thetwo bending methods. Figure 5 shows the distribution ofthickness increase and decrease ratio at the compression andtension sides for a bending radius 3 times the originaldiameter (3DR) and a 90-degree bending angle made usingSTKM11A electric resistance welded steel tubes with a60.5mm outer diameter and a 2.0mm thickness.15)
STKM11A is one of Japanese industrial standard (JIS) forcarbon steel tubes for machine structural purpose. Theincrease and decrease ratio is defined as the ratio of changein thickness after bending compared to the original thickness.In intrusion bending, the constant ratio is 3 times the originaltube’s diameter. From these figures, we can see that thethickness increase ratio at the compression side is almost the
Table 1 Sizes and mechanical properties of tube.
/mm
513.490 63.5 77.8
63.5
254.9
247
63.5
φ63.5
90
R5.5R152
247 A
A42°
A-A
Fig. 2 Shape of hydroformed part.
(a)
(b)
Pressure die
Ball
Clamping die
Bending die
Wiper
TubePusher
Mandrel
BallMandrelTubePusher
Movement
Rotation
GyroGuide cylinder
Fig. 3 Schematics of bending method. (a) Rotary draw bending, (b)Intrusion bending.
M. Mizumura and Y. Kuriyama516
same as the thickness decrease ratio at the tension side forrotary draw bending. On the other hand, the thicknessincrease ratio at the compression side is much larger than the
thickness decrease ratio at the tension side for intrusionbending. Because it is bent with compression from the endof the tube, the thickness increases overall. In addition, thethickness increase/decrease ratio is constant in rotary drawbending, but is not in intrusion bending.
Now we will discuss S-shape. The final radius of 152mmis the hydroformed shape, as shown in Fig. 2, but the radiusduring the bending process need not be 152mm. Aspreviously reported,10) a bending shape that fits the hydro-forming die at the compression side is desirable because thetube is pushed by axial feeding during the hydroformingprocess. As a result of that, the bent shape is set as shown inFig. 6. In rotary draw bending, the bending radius was254mm, which was larger than the radius of the hydro-forming shape. Thickness reduction at the thinnest areascould be suppressed by this bending design more than with abending radius of 152mm. On the other hand, intrusionbending enabled a larger bending radius through utilization ofthe aforementioned transient bending range in the beginningand end of the constant bending radius. The constant bendingradius could be realistically set at 311mm. As describedabove, and from the viewpoint of the bending shape formedbefore hydroforming, in this study, intrusion bending couldsuppress thickness reduction more than rotary draw bendingdue to the ability to set a larger bending radius.
2.4 Hydroforming procedureS-shape bent tube made by each bending method was set
in a hydroforming die with the same cavity shape as thatshown in Fig. 2, then hydroformed. In the hydroformingprocess, internal pressure p and axial feeding from both ends¤ are controlled while being subjected to load. This loadingpath is shown in Fig. 7. First the pressure was increased tothe specified pressure with short axial feeding for sealing.Next, axial feeding was performed while maintaining thepressure and stopped at the specified stroke. Finally, onlypressure was increased until burst occurred. In this loadingpath, the holding pressure and final axial stroke are definedas pH and ¤F, respectively. In general hydroforming paths, the
(a)
(b)
-5
0
5
10
15
20
25
0 50 100 150 200 250
Thic
knes
s inc
reas
e an
d de
crea
se ra
tioτ/
%
Axial position from bending start xb /mm
Thickness decrease ratio at tension side
Thickness increase ratio at compression side
R/D = 3
-5
0
5
10
15
20
25
0 100 200 300 400
Thic
knes
s inc
reas
e an
d de
crea
se ra
tio τ
/%
Axial position from bending start xb /mm
Thickness increase ratio at compression side
Thickness decrease ratio at tension side
R/D = 3 (uniform bending area)
Fig. 5 Distribution of thickness increase and decrease ratios after bending(¤60.5, t2.0, STKM11A).15) (a) Rotary draw bending, (b) Intrusionbending.
(a)
(b)
R254
206
41°Narrow gap at
compression side
Hydroforming die
/mm
R311
65
Narrow gap at compression side
Uniform bending
area
Transient bending area
Hydroforming die
/mm
Fig. 6 S-shape made by each bending method to fit hydroforming die.(a) Rotary draw bending, (b) Intrusion bending.
0
5
10
15
20
25
30
35
0 10 20 30 40
Gyr
o m
ovin
g di
stan
ce a
/mm
,G
yro
rota
tion
angl
e B
/deg
Test time T /sec
70
60
5040
30
20
10
0A
xial
mov
ing
dist
ance
of p
ushe
rxp
/mm
Gyro rotation angle B
Gyro moving distance a
Axial moving distance of pusher xp
Transient bending area
Straight area
Uniform bending area
Straight area
Transientbending area
Uniform bendingradius
Fig. 4 Example of intrusion bending conditions and bending shape.
Effect of Bending Method on Tube Hydroforming 517
pressure is increased during axial feeding.16) However, weadopted the loading path shown in Fig. 7 because the laterdiscussed hydroforming range in this loading path isexpressed by only two parameters, pH and ¤F.
The reason that the pressure is increased until burst occursis because the corner R limit and the wrinkle limit can beobtained by seeing if the corner R is less than the target sizeor if wrinkles have been removed when the tube has beensubjected to enough pressure to cause this burst. Addition-ally, the burst limit is the holding pressure limit during axialfeeding and the buckling limit is the limit of excessivethickness at tube ends. Those included, the authors developed4 kinds of forming limits that are all expressed with holdingpressure pH in the vertical axis and final axial stroke ¤F in thehorizontal axis in a previous paper.17) A typical example isshown in Fig. 8. The area surrounded by the 4 forming limitlines is the hydroforming range, and the hydroformingallowance can be evaluated by comparing area size. Throughthis method, many comprehensive tests under a matrix ofchanging conditions are necessary to obtain the 4 forminglimits. To simplify this process, the final axial stroke ¤F wasfixed at 60mm, and the bust, corner R and wrinkle limitswere obtained at this axial stroke. The range of holdingpressure pH is expressed as 2 arrows (dashed and dotted), asshown in Fig. 8. For the long dashed left arrow with the lowpressure corner R limit, the range of the original hydro-forming range has expanded to the left. On the other hand,the long dotted arrow with the low wrinkle limit means thatthe hydroforming area has expanded to the right. Thebuckling limit was not apparent in these tests, as the tubes
were a thin 1.4mm. As described above, we conductedsimple evaluation of hydroforming allowance by using the2 forming ranges of holding pressure pH obtained by bustlimit, corner R limit and wrinkle limit at a 60mm final axialstroke ¤F.
2.5 Finite element method procedureWe conducted analysis of the results of this experiment
using the finite element method (FEM). Dynamic explicitanalysis software, PAM-STAMP, was used for this FEManalysis. As shown in Fig. 9, S-shape bent tube with thethickness and strain calculated by analysis of each bendingprocess was inserted in a hydroforming die and analyzed.Shell elements of about 2.5mm were used. The mechanicalproperties of the tube were approximated with the Swiftformula.
3. Results and Discussions
3.1 Effect on distribution of thicknessThe FEM result of thickness distribution after each
bending process is shown in Fig. 10. In rotary draw bending,thickness was decreased at the tension side and increased at
Holding pressure pH
Final axial stroke δF
Sealing position
Raise until burst
Axial stroke δ /mm
Inte
rnal
pre
ssur
e p
/MPa
Axial stroke δ Axial stroke δ
Internal pressure p
Hydroforming dieBending tube
Fig. 7 Loading path of hydroforming.
Hol
ding
pre
ssur
ep H
Final axial stroke δF
Burst limit line
Wrinkle limit line
: Defect: Sound
δF = constant (60 mm)
Corner R limit line
Buckling limit line
Burst limit
Wrinkle limit
Corner R limit
Fig. 8 Hydroforming allowance.
Hydroforming die
BallBallMandrelMandrel
Pressure dieTube
Tube
Bending tube
WiperBending die GyroGuide cylinder
Rotary draw bending Intrusion bending
Hydroforming
Fig. 9 FEM models of bending and hydroforming.
(a)
(b)
Wall thickness/mm
Wall thickness/mm
Fig. 10 Distributions of wall thickness after bending (FEM). (a) Rotarydraw bending, (b) Intrusion bending.
M. Mizumura and Y. Kuriyama518
the compression side. However, in intrusion bending, therewas almost no decrease in thickness at the tension side andextreme increase at the compression side. In draw bending,S-shape Bends No. 1 and No. 2 were independent of eachother, so the thickness distributions were almost the same. Onthe other hand, in case of intrusion bending, it was expectedthat Bends No. 1 and No. 2 are dependent upon each otherbecause the tube is bent continuously, but there was nodifference in the distribution of thickness. The distancebetween the guide cylinder and gyro was 25mm during zerogyro movement and rotation. The distance between BendsNo. 1 and No. 2 is 65mm, as shown in Fig. 6(b), which islonger than the distance between the guide cylinder and gyro.Bends No. 1 and No. 2 are regarded to be considerablyindependent of each other in this intrusion bending.
Figure 11 shows the results of the experiment and FEM fordistribution of thickness strain in the center section of BendNo. 1 after bending and hydroforming. The hydroformingconditions after each bend were different. This will bedescribed in 3.3, but the holding pressure pH of intrusion benttube must be higher than that of rotary draw bending. Toensure conditions where the tube does not burst, the holdingpressure pH selected was 15MPa for rotary draw bending and18MPa for intrusion bending. In rotary draw bending, thethickness strain was negative at the tension side, positive atthe compression side and these absolute values were almostthe same. In intrusion bending, however, the thickness strainwas positive at the compression side, but was almost zeroat the tension side. These trends and absolute valuescorresponded well in the results of the experiment and theFEM.
Next, we’ll discuss the thickness strain distribution afterhydroforming. In rotary draw bending, the thickness strain atthe compression side changed from positive to negative, butwas almost constant at the tension side from the time ofbending. Our previous report10) mentioned that thickness atthe tension side did not decrease due to axial feeding aftercontact with the hydroforming die, but during the finalpressure increase, a gap developed between the tube and dieat the compression side due to decreased thickness. On theother hand, the gap did not grow in intrusion bending due toa holding pressure pH that was higher than in rotary drawbending. As a result, thickness strain did not progress at thecompression side, which was comparatively thicker afterbending, and negative strain progressed at the intermediateand tension sides. Trends and absolute values for strain at thecompression side in the experiment and FEM corresponded,but strain at the tension and the intermediate sides was higherin the experiment and FEM, respectively. It is assumed thatthese differences are due to the timing of contact with the dieinfluencing strain at the tension and intermediate sides.
3.2 Effect on fracture positionFigure 12 shows the test samples that burst during axial
feeding of hydroforming. Burst during axial feeding occurreddue to excessive high holding pressure pH. This occurred inrotary draw bending at 16MPa or higher and in intrusionbending at 20MPa or higher. These bursts occurred at theintermediate side in all cases. These results corresponded tocases with 1 bend as mentioned in our previous report.10) TheFEM results in Fig. 13 show that the most extreme decreasein thickness was at the intermediate side during axial feedingno matter the bending case.
Next, we’ll discuss the positions where burst occurredduring final pressure increase. Some examples are shown inFig. 14. As indicated in the previous report,10) burst occurredat the compression side or near the R stop of the compressionside because the position at which the gap increased by axialfeeding expanded further during final pressure increase.Particularly in rotary draw bending, cases were observedwhere increased strain on the compression side resulted inburst (Fig. 14(a) below). In all cases of intrusion bending,burst occurred at the R stop near the compression side along
(a)
(b)
-0.3
-0.2
-0.1
0.0
0.1
0.2
0 45 90 135 180
Thic
knes
s stra
in ε t
Circumferential position θ /deg
Compression side
, Experiment：FEM Tension side
After bending
After hydroforming pH = 15 MPa
-0.3
-0.2
-0.1
0.0
0.1
0.2
0 45 90 135 180
Thic
knes
s stra
in ε t
Circumferential position θ /deg
Compression side Tension side
After bending
After hydroforming
, Experiment：FEM
pH = 18 MPa
Fig. 11 Circumferential distributions of wall thickness after bending andhydroforming (experiment and FEM). (a) Rotary draw bending, (b)Intrusion bending.
(a)
(b)
Top offorming
Bottom of forming
pH = 16 MPa
Burst
pH = 20 MPa
Top offorming
Bottom of forming
Burst
Fig. 12 Examples in which bursts occurred during axial feeding. (a) Rotarydraw bending, (b) Intrusion bending.
Effect of Bending Method on Tube Hydroforming 519
the area between the two bent parts due to the lowprogression of strain at the compression side, as describedin the section above. This is because the thickness in thestraight area is generally less than that at the bent positions.It is estimated that the straight area between the two bentparts was more easily burst because effective axial feedingwas more difficult. Figure 15 shows the FEM results forthickness distribution after hydroforming. It is observed thatthe thickness decreased significantly as the same positionswhere burst occurred in the experiments.
3.3 Effect on hydroforming allowanceThe effect of the bending method on hydroforming
allowance was investigated using results above. As
mentioned in 2.4, the authors evaluated the allowance bycomparing the length of the two arrows (dashed and dotted)for holding pressure pH. The dashed arrow means the areafrom the burst limit to the corner R limit and the dotted arrowmeans the area from the burst limit to the wrinkle limit undera 60mm final axial stroke ¤F. The results are shown inFig. 16. For the burst limit, the pressure was higher inintrusion bending due to relatively higher thickness, so theallowance tended to be larger. For the lower limit, however,the corner R limit pressure was lower in intrusion bending,while the wrinkle limit pressure was lower in rotary drawbending. As mentioned above, the corner R became smallerbecause intrusion bent thickness enabled load to be withstooduntil final application of high pressure. However, this wasbelieved to make wrinkles develop more readily duringintrusion bending. Generally speaking, this is because oflower die restraint. Sharp wrinkles were not observed inany kind of bending, however small wrinkles grew duringthe hydroforming process. Figure 17 shows FEM resultsof deformation in Bend No. 1 at the beginning of axialfeeding. From this figure, we can see that wrinkles appearedto develop more easily at the compression side of intrusionbending.
To summarize the findings above, rotary draw bendingis advantageous to the wrinkle limit, however the totalallowance of intrusion bending is greater. In addition, wefound that high internal pressure is necessary for the
(a)
(b)
pH = 20 MPa
Top offorming
Bottom of forming
Wall thickness/mm
Burst
pH = 20 MPa
Top offorming
Bottom of forming
Wall thickness/mm
Burst
Fig. 13 FEM results in which bursts occurred during axial feeding. (a)Rotary draw bending, (b) Intrusion bending.
(a)
(b)
Top of forming
Bottom of forming
pH = 11 MPa
Burst
Top of forming
Bottom of forming
pH = 15 MPa
Burst
Top of forming
Bottom of forming
Burst
pH = 19 MPa
Fig. 14 Examples in which bursts occurred during final raising of pressure.(a) Rotary draw bending, (b) Intrusion bending.
pH = 17 MPa
Top offorming
Bottom of forming
Wall thickness/mm
Burst
pH = 17 MPa
Top offorming
Bottom of forming
Wall thickness/mm
Burst
(a)
(b)
Fig. 15 FEM results in which bursts occurred during final raising ofpressure. (a) Rotary draw bending, (b) Intrusion bending.
4
8
12
16
20
24
Hol
ding
pre
ssur
ep H
/MPa
δF = constant (60 mm)
Burst limit
Burst limit
Corner R limit Wrinkle
limitCorner R limit
Wrinkle limit
Rotary draw bending Intrusion bending
Fig. 16 Hydroforming allowance in rotary draw bending and intrusionbending.
M. Mizumura and Y. Kuriyama520
hydroforming loading path in intrusion bending. This isbecause thickness reduction during bending process issuppressed in intrusion bending.
4. Conclusion
In order to investigate the effect of bending method onhydroforming in subsequent processes, S-shape tubes werehydroformed with the same die after application of two kindsof bending methods, rotary draw bending and intrusionbending. We made the following conclusion from the resultsof experiments and FEM.(1) Regarding distribution of wall thickness after hydro-
forming, wall thickness of the tube is thinnest on thecompression side for rotary draw bending and on thetension or intermediate sides for intrusion bending.
(2) Regarding burst position, burst occurs at the inter-mediate side during axial feeding no matter the bendingmethod. In rotary draw bending, burst occurs at thecompression side or at the nearby R stop, however, in
intrusion bending, burst does not occur at thecompression side, but occurs at the nearby R stopduring the final increase of internal pressure.
(3) Intrusion bending results in a larger hydroformingallowance than rotary draw bending. In addition, higherinternal pressure is necessary for intrusion bent tube.This is because the wall thickness after intrusionbending is greater than that after rotary draw bending.
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Hydroforming die Hydroforming die
Small wrinkle
(a) (b)
Fig. 17 Forming shapes at compression side of 1st bending under theconditions of 15MPa holding pressure and 20mm axial feeding (FEM).(a) Rotary draw bending, (b) Intrusion bending.
Effect of Bending Method on Tube Hydroforming 521
