4TH INTERNATIONAL CONFERENCE ON TUBE HYDROFORMING (TUBEHYDRO 2009)
September 6-9, 2009, Kaohsiung, Taiwan.

Effects of Draw Bending Conditions of Tube on Deformation of theBent Tube during the Subsequent Hydroforming Process
Katsushi Ishigaki*1, Naoyoshi Sakaguchi1 , Naoto Kaneda1 and Masayasu Kojima1
1
Yamamoto Hydraulic Machinery Works Co.,LTD
Abstract: This paper describes a sequential FEM simulation of draw bending of tube andhydroforming of the bent tube. The effects of draw bending conditions such as mandrel inserted thetube and axial compression applied to the end of the tube on the thinning behavior during thehydroforming are made clear. Minimizing the amount of flattening of the bend by using a multiple
ball mandrel is effective to decrease thinnings of the outside and the side walls of the bend during
the hydroforming. Increasing the axial compression of the tube during the draw bending is effective
to increase the thicknesses of the outside and the side walls of the bend after the hydroforming.
Keywords: Draw bending, hydroforming, ball mandrel, axial compression, flattening.
1.

Introduction
Structural parts with hollow section for auto-body manufactured by tube hydroforming process
have two or more bends along the axis. Prior to the hydroforming of these parts, a straight tube
blank for each part is bent on a draw bending machine to approximately the final shape of the part.
During the bending operation, non-uniform circumferential distributions of wall thickness andwork-hardening are formed in the bend, therefore, expansion ratio of the bend in the subsequenthydroforming process should be limited to prevent localized thinning or bursting. In this paper, asequential FEM simulation of draw bending and hydroforming is performed for the purpose of
making clear the suitable draw bending conditions to decrease the thinning of the bend during thehydroforming and to increase the thickness of the bend after the hydroforming.
2.

Simulation model (Solver=LS-DYNA)

2.1 Tube blank
Steel tube with diameter of 60.5mm, wall thickness of 2mm, and length of 418mm is modelled byshell elements. The periphery of the tube is composed of 120 elements with axial edge length of2mm. Stress-strain relationship of the tube is shown in Fig.1. Yield point σy, Young’s modulus E,
slope of the linear work-hardening Et, and Poisson’s ratio ν are listed in Table 1.
Table 1 Mechanical properties of tube

σσytan-1Etan-1Et
εFigure 1 Stress-strain relationship of tube

Yield point σyYoung’s modulus E
Slope of linear work-hardening Et
Poisson’s ratio ν354 [MPa]206 [GPa]
1.26 [GPa]0.3

2.2 Draw bending
The tube blank is bent at an angle of 90° with a centerline radius of 120mm as shown in Fig.2.
Fig.2 (a) shows tooling before starting the bending operation. Bending tools are bending form,clamp die, movable pressure die, wiper die, and flexible ball mandrel. The surfaces of the bending
tools are modeled by rigid shell elements. The wiper die is fixed to the main body of the bender witha heel angle of 0.5°. Nodes at the top of the tube are fixed with both the straight clamping sectionof the bending form and the mating clamp die. Table 2 shows coefficient of friction in the contact
interfaces between the tube and the bending tools. In this simulation, four kinds of mandrel
conditions are studied. They are 1-ball, 2-ball, 3-ball shown in Fig.3 and without mandrel. The ball
mandrel consists of a shank and ball segments. The shank and the ball segments are connectedwith ball joints. The clearance between the tube and the ball mandrel is 0.5mm. The ball mandrel
supported by a rod is positioned as shown in Fig.2. In this study, axial compressive stress fb applied
to the end of the tube is considered as another bending condition by which the thickness of the bend
after hydroforming will be controlled. The magnitude of fb is constant during the draw bending
process.

R120

Tangent point

Bending form
Wiper die
Tube
0.5°
fbfb

(a) φ60.5(b)115

Clamp die450

Rod

Ball mandrel

Pressure die

Figure 2Pf(+)
Frictional force

Simulation model of draw bending of tube

Table 2 Coefficient of friction during bending
Bending tools
Bending form
Clamp diePressure die
Wiper dieBall mandrel

Pf(-)
Ls

Coefficient of friction
0.1
0.5
0.2
0.1
0.1

Ball segment

Tangent point
φ56

14R2
R2855

150

Shank Rod

Figuremandrel(1-ball,2-ball,3-ball)Fig.3 3BallBall
mandrel（1-ball、2-ball、3-ball）

Fig.2 (b) shows the final state of the draw bending operation. In this simulation, the pressure die ismoved with a constant velocity during the rotation of the bending form. Displacement of thepressure die (Ls) for the bending angle of 90° can be determined arbitrarily. In this study, themagnitude of the displacement of the pressure die is expressed by non-dimensional γ defined byEq.1.
γ=Ls/(Rθ)(1)

Where R is bending radius (=120mm), θ is bending angle in radian (=π/2 ). Depending on themagnitude of γ, velocity of the pressure die to the tube is varied, and consequently, the longitudinalfrictional force Pf (see Fig.2 (b)) applied to the pressure die from the tube is varied. In the simulation,
the direction of Pf is distinguished by the sign of plus or minus. Minus Pf is forward frictional force
and plus Pf is backward frictional force. As the direction of the frictional force applied to the tube
from the pressure die is reverse to the direction of Pf, minus Pf and plus Pf act as backward tension
and forward compression for the tube respectively.
2.3 Hydroforming
Dimensions of the hydroformed workpiece are shown in Fig.4. The bent tube illustrated by dottedline is set in the hydroforming die and the bend of the bent tube is expanded to 1.1 times thediameter of the tube blank by increasing the internal pressure. The edge nodes in the bent tube arefixed to the hydroforming die to simulate the hydroforming without axial feeding. Coefficient offriction in the contact interface between the tube and the die is 0.1.

115
30
Bent tube（dotted line）
aOutside Sidebwall
wall
R120c
ac

Hydroformed workpiecedInsidewall

φ66.6

Fig.44 Dimensionsof ofhydroformed
workpiece
FigureDimensionshydroformed
workpiece

Lc
45°ac Dbd

Dac
Reduction.of
Reduction
ofD
Periphperipheral lengtha
β=1-Lc／(π・ D)
Fig.5
of 45°crosssectionof bendFigureDimensions
5 Dimensionsof 45°crosssectionofbendc

3.

Simulation results on the effects of mandrel conditions

3.1 Flattening of the bend in draw bending
The role of the mandrel in the draw bending is reduction of the amount of flattening[1]. In thisstudy the flatness of the bend is defined by Eq.2.
α=(Dbd-Dac)/D(2)

(a)

0.2
0.1
00.90

0.95

1.00

Displacement of pressure die γ

Figure 6

Variations of frictional force
Pf and flatness α with γ (fb=0)

β0.2

0.04
β

α

0.1

0.02

00

Mandrel conditions

Figure 73ba
ll(b)

0.06

1ba
ll
2ba
ll

Flatnessα

0.3

0.3

ithout0.95

Without
1-ball2-bal
3-ball
1.00

W

15
10
5
0-5-10-15
0.90

Flatness α

Pf (kN)

Where Dac and Dbd are diameters at 45° cross section shown in Fig.5, and D is diameter of thetube blank. Fig.6 (a) and (b) show the variations of Pf and flatness α with γ respectively. From Fig.6(a) and (b), it is observed that α decreases with the change of the sign of Pf from minus to plus, andthe variations of α with Pf are reduced with increasing the number of the ball segment. In this study,
the effects of the mandrel condition on α are evaluated at critical γ(=γcr) which makes Pf zero. Fig.7
shows variations of α, reduction of peripheral length β(see Fig.5), and shape of 45° cross section ofthe bend with mandrel conditions. In the case of bending without mandrel, concaved deflection isobserved on the flattened outside wall. From Fig.7, it is clear that large α brings large β, andconsequently, increases the actual expansion ratio during the subsequent hydroforming process.

Variations of flatness and reductionof peripheral lengthβwith mandrel
conditions (fb=0, γ=γcr)

3.2 Expanding behavior of the bend during the hydroforming
Enlargement of the cross section of the bend is observed by measuring the clearance between
the wall of the bend and the wall of the die cavity at 45° cross section. Fig.8 (a), (b), and (c) showvariations of the clearance δ at the outside, the side, and inside walls respectively, with the increaseof the internal pressure p. In Fig.8 (a), difference of the initial δ at p=0 among the mandrel conditions
is due to the difference of α shown in Fig.7. The larger the initial δ, the faster the flattened outside
wall is expanded out with increasing p. It seems that the outside, the side, and the inside walls
contact with the mating wall of the die cavity at almost the same p for the mandrel conditions of
1-ball, and 3-ball. Fig.9 (a), (b), and (c) show variations of longitudinal strain εl on the outside, theside, and the inside walls at 45° cross section with increasing p for the condition of without mandrel,1-ball, and 3-ball respectively. For all mandrel conditions, the change of εl during the hydroformingis plus at the outside wall, nearly zero at the side wall, and minus at the inside wall, as expectedfrom the difference of the longitudinal curvature radius between the bent tube and the hydroformed
tube shown in Fig.4. In the condition without mandrel shown in Fig.9 (a), increase of εl starts at low
pressure (less than 20MPa) corresponding to the reduction of δ at the initial stage of increasing p
shown in Fig.8 (a). Comparing Fig.9 (a), (b), and (c), it is observed that the increase of εl on theoutside wall during hydroforming is reduced by using a multiple ball mandrel.

Fig.10 (a), (b), and (c) show variations of circumferential strain εθ on the outside, the side, and theinside walls at 45° cross section with increasing p for the condition of without mandrel, 1-ball, and3-ball respectively. It is observed that εθ on the side wall starts to increase at less p than that on theoutside and the inside walls, and that the increase of εθ on the side wall is noticeably larger thanthat on the outside and the inside walls. It is considered that the phenomenon of increasing εθ onthe side wall is mainly due to the fact that the work-hardening during the draw bending of the sidewall is noticeably less than that on the outside and the inside walls.

Clearance δ(mm)(a) Outside wall

Without mandrel
1-ball mandrel
3-ball mandrel

1055500040p(MPa)Figure 80.20.2

2040p(MPa)Figure 9-0.3
02040p(MPa)060(b) 1-ball mandrel

0.2

Side wall-0.1

2040p(MPa)60

Inside wall

0.1

Inside wall

0Side wall

0Side wall

-0.2
2040p(MPa)60

Outside wall

-0.1

Outside wall

Outside wall

-0.2(c) 3-ball mandrel

0.2

0.1

-0.1

0

Inside wall

-0.2

Variations of longitudinal strain at 45°cross section of bent tube withincrease of internal pressure (fb=0, γ=γcr)

Inside wall

0Side wall0

Inside wall

-0.2
60

Outside wall

-0.1

-0.1

(a) Without mandrel

0.1

60

0.1

-0.3

0.240p(MPa)(c) 3-ball mandrel

0.2

Side wall

0-0.3
0200.3

Outside wall

0.1

Inside wall

-0.260(b) 1-ball mandrel

0.3

Side wall

040p(MPa)

10Variations of clearance between wall of die cavity and bent tube withincrease of internal pressure (fb=0, γ=γcr)

Outside wall

0.1

2060(a) Without mandrel

0.3

-0.1

Circumferential strain εθ(c) Inside wall

1020

Longitudinal strain εl(b) Side wall

-0.2
02040p(MPa)6002040p(MPa)Figure 10 Variations of circumferential strain at 45°cross section of bent tube
with increase of internal pressure (fb=0, γ=γcr)

60

In Fig.10, it is also observed that the increase of εθ on the side wall is reduced by using a multiple
ball mandrel. In the condition without mandrel shown in Fig.10 (a), it must be noticed that εθ on theoutside wall is reduced at low pressure (less than 20MPa). This means that the peripheral length of
the bend, which is reduced largely during the bending without mandrel, is reduced again at the initialstage of the hydroforming. The reduction of the peripheral length of the bend due to the reduction ofεθ on the outside wall increases the total expansion ratio during the hydroforming. Fig.11 (a), (b),and (c) show variations of the thickness strain at 45° cross section of the bent tube and thehydroformed tube with mandrel conditions on the outside, the side, and the inside walls respectively.
In the case of the circular expansion by the hydroforming in this study, the most thinned area after
the hydroforming is the outside wall for all mandrel conditions. From Fig.11 (a), it is noticed that thedegree of thinning of the outside wall after the hydroforming is hardly affected by the mandrel
conditions, while the thinning of the outside wall after bending increases by using a multiple ball
mandrel. In other words, it can be said that the larger the amount of flattening in the draw bending,the larger the thinning of the outside wall during the hydroforming. Comparing the differences
between the thickness strain after draw bending and that after hydroforming in Fig.11 (a), (b), and(c), it is clearly observed that the thinning during the hydroforming of the side wall is noticeably
larger than that of the outside and inside walls. From Fig.11 (b), it is noticed that the thinning of theside wall during the hydroforming is reduced by using the multiple ball mandrel. The thinning of theinside wall during the hydroforming is small and is hardly affected by the mandrel conditions asshown in Fig.11 (c).

Outside wall

-0.1
-0.2

Bent tube
Hydroformed tube

-0.3
1-ball2-ball3-ball(b)0
Bent tube

-0.1

(a)

20
fb=0

15
10
50-5-100.9

Side wall

0.95
1
1.05
1.1
Displacement of pressure die γ-0.2
Hydroformed tube

-0.3
without

1-ball2-ballBent tube0.2
0.13-ballInside wall

Hydroformed tube
1-ball2-ballInside wall

0.2
0.1

fb=0
fb=66.7[MPa]fb=133[MPa]0Outside wall

-0.1
-0.2

0without(b)0.3(c)

0.3

fb=66.7 fb=133[MPa] [MPa]-15

Thickness strain εt

Thickness strain εt

without

Frictional force Pf (kN)(a)

03-ballFigure 11 Variations of thickness strain at 45°
cross section of bent tube and hydroformedtube with mandrel conditions in draw bending(fb=0, γ=γcr)

0.9

0.95
1
1.05
1.1
Displacement of pressure die γFigure 12 Effects of axial compressive
stress fb on variations of frictional
force Pf and thickness strain with γ(3-ball mandrel)

4.
Simulation results on the effects of axial compression applied to the tube during
bending
4.1 Thinning and thickening in draw bending
It is known that the compressive stress applied to the tube by using a booster decreases thethinning of the outside wall of the bend and increases the thickening of the inside wall of the bend[2]. Both the thinning and the thickening are also affected by the direction of the frictional force Pf.
Fig.12 (a) and (b) show effects of the compressive stress (fb) on the variations of Pf and thickness
strain of the bend respectively, with the non-dimensional displacement (γ) of the pressure die in thedraw bending with 3-ball mandrel. In Fig.12 (a), it is clear that γcr, which makes Pf zero, increases
with the increase of fb. And in Fig.12 (b), it is observed that the thinning of the outside wall isdecreased and the thickening of the inside wall is increased by the change of the sign of Pf fromminus to plus accompanied with the increase of γ. The effects of fb on the thinning and thethickening of the bend should be evaluated by the thickness strain obtained at the condition of γcr foreach value of fb.
4.2 Thickness strain of the bend after hydroforming
Fig.13 (a), (b), and (c) show variations of thickness strain at 45° cross section of the bent tube
and the hydroformed tube with fb on the outside wall, the side wall, and the inside wall respectively.
Increase of fb is effective to increase the thickness of the outside wall and that of the side wall after
the hydroforming. Differences of the thickness strain between the bent tube and the hydroformed
tube on the outside, the side, and the inside walls are hardly affected by the magnitude of fb.
(a) Outside wall

Thickness strain εt0.30.3(b) Side wall

0.2

0.2

0.1

0.1

000

-0.1

-0.1

Bent tube

-0.1
-0.2

Hydroformed tube

-0.3
050

100

150

-0.2
-0.3

(c) Inside wall

0.3

Bent tube

0.2
Bent tube

Hydroformed tube

0.1

Hydroformed tube

-0.2
-0.3

050
100
150
Axial compressive stress fb (MPa)050

100150Figure 13 Variations of thickness strain at 45°cross section of the bent tube and the hydroformed
tube with axial compressive stress at tube end in draw bending(3-ball mandrel, γ=γcr)
5.

SUMMARY
Effects of the mandrel conditions and the compressive stress applied to the end of tube in thedraw bending on the thinning behavior of the bend during the subsequent hydroforming areinvestigated by the sequential FEM simulation.
(1) The most thinned area after hydroforming is the outside wall and the most thinned area duringhydroforming is the side wall for all mandrel conditions. Minimizing the amount of flattening of
the bend by using a multiple ball mandrel is effective to decrease thinnings of the outside andthe side walls during the hydroforming.
(2) Increasing the axial compression applied to the end of the tube during the draw bending iseffective to increase the thicknesses of the outside and the side walls of the bend after thehydroforming.
REFERENCES[1] R.J.Kervick, R.K.Springborn, 1966, “Cold bending and forming tube and other sections”, ASTME[2] D.Park, Y.Kim, 2005, Effect analysis of bending process on hydroforming, “Proceedings ofTUBEHYDRO2005“, PP.18-22