1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 5, September - October (2013), pp. 250-256
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IJMET
©IAEME
BRANCH HEIGHT OPTIMIZATION OF COPPER TUBE HYDROFORMING
USING SIMULATION THROUGH TAGUCHI TECHNIQUE
PARTHASARATHY GARRE
Department of Mechanical Engineering, MLR Institute of Technology, Affiliated to JNTUH,
Hyderabad, India
ABSTRACT
Tubehydroforming is a process in which a hollow work piece is expanded into a useful form
in a die under high internal hydraulic pressure until the work piece balloons out to reach a desired
final shape. Though the process is used for manufacturing complex parts, predictions of wall
thickness and branch height development of tube are quite limited. Also, it is quite expensive to
experimentally validate a process and thus finite element simulation alone can provide a valuable
insight. In this work, + shaped component was taken up for tubehydroforming with boundary
conditions available from the literature and the process was simulated using HYPERFORM and
LSDYNA. After conducting simulation for the process, Taguchi technique was selected to determine
the optimum branch height of the copper tubehydroforming.
KEYWORDS: ANOVA, FEA, HYPERFORM, LSDYNA, L9, THF.
1. INTRODUCTION
1.1 Tubehydroforming
In tube hydroforming (THF), a tubular blank is placed between two dies, sealed and filled by
injecting pressurized water up to 1200MPa into it, deforming its walls and calibrating them to shape
the die cavities [1]. The process sequence from 1 to 6 for a typical tubehydroforming operation
follows as shown in Fig.1. The typical process cycle includes placing the blank onto the lower tool,
closing the die, and applying fluid pressure into tubular section. The pressure is sufficient to cause
the blank to deform plastically and take the shape of the tool cavity.
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
Fig.1.1: The process sequence for a typical hydroforming operation
1.2. Failure Modes of Tubehydroforming
It is required that the tubular blank should be formed into a die cavity of desired shape
without any kind of defects such as bursting, wrinkling or buckling. Since bursting is a consequence
of necking, which is a condition of local instability under excessive tensile stresses, prediction of
necking initiation is an important issue before designing the details of processes [2]. The potential of
the expansion process for forming work pieces is limited by the failure modes of Buckling,
Wrinkling and Bursting as shown in Fig.1.2. The tube hydroforming processes has two loading
variables, i.e. the internal pressure and the axial feeding distance [3].
Fig.1.2: Common failure modes in THF process are wrinkling, buckling, and bursting
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3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
A successful tubular hydroforming depends on a reasonable combination of the internal
pressure and the axial compression force at the tube ends. Thus, the information on the tubular
hydroforming limit, the final wall thickness distribution and the final contact quality between the
deformed tube and the tools is necessary for a designer [4]. Determining the range of values for each
of the above parameters and getting a right combination of them is taken up as the problem for this
work. Finite element analysis in conjunction with experimental validation can provide a better
understanding of the process. It should be noted, however, that it is quite expensive to experimentally
validate a process where the geometry is complex in nature, and thus finite element simulation alone
can provide a valuable insight and understanding of the process and help in new prototype or product
design and development [5]. Thus the process is to be simulated using Altair’s HYPERFORM and
LSDYNA. Taguchi method is used to determine the process parameters with optimal branch height
[6] without any defect. In the process of THF, which is usually characterized by the reduction in wall
thickness and increase in internal volume and surface area of the tube, the internal pressure will drop
quickly if no extra fluid flows into the tube timely with the augment of the tube volume, and then the
overall process has to be suspended in the case of free bulge forming (FBF) operation when it drops
to a minimal pressure level required for the plastic forming, or when severe buckling or wrinkling
takes place in the case of bulge forming with axial loading (BFAL) operation. In fact, metal tube is
strain-hardened in cold THF process, in which a climbing pressure is required to continue the plastic
forming. Therefore, the timely supply of pressurized fluid into the deforming tube and proper control
of the internal pressure are critical to carry the process to the end [7]. The material properties, that
are generally required to assess the component stiffness and strength characteristics under various
loading conditions, as such copper is considered as material in tubehydroforming.
1.3. Finite Element Analysis
FEA simulations provide insights on the necessary process parameters/ loading paths (i.e.
internal pressure and axial feed), part geometry, and part formability by analyzing the thinning,
thickening, and strain distribution in the deformed tube. Tubehydroforming process can be simulated
using Hyperform with incremental analysis and LS-DYNA software.
1.4. Taguchi Technique
In the present work, the Taguchi Technique has been applied to Tubehydroforming process.
The application steps are selecting projects, planning the experiment, designing the experiment,
conducting the trail run of experiment, analyzing the results (ANOVA) and confirmation test. An
orthogonal array is a matrix of numbers arranged in columns and rows. The array is called
orthogonal because the levels of various factors are balanced and can be separated from the effects of
the other factors within the experiment. In this case L9 standard orthogonal array is considered.
2. RESULTS AND DISCUSSION
The first objective of Taguchi methods is to reduce the variability in quality. In order to find
out variability, standard L9 array was chosen and formulated and then simulation results were
included in it and then conducting ANOVA to determine the contribution of each variable for the
optimized process parameters. The formulated orthogonal array TABLE 2.1 is shown below.
Column I represents the internal pressure, column II represents axial pressure and column III
represents thickness of the blank. The number below the roman letters represents the levels of each
factor.
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4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
Table 2.1: Formulated L9 array table for all factors
Experiment
columns
I
II
III
1
190
8
0.8
2
190
10
1
3
190
12
1.5
4
200
8
1
5
200
10
1.5
6
200
12
0.8
7
210
8
1.5
8
210
10
0.8
9
210
12
1
2.1. Results of Simulation
The simulation results from the above L9 array table for values internal pressure, axial feed
and thickness as (190, 8, 0.8) to get branch height as 10.48 is shown in Fig.2.1.
Fig.2.1: Deformed blank and FLD at ip=190; af=8; t=0.8
The simulation results for values internal pressure, axial feed and thickness as (190, 10, 1) to
get branch height as 10.2166 is shown in Fig.2.2.
Fig.2.2: Deformed blank and FLD at ip=190; af=10; t=1
Similarly the simulation results for values for the rest of the internal pressure, axial feed and
thickness as in the L9 array TABLE 2.2 shown below.
2.2. Formulated Array with Response Factor
The formulated L9 array with all factors and response factor that is branch heights are shown
in the following table. The response factors are from simulation results as said above.
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5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
Table 2.2: Formulated L9 array of all factors and response factor
Experiments
Factor I Factor II Factor III Response Factor(Y)
1
190
8
0.8
10.48
2
190
10
1
10.2166
3
190
12
1.5
11.4066
4
200
8
1
10.43
5
200
10
1.5
10.39
6
200
12
0.8
10.0116
7
210
8
1.5
11.34
8
210
10
0.8
10.1766
9
210
12
1
10.2633
2.3. ANOVA
Generating the response table as per the standard format of L9 array for various factors and
levels are as shown in TABLE 2.3.
Table 2.3: Calculated response table
Levels
Factor I
Factor II
Factor III
1
10.7011
10.2227
10.3777
2
10.2772
10.3033
10.5227
3
10.5933
11.0455
10.6711
Preparing the ANOVA table as per standard L9 array and included in the following TABLE
2.4 as shown below.
Table 2.4: Final results in ANOVA table
SOURCE
DOF
SS
MSS
F ratio
Internal
2
0.3039 0.15195 0.869
pressure
Axial
feed
Thickness
Error
2
1.2407
0.62035
3.5479
2
2
0.1354
0.3497
0.0677
0.1749
0.3872
-
2.4. RESPONSE GRAPHS
The response graphs are drawn as shown in GRAPHS 2.1, 2.2 and 2.3 with the appropriate
confidence intervals for the factors and levels. This gives a graphical representation of the
differences between the factor levels.
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6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
Response factor I graph
10.8
10.7
B ch h h
ran
eig t
10.6
10.5
10.4
Series2
10.3
10.2
10.1
10
1
Series2
10.7011
2
3
10.2772
10.5933
Internal pressue
Graph 2.1: Graph between branch height Vs internal pressure
Response factor II graph
11.2
11
Branch height
10.8
10.6
Series3
10.4
10.2
10
9.8
1
Series3
10.2227
2
3
10.3003
11.0455
Axial feed
Graph 2.2: Graph between branch height Vs axial feed
Response factor III graph
10.7
10.65
Branch height
10.6
10.55
10.5
10.45
Series2
10.4
10.35
10.3
10.25
10.2
1
Series2
10.3777
2
3
10.5227
10.6711
Thickness
Graph 2.3: Graph between branch height Vs thickness
3. CONCLUSION
The inference from the results obtained from the application of Taguchi technique to the THF
process is discussed here. The predicted mean value (190, 12, 1.5) of the branch height is 11.4066
and the confirmation experiment value (190, 12, 1.5) of the branch height is 11.44 as shown in the
Fig.3.1.
Fig 3.1: Deformed blank and FLD at ip=190; af=12; t=1.5
Here the range overlaps and then the experiment can be regarded as reproducible. Hence by
using Taguchi technique we can determine the optimized process parameters.
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7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
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