Optimization of Variation in Wall Thickness of a Deep Drawn

IRACST – Engineering Science and Technology: An International Journal (ESTIJ), ISSN: 2250-3498
Vol.4, No.5, October 2014
Optimization of Variation in Wall Thickness of a
Deep Drawn Cup using Virtual Design of
Experiments
Mrs. Ketaki N. Joshi
Assistant Professor
Lokmanya Tilak College
of Engineering
Navi Mumbai, India
Dr. Bhushan T. Patil
Associate Professor
Fr.Conceicao
Rodrigues College of
Engineering, Bandra
Mumbai , India
Abstract— This paper presents an investigation of the effect of die
draw radius, sheet thickness and blank holder force on the
variation in wall thickness of a deep drawn cup using finite
element simulations. The variation in wall thickness is minimized
by carrying out analysis of variance (ANOVA) for individual
factors and their interactions.
Keywords- Metal forming process; Deep drawing; finite element
simulations;design of experiments; Hyperform; ANOVA; Wall
thickness Variation
I.
INTRODUCTION
Deep drawing is one of the metal forming processes used to
produce a cup like cylindrical component by radially drawing
metal blank into the die cavity with the help of a punch. The
cup shaped part produced by this process has the depth greater
than half of its diameter. The change in cross-section of the
metal is achieved by plastic deformation of the initial blank.
Optimization of the process plays an essential role in
improving industrial performance measures such as
productivity and cost. In order to improve the process
outcome, a number of process parameters such as blank shape,
sheet dimensions, blank holding force, lubrication and
punch/die design need to be controlled and optimized. [5] It is
difficult yet essential to analyze the effect of various
parameters on the process output and select their optimal
values due to complexity of process and large number of
factors involved in it. Finite element analysis is nowadays
accepted and preferred by the industry over analytical and
experimental approaches being more economic, time saving
and equally effective in predicting the process output.
Numerical simulation technology combined with optimization
techniques has been applied in sheet metal forming processes
Mr. Sunil Satao
Dr. Chandrababu. D
Assistant Professor
Lokmanya Tilak College
of Engineering
Navi Mumbai, India
Head of Department
(Mechanical)
Lokmanya Tilak College
of Engineering
Navi Mumbai, India
in order to improve design quality and shorten design cycle.
[29]
II.
LITERATURE REVIEW
A. Review of Parameters Investigated
F. Ayari et al. (2009) [22] conducted a parametric study of
deep drawing using FEM model which is built using
ABAQUS/ Explicit standard code. In that they considered
influential parameters such as geometric, material parameters
and coefficient of friction and validated them against
experimental results.
Kopanathi Gowtham et al. (2012) [24] studied the effect of
variation in die radius on effective stress, effective strain, max.
principal stress, max. principal strain, damage value and load
required. They concluded that die radius is an important design
parameter and they also optimized it using FE simulations.
Pandhare et al. (2012) [25] used FE simulations to optimize
blank holder force in deep drawing process using friction
property of CRDQ steel. They studied FLD for different values
of µ and found that BHF first increases upto a certain limits
and then decreases. For low BHF values, wrinkling defect is
observed whereas high values of BHF result into failure, the
optimum value is the one which reduces the probability of both
the defects.
R. Padmanabhan et al. (2007) [30] studied the significance
of three parameters die radius, blank holder force and friction
coefficient on deep-drawing characteristics of a stainless steel
axi-symmetric cup using finite element method combined with
Taguchi technique. They carried out a reduced set of finite
element simulations based on the fractional factorial design of
L9 orthogonal array and analyzed the relative importance of the
selected parameters on thickness distribution using ANOVA.
From the analysis they concluded that die radius has the
124
IRACST – Engineering Science and Technology: An International Journal (ESTIJ), ISSN: 2250-3498
Vol.4, No.5, October 2014
greatest influence on the deep drawing of stainless steel blank
sheet which is followed by the blank holder force and then the
friction coefficient.
P V R Ravindra Reddy et al. (2012) [32] have studied the
effect of blank holding force and die draw radius on the limit
strains in deep drawing process using an explicit finite element
code LSDYNA. They have validated the results of the
simulations with the strain values obtained by analytical
formulae for power law plasticity models. The observations
from the investigation were increase in limit strains with
increase in die corner radius. They also concluded that even
though safer deformation zone increases with blank holder
force (BHF), limit strains are independent of BHF at lower
ratio of principal strains.
IV.
RESEARCH METHODOLOGY
The research methodology used for the current work is as
shown in the figure 1 below.
R. Venkat Reddy et al. (2013) [33] have conducted a
parametric study of BHF, sheet thickness, die profile radius,
punch profile radius, initial yield stress, sheet anisotropy and
imperfections. They found that maximum cup height at the
onset of wrinkling increases with Blank Holding Force (BHF),
sheet thickness and an increase in the die profile radius as well
as punch profile radius. They also concluded that die profile
radius is more significant and resistance to wrinkling also
depends on anisotropy.
From above discussion and findings, it is clear that
researchers have mainly worked towards improvement in
formability and elimination of various defects such as
wrinkling, fracture, thickness variation and other surface
defects by careful selection of sheet material and process
parameters such as friction, blank holder force, die draw radius,
punch radius, blank shape and number of redrawing steps. It is
also evident that researchers are successfully using FE
approach to optimize the deep drawing process to reduce costly
and time consuming experimental trial and errors and
simulations can be combined with various optimization
techniques such as design of experiments, analysis of variance,
Taguchi's robust design for improving design quality and
reducing design cycle time.
III.
RESEARCH GAP
After a thorough analysis of the literature, it was found that
researchers have investigated the effect of various process and
design parameters on the process output using FE simulations
but very few researchers have carried out a comprehensive
parametric study to find the relative importance of the
parameters using finite element method coupled with Taguchi’s
techniques. There lies a future scope of conducting a more
comprehensive parametric study of the deep drawing process
parameters using finite element simulations and their
interactions for optimizing the process using full factorial
design of experiments. Hence, the aim of the present work is to
investigate the effect of die draw radius, blank thickness and
blank holder force on variation in wall thickness of the deep
drawn cup and select their optimal values using full factorial
design.
Figure 1: Deep Drawing Simulation Methodology
The geometry of the die and blank is prepared using
modeling software PRO-E and then is imported into the
preprocessor Hyperform. There all the preprocessing steps are
carried out and then the analysis is carried out using LSDYNA
solver. The output of the analysis stage is viewed using
postprocessor Hyperview. The simulations are carried out
based on full factorial design of L27 orthogonal array and then
the relative importance of the selected parameters and their
optimal values are analyzed using ANOVA.
The parameters selected for the investigation are as follows:
Dependent Variables
Dependent variables are the ones that depend on other
variables. The dependent variable selected for the present work
is percent thickness variation which gives the variation in the
wall thickness of a deep drawn cup as a percent of original
blank thickness. During deep drawing, tensile and compressive
stresses developed in them metal result into uneven thickness
of the formed component, which may result into failure of the
component in working condition. Hence the aim is to always
select design parameters and control the process variables such
that variation in the wall thickness is minimum.
Independent Variables
Independent variables are not dependent on any other
parameter. These are the inputs to the analysis and mainly
contribute to measurement of model.
125
IRACST – Engineering Science and Technology: An International Journal (ESTIJ), ISSN: 2250-3498
Vol.4, No.5, October 2014
In the present work, independent variables selected are as
follows:
¾
Die draw radius
¾
Blank thickness
¾
Blank holder force
The chart below clearly indicates that, percent thickness
variation first increases as the level of factor A (die draw
radius) changes from 1 to 2 and then decreases as the level
changes from 2 to 3. Whereas % thickness variation increases
as the level changes from 1 to 2 and from 2 to 3 for both factor
B (Sheet thickness) and factor C (BHF).
The model of the deep drawing process, which is the
outcome of the preprocessing step, used for the finite element
analysis is as shown in the figure 2 below:
Figure 2: Outcome of the preprocessor used for
FE analysis
V.
Results of Analysis of variance considering the effect of
individual factors and their interactions are as given in Table 3
below:
Table 3: Modified ANOVA Summary Table for Percent
Thickness Variation
DATA COLLECTION AND ANALYSIS
Full factorial design is used for analysis of variance in the
present work. The material of the deep drawn componenet
selected for the study is CRDQ steel. Three parameters with
their three levels selected for this purpose are given in the table
1 below:
MODIFIED ANOVA SUMMARY TABLE
SS
D.
F.
M.S.S
.
F
al
Total
LEVELS
1
2
3
A
Die Draw Radius (mm)
4
5
6
B
Sheet Thickness (mm)
1
1.2
1.4
C
Blank Holder Force (KN)
20
30
40
The results for average response of percent thickness
variation for individual factors are as given in the table 2
below.
Table 2: Average Response of Percent Thickness Variation
for individual Factors
FACTORS
A
B
C
Average Response ( % Thickness Variation)
Level 1
Level 2
Level 3
23.6449
24.7633
24.8685
26.9151
25.0861
25.5394
26.1466
26.8571
26.2987
at
α=
0.05
Table 1: Factors and their levels selected for simulation
FACTORS
Fcritic
A
B
C
AXB
AXC
BXC
Error
99.0161
52.6270
22.8743
9.2158
12.0718
0.4653
1.5026
0.2593
26
2
2
2
4
4
4
8
26.3135
11.4372
4.6079
3.0179
0.1163
0.3756
0.0324
811.75228
352.8282
142.1500
93.1013
3.5886
11.5885
4.46
4.46
4.46
3.84
3.84
3.84
Significant
Significant
Significant
Significant
Insignificant
Significant
For studying the interaction effects pair-wise comparisons
are useful. For this study, we need to make a distinction
between focal independent variable and moderate variable. The
focal independent variable can be 'assigned-active distinction'.
The assigned independent variable i.e. a characteristic intrinsic
to the participant such as sheet thickness in this case and the
active independent variable i.e. the one assigned or designed by
the researcher such as die radius or blank holder force will be
considered as the focal variable. In the current analysis, sheet
thickness is designated as moderator variable and die draw
radius and blank holder force are designated as focal
independent variables.
From the above analysis, it is clear that interaction AXC
(die radius with BHF) is insignificant. Hence interaction effect
of AXB and BXC is studied further. For each sheet thickness
126
IRACST – Engineering Science and Technology: An International Journal (ESTIJ), ISSN: 2250-3498
Vol.4, No.5, October 2014
one-way ANOVA is carried out for interactions AXB and BXC
for each sheet thickness to conclude on the effect. From the
analysis, it is clear that the interaction effect AXB is significant
at each level of sheet thickness and hence post-hoc analysis by
doing pairwise comparison is carried out to determine the
optimal values. The details are given in table 4 to 6 below.
Table 4: Pairwise Comparison (AXB) for % Thickness
Variation for 1 mm Sheet Thickness
Pairwise
Comparison
Difference
Level1 - Level2
22.8733 - 25.5400 =
-2.6667
25.5400 - 25.8767 =
-0.3367
22.8733 - 25.8767 =
-3.0033
Level2 - Level3
Level1 - Level3
95 % confidence
interval (difference
±0.3336)
(-3.0419, -2.2914)
Level1 - Level2
22.1806 - 26.9194 =
-4.7389
26.9194 - 26.1583 =
0.7611
22.1806 - 26.1583 =
-3.9778
Level2 - Level3
Level1 - Level3
(-3.3786, -2.6281)
1.
When any sheet
thickness is permitted
2.
When Sheet Thickness
of 1 mm is permitted
3.
When Sheet Thickness
of 1.2 mm is permitted
4.
When Sheet Thickness
of 1.4 mm is permitted
(0.3859, 1.1363)
(-4.3530, -3.6025)
It is clear that all the three differences are significant and
the mean for level 1 of factor A (die draw radius - 4 mm) is the
lowest (22.1806).
Table 6: Pairwise Comparison (AXB) for % Thickness
Variation for 1.4 mm Sheet Thickness
Pairwise
Comparison
Difference
Level1 – Level2
25.8810 - 28.2857 =
-2.4028
28.2857 - 26.4048 =
1.8810
25.8810 - 26.4048 =
-0.5238
Level2 - Level3
Level1 - Level3
Table 7: Summary of Optimal Combinations for Minimum
Percent Thickness Variation
Details of the
Requirements
95 % confidence
interval (difference
±0.3336)
(-5.1141, -4.3636)
95 % confidence
interval (difference
±0.3336)
(-2.7800, -2.0295)
it is clear that all the three differences are significant and
the mean for level 1 of factor A (die draw radius - 4 mm) is the
lowest (25.8810).
Optimal Combination of Factors
and levels for Minimum Percent
Thickness Variation
Factor A - Level 1
Factor B - Level 2
Factor C - Level 1
Factor A - Level 1
Factor B - Level 1
Factor C - Level 1
Factor A - Level 1
Factor B - Level 2
Factor C - Level 2
Factor A - Level 1
Factor B - Level 3
Factor C - Level 3
To conclude, in the present paper the effect of die draw
radius, sheet thickness and blank holder force on the material
thinning in deep drawing, individually and interactions is
analyzed by using finite element analysis coupled with design
of experiments. Optimal combination of the parameters is
suggested based on ANOVA of the results obtained.
REFERENCES
[1]
[2]
[3]
[4]
(1.5056, 2.2562)
(-0.8991, -0.1486)
CONCLUSION
Summary of the optimal combination of selected
parameters for minimum percent thickness variation is
tabulated in table 7 below.
Sr.
No.
Table 5: Pairwise Comparison (AXB) for % Thickness
Variation for 1.2 mm Sheet Thickness
Difference
VI.
(-0.7119, 0.0386)
It is clear that the differences between level 2 and level 3 is
insignificant and the mean for level 1 of factor A (die draw
radius - 4 mm) is significantly lower (22.8733) than the other
two values
Pairwise
Comparison
different for different sheet thicknesses and there is not much
difference in the group means. Hence it is advisable to select
the blank holder force as calculated by the empirical formula.
[5]
[6]
[7]
Conry T. F., Odell E.I., and Davis W.J. (1980), “Optimization of die
profiles for deep drawing",Journal of mechanical design, Vol. 102, no. 3,
pp. 452-459.
Plevy T.A.H. (1980), “Role of friction in metal working with particular
reference to energy saving in deep drawing", Wear, Vol. 58, no. 2, pp.
359-380
Doege E. and Sommer N. (1983), “Optimization of theBlank-holder
Force during Deep Drawing of Rectangular Parts. [in German]", Stahl
und Eisen, Vol.103, no. 3, pp. 139-142.
Bauer D. and Mueller M. (1990), “Computer-optimized hold-down force
prevents wrinkling in deep drawing[in German]”, Baender Bleche
Rohre, Vol. 31, no. 9,pp. 48-51.
Abdalla S. Wifi, Tamer F. Abdelmaguid, Ahmed I. El-Ghandour, “A
review of the optimization techniques applied to the deep drawing
process”, Proceedings of the 37th International Conference on
Computers and Industrial Engineering,October 20-23, 2007
Bauer D. and Krebs R. (1994), “Optimization of deep-drawing presses
through statistical test planning”, Bander Bleche Rohre, Vol. 35, no. 10,
pp.18-29.
Iseki H., Murota T. (1986), “Determination of the optimum blank shape
of non axi symmetric drawn cup by the finite element method”, Bull
JSME, Vol. 29, pp.1033-1040.
Similarly One-way ANOVA of BXC for each sheet
thickness shows that optimal value of blank holder force is not
127
IRACST – Engineering Science and Technology: An International Journal (ESTIJ), ISSN: 2250-3498
Vol.4, No.5, October 2014
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
M.M. Moshksar, A. Zamanian (1996), “Optimization of the Tool
Geometry in the Deep Drawing of Aluminum”, Journal of Materials
Processing Technology
Eriksen M. (1997), “The influence of die geometry on tool wear in deep
drawing”, Vol. 207, no. 2, pp. 10-15.
Gea, H. C. and Ramamurthy R. (1998), “Blank design optimization on
deep drawing of square shells”, IIE transactions, Vol. 30, no. 10, pp.
913-921
M. R. Jensen, F.F Damborg, K.B Nielsen, J Danckert (1998),
“Optimization of the draw-die design in conventional deep-drawing in
order to minimise tool wear”, Journal of Materials Processing
Technology. Volume 83, Issues 1–3, 1 November 1998, Pages 106–114
S.H. Park, J.W. Yoon, D.Y. Yang and Y.H. Kim(1999), “Optimum
blank design in sheet metal forming by the deformation path iteration
method”, Inte. J. Mech. Sci., Vol 41, no. 10, pp 1217-1232
Doege E. and Elend L. (2001), “Design and application of pliable blank
holder systems for the optimization of process conditions in sheet metal
forming”, Journal of Materials Processing Technology, Vol. 111, no. 3,
pp. 182-187.
Cao J., Li S. Xia, Z.C. and Tang S.C. (2001), “Analysis of an
axisymmetric deep-drawn part forming using reduced forming steps”,
Journal of Materials Processing Technology, Vol. 117, no. 2, pp. 193200.
Gašper Gantar , Tomaž Pepelnjak, Karl Kuzman (2002) , “Optimization
of sheet metal forming processes by the use of numerical simulations”,
Journal of Materials Processing Technology, Volumes 130–131, 20
December 2002, Pages 54–59
Naval Kishor, D. Ravi Kumar (2002), “Optimization of initial blank
shape to minimize earing in deep drawing using finite element method”,
Journal of Materials Processing Technology 130-131 (2002) 20-30
Pegada V.P., Chun Y. and Santhanam S. (2002), “An algorithm for
determining the optimum blank shape for deep drawing of aluminum
cups”, Journal of Materials Processing Technology, vol. 125-126, pp.
743-750
H. Naceura, A. Delamézierec, J.L. Batozc, Y.Q. Guob, C. KnopfLenoira (2004), “Some improvements on the optimum process design in
deep drawing using the inverse approach”, Journal of Materials
Processing Technology, Volume 146, Issue 2, 28 February 2004, Pages
250–262
Chengzhi S., Guanlong C., and Zhongqin L. (2005), “Determining the
optimum variable blankholder forces using adaptive response surface
methodology(ARSM)”,
International
Journal
of
Advanced
Manufacturing Technology, Vol. 26, no. 2, pp. 23–29
H. K. Kim, S. K. Hong (2007), “FEM based optimum design of multistage deep drawing process of molybdenum sheet”, Journal of Material
Processing Technology. Vol 184, pp. 354–362.
Chen L. J.C., Yang J. C., L.W. Zhang L. W, and Yuan S.Y. (2007),
“Finite element simulation and model optimization of blank holder gap
and shell element type in the stamping of a washing-trough”, Journal of
Materials Processing Technology, Vol. 182, no. 3, pp.637–643
F. Ayari a, T. Lazghab b, E. Bayraktar (2009), “Parametric Finite
Element Analysis of square cup deep drawing”, International scientific
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
journal by association of Computational materials science and surface
engineering, vol. 1, issue 2, 2009, 106-111
GAO En-zhi (2009), “Influences of material parameters on deep drawing
of thin-walled hemispheric surface part”, Trans. Nonferrous Met. Soc.
China 19(2009) 433−437
Kopanathi Gowtham, K.V.N.S. Srikanth & K.L.N. Murty (2012),
“Simulation of the effect of DIE Radius on Deep Drawing process”,
International Journal of Applied Research in Mechanical Engineering
(IJARME) ISSN: 2231 –5950, Volume-2, Issue-1, 2012
Prasad S. Pandhare, Vipul U. Mehunkar, Ashish S. Joshi, Amruta M.
Kirde & V. M. Nandedkar (2012), “Optimization of Blank Holding
Force in Deep Drawing Process Using Friction Property of Steel
Blank”, International Journal on Theoretical and Applied Research in
Mechanical Engineering (IJTARME), ISSN : 2319 – 3182, Volume-1,
Issue-2, 2012
Browne M.T. and Hillery M.T. (2003), “Optimising the variables when
deep-drawing C.R.1 cups”, Journal of Materials Processing Technology,
Vol. 136, no. 3, pp.64-71.
Ohata T., Nakamura Y., Katayama T., Nakamachi E.and Nakano K.
(1996), “Development of optimum process design system by numerical
simulation”, Journal of Materials Processing Technology, Vol. 60,no. 4,
pp. 543-548.
Ohata T., Nakamura Y., Katayama T., Nakamachi E.and Omori, N.
(1998), “Improvement of optimum process design system by numerical
simulation”, Journal of Materials Processing Technology, Vol. 80-81,
pp. 635-641
Y. Q. Li, Z. S. Cui, X. Y. Ruan, D. J. Zhang (2006), “CAE-Based six
sigma robust optimization for deep- drawing process of sheet metal”,
The International Journal of Advanced Manufacturing Technology,
October 2006, Volume 30, Issue 7-8, pp 631-637
R. Padmanabhan, M.C. Oliveira, J.L. Alves, L.F. Menezes (2007),
“Influence of process parameters on the deep drawing of stainless steel”,
Finite Elements in Analysis and Design 43 (2007) 1062 – 1067
Susheel Magar, Mohan Khire (2010), “Deep drawing of cup shaped steel
component: finite element analysis and experimental validation”,
International Journal on Emerging Technologies 1(2): 68-72(2010) ISSN
: 0975-8364
P V R Ravindra Reddy, G Chandra Mohan Reddy, T A Janardhan Reddy
(2012), “Studies on the effect of die corner radius and blank holding
force on limit strains in deep drawing process”, Indian Journal of
Engineering & Materials Sciences, Vol. 19, February 2012, pp. 24-30
R. Venkat Reddy , Dr. T. A. Janardhan Reddy (2013), “Effect of various
parameters on Wrinkling with imperfections in Deep Drawing of
Cylindrical Cup”, International Journal of Emerging Technology and
Advanced Engineering, ISSN 2250-2459, ISO 9001:2008 Certified
Journal, Volume 3, Issue 5, May 2013
Abdullah A. Dhaiban, M.-Emad S. Soliman, M.G. El-Sebaie (2014),
“Finite element modeling and experimental results of brass elliptic cups
using a new deep drawing process through conical dies”, Journal of
Materials Processing Technology,Volume 214,Issue 4,April 2014, Pages
828–838
128
Download PDF