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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 9, Issue 6, June 2018, pp. 92–101, Article ID: IJMET_09_06_012
Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=6
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
EFFECT OF UNCERTAINTY PARAMETERS ON
THE PART QUALITY IN A DEEP DRAWING
PROCESS FOR A LOW CARBON STEEL SHEET
Kotchakorn Wiratchakul, Thanasan Intarakumthornchai
Department of Industrial Engineering, KMUT’NB University, Thailand
Yingyot Aue-u-lan
Department of Mechanical and Process Engineering, The Sirindhorn International Thai-
German Graduate School of Engineering, KMUT’NB University, Thailand
ABSTRACT
Reliability and robustness of deep drawing process depend on uncertainty of
material properties and lubrication conditions. Practically, there are no principles or
guidelines to know how much variance of factor should be controlled to increase the
productivity and decrease waste. This Research presents the effect of uncertainty from
material properties and friction coefficient on the thinning of round cup by Finite
Element Method (FEM). The material properties are consisted of the strength
coefficient (K), strain hardening exponent (n), and normal anisotropy (rm). The
friction coefficient (µs) of the deep drawing process is composed of 3 pairs;
punch/blank (µs(P/B)), die/blank (µs(D/B)) and binder/blank (µs(B/B)) interface. Simulation-
optimization Technique is used by Response Surface Method (RSM) to create
Surrogate Model to combine the objective function with Monte Carlo Simulation
(MCS) to simulate the distribution according to the occurred variance of each factor.
The results, it was demonstrated that DR is important to deep drawing process highly.
Moreover, the variance control of friction coefficients for 3 interfaces properly (1%-
5%) can increase the variance of material properties that affects the cost. So the
manufacturers should control the lubrication condition in the proper range to achieve
the target efficiency and sustainably.
Key words: Simulation-optimization, Deep Drawing Process, and Uncertainty
Parameters
Cite this Article: Kotchakorn Wiratchakul, Thanasan Intarakumthornchai and Yingyot
Aue-u-lan, Effect of Uncertainty Parameters on the Part Quality in a Deep Drawing
Process for a Low Carbon Steel Sheet, International Journal of Mechanical
Engineering and Technology 9(6), 2018, pp. 92–101.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=6
Effect of Uncertainty Parameters on the Part Quality in a Deep Drawing Process for a Low Carbon Steel Sheet
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1. INTRODUCTION
Uncertainty or Stochasticity is a situation in which something is unknown information that
involves variances. In the manufacturers of automotive and electronic part face the
uncertainty problem whether it is the variance within the lot or between lots and process
parameters. For example, the study of Majeske and Hammett [1] who studied the process of
many leading automotive manufacturers found the scrap was high up to 21% although used
material from the same lots, same die and process setup. So the variance problems needed to
be fixed by the proper way to increase the efficiency
Reliability and robustness is the main target for every industry because this concept can
reduce mistakes of decision making under the variance from factors. Moreover, it can increase
the quality of workpieces and reduce the cost. Therefore, researchers developed many
techniques to make processes achieved the target. In the past, statistical techniques were
applied for metal forming simulation such as tsegin ox xpsngmsnDs (DOE), hypothesis test and
enllyege ox slnglnns (ANOVA). To consider relationships of each factor of forming process to
reduce the unnecessary simulation [2-4], the difficulty of applying statistical techniques was
design space because large scaled problems lead to the big problem which could not be
solved. Besides statistical techniques, opDgmgzlDgon was applied as well to find the
appropriation of process such as tool dimensions and process parameters [5-6]. Moreover, the
researchers who combined 2 methods [7-8] by using the concept of DOE for screening factors
which not affect to reduce unnecessary procedures and improve the efficiency of solutions.
Mentioned optimization is a deterministic approach which is effective when parameters and
solutions were certain while it was not proper for a variance. Statistical techniques were
applied to increase the efficiency for a long time. Last 10 years, the new technique was found
and used to deal with uncertainty problem effectively [9-10]. That technique is Simulation-
optimization Technique which was the simulation combine optimization. Generally, this
technique was applied to complicated and big problems to calculate decision variables by
maximizing or minimizing objective functions. So, simulation-optimization is accepted in the
present and there are developments in this field. It can be classified into 2 types, Reliability
Base Design Optimization (RBDO) [11-14] and Robustness Optimization [15-19] The
classification is done by objective functions those are optimization by shifting response
average to make the range of waste possibility acceptable and optimization to minimize the
variance of response respectively.
The research interests simulation-optimization that applies pnoblbglgetgn appnolnh and
opDgmgzlDgon together to study the effect of uncertainty factors on part quality from mlDsngll
pnopsnDgse and friction coefficient in deep drawing process by Finite Element Method (FEM).
Firstly, Response Surface Method (RSM) to generate a sunnoilDs modsl for the objsnDgvs
function. Then, simulate the distribution of every factor with MonDs Clnlo SgmullDgon (MCS).
Finally, find the maximum occurred variance without the crack by simulation-optimization
technique. From analysis, obtain the factors affect the most of deep drawing process that
should be controlled and also kwon the factors can be slightly ignored. In addition, it is the
quality control of workpieces, reduce the cost in the long term, and lead to rslglbglgDy and
robueDnsse.
2. RELIABILITY
In the real condition, operations in the manufacturer found with the uncertainty of factors both
of conDnolllbls flnDone and unnonDnolllbls flnDone in the process which increase the waste,
rework, and loss of gross profit. Therefore, it is important to deal with this problem. This
study presents the method which finds the proper variance of factors for deep drawing process
Kotchakorn Wiratchakul, Thanasan Intarakumthornchai and Yingyot Aue-u-lan
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to achieve the rslglbglgDy and robueDnsse. Proposed research methodology can be shown in
Figure 1.
Figure 1 Proposed research methodology
SgmullDgon-opDgmgzlDgon technique consists of 3 components as objective function,
constrain, and decision variable. From Figure 1, objective function is defined with a surrogate
model that is generated by RSM and pnoblbglgeDgn appnolnh to simulate the data distribution by
MCS as each decision variables. Constraints set that the workpieces are not crack. Simulation-
optimization finds the maximum occurred variance of each factor which not causes the
failures.
2.1. Surrogate Models
Surrogate Model or MsDl-modsl is the mlDhsmlDgnll modsl which used to simulate, explain, and
compare events by terms of equations. Mostly, engineering problems are non-linear as the
response from F M. Surrogate models can be generated by many ways. However, there are 3
popular techniques consist of RSM, Kriging, and Artificial Neural Networks (ANN). The
method which many researchers agree to generate for surrogate models is RSM because its
simplicity applies with tO and less experiments. Moreover, Kriging and ANN, tend to take
long time in case of many interested factors. In this study, RSM is used to develop surrogate
model.
2.1.1. Define Variables
This research is study effect of factors on part quality for deep drawing process.
2.1.2. Define variance
Variance of each factor is defined by Coefficient of Variation (CV) form, so this study will
consider that every factor is normal distribution.
2.1.3. Design of experiment
Central Composite Design (CCD) was used to design of experiment. This design is similar to
factorial design. The difference is CCD does not experiment all cases that is the selection of
some necessary cases for the sufficiency of statistical analysis. So CCD can analyze the
relationship between main term, interaction term, and quadratic terms with not too high
resource. Therefore, it is appropriate to use with FEM because each case takes a long time
that is not suitable for factorial design.
2.1.4. Mathematical model generation
RSM is used to the analysis for mathematical model. The model consists of only affected
factors. In this study use RSM model as follows Equation (1)
Reliability
Surrogate Model Probabilistic Approach
Objective Functions Constrains Decision Variables
Simulation Optimization
A Best Set of Values for Decision Variables
Probabilistic Approach
Effect of Uncertainty Parameters on the Part Quality in a Deep Drawing Process for a Low Carbon Steel Sheet
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2
0
1 1 2
( )k k k
j j jj jj ij i j
j j i j
f x y x x x x
(1)
2.1.5. Model Adequacy Checking
This procedure is residual or error validation. There are all 3 major assumptions which consist
of normal distribution, independence, and constant variance. This checking will be completed
before using mathematical models. In case some assumption is failed, data transformation is
required and analysis by RSM again for the new model until the validation has all 3
assumptions and can be used for models effectively.
2.2. Probabilistic Approach
Engineering problems involve uncertainty parameters that make more complication.
Therefore, it is difficult to solve problems by dsDsnmgngeDgn approach which is not sufficient to
deal with this challenge. Thus, pnoblbglgeDgn appnolnh is considered to study the effect of
variance as the probability [20]. This technique uses sDlDgeDgnll and probability, which one to
find statistical parameters. The probability use statistical parameters to generate the
dgeDngbuDgon. The widely approaches used in this field have 2 techniques as Monte Carlo
Simulation (MCS) and First-order Reliability Method (FORM) have appropriate with each
problem as the study of Jang et al. [21] which identified that FORM needed less data for
number of iterations and the efficiency was better than MSC when the numbers which lower
than 100 samples were random [22-23]. This study focuses on deep drawing process so
sample size is large. Therefore, MCS is more suitable than FORM. MCS is the simulation to
explain the events from the variance by generating the distribution for input data through the
model.
2.3. Optimization
This study does simulation-optimization by OptQuest function in Crystal Ball software. The
concept of this function is applying search algorithm for the better solution by using Scatter
Search with Tabu Search for local optimum. Then, collecting good solutions and comparing
with new solution for the better solution. Then, collect all solutions as database for ANN to
learn by Adaptive Memory concept. The solution is a global solution or the close one which
needs less time.
3. THE FINITE ELEMENT MODELLING
The deep drawing process was an example used to verify the methodology proposed. It uses
to evaluate the friction behavior in sheet metal forming. Moreover, before the new developed
surrogate model, the validation is always required.
3.1. Finite Element Modelling
The deep drawing process of round cup has shape and size of forming process as Figure 2.
Material is low carbon steel sheet with ASTM A1011 DS type-B, the thickness is 2.17 mm as
material properties tabulated in Table 1. Defining of pnonsee plnlmsDsne will use Blank Holder
Force (BHF) as constant forces 3 levels, 30, 50, and 80 tone. Friction coefficient (µs) for 3
interfaces consist of punch/blank (µs(P/B)), die/blank (µs(D/B)), and blank holder plate/blank (µs(B/B))
are 0.06, 0.07, 0.09, 0.10, 0.16, and 0.18. F M model is analyzed by LS-DYNA which is ¼
because the workpiece is symmetry for both axes. To reduce the calculation time, Mesh is
defined as quadrilateral as Figure 3.
Kotchakorn Wiratchakul, Thanasan Intarakumthornchai and Yingyot Aue-u-lan
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Table 1 Material properties of a low carbon steel sheet according to ASTM A1011 DS type-B
Material Properties: ASTM A1011 DS type-B
Young’s modulus (E) 210 GPa
Strength Coefficient (K) 498.8 MPa
Strain Hardening Component (n) 0.131
Normal anisotropy (rm) 1.5
Figure 2 Shape and dimension of deep drawing process
Figure 3 FEM model of this research
3.2. Model Validation
The correction of developed models can be investigated by comparing with response between
FEM model and experiments. A response which compared is dnlw-gn lsniDh and perimeter of
workpiece after forming. Both of responses measured as the average (0, 45, and 90 degrees)
because of anisotropy of material. The results of validation show that shown in Table 2.
Table 2 The results of validation between FEM model and experiment
Parameters Draw in Length (mm) Perimeter (mm)
BHF (Ton) µs FEM Model Experiment FEM Model Experiment
30 0.06 36.83 35.8 689.48 671
30 0.07 36.7 35.5 690.25 673
50 0.07 35.7 34.7 696.23 678
50 0.1 34.36 32.2 704.23 692
80 0.09 32.07 31.2 717.88 698
80 0.1 30.5 29.4 727.25 708
From the comparison in Table 2, responses from FEM model are not significantly
different from the experiment. Therefore, the developed FEM model can be substituted real
forming processes effectively to be a part of surrogate model development for objective
function in simulation-optimization.
Blank Sharpe
304.8 mm
Thickness 2.17 mm
Punch
Binder
Die
Blank
BHF (Tons)
Time (s)
Effect of Uncertainty Parameters on the Part Quality in a Deep Drawing Process for a Low Carbon Steel Sheet
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4. SIMULATION OPTIMIZATION APPROACH
In this chapter, the presented method application is explained that is finding solutions by
simulation-optimization which the concept is shown as Figure 1. It can be seen that solution
calculation needs responses from the simulation which used to measure the appropriated input
data with previous evaluation. Then, set new sets of input variables to the system again. Every
sequence is repeated until the conditions of terminating conditions are achieved such as
getting solutions according to conditions or achieving target time. Simulation-optimization
consists of 3 components as mentioned. Each sequence can be explained as follows;
4.1. Response Surface Method
4.1.1. Effect factors in the deep drawing process.
Gantar and Kuzman [24] study the variance in factors of deep drawing processes, there were
12 factors. It was found that material properties and lubngnlDgon had influence to the process.
Therefore, factors which need to be studied are material properties which consist of strength
K, n and rm For lubrication of deep drawing process, there are friction coefficient for 3 pairs
of interface which consist of µs(P/B), µs(D/B) and µs(B/B)
4.1.2. Defining the variance
Cao and Kinsey [25] studied the variance of K and n up to 20% and 16% respectively. For the
friction coefficient, it equaled to 65%. This study defines variances of each factor as Clo but
the difference is the variance of material properties will be defined equally that is 20% for all
factors because the convenience and simple to design of experiment in the next step.
Moreover, another factor is added that is Drawing Ratio (DR) which identifies the difficulty
of forming. Usually, this value will equal to 1.8-2.2 for low carbon steel sheet. This study
focuses on 7 factors which affect the process. Material properties are according to Table 1.
Friction coefficient is set to 0.125 (generally, the value in deep drawing process is 0.04-0.15.
the reason to choose 0.125 because this value is in the range and the default value of LS-Dyna
program). So that detail of each factor can be shown as Table 3.
Table 3 Detail of each factor in this study for the deep drawing process
Factors Materials Properties Friction Coefficient
DR K n rm µs(P/B) µs(D/B) µs(B/B)
Mean 498.8 0.131 1.25 0.125 0.125 0.125
1.8-2.2 SD 99.76 0.03 0.25 0.08125 0.08125 0.08125
CV 20% 20% 20% 65% 65% 65%
4.1.3. Design of experiment
According to Table 3, design of experiment by CCD concept that does normalization for all
data in terms of , –1, 0, 1 and . ( 3.364 ). The numbers of experiments are 152 because
there are 7 factors.
4.1.4. RSM analysis
The response which used to measure the quality of workpiece after FEM is thinning as
psnnsnDage (%) because this value can indicate the mistake that cause the worst damage
(crack). The thinning of this damage is higher than 20%. After the analysis, the mathematical
model will be provided that consists of factors which affect to be sunnoilDs modsl. Next step is
model adequacy checking needs to analyze for 3 assumptions. In case of incomplete, data
transformation is required by Box Cox method to analyze new surrogate model. Then, check
Kotchakorn Wiratchakul, Thanasan Intarakumthornchai and Yingyot Aue-u-lan
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all assumptions for model adequacy checking again which can be shown in Figure 4. The
results show that the new developed model is sufficiently correct and can be used to predict
effectively can be shown as Equation (2).
Figure 4 Results from model adequacy checking after data transformation
1.74
( / ) ( / )0.0145 0.00856 0.0031 0.0056 0.000398 0.00915'
s P B s D BmK n ry Thinning
(2)
( / ) ( / )
0.0416 0.012 0.00076 * 0.00168 * 0.00243 *s B B s D BmDR K n K r K
( / ) ( / )
0.000651 * 0.0054 * 0.000822 * 0.00105 *s B B s D BmK K DR n r n
( / ) ( / )
0.0019 * 0.00215 * 0.00111 * 0.0023 *s D B s B Bm m mn DR r r r DR
( / ) ( / ) ( / ) ( / )
0.001596 * 0.00455 * 0.00251 *s D B s B B s D B s B B
DR DR
( / ) ( / )
2 2 2 20.00163 0.0033 0.0463 0.0036
s P B s D Bn DR
4.2. Monte Carlo Simulation
MCS is a simulation by random variables from Probability Density Function (PDF). This
study uses MCS to simulate on the surrogate model. The distribution of 6 factors (K, n, rm,
µs(P/B), µs(D/B) and µs(B/B)) is defined as normal distribution because it plays the important role in
applied statistics. For DR factors, it will be adjusted according to the change of the process.
MCS simulate random variable X which the distribution is normal by parameters and 2
that written by 2( , )X N .
4.3. Optimization Problem Setup
This study presents simulation-optimization technique which different from other researches.
Decision variables ( X ) are the variances of 6 factors in terms of CV which maximize the
variance of the objective function (σf(x)) under constrain that probability ( Pr ) causes rsigon ox
uneunnsee ( ( ) 0g x ) equal to 0 as Figure 5.
Effect of Uncertainty Parameters on the Part Quality in a Deep Drawing Process for a Low Carbon Steel Sheet
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Figure 5 Objective function for simulation-optimization technique in this study
5. RESULTS AND CONCLUSIONS
This research studies the effect on the variance of material properties and friction coefficient
on deep drawing process of round cup by FEM with optimization-simulation technique to find
the maximum occurred variance of each factor to be the guideline of the operation. It can be
classified into 3 cases as the following; constant material properties, constant friction
coefficients and adjusting DR. The first and second case has 3 decision variables. For both
cases, DR is 2.00 only (according to experimental model). The last case is adjusting DR for 3
levels, 1.80, 2.00, and 2.20. The results of simulation optimization can be shown in Table 4–6
respectively.
Table 4 The results of simulation optimization in case of constant friction coefficient
Decision Variable Fix
K n rm µs(P/B) µs(D/B) µs(B/B)
12.22% 11.20% 13.85% 1.00%
11.58% 10.88% 14.10% 5.00%
10.61% 0.11% 13.79% 10.00%
Constant friction coefficient case as Table 4 shows that the reducing of friction coefficient
variation does not increase the variance of material properties. However, friction coefficient
should not be too high because n will have more influence (variance of n reduces equal to
011%). Therefore, in case lubrication condition variance can be controlled to occur with the
properly for the variance of material properties can reduce the effect of workpiece quality.
The proper range of variance is 1% to 5%. Therefore, the manufacturers should consider the
lubrication control to keep it in the appropriate condition which allows to use a lower quality
of material (the variance is high) but the productivity still the same. This can create rslglbglgDy
and robueDnsse. In addition, it can reduce the production cost by using the lower quality
material.
Table 5 The result of simulation optimization in case of constant material properties
Fix Decision Variable
K n rm µs(P/B) µs(D/B) µs(B/B)
1.00% 6.54% 39.34% 34.34%
5.00% 6.86% 37.11% 32.12%
10.00% 6.28% 30.92% 25.93%
Optimized ProcessOriginal Process
Maximum( )f x
1 2 6[ , ,..., ]x x x
Kotchakorn Wiratchakul, Thanasan Intarakumthornchai and Yingyot Aue-u-lan
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In case material properties variation can be controlled, it can be seen that the variance of
friction coefficient is not affected significantly. That means no matter how much the variance
of material properties be controlled that the occurred variance of friction coefficient does not
change as Table 5. Thus, the high-quality material does not guarantee the increasing of the
productivity if the process does not have the proper lubrication control. If friction coefficient
variation needs to be reduced, other factors should be considered such as DR reducing because
it can reduce the cost due to the decreasing of bllnk sgzs as Table 6.
Table 6 The results of simulation optimization in case of DR adjustment
DR K n rm µs(P/B) µs(D/B) µs(B/B)
1.80 10.18% 7.59% 22.64% 4.74% 50.41% 45.41%
2.00 6.27% 2.71% 13.77% 3.17% 38.15% 33.17%
2.20 12.86% 1.45% 1.72% 1.00% 28.00% 29.27%
From table 6, adjustment of DR affects the variance of material properties and friction
coefficient. DR increases, the variance of these two more affect the workpiece quality. The
factors which highly affect the process are µs(P/B), n, and rm.as 1.00%, 1.45% and 1.72%
respectively. Form the results found that µs(P/B) is a factor that enhance the sensitivity of the
variances of n and rm. Moreover, DR is close to LgmgDgni tnlwgng RlDgo (LDR) that makes more
difficult to forming. Therefore, it is necessary to prioritize the forming ability (n and rm).
Consequently, DR is the important factor to the deep drawing process. It makes the quality
control can be performed effectively in the practice. Manufacturing should consider the
proper DR in each production because each DR affects the factors which different ways.
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