EFFECT OF UNCERTAINTY PARAMETERS ON THE PART QUALITY … · function. Then, simulate the distribution of every factor with MonDs Clnlo SgmllDgon (MCS). Finally, find the maximum occurred

http://www.iaeme.com/IJMET/index.asp 92 [email protected]

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


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


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



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.



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)



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



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.



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



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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Documents

EFFECT OF UNCERTAINTY PARAMETERS ON THE PART QUALITY … · function. Then, simulate the distribution of every factor with MonDs Clnlo SgmllDgon (MCS). Finally, find the maximum occurred