Tối ưu hóa đa mục tiêu quá trình khoan xung cho vật liệu làm khuôn để nâng cao năng suất và chất lượng lỗ gia công

 CÔNG NGHỆ 
 Tạp chí KHOA HỌC & CÔNG NGHỆ ● Số 51.2019 44
KHOA HỌC
MULTI-RESPONSE OPTIMIZATION OF EDD PROCESS 
OF DIE STEEL FOR IMPROVING PRODUCTION RATE 
AND HOLE QUALITY 
TỐI ƯU HÓA ĐA MỤC TIÊU QUÁ TRÌNH KHOAN XUNG CHO VẬT LIỆU LÀM KHUÔN 
ĐỂ NÂNG CAO NĂNG SUẤT VÀ CHẤT LƯỢNG LỖ GIA CÔNG 
Tran Van Tuan1, 
Nguyen Long Hai2, Nguyen Trung Thanh2,* 
1. INTRODUCTION 
Electrical discharge machining (EDM) is 
an efficient machining method, in which the 
removal of the material is performed based 
on melting and evaporation processes. The 
conversion of electrical energy to thermal 
energy is conducted by electrical sparks 
between the electrode and the workpice in 
the dielectric liquid [1]. The electrical 
discharge drilling (EDD) process has the 
same working principle as EDM process. The 
EDD process is specifically designed to 
quickly drill the holes in the production of 
turbine blades, fuel injectors, coolant lines, 
and plastic molds [2]. 
The effects of machining conditions on 
the criteria outputs of the EDD processes 
have been explored by many researchers. 
Yılmaz et al. [3] investigated the drillability of 
Hadfield steel for the EDD operation of the 
deep-holes. The effect of input values for 
deep-hole drilling of Inconel 718 was 
examined by Kuppan et al. [4]. Asokan et al. 
[5] analyzed the impacts of process 
parameters on performance characteristics 
in EDD process the titanium alloy. Mohan et 
al. [6, 7] investigated the machinability for 
EDD process of AlSiC metal matrix 
composite. Lee et al. [8] proposed the 
estimating model for the electrode wear in 
the EDM drilling. The optimization of 
parameters was performed to improve the 
technical outputs for EDD process of Ti-
6Al04V [9] and PCDS [10]. As a result, the 
factors optimized are the process 
parameters (the pulse on time, the pulse off 
time, the current, and the voltage), the 
ABSTRACT 
Improving the technical outputs of the electrical discharge drilling (EDD) process is an effective 
solution to decrease manufacturing costs. This paper presented a multi-response optimization to 
simultaneously improve the material removal rate (MRR) and decrease the dilation of hole (DH). 
The processing conditions considered include the pulse on time (TON), the current (AMP), the gap 
voltage adjustor (GAP), and the pulse off time (TOFF). An EDD drilling machine was adopted in 
conjunction with the Box-Behnken matrix to conduct experimental trails for machining of SKD61 
steel. The highly nonlinear relationships between the process parameters and criteria outputs were 
developed using the Kriging models. Finally, an archive-based micro-genetic algorithm (AMGA) 
was used to determine the optimal values of the processing factors. The results showed that DH
could be approximately decreased 12.26%, while (MRR) is around improved 32.17%. The 
combination of the Kriging model and AMGA could be considered as an intelligent approach for 
modeling EDD processes and generating reliable optimal results. 
Keywords: EDD, dilation of hole, material removal rate, Kriging model, mold steel. 
TÓM TẮT 
Nâng cao các chỉ tiêu kỹ thuật của quá trình khoan xung là một giải pháp hiệu quả để giảm chi 
phí sản xuất. Nghiên cứu này đề cập đến bài toán tối ưu hóa đa mục tiêu để nâng cao tốc độ bóc 
tách vật liệu và giảm độ mở rộng của lỗ. Các thông số công nghệ bao gồm cường độ dòng điện, độ 
kéo dài xung, khoảng cách xung và hệ số điều chỉnh điện áp. Quá trình thực nghiệm được tiến hành 
trên máy khoan xung EDD theo ma trận quy hoạch Box-Behnken. Mối quan hệ phi tuyến tính giữa 
các thông số công nghệ và hàm mục tiêu được xây dựng thông qua mô hình Kriging. Cuối cùng, một 
thuật toán di truyền vi mô dựa trên kho lưu trữ (AMGA) đã được sử dụng để giải quyết mối tương 
quan giữa các yếu tố đầu ra xác định các thông số tối ưu. Kết quả cho thấy, độ mở rộng của lỗ có thể 
giảm khoảng 12,26%, trong khi tốc độ bóc tách vật liệu được cải thiện khoảng 32,17%. Sự kết hợp 
giữa mô hình Kriging và AMGA có thể được coi là một cách tiếp cận thông minh để mô hình hóa các 
quy trình khoan xung và tạo ra kết quả tối ưu đáng tin cậy. 
Từ khóa: Khoan xung, độ giãn nở của lỗ, tốc độ bóc tách vật liệu, mô hình Kriging, thép làm 
khuôn. 
1Faculty of Mechanical Engineering, Military Industrial College 
2Faculty of Mechanical Engineering, Le Quy Don Technical University 
*Email: trungthanhk21@mta.edu.vn 
Received: 25 February 2019 
Revised: 14 April 2018 
Accepted: 25 April 2019 
SCIENCE TECHNOLOGY 
Số 51.2019 ● Tạp chí KHOA HỌC & CÔNG NGHỆ 45
electrode characteristics (the geometry and the material), 
dielectric properties (type, dielectric strength, and 
viscosity), and the workpiece properties. The technological 
responses considered are surface roughness properties and 
the hole quality. 
In the current work, a multiple-response optimization of 
process parameters for the EDD process of the die material 
has performed to improve the MRR and reduce the DH. The 
inputs may have complicated impacts on the outputs and an 
effective approach for modeling EDD process behavior and 
the optimizing processing factors in terms of improving 
working performances still is a significant contribution. 
2. MATERIALS AND METHODS 
2.1. Optimization framework 
The procedure for generating optimal values is shown 
in Fig. 1. The experimental matrix generated by the Box-
Behnken method is applied to save the experimental costs 
[11, 12]. Process parameters, including the AMP, TON, TOFF 
and GAP as well as three levels (-1; 0; +1) were shown in 
Table 1. The chemical compositions of SKD61 material are 
shown in Table 2. The parameter ranges are chosen based 
on the machine tool’s characteristics, the 
recommendations of the electrode’s manufacturer, and 
material properties. The predictive models of DH and MRR 
are then developed with respect to process parameters 
using the experimental data. 
In this paper, the AMGA is applied to find a set of 
feasible solutions, which can be used to enhance surface 
integrity. AMGA is an evolutionary optimizing technique, in 
which each response is resolved individually and a set of 
feasible solutions is observed. The operating mutation and 
solution are performed by means of the chosen designs. 
The search history and solution selection are conducted 
using a myriad of different heuristics. The best values of the 
responses were determined at the end of the convergent 
run. Many researchers indicated that AMGA possesses high 
computational efficiency and provides the globally optimal 
solutions, as compared to other optimization algorithms 
[13, 14]. 
Figure 1. Systematic optimization procedure 
Table 1. Process parameters and their levels 
Symbol Parameters level -1 level 0 level +1 
AMP Current (A) 2 5 8 
TON Pulse on time (µs) 40 90 140 
GAP Gap voltage adjustor 2 5 8 
TOFF Pulse off time (µs) 15 65 115 
Table 2. Chemical compositions of SKD61 
C Si Mn P S Cr Mo Cu V 
0.38 0.9 0.28 0.03 0.02 4.9 1.2 0.26 0.95 
2.2. Experiments and measurements 
The CNC EDM machine, namely MAX S.E.E S36 is used to 
perform the experimental runs as depicted in Fig. 2. The 
brass electrode of 1 mm diameter and 400 mm length is 
used as tool material. The vertical axis movement of the 
electrode is controlled using the servo motor and the 
desired depth of 10 mm is set for each run. The debris is 
removed with the aid of the fluid. 
The holes are drilled on the workpiece having the 
dimensions of 20 x 10 x 100 mm. All faces of the specimens 
are ground and polished before the EDM drillings. The 
workpiece having the mating interface is used to measure 
the length of the drilling hole. 
 The DH is an indicator of the machined part quality. The 
diameter of each hole is measured at different positions 
and the average value (ΔD) is calculated to find the mean 
diameter of the hole at the top as well as the bottom. The 
value of DH is estimated using the following equation, as 
depicted in Fig. 2: 
eDH D D= (1) 
where De is the original diameter of the electrode. ΔD is the 
circularity of drilled hole and calculated using Eq. (2): 
....1 2 nD D DD
n
+ + +
 = 
(2) 
where n is the number of measuring points. 
The machined holes are dried, cleansed, scanned using 
a 3D high-resolution scanner, namely 450V. The captured 
images are used to the diameters and the length of each 
hole. 
Generally, the MRR is generally considered as an 
important indicator of the production rate. The MRR 
(mm3/s) is calculated using the following equation: 
( )22 top bottoma a D D LV D LMRR
t 4t 16t
 + 
= = = 
(3) 
where Da (mm), L (mm), and t (s) are the average diameter 
of the hole, the length of the hole, and machining time, 
respectively. ΔDtop and ΔDbottom are the top and bottom 
circularity of each hole, respectively. 
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2.3. Kriging Model 
The Kriging models of DH and MRR in terms of 
processing factors are proposed using the experimental 
data. It can be described by means of equation 4: 
( ) ( ) ( )y x p x z x= + (4) 
where y(x) denotes the polynomial function to be 
developed, p(x) presents a known polynomial function and 
z(x) is the realization of a normally distributed stochastic 
process [15]. 
The Kriging predictor at a specific value of x is 
calculated by: 
 (x) ( ) ( )T 1y β r x R f pβ = +  (5) 
where f denotes the column vector containing the sample 
data and p presents the filled column vector. The factor β is 
calculated using the following equation: 
 ( )T 1 1 T 1yβ p R p p R = (6) 
rT(x) is the correlation vector and estimated by: 
T 1 2 N Tr (x) [R(x,x ),R(x,x ),...,R(x,x )]= (7) 
In this paper, the Gaussian correlative function is used 
and defined as: 
m
i j 2
k k k
k 1
R(θ) exp[ θ (x x ) ]
=
=  
(8) 
The estimated variance of the proposed model is 
calculated by: 
12 (y pβ)R (y pβ)σ
N
=
 
 
(9) 
The correlation factor θk is estimated by: 
 2
k
[Nln(σ ln R ]max (θ ) 2
+
 = 
(10) 
where 
2
σ and R are the function of θk. 
Figure 2. Experiments 
3. RESULTS AND DISCUSSION 
3.1. Development of Kriging models 
The DOE matrix and experimental results of the EDD 
process are given in Table 3. For constructing a Kriging 
surrogate, it is necessary to obtain the unknown correlation 
parameter θk and scalar factor β in Eqs. 6 & 10. The 
correlation parameter θk and scalar factor β were observed 
using the maximum likelihood method, as shown in Table 4. 
Table 3. Experimental results 
No. AMP 
(A) 
TON 
(µs) 
TOFF 
(µs) 
GAP 
DH 
(mm) 
MRR 
(mm3/s) 
1 5 90 65 5 0.601 0.5400 
2 2 90 65 2 0.392 0.4651 
3 5 90 15 2 0.513 0.3515 
4 5 90 65 5 0.604 0.5588 
5 5 90 115 8 0.599 0.8867 
6 5 90 115 2 0.346 0.2005 
7 5 140 65 8 0.824 1.5965 
8 2 90 15 5 0.611 0.3046 
9 5 40 115 5 0.352 0.1806 
10 8 90 115 5 0.674 0.9454 
11 5 40 65 2 0.291 0.1688 
12 5 90 65 5 0.603 0.5478 
13 2 90 65 8 0.726 0.5319 
14 8 90 65 8 0.986 2.6267 
15 2 40 65 5 0.322 0.1289 
16 8 140 65 5 0.891 1.5989 
17 5 90 15 8 0.848 1.4265 
18 2 90 115 5 0.321 0.1198 
19 8 90 15 5 0.925 1.3470 
20 5 40 65 8 0.691 0.7566 
21 8 90 65 2 0.776 0.7113 
22 5 140 115 5 0.479 0.4506 
23 2 140 65 5 0.574 0.3242 
24 5 140 15 5 0.802 0.8073 
25 5 90 65 5 0.608 0.5531 
26 8 40 65 5 0.664 0.8438 
27 5 40 15 5 0.461 0.3541 
28 5 140 65 2 0.601 0.3982 
29 5 90 65 5 0.607 0.5393 
Table 4. The parameters of the Kriging models 
Responses Correlation parameter θk Scalar 
factor β AMP GAP TON TOFF 
DH 0.124259 0.118648 0.105811 0.121930 0.014445 
MRR 0.217231 0.204221 0.071491 0.060502 0.127774 
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(a) For the dilation of hole 
(b) For the material removal rate 
Figure 3. Investigations of the model accuracy for the Kriging models 
3.2. Model fitness 
The adequacy of the Kriging models can be evaluated 
using the R2-values. The R2-values of DH and MRR are 0.9886 
and 0.9874, respectively. Additionally, the observed data 
distributed on the straight lines, as exhibited in Fig. 3. It can 
be stated that there is a good agreement between 
predicted and measured values. Therefore, the fidelity of 
the Kriging models proposed for the machining responses 
is acceptable. 
3.3. The effects of process parameters on the technical 
responses 
The effects of processing factors on the DH are shown in 
Figs. 4a and b. At a higher value of AMP, GAP, and TON, the 
discharge energy will increase, leading to excessive 
material removal, which results in larger dimensions. In 
contrast, the decreased DH is associated with an increased 
TOFF. The longer the TOFF, the smaller discharge energy 
becomes, which decreases the evaporating of materials, 
leading to smaller diameters. 
The effects of processing factors on the material 
removal rate are shown in Figs. 4 c and d. An increase in the 
AMP, GAP, and TON causes higher discharge energy, which 
leads to an increment in the rate of melting and 
evaporation. A higher pulse off time decreases the 
discharge energy, leading to a slower MRR. 
The contributions of inputs are depicted using Pareto 
charts, as shown in Fig. 5. The blue bar shows that the 
process parameters have a positive effect on the objective, 
while the red denotes a negative influence. As a result, the 
percentage contributions of AMP, GAP, TOFF, and TON are 
17.90%, 16.44%, 14.15%, and 13.89%, respectively. The AMP 
2 account for the highest percentage contribution with 
respect to quadratic terms (7.20%); this followed by TOFF2 
(4.90%), TON2 (4.63%), and GAP2 (3.70%). The contributions 
of the interaction terms, including GAP-TON and GAP-TOFF 
are 4.60% and 2.13%, respectively, which have a negative 
effect on the dilation of hole. 
As shown in Fig. 5b, the AMP has the largest effect on 
MRR with a percentage of 14.92%, followed by GAP 
(11.95%), TON (9.20%), and TOFF (7.47%). The GAP2 is the 
most affected factor due to the highest contribution 
(9.28%) with regard to the quadratic term, followed by 
AMP2 (8.51%). 
(a) DH versus AMP and GAP 
(b) DH versus TON and TOFF 
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(c) MRR versus AMP and GAP 
(d) MRR versus TON and TOFF 
Figure 4. Interaction effects of each machining parameters on the objectives 
(a) Pareto chart for DH 
(b) Pareto chart for AMRR 
Figure 5. Pareto charts for the objectives 
4. OPTIMIZATION RESULTS 
The developed models for the DH and MRR are 
optimized using AMGA, which has the capacity of finding 
the optimal solution of a multi-objective problem. It is 
tough work to determine the optimal process parameters 
for simultaneous improving machining responses. 
Additionally, processing factors have complex effects on 
the technical outputs. The optimizing issue can be 
described as follows: 
Find X = [AMP, TON, TOFF, GAP] 
Maximize MRR; Minimize DH 
2 ≤ AMP ≤ 8 (A), 40 ≤ TON ≤ 140 (µs), 15 ≤ TOFF ≤ 115 
(µs), 2 ≤ GAP ≤ 8. 
Figure 6. Pareto fonts generated by AMGA 
SCIENCE TECHNOLOGY 
Số 51.2019 ● Tạp chí KHOA HỌC & CÔNG NGHỆ 49
Table 5. Optimization results 
Method 
Optimization parameters Responses 
AMP 
(A) 
TON 
 (µs) 
GAP 
TOFF 
 (µs) 
DH 
(mm) 
MRR 
(mm3/s) 
AMGA 6 139 6 114 0.5273 0.7961 
Initial 5 90 5 65 0.6010 0.5400 
Improvement (%) -12.26 32.17 
The developed equations showing the relationship 
between process parameters and machining responses are 
used to find optimal parameters by means of the AMGA. 
The operating values of AMGA parameters, including the 
population size, number of generations, crossover 
probability, crossover distribution index, and mutation 
distribution index, are 20, 40, 0.9, 10, and 20, respectively. 
The Pareto front generated by the AMGA algorithm was 
exhibited in Fig. 6, in which the pink points are feasible 
solutions. The optimization results are listed in Table 5. The 
dilation of the hole is decreased around 12.26% and the 
material removal rate is approximately increased 32.17%. 
5. CONCLUSION 
This paper presented a machining parameters-based 
optimization for the electrical discharge drilling of SKD61 
material in order to decrease the DH and the MRR. The 
Kriging models of two responses were developed in terms 
of processing factors, including the TON, the AMP, the GAP, 
and the TOFF. An AMGA was used to predict the optimal 
values. The conclusions of this research can be listed as 
follows: 
1. The predictive models for the dilation of the hole and 
the material removal rate having R²-values of 0.9886 and 
0.9874, respectively indicate a good correlation between 
the predicted and experimental values. The models 
proposed are effectively exhibited the nonlinear 
relationships in terms of process parameters. The predictive 
models developed can be used for the electrical discharge 
drilling process of SKD61 material to forecast the optimal 
process parameters with the acceptable accuracy. 
2. The Pareto fronts generated by the AMGA can 
significantly support the EDD operators to select 
appropriate parameters to decrease the dilation of the hole 
and increase the material removal rate. The selection of 
optimal parameters can decrease the efforts required and 
machining costs as well as machining time. 
3. The hybrid approach consisting the Kriging models 
and AMGA can widely apply for the optimization of the 
electrical discharge drilling process instead of using 
practical experience and operating guide. The method 
approach in this research is multi-purposeful and can be 
used in all cases of electrical discharge drilling processes 
with different materials. 
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THÔNG TIN TÁC GIẢ 
Trần Văn Tuấn1, Nguyễn Long Hải2, Nguyễn Trung Thành2 
1Khoa Cơ khí, Trường Cao đẳng Công nghiệp Quốc phòng 
2Khoa Cơ khí, Học viện Kỹ thuật Quân sự