PARAMETRIC OPTIMIZATION OF WIRE ELECTRICAL DISCHARGE
MACHINING PROCESS ON AISI H13 TOOL STEEL USING
WEIGHTED PRINCIPAL COMPONENT ANALYSIS
(WPCA) AND TAGUCHI METHOD
Nuraini Lusi
1, Khairul Muzaka
1and Bobby Oedy Pramoedyo Soepangkat
2 1State Polythecnic of Banyuwangi, Jalan Raya Jember Kabat Labanasem, Banyuwangi, Indonesia
2
Manufacturing Laboratory, Mechanical Engineering Department, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia E-Mail: [email protected]
ABSTRACT
Wire Electrical Discharge Machining (WEDM) plays a significant role in the manufacturing process for various industries. In the WEDM process, the objective is always to get improved Material Removal Rate (MRR) along with achieving better surface quality of machined component. An Experimental Investigation was conducted to determine the setting parameters appropriate WEDM process to maximize the material removal rate, minimize kerf and surface roughness of workpiece material. The experimental design used is based on orthogonal matrix L18 design. WEDM process parameters to be determined the setting are the arc on time, on time, open voltage, off time and servo voltage. The results showed have shown that the parameters arc on time, on time, open voltage, and off time have the greatest contribution in reducing the variation of responses were observed simultaneously.
Keywords: WEDM, AISI H13 tool steel, taguchi, WPCA.
INTRODUCTION
Metal cutting is one of the most important manufacturing processes in the industrial world. The study of metal cutting is often focused on the composition and mechanical properties of the workpiece, as well as all the machining parameters that affect the efficiency of the process and quality of product. WEDM is widely used to manufacture components with intricate shapes and profiles. It has been commonly used in the automotive, aerospace, mould, tool and die making industries. Applications can also be found in the field of medical, optical, jewellery and dental parts processing. Owing to high process capability, it is widely used in manufacturing of cam wheels, special gears, bearing cage, various press tools, dies, and similar intricate parts [1]. The movement of work piece is controlled by computer numerical control
system (with positional accuracy of ± 0.5 μm) and wire is
fed continuously through the work piece by a micro processor, enabling parts of complex shapes to be machined with high accuracy [2].
AISI H13 steel is one kind of steel that has high conductivity, has a high wear resistance and has a high stability in hardening. This steel categorised as difficult to machine material, its has greater strength and toughness. AISI H13 widely used in the blanking and cold-forming dies manufacturing for a wide range of automotive and electronic components production.
In the wire electrical discharge machining (WEDM) process, it is important to select proper combination of machining parameters for achieving optimum machining performance measures. The proper selection of machining parameters is essential to increase production rate and to improve product quality.
Particularly in rough cutting machining with WEDM, the goal is to produce the higher material removal rate (MRR) and to obtain best surface finish. MRR determines the economics cost of machining and time rate of production. Surface roughness is a measure of the technological quality of a machining parameters that greatly influences manufacturing cost and quality. Surface roughness is a key factor in the machining process while considering machining performance [3]. In the WEDM process, kerf denotes degree of precision. The accuracy of the dimensions are highly depend on cutting width. The kerf is one of the performance measures which is very important in determining the accuracy of the dimension and the precision of the finishing part [4]. The kerf can be considered as a limiting factor in producing the internal corner radius during WEDM process. This means that the rough cutting operation is more challenging because three goals must be satisfied simultaneously.
However, the optimal selection of machining parameters which conducted by traditional Taguchi method cannot solve multi-response optimization problems.
Multi-response methods based on a weighted principal component analysis (WPCA) method coupled with Taguchi method to optimize the multi-response problem can effectively address above issues. PCA method is a way of identifying patterns in the correlated data, and expressing the data in such a way so as to highlight their similarities and differences [7]. Based on WPCA method, the normalized multi-response values are transformed into uncorrelated linear combinations known as principal components (PCs) [8]. Principal components are found out which are independent quality indices.
EXPERIMENTATION
Experimental Set Up
During this study, all the experiments were conducted on a CHMER CW32F WEDM machine tool. In this WEDM machine, all the axes are controlled by servo and can be programmed to follow a CNC code which is fed through the control panel. The work piece has been made by AISI H13 tool steel material. The work piece material chemical composition of the material is Fe: 90.95%, Cr: 5%, Mo: 1.35%, V: 1%, C: 0.4%, Si: 1%, Mn: 0.3%. The size of the work piece considered for experimentation on the wire-cut EDM is 200 mm x 30 mm x 15 mm. The electrode taken was Seiki Denko HSD-25P-5RT brass wire with diameter of 0.25 mm. 10 mm length of cut with 15 mm depth of cut was made along the longer length of the work piece. After removing material from the work piece, the surface roughness was measured using a Mitutoyo Surftest 301 with a cut-off length of 0.8 mm and sampling length of 5 mm.
Machining Parameters Selection
Arc on time, on time, open voltage, off time and servo voltage were used as input machining parameters in the experiments. Input levels are decided based on the design of experiments. The input parameters and their level are presented in Table 1. These parameters and their level were chosen based on the recommendation of the machine tool manufacturer and as per the few preliminary pilot experiments that were carried out by varying the machining parameters to find their significance and relevance to the response parameters.
Table-1. Machining parameters and their level.
WEDM parameters Level Unit
1 2 3
Arc on time (AN) 2 3 - s
On time (ON) 0.3 0.4 0.5 s
Open voltage (OV) 90 100 110 volt
Off time (OFF) 8 9 10 s
Servo voltage (SV) 32 36 40 volt
Table-1 shows that one parameter was set at two different levels while the other four were set at three different levels. Hence, the total degrees of freedom were eight.
Design of Experiments
A L18 orthogonal array has been selected based on Taguchi quality design concept for the experimentation purpose. The interaction effect of process parameters has been assumed to be negligible. Table 2 shows the orthogonal array that used for experimention and led to a total of 18 tests. The tests were run randomly and repeated two times to achieve validity and accuracy of the experiment.
Taguchi design method is to identify the machining parameter settings which render the quality of the product or process robust to unavoidable variations in external noise. The relative quality of a particular parameter design is evaluated using a generic signal to noise (S/N) ratio. Depending on the particular design problem, different S/N ratiosare applicable, including larger is better and smaller is better. The S/N ratios calculations for each type of characteristic are shown as follows [9]:
Larger is better (maximize):
S/N= − log [∑ 1/��2
=1 ], (1) and
Smaller is better (minimize):
S/N= − log [∑ i2
Table-2. L18 orthogonal array.
No Machining parameter
AN ON OV OFF SV
1 2 0.3 90 8 32
2 2 0.3 100 9 36
3 2 0.3 110 10 40
4 2 0.4 90 8 36
5 2 0.4 100 9 40
6 2 0.4 110 10 32
7 2 0.5 90 9 32
8 2 0.5 100 10 36
9 2 0.5 110 8 40
10 3 0.3 90 10 40
11 3 0.3 100 8 32
12 3 0.3 110 9 36
13 3 0.4 90 9 40
14 3 0.4 100 10 32
15 3 0.4 110 8 36
16 3 0.5 90 10 36
17 3 0.5 100 8 40
18 3 0.5 110 9 32
EXPERIMENTAL RESULT AND DISCUSSIONS
Since the range of data series is too large and the optimal value of the quality characteristics is also too large, hence the influence of some parameters might be ignored. It is necessary to normalize the experimental data to eliminate the aforesaid effect. A linear normalization of the S/N ratio of experimental result for the experiment for the responses are performed in the range between 0 and 1. There are three different types of data normalization as required, i.e., the SB (smaller is better), the LB (larger is better) and NB (nominal is the best). The following equation is applied to normalize the S/N ratio obtained from Table-3 [9]:
∗ � = �� − i ��
a �� − i �� (3)
Here, i = 1, 2 ...m; k = 1, 2 ...n
Xi *(k) is the normalized data of the k th element in the i th sequence.
The experimental result, S/N ratio and the normalization data for the MRR, kerf and SR are presented in Table 3, 4 and 5. Since the performance characteristics of MRR are larger is better, kerf and SR is smaller is better. Here n denotes the number of measurements and yi is the measured characteristic value.
Table-3. Experimental results of MRR.
No MRR
(mm3/min) S/N Xi
1 13.2 22.4002 0.0035
2 13.43 22.5544 0.0331
3 13.16 22.3821 0
4 18.16 25.1827 0.5377
5 17.32 24.7694 0.4584
6 18.4 25.2962 0.5595
7 19.35 25.7297 0.6428
8 21.4 26.6099 0.8117
9 20.39 26.1867 0.7305
10 15.09 23.5585 0.2259
11 17.37 24.7968 0.4636
12 16.72 24.4607 0.3991
13 18.96 25.5547 0.6091
14 22.12 26.8946 0.8664
15 22.5 27.0374 0.8938
16 23.54 27.4326 0.9697
17 23.54 27.433 0.9698
18 23.96 27.5904 1
Table-4. Experimental results of Kerf.
No Kerf
(µm) S/N Xi
1 338 -50.5741 1
2 341 -50.6551 0.8948
3 347 -50.7983 0.709
4 353 -50.9555 0.5049
5 356 -51.0168 0.4253
6 359 -51.0979 0.3201
7 363 -51.1862 0.2055
8 365 -51.234 0.1434
9 369 -51.3405 0.0051
10 351 -50.9144 0.5582
11 346 -50.7773 0.7361
12 350 -50.8689 0.6172
13 361 -51.1461 0.2574
14 362 -51.1822 0.2106
15 365 -51.2538 0.1177
16 369 -51.3445 0
17 366 -51.2578 0.1125
18 368 -51.317 0.0357
No SR
(µm) S/N Xi
1 2.26 -7.0584 0.9899
2 2.25 -7.0114 1
3 2.67 -8.5414 0.6693
4 2.48 -7.8775 0.8128
5 2.67 -8.5509 0.6672
6 2.59 -8.2441 0.7335
7 2.5 -7.9838 0.7898
8 2.88 -9.1984 0.5273
9 3.71 -11.372 0.0574
10 2.6 -8.2831 0.7251
11 2.41 -7.6464 0.8628
12 2.61 -8.3331 0.7143
13 2.55 -8.1316 0.7579
14 2.57 -8.2068 0.7416
15 3.46 -10.7859 0.1841
16 2.66 -8.4994 0.6784
17 3.82 -11.6375 0
18 3.67 -11.2823 0.0768
The next step is optimization process of multiple performance characteristics with WPCA method. After data normalization a check has to be made whether responses are correlated or not. The correlation coefficient between two quality characteristics is calculated by using the following equation [10]:
(4)
j = 1, 2, 3 ... n k = 1, 2, 3 ... n j ≠ k
Here, ρjk representing the correlation coefficient between quality characteristic j and quality characteristic k; Cov(Qj Qk) is the covariance of quality characteristic j
and quality characteristic k; σQj and σQk are the standard deviations of quality characteristic j and quality characteristic k, respectively.
The correlation is proved by testing the following hypothesis:
H0ρjk = 0 (There is no correlation) H1ρjk≠ 0 (There is correlation)
Table-6 shows the Pearson’s correlation coefficient between the responses. In all cases non-zero value of correlation coefficient indicates that all response features are correlated to each other [11].
Table-6. Experimental results of SR.
NO Correlation
between
Pearson’s
correlation
coefficient Remarks
(ρ)
1 Xi*1 & Xi*2 -0.923 Correlation
2 Xi*1 & Xi*3 -0.669 Correlation
3 Xi*2 & Xi*3 0.718 Correlation
In order to eliminate response correlations between the quality characteristics, it is necessary to derive three independent quality indices called principal component by applying principal component analysis. The independent quality indices are denoted as PC1, PC2 and PC3. Principal components are independent (uncorrelated) of each other. The explained variance of each principal component for the total variance of the responses is also obtained simultaneously. To calculate the value of principal component scores using the following equation [11]:
� = ∑=1 ∗ j (5)
for j= 1, β,…k, the coefficient ij is called eigenvector. The results of PCA (Eigen value, Eigen vector, accountability proportion AP and cumulative accountability proportion CAP) are presented in Table-7.
Table-7. Results of Principal Component Analysis.
Y1 Y2 Y3
Eigen value 2.5452 0.3805 0.0743
Eigen vector
-0.592 0.445 -0.672 0.602 -0.310 -0.736 0.536 0.840 0.084
AP 0.848 0.127 0.025
CAP 0.848 0.957 1
Based on weighted principal component method, all principal components will be used, thus the explained variance can be completely explained in all responses. Accountability proportion (W) of individual principal components has been treated as individual priority weights [6]. Finally, multi-response performance index (MPI) has been calculated using the following equation [6]:
��� = ∑ =1 (6)
MPI has been treated as single objective function for optimization in order to maximize it. This has been calcculated using Taguchi method. Table-8represents the values of these independent principal components and MPI for 18 experimental runs.
No PC1 PC2 PC3 MPI
Y1 Y2 Y3
1 -0.2223 -1.0365 0.9250 -0.2970
2 -0.2934 -0.9935 0.8534 -0.3536
3 -0.1343 -0.7124 0.6518 -0.1880
4 -0.6398 -0.4310 0.7806 -0.5778
5 -0.5305 -0.3469 0.6590 -0.4774
6 -0.6817 -0.3023 0.6304 -0.6007
7 -0.8198 -0.2580 0.5835 -0.7134
8 -0.7711 0.0561 0.5998 -0.6317
9 -0.4688 0.3959 0.4007 -0.3372
10 -0.3726 -0.5707 0.6509 -0.3722
11 -0.5267 -0.5841 0.9393 -0.4973
12 -0.4416 -0.4768 0.7924 -0.4152
13 -0.7554 -0.2709 0.6064 -0.6598
14 -0.9175 -0.0895 0.7036 -0.7719
15 -0.6005 0.3661 0.5934 -0.4479
16 -1.0299 0.0845 0.5767 -0.8483
17 -0.5241 0.5489 0.6143 -0.3593
18 -0.6277 0.5344 0.5724 -0.4501
Performing analysis of variance
Finally, with the application of Analysis of Variance (ANOVA), the significant machining parameters in this quality index and their contribution percentages for total variation in MPI can be obtained. The purpose of ANOVA is to identify which machining parameters significantly affecting the machining performance characteristics such as material removal rate, surface roughness and kerf. This is accomplished by separating the total variability of the multi-response performance from the total mean of the MPI, which is measured by the sum
of the squared deviations from the total mean of the MPI, into contributions by each of the machining parameters and the error [6]. In addition, the Fisher's F-test can also be used to determine which machining parameters have a significant effect on the performance characteristic. F- value is defined as the ratio of mean square for the term to mean square for the error term. According to ANOVA, large F-value indicates that the variation of the process parameter makes a big change on the performance characteristics. Table 9 represent the ANOVA of the MPI for the WEDM process for AISI H13.
Table-9. ANOVA for the MPI.
WEDM
parameters DF SS MS F
Contribution
(%) AN 1 0.02311 0.02311 2.78 2.77
ON 2 0.19512 0.09756 11.73 35.03
OV 2 0.09038 0.04519 5.43 15.38
OFF 2 0.06816 0.03407 4.1 11.22
SV 2 0.09197 0.04598 5.53 15.68
Error 8 0.06655 0.00831 19.89
Table-9 also shows the degree of contribution of the most significant machining parameters for the MPI of WEDM AISI H13. Based on that table, the contribution of machining parameters in order are on time, servo voltage, open voltage, off time and arc on time. Figure-1 performed ratio plot of MPI. Optimal setting has been evaluated from this plot. In the MPI graph (Figure-1), it is clearly mentioned that the optimal combination of process parameters for multiple performance characteristics are second level of arc on time, second level of on time, first level of open voltage, third level of off time and first level servo voltage (AN 2 ON 2 OV1 OFF3 SV1).
2 1 0,6
0,5
0,4
3 2
1 1 2 3
3 2 1 0,6
0,5
0,4
3 2 1 A
M
e
a
n
o
f
M
e
a
n
s
B C
D E
Main Effects Plot for Means
Data Means
Figure-1. MPI of multiple performance characteristics.
Confirmation Experimets
After the optimal level of machining parameters has been identified, a verification test needs to be carried out in order to check the accuracy of analysis. The purpose of these tests also to predict and verify the improvement of the performance characteristic using the optimal level of the machining parameters. The estimated MPI (̂) using the optimal level of the machining parameters can be calculated as [6]:
(7)
where is the total mean of MPI, ̅� is the mean of the MPI at the optimal level, and i is the number of the machining parameters that significantly affects the multiple performance characteristics of WEDM process.
The results of the confirmation test using the optimal machining parameters, and also a comparison of the multiple process responses for initial and optimal machining parameters are shown in Table-10. It can be seen in Table-10 that MRR is increased 12 % from 18.17 to 20.65 mm3/min, kerf is decreased 1.3% from 366 to 361 µm and SR is decreased 63.18% from 2.58 to 2.24 µm. Therefore, it can be concluded that the multiple performance characteristic of the WEDM process such as material removal rate, kerf and surface roughness are improved simultaneously by using this approach.
Table-10. Result of confirmation tests.
Initial Optimal process condition
Prediction Experiment
Setting Level of process parameters
AN1ON1 OV1 OFF2SV1
AN2ON2OV1 OFF3SV1
AN2ON1OV1 OFF3SV1 Material Removal
Rate (mm3/min) 18.17 20.65
Kerf (µm) 366 361
Surface Roughness
(µm) 2.58 2.25
MPI -0.0137 -0.1447
CONCLUSIONS
The usage of orthogonal array by Taguchi method with principal component analysis to optimize the WEDM process with the multiple performance characteristics has been reported in this paper. A principal component analysis of the experimental results of MRR, kerf and surface roughness can convert optimization of a single performance characteristic called the MPI. As a result, optimization of the complicated multiple performance characteristics can be greatly simplified
through this approach. The conclusions of the study are as follows:
The combination of machining parameters for maximizing metal removal rate, minimizing kerf and surface roughness for WEDM of AISI H13 tool steel are arc on time of 2 µs, on time of 0.4 µs, open voltage of 90 volt, off time of 10 µs and servo voltage of 32 volt.
The combination of Taguchi method and WPCA facilitates simultaneous acquisition of high metal removal rate, low kerf and surface roughness.
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