- Email: [email protected]
Parametric Appraisal of WEDM Taper Cutting Process Using Maximum Deviation Method
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 5 (2018) 11601–11607
www.materialstoday.com/proceedings
ICMMM - 2017
Parametric Appraisal of WEDM Taper Cutting Process Using Maximum Deviation Method Bijaya Bijeta Nayaka*, Kumar Abhishekb, Siba Sankar Mahapatrac a
School of Mechanical Engineering, KIIT University, Bhubaneswar, Odisha, India b School of Mechanical Engineering Ahmedabad, Gujurat, India c Department of Mechanical Engineering, National Instutute of Technology, Rourkela, Odisha, India
Abstract The present study highlights a multi-response optimization approach to determine optimal process parameters in taper cutting of AISI D2 tool steel as work piece material using wire electrical discharge machine. Experiments have been conducted considering six input parameters such as part thickness, taper angle, pulse duration, discharge current, wire speed and wire tension each at three levels for obtaining desired value of performance measures such as angular error (AE), surface roughness (SR), cutting rate (CR) and white layer thickness (WLT). Taguchi’s L27 orthogonal array is used to gather information regarding the process with less number of experimental runs. However, Traditional Taguchi method fails to optimize multiple performance measures simultaneously. In order to overcome this limitation, the present work proposes a maximum deviation method (MDM) for converting multiple performance measures into equivalent single performance measure known as composite score (CS). The effect of input parameters on composite score (CS) values has been studied in detail by using taguchi method. Analysis of Variance (ANOVA) is also conducted to determine the statistical significance of process parameters during taper cutting in WEDM process. © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Materials Manufacturing and Modelling (ICMMM - 2017).
Keywords:Wire electrical discharge machining; Taper cutting; Maximum deviation method; Composite score
*
Corresponding author. Tel.: +0-661-246-2512; fax: +0-661-246-2926. E-mail address: [email protected]
2214-7853© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Materials Manufacturing and Modelling (ICMMM - 2017).
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Bijaya Bijeta Nayak et al. / Materials Today: Proceedings 5 (2018) 11601–11607
1. Introduction Wire electrical discharge machining (WEDM) has become an important non-traditional machining process as it provides aneffective solution for producing components made of difficult-to-machine materials like titanium, zirconium, tungsten etc. and intricateshapes which are not possible by conventional machining methods. It is basically a thermo- electrical process in which material is eroded by aseries of sparks between the work piece and the wireelectrode (tool).WEDM has become one of the popular processes for producing precise complex geometries with inclined surfaces in hard materials such as those used in the tooling industry. The socalled tapercutting involves the generation of inclined surfaces and possesses significant bearing in manufacturing of tooling requiring taper or draft angles. In this case, the taper angle is achieved by applying a relative movement between the upper and lower guides as shown in figure 1.During taper cutting operation in wire-EDM, the wire is subjected to deformation resulting deviations in the inclination angle of machined parts.As a result, the machined part losses its precision.The problem of prediction of angular error in tapercutting was investigated by Kinoshita et al. [1].They proposed a linear model of wire deformation neglecting the forces produced during the process.Sanchez et al. [2] presented a approach for the prediction of angular error in wire-EDM taper cutting. They analyzed the factors that influence angular error in taper cutting that leads to the development of experimental and numerical methods for the prediction of the error.Plaza et al. [3] developed two models for the prediction of angular error in WEDM tapercutting and found that part thickness and taper angle are most influencing variables.A computer simulation approach is adopted by Sanchez et al. [4] for analysis of angular error in wire-EDM taper cutting to minimize verification by experimentation.However a few researchers discussed about the problem of simultaneous optimization of various response during taper cutting operation in WEDM process. Therefore, in the present work maximum deviation method is used to simultaneously improve more than one performance measures at a time. 2. Proposed methodology Usually the weights assigned in the multi attribute decision making (MADM) are quite subjective in nature and affect the decision of ranking the alternative solutions. Therefore to avoid the embedded uncertainty and due to the subjective assigning of weights from the experts and to extract the accurate information from the available numerical data, maximum deviation method was proposed by Wang [5]. The little difference in the performance value of each alternative under an attribute shows the significance of that attribute in the priority ranking of alternatives. Contrariwise, higher difference in the performance value of alternatives in an attribute dictates the higher significance of that attribute in selection of best alternative. Therefore, the attribute having similar values across all alternatives should be assigned a smaller weight in comparison to the attribute having larger deviations. Especially, if the attribute values of all alternatives are equal with respect to a given attribute will be judged unimportant by most decision makers. In other word, such an attribute should be assigned a very small weight. Wang [5] suggests that zero weight should be assigned to the corresponding attribute. Hence to obtain the response weight for the given problem the following steps are suggested. Step-1: Normalization of the response variables The normalization process is needed to transform different scales and units among various attributes into common measurable units to allow the comparisons of different attributes. The decision matrix is obtained from the experimental results. Each element of the decision matrix represents the value of attribute of alternative, where = 1,2 … … . . and = 1,2 … … . To normalize the evaluation matrix following equations are used. =
For non-beneficial attributes
(1)
=
For beneficial attributes
(2)
Step-2: Weights determination through maximum deviation method In the present work, maximum deviation method is considered to compute the differences of performance values of each alternative. For the attribute | = 1,2, … … , , the deviation value of the alternative | = 1,2, … … from all the other alternatives can be computed as follows
Bijaya Bijeta Nayak et al./ Materials Today: Proceedings 5 (2018) 11601–11607
11603
= ∑ , (3) Then the total deviation values of all alternatives with respect to other alternatives for the attribute | = 1,2, … … , , can be defined = ∑ = ∑ ∑ , (4) The deviation of all the attributes along all the alternatives can be represented as = ∑ = ∑ ∑ ∑ , (5) Based on the above analysis, we have to choose the weight vector to maximize all deviation values for all the attributes, for which we can construct a linear model as follows = ∑ ∑ ∑ , (6) . ∑ = 1, ≥ 0, = 1,2, … … . , To solve the above model, we construct the Lagrange function: , =∑ ∑ ∑ , + ∑ −1 (7) where is the Lagrange multiplier. The partial derivative of , with respect to and are: =∑ ∑ , +2 =0 (8) = ∑ −1=0 Thus from Eq (7) and (8) w and λ can be determined as 2
∑
=
∑ ∑
∑
∑ ∑
∑
, (9)
, ∑
,
Further the normalized attribute weights from the above can be determined as follows: =∑
∑
∑ ∑
, ∑
(10)
,
Step-3: Calculation of composite score Finally the multi-responses are converted into single equivalent response by determining the composite score of each experiment by summing the weighted performance in all the attributes. 3. Experimentation The experiments were coducted on AC Progress V2 high precision CNC WEDM, which is manufactured by Agie-Charmilles Technologies Corporation. A wire commonly used now a days for taper cutting , the coated Broncocut-W (by Bedra), diameter 0.2mm, has been used for the experiment. Deionized water is used as di-electric medium. AISI D2 tool steel [Carbon 1.55%, Manganese 0.6%, Silicon 0.6%, Chromium 11.8%, Molybdenum 0.8%, Vanadium 0.8% and rest is iron] of diameter 25mm and thickness of 20mm, 30mm and 40 mm respectively has been chosen as work piece material. The input parameters used in the present study are shown in Table 1. These were chosen through review of literature, experience, and some preliminary investigations.Their limits were set on the basis of capacity and limiting conditions of the WEDM, ensuring continuous cutting by avoiding the breakage of the wire. Table 1. Input parameters with their levels Input variables
Unit
Symbol
Part Thickness Taper Angle Pulse Duration Discharge Current Wire Speed Wire Tension
mm Degree µs Amp mm/s N
A B C D E F
Level I 20 5 24 14 90 12
Levels Level II 30 6 28 16 120 14
Level III 40 7 32 18 150 16
In the present work, Taguchi’s L27 orthogonal array is used to gather maximum information regarding the process with less number of experimental run. The factors and their interaction are assigned to the columns by using the
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standard linear graph [6-7]. According to the Taguchi design concept, a L27 orthogonal array was chosen for the experiments as shown in Table 2. Angular error (AE), surface roughness (SR), cutting speed (CS) and white layer thickness (WLT) were considered the four important performance measures for optimizing machining parameters of WEDM taper cutting process. The angular error can be expressed in minute and calculated by the following formula: Angular error = Ф - θ where θ is the programmed angle or the angle expected in the machined part. Фis the actual angle obtained in the machined part due to the wire deformation After machining, the angle of the inclined surface (Ф) is measured with respect to the top surfaces using a Zeiss 850 CNC coordinate measuring machine. The surface roughness value (in µm) has been obtained by measuring the mean absolute deviation, Ra (surface roughness) from the average surface level using SURFCOM 130A. For WEDM cutting speed is also a desirable characteristic and it should be as high as possible to give least machine cycle time leading to increased productivity. In the present study cutting rate is a measure of job cutting which is digitally displayed on the screen of the machine and is given in mm/min. To measure the white layer thickness, cross section of work piece samples were polished successively with silicon carbide emery papers of grit sizes 80, 120, 220, 320, 400, 600, 800, 1000, 1200 and 1500 using automatic polishing machine. The surface was subsequently electro polished using automatic polishing machine with various grades of diamond paste (5, 3, 1µm respectively) to have mirror finish. Thereafter, these faces were etched with nital solution (97% ethyl alcohol and 3% nitric acid) for 20 to 25 seconds. A Scanning Electron Microscope (SEM) (Model-JSM-6480LV, Japan) with a magnification 500x is employed to analyse the white layer. The depths of white layer were measured carefully from the micrographs using image processing in MATLAB 13 and the maximum depth was considered as the white layer thickness. The experimental results of performance measures during taper cutting of AISI D2 tool steel using WEDM are presented in Table 2. Table 2. Experimental results of performance measures Angular Error
Surface
Cutting Speed
White layer
(minute)
Roughness(µm)
(mm/min)
Thickness(µm)
1
29.81
2.406
0.7644
9.56
2
2
44.36
2.219
0.8951
12.5
3
3
3
42.11
2.897
1.5764
14.13
2
2
3
45.15
2.968
0.8616
12.9
2
3
3
1
47.33
2.866
0.9515
13.6
2
3
1
1
2
48.79
3.008
0.9986
11.4
3
1
3
3
2
52.65
2.994
0.9412
9.81
3
2
1
1
3
49.63
2.706
0.8664
8.95
Exp.no
A
B
C
D
E
F
1
1
1
1
1
1
2
1
1
2
2
3
1
1
3
4
1
2
1
5
1
2
6
1
7
1
8
1
9
1
3
3
2
2
1
50.86
3.219
1.1892
7.6
10
2
1
1
2
3
2
54.63
2.841
0.7828
9.77
11
2
1
2
3
1
3
57.25
2.912
0.9508
10.55
12
2
1
3
1
2
1
41.99
3.205
0.9768
8.25
13
2
2
1
3
1
1
52.61
3.451
0.7489
9.92
14
2
2
2
1
2
2
54.56
3.527
0.8808
6.25
15
2
2
3
2
3
3
50.25
3.661
1.1932
12.89
16
2
3
1
1
2
3
25.86
2.824
0.7644
10.58
17
2
3
2
2
3
1
34.21
3.004
0.8648
12.44
18
2
3
3
3
1
2
26.25
3.678
0.9673
17.35
19
3
1
1
3
2
3
30.99
2.433
0.8164
11.29
Bijaya Bijeta Nayak et al./ Materials Today: Proceedings 5 (2018) 11601–11607
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20
3
1
2
1
3
1
22.14
2.182
0.919
9.45
21
3
1
3
2
1
2
24.24
2.339
1.0156
13.88
22
3
2
1
1
3
2
43.01
2.515
0.8952
5.21
23
3
2
2
2
1
3
52.29
2.608
0.9518
11.85
24
3
2
3
3
2
1
35.32
2.963
1.3104
19.56
25
3
3
1
2
1
1
42.23
2.845
0.5616
11.57
26
3
3
2
3
2
2
39.94
2.971
0.9812
13.63
27
3
3
3
1
3
3
31.71
3.156
1.1156
14.89
4. Results and Discussion The experiments are conducted using Taguchi’s L27 orthogonal array design of experiment and the response values are calculated as described in section 3. Present work aims at simultaneously minimizing the angular error, surface roughness and white layer thickness as well as maximizing the cutting speed during taper cutting in WEDM process. To achieve the above goal, composite score of the responses are calculated which is treated as equivalent single response for the above problem. Initially all the response variables are normalized by using Eqs. (1-2) to avoid the scaling effect.The objective weights are determined for the normalized values of responses by applying maximum deviation method using Eqs. (3-10). The weights obtained through the maximum deviation method are 0.315, 0.279, 0.184 and 0.223for angular error, surface roughness, cutting speed and white layer thickness respectively.The weighted normalized objective values are calculated by multiplying the normalized objective values and the objective weights as shown in Table 3. The composite score is obtained by summing all the weightedobjective function values for each alternative which is treated as the equivalent single performance characteristic for optimization. The values of composite scores are also listed in Table 3. Table 3. Calculation of Composite score of responses Exp. No
Normalized response values Angular Surface Cutting error Roughness speed
White layer thickness
Angular error
Weighted Normalized response values Surface Cutting White layer Roughness speed thickness
Composite score
1
0.782
0.850
0.200
0.697
0.246
0.237
0.037
0.155
0.675
2
0.367
0.975
0.329
0.492
0.116
0.272
0.061
0.109
0.557
3
0.431
0.522
1.000
0.378
0.136
0.145
0.184
0.084
0.550
4
0.345
0.475
0.296
0.464
0.108
0.132
0.054
0.103
0.398
5
0.283
0.543
0.384
0.415
0.089
0.151
0.071
0.092
0.403
6
0.241
0.448
0.431
0.569
0.076
0.125
0.079
0.127
0.406
7
0.131
0.457
0.374
0.679
0.041
0.127
0.069
0.151
0.389
8
0.217
0.650
0.300
0.739
0.068
0.181
0.055
0.165
0.469
9
0.182
0.307
0.618
0.833
0.057
0.086
0.114
0.185
0.442
10
0.075
0.559
0.218
0.682
0.023
0.156
0.040
0.152
0.371
11
0.000
0.512
0.384
0.628
0.000
0.143
0.071
0.140
0.353
12
0.435
0.316
0.409
0.788
0.137
0.088
0.075
0.175
0.476
13
0.132
0.152
0.185
0.672
0.042
0.042
0.034
0.149
0.267
14
0.077
0.101
0.315
0.928
0.024
0.028
0.058
0.206
0.317
15
0.199
0.011
0.622
0.465
0.063
0.003
0.115
0.103
0.284
16
0.894
0.571
0.200
0.626
0.281
0.159
0.037
0.139
0.616
17
0.656
0.451
0.299
0.496
0.207
0.126
0.055
0.110
0.497
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18
0.883
0.000
0.400
0.154
0.278
0.000
0.074
0.034
0.386
19
0.748
0.832
0.251
0.576
0.235
0.232
0.046
0.128
0.642
20
1.000
1.000
0.352
0.705
0.315
0.279
0.065
0.157
0.815
21
0.940
0.895
0.447
0.396
0.296
0.249
0.082
0.088
0.716
22
0.406
0.777
0.329
1.000
0.128
0.217
0.061
0.223
0.627
23
0.141
0.715
0.385
0.537
0.044
0.199
0.071
0.120
0.434
24
0.625
0.478
0.738
0.000
0.197
0.133
0.136
0.000
0.466
25
0.428
0.557
0.000
0.557
0.135
0.155
0.000
0.124
0.414
26
0.493
0.473
0.413
0.413
0.155
0.132
0.076
0.092
0.455
27
0.727
0.349
0.546
0.325
0.229
0.097
0.101
0.072
0.499
The optimal machining parameter has been obtained from mean effect plot of composite score as shown in Fig. 1. The optimal input parameter setting is part thickness at level 1, taper angle at level 1, pulse duration at level 3, discharge current at level 1, wire speed at level 3 and wire tension at level1 for minimizing angular error, surface roughness, white layer thickness and maximizing cutting speed simultaneously.
Fig.1. Mean effect plot for composite score Analysis of variance (ANOVA) is a particular form of statistical hypothesis testing heavily used in the analysis of experimental data. ANOVA is used to investigate which machining parameters significantly affect the performance characteristics. From Table 4, it is evident that part thickness and taper angle are the significant factors for composite score during taper cutting process in WEDM. Table 4. ANOVA Table Factor
DF
Seq SS
Adj SS
Adj MS
F
P
Part thickness
(A)
2
0.1250
0.1250
0.0625
6.64
0.009
Taper angle
(B)
2
0.1369
0.1369
0.0684
7.27
0.007
Pulse duration
(C)
2
0.0017
0.0017
0.0008
0.09
0.913
Discharge current (D)
2
0.0607
0.0607
0.0303
3.23
0.070
Wire speed
(E)
2
0.0061
0.0061
0.0030
0.33
0.727
Wire tension
(F)
2
0.0036
0.0036
0.0018
0.19
0.828
Error
6
0.1318
0.1318
0.0094
Total
26
0.4660
Bijaya Bijeta Nayak et al./ Materials Today: Proceedings 5 (2018) 11601–11607
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5. Conclusions This research work offers an effective guideline to select optimum parameter settings for achieving the minimum angular error, surface roughness, white layer thickness and maximum cutting rate during taper cutting in AISI D2 tool steel using WEDM process to the experimenter and practitioners.The maximum deviation method integrated Taguchi method seems to be an efficient methodology to find out the optimum cutting parameters for taper cutting operation as experiment was based on minimum number of trails conducted to obtain optimum setting for cutting parameters. References [1] [2] [3] [4] [5] [6] [7]
N. Kinoshita, M. Fukui, T. Fujii,CIRP Annals-Manufacturing Technology, 36 (1987) 119-122. J. A. Sanchez, S. Plaza, N. Ortega, M. Marcos, J. Albizuri, International Journal of Machine Tools and Manufacture, 48 (2008) 14201428. S. Plaza, N. Ortega, J. A. Sanchez, I. Pombo, A. Mendikute, International Journal of Advanced Manufacturing Technology, 44 (2009) 529-538. J. A. Sanchez, J. L. Rodil, A. Herrero, L.N. Lopez de Lacalle, A. Lamikiz, Journal of Materials Processing Technology, 182 (2007) 574-579. Y.M. Wang, Systems Engineering and Electronics. 20 (1998), 24-26. S.G. Peace, Taguchi methods: a hands on approach, Addison-Wesley, New York 1993. M.S. Phadke, Quality engineering using robust design, Prentice Hall Eaglewood Cliffs, New Jersey 1989.
ScienceDirect Materials Today: Proceedings 5 (2018) 11601–11607
www.materialstoday.com/proceedings
ICMMM - 2017
Parametric Appraisal of WEDM Taper Cutting Process Using Maximum Deviation Method Bijaya Bijeta Nayaka*, Kumar Abhishekb, Siba Sankar Mahapatrac a
School of Mechanical Engineering, KIIT University, Bhubaneswar, Odisha, India b School of Mechanical Engineering Ahmedabad, Gujurat, India c Department of Mechanical Engineering, National Instutute of Technology, Rourkela, Odisha, India
Abstract The present study highlights a multi-response optimization approach to determine optimal process parameters in taper cutting of AISI D2 tool steel as work piece material using wire electrical discharge machine. Experiments have been conducted considering six input parameters such as part thickness, taper angle, pulse duration, discharge current, wire speed and wire tension each at three levels for obtaining desired value of performance measures such as angular error (AE), surface roughness (SR), cutting rate (CR) and white layer thickness (WLT). Taguchi’s L27 orthogonal array is used to gather information regarding the process with less number of experimental runs. However, Traditional Taguchi method fails to optimize multiple performance measures simultaneously. In order to overcome this limitation, the present work proposes a maximum deviation method (MDM) for converting multiple performance measures into equivalent single performance measure known as composite score (CS). The effect of input parameters on composite score (CS) values has been studied in detail by using taguchi method. Analysis of Variance (ANOVA) is also conducted to determine the statistical significance of process parameters during taper cutting in WEDM process. © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Materials Manufacturing and Modelling (ICMMM - 2017).
Keywords:Wire electrical discharge machining; Taper cutting; Maximum deviation method; Composite score
*
Corresponding author. Tel.: +0-661-246-2512; fax: +0-661-246-2926. E-mail address: [email protected]
2214-7853© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Materials Manufacturing and Modelling (ICMMM - 2017).
11602
Bijaya Bijeta Nayak et al. / Materials Today: Proceedings 5 (2018) 11601–11607
1. Introduction Wire electrical discharge machining (WEDM) has become an important non-traditional machining process as it provides aneffective solution for producing components made of difficult-to-machine materials like titanium, zirconium, tungsten etc. and intricateshapes which are not possible by conventional machining methods. It is basically a thermo- electrical process in which material is eroded by aseries of sparks between the work piece and the wireelectrode (tool).WEDM has become one of the popular processes for producing precise complex geometries with inclined surfaces in hard materials such as those used in the tooling industry. The socalled tapercutting involves the generation of inclined surfaces and possesses significant bearing in manufacturing of tooling requiring taper or draft angles. In this case, the taper angle is achieved by applying a relative movement between the upper and lower guides as shown in figure 1.During taper cutting operation in wire-EDM, the wire is subjected to deformation resulting deviations in the inclination angle of machined parts.As a result, the machined part losses its precision.The problem of prediction of angular error in tapercutting was investigated by Kinoshita et al. [1].They proposed a linear model of wire deformation neglecting the forces produced during the process.Sanchez et al. [2] presented a approach for the prediction of angular error in wire-EDM taper cutting. They analyzed the factors that influence angular error in taper cutting that leads to the development of experimental and numerical methods for the prediction of the error.Plaza et al. [3] developed two models for the prediction of angular error in WEDM tapercutting and found that part thickness and taper angle are most influencing variables.A computer simulation approach is adopted by Sanchez et al. [4] for analysis of angular error in wire-EDM taper cutting to minimize verification by experimentation.However a few researchers discussed about the problem of simultaneous optimization of various response during taper cutting operation in WEDM process. Therefore, in the present work maximum deviation method is used to simultaneously improve more than one performance measures at a time. 2. Proposed methodology Usually the weights assigned in the multi attribute decision making (MADM) are quite subjective in nature and affect the decision of ranking the alternative solutions. Therefore to avoid the embedded uncertainty and due to the subjective assigning of weights from the experts and to extract the accurate information from the available numerical data, maximum deviation method was proposed by Wang [5]. The little difference in the performance value of each alternative under an attribute shows the significance of that attribute in the priority ranking of alternatives. Contrariwise, higher difference in the performance value of alternatives in an attribute dictates the higher significance of that attribute in selection of best alternative. Therefore, the attribute having similar values across all alternatives should be assigned a smaller weight in comparison to the attribute having larger deviations. Especially, if the attribute values of all alternatives are equal with respect to a given attribute will be judged unimportant by most decision makers. In other word, such an attribute should be assigned a very small weight. Wang [5] suggests that zero weight should be assigned to the corresponding attribute. Hence to obtain the response weight for the given problem the following steps are suggested. Step-1: Normalization of the response variables The normalization process is needed to transform different scales and units among various attributes into common measurable units to allow the comparisons of different attributes. The decision matrix is obtained from the experimental results. Each element of the decision matrix represents the value of attribute of alternative, where = 1,2 … … . . and = 1,2 … … . To normalize the evaluation matrix following equations are used. =
For non-beneficial attributes
(1)
=
For beneficial attributes
(2)
Step-2: Weights determination through maximum deviation method In the present work, maximum deviation method is considered to compute the differences of performance values of each alternative. For the attribute | = 1,2, … … , , the deviation value of the alternative | = 1,2, … … from all the other alternatives can be computed as follows
Bijaya Bijeta Nayak et al./ Materials Today: Proceedings 5 (2018) 11601–11607
11603
= ∑ , (3) Then the total deviation values of all alternatives with respect to other alternatives for the attribute | = 1,2, … … , , can be defined = ∑ = ∑ ∑ , (4) The deviation of all the attributes along all the alternatives can be represented as = ∑ = ∑ ∑ ∑ , (5) Based on the above analysis, we have to choose the weight vector to maximize all deviation values for all the attributes, for which we can construct a linear model as follows = ∑ ∑ ∑ , (6) . ∑ = 1, ≥ 0, = 1,2, … … . , To solve the above model, we construct the Lagrange function: , =∑ ∑ ∑ , + ∑ −1 (7) where is the Lagrange multiplier. The partial derivative of , with respect to and are: =∑ ∑ , +2 =0 (8) = ∑ −1=0 Thus from Eq (7) and (8) w and λ can be determined as 2
∑
=
∑ ∑
∑
∑ ∑
∑
, (9)
, ∑
,
Further the normalized attribute weights from the above can be determined as follows: =∑
∑
∑ ∑
, ∑
(10)
,
Step-3: Calculation of composite score Finally the multi-responses are converted into single equivalent response by determining the composite score of each experiment by summing the weighted performance in all the attributes. 3. Experimentation The experiments were coducted on AC Progress V2 high precision CNC WEDM, which is manufactured by Agie-Charmilles Technologies Corporation. A wire commonly used now a days for taper cutting , the coated Broncocut-W (by Bedra), diameter 0.2mm, has been used for the experiment. Deionized water is used as di-electric medium. AISI D2 tool steel [Carbon 1.55%, Manganese 0.6%, Silicon 0.6%, Chromium 11.8%, Molybdenum 0.8%, Vanadium 0.8% and rest is iron] of diameter 25mm and thickness of 20mm, 30mm and 40 mm respectively has been chosen as work piece material. The input parameters used in the present study are shown in Table 1. These were chosen through review of literature, experience, and some preliminary investigations.Their limits were set on the basis of capacity and limiting conditions of the WEDM, ensuring continuous cutting by avoiding the breakage of the wire. Table 1. Input parameters with their levels Input variables
Unit
Symbol
Part Thickness Taper Angle Pulse Duration Discharge Current Wire Speed Wire Tension
mm Degree µs Amp mm/s N
A B C D E F
Level I 20 5 24 14 90 12
Levels Level II 30 6 28 16 120 14
Level III 40 7 32 18 150 16
In the present work, Taguchi’s L27 orthogonal array is used to gather maximum information regarding the process with less number of experimental run. The factors and their interaction are assigned to the columns by using the
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standard linear graph [6-7]. According to the Taguchi design concept, a L27 orthogonal array was chosen for the experiments as shown in Table 2. Angular error (AE), surface roughness (SR), cutting speed (CS) and white layer thickness (WLT) were considered the four important performance measures for optimizing machining parameters of WEDM taper cutting process. The angular error can be expressed in minute and calculated by the following formula: Angular error = Ф - θ where θ is the programmed angle or the angle expected in the machined part. Фis the actual angle obtained in the machined part due to the wire deformation After machining, the angle of the inclined surface (Ф) is measured with respect to the top surfaces using a Zeiss 850 CNC coordinate measuring machine. The surface roughness value (in µm) has been obtained by measuring the mean absolute deviation, Ra (surface roughness) from the average surface level using SURFCOM 130A. For WEDM cutting speed is also a desirable characteristic and it should be as high as possible to give least machine cycle time leading to increased productivity. In the present study cutting rate is a measure of job cutting which is digitally displayed on the screen of the machine and is given in mm/min. To measure the white layer thickness, cross section of work piece samples were polished successively with silicon carbide emery papers of grit sizes 80, 120, 220, 320, 400, 600, 800, 1000, 1200 and 1500 using automatic polishing machine. The surface was subsequently electro polished using automatic polishing machine with various grades of diamond paste (5, 3, 1µm respectively) to have mirror finish. Thereafter, these faces were etched with nital solution (97% ethyl alcohol and 3% nitric acid) for 20 to 25 seconds. A Scanning Electron Microscope (SEM) (Model-JSM-6480LV, Japan) with a magnification 500x is employed to analyse the white layer. The depths of white layer were measured carefully from the micrographs using image processing in MATLAB 13 and the maximum depth was considered as the white layer thickness. The experimental results of performance measures during taper cutting of AISI D2 tool steel using WEDM are presented in Table 2. Table 2. Experimental results of performance measures Angular Error
Surface
Cutting Speed
White layer
(minute)
Roughness(µm)
(mm/min)
Thickness(µm)
1
29.81
2.406
0.7644
9.56
2
2
44.36
2.219
0.8951
12.5
3
3
3
42.11
2.897
1.5764
14.13
2
2
3
45.15
2.968
0.8616
12.9
2
3
3
1
47.33
2.866
0.9515
13.6
2
3
1
1
2
48.79
3.008
0.9986
11.4
3
1
3
3
2
52.65
2.994
0.9412
9.81
3
2
1
1
3
49.63
2.706
0.8664
8.95
Exp.no
A
B
C
D
E
F
1
1
1
1
1
1
2
1
1
2
2
3
1
1
3
4
1
2
1
5
1
2
6
1
7
1
8
1
9
1
3
3
2
2
1
50.86
3.219
1.1892
7.6
10
2
1
1
2
3
2
54.63
2.841
0.7828
9.77
11
2
1
2
3
1
3
57.25
2.912
0.9508
10.55
12
2
1
3
1
2
1
41.99
3.205
0.9768
8.25
13
2
2
1
3
1
1
52.61
3.451
0.7489
9.92
14
2
2
2
1
2
2
54.56
3.527
0.8808
6.25
15
2
2
3
2
3
3
50.25
3.661
1.1932
12.89
16
2
3
1
1
2
3
25.86
2.824
0.7644
10.58
17
2
3
2
2
3
1
34.21
3.004
0.8648
12.44
18
2
3
3
3
1
2
26.25
3.678
0.9673
17.35
19
3
1
1
3
2
3
30.99
2.433
0.8164
11.29
Bijaya Bijeta Nayak et al./ Materials Today: Proceedings 5 (2018) 11601–11607
11605
20
3
1
2
1
3
1
22.14
2.182
0.919
9.45
21
3
1
3
2
1
2
24.24
2.339
1.0156
13.88
22
3
2
1
1
3
2
43.01
2.515
0.8952
5.21
23
3
2
2
2
1
3
52.29
2.608
0.9518
11.85
24
3
2
3
3
2
1
35.32
2.963
1.3104
19.56
25
3
3
1
2
1
1
42.23
2.845
0.5616
11.57
26
3
3
2
3
2
2
39.94
2.971
0.9812
13.63
27
3
3
3
1
3
3
31.71
3.156
1.1156
14.89
4. Results and Discussion The experiments are conducted using Taguchi’s L27 orthogonal array design of experiment and the response values are calculated as described in section 3. Present work aims at simultaneously minimizing the angular error, surface roughness and white layer thickness as well as maximizing the cutting speed during taper cutting in WEDM process. To achieve the above goal, composite score of the responses are calculated which is treated as equivalent single response for the above problem. Initially all the response variables are normalized by using Eqs. (1-2) to avoid the scaling effect.The objective weights are determined for the normalized values of responses by applying maximum deviation method using Eqs. (3-10). The weights obtained through the maximum deviation method are 0.315, 0.279, 0.184 and 0.223for angular error, surface roughness, cutting speed and white layer thickness respectively.The weighted normalized objective values are calculated by multiplying the normalized objective values and the objective weights as shown in Table 3. The composite score is obtained by summing all the weightedobjective function values for each alternative which is treated as the equivalent single performance characteristic for optimization. The values of composite scores are also listed in Table 3. Table 3. Calculation of Composite score of responses Exp. No
Normalized response values Angular Surface Cutting error Roughness speed
White layer thickness
Angular error
Weighted Normalized response values Surface Cutting White layer Roughness speed thickness
Composite score
1
0.782
0.850
0.200
0.697
0.246
0.237
0.037
0.155
0.675
2
0.367
0.975
0.329
0.492
0.116
0.272
0.061
0.109
0.557
3
0.431
0.522
1.000
0.378
0.136
0.145
0.184
0.084
0.550
4
0.345
0.475
0.296
0.464
0.108
0.132
0.054
0.103
0.398
5
0.283
0.543
0.384
0.415
0.089
0.151
0.071
0.092
0.403
6
0.241
0.448
0.431
0.569
0.076
0.125
0.079
0.127
0.406
7
0.131
0.457
0.374
0.679
0.041
0.127
0.069
0.151
0.389
8
0.217
0.650
0.300
0.739
0.068
0.181
0.055
0.165
0.469
9
0.182
0.307
0.618
0.833
0.057
0.086
0.114
0.185
0.442
10
0.075
0.559
0.218
0.682
0.023
0.156
0.040
0.152
0.371
11
0.000
0.512
0.384
0.628
0.000
0.143
0.071
0.140
0.353
12
0.435
0.316
0.409
0.788
0.137
0.088
0.075
0.175
0.476
13
0.132
0.152
0.185
0.672
0.042
0.042
0.034
0.149
0.267
14
0.077
0.101
0.315
0.928
0.024
0.028
0.058
0.206
0.317
15
0.199
0.011
0.622
0.465
0.063
0.003
0.115
0.103
0.284
16
0.894
0.571
0.200
0.626
0.281
0.159
0.037
0.139
0.616
17
0.656
0.451
0.299
0.496
0.207
0.126
0.055
0.110
0.497
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18
0.883
0.000
0.400
0.154
0.278
0.000
0.074
0.034
0.386
19
0.748
0.832
0.251
0.576
0.235
0.232
0.046
0.128
0.642
20
1.000
1.000
0.352
0.705
0.315
0.279
0.065
0.157
0.815
21
0.940
0.895
0.447
0.396
0.296
0.249
0.082
0.088
0.716
22
0.406
0.777
0.329
1.000
0.128
0.217
0.061
0.223
0.627
23
0.141
0.715
0.385
0.537
0.044
0.199
0.071
0.120
0.434
24
0.625
0.478
0.738
0.000
0.197
0.133
0.136
0.000
0.466
25
0.428
0.557
0.000
0.557
0.135
0.155
0.000
0.124
0.414
26
0.493
0.473
0.413
0.413
0.155
0.132
0.076
0.092
0.455
27
0.727
0.349
0.546
0.325
0.229
0.097
0.101
0.072
0.499
The optimal machining parameter has been obtained from mean effect plot of composite score as shown in Fig. 1. The optimal input parameter setting is part thickness at level 1, taper angle at level 1, pulse duration at level 3, discharge current at level 1, wire speed at level 3 and wire tension at level1 for minimizing angular error, surface roughness, white layer thickness and maximizing cutting speed simultaneously.
Fig.1. Mean effect plot for composite score Analysis of variance (ANOVA) is a particular form of statistical hypothesis testing heavily used in the analysis of experimental data. ANOVA is used to investigate which machining parameters significantly affect the performance characteristics. From Table 4, it is evident that part thickness and taper angle are the significant factors for composite score during taper cutting process in WEDM. Table 4. ANOVA Table Factor
DF
Seq SS
Adj SS
Adj MS
F
P
Part thickness
(A)
2
0.1250
0.1250
0.0625
6.64
0.009
Taper angle
(B)
2
0.1369
0.1369
0.0684
7.27
0.007
Pulse duration
(C)
2
0.0017
0.0017
0.0008
0.09
0.913
Discharge current (D)
2
0.0607
0.0607
0.0303
3.23
0.070
Wire speed
(E)
2
0.0061
0.0061
0.0030
0.33
0.727
Wire tension
(F)
2
0.0036
0.0036
0.0018
0.19
0.828
Error
6
0.1318
0.1318
0.0094
Total
26
0.4660
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5. Conclusions This research work offers an effective guideline to select optimum parameter settings for achieving the minimum angular error, surface roughness, white layer thickness and maximum cutting rate during taper cutting in AISI D2 tool steel using WEDM process to the experimenter and practitioners.The maximum deviation method integrated Taguchi method seems to be an efficient methodology to find out the optimum cutting parameters for taper cutting operation as experiment was based on minimum number of trails conducted to obtain optimum setting for cutting parameters. References [1] [2] [3] [4] [5] [6] [7]
N. Kinoshita, M. Fukui, T. Fujii,CIRP Annals-Manufacturing Technology, 36 (1987) 119-122. J. A. Sanchez, S. Plaza, N. Ortega, M. Marcos, J. Albizuri, International Journal of Machine Tools and Manufacture, 48 (2008) 14201428. S. Plaza, N. Ortega, J. A. Sanchez, I. Pombo, A. Mendikute, International Journal of Advanced Manufacturing Technology, 44 (2009) 529-538. J. A. Sanchez, J. L. Rodil, A. Herrero, L.N. Lopez de Lacalle, A. Lamikiz, Journal of Materials Processing Technology, 182 (2007) 574-579. Y.M. Wang, Systems Engineering and Electronics. 20 (1998), 24-26. S.G. Peace, Taguchi methods: a hands on approach, Addison-Wesley, New York 1993. M.S. Phadke, Quality engineering using robust design, Prentice Hall Eaglewood Cliffs, New Jersey 1989.