Determination of multi-performance characteristics for ...

Original Article

Determination of multi-performance characteristics for powder mixed electric discharge machining of tungsten carbide alloy

Proc IMechE Part B: J Engineering Manufacture 2016, Vol. 230(2) 303–312 Ó IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954405414554017 pib.sagepub.com

Rajiv Kumar Sharma and Jagdeep Singh

Abstract This article aims to develop a method that optimize the multi-performance characteristics, that is, micro-hardness and surface roughness of powder mixed electric discharge machining process. For experimentation, four input parameters— (a) pulse-on time, (b) pulse-off time, (c) current and (d) powder—are considered to investigate the improvement in multi-performance characteristics using Taguchi’s L27 orthogonal array design. Furthermore, to optimize these parameters and to handle the element of uncertainty associated with multi-input and discrete data, a method combining the grey and Taguchi experimental design was established. Theoretical prediction of results obtained from grey relational grade approach shows that the proposed approach proved useful for optimizing surface roughness and micro-hardness. In addition, analysis of variance is used to find the percentage contribution of process parameters. Finally, from analytical and experimental results, it is concluded that the pulse-on, powder and current are the most influencing parameters in powder mixed electric discharge machining of cobalt-bonded tungsten carbide.

Keywords Electric discharge machining, powders, dielectric, analysis of variance, surface roughness, micro-hardness, tungsten carbide

Date received: 15 January 2014; accepted: 9 September 2014

Introduction Electric discharge machining, popularly known as EDM, is one of the most versatile non-traditional machining process in which the material removal takes place by a succession of electrical discharges, which occur between the electrode and the workpiece immersed in a dielectric. A spark is produced at the point of smallest inter-electrode gap, generating temperature in the range of 8000 °C–12,000 °C, causing erosion and vaporization of material.1 Because of its ability to machine high strength temperature resistant (HSTR) alloys and hard materials and to produce geometrically complex shapes, the process is most widely used in mold and die making industry and in manufacturing automotive, aerospace and surgical components. However, its low machining efficiency and poor surface finish restricted its further industrial applications.2–4 Because of complex and stochastic nature of EDM, numerous studies have been undertaken by various researchers to establish control over machining parameters, which results in better machining

performance.5,6 Among the different EDM variants— (a) die sinking, (b) additive/powder mixed and (c) wire EDM—powder mixed electrical discharge machining (PMEDM) process has been used to overcome some of the limitations of conventional EDM.7–9 In PMEDM, the material in powder form is mixed into the dielectric fluid in separately built tank. The powder improves the break down characteristics of the dielectric fluid, that is, the insulating strength of the dielectric fluid decreases, and consequently, the spark gap distance between the electrode and workpiece increases, which makes the flushing of debris uniform. As a result, the process becomes more stable, thereby improving machining rate and surface finish. Moreover, the

Department of Mechanical Engineering, National Institute of Technology Hamirpur, India Corresponding author: Jagdeep Singh, Department of Mechanical Engineering, National Institute of Technology Hamirpur, Himachal Pradesh 177005, India. Email: [email protected]

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surface produced by PMEDM has high resistance to corrosion and abrasion.10–14 Despite the better processing results of PMEDM process, it is used in industry at slow pace.15,16 Thus, fundamental issues related with process variables require further investigation. Optimization of PMEDM process has been reported using response surface methodology,3,17 analytical hierarchy process18,19 and multiobjective optimization methods.20,21 Kansal et al.22 and Kumar et al.6 carried out a detailed review on current research developments in additive mixed EDM/ PMEDM. Pecas and Henriques23 analyzed the presence of powder particles in dielectric fluid and stated that the concentration of powder creates conditions suitable for achieving better surface quality in the machined area. Wu et al.24 achieved the electrical discharge distribution effects by the addition of Al powder in the dielectric on SKD61 workpiece with copper as tool material. They found that quality of surface roughness (SR) has been improved up to 60% as compared to that of electrical discharge machined surface under pure dielectric. Mahdavinejad and Mahdavinejad25 investigated the instability of EDM process during machining WC–Co composite of different compositions. Assarzadeh and Ghoreishi26 optimized process parameters in EDM of WC–Co composite by response surface methodology and analyzed the results of material removal rate, tool wear rate and SR. Bhattacharya et al.27 studied the surface characterization and material migration during surface modification of die steels with silicon, graphite and tungsten powder in EDM process and further analyzed the two output responses, micro-hardness and SR. From the above literature studies, it is observed that a lot of work has been undertaken by various authors to investigate the various performance characteristics, but a limited work21,28,29 which deals with handling the demerit of uncertainty associated with the uncertain, multi-input and discrete data using the grey approach is reported. Furthermore, to abridge the gap between theory and practice and to handle multi-input and discrete data, the authors in this article developed a sixstep procedure (Figure 1) based upon grey relational approach. An application of PMEDM of tungsten carbide (65% WC–10%Co) is used to investigate the multi-performance characteristics (MPCs), that is, micro-hardness and surface finish, with a particular combination of control settings in the Taguchi L27 orthogonal array (OA) parameter design. Analysis of variance (ANOVA) is used to ascertain the percentage contribution of the most significant factor.

Research methodology The framework shown in Figure 1 provides the details of research methodology adopted in the study. The steps involved in the framework are described briefly as follows:

1. Selection of factors and their levels

Performing pilot experiments with L9 OA

2. Selection of orthogonal arrays

3. Conduct Experiments

4. Perform Grey relational Analysis a. Normalize the experimental results b. Generate grey relational coefficient. c. Calculate grey relation grade d. Select optimal level of parameter

Performing experiments with L27 OA

Grey relational grade

5. Theoretical prediction

6. ANOVA for percentage of contribution

Figure 1. Framework for grey relation approach.

1. 2. 3. 4.

5. 6.

First L9 OA is designed for the pilot experimentation. Most contributing factors and their levels are identified with the help of pilot experiments. Furthermore, Taguchi L27 OA is selected for performing the experimental work. A total of 27 experiments are performed on the tungsten carbide (65% WC–10% Co) with the help of four input parameters. Grey relational analysis is performed on the values of micro-hardness and SR, and a grey relational grade (GRG) as the output value is found out. Furthermore, optimal parameters are selected with the help of grey relational response table. The theoretical prediction is done to show the overall improvement using grey approach. To determine the percentage contribution of most significant factors, ANOVA analysis has been done.

Basic concepts of grey relational method This section provides details to basic concepts related to grey relational method which are required to understand the proposed methodology.

Grey relational analysis Grey relational analysis based upon grey theory provides an effective way to handle uncertainty associated with multi-input and discrete data. The theory proposed by Deng30 also deals with making decisions characterized by incomplete and partially known information. It explores system behavior using relation analysis and model construction.31 In the literature, the use of grey theory has been observed in various fields

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such as forecasting,32–34 industrial applications35 and engineering applications.36–38 The steps involved in grey analysis are as follows: 1. 2.

3. 4. 5.

Normalize the experimental results so that they can be converted into the comparison form. Calculate the grey relational coefficients for the performance characteristics to represent the relation between the ideal and normalized experimental results. Calculate the GRG by averaging the corresponding grey relational coefficients. Analyze the experimental results using the GRG. Select the optimal levels of process parameters from grey response table.

Data pre-processing. In grey relational analysis, when the range of the sequence is large or the standard value is enormous, the function of factors is neglected. However, if the factors, goals and directions are different, the grey relation might produce incorrect results. Therefore, one has to pre-process the data which are related to a group of sequences, which is called ‘‘grey relational generation.’’39 Data pre-processing is a process of transferring the original sequence to a comparable sequence. For this purpose, the experimental results are normalized in the range between 0 and 1. If the target value of original sequence is infinite, then it has a characteristic of ‘‘higher-the-better.’’ The normalized experimental results obtained in step-1 can be expressed using equation (1) for ‘‘higherthe-better’’ characteristics, that is, for micro-hardness and if the expectancy is the ‘‘lower-the-better’’ characteristics, that is, for SR can be expressed using equation (2) xi ðkÞ =

xi ðkÞ  max x0i ðkÞ

min x0i (k)  min x0i (k)

ð1Þ

xi ðkÞ =

max x0i ðkÞ  x0i (k) max x0i ðkÞ  min xoi (k)

ð2Þ

where xi (k) is the value after the grey relational generation (data pre-processing), max x0i (k) is the largest value of x0i (k), min x0i (k) is the smallest value of x0i (k) and x0 is the desired value. (Suffix i stands for run/ experiment number and suffix k stands for response.) Grey relational coefficient and GRG. The grey relation coefficient ji(k) is calculated to express the relationship between the ideal (best) and actual normalized experimental results which can be expressed as follows40 in equation (3) ji ðkÞ =

Dmin ðkÞ + z  Dmax D0i ðkÞ + z  Dmax

ð3Þ

where D0i(k) is the deviation sequence of the reference sequence x0 (k) and the comparability sequence xi (k), namely   D0i (k) = x0 ðkÞ  xi ðkÞ ð4Þ    Dmax = max8j2i maxx0 ðkÞ  x0i ðkÞ ð5Þ 8k   Dmin = min8j2i min8k x0 ðkÞ  xi ðkÞ ð6Þ z is distinguishing or identification coefficient: z 2 ½0, 1. z = 0.5 is generally used,41 and in this study also, z is taken as 0.5. The coefficient j lies between 0 and 1, which is to expand or compress the range of grey relation coefficient. Then the GRG is computed by averaging the grey relational coefficient (corresponding to each performance characteristic) as shown in equation (7) gi =

m 1 X j (k) m k=1 i

ð7Þ

where g i is the GRG for the ith experiment and m is the number of responses. In the grey relational analysis, the GRG is used to show the relationship among the sequences. If the two sequences are identical, then the value of GRG is equal to 1. The GRG also indicates the degree of influence that the comparability sequence could exert over the reference sequence. Therefore, if a particular comparability sequence is more important than the other comparability sequences to the reference sequence, then the GRG for that comparability sequence and reference sequence will be higher than other GRGs.42

Experimental details PMEDM mechanism PMEDM is also known as ‘Additive’ process; during this process, a voltage of 80–320 V is applied between the workpiece and the electrode, and electrical intensity in the range of 105–107 V/m is generated. Spark gap which is of the order of 25–50 mm is filled up with the additive particles suspended through flushing. Under the influence of high potential intensity, the particle becomes charged, gets accelerated, moves in zigzags fashion and may act as conductors.6 Under the influence of electrical forces, the powder particles arrange themselves in the form of chains at the different places under the sparking area. Due to this bridging effect, the gap voltage and insulating strength of the dielectric fluid decrease. A series of sparking occurs between the tool and the workpiece due to the short-circuit phenomena. As there is increase in the frequency of discharging, the faster erosion of material takes place from the workpiece and, at the same time, additives or powders modify the plasma channel.15 Gap contamination facilitates the ignition process and increases gap size, thereby improving the process stability. The

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Figure 2. Schematic diagram of PMEDM setup. PMEDM: powder mixed electrical discharge machining [15].

samples formed by the indenter. The indents are formed in the pyramid shape; the use of a diamond pyramid with the apex angle of 136° leads to the Vickers microhardness Hv (MPa)43 Hv = 1854

P d2

ð8Þ

where the units of force P and of impression diameter d are newton (N) and millimeters (mm), respectively. Micro-hardness was measured on a computer interfaced micro-hardness tester (Model MVH-2) of Meta Tech Industries, Pune, India. Indent was measured with Quantimet software using a load of 1 kg for 25 s. Micro-hardness is measured at two places on all the 27 samples: one at the center and other at the corner. Figure 3. Experimental setup (model no. T-3822).

absence of debris may result in arcing due to the absence of precise feeding mechanism with highly position resolution. However, excessive contamination may increase spark concentration, that is, arcing, leading to unstable and inefficient process. In PMEDM process, powders are mixed into the dielectric fluid in the tank, and to avoid mixing of the powder into the filtering system, a transparent bath like container (10 L capacity), called machining tank, is placed in the work tank of EDM, and the machining is performed in this container. For better circulation of the powder mixed in the dielectric, a stirrer is also used to shake the powder continuously in the box whose revolutions per minute is controlled by a heavy duty regulator. The schematic diagram for powder EDM is shown in Figure 2. The experiments have been conducted on electrical discharge machine model no. T-3822 of Victory Electromech, as shown in Figure 3.

Performance measurement metrics Micro-hardness. The micro-hardness measurement is dependent on the diameter of the indentation on the

SR. Generally, SR is measured in terms of arithmetic mean (Ra) which according to the International Organization for Standardization (ISO) 4987:1999 is defined as the arithmetic average roughness of the deviations of the roughness profile from the central line along the measurement.22 It is shown as ðL 1 Ra = jhðxÞdxj L

ð9Þ

0

where h(x) is the value of the roughness profile and L is the evaluation length. The SR of the workpiece can be expressed in different ways like, arithmetic average (Ra), average peak-to-valley height (Rz), peak roughness (Rp) and so on. In the study, it was measured using the Perthometer (Model SJ-400 of Mitutoyo, Japan). The equipment uses stylus method of measurement, has profile resolution of 12 nm and measures roughness up to 100 mm. A tracing length of 0.24 mm was used for analysis. SR is measured at two places on the all 27 samples, one in vertical and other in horizontal direction. Cobalt-bonded tungsten carbide is used as workpiece material, and the electrolytic copper tool is used

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Table 1. Composition of workpiece. Serial number

% Composition

1

W

Cu

Nb

Co

Ti

65.50

3.66

4.69

10.07

15.47

Table 2. Abrasives used for PMEDM properties. Powder

Particle size (nm)

Density (g/cm3)

Thermal conductivity (W cm21 K21)

Electrical conductivity (mO21 cm21)

Melting point (°C)

Specific heat (J kg21 K21)

C Al2O3

55 25

2.25 3.89

1.50 0.35

3 3 1023 1 3 1028

3652 2054

710 880

PMEDM: powder mixed electrical discharge machining.

Table 3. Process parameters and their levels.

Table 5. Constant input parameters.

Levels

Serial number

Parameter

Value

1 2 3 4 5

Open circuit voltage Polarity Tool Machining time Powder concentration

135 6 5% Positive Copper 10 min 15 gm/L

Factors

Process parameter

1

2

3

A B C D

Pulse-on time (ms) Pulse-off time (ms) Current (A) Powders

15 10 3 C

50 50 6 Al2O3

100 75 9 –

C: graphite, Al2O3: aluminum oxide; –: no powder.

Table 4. L9 orthogonal array experimental design. Serial number

Pulse-on (ms)

Pulse-off (ms)

Current (A)

Powder

1 2 3 4 5 6 7 8 9

15 15 15 50 50 50 100 100 100

10 50 75 10 50 75 10 50 75

3 6 9 6 9 3 9 3 6

C Al2O3 – – C Al2O3 Al2O3 – C

C: graphite, Al2O3: aluminum oxide; –: no powder.

for machining the workpiece (65% WC–10% Co). The composition of workpiece is shown in Table 1, and Table 2 shows the properties and particle size of powders used in PMEDM process.

Setting of the process parameters and their levels To study the MPCs, that is, micro-hardness (m-H) and SR of PMEDM process, four input parameters used are (a) pulse-on, (b) pulse-off, (c) current and (d) powder. The various parameters and their levels are mentioned in Table 3. The design for pilot experiments with L9 OA is shown in Table 4. The constant input parameters used in the experiments are presented in Table 5.

Taguchi L9 OA shown in Table 4 is used for performing pilot experiments and based upon them, the parameters, that is, pulse-on time, pulse-off time, current and powder, were identified as one of the contributing factors which affect the micro-hardness and SR. There are four factors with three levels which have been finalized on the basis of pilot experimentation. The number of factors and their levels determine the total degree of freedom (DOF) for the experiment. As DOF for each factor is given by K-1, where K is the number of level for each response; therefore, the total DOF is 8; so according to Ross,44 OA L27 is capable to handle these factors. Table 6 shows the L27 OA experimental design used in the study. Table 7 shows the values of m-H and SR obtained for all the 27 experiments.

Determination of optimal PMEDM parameters In this section, the use of grey relational approach for optimizing MPCs of PMEDM parameters is presented.

Grey relational analysis The L27 OA gives 27 experimental result values for m-H and SR which are normalized in the range of 0–1 using equations (1) and (2), mentioned in section ‘Grey relational analysis’. To express the relationship between the desired and actual experimental data, grey relational coefficients are found out for both using equation (3).

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Table 6. Taguchi L27 orthogonal array experimental design. Serial number

Pulse-on time (ms)

Pulse-off time (ms)

Current (A)

Powder

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

15 15 15 15 15 15 15 15 15 50 50 50 50 50 50 50 50 50 100 100 100 100 100 100 100 100 100

10 10 10 50 50 50 75 75 75 10 10 10 50 50 50 75 75 75 10 10 10 50 50 50 75 75 75

3 6 9 3 6 9 3 6 9 3 6 9 3 6 9 3 6 9 3 6 9 3 6 9 3 6 9

C Al2O3 – – C Al2O3 Al2O3 – C Al2O3 – C C Al2O3 – – C Al2O3 – C Al2O3 Al2O3 – C C Al2O3 –

C: graphite, Al2O3: aluminum oxide; –: no powder.

Table 8 presents the normalized values of m-H and SR along with grey relation coefficients and grades. GRG is calculated by the addition of both the values of grey relation coefficient and then divided by the total number of outputs which are observed, as shown in equation (7). Table 9 indicates the average response values for the GRG; here, the value indicated by the ‘star’ (*) indicates the best or optimal level for each parameter. It shows that if process parameters, that is, pulse-on time, are maintained at level-3 (100 ms), that is, 0.6860, pulseoff time is maintained at level-2 (50 ms), that is, 0.6184, current is maintained at level-3 (9 A), that is, 0.6479, and powder is maintained at level-1 (C), that is, 0.6359, than optimum output is produced. In Table 9, maximum–minimum column indicates that pulse-on time is the most significant factor among four input variables. Table 8 indicates the values for GRG for all the 27 experiments and their ranking also. Higher value gets higher rank. Experiment 24 shows highest value, that is, 0.7819, which indicates that experiment 24 has optimum combination of all the parameters like pulseon time, pulse-off time, current and powder in order to produce higher micro-hardness and lower SR.

Theoretical Prediction of GRG From the response table for the GRG, that is, Table 9, the optimal machining parameter setting is found for the PMEDM of tungsten carbide. Now after finding

the optimal factor combination, it is necessary to predict the grey reasoning grade theoretically. The theoretical prediction of GRG is predicted using the following equation (10)28 ^ = gm + g

q X 

gj  gm



ð10Þ

j=1

where g m is the average of GRG values and g j is the mean of the GRG at the optimum level and q is the number of influential parameters that significantly affect the MPCs. Table 10 provides the results of initial and optimal machining parameters (both prediction and experimental values). In Table 10, A1B1C1D1 are taken as initial machining parameters, and A3B2C3D1 are taken as optimal machining parameters; it is seen that micro-hardness in the initial setting level of A1 B1 C1 D1 increases from 1186 to 1332 (experiment no. 24), SR decreases from 3.25 to 3.08 and GRG is also improved from 0.5363 to 0.7819, that is, 24.56% for optimal machining parameters. From the above results, it has been asserted that the grey relational analysis can be useful for optimizing the multiple performances in PMEDM of cobaltbonded tungsten carbide.

Analysis of results ANOVA is used to find the most contributing factor which may affect the MPCs of PMEDM process. This

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Table 7. Experimental values of micro-hardness and surface roughness (SR). Serial number

m-H-1

m-H-2

m-H mean (HVN)

SR-1

SR-2

SR-mean (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

1147 1206 1240 1124 1238 1170 1195 1049 1236 1204 1120 1252 1254 1206 1246 1232 1262 1274 1268 1289 1276 1163 1275 1338 1290 1278 1269

1225 1266 1276 1182 1206 1098 1129 1019 1112 1258 1131 1224 1302 1220 1296 1152 1280 1315 1278 1303 1258 1109 1329 1326 1278 1266 1263

1186 1236 1258 1153 1222 1134 1162 1034 1174 1231 1125 1238 1278 1213 1271 1192 1271 1294 1273 1296 1267 1136 1302 1332 1284 1272 1266

2.94 3.72 2.67 6.80 2.74 1.79 5.32 5.03 3.20 5.53 2.76 1.85 5.07 2.68 1.96 5.29 2.79 3.10 2.28 3.26 2.40 1.56 3.54 3.81 2.90 3.56 2.82

3.56 4.10 3.51 5.88 3.80 2.71 4.56 5.25 2.76 5.29 1.49 2.65 3.77 2.96 4.22 2.55 3.03 3.26 2.88 3.54 3.38 1.14 3.30 2.75 2.92 2.74 3.78

3.25 3.91 3.09 6.34 3.27 2.25 4.94 5.14 2.98 5.41 2.12 2.25 4.42 2.82 3.09 3.92 2.91 3.18 2.58 3.40 2.89 1.35 3.42 3.08 2.91 3.15 3.30

Table 8. Grey relational values for micro-hardness (m-H) and surface roughness (SR). Serial number

Normalized value m-H,

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

xi

0.5100 0.6778 0.7516 0.3993 0.6308 0.3355 0.4295 0.0000 0.4697 0.6610 0.3053 0.6845 0.8187 0.6006 0.7953 0.5302 0.7953 0.8724 0.8020 0.8791 0.7818 0.3422 0.8993 1.0000 0.8389 0.7986 0.7785

(1)

Grey relational coefficient SR,

xi

(2)

0.6192 0.4869 0.6513 0.0000 0.6152 0.8196 0.2805 0.2404 0.6733 0.1863 0.8456 0.8196 0.3847 0.7054 0.6513 0.4849 0.6873 0.6332 0.7535 0.5891 0.6913 1.0000 0.5851 0.6132 0.6873 0.6329 0.6092

m-H, ji (1)

SR, ji (2)

0.5050 0.6081 0.6680 0.4542 0.5752 0.4293 0.4670 0.3333 0.4852 0.5959 0.4185 0.6131 0.7338 0.5559 0.7095 0.5155 0.7095 0.7966 0.7163 0.8056 0.6961 0.4321 0.8323 1.0000 0.7563 0.7128 0.6930

0.5676 0.4935 0.5891 0.3333 0.5650 0.7348 0.4100 0.3969 0.6048 0.3806 0.7640 0.7348 0.4483 0.6292 0.5891 0.4925 0.6153 0.5768 0.6697 0.5489 0.6182 1.0000 0.5465 0.5638 0.6152 0.5808 0.5612

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Grey relational grade, gi

Rank

0.5363 0.5508 0.6285 0.3937 0.5701 0.5820 0.4385 0.3651 0.5450 0.4882 0.5912 0.6739 0.5910 0.5925 0.6493 0.5040 0.6624 0.6867 0.6930 0.6772 0.6571 0.7160 0.6894 0.7819 0.6857 0.6468 0.6271

22 20 13 26 19 18 25 27 21 24 16 8 17 15 11 23 9 5 3 7 10 2 4 1 6 12 14

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Table 9. Average response values of grey relational grade. Factors

Process parameters

Level-1

Level-2

Level-3

Maximum–minimum

A B C D

Pulse-on time (ms) Pulse-off time (ms) Current (Amp) Powder

0.5122 0.6106 0.5607 0.6359a

0.6043 0.6184a 0.5939 0.5954

0.6860a 0.5734 0.6479a 0.5712

0.1738a 0.0450 0.0872 0.0647

a

Indicates the optimum levels.

Table 10. Results of the initial and optimal machining performance. Process parameters

Micro-hardness (HVN) Surface roughness (Ra) Grey relational grade

Initial machining

Optimal machining parameters

A1B1C1D1

Prediction A3B2C3D1

Experiment A3B2C3D1

1186 3.25 0.5363

– – 0.7858

1332 3.08 0.7819

Table 11. ANOVA for grey relational grade. Factors

DOF

Sum of Squares (SS)

Mean Square (MS)

F

% of contribution

Status

Pulse-on, A Pulse-off, B Current, C Powder, D Residual error Total

2 2 2 2 18 26

0.136093 0.010397 0.019234 0.034890 0.058625 0.259240

0.068047 0.005198 0.009617 0.017445

20.89 1.60 3.95 5.36

52.49 4.01 7.41 13.45

O 3 O O

100

ANOVA: analysis of variance; DOF: degree of freedom; SS: Sum of Squares; MS: Mean Square; Here F represents the statistical test; here O represents a significant term and 3 represents the insignificant term.

is accomplished by separating the total variability of GRGs, which is measured by sum of squared deviations from the total mean. The results of ANOVA for GRG values with pulse-on time, pulse-off time, current and powder are shown in Table 11. The percentage contribution of each of the process parameter is also calculated and shown in Table 11, as from ANOVA Table pulse-on time, powder and current are the significant factors which affect the performance, at 95% confidence interval, F-test , here F-critical value selected is 3.55.44 Results show that pulse-on time (52.49%) is the most contributing factor, followed by the powder (13.45%) and then current (7.41%), which affects the multi-response characteristics in this study.

value of GRG with optimal setting of parameters, that is, pulse-on time (100 ms), pulse-off time (50 ms), current (9 A) and powder (graphite). Furthermore, ANOVA analysis has been done to find the most contributing factor. ANOVA result shows that pulse-on, powder and current were significant and contributing factors of PMEDM of 65% WC–10% Co. Declaration of conflicting interests The authors declare that there is no conflict of interest. Funding This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Conclusion The main aim of this study was to present a framework which not only helps to obtain optimal combinations of process parameters but also to handle the element of uncertainty associated with multi-input data. An application of PMEDM of tungsten carbide alloy was used to study the proposed framework. Optimal settings of parameters for the output responses, that is, microhardness and SR, were obtained. Experimental investigation shows that experiment no. 24 provides highest

References 1. Batish A, Bhattacharya A, Singla VK, et al. Study of material transfer mechanism in die steels using powder mixed electrical discharge machining. Mater Manuf Process 2012; 27: 449–456. 2. Singh S, Maheshwari S and Pandey PC. Some investigations into the electric discharge machining of hardened tool steel using different electrode materials. J Mater Process Tech 2004; 149: 272–277.

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