Statistical multi-objective optimization of electrical discharge machining parameters in machining titanium grade 5 alloy using graphite electrode

Abstract

In industrial applications, particularly in aero, marine and medical industries, titanium has received great attention as a useful material and electrical discharge machining as its machining process. Selection of optimal machining parameters in a multi-objective environment is essential for specific workpiece and tool material combination, which is the concern of industries to improve the overall productivity at less cost. In this article, optimization of critical electrical discharge machining parameters such as pulse current, on time of pulse, off time of pulse and tool geometry depending on the responses such as titanium machining rate, graphite wear rate, surface roughness and deviation between entry and exit while machining titanium grade 5 alloy with graphite tool electrode at negative polarity is presented. Taguchi’s L27 orthogonal array was used to design the experiment with interaction between factors. The weighing method was used to integrate different objectives into one performance. The optimal combination of process parameters was found statistically using signal-to-noise ratios. Significance was checked by analysis of variance. Optimum parameters were found to be pulse current 15 A, on time of pulse 50 µs, off time of pulse 200 µs and cylindrical tool geometry. Resultant percentage improvements in different responses were presented.

Keywords

electrical discharge machining titanium grade 5 alloy graphite electrode Taguchi L27 array analysis of variance statistical multi-objective optimization

Introduction

Titanium alloys possess a combination of most useful properties such as great weldability, lightweight, extraordinary corrosion resistance, high tensile strength, high hardness at extreme temperatures and high toughness,¹ which are very suitable for aero, marine and medical implants’ manufacturing applications. Electrical discharge machining (EDM) is a suitable process to machine titanium alloys.² Among the 38 different grades of titanium alloys, the most common in industrial applications are the titanium grade 5 alloys.² Review articles were published^3,4 in 2010 elaborating the status of research in the field of EDM. As per the literature survey, a study of the machinability of titanium alloys using EDM with different tool materials under different conditions has been carried out^5–8 in the literature. However, one important concern of industries is to find the optimum machining parameters to improve the overall productivity at less cost. In the past, a lot of research was done in the field of optimization that saw numerous algorithms, and their effectiveness was studied in different areas of applications.^9–12 In EDM field too optimization of machining parameters was done for different work materials and tool combinations using different techniques/algorithms.^13–15 In most of these researches, many input parameters were considered for optimization, but when it comes to output parameters, mostly one output parameter or two output parameters such as metal removal rate (MRR) and surface roughness (SR) were considered. This is because of the difficulties associated with multi-objective optimization. In this work on optimization, the four objectives, namely, titanium machining rate (TMR), graphite wear rate (GWR), SR and deviation between entry and exit (EED), were considered in the EDM of titanium grade 5 alloy using graphite electrode. The input parameters considered were pulse current, on time of pulse, off time of pulse and tool cross-sectional area.

Experiment details

The experiment was conducted in V5030 EDM machine made by Electronica Corporation, India. Three titanium grade 5 alloy sheets of dimension 100 × 50 × 3mm³ were used as a workpiece. Kerosene was the dielectric with side flushing option. Table 1 provides chemical composition for the titanium grade 5 alloy workpiece.

Table 1.

Chemical composition of titanium grade 5 alloy (by weight—measured using OES—Foundry Master, UV, Germany).

C	0.001%
Mn	0.007%
Si	0.005%
Cr	0.043%
Mo	0.012%
Ni	0.0275%
Al	5.841%
Cu	0.0021%
Fe	0.155%
V	3.641%
Zr	0.019%
Sn	0.019%
Ti	90.23%

OES: optical emission spectroscopy.

Graphite electrodes of geometrical shapes such as square (8 × 8 mm²), circular (8 mm diameter) and rectangular (8 × 5 mm²) were used as tool material. Its properties are given in Table 2. Nine electrodes per geometry were used in the experiment.

Table 2.

Properties of graphite material used as tool electrode.

Density	1880 kg/m³
Melting point	3300 °C
Electrical resistivity	1400 µΩ cm
Particle size	20 µm

Three levels of four experimental parameters, on time of pulse, off time of pulse, current and tool cross section, were considered. Table 3 provides parameter details. The ranges of level values were chosen based on the work done by Ahmed and Ulas.¹⁶

Table 3.

Experimental parameters.

Parameters	Level 1	Level 2	Level 3
Pulse current (A)	15	20	25
Pulse on time (µs)	50	100	200
Pulse off time (µs)	50	100	200
Geometry (area in mm²)	Rectangle (40)	Circle (50.26)	Square (64)

L27 orthogonal array model of Taguchi was chosen while designing the experiment in order to reduce the number of experiments required to cover all experimental combinations. Coded experimental parameters are shown in Table 4.

Table 4.

Taguchi experiment model (L27 array with interaction between factors).

Exp. no.	Pulse current	Pulse on time	Pulse off time	Geometry
1	1	1	1	3
2	1	1	2	1
3	1	1	3	2
4	1	2	1	1
5	1	2	2	2
6	1	2	3	3
7	1	3	1	2
8	1	3	2	3
9	1	3	3	1
10	2	1	1	1
11	2	1	2	2
12	2	1	3	3
13	2	2	1	2
14	2	2	2	3
15	2	2	3	1
16	2	3	1	3
17	2	3	2	1
18	2	3	3	2
19	3	1	1	2
20	3	1	2	3
21	3	1	3	1
22	3	2	1	3
23	3	2	2	1
24	3	2	3	2
25	3	3	1	1
26	3	3	2	2
27	3	3	3	3

During the experiment, the workpiece was connected to positive and the tool was connected to negative terminals. After the experiment, the workpiece and the tool were washed with dielectric, dried and weighed using electronic balance. A digital watch was used to record the machining time. In random, nine experiments with three experiments/geometry were conducted on each sheet.

After all the holes were made, TMR and GWR were calculated using equations (1) and (2), respectively⁸

TMR = \frac{WMR}{(ρ_{w} \times t)}

(1)

GWR = \frac{WTR}{(ρ_{t} \times t)}

(2)

where WMR is the weight of metal removed in grams, ρ_w is the density of the workpiece in gram per cubic millimeter, t is the machining time in minutes, WTR is the weight of tool material lost during EDM and ρ_t is the density of the tool in gram per cubic millimeter. WMR and WTR were calculated by measuring the difference in weight before and after machining. Perthometer MarSurf PS1 with 4-µm stylus tip was used to measure the SR of the inner surface of the holes with cutoff length 2.5 mm.

Accurate spectra coordinate measuring machine with TP8 probe head was used to measure entry and exit deviation in the holes. Table 5 shows the results of all the 27 experiments.

Table 5.

Experiment results.

Exp. no.	TMR (mm³/min)	GWR (mm³/min)	SR (µm)	EED (°)
1	0.6642	0.0585	2.870	0.5548
2	0.7966	0.0625	2.601	0.5154
3	0.3914	0.0411	1.407	0.2146
4	0.8342	0.0638	2.729	0.4604
5	0.9646	0.0665	2.351	0.4085
6	0.5666	0.0537	1.819	0.2161
7	1.0646	0.0703	2.979	0.4510
8	1.1968	0.0819	2.346	0.2473
9	0.7964	0.0613	1.554	0.0725
10	0.7294	0.1285	2.794	0.7308
11	0.8558	0.1387	2.686	0.5121
12	0.4578	0.1197	1.639	0.3372
13	0.8954	0.1409	2.946	0.6054
14	1.0332	0.1444	2.417	0.5236
15	0.6356	0.1235	1.889	0.2129
16	1.1292	0.1492	3.205	0.4502
17	1.2636	0.1519	2.577	0.3919
18	0.8624	0.1384	1.634	0.1795
19	0.7886	0.2100	3.021	0.6766
20	0.9252	0.2086	2.648	0.6567
21	0.5472	0.1889	1.974	0.4643
22	0.9658	0.2109	3.276	0.7201
23	1.1000	0.2225	2.502	0.5023
24	0.6980	0.2019	1.868	0.3571
25	1.1964	0.2264	3.025	0.5883
26	1.3280	0.2308	2.913	0.5323
27	0.9330	0.2084	1.704	0.1822

TMR: titanium machining rate; GWR: graphite wear rate; SR: surface roughness; EED: deviation between entry and exit.

Statistical multi-objective optimization methodology

The methodology used here for performing the required multi-objective optimization is signal-to-noise (S/N) ratio–based Taguchi analysis. S/N ratio is used to measure the response variation based on the influence of the noise factors, where S is the measure of the mean of desirable output characteristics called signal and N stands for noise, which is undesirable.⁸ The larger the S/N ratio, the better the product quality, in other words, the higher the performance robustness.⁹ Therefore, the largest level setting of S/N ratio can optimize the quality characteristic of an experiment. In this work, experiment outputs were transformed to S/N ratio values. Following are the step-by-step method used to find out the optimum parameters.

Step 1. Transform all the experiment output data of various responses into S/N ratios using the following equations.

For TMR values, the objective is to maximize the titanium alloy machining rate, so “larger the better approach” was used. The formula used for that approach is given in equation (3), where m is the total number of replications and y_ij is the value of response in ith replication and jth experimental condition⁹

(\frac{S}{N}) j = - 10 \log_{10} (\frac{1}{m} \sum_{i = 1}^{m} \frac{1}{y_{ij}^{2}})

(3)

For GWR, SR and EED values, the objective is to minimize all of these, so “smaller the better approach” was used. The formula used for that approach is given in equation (4)⁹

(\frac{S}{N}) j = - 10 \log_{10} (\frac{1}{m} \sum_{i = 1}^{m} y_{ij}^{2})

(4)

Step 2. Normalize the S/N ratio values for all responses. This is a transformation done on every single data (S/N ratio) to distribute it evenly and scale it into an acceptable range for further analysis without affecting the characteristics of data. In normalization, $y_{ij}$ is normalized to $Z_{ij} (0 \leq Z_{ij} \leq 1)$ by using equation (5), which avoids the effect of adopting different units and reduces the variability. Here, an appropriate value is deducted from the S/N ratios in the same array to make the new array values approximated to 1. Since the normalization affects the rank, the sensitivity of the normalization process was analyzed in results’ sequencing. For larger the better approach S/N ratio values (like for TMR), equation (5) was used to normalize⁹

Z_{ij} = \frac{y_{ij} - \min (y_{ij}, i = 1, 2, \dots, m)}{\max (y_{ij}, i = 1, 2, \dots, m) - \min (y_{ij}, i = 1, 2, \dots, m)}

(5)

For smaller the better approach S/N ratio values (like for GWR, SR and EED), equation (6) was used in the normalization⁹

Z_{ij} = \frac{\max (y_{ij}, i = 1, 2, \dots, m) - y_{ij}}{\max (y_{ij}, i = 1, 2, \dots, m) - \min (y_{ij}, i = 1, 2, \dots, m)}

(6)

Step 3. Use the weighing method to convert the multi-objective multiple response into a single performance index. Usually, the weights are determined purely based on engineering judgment¹⁷ and available data based on application requirement. In case of titanium grade 5 alloy, such data are not available in data books as well as in the literature. So, it is not easy to determine a definite weight for each response in reality.

Step 4. Calculate the weighted values (from normalized S/N ratios) using the weights $(w_{1}, w_{2}, \dots, w_{j})$ given in Table 8 using equation (7)

WS N_{i} = W_{1} Z_{11} + W_{2} Z_{12} + \dots + W_{j} Z_{ij}

(7)

Step 5. Estimate the effect of each factor, level by level, for each case. To do that, first calculate the average of weighted S/N ratio (WSN) values for each level j, mentioned as $WS N_{ij}$ . Then calculate the effect of E_i using equation (8)

E_{i} = \max (WS N_{ij}) - \min (WS N_{ij})

(8)

Based on the maximum effect value for each factor, determine the optimal level combination for the factors. That is, if j is the factor, then the best level j^* is determined by using equation (9)

j * = \max (WS N_{ij})

(9)

Step 6. Through analysis of variance (ANOVA) confirm the significance of the factors case by case using p values; p value is the probability measure of the variation between conditions, which may have occurred by chance. It is a practice to accept the factor effect as significant if the p value is less than 5%.⁸

Results

As mentioned in the previous section, at the first step, TMR values were transformed to S/N ratio values using Taguchi’s larger the better approach formula as shown in equation (3). Similarly, GWR values, SR values and EED values were transformed using Taguchi’s smaller the better approach formula as shown in equation (4). The values were tabulated in Table 7.

As the second step, those transformed S/N ratio values of different responses were normalized using equation (5) for TMR and equation (6) for GWR, SR and EED as they belong to smaller the better category. These values are also tabulated in Table 6.

Table 6.

Analysis data.

Exp. no.	TMR (mm₃/min)	GWR(mm₃/min)	SR(micro meter)	EED(degree)	S/N ratio for TMR	S/N ratio for GWR	S/N ratio for SR	S/N ratio for EED	Normalized values of S/N ratio for TMR	Normalized values of S/N ratio for GWR	Normalized values of S/N ratio for SR	Normalized values of S/N ratio for EED	Weighted S/N ratio
Exp. no.	TMR (mm₃/min)	GWR(mm₃/min)	SR(micro meter)	EED(degree)	S/N ratio for TMR	S/N ratio for GWR	S/N ratio for SR	S/N ratio for EED	Normalized values of S/N ratio for TMR	Normalized values of S/N ratio for GWR	Normalized values of S/N ratio for SR	Normalized values of S/N ratio for EED	0.7 TMR+ 0.1 GWR+ 0.1 SR+ 0.1 EED	0.5 TMR+ 0.15 GWR+ 0.2 SR+ 0.15 EED	0.6 TMR+ 0.05 GWR+ 0.3 SR+ 0.05 EED
1	0.66420	0.05850	2.87000	0.55480	−3.554	24.657	−9.158	5.1173	0.56712	0.79542	0.15655	0.11925	0.50410	0.45207	0.43297
2	0.79660	0.06250	2.60100	0.51540	−1.975	24.082	−8.303	5.7571	0.41833	0.75709	0.27300	0.15113	0.41095	0.40000	0.37831
3	0.39140	0.04110	1.40700	0.21460	−8.148	27.723	−2.966	13.367	1.00000	1.00000	1.00000	0.53033	0.95303	0.92955	0.97652
4	0.83420	0.06380	2.72900	0.46040	−1.575	23.904	−8.72	6.7373	0.38058	0.74516	0.21616	0.19997	0.38254	0.37529	0.34045
5	0.96460	0.06650	2.35100	0.40850	−0.313	23.544	−7.425	7.7762	0.26170	0.72114	0.39257	0.25174	0.31973	0.35529	0.32343
6	0.56660	0.05370	1.81900	0.21610	−4.934	25.401	−5.197	13.307	0.69721	0.84503	0.69612	0.52732	0.69489	0.69368	0.69578
7	1.06460	0.07030	2.97900	0.45100	0.5437	23.061	−9.481	6.9165	0.18096	0.68893	0.11245	0.20890	0.22770	0.24764	0.18720
8	1.19680	0.08190	2.34600	0.24730	1.5604	21.734	−7.407	12.136	0.08515	0.60042	0.39508	0.46895	0.20605	0.28200	0.22308
9	0.79640	0.06130	1.55400	0.07250	−1.977	24.251	−3.829	22.793	0.41854	0.76832	0.88242	1.00000	0.55805	0.65100	0.60427
10	0.72940	0.12850	2.79400	0.73080	−2.741	17.822	−8.925	2.724	0.49047	0.33939	0.18830	0.00000	0.39610	0.33380	0.36774
11	0.85580	0.13870	2.68600	0.51210	−1.353	17.158	−8.582	5.8129	0.35966	0.29512	0.23495	0.15391	0.32016	0.29417	0.30873
12	0.45780	0.11970	1.63900	0.33720	−6.786	18.438	−4.292	9.4422	0.87173	0.38050	0.81941	0.33475	0.76368	0.70704	0.80463
13	0.89540	0.14090	2.94600	0.60540	−0.96	17.022	−9.385	4.3592	0.32263	0.28600	0.12563	0.08147	0.27515	0.24156	0.24964
14	1.03320	0.14440	2.41700	0.52360	0.2837	16.809	−7.666	5.62	0.20546	0.27178	0.35981	0.14430	0.22141	0.23710	0.25202
15	0.63560	0.12350	1.88900	0.21290	−3.936	18.167	−5.525	13.436	0.60314	0.36239	0.65144	0.53378	0.57696	0.56628	0.60213
16	1.12920	0.14920	3.20500	0.45020	1.0554	16.525	−10.12	6.9319	0.13274	0.25283	0.02592	0.20967	0.14176	0.14093	0.11054
17	1.26360	0.15190	2.57700	0.39190	2.0322	16.369	−8.222	8.1365	0.04069	0.24243	0.28396	0.26969	0.10809	0.15396	0.13521
18	0.86240	0.13840	1.63400	0.17950	−1.286	17.177	−4.265	14.919	0.35337	0.29637	0.82303	0.60763	0.42006	0.47689	0.50413
19	0.78860	0.21000	3.02100	0.67660	−2.063	13.556	−9.603	3.3934	0.42659	0.05473	0.09588	0.03335	0.31701	0.24569	0.28913
20	0.92520	0.20860	2.64800	0.65670	−0.675	13.614	−8.458	3.6527	0.29583	0.05861	0.25181	0.04627	0.24275	0.21401	0.25829
21	0.54720	0.18890	1.97400	0.46430	−5.237	14.475	−5.907	6.664	0.72572	0.11610	0.59936	0.19632	0.59918	0.52960	0.63086
22	0.96580	0.21090	3.27600	0.72010	−0.302	13.518	−10.31	2.8521	0.26068	0.05226	0.00000	0.00638	0.18834	0.13914	0.15934
23	1.10000	0.22250	2.50200	0.50230	0.8279	13.053	−7.966	5.9807	0.15418	0.02123	0.31891	0.16227	0.15817	0.16840	0.19736
24	0.69800	0.20190	1.86800	0.35710	−3.123	13.897	−5.428	8.9442	0.52649	0.07753	0.66467	0.30994	0.47376	0.45430	0.53467
25	1.19640	0.22640	3.02500	0.58830	1.5575	12.902	−9.615	4.608	0.08542	0.01116	0.09431	0.09387	0.07973	0.07733	0.08480
26	1.32800	0.23080	2.91300	0.53230	2.464	12.735	−9.287	5.4769	0.00000	0.00000	0.13895	0.13717	0.02761	0.04837	0.04854
27	0.93300	0.20840	1.70400	0.18220	−0.602	13.622	−4.629	14.789	0.28896	0.05917	0.77339	0.60117	0.34565	0.39821	0.43841

TMR: titanium machining rate; GWR: graphite wear rate; SR: surface roughness; EED: deviation between entry and exit; S/N: signal-to-noise.

In step 3, to convert multi-response into a single performance index, three different sets (cases) of weights were assumed for the responses, which are shown in Table 7. As this step needs to be done based on engineering judgment,¹⁵ these three cases were considered based on the three production requirements such as mass production, batch and job shop productions.

Table 7.

Weight age of output responses.

Case no.	TMR	GWR	SR	EED
1	0.7	0.1	0.1	0.1
2	0.5	0.15	0.20	0.15
3	0.6	0.05	0.3	0.05

TMR: titanium machining rate; GWR: graphite wear rate; SR: surface roughness; EED: deviation between entry and exit.

In step 4, WSN values were calculated based on assumed weights and as per equation (7). All these values for all the three cases assumed are given in Table 6.

In step 5, as per equations (8) and (9), effects in terms of S/N ratio values for each studied factor such as pulse current, on time of pulse, off time of pulse and geometry at each parameter level were found out, case by case. From these tabulated values, optimal level combination of the factors was determined based on the maximum tabulated value for a particular factor. Tables 8 –10 show the S/N ratio values calculated by following all the previous steps for case 1, case 2 and case 3, respectively. In all these tables, values represented in boldface are the largest values indicating the maximum factor effect and thus the optimum factor level. Through all these tables, corresponding to different cases, the optimal combination of factor level was found out to be A₁B₁C₃D₂ where the capital alphabets indicate the factors such as A for pulse current, B for on time of pulse, C for off time of pulse and D for tool geometry, and the suffix numerals are the level of those factors. Since the optimum factor level combination obtained through the analysis (1 1 3 2) was one among 27 experiments which is experiment number 3, confirmatory experiment was not required.

Table 8.

S/N response table for case 1.

Machining parameters	Level 1	Level 2	Level 3
Pulse current	0.4730	0.3581	0.2702
Pulse on time	0.5007	0.3656	0.2349
Pulse off time	0.2791	0.2238	0.5983
Geometry	0.3633	0.3704	0.3676
Setting	A₁B₁C₃D₂

Note: The values represented in boldface are the largest values indicating the maximum factor effect and thus the optimum factor level.

Table 9.

S/N response table for case 2.

Machining parameters	Level 1	Level 2	Level 3
Pulse current	0.4873	0.3501	0.2527
Pulse on time	0.4562	0.3590	0.2751
Pulse off time	0.2503	0.2392	0.6007
Geometry	0.3617	0.3659	0.3626
Setting	A₁B₁C₃D₂

Table 10.

S/N response table for case 3.

Machining parameters	Level 1	Level 2	Level 3
Pulse current	0.4624	0.3705	0.2934
Pulse on time	0.4941	0.3727	0.2595
Pulse off time	0.2468	0.2361	0.6434
Geometry	0.3712	0.3802	0.3750
Setting	A₁B₁C₃D₂

In step 6, significance of the studied factor effects over responses was tested using statistical ANOVAs. Tables 11 –13 are the ANOVA tables for cases 1, 2 and 3, respectively. Through ANOVA, significance of individual factor effects as well as interactive factor effects was analyzed. The results show that the effects of the first three factors, pulse current, on time of pulse and off time of pulse, are highly significant as their p values are at very high confidence level in all the three cases, which means the optimum level values found for pulse current, on time of pulse and off time of pulse are reliable, whereas the fourth factor tool geometry/cross-sectional area along with other interactive effects was found to be insignificant.

Table 11.

Analysis of variance for case 1.

Machining parameters	DF	Sum of square	Mean square	F	p value
Pulse current (A)	2	194.01	97.003	23.98	0.001
Pulse on time (B)	2	337.83	168.913	41.75	0.000
Pulse off time (C)	2	481.18	240.590	59.47	0.000
Geometry (D)	2	3.74	1.869	0.46	0.651
A × B	4	32.80	8.200	2.03	0.210
A × C	4	24.42	6.105	1.51	0.310
B × C	4	40.61	10.152	2.51	0.151
Error	6	24.27	4.045
Total	26	1138.85

DF: degrees of freedom.

Table 12.

Analysis of variance for case 2.

Machining parameters	DF	Sum of square	Mean square	F	p value
Pulse current (A)	2	228.615	114.308	35.61	0.000
Pulse on time (B)	2	161.132	80.566	25.10	0.001
Pulse off time (C)	2	451.156	225.878	70.27	0.000
Geometry (D)	2	1.067	0.534	0.17	0.851
A × B	4	18.657	4.664	1.45	0.325
A × C	4	10.810	4.952	1.54	0.302
B × C	4	25.037	6.259	1.95	0.222
Error	6	19.261	3.210
Total	26	924.735

DF: degrees of freedom.

Table 13.

Analysis of variance for case 3.

Machining parameters	DF	Sum of square	Mean square	F	p value
Pulse current (A)	2	121.430	60.715	16.06	0.004
Pulse on time (B)	2	249.803	124.901	33.03	0.001
Pulse off time (C)	2	529.887	264.943	70.07	0.000
Geometry (D)	2	0.960	0.480	0.13	0.883
A × B	4	14.067	3.517	0.93	0.505
A × C	4	13.237	3.309	0.88	0.530
B × C	4	37.368	9.342	2.47	0.155
Error	6	22.686	3.781
Total	26	989.438

DF: degrees of freedom.

Table 14 shows the findings in optimization of machining parameters in EDM of titanium grade 5 alloy using graphite electrode at the negative polarity experiment and analysis.

Table 14.

Optimum parameters and responses.

Parameter	Pulse current-Amps (A)	Pulse on time-micro seconds (B)	Pulse off time- micro seconds (C)	Geometry-mm₂ (D)	TMR(mm₃/min)	GWR (mm₃/min)	SR (micro m)	EED
A₁B₁C₃D₂	15	50	200	50.26	0.39128 (45%)	0.04103 (29%)	1.40721 (57%)	0.21451 (49%)
Average	For all 27 experiments				0.87481	0.13716	2.4226	0.43571

TMR: titanium machining rate; GWR: graphite wear rate; SR: surface roughness; EED: deviation between entry and exit.

The first row in this table shows the optimum parameter levels and resultant response values. The second row in this table shows the average response values of all the 27 experiments. The percentage values mentioned in brackets indicate the percentage of optimum response values from the average.

Discussion

Through this experiment and statistical multi-objective optimization, a reliable approach was found to optimize the parameters when there are multiple objectives. The optimized values found resulted in the following percentage reductions compared to the average values of all 27 experiments in three important responses out of the four studied as shown in Table 14.

In GWR, 71%.

In SR, 43%.

In EED, 51%.

On the negative side, these optimum values resulted in 55% reduction in titanium alloy machining rate compared to the average TMR in all the 27 experiments, which was a compromise for the benefits achieved in other three responses. Therefore, this method can be used to optimize the parameters for any number of objectives, provided weighing details are available either by experience or based on the data available in the data books or in the literature. So, the proposed methodology is very useful for small- and medium-scale industries that normally will not spend on research and will have their experience-based weighing data, and also, this work is useful for the industries that are working with titanium grade 5 alloy. One of the findings in this research through ANOVA testing is that the tool geometry is not significantly influencing the optimization except that cylindrical shapes can give better responses. This infers that while designing the tool electrodes, the sharp edges need to be rounded off to get better responses. In addition, optimized parameters found resulted in remarkable improvements in graphite (tool) wear rate, SR and EED, which is an important requirement in high-end applications such as space, aero and marine industries where little trade-off can be tolerated with less TMR in order to achieve better results in above responses. However, by suitable changes at weighing stage, optimized parameters suitable to other industries also can be found.

Conclusion

In this work, multi-objective optimization of operation parameters for EDM of titanium grade 5 alloy using graphite electrode had been achieved. The application of S/N and ANOVA was proved to be useful for achieving the optimal EDM process parameters for desired responses. The findings are summarized below.

The optimum conditions found out in the study were as follows:

Pulse current: 15 A

On time of pulse: 50 µs

Off time of pulse: 200µs

Tool geometry: cylindrical

Electrical parameters were found to be the most significant control parameters in obtaining desired SR, TMR, EED and GWR.

The order of influence among the electrical parameters over the studied four responses was on time of pulse, pulse current and off time of pulse.

Footnotes

Appendix 1 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.

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Exp. no.	Pulse current	Pulse on time	Pulse off time	Geometry
1	1	1	1	3
2	1	1	2	1
3	1	1	3	2
4	1	2	1	1
5	1	2	2	2
6	1	2	3	3
7	1	3	1	2
8	1	3	2	3
9	1	3	3	1
10	2	1	1	1
11	2	1	2	2
12	2	1	3	3
13	2	2	1	2
14	2	2	2	3
15	2	2	3	1
16	2	3	1	3
17	2	3	2	1
18	2	3	3	2
19	3	1	1	2
20	3	1	2	3
21	3	1	3	1
22	3	2	1	3
23	3	2	2	1
24	3	2	3	2
25	3	3	1	1
26	3	3	2	2
27	3	3	3	3

Exp. no.	Pulse current	Pulse on time	Pulse off time	Geometry
1	1	1	1	3
2	1	1	2	1
3	1	1	3	2
4	1	2	1	1
5	1	2	2	2
6	1	2	3	3
7	1	3	1	2
8	1	3	2	3
9	1	3	3	1
10	2	1	1	1
11	2	1	2	2
12	2	1	3	3
13	2	2	1	2
14	2	2	2	3
15	2	2	3	1
16	2	3	1	3
17	2	3	2	1
18	2	3	3	2
19	3	1	1	2
20	3	1	2	3
21	3	1	3	1
22	3	2	1	3
23	3	2	2	1
24	3	2	3	2
25	3	3	1	1
26	3	3	2	2
27	3	3	3	3

Exp. no.	Pulse current	Pulse on time	Pulse off time	Geometry
1	1	1	1	3
2	1	1	2	1
3	1	1	3	2
4	1	2	1	1
5	1	2	2	2
6	1	2	3	3
7	1	3	1	2
8	1	3	2	3
9	1	3	3	1
10	2	1	1	1
11	2	1	2	2
12	2	1	3	3
13	2	2	1	2
14	2	2	2	3
15	2	2	3	1
16	2	3	1	3
17	2	3	2	1
18	2	3	3	2
19	3	1	1	2
20	3	1	2	3
21	3	1	3	1
22	3	2	1	3
23	3	2	2	1
24	3	2	3	2
25	3	3	1	1
26	3	3	2	2
27	3	3	3	3