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SN Applied Sciences

, 2:99 | Cite as

Optimization of relative wear ratio during EDM of titanium alloy using advanced techniques

  • Neeraj AgarwalEmail author
  • Nitin Shrivastava
  • M. K. Pradhan
Research Article
  • 145 Downloads
Part of the following topical collections:
  1. 3. Engineering (general)

Abstract

This study presents the relative wear ratio (RWR) optimization of Titanium alloy 685 for electric discharge machining (EDM). Titanium alloys are widely used in modern industry due to its excellent engineering property like high strength to weight ratio, corrosion resistance. There is difficulty in the machining of titanium alloy with conventional machining processes, hence EDM used to machine titanium alloy. The objective is to maximize the material removal rate (MRR) while the tool wear rate (TWR) should be minimized. The machined surface is an exact replica of the tool face. If TWR increases then the quality of the machined surface deteriorate. A new term introduces a RWR which represents the ratio of MRR to the TWR. The high value of RWR is desired to improve the quality of the machined surface. In this paper RWR is optimized. Response surface model used to develop a regression model of RWR. Optimization of RWR is done by advanced optimization techniques, Jaya Algorithm, teaching-learning-based optimization and response optimizer. Parameters optimization of peak current (Ip), pulse on time (Ton), duty factor (t) and voltage (V) done in this study to maximize RWR.

Keywords

EDM Electric discharge machining Modelling Optimization Advanced optimization Relative wear ratio (RWR) Titanium alloy 685 Jaya Algorithm 

1 Introduction

Nowadays there are requirements of advanced materials like superalloys, Titanium alloy, ceramic, etc with excellent engineering property like hardness, strength, high strength to weight ratio, etc. Due to the hardness of these materials, machining is extremely difficult and even sometimes not possible to machine, with conventional machining processes. These materials can be machined by unconventional machining processes like Electrical Discharge Machining (EDM), Electro-Chemical Machining (ECM), Laser Beam machining (LBM), etc [1, 2]. EDM is most popular because of its machining capabilities and comparatively low cost. EDM is a nonconventional machining process, which is used to machine extremely hard material [3, 4, 5]. There are two electrodes, one is a workpiece and the other is the tool electrode. Two electrodes are completely submerged in a dielectric fluid. A gap is maintained between two electrodes. Voltage is gradually applied between two electrodes. Due to this potential difference, there is a series of sparking takes place between two electrodes (one is a workpiece and the other is known as a tool/electrode). Due to this sparking, some material from the surface of the workpiece is melt and flushed away from the machining area [6] and some material from the tool surface also removed [7]. There are many control parameters of electrical discharge machining (EDM). Peak current (Ip) is the maximum current flow between electrodes, pulse on time (Ton) is the time interval during each spark, duty factor (t) is the percentage of the ratio between pulse duration and total cycle time, voltage (V) is applied a potential difference between both electrodes [8].

Higher material removal rate (MRR) is desirable, but higher MRR also leads to a higher tool wear rate (TWR). High TWR deforms the tool shape, which affects the machining quality of the workpiece. Because the machined surface is an exact replica of the tool surface. This limitation can be overcome by maximizing the relative wear ratio (RWR). RWR is the ratio of MRR to TWR (in other words RWR = MRR/TWR). There is a challenge to maximize RWR. Qudeiri Jaber E. Abu et al. reviewed the EDM machinability of Titanium alloy [9]. Relative wear ratio is a very important term for electrical discharge machining (EDM). A higher value of RWR ensures a better quality of EDM machining. To understand the behavior of the process, it is required to develop a model between the process parameters and response measure. Muthuramalingam and Mohan reviewed on the influence of various electrical process parameters in the EDM process [10]. Ghoreishi and Atkinson used RSM to develop a regression model for MRR, TWR, and SR during UAEDM of tool and die steel [11]. Pradhan and Biswas used RSM to development of the model and work on multi-objective optimization of MRR and surface roughness [12]. EDM has many control parameters like peak current, discharge voltage, pulse on-time, pulse-off time, electrode polarity, electrode gap, dielectric [13]. Four important control parameter Peak current (Ip), discharge voltage (V), pulse on time (Ton) and duty factor (t) is selected as control parameter; RWR is selected as quality measures. To prepare the empirical model, thirty experiments were conducted using a design of experiment with central composite design (CCD) [14]. Once the model is prepared, the developed model is used for optimization.

Optimization is the process of finding the best result within the given resources. Rajesh and Dev optimize MRR and surface roughness (Ra) on the EDM process [15]. Kao et al. optimized electrode wear ratio (EWR), MRR and Ra [16]. Tarng et al. find the optimum level of control parameters in wire electrical discharge machining [17]. Many researchers applied different optimization techniques like Genetic Algorithm (GA), simulated annealing (SA), particle swarm analysis (PSA) and many more. These optimization techniques have algorithm-specific parameters and complicated in nature. Rao invented an optimization algorithm, known as Jaya algorithm in 2016. Jaya algorithm is an advanced optimization technique and simpler to implement, further, it requires fewer parameters. Jaya Algorithm is successfully used in constrained optimization as well [18, 19, 20]. Teaching–learning- based optimization (TLBO) is an advanced optimization technique that is based on the process of teaching and learning of a student [21, 22].

In this paper, RWR has been optimized, through advanced optimization technique Teaching learning based optimization (TLBO) and Jaya Algorithm. RWR optimization of Titanium alloy 685 is discussed in this research paper. No work has been reported on EDM machinability of Titanium alloy 685. Many researchers worked on the optimization of MRR and surface roughness but very few research work reported on RWR optimization. The researcher involves maximizing MRR only (this also maximizes TWR with poor machining quality especially for complicated tool shape). This paper maximizes MRR while TWR is minimized simultaneously.
Fig. 1

Workpiece

2 Experimental setup

Titanium alloy 685 is selected as a workpiece and a copper rod of 10 mm diameter is selected as an electrode. Thirty experiments were conducted as per the design of experiments (DOE) shown in Table 2. Four important parameter Ip, Ton, t, and V are selected as control parameters. Table 1 shows the corresponding range of variables. Each experiment was conducted for thirty minutes. The workpiece is shown in Fig. 1. The material removal rate (MRR) and tool wear rate (TWR) is recorded for each experiment. The MRR is calculated as following
$$\begin{aligned} MRR = \frac{M_{fw}-M_{iw}}{T_{p}}\ \end{aligned}$$
(1)
where \(M_{fw}\) = Final weight of workpiece after machining, \(M_{iw}\) = Intial weight of workpiece, \(T_{p}\) = Time period of machining in minutes.
The TWR is calculated as following
$$\begin{aligned} TWR = \frac{E_{fw}-E_{iw}}{T_{p}}\ \end{aligned}$$
(2)
where \(E_{fw}\) = Final weight of tool electrode after machining, \(E_{iw}\) = Intial weight of electrode, \(T_{p}\) = Time period of machining in minutes.

Relative wear ratio (RWR) is the ratio of MRR to TWR. RWR is calculated for each experiment and inserted into Table 2 to show the experimental result.

RWR is calculated as follwing
$$\begin{aligned} RWR = \frac{MRR}{TWR}\ \end{aligned}$$
(3)
Table 1

Control parameters and their ranges

Parameter

Level 1

Level 2

Level 3

Ip (Ampere)

4

6

8

Ton (\(\mu \) seconds)

50

100

150

Duty Factor (%)

25

37.5

50

V (Volt)

40

70

100

Table 2

Experimental details

Exp.

Ip (Amp)

Ton (\(\upmu \)s)

t (%)

V (V)

RWR

1

4

50

25

40

7.4365

2

4

50

50

40

7.9299

3

4

150

25

40

21.4429

4

4

150

50

40

34.4082

5

4

100

37.5

70

31.2013

6

4

50

25

100

6.8743

7

4

50

50

100

9.5447

8

4

150

25

100

15.7667

9

4

150

50

100

28.2391

10

6

100

37.5

40

9.8320

11

6

50

37.5

70

5.2024

12

6

100

25

70

8.6039

13

6

100

37.5

70

10.0938

14

6

100

37.5

70

9.2377

15

6

100

37.5

70

8.8455

16

6

100

37.5

70

10.4862

17

6

100

37.5

70

9.2038

18

6

100

37.5

70

9.6536

19

6

100

50

70

11.8069

20

6

150

37.5

70

15.2702

21

6

100

37.5

100

9.6188

22

8

50

25

40

3.2859

23

8

50

50

40

4.3258

24

8

150

25

40

8.1091

25

8

150

50

40

13.1414

26

8

100

37.5

70

6.5890

27

8

50

25

100

3.2556

28

8

50

50

100

9.3455

29

8

150

25

100

9.8446

30

8

150

50

100

13.4870

3 Modelling and optimization

3.1 Modelling

In response surface methodology, The relation between the quality measures and process control parameters is express as following:
$$\begin{aligned} y = f (x_{1},x_{2},x_{3},x_{4},x_{5},\ldots x_{n})\ \end{aligned}$$
(4)
where \(x_{1}, x_{2}, x_{3}, x_{4}, x_{5},\ldots , x_{n}\) are input parameters and y is output response. With plotting the response ‘y’, a surface is obtained which is known as response surface. Function of ’y’ may be very complicated and unknown. The RSM aims is to approximating f by a suitable lower order equation. A second order regression model is represented as following:
$$\begin{aligned} y = b_{0}+\sum _{i = 1}^{p} b_{i}x_{i}+\sum _{i = 1}^{p} b_{ii}x_{i}^2+\sum _{i}\sum _{j}b_{ij}x_{i}x_{j} \end{aligned}$$
(5)
where \(b_{0}\) is constant and all b’ are regression coefficient.
Response surface methodology (RSM) used to develop a regression model. Commercial statistical software Minitab 18 is used to develop a regression model as following.
$$\begin{aligned} RWR& = 39.4*21.62*Ip+0.669*V+0.235*Ton\\&\quad -0.027*t+1.699*Ip*Ip-0.00516*V*V\\&\quad +0.0186*Ip*V-0.0273* Ip*Ton\\&\quad -0.000659*V*Ton +0.00238*Ton*t \end{aligned}$$

3.2 Optimization using Jaya Algorithm

Jaya algorithm is an advanced optimization technique and found suitable for engineering optimization. Figure 2 shows flow diagram of Jaya Algorithm.
Fig. 2

Flow diagram of Jaya Algorithm

  • Step 1: Initial population is generated randomly with in the range as per Table 1

  • Step 2: The objective is to maximize RWR as per equation 6. The highest value of RWR, considered as best and lowest RWR considered as worst. Candidate 4 having best value of RWR and corresponding variables of candidate 4 have Ip_best = 4.9262, Ton_best = 142.7235, t_best = 47.38632, V_best = 71.1816. Candidate 5 having minimum RWR, hence Ip_worst = 4.8570, Ton_worst = 67.9034, t_worst = 39.2846, V_worst = 51. 5042.

Table 3

Initial solution

Can.

Ip

Ton

t (%)

V

RWR

1

7.7104

112.6811

49.9706

45.6465

11.4634

2

4.1532

85.3170

47.0505

97.7998

15.7032

3

4.0926

101.5753

41.7021

62.5484

23.0844

4

4.9262

142.7235

47.8632

71.1816

24.7406

5

4.8570

67.9034

39.2846

51.5042

9.8303

Now Consider two random numbers r1 = 0.7332, r2 = 0.4231. Calculate the new value of all parameters candidate as per equation (7). All values of newly calculated parameters should be within the range as per Table 1. If new values fall below the lower limit then assign a lower limit to a new variables value. If new values of variable go beyond the upper limit of variables then assign an upper limit to the given variable as per Table 1.
$$\begin{aligned} X'j,k,i& = Xj,k,i + r1,j,i (Xj,best,i - |Xj,k,i|) \\&- r2,j,i (Xj,worst,i - |Xj,k,i|) \end{aligned}$$
  • Candidate 1 Ip = 7.7104 + 0.7332(4.9262 − | 7.7104|) − 0.4231(4.8570 − |7.7104|)  = 6.8764

  • Candidate 2 Ip  = 4.1532 + 0.7332(4.9262 − | 4.1532|) − 0.4231(4.8570 − |4.1532|)  = 4.4222

  • Candidate 3 Ip  = 4.0926 + 0.7332(4.9262 −  | 4.0926 |)  −  0.4231(4.8570 − |4.0926|)  = 4.3804

  • Candidate 4 Ip  = 4.9262 + 0.7332(4.9262 −  | 4.9262|)  −  0.4231 (4.8570 − |4.9262|)  = 4.9555

  • Candidate 5 Ip  = 4.8570 + 0.7332(4.9262 −  | 4.8570 |)  −  0.4231(4.8570 − |4.8570|)  = 4.9077

  • Candidate 1 Ton  = 112.6811 + 0.7332(142.7235 − |112.6811|) −  0.4231(67.9034 − |112.6811|) = 153.6536326 ( = 150 because maximum Ton = 150)

  • Candidate 2 Ton  = 85.3170 + 0.7332(142.7235 − |85.3170|) −  0.4231(67.9034 − |85.3170|) = 134.77514

  • Candidate 3Ton = 101.5753 + 0.7332(142.7235 − |101.5753|) −  0.4231(67.9034 − |101.5753|) = 103.6817411

  • Candidate 4 Ton = 142.7235 + 0.7332(142.7235 − |142.7235|) −  0.4231(67.9034 − |142.7235|) = 174.3798843 ( = 150 because maximum Ton = 150)

  • Candidate 5 Ton = 67.9034 + 0.7332(142.7235 − |67.9034|) −  0.4231(67.9034 − |67.9034|) = 122.7614973

  • Candidate 1 t = 49.9706 + 0.7332(47.38632  − |49.9706|) −  0.4231(39.2846 − |49.9706|) = 52.9467 ( = 50 because maximum t = 50)

  • Candidate 2 t = 47.0505 + 0.7332(47.38632  − |47.0505|) −  0.4231(39.2846 − |47.0505|) = 50.9321 ( = 50 because maximum t = 50)

  • Candidate 3 t = 41.7021 + 0.7332(47.38632  − |41.7021|) −  0.4231(39.2846 − |41.7021|) = 47.2422

  • Candidate 4 t = 47.8632 + 0.7332(47.38632  − |47.8632|) −  0.4231(39.2846 − |47.8632|) = 51.4928 ( = 50 because maximum t = 50)

  • Candidate 5 t = 39.2846 + 0.7332(47.38632  − |39.2846|) −  0.4231(39.2846 − |39.2846|) = 45.5744

  • Candidate 1 V = 45.6465 + 0.7332 (71.1816 −  | 45.6465 |) −  0.4231(51.5042 −  |45.6465|) = 61.8904

  • Candidate 2 V = 97.7998 + 0.7332(71.1816 −  | 97.7998 |) −  0.4231 (51.5042 −  |97.7998|) = 97.8710

  • Candidate 3 V = 62.5484 + 0.7332(71.1816 −  | 62.5484 |) −  0.4231(51.5042 −  |62.5484|) = 73.5510

  • Candidate 4 V = 71.1816 + 0.7332 (71.1816 −  | 71.1816 |) −  0.4231(51.5042 −  |71.1816|) = 79.5071

  • Candidate 5 V = 51.5042 + 0.7332 (71.1816 − | 51.5042|) −  0.4231(51.5042 − |51.5042|) = 65.9316

Now insert calculated new value into Table 4.
Table 4

New values of all parameter and corresponding objective function RWR (first iteration)

Can.

Ip

Ton

t (%)

V

RWR

1

6.8764

150.0000

50.0000

61.8904

18.0981

2

4.4222

134.7751

50.0000

97.8713

22.5136

3

4.3804

45.9918

47.2422

73.5511

29.4930

4

4.9555

150.0000

50.0000

79.5073

25.4826

5

4.9077

122.7613

45.5744

65.9316

21.0654

Step 3: Compare every candidate and select with better RWR (objective function). Candidate 1 from Table 4 has better objective value compare to candidate 1 of Table 3, hence inserted into Table 4 as candidate 1. Similarly candidate 2, 3, 4, and 5 of Table 4 has also better RWR as compare to candidate 2, 3, 4, 5 of Table 3, hence candidate 2, 3, 4 and 5 of Table 3 inserted into Table 5. First iteration is over.
Table 5

Updated values of all variables and corresponding RWR (first iteration)

Can.

Ip

Ton

t (%)

V

RWR

1

6.8764

150

50

61.8904

18.0981

2

4.4222

134.7751

50

97.8713

22.5136

3

4.3804

145.9918

47.2422

73.5511

29.493

4

4.9555

150

50

79.5073

25.4826

5

4.9077

122.7613

45.5744

65.9316

21.0654

Step 4: Consider Table 5 as input to second iteration. Consider r1 = 0.5058, r2 = 0.4807 and repeat the same procedure as per step 2 and step 3. Table 6 represent new value of all variables. Now compare each candidate from Table 5 and Table 6. Select better RWR for each candidate and insert into Table 7.
Table 6

New values of all variables for second iteration

Can.

Ip

Ton

t (%)

V

RWR

1

5.6138

147.9726

48.605

67.7887

21.5808

2

4

133.1297

48.605

100

24.9066

3

4

144.065

45.9165

79.1568

31.7298

4

4

147.9726

48.605

84.9635

32.1518

5

4

121.4175

44.2905

71.7286

28.0169

Table 7

Updated values of all variables and corresponding RWR for second iteration

Can.

Ip

Ton

t (%)

V

RWR

1

5.6138

147.9726

48.605

67.7887

21.5808

2

4

133.1297

48.605

100

24.9066

3

4

144.065

45.9165

79.1568

31.7298

4

4

147.9726

48.605

84.9635

32.1518

5

4

121.4175

44.2905

71.7286

28.0169

3.3 Optimization using TLBO algorithm

Teaching-learning-based optimization (TLBO) is two-phase optimization algorithm, first is teacher phase and second is the learner phase. Figure 3 shows flow diagram of TLBO Algorithm.

Step 1: Initial population is randomly generated in between upper bound and lower bound of variables as shown in Table 1. Calculate the mean of all variables.
Fig. 3

Flowchart of TLBO algorithm

Fig. 4

Effect of various control parameters on RWR

Table 8

Initial population

Can.

Ip

Ton

t (%)

V

RWR

1

5.8033

75.6442

30.6602

40.7974

2.7112

2

4.8153

85.5584

33.0294

46.5677

10.8899

3

6.1957

76.3754

30.6019

83.3591

5.7567

4

7.6135

135.5253

30.5221

99.1143

6.7809

5

6.7352

63.1263

46.2953

65.3627

6.9415

Mean

6.2326

87.24592

34.22178

67.04024

6.2326

Step 2: Objective is to maximize RWR as per equation 6. Candidate 2 has maximum RWR value hence selected as teacher. Value of Ip = 4.8153, Ton = 85.5584, t = 33.0294, V = 46.5677 selected as teacher’s variables value. Calculated mean value of Ip, Ton, t and V are 6.2326, 87.24592, 34.22178, 67.04024 respectively. Consider four random numbers r1 = 0.6476, r2 = 0.9520 r3 = 0.1991 and r4 = 0.0000 for Ip, Ton, t and V respectively. The difference mean values of Ip, Ton, t and V calculated as following.
  • Difference mean (Ip) = 0.6476*(4.8153-6.2326)

  • Difference mean (Ton) = 0.9520*(85.5584-87.24592)

  • Difference mean (t) = 0.1991*(33.0294-34.22178)

  • Difference mean (V) = 0.0000*(46.5677-67.04024)

The values of difference mean (Ip) is added to all parameter of Ip (first column) similarly difference mean (Ton) is added to all values of Ton (second column), difference mean (t) is added to all values of t and difference mean (V) is added to all values of V of Table 8. Thus Table 9 is prepared shows the new values of all variables.
Table 9

New values of the input variables and the objective function (teacher phase)

Can.

Ip

Ton

t (%)

V

RWR

1

4.8854

74.0377

30.4228

40

6.5787

2

4

83.9519

32.792

40

15.5988

3

5.2778

74.7689

30.3645

75.9497

8.7602

4

6.6956

133.9188

30.2848

91.7049

7.9195

5

5.8174

61.5198

46.058

57.9533

6.6744

  • Step 3: Now compare Tables 8 and 9 for better values of RWR. The better value of RWR is placed in Table 10 for each candidate. Table 9 has a better RWR value for each candidate as compared to Table 8. Hence select all candidate from Table 9 and inserted into Table 10. The teacher phase is over now.

  • Step 4: Learner phase is started now. Every learner (candidate) has to interact with any other learner (candidate) and every learner interacts with anyone learner. Here, the interaction between learner 1 and learner 2, learner 2 and learner 3, learner 3 and Lerner 4, learner 4 and learner 5 and interaction between learner 5 and learner 1 is considered. Consider random numbers r5 = 0.3653, r6 = 0.1889, r7 = 0.2440 and r8 = 0.5060 for Ip, Ton, t and V respectively.

Table 10

Updated values of the variables and the objective function based on best of two (teacher phase)

Can.

Ip

Ton

t (%)

V

RWR

1

4.8854

74.0377

30.4228

40

6.5787

2

4

83.9519

32.792

40

15.5988

3

5.2778

74.7689

30.3645

75.9497

8.7602

4

6.6956

133.9188

30.2848

91.7049

7.9195

5

6.7352

63.1263

46.2953

65.3627

6.9415

After a comparison between learner 1 and learner 2, learner 2 has better RWR hence
  • (Ip) new for learner 1 = 4.8854+ r5*(4-4.8854) = 4.5621

  • (Ton) new for learner 1 = 74.0377+ r6*(83.9519-74.0377) = 75.9102

  • (t) new for learner 1 = 30.4228+ r7*(32.792-30.4228) = 31.0009

  • (V) new for learner 1 = 40+ r8*(40-40) = 40

Similarly calculated new values of all variables of candidate 2, candidate 3, candidate 4, and candidate 5 is inserted into Table 11. It is noted that the new value of variables should be within the range of input as per Table 1. If the value falls below lower limit the assign lower bound and if it goes beyond the upper limit then assign an upper limit to the variable.
Table 11

New values of the variables and the objective function (learner phase)

Can.

Ip

Ton

t (%)

V

RWR

1

4.5621

75.9102

31.0009

40

9.1741

2

4

85.6863

33.3843

40

16.0114

3

5.7955

85.9405

30.3451

83.9219

7.2491

4

6.6811

147.2893

26.3784

100

5.0965

5

7.4107

61.0655

50

78.1963

8.7936

Step 5: Now compare Tables 10 and 11 for better values of f(x) and better value of f(x) is placed in Table 12 for each candidate. Learner phase is over now. Iteration one is over.
Table 12

Updated values of the variables and the objective function based on fitness comparison (learner phase)

Can.

Ip

Ton

t (%)

V

RWR

1

4.5621

75.9102

31.0009

40

9.1741

2

4

85.6863

33.3843

40

16.0114

3

5.2778

74.7689

30.3645

75.9497

8.7602

4

6.6956

133.9188

30.2848

91.7049

7.9195

5

7.4107

61.0655

50

78.1963

8.7936

Step 6: Table 12 would be input to next iteration and repeat step 2,3,4 and step 5. Continue procedure for 100 iterations and report optimum solution.

3.4 Optimization using Minitab 18

Response optimizer of commercial software Minitab 18 optimizes response measures RWR = 35.5719 and corresponding four control parameters are Ip = 4 A, V = 62.4242 v, Ton = 150 \(\mu \) seconds and t = 50 %.

4 Discussion

MRR increases with the increase of peak current (Ip), but TWR also increases with Ip increases [10]. Many authors maximize MRR with compromisation to TWR and quality. The quality of the machined surface deteriorates if TWR has a higher value. Hence in this study, we consider RWR (RWR = MRR/TWR) optimization. This optimization ensures to maximize MRR while the quality of the machined surface maintained at the best level. This section discusses the effect of four control parameters individually on RWR. Figure 4 shows the effect of all parameters on RWR value. RWR decreases with the increment of peak current (Ip), RWR increases with the increases of pulse on time (Ton), RWR increases with the increases of duty factor (t) and the optimum value of voltage (v) observes at V = 62.4242 V, as shown in Figure 4.
Table 13

Optimum result

Algorithm

Ip

Ton

t (%)

V

RWR

Jaya Algorithm

4

150

50

62.4614

35.6021

TLBO

4

150

50

62.4564

35.6021

Response Opt.

4

150

50

62.4242

35.5719

5 Results

Optimization results are shown in tabular form. Table 13 shows the comparison and result produced by the different optimization algorithm.

6 Conclusion

The optimization of RWR using response surface modeling, Jaya Algorithm and teaching-learning-based optimization algorithm (TLBO) has been done. All three optimization methods show the same result. Maximum RWR is 35.6021 at an optimum level of Ip = 4 amp, Ton = 150 \(\mu \) s, duty factor t = 50 % and V = 62.4614V.

Jaya Algorithm converges the optimization quickly in just 15 iterations and found suitable for engineering optimization. RWR decreases with the increase of peak current, RWR increases with the increases of Ton and duty factor (t) while the optimum value of voltage (V) observed at 62.4614 V.

Notes

Acknowledgements

The authors would like to thanks the anonymous reviewers for their constructive comments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University Institute of Technology, Rajiv Gandhi Proudyogiki VishwavidyalayaBhopalIndia
  2. 2.Maulana Azad National Institute of TechnologyBhopalIndia

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