# Optimization of Machine Process Parameters in EDM for EN 31 Using Evolutionary Optimization Techniques

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Need for Optimization

## 3. Literature Survey

## 4. Research Gap

## 5. Experimental Setup

#### 5.1. Input& Output Parameters

#### 5.1.1. Output Parameters

#### 5.1.2. Output Parameters

#### Material Removal Rate (MRR)

_{i}is the initial weight of the work piece before machining, W

_{f}is the final weight of the work piece after machining, and t is the time period of trials.

#### Average Roughness (Ra)

#### 5.2. Experimentation

#### 5.3. Regression Model

#### 5.4. PSO Technique

_{1}and r

_{2}are generated randomly and lie in the range [0, 1]. c

_{1}and c

_{2}are the acceleration constants that weights the acceleration terms. The confidence of the particle in itself is represented by c

_{1}whereas c

_{2}represents the confidence a particle has in a swarm. c

_{1}and c

_{2}are referred to as cognitive and social parameters, respectively. The values of these two parameters determines the change in amount of tension in the system. The low values of the parameters result in the particles roaming far away from the target regions whereas a higher value results in an abrupt movement towards the target solution [33]. The exploration abilities of the swarm particles are controlled by the inertia weight w and is therefore very critical in determining the convergence behaviour of PSO. The lower values of w restrict the velocity updates to nearby region in the search space, whereas higher values result in velocity updates for a wider space in the problem space. Berg and Engelbrecht [34] have investigated the effect on convergence if benchmark functions of w, c

_{1}, and c

_{2}.

_{1}, c

_{2}, and w but these are applicable for single-objective optimization problems only. Determination of the parameters and the inertia weights for multi-objective optimization problems is relatively difficult and therefore a time variant of PSO has been described by Tripathi et al. [35]. In this variant of PSO, the parameters and the inertia weights are adaptive and changes with the iterations. The search space can be explored more efficiently with the adaptive nature of the time variant PSO technique. The premature convergence was taken care off by the mutation operator.

#### 5.5. BBO Technique

- m
_{k}= mutation rate, - m
_{max}= maximum mutation rate, - P
_{k}= probability of number of species, - P
_{max}= maximum probability,

_{k}).

_{S}(t), and λ

_{S}and µ

_{S}are consecutively the immigration and emigration rates at the presence of S species on that particular island. Then the variation from P

_{S}(t) to P

_{S}(t + Δt) can be described in Equation(7) below:

_{S}(t) and $\dot{P}$

_{S}(t), the value of Ps(t + Δt) given in Equation (7) can be approximated as:

_{S}(t + Δt). The algorithm for the BBO is shown below in Figure 3:

## 6. Optimization of Mrr and Ra Using PSO and BBO

_{1}= c

_{2}= 1.49445, number of iterations =100 and population size = 50 particles.

_{1}and f

_{2}are normalized values of MRR and Ra. The values of inertia weights considered are 0.5 for MRR and 0.5 for Ra as we have given equal importance to both the parameters. The initial values have been tabulated in the Table 6.

## 7. Results and Discussion

_{A}= 40, Gbest

_{B}= 110, Gbest

_{C}= 230, Gbest

_{D}= 50 (GBEST archive), are selected as optimal values. The values corresponding to the optimised value of MRR & Ra for the various input parameters are: A = 40; B = 110; C = 230; D = 50. MRR obtained through these parameters 235 mm

^{3}/min and Ra is 18.4 µm.

^{3}/min and Ra 17.98 µm were obtained using these parameters.

## 8. Conclusions

## 9. Scope of Future Research

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**3D contour plots or surfaces showing relationship between different input and output process parameters (

**a**) MRR with Gap Voltage and Pulse Current; (

**b**) MRR with Pulse-on-time and Pulse-off-time; (

**c**) Ra with Gap Voltage and Pulse Current;and (

**d**) Ra with Pulse-on-time and Pulse-off-time.

**Figure 6.**SEM images: (

**a**) before machining; (

**b**) after machining with initial parameters; (

**c**) after machining with optimal parameters computed using BBO; and (

**d**) after machining with optimal parameters computed using PSO.

Elements | C | Mn | Si | P | S | Cr | Fe |
---|---|---|---|---|---|---|---|

Chemical Composition (wt. %) | 1.07 | 0.58 | 0.32 | 0.04 | 0.03 | 1.12 | 96.84 |

Thermal Conductivity (w/mk) | 46.6 |

Density (gm/cc) | 7.81 |

Electrical Resistivity (ohm-cm) | 0.0000218 |

Specific heat capacity (j/gm-°C) | 0.475 |

Copper (99% Pure) | |
---|---|

Thermal Conductivity (w/mk) | 391 |

Density (gm/cc) | 1083 |

Electrical Resistivity (ohm-cm) | 1.69 |

Specific heat capacity (j/gm-°C) | 0.385 |

Machining Conditions | |
---|---|

Machine Used | CNC EDM (EMT 43) (Electronica) |

Electrode | Polarity Positive |

Dielectric | EDM Oil |

Work piece | Oil Hardened Non Shrinking Steel (48–50 HRC) |

Electrode | Electrolytic Copper (99.9% Purity) |

Flushing Condition | Pressure Flushing through 6 mm hole through work piece |

S. No. | IP (A) [A] | T_{on} (µs) [B] | T_{off} (µs) [C] | V (V) [D] | MRR mm^{3}/min | (Ra) (µm) | S. No. | IP (A) [A] | T_{on} (µs) [B] | T_{off} (µs) [C] | V (V) [D] | MRR mm^{3}/min | (Ra) (µm) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 5 | 11 | 60 | 1.2 | 1.97 | 26 | 6 | 200 | 425 | 50 | 25.0 | 10 |

2 | 1 | 10 | 22 | 55 | 2.5 | 2.4 | 27 | 10 | 50 | 107 | 50 | 50.0 | 10 |

3 | 1 | 20 | 43 | 55 | 2.1 | 3.1 | 28 | 10 | 75 | 160 | 50 | 48.0 | 10 |

4 | 1 | 30 | 64 | 55 | 2.3 | 2.7 | 29 | 10 | 100 | 213 | 50 | 60.0 | 11.6 |

5 | 1 | 50 | 107 | 55 | 3.1 | 2.9 | 30 | 10 | 150 | 319 | 50 | 58.0 | 13.1 |

6 | 1.5 | 5 | 11 | 60 | 2.0 | 2.4 | 31 | 10 | 200 | 425 | 50 | 56.0 | 14.4 |

7 | 1.5 | 10 | 22 | 55 | 4.9 | 3.0 | 32 | 20 | 100 | 213 | 50 | 133.0 | 15 |

8 | 1.5 | 20 | 43 | 55 | 4.7 | 3.1 | 33 | 20 | 150 | 319 | 50 | 121.0 | 16.8 |

9 | 1.5 | 50 | 107 | 55 | 6.2 | 3.1 | 34 | 20 | 200 | 425 | 50 | 132.0 | 18.0 |

10 | 1.5 | 100 | 213 | 55 | 4.0 | 3.3 | 35 | 20 | 500 | 1063 | 50 | 124.0 | 23.7 |

11 | 2 | 5 | 11 | 60 | 2.3 | 2.6 | 36 | 30 | 150 | 319 | 50 | 182.0 | 18.8 |

12 | 2 | 10 | 22 | 55 | 7 | 2.6 | 37 | 30 | 200 | 425 | 50 | 174.0 | 20.5 |

13 | 2 | 20 | 43 | 55 | 8 | 3 | 38 | 30 | 500 | 1063 | 50 | 187.0 | 27.4 |

14 | 2 | 50 | 107 | 55 | 9 | 3.6 | 39 | 30 | 1000 | 2125 | 50 | 158.0 | 34.2 |

15 | 3 | 5 | 11 | 50 | 7.8 | 2.2 | 40 | 40 | 100 | 213 | 50 | 244.0 | 18 |

16 | 3 | 10 | 22 | 50 | 11.5 | 2.7 | 41 | 40 | 150 | 319 | 50 | 240.0 | 20.4 |

17 | 3 | 20 | 43 | 50 | 12.6 | 3.7 | 42 | 40 | 200 | 425 | 50 | 218.0 | 22.3 |

18 | 3 | 50 | 107 | 50 | 13.7 | 4.9 | 43 | 40 | 500 | 1063 | 50 | 270.0 | 29.6 |

19 | 3 | 100 | 213 | 50 | 10.3 | 6 | 44 | 40 | 1000 | 2125 | 50 | 216.0 | 36.5 |

20 | 6 | 5 | 11 | 50 | 17.0 | 2.8 | 45 | 40 | 2000 | 4250 | 50 | 240.0 | 45 |

21 | 6 | 10 | 22 | 50 | 26.0 | 3.6 | 46 | 50 | 200 | 425 | 50 | 330.0 | 25 |

22 | 6 | 20 | 43 | 50 | 29.0 | 4.5 | 47 | 50 | 400 | 850 | 50 | 350.0 | 32 |

23 | 6 | 50 | 107 | 50 | 31.0 | 6.3 | 48 | 50 | 500 | 1063 | 50 | 310.0 | 32 |

24 | 6 | 100 | 213 | 50 | 32.0 | 7.7 | 49 | 50 | 1000 | 2125 | 50 | 310.0 | 41 |

25 | 6 | 150 | 319 | 50 | 28.0 | 8.7 | 50 | 50 | 2000 | 4250 | 50 | 300.0 | 50 |

Particle | A | B | C | D | MRR | Ra | Fitness Value |
---|---|---|---|---|---|---|---|

1 | 30 | 500 | 1063 | 50 | 187 | 27.4 | 0.6814 |

2 | 40 | 1000 | 2125 | 55 | 216 | 36.5 | 0.5038 |

3 | 50 | 2000 | 4250 | 60 | 300 | 50 | 0.5672 |

Particle | A | B | C | D |
---|---|---|---|---|

1 | 2.92 | 60 | 75 | 5.5 |

2 | 2.4 | 30 | 35 | −4.5 |

3 | 0.5 | 0.5 | 0.5 | 0.05 |

Particle | A | B | C | D | MRR | Ra | Fitness Value |
---|---|---|---|---|---|---|---|

1 | 32.92 | 560 | 1138 | 55.50 | 184.25 | 26.50 | 0.768 |

2 | 42.40 | 1030 | 2160 | 50.50 | 216.35 | 34.50 | 0.659 |

3 | 50.50 | 2000.50 | 4250.5 | 60.05 | 302.30 | 48.75 | 0.724 |

I | T_{on} | T_{off} | V | MRR | Ra | ||||
---|---|---|---|---|---|---|---|---|---|

40 | 110 | 230 | 50 | Experimental | Optimized | %Error | Experimental | Optimized | %Error |

238 | 235 | 1.26 | 18.4 | 18.1 | 1.63 |

I | T_{on} | T_{off} | V | MRR | Ra | ||||
---|---|---|---|---|---|---|---|---|---|

40 | 100 | 210 | 50 | Experimental | Optimized | %Error | Experimental | Optimized | %Error |

240 | 242 | 0.83 | 18.01 | 17.98 | 0.166 |

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**MDPI and ACS Style**

Faisal, N.; Kumar, K.
Optimization of Machine Process Parameters in EDM for EN 31 Using Evolutionary Optimization Techniques. *Technologies* **2018**, *6*, 54.
https://doi.org/10.3390/technologies6020054

**AMA Style**

Faisal N, Kumar K.
Optimization of Machine Process Parameters in EDM for EN 31 Using Evolutionary Optimization Techniques. *Technologies*. 2018; 6(2):54.
https://doi.org/10.3390/technologies6020054

**Chicago/Turabian Style**

Faisal, Nadeem, and Kaushik Kumar.
2018. "Optimization of Machine Process Parameters in EDM for EN 31 Using Evolutionary Optimization Techniques" *Technologies* 6, no. 2: 54.
https://doi.org/10.3390/technologies6020054