# Optimization of machining parameters and wire vibration in wire electrical discharge machining process

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## Abstract

### Background

Wire Electrical discharge machining (WEDM) has higher capability for cutting complex shapes with high precision for very hard materials without using high cost of cutting tools. During the WEDM process, the wire behaves like a metal string, straightened by two axial pulling forces and deformed laterally by a sum of forces from the discharge process. Major forces acting on the wire can be classified into three categories. The first is a tensile force, pulling the wire from both sides in axial direction and keeping it straight. The second is the dielectric flushing force that comes from circulation of the dielectric fluid in the machining area. The third category consists of forces of different kinds resulting from sparking and discharging. Large amplitude of wire vibration leads to large kerf widths, low shape accuracies, rough machined surfaces, low cutting speeds and high risk of wire breakage. Such tendencies for poor machining performance due to wire instability behavior appear with thinner wires.

### Methods

The present work investigates a mathematical modeling solution for correlating the interactive and higher order influences of various parameters affecting wire vibration during the WEDM process through response surface methodology (RSM). The adequacy of the above proposed model has been tested using analysis of variance (ANOVA).

### Results

Optimal combination of machining parameters such as wire tension, wire running speed, flow rate and servo voltage parameters has been obtained to minimize wire vibration.

### Conclusions

The analysis of the experimental observations highlights that the wire tension, wire running speed, flow rate and servo voltage in WEDM greatly affect average wire vibration and kerf width.

## Keywords

Wire electrical discharge machining (WEDM) Mathematical modeling Wire vibration Kerf width and response surface methodology (RSM)## Abbreviations

- CCD
Central composite designs

- F
_{r} Flow rate

- S
_{v} Servo voltage

- W
_{s} Wire running speed

- W
_{t} Wire tension

## Background

Wire electrical discharge machining is a thermo-electrical process in which material is eroded from the workpiece through a series of discrete sparks occurring between the workpiece and the wire electrode (tool). The tool is separated by a thin film of dielectric fluid which is continuously fed to the area being machined in order to flush away the eroded particles. The movement of the wire is numerically controlled to achieve the desired three-dimensional shape and accuracy of the workpiece. The most important performance factors effecting WEDM are discharge current, pulse duration, pulse frequency, wire speed, wire tension, type of die electric fluid and dielectric flow rate. However, wire EDM owing a large number of variables and the stochastic nature of the process, even a highly trained operator will still find it difficult to attain an optimal processing and avoid wire breakage.

Geometrical inaccuracy due to wire lag phenomenon in wire-cut electrical discharge machining has been analyzed and optimized by (Puri & Bhattacharyya 2003). Also, the trend of variation of the geometrical inaccuracy caused due to wire lag with various machine control parameters has been studied. Shichun et al. (2009) analyzed kerf width of micro wire EDM. They developed mathematical model of wire lateral vibration in machining process. Kumar et al. (2013) studied describes the effect of six input parameters such as pulse-on time, pulse-off time, peak current, spark gap voltage, wire feed and wire tension on wire breakage frequency and the surface integrity of wear out wire during machining of pure titanium. Wentai et al. (2015) investigated wire tension change in high speed wire EDM. They developed simulation model for the process and redesigned wire winding mechanism to improve cutting stability as well as the consistency of workpiece dimension in multi-cutting process. In addition, the higher tension decreases the wire vibration amplitude and hence decreases the cut width so that the speed is higher for the same discharge energy. However, if the applied tension exceeds the tensile strength of the wire, it leads to wire breakage. Kumar & Singh (2012) investigated the variation of cutting performance with pulse on time, pulse off time, open voltage, feed rate override, wire feed, servo voltage, wire tension and flushing pressure. They used Taguchi approach of L18 orthogonal array under different conditions to obtain optimal combination of parameters. Nain et al (2015) reviews the effect of process parameters on the performance characteristics such as surface integrity characteristics and roughness, material removal rate, kerf width and wire wear rate of wire EDM process.

Wire movements vibration during wire EDM process were directly observed by (Habib & Okada 2016a; Habib & Okada 2016b) using a high-speed video camera. High-speed observation model was built, and the wire movements during machining were observed and recorded. By analyzing the recorded images, the effects of machining conditions such as wire tension, wire running speed, flow rate of jet flushing and servo voltage on the wire vibration amplitude and machined kerf width were developed. In this work, mathematical models for correlating these machining conditions with wire vibration amplitude and machined kerf width were developed. Response surface methodology was used to optimize machining conditions utilizing the relevant experimental data as obtained through experimentation. The adequacy of the developed mathematical models has also been tested by the analysis of variance test.

## Methods

Properties of dielectric fluid

Dielectric fluid property | Value |
---|---|

Flushing point | 125 °C |

Melting point | -51 °C |

Boiling point | 300 °C |

Appearance | colorless |

Specific Gravity | 0.8236 |

Odor | odorless |

Experimental working conditions

Working conditions | Value |
---|---|

Machining length | 5.0 mm |

Workpiece material | SKD11 (JIS) |

Workpiece thickness | 1.0 mm |

Pulse duration t | 1.0 μs |

Discharge current i | 20 A |

Wire diameter | 0.5 mm |

Wire material | Tungsten |

Wire tension W | 0.5–4.0 N |

Wire running speed W | 1.0–15.0 m/min |

Servo voltage S | 50–90 V |

Flow rate F | 0–8.0 L/min |

Dielectric fluid | Kerosene |

Digital video camera recording conditions

Recording conditions | Value |
---|---|

Recording speed | 8,000 fps |

Shutter speed | 1/40,000 s |

Recording time | 2.0 s |

View size | 0.4 × 0.2 mm |

## Response surface modelling and experimental design

Response surface methodology (RSM) is a collection of mathematical and statistical techniques for empirical model building. By careful design of experiments, the objective is to optimize a response (output variable) which is influenced by several independent variables (input variables). An experiment is a series of tests, called runs, in which changes are made in the input variables in order to identify the reasons for changes in the output response (Mahfouz 1999). In this work response surface methodology was chosen meanwhile many other techniques are available because it explores the relationships between several explanatory variables and one or more response variables. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response.

Most of the criteria for optimal design of experiments are associated with the mathematical model of the process. Generally, these mathematical models are polynomials with an unknown structure, so the corresponding experiments are designed only for every particular problem. The choice of the design of experiments can have a large influence on the accuracy of the approximation and the cost of constructing the response surface. A second-order model can be constructed efficiently with central composite designs (CCD) (Montgomery 1997). CCD are first-order (2^{K}) designs augmented by additional centre and axial points to allow estimation of the tuning parameters of a second-order model. the design involves 2^{K} factorial points, 2 K axial points and 1 central point repeated 7 times (Habib 2009).

Coding levels of input variables

Level | Wt | Ws | Fr | Sv |
---|---|---|---|---|

-2 | 0.5 | 1 | 0 | 50 |

-1 | 1.5 | 3 | 2 | 60 |

0 | 2 | 7 | 4 | 70 |

1 | 3 | 11 | 6 | 80 |

2 | 4 | 15 | 8 | 90 |

_{u}is the corresponding response, e.g. the Aa and Wk produced by the various input variables and the x

_{i}(1,2, …k) are coded levels of k quantitative process variables, the terms β

_{°}, β

_{i}, β

_{ii}and β

_{ij}are the second order regression coefficients. The second term under the summation sign of this polynomial equation is attributable to linear effect, whereas the third term corresponds to the higher-order effects; the fourth term of the equation includes the interactive effects of the process parameters. In this work, Eq. (2) can be rewritten according to the four variables used as:

Where: X_{1}, X_{2}, X_{3} and X_{4} are wire tension, wire running speed, flow rate and servo voltage respectively.

## Result and Discussion

### Mathematical formulation

Plan for central composite rotatable second-order design: different controlling parameters and results

Experiment No. | Wt | Ws | Fr | Sv | Response Aa (μm) | Response Wk (μm) |
---|---|---|---|---|---|---|

1 | -2 | 0 | 0 | 0 | 3.66540 | 71.5790 |

2 | 0 | 0 | 0 | 0 | 2.37396 | 68.0022 |

3 | -1 | 1 | 1 | -1 | 2.54925 | 68.3599 |

4 | 0 | 0 | 0 | 0 | 2.37396 | 68.0022 |

5 | -1 | -1 | 1 | -1 | 2.93253 | 70.4804 |

6 | -1 | -1 | -1 | -1 | 2.70124 | 69.2480 |

7 | 2 | 0 | 0 | 0 | 2.17943 | 65.7750 |

8 | 0 | 0 | 0 | 0 | 2.37396 | 68.0022 |

9 | -1 | 1 | -1 | -1 | 2.70124 | 69.2480 |

10 | -1 | 1 | -1 | 1 | 2.66031 | 69.1647 |

11 | 0 | 0 | 0 | 0 | 2.37396 | 68.0022 |

12 | 1 | 1 | 1 | 1 | 2.01800 | 66.6289 |

13 | 1 | 1 | 1 | -1 | 1.84065 | 65.8024 |

14 | 0 | 2 | 0 | 0 | 2.51052 | 68.3176 |

15 | 0 | 0 | -2 | 0 | 2.62025 | 68.8408 |

16 | 0 | 0 | 0 | 0 | 2.37396 | 68.0022 |

17 | 0 | 0 | 0 | 0 | 2.37396 | 68.0022 |

18 | -1 | -1 | -1 | 1 | 2.66031 | 69.1647 |

19 | 0 | 0 | 0 | -2 | 2.43437 | 68.1575 |

20 | -1 | 1 | 1 | 1 | 2.83786 | 69.6149 |

21 | 0 | 0 | 0 | 2 | 2.60788 | 69.0435 |

22 | -1 | -1 | 1 | 1 | 2.95642 | 70.7109 |

23 | 1 | -1 | -1 | -1 | 2.24741 | 67.2592 |

24 | 1 | 1 | -1 | -1 | 2.04350 | 66.4264 |

25 | 1 | -1 | -1 | 1 | 2.09522 | 66.7474 |

26 | 0 | 0 | 0 | 0 | 2.37396 | 68.0022 |

27 | 0 | -2 | 0 | 0 | 2.55843 | 69.1749 |

28 | 0 | 0 | 2 | 0 | 2.64001 | 69.5402 |

29 | 1 | 1 | -1 | 1 | 2.15603 | 66.9390 |

30 | 1 | -1 | 1 | -1 | 2.69919 | 69.1595 |

31 | 1 | -1 | 1 | 1 | 2.61182 | 68.9616 |

### Checking the accuracy of the model

^{2}). In all the three cases that the values of determination coefficient (R

^{2}) and adjusted determination coefficient (adj. R

^{2}) are more than 90% which confirms good significance of the model. The results of the analysis justifying the closeness of fit of the mathematical models have been enumerated, as shown in Tables 6 and 7. The

*p*-values of the models are also found to be less than 0.05, which verifies that the model is acceptable. It is concluded that the evolved models given by Eqs. (4) and (5) are quite adequate and demonstrate the independent, quadratic and interactive effects of the different machining parameters on the average wire amplitude and kerf width criteria values.

ANOVA analysis for Wire amplitude (A_{a})

Source | Sum of squares | Degree of freedom | Mean Square | | | |
---|---|---|---|---|---|---|

Model | 2.45 | 14 | .31 | 32.78 | <.0001 | Significant |

Pure error | .17 | 16 | ||||

Cor total | 2.62 | 30 | ||||

R-Squared = .9358 | Adj R –Squared = .9072 |

ANOVA analysis for Kerf width (Wk)

Source | Sum of squares | Degree of freedom | Mean Square | | | |
---|---|---|---|---|---|---|

Model | .56 | 14 | .070 | 1202.36 | <.0001 | Significant |

Pure error | .00104 | 16 | ||||

Cor total | .56 | 30 | ||||

R-Squared = .9981 | Adj R –Squared = .9973 |

### Parametric influence on average wire amplitude

When the wire running speed has a lower value, the amplitude slightly increases. The debris exclusion from the discharge gap is a little difficult at lower wire running speed because there is no high-speed flow of working fluid around the wire. Then, the debris stagnation occurs around the wire, which causes unstable machining and larger amplitude of wire vibration. When the wire running speed is higher, the debris is smoothly excluded.

Dielectric flow rate is the rate at which the dielectric fluid is circulated. Flow rate of the working fluid from jet nozzles is important for efficient machining. One of the forces exerted on the wire is the dielectric flow such that as the flow rate increases around the wire, the movement of the wire speeds up and thus the average wire amplitude increases.

Servo voltage acts as the reference voltage to control the wire advances and retracts. Figure 3 shows that there is little decrease of average wire amplitude with change of servo voltage from 50 to 70 V. After that, the average wire amplitude increases slightly.

### Parametric influence on kerf width

### Optimality search

Optimal values of WEDM parameters

Process parameters | Value obtained | |
---|---|---|

Average wire amplitude | Kerf width | |

Wire tension, | 3.5–4.0 | 3.5–4.0 |

Wire running speed, m/min | 4.0–15.0 | 10.5–11.5 |

Flow rate, L/min | 0 to 8.0 | 1.5–2.5 |

Servo voltage, V | 65–75 | 65–75 |

## Conclusions

- 1.
Average wire amplitude decreases with the increase of wire tension and wire running speed. However, average wire amplitude increases with dielectric flow rate. Servo voltage has a weak influence on average wire amplitude.

- 2.
Kerf width decreases directly with the increase of wire tension and wire running speed. However, kerf width increases with the increase of flow rate and servo voltage.

- 3.
To minimize average wire amplitude, the value of wire tension is recommended to range between 3.5–4.0 N in addition with a servo voltage ranging between 65–75 V.

- 4.
When the value of wire running speed ranges between 4.0 and 15.0 m/min for the range of dielectric flow rate from 0–8.0 L/min, minimum average wire amplitude has been achieved.

- 5.
Minimum kerf width values resulted under wire tensions ranging between 3.5–4.0 N while the servo voltages ranged between 65–75 V.

- 6.
For minimal kerf widths, the WEDM process is preferred to operate under wire running speeds between 10.5–11.5 m/min in addition to dielectric flow rates ranging between 1.5–2.5 L/min.

## Notes

### Funding

This research got no financial help from any funding organization for the authorship or publication of this article.

### Authors’ contributions

There only one author for this manuscript, Prof. SSH.

### Competing interests

The author declares that he/she has no competing interests.

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