Optimization of machining parameters and wire vibration in wire electrical discharge machining process
 Sameh Habib^{1}Email authorView ORCID ID profile
DOI: 10.1186/s4075901700171
© The Author(s). 2017
Received: 11 November 2016
Accepted: 12 January 2017
Published: 28 January 2017
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)Background
Wire electrical discharge machining is a thermoelectrical 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 threedimensional 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 wirecut 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 pulseon time, pulseoff 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 multicutting 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 highspeed video camera. Highspeed 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_{e}  1.0 μs 
Discharge current i_{e}  20 A 
Wire diameter  0.5 mm 
Wire material  Tungsten 
Wire tension W_{t}  0.5–4.0 N 
Wire running speed W_{s}  1.0–15.0 m/min 
Servo voltage S_{v}  50–90 V 
Flow rate F_{r}  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 secondorder model can be constructed efficiently with central composite designs (CCD) (Montgomery 1997). CCD are firstorder (2^{K}) designs augmented by additional centre and axial points to allow estimation of the tuning parameters of a secondorder 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 
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 secondorder 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
ANOVA analysis for Wire amplitude (A_{a})
Source  Sum of squares  Degree of freedom  Mean Square  F value  P value  

Model  2.45  14  .31  32.78  <.0001  Significant 
Pure error  .17  16  
Cor total  2.62  30  
RSquared = .9358  Adj R –Squared = .9072 
ANOVA analysis for Kerf width (Wk)
Source  Sum of squares  Degree of freedom  Mean Square  F value  P value  

Model  .56  14  .070  1202.36  <.0001  Significant 
Pure error  .00104  16  
Cor total  .56  30  
RSquared = .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 highspeed 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, N  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.
Abbreviations
 CCD:

Central composite designs
 F_{r} :

Flow rate
 S_{v} :

Servo voltage
 W_{s} :

Wire running speed
 W_{t} :

Wire tension
Declarations
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.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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