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Experimental Investigation of the Dry Electric
Discharge Machining (Dry EDM) Process
A Thesis Submitted
in Partial Fulfillment of the Requirements
for the Degree of
Master of Technology
by
Sourabh Kumar Saha
to the
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016 (INDIA)
April 2008
Abstract Electric Discharge Machining (EDM) is a thermo-electric non-traditional machining
process in which material removal takes place through the process of controlled spark
generation between a pair of electrodes which are submerged in a dielectric medium. Use
of mineral oil based dielectric liquids is the major cause of environmental concerns
associated with the EDM process. Dry EDM is an environment-friendly modification of
the oil EDM process in which a gaseous medium replaces the liquid dielectric. In the
current work, an independent machining unit has been designed and developed for
implementing the dry EDM process on an existing oil EDM machine. The unit has been
designed to satisfy the basic requirements for dry EDM, i.e. high velocity gas flow
through a rotating tubular tool. Parametric analysis has been done by conducting a set of
experiments using air as the dielectric medium. Effect of gap voltage, discharge current,
pulse-on time, duty factor, air pressure and spindle speed on material removal rate
(MRR) and surface finish (Ra) has been studied. Empirical models for MRR and Ra have
been developed by conducting a designed experiment based on the Central Composite
Design. Genetic Algorithm (GA) based multi-objective optimization for maximization of
MRR and minimization of Ra has been done by using the developed empirical models.
Optimization results have been used for identifying the rough and finish machining
conditions. For verification of the empirical models and the optimization results, focused
experiments have been conducted in the rough and finish machining regions. Finally, a
comparison of the process performance in dry EDM and oil EDM has been made. It was
experimentally found that although the MRR is lower in dry EDM, surface finish and tool
wear rate are much better than in oil EDM.
Acknowledgement I wish to express my sincere gratitude and regards to my thesis supervisor, Prof. S.K.
Choudhury. His guidance and support throughout the program has been a major factor in
the successful completion of the present work. This work would not have culminated into
the present form without his invaluable suggestions and generous help.
I am thankful to the faculty of IIT Kanpur for providing me with an excellent education
during my M.Tech and B.Tech program.
I am grateful to Mr. R.C. Sharma and the staff at the Central Workshop facility for
extending their utmost cooperation during the fabrication of the experimental set-up. I
would also like to thank Mr. B.S. Bhadauria, Mr. Sanjeev Verma and Mr. Virender Singh
of the Manufacturing Science lab for their help during the assembly and operation of the
set-up.
I am thankful to all my seniors and colleagues at the Manufacturing Science lab who not
only provided valuable suggestions and constant help during my work but also made my
stay at the lab an enjoyable experience.
Above all, I am forever thankful to my parents for their love and encouragement.
Sourabh Kumar Saha
Dedication
This work is dedicated to my parents.
Contents
List of Figures ix
List of Tables xii
Nomenclature xiv 1 Introduction 1
1.1 Introduction 1
1.2 Electric Discharge Machining 2
1.3 Dry Electric Discharge Machining 4
1.4 Literature Review 5
1.5 Aims and Objective of Current Work 10
2 Theoretical Background 12
2.1 EDM Discharge Phenomena 12
2.1.1 Phases of discharge 12
2.1.2 Effect of input parameters 14
2.2 Dielectric Medium in EDM 16
2.2.1 Functions of dielectric 16
2.2.2 Properties of dielectric 16
2.2.3 Types of dielectric 17
2.3 Mathematical Models 18
2.3.1 Model for MRR 18
2.3.2 Model for surface roughness 19
2.4 Design of Experiments (DOE) 21
2.4.1 DOE principles 21
2.4.2 Response Surface Methodology 22
2.4.3 Central Composite Design 23
2.5 Optimization 24
2.5.1 Optimization Terminology 24
2.5.2 Genetic Algorithms as Optimizers 24
2.5.3 Real parameter single objective GA 26
2.5.4 Multi-objective Optimization 27
2.5.5 Non-Dominated Sorting Genetic Algorithm II (NSGA II) 29
3 Experimental Set-up and Procedure30
3.1 Experimental Set-Up 30
3.1.1 EDM Machine 30
3.1.2 Dry EDM Unit Attachment 32
3.1.3 Spindle Rotation and High Pressure Air Source 35
3.1.4 Workpiece and Tool 36
3.2 Experimental Procedure 40
3.2.1 Conducting Experiments: Standardization 40
3.2.2 MRR and TWR Calculation 42
3.2.3 Surface Roughness measurement 43
4 Plan of Experiments and Genetic Algorithm (GA) Based
Optimization Strategy 44 4.1 Plan of Experiments 44
4.2 Exploratory Experiments 45
4.2.1 Parameter selection and range selection 45
4.2.2 One Variable At a Time (OVAT) 46
4.2.3 Tool face geometry 46
4.2.4 Depth of cut and Machining time 47
4.3 Parametric Analysis 48
4.3.1 CCD Coded Variables 48
4.3.2 CCD Modified Variables 49
4.3.3 Corrected Table 50
4.3.4 Response Surface and Regression Analysis 50
4.4 GA Based Optimization 52
4.4.1 Single Objective Optimization 52
4.4.2 Multi-objective Optimization 53
4.5 Focused Experiments 54
4.5.1 Finish cutting region 54
4.5.2 Rough cutting region 55
5 Results and Discussion 56
5.1 Exploratory Experiments 56
5.1.1 Depth of cut and machining time 56
5.1.2 One Variable At a Time (OVAT) 58
5.1.3 Tool face geometry 65
5.2 Parametric Analysis 68
5.2.1 CCD Observations 68
5.2.2 Regression analysis and Model fitting 71
5.2.3 Response surface analysis 78
5.3 GA based Optimization 85
5.3.1 Single objective optimization 85
5.3.2 Multi-objective optimization 90
5.4 Focused Experiments 93
5.4.1 Finish machining region 93
5.4.2 Rough machining region 97
5.5 Comparison with oil EDM 100
6 Conclusion 103
7 Scope for Future Work 105 References 107
Appendix A 109
ix
List of Figures Figure 1.1 Tool shape and corresponding cavity formed on workpiece after
EDM operation
3
Figure 1.2 Schematic of an Electric Discharge Machining (EDM) machine tool
4
Figure 1.3 Schematic of dry EDM process
5
Figure 2.1 Phases of a discharge during EDM. (a) Preparation phase (b) Discharge phase (c) Interval phase
13
Figure 2.2 Pareto-optimal front for multi-objective optimization of functions f1 and f2.
28
Figure 3.1
Idealized voltage pulse generated by the EDM machine power supply and the corresponding variation in current with time obtained during machining
31
Figure 3.2
Experimental Set-Up showing (a) Dry EDM spindle attachment (b) Machining in progress and (c) ZNC EDM machine
33
Figure 3.3 Dry EDM machine unit showing various parts
34
Figure 3.4 Formation of central core. (a) Machining with a centrally located single hole tube electrode (b) Machining with a non-centrally located multi-holed tube electrode
37
Figure 3.5 Insert-type tool electrode showing the tool shank and the insert
39
Figure 3.6 Single tube multiple-hole tool electrode with non-central holes
40
Figure 4.1
Tool face showing size and position of the non-central holes for air flow (a) one hole, (b) two holes 180o apart, (c) three holes 120o apart and (d) four holes 90o apart
47
Figure 5.1 Increase in depth of cut with time during machining
57
Figure 5.2 Effect of machining time on material removal rate and surface finish
58
Figure 5.3 Effect of discharge current on MRR and Ra 59
x
Figure 5.4 Effect of gap voltage on MRR and Ra
60
Figure 5.5 Effect of pulse-on time on MRR and Ra
61
Figure 5.6 Effect of pulse-off time on MRR and Ra
63
Figure 5.7 Effect of air inlet pressure on MRR and Ra
64
Figure 5.8 Effect of spindle speed on MRR and Ra
65
Figure 5.9 Effect of tool electrode outer diameter on MRR, TWR and Ra
66
Figure 5.10 Effect of number of holes in tool electrode on MRR and Ra
68
Figure 5.11 Response surface of MRR versus gap voltage and discharge current
79
Figure 5.12 Response surface of MRR versus gap voltage and pulse-on time
80
Figure 5.13 Response surface of MRR versus discharge current and duty factor setting
81
Figure 5.14 Response surface of MRR versus discharge current and air inlet pressure
81
Figure 5.15 Response surface of MRR versus discharge current and spindle speed
82
Figure 5.16 Response surface of MRR versus pulse-on time and duty factor setting
82
Figure 5.17 Response surface of Ra versus gap voltage and discharge current
84
Figure 5.18 Response surface of Ra versus pulse-on time and air inlet pressure
84
Figure 5.19 Variation in population best and population average with generation for maximization of MRR
86
Figure 5.20 Variation in population best and population average with generation for minimization of Ra
88
Figure 5.21 Variation of success rate of convergence with population size for minimization of Ra
90
xi
Figure 5.22 Pareto-optimal front for minimization of 1/MRR and Ra obtained by plotting the non-dominated solutions from NSGA II run
92
Figure 5.23 Effect of gap voltage on Ra in finish machining region
95
Figure 5.24 Effect of discharge current on Ra in finish machining region
96
Figure 5.25 Interaction plot for Ra in finish machining region
96
Figure 5.26 Effect of gap voltage on MRR in rough machining region
98
Figure 5.27 Effect of pulse-on time on MRR in rough machining region
99
Figure 5.28 Effect of pulse-off time on MRR in rough machining region
100
Figure 5.29 Comparison of dry EDM with oil die-sinking EDM 102
xii
List of Tables Table 2.1 Comparison of electrical, thermal and mechanical properties of
mineral oil, deionized water and air
17
Table 2.2 Parameters and their corresponding dimensions for dimensional analysis of surface roughness value
19
Table 3.1 Range of values available on the ZNC EDM machine on which experiments have been conducted
32
Table 4.1 Range of parameters over which experiments were conducted
46
Table 4.2 List of calculated parameter values corresponding to the coded levels in CCD
49
Table 4.3 List of actual parameter values used corresponding to the coded levels in CCD due to constraints on the available parameter setting values
49
Table 4.4 CCD run design table with the modified coded factor levels used for conducting experiments
50
Table 5.1 MRR, Ra and TWR observations of the CCD runs
69
Table 5.2 Sequential Model Sum of Squares for MRR
71
Table 5.3 Comparison of regression statistics for the full two factor interaction model and reduced two-factor interaction model for MRR
72
Table 5.4 Analysis of variance table for response surface reduced two-factor interaction model of MRR
73
Table 5.5 Sequential Model Sum of Squares for Ra
75
Table 5.6 Comparison of regression statistics for the reduced quadratic, reduced two-factor interaction, reduced linear and linear Ra models
76
Table 5.7 Analysis of variance table for response surface reduced quadratic model of Ra
76
Table 5.8 Sequential Model Sum of Squares for TWR 77
xiii
Table 5.9 Comparison of regression statistics for the reduced quadratic,
reduced two-factor interaction and linear TWR models
77
Table 5.10 Values of input parameters and response variables at the operating point corresponding to maximum MRR obtained through optimization
86
Table 5.11 Values of input parameters and response variables at the operating point corresponding to minimum Ra obtained through optimization
89
Table 5.12 MRR, Ra and input parameter values corresponding to the finish machining region obtained from Pareto-front analysis
93
Table 5.13 MRR, Ra and input parameter values corresponding to the rough machining region obtained from Pareto-front analysis
93
Table 5.14 Experimental observations for CCD runs in the finish machining region
94
Table 5.15 Experimental observations for factorial runs in the rough machining region
97
xiv
Nomenclature
D Duty factor setting
d Duty factor
dc Depth of cut (μm)
Es Energy of a single spark (J)
f Spark frequency (Hz)
Id Discharge current (A)
M, L, T Dimensions of mass, length and time respectively
MRR Material removal rate (mm3/min)
N Spindle rotational speed (rpm)
n Number of axial holes for gas flow in the tool electrode
P Gas inlet pressure (kgf/cm2)
Ra Center line average surface roughness (μm)
Ton Pulse-on time (μs)
Toff Pulse-off time (μs)
TWR Tool wear rate (mm3/min)
Vc Volume of discharge crater (mm3)
Vg Gap voltage (V)
W Input electric power during machining (W)
Greek symbols α, β, γ Exponents of electric power, pulse-on time and gas pressure in
dimensional analysis of surface roughness
αd Distance of axial points from the center point in central composite design
(CCD) of experiments
ηc, ηm Parameter values for SBX and polynomial mutation operators in GA
π1, π2, π3 Dimensionless π parameters in the dimensional analysis of surface
roughness
1
Chapter 1 Introduction and Literature Review
1.1 Introduction
Fuelled by a growing need for high strength materials in technologically advanced
industries and supported by the advances in the field of material science, there has
been an increase in the availability and use of difficult-to-machine materials. Non-
traditional machining processes are necessary for machining of such materials.
Electrical Discharge Machining (EDM) is one such process which is widely used to
machine electrically conductive materials. EDM is a thermo-electric process in which
material removal takes place through the process of controlled spark generation. It is
one of the most popular non-traditional machining processes being used today in the
industry. EDM is commonly used in mould and die making industry and in
manufacturing automotive, aerospace and surgical components. Since there is no
mechanical contact between the tool and the workpiece, thin and fragile components
can be machined without the risk of damage.
EDM has achieved a status of being nearly indispensable in the industry because of
its ability to machine any electrically conductive material irrespective of its
mechanical strength. Despite its advantages, environmental concerns associated with
the process have been a major drawback of EDM [1]. The dielectric fluid used in
EDM is the primary source of pollution from the process. Hydrocarbon based oils are
the most commonly used EDM dielectric. Dielectric wastes generated after
machining are very toxic and cannot be recycled. Also, toxic fumes are generated due
to high temperature chemical breakdown of dielectric during machining. The use of
oil as the dielectric fluid also makes it necessary to take extra precaution to prevent
fire hazards. Since an environment friendly alternative for replacing the EDM process
2
is not available, changing or totally eliminating the liquid dielectric medium provides
a feasible solution.
Deionized water has been used as a dielectric fluid for quite some time now.
However, process performance is generally found to decrease on using water as the
dielectric. Replacing liquid dielectric by gases is an emerging field in the
environment-friendly EDM technology [2-13]. High velocity gas flow through the
tool can be used to replace liquid dielectric. Such a dry EDM technology would leave
behind no toxic waste material. Experimental results demonstrating the feasibility of
the dry EDM process are available from a few research groups. However, literature in
this field is insufficient and further research is required to make this process
commercially feasible.
1.2 Electric Discharge Machining
Electric discharge machining is a thermo-electric non-traditional machining process.
Material is removed from the workpiece through localized melting and vaporization
of material. Electric sparks are generated between two electrodes when the electrodes
are held at a small distance from each other in a dielectric medium and a high
potential difference is applied across them. Localized regions of high temperatures
are formed due to the sparks occurring between the two electrode surfaces.
Workpiece material in this localized zone melts and vaporizes. Most of the molten
and vaporized material is carried away from the inter-electrode gap by the dielectric
flow in the form of debris particles. To prevent excessive heating, electric power is
supplied in the form of short pulses. Spark occurs wherever the gap between the tool
and the workpiece surface is smallest. After material is removed due to a spark, this
gap increases and the location of the next spark shifts to a different point on the
workpiece surface. In this way several sparks occur at various locations over the
entire surface of the workpiece corresponding to the workpiece-tool gap. Because of
the material removal due to sparks, after some time a uniform gap distance is formed
throughout the gap between the tool and the workpiece. Thus, a replica of the tool
surface shape is formed on the workpiece as shown in Figure 1.1. If the tool is held
3
stationary, machining would stop at this stage. However if the tool is fed continuously
towards the workpiece then the process is repeated and more material is removed.
The tool is fed until the required depth of cut is achieved. Finally, a cavity
corresponding to replica of the tool shape is formed on the workpiece.
Figure 1.1: Tool shape and corresponding cavity formed on workpiece after EDM
operation
The schematic of an EDM machine tool is shown in Figure 1.2. The tool and the
workpiece form the two conductive electrodes in the electric circuit. Pulsed power is
supplied to the electrodes from a separate power supply unit. The appropriate feed
motion of the tool towards the workpiece is generally provided for maintaining a
constant gap distance between the tool and the workpiece during machining. This is
performed by either a servo motor control or stepper motor control of the tool holder.
As material gets removed from the workpiece, the tool is moved downward towards
the workpiece to maintain a constant inter-electrode gap. The tool and the workpiece
are plunged in a dielectric tank and flushing arrangements are made for the proper
flow of dielectric in the inter-electrode gap.
Typically in oil die-sinking EDM, pulsed DC power supply is used where the tool is
connected to the negative terminal and the workpiece is connected to the positive
terminal. The pulse frequency may vary from a few kHz to several MHz. The inter-
electrode gap is in the range of a few tens of micro meter to a few hundred micro
meter. Material removal rates of up to 300 mm3/min can be achieved during EDM.
4
The surface finish (Ra value) can be as high as 50 μm during rough machining and
even less than 1 μm during finish machining.
Figure 1.2: Schematic of an Electric Discharge Machining (EDM) machine tool
1.3 Dry Electric Discharge Machining
Dry Electric Discharge Machining (dry EDM) is a modification of the oil EDM
process in which the liquid dielectric is replaced by a gaseous dielectric. High
velocity gas flowing through the tool electrode into the inter-electrode gap substitutes
the liquid dielectric. The flow of high velocity gas into the gap facilitates removal of
debris and prevents excessive heating of the tool and workpiece at the discharge
spots. Providing rotation or planetary motion to the tool has been found to be
essential for maintaining the stability of the dry EDM process. The dry EDM process
schematic is shown in Figure 1.3. Tubular tools are used and as the tool rotates, high
velocity gas is supplied through it into the discharge gap. Gas in the gap plays the role
of the dielectric medium required for electric discharge. Also, continuous flow of
fresh gas into the gap forces debris particles away from the gap. Tool rotation during
5
machining not only facilitates flushing but also improves the process stability by
reducing arcing between the electrodes.
Figure 1.3 Schematic of dry EDM process [4]
Dry EDM is an environment-friendly EDM technique because of the absence of
mineral oil-based liquid dielectric. Environmentally harmful oil-based dielectric
wastes are not produced in dry EDM. Also, the process does not pose a health hazard
since toxic fumes are not generated during machining. Additionally, absence of
mineral oil-based dielectrics drastically reduces fire hazards during the process.
1.4 Literature Review
It is conventional wisdom in the EDM community that a liquid dielectric is essential
for conducting EDM operation. The first reference to dry EDM can be found in a
1985 NASA Technical report [2]. It is briefly reported that argon and helium gas
were used as dielectric medium to drill holes using tubular copper electrode. Further
details are however not available. Later in 1991, Kunieda et. al. [3] showed that
introducing oxygen gas into the discharge gap improves MRR in a water based
dielectric medium. It was in 1997 that the feasibility of using air as the dielectric
medium was first demonstrated by Kunieda et al. [4]. High velocity gas jet through a
thin walled tubular electrode was used to serve the purpose of a dielectric. Further
research in this field has brought out some of the essential features of the process. It is
now known that some of the advantages of the dry EDM process are: low tool wear,
lower discharge gap, lower residual stresses, smaller white layer and smaller heat
6
affected zone [4-7]. Also, several studies have been made to improve the performance
of the process [8-13]. However, the knowledge base in dry EDM is still limited to
such an extent that an accurate prediction of process performance is not possible for a
given set of input variables. The relevant literature and its significance in dry EDM
research have been discussed below.
The work by Kunieda et. al. [3] not only demonstrated that EDM in gaseous medium
is possible but also brought out some of the advantages of the process. Their work
showed that high velocity gas flow through tool electrode reduces debris reattachment
after a spark, thus considered to be effective in flushing. The debris reattachment is
much lower for a thin walled tube and this increases the MRR. It was found that the
probability of short circuits reduces when rotation or planetary motion is given to the
tool electrode. It was also shown that the tool wear ratio (TWR) is almost zero in dry
EDM. MRR is shown to increase when oxygen gas is used and it is suggested that the
heat generated by oxidation is responsible for the increased MRR. Dry EDM was
applied to 3D machining using an NC tool path and precise machined shapes were
obtained. It was also observed by them that the MRR increases when the
concentration of oxygen in the dielectric gas mixture is increased.
The effect of tool rotation on MRR, tool wear and surface finish has been
experimentally studied in oil-die sinking EDM by Soni et al. [14]. Experiments were
conducted with a rotating copper-tungsten tool electrode for oil die-sinking EDM of
titanium workpiece. Designed experiments were conducted to compare rotary EDM
with stationary tool EDM. It was found that rotation of the tool leads to a higher
sparking efficiency and a better flushing of debris from the discharge gap
consequently leading to a higher MRR. However, a poorer surface finish was
obtained with a rotating tool. It was also observed that a statistically significant effect
of tool rotation on tool wear did not exist.
Kunieda et. al. [5] proposed that dry EDM is not only a thermal process but also a
chemical process. With oxygen gas used as the dielectric medium, three distinct
modes of material removal were observed depending on the discharge power density:
normal mode, quasi-explosion mode and explosion mode. Thermally activated
oxidation of workpiece material becomes uncontrolled at very high discharge powers
7
leading to uncontrolled arcing in the explosion mode. In the quasi-explosion mode
there is no discharge delay time and the oxidation reaction is controllable since the
reaction stops as soon as the power is switched off. The material removal rate during
quasi-explosion mode was found to be as high as in a conventional milling process;
however the tool wear was still low. Also, an alternate ‘intake method’ of gas supply
in the gap was proposed for improving the accuracy. Instead of supplying gas through
the hollow tool electrode, gas was sucked into the tool electrode in the ‘intake
method’.
Yu et. al. [6] demonstrated the effectiveness of the dry EDM method in machining of
cemented carbide. Dry EDM was used for groove milling and three- dimensional
milling. Copper-tungsten tubes were used as tool electrodes and high velocity oxygen
gas was used as the dielectric. Dry EDM performance was compared to oil die
sinking EDM and oil EDM milling. It was found that dry EDM milling produces the
smallest form deviation due to very low tool wear ratio. The machining speed in dry
EDM is higher than for oil milling EDM but lower than oil die-sinking EDM.
However, it was argued that the total time required for making multiple electrodes in
die-sinking EDM puts it at a disadvantage to dry EDM milling. Fewer tool electrodes
are required in dry EDM due to lower tool wear. The total machining time for dry
EDM may then be lower than die-sinking EDM.
Kunieda et. al. [7] have used a piezoelectric actuator to improve the dry EDM
characteristics by controlling the discharge gap distance. The workpiece was mounted
on a piezoelectric element and the control signal to the element was provided by a
feedback from the actual average gap voltage. The element had a high frequency
response (natural frequency of 500MHz) and the control system was responsible for
providing the displacement command signal to the piezoelectric element.
Experiments were conducted with the piezo control. It was found that presence of the
actuator leads to a reduction in the arcing probability and increases the MRR by
improving the stability of the process. The arcing probability and MRR improvement
were also predicted through simulation of the process. It was found that the
simulation over-estimates the performance improvement. From simulations it was
also found that conventional is stable enough even in the absence of the piezoelectric
8
servo system. Based on experiments and simulation it was found that monotonous
oscillations (such as a sine wave) of the piezo element were not as advantageous in
improving process stability as the servo control system.
Zhanbo et. al. [8] demonstrated the feasibility of 3D surface machining using dry
EDM. The developed process was used for micromachining applications. Parametric
analysis was done to observe the effect of gas pressure, depth of cut, pulse duration,
pulse interval and rotational speed of tool electrode on MRR and tool wear ratio
(TWR). It was found that optimum conditions exist for gas pressure, depth of cut and
pulse duration for achieving maximum MRR and minimum TWR. It is suggested that
at high gas pressure debris removal is enhanced, however frequent short circuits were
observed for very high pressure values. MRR is found to saturate to a constant value
for tool rotational speeds above 500 RPM. At very low RPM values, frequent short
circuits occur due to poor debris removal. The dry EDM process has been used for
EDM milling and contouring on micro scales.
Zhang et. al. [9] and Zhang et. al. [10] proposed an improvement over dry EDM by
introducing ultrasonic vibrations to the workpiece. A mathematical model for MRR in
terms of process parameters (open voltage, discharge current, pulse duration and
pulse interval) was also developed. It was experimentally found that MRR increases
with decrease in tool wall thickness and increase in open voltage, pulse duration,
discharge current and amplitude of ultrasonic vibration. It was also found that surface
roughness increases with pulse duration. Surface roughness however does not show
any clear dependence on amplitude of vibration or tool wall thickness. This work
presented ultrasonic EDM in gas however it failed to compare the performance of dry
UEDM with liquid-dielectric EDM processes.
The dry EDM process has been used for precision wire EDM (WEDM) cutting by
Kunieda et. al [11]. Lower reaction forces and electrostatic forces are produced
during dry WEDM as compared to conventional WEDM with water. Dry WEDM
was performed with brass wire in the atmosphere without any external dielectric
supply to the discharge gap. WEDM experiments were performed with water as
dielectric and in the dry conditions. Effects of current, wire winding speed and depth
of cut on MRR, straightness, surface roughness, waviness and gap length were
9
investigated. It was found that better straightness of cut and surface finish is obtained
in dry WEDM and the gap length is narrower in dry WEDM. In addition, no over-cut
was observed in dry WEDM because of smaller distortion and vibration of the wire.
However, it was found that the waviness and the MRR were poorer in dry WEDM
due to frequent short circuiting. Improving the frequency response of the wire feed
control has been suggested to reduce short circuiting. From the experiments it was
also found that increasing the wire winding speed and decreasing the depth of cut
could lead to an improvement in MRR and waviness.
Kao et. al. [12] have further investigated the dry WEDM process for thin work pieces.
Experiments were carried on with different workpiece materials and it was found that
workpiece thickness, melting temperature and heat capacity had significant effect on
machinability. Dry WEDM experiments were performed using a copper electrode
wire in stationary air or with an assisting air jet. Experiments were performed to
investigate the effects of duty factor, pulse-on time, air flow rate and workpiece
thickness on MRR, groove width, debris deposition and the rate of spark, arc and
short pulses. Analysis of the measured voltage and current was done to identify the
spark, arc and short pulses. Lower values of MRR were obtained in dry WEDM, but
the MRR could be slightly improved by the use of air flow. It was found that MRR
reduces with an increase in the workpiece thickness and the workpiece melting
temperature. The MRR was found to be related to the rate of spark, arc and short
pulses.
Very recently, Tao et. al. [13] have experimentally investigated the dry and near dry
EDM process. A two phase gas-liquid mixture was used as the dielectric medium in
near dry EDM. Commercially available rotary spindle with through-spindle flushing
capability was used for implementing dry and near dry EDM. The effect of discharge
current, pulse-duration, pulse interval, gap voltage and open circuit voltage was
investigated at constant values of gas pressure and tool rpm by using a 25-1 fractional
factorial designed experiment. Separate set of input parameter values and tool-
dielectric combinations were identified for finish and rough machining. It was found
that copper tool and oxygen gas dielectric with a high current and low pulse off time
were suitable for rough machining with a high MRR. Graphite tool and water-
10
nitrogen gas mixture was found to give a better surface finish. Low current, low
pulse-on time and high pulse-off time was found to be suitable for finishing
operations. Ra values, as low as 0.8 μm, have been reported in the near dry EDM
finishing conditions.
1.5 Aims and Objectives of Current Work
From the available literature it can be seen that EDM in gas is a feasible process. It is
also fairly established that high velocity gas flow through the tool electrode and
rotation of tool are essential for the dry EDM process. Apart from being an
environment friendly process, dry EDM also has additional performance advantages
in precision cutting. However, the current literature in the field is still insufficient in
order to make dry EDM a commercially viable process. Suitable process models for
accurately predicting the process performance (such as material removal rate and
surface finish) for a given set of input parameters are still not available. A limited
knowledge base in parametric analysis makes it difficult to choose input process
parameter values for obtaining a high performance. Also, sufficient work is lacking in
the area of dry EDM process optimization.
The current work aims to develop a machining unit for dry EDM, perform parametric
analysis using experimental results, develop empirical models for performance
variables and finally to optimize the process using Design of Experiments (DOE) and
Genetic Algorithm (GA) methods.
In the current work, an independent machining unit has been designed and developed
for implementing the dry EDM process on an existing oil EDM machine. The unit has
been designed to satisfy the basic requirements for dry EDM, i.e. high velocity gas
flow through a rotating tubular tool. Parametric analysis has been done by conducting
a set of experiments using air as the dielectric medium. Effect of the input parameters
such as gap voltage, discharge current, pulse-on time, duty factor, inlet air pressure
and spindle speed on material removal rate (MRR) and surface finish (Ra) has been
studied. An empirical model for MRR and Ra has then been developed by conducting
a designed experiment based on the Central Composite Design (CCD). Genetic
algorithm (GA) based multi-objective optimization has been done by using the
11
developed empirical models for MRR and Ra. Optimization results have been used
for identifying the parameter values corresponding to rough and finish machining
conditions. For verification of the empirical models and the optimization results,
focused experiments have been conducted in the rough and finish machining regions.
Finally, a comparison of the process performance in dry EDM and oil EDM has been
made.
12
Chapter 2 Theoretical Background 2.1 EDM Discharge Phenomena
2.1.1 Phases of discharge
The discharge process during EDM can be separated into three main phases [15].
They are: preparation phase, discharge phase and interval phase. Details of each
phase are discussed below.
Preparation phase
On switching on the power supply, electric field is set-up in the gap between the
electrodes. The electric field reaches maximum value at the point where the gap
between the electrodes is smallest. Spark location is determined by the gap
distance and the gap conditions. In the presence of electrically conductive
particles in the gap, thin particle bridges are formed. When the strength of the
electric field exceeds the dielectric strength of the medium, electric breakdown of
the medium takes place. Ionization of the particle bridges takes place and a
plasma channel is formed in the gap between the electrodes. The steps in the
phase are shown in Figure 2.1 (a).
Discharge phase
During the discharge phase (Figure 2.1 (b)), a high current flows through the
plasma channel and produces high temperature on the electrode surfaces. This
creates very high pressure inside the plasma channel creating a shock wave
distribution within the dielectric medium. The plasma channel keeps
continuously expanding and with it the temperature and current density within
the channel decreases. Plasma channel diameter stabilizes when a thermal
13
Figure 2.1: Phases of a discharge during EDM. (a) Preparation phase
(b) Discharge phase (c) Interval phase
equilibrium is established between the heat generated and the heat lost to
evaporation, electrodes and the dielectric. This enlarged channel is still under
high pressure due to evaporation of the liquid dielectric and material from the
electrodes. The evaporated material forms a gas bubble surrounding the plasma
14
channel. During this phase, high energy electrons strike the workpiece and the
positively charged ions strike the tool (for negative tool polarity). Due to low
response time of electrons, smaller pulses show higher material removal from the
anode where as, longer pulses show higher material removal from the cathode.
Interval phase
The plasma channel de-ionizes when power to the electrodes is switched off. The
gas bubble collapses and material is ejected out from the surface of the electrodes
in the form of vapors and liquid globules. The evaporated electrode material
solidifies quickly when it comes in contact with the cold dielectric medium and
forms solid debris particles which are flushed away from the discharge gap.
Some of the particles stay in the gap and help in forming the particle bridges for
the next discharge cycle. Power is switched on again for the next cycle after
sufficient de-ionization of dielectric has occurred. The steps in the phase are
shown in Figure 2.1 (c).
2.1.2 Effect of input parameters
Based on the discharge phenomena discussed above, the effect of various input
parameters on material removal rate (MRR) and surface roughness (Ra) is
discussed below.
Discharge Current
The discharge current (Id) is a measure of the power supplied to the discharge
gap. A higher current leads to a higher pulse energy and formation of deeper
discharge craters. This increases the material removal rate (MRR) and the surface
roughness (Ra) value. Similar effect on MRR and Ra is produced when the gap
voltage (Vg) is increased.
Pulse-on time
Machining takes place only during the pulse-on time (Ton). When the tool
electrode is at negative potential, material removal from the anode (workpiece)
takes place by bombardment of high energy electrons ejected from the tool
15
surface. At the same time positive ions move towards the cathode. When pulses
with small on times are used, material removal by electron bombardment is
predominant due to the higher response rate of the less massive electrons.
However, when longer pulses are used, energy sharing by the positive ions is
predominant and the material removal rate decreases. When the electrode
polarities are reversed, longer pulses are found to produce higher MRR.
Pulse-off time
A non-zero pulse off time is a necessary requirement for EDM operation.
Discharge between the electrodes leads to ionization of the spark gap. Before
another spark can take place, the medium must de-ionize and regain its dielectric
strength. This takes some finite time and power must be switched off during this
time. Too low values of pulse-off time may lead to short-circuits and arcing. A
large value on the other hand increases the overall machining time since no
machining can take place during the off-time.
The surface roughness is found to depend strongly on the spark frequency. When
high frequency sparks are used lower values of Ra are observed. It is so because
the energy available in a given amount of time is shared by a larger number of
sparks leading to shallower discharge craters.
Gas Pressure
Apart from the electrical parameters, pressure of the gaseous dielectric may have
an effect on the process performance during dry EDM. Velocity of the gas jet
(Figure 1.3) is directly proportional to the inlet gas pressure. A high velocity gas
jet would lead to better flushing of debris from the discharge gap thus improving
the MRR and Ra values. Forced flow of gas also helps in reducing the time
required for recovery of dielectric strength of the medium since fresh and
previously non-ionized medium is continuously supplied to the gap. This leads to
higher process stability. Also, it is found that the dielectric strength of air is
dependent on the pressure and increases with an increase in the pressure. This
favors an increase in the MRR of the process.
16
Tool rotation
Tool electrode rotation is commonly used in small-hole EDM drilling operations.
Tool rotation improves flushing and leads to a more uniform electrode wear. The
effects of improved flushing are an increased MRR and lower Ra value. At the
same time, process stability increases because tool rotation makes it easier to
introduce fresh dielectric into discharge gap as the used up dielectric is thrown
out due to the centrifugal force. Thus, even with low pulse off times and poor
flushing conditions good machining performance is obtained.
2.2 Dielectric Medium in EDM
2.2.1 Functions of dielectric
Dielectric fluid plays an important role in the EDM process. Because of a high
dielectric strength, the dielectric medium prevents premature discharge between
the electrodes until a low discharge gap is established between them. Continuous
dielectric flow in the discharge gap helps in carrying away the debris formed
during the discharge and ensures a proper flushing. Also, dielectric medium cools
the machining zone by carrying away excess heat from the tool electrode and the
workpiece.
2.2.2 Properties of dielectric
The most important properties of dielectric are its dielectric strength, viscosity,
thermal conductivity and thermal capacity. Dielectric strength characterizes the
fluid’s ability to maintain high resistivity before spark discharge and the ability
to recover rapidly after the discharge. High dielectric strength leads to a lower
discharge gap which in turn leads to a low gap resistance. Hence, high discharge
currents may flow leading to a higher material removal rate. Also, fluids with
high dielectric strength need lower time for the recovery of dielectric strength.
Thus, low pulse-off times are sufficient. This not only improves the MRR but
also provides better cutting efficiency because of a reduced probability of arcing.
Liquids with low viscosity generally provide better accuracies because of a better
17
flow ability of the oil leading to improved flushing. Also, the sideward expansion
of the discharge plasma channel is restricted by high viscosity fluids. This
focuses the discharge energy over a small region and leads to a deeper crater
which reduces the surface finish. [4]. Dielectric fluids with high thermal
conductivity and thermal heat capacity can easily carry away excess heat from
the discharge spot and lead to a lower thermal damage.
2.2.3 Types of dielectric
Selection of dielectric medium is an important consideration for EDM
performance. Mineral oils are commonly used as the dielectric medium for die-
sinking EDM operations. Mineral oils exhibiting high dielectric strength and a
low viscosity are preferred because of their higher performance. For safety
reasons oils with a high flash point are usually used. Kerosene is one such oil
which is used commonly for EDM. Water based dielectrics are used almost
extensively for wire EDM operations. Water has a high specific heat capacity
which leads to a better cooling effect required for wire cut operations. To prevent
chemical reactions, deionized water is used in such applications.
Table 2.1: Comparison of electrical, thermal and mechanical properties of mineral oil, deionized water and air
Dielectric Strength
Dynamic Viscosity
Thermal Conductivity
Specific heat capacity
Properties Medium (MV/m) g/m-s W/m-K J/g-K Kerosene 14-22 1.64 0.149 2.16 Deionized water
13 0.92 0.606 4.19
Air 3 0.019 0.026 1.04
In comparison to mineral oils and water, air has the lowest dielectric strength,
viscosity, thermal conductivity and thermal capacity as shown in Table 2.1. A
low viscosity air medium favors higher cutting accuracy and better surface finish.
However, low dielectric constant suggests a lower MRR with air medium. Low
thermal capacity and thermal conductivity suggests higher thermal damage of
workpiece. However, for a complete analysis of the thermal damage an opposing
18
effect caused by the expansion of plasma channel due to low viscosity must also
be accounted. Thus, overall it seems that using air as dielectric may be a better
alternative for improving some of the process performance such as surface finish
and accuracy at the expense of the MRR.
2.3 Mathematical Models
2.3.1 Model for MRR
Material removal rate (MRR) refers to the amount of material removed from the
workpiece per unit time. It can be estimated in terms of the electrical parameters
as: the amount of material removed per spark multiplied by the number of sparks
per unit time. The amount of material removed per spark is proportional to the
volume of the discharge crater (Vc). The volume of discharge crater depends on
the spark energy (Es). This gives:
1
1 is the proportionality constant., c sV k E
Where k=
(2.1)
The spark energy is given by:
s g d onE V I T= (2.2)
Assuming that one spark occurs over each pulse-on time, the spark frequency (f)
is given by:
1
on off
fT T
=+
(2.3)
Since,
is the proportionality constant.,
g d on
on off
MRR fVcV I T
MRR kT T
Where k
=
∴ =+
(2.4)
Effect of the non-electrical parameters such as inlet gas pressure (P) and spindle
rpm (N) is included in the proportionality constant ‘k’.
19
It is interesting to note at this stage that Eq. 2.3 may not give an accurate estimate
of spark frequency for a rotating tool. For stationery tool EDM, spark can occur
continuously throughout the spark-on time and the assumption that only one spark
occurs over a pulse-on time can be justified. However, for a rotating tool the spark
may be interrupted due to the movement of the tool during the pulse-on time.
Under such circumstances, several short sparks may occur over a single spark-on
time, at locations where the instantaneous spark gap is lowest. Thus the spark
frequency may be much higher than given by Equation 2.3. Such an anomaly
would be more pronounced at higher pulse-on times and Equation 2.3 is expected
to be in reasonable agreement with experiments at low pulse-on time values.
2.3.2 Model for surface roughness
Roughness of the surface obtained after performing dry EDM is quantified by the
center line average roughness value (Ra). The functional dependence of Ra on
the parameters can be estimated by performing a dimensional analysis based on
the Buckingham π theorem. With six parameters and three dimensions: mass
(M), length (L) and time (T), three dimensionless π parameters would be
required. The parameters and their corresponding dimensions are shown in Table
2.2. The basis chosen for dimensional analysis is: (W, Ton, P).
Table 2.2: Parameters and their corresponding dimensions for dimensional analysis of surface roughness value
Parameter Symbol Unit Dimension Surface roughness Ra μm L
Electric power W(=Vg*Id) watt ML2T-3 Pulse-on time Ton μs T Pulse-off time Toff μs T Gas pressure P kgf/cm2 ML-1T-2 Spindle rpm N rpm T-1
20
The π parameters can be represented as:
( )1 1 1
2 2 2
3 3 3
1
2
3
: , ,on
on
on off
on
basis W T P
W T P Ra
W T P T
W T P N
α β γ
α β γ
α β γ
π
π
π
=
=
= (2.5)
Substituting the dimensions for each parameter and equating dimensions on both
sides of the equations gives:
( ) ( )
( ) ( )( ) ( )
1 1 1
2 2 2
3 3 3
1, , 1, 1,13
, , 0, 1,0
, , 0,1,0
α β γ
α β γ
α β γ
= − −
= −
=
Thus, the dimensionless π parameters are: 1
3
1
2
3
g d on
off
on
on
P RaV I T
TTT N
π
π
π
⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠
=
= (2.6)
Representing π1 as a function of π2 and π3 and substituting for the π parameters
gives:
( )1 2 3
13
,
,g d on offon
on
f
V I T TRa f T N
P T
π π π=
⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠ (2.7)
21
Volume of the discharge crater is proportional to the spark energy and the depth
of crater scales as 1/3rd of the crater volume. Hence, surface roughness is
expected to be proportional to cube root of current and voltage. Dimensional
analysis yields a similar dependence of Ra on Vg and Id. Eq. (2.7) also shows that
the Ra value decreases with an increase in the gas inlet pressure (P). Additional
information (such as from experiments) is required to obtain the exact form of
the function ‘f’.
2.4 Design of Experiments (DOE)
2.4.1 DOE principles
Design of Experiments (DOE) refers to planning, designing and analyzing an
experiment so that valid and objective conclusions can be drawn effectively and
efficiently [16]. In performing a designed experiment, changes are made to the
input variables and the corresponding changes in the output variables are
observed. The input variables are called factors and the output variables are
called response. Factors may be either qualitative or quantitative. Qualitative
factors are discrete in nature (such as type of material, color of sample). Each
factor can take several values during the experiment. Each such value of the
factor is called a level. A trial or run is a certain combination of factor levels
whose effect on the output is of interest. It is convenient to represent the high
level value of a factor as +1 and the low level value as -1, and transforming all
the factors into the same [-1 1] coded range. It is essential to incorporate
statistical data analysis methods in the experimental design in order to draw
statistically sound conclusions from the experiment. Some of the advantages of
DOE over One-Variable-At-a-Time approach (OVAT) are that a DOE approach
enables to separate the important factors from the unimportant ones by
comparing the factor effects. Also, interaction effects among different factors can
be studied through designed experiments.
22
2.4.2 Response Surface Methodology
Response Surface Methodology (RSM) is a collection of statistical and
mathematical techniques useful for developing, improving and optimizing
processes [17]. RSM is useful for the modeling and analysis of experiments in
which a response of interest is influenced by several variables and the objective
is to optimize this response.
Consider a process where the response variable (output) y depends on the
controllable (input) variables x1, x2, …, xk. The relationship is:
1 2( , , , )ky f x x x= … (2.8)
The true form of the response variable y is seldom known for a process. In RSM,
the true relationship between y and the independent variables is generally
approximated by the lower-order polynomial models such as:
(2.9)
Here, the βs are the unknown parameters. These parameters are estimated by first
collecting data on the system and then performing statistical model building by
using regression analysis. Response surface designs are special types of
experimental designs which are commonly used for the data collection phase.
Polynomial models are generally linear functions of the unknown βs. Hence
linear regression is used for the model building phase.
A linear regression model may be written in matrix notation as:
0 1 1
20
1 1
Where ε represents the statistical error term
k kk k
i i ii i ij i ji i i j
y x x
y x x x x
β β β ε
β β β β ε= = <
= + + + +
= + + + +∑ ∑ ∑
23
( )
( ) ( )
11 1
1
1 2 n
0 1 0 1
1
, y , , y
1
, , , , , ,
,
,
k
n nk
T
T Tk n
x
y
x
Wherex
x
y X
y X
β β β ε ε εβ
β ε
ε
= +
⎛ ⎞⎜ ⎟= = ⎜ ⎟⎜ ⎟⎝ ⎠
= =
…
(2.10)
In general, y is an (n x 1) vector of the responses, X is an (n x p) matrix of the
levels of the independent variables, β is a (p x 1) vector of the regression
coefficients and ε is an (n x 1) vector of random errors, with p=k+1.
The least square estimate of the β parameters is: 1( )' 'b X X X y−= (2.11)
The fitted regression model is: ^y Xb= (2.12)
2.4.3 Central Composite Design
The central composite design (CCD) is one of the most popular classes of
designs used for a second-order model. CCD designs comprise a set of two-level
factorial points, axial points and center runs. The factorial points contribute to the
estimation of linear terms and two-factor interactions. Factorial points are the
only points which contribute to estimation of the interaction terms. The axial
points contribute to the estimation of quadratic terms. In the absence of axial
points, only the sum of the quadratic terms can be estimated. The center runs
provide an internal estimate of pure error and contribute towards the estimation
of quadratic terms.
The number of factorial runs depends on the type of factorial design used and the
number of factors. A minimum design resolution of V is required for the factorial
fraction. For a full factorial, there are 2k factorial points. The number of axial
points is 2k and the number of center runs (nc) depends on the number of factors.
24
For up to four factors, three to five center runs are sufficient. Higher number of
center runs is preferable if there are more than four factors.
The axial points lie at a distance of ± α from the center point (zero level for all
factors). The value of α generally varies from 1 to √k. In the coded space, axial
points are obtained by taking ± α level for one factor and the zero level for all
other factors. Thus, there are 2k axial points, two points (one +α and one -α) for
each factor. Each factor is varied over five levels: ± α (axial points), ± 1
(factorial points) and the center point.
2.5 Optimization
2.5.1 Optimization Terminology
Optimization is the process of finding the minimum or maximum of a function
by systematically choosing the values of the variables from within an allowed
set. The function which has to be optimized is called the objective function and
the variables on which the objective function depends are called the parameters.
The possible set of values of the parameters forms the search space. In addition if
there are any constraints then they must also be satisfied by the optimum
solution.
Optimization can be considered to be a ‘search’ process wherein we are
interested in finding that particular solution (out of the entire search space) which
makes the objective function minimum or maximum. Classical optimization
methods are primarily of two types: direct and gradient based search methods. In
direct search methods, only objective function and constraint values are used to
guide the search strategy, where as gradient-based methods use the first and/or
second-order derivatives of the objective function and/or constraints to guide the
search process.
2.5.2 Genetic Algorithms as Optimizers
Genetic algorithm (GA) is a subclass of population based stochastic search
procedure which is closely modeled on the natural process of evolution with
25
emphasis on breeding and the survival of the fittest. Instead of starting with a
single point, the algorithm starts with a set of initial solutions. Also, instead of a
deterministic result at each iteration, GA operators produce probabilistic results
leading to stochasticity. Proper search direction can be provided to the GA by
simulating the natural process of evolution. In the process of evolution the
organisms which are better able to adapt to the environment have a higher chance
of survival. This leads to a higher chance of breeding for such organisms and an
increased probability of their traits being carried over to the next generation
through their offspring. Thus a trait which leads to a better organism has higher
chances of making it to the next generation. Moreover, due to mating of two
different organisms with better fitness leads to intermixing of favorable traits
which hopefully would lead to better offspring. In case the new members are
poorer, they would be lost in the next generation. At the same time, it is
important to maintain diversity in the population so that potentially important
regions of the search space are not eliminated during the initial stages.
To keep a track of which traits are favorable and which are not, traits are coded
in the form of genetic material which is stored in a chromosome. Due to selection
of better traits and intermixing, eventually the entire population has the same
chromosome set which is also the best possible trait combination.
To incorporate the idea of natural evolution GA must have the following
essential features:
a) Encoding of solution: To keep track of favorable solutions
b) Assigning fitness to a solution: To determine the chances of survival of the
solution
c) Selection operator: To select the fit solutions for mating
d) Crossover or Recombination operator: For mixing of traits through mating of
two different solutions
e) Mutation operator: Random variations in encoded solutions to obtain new
solutions
26
f) Survivor operator: To determine the members which die off and those which
go to the next generation
These operators are responsible for providing the search direction to a GA.
Selection operator selects good solutions and crossover operator recombines
good genetic material from two good solutions to (hopefully) form a better
solution. Mutation operator alters a string locally to (hopefully) create a better
string. If bad strings are created they are be eliminated by the reproduction
operator in the next generation and if good strings are created, they are
emphasized.
2.5.3 Real parameter single objective GA
In real parameter GA, solutions are represented as real numbers instead of using
a binary string representation. Real parameter GA has an edge over binary coded
GA because of the higher precisions possible through real parameter
representations. Also, problems such as hamming cliff are not present in a real
parameter GA [18].
The selection and survivor operators require no modification for real
representations. However, modified crossover and mutation operators are
necessary to handle real parameters. Simulated binary crossover (SBX) is one of
the cross-over operators used for real parameters. SBX imitates the working
principle of a binary crossover in real paradigm. The operator produces two
children from two parent solutions by generating a random cross-site lying
between the two parents. The nearness of the cross-site to the parents is
determined by the factor ηc. A large value of ηc produces children nearer to the
parents indicating a higher degree of recombination. Polynomial mutation
operator is used to implement mutation for real parameters. Similar to the SBX
operator, a mutated solution is obtained from a parent solution by generating a
random number and using a polynomial probability distribution. This mutation
operator creates a mutated child in the vicinity of a parent. The nearness of the
child to the parent is determined by the factor ηm. A large value indicates that the
27
child is nearer to the parent. Details of the SBX and polynomial mutation
operator have been discussed by Deb [18-19].
2.5.4 Multi-objective Optimization
When two or more objective functions are simultaneously optimized, the
resulting optimization problem is called a multi-objective optimization problem.
Generally such problems consist of conflicting objectives so that it is not possible
to obtain a single solution which is optimum in all the objectives. For example,
during optimization of machining cost and product quality it is not possible to
obtain a solution which is better in both cost and quality. If only cost is
optimized, the quality suffers and vice-versa. Instead of a single optimum
solution, a set of optimum solutions exists in such cases. Such set of optimum
solutions is called as the Pareto-Optimal set.
As opposed to the single objective optimization, in multi-objective optimization
optimality criterion can seldom be in the form of a single point which is
minimum (or maximum) in all the objectives. Instead, optimality is expressed in
terms of Pareto-optimality. A solution S1 is said to be Pareto-optimal if there is
no other solution S2 which dominates the solution S1. A solution A dominates a
solution B, if it is better than B in at least one objective function and not worse
with respect to all other objective functions. The set of all Pareto-optimal points
is called the Pareto set and the front so obtained is called the Pareto front.
A Pareto front is shown in Figure 2.2 for minimization of the objective functions
f1 and f2. Each box represents a feasible solution. From the figure it can be seen
that solution A is better than B in f1 and not worse than B in f2. Hence solution A
dominates solution B. Solution A is better than S1 in f1 but poorer than S1 in f2.
Neither of them dominates each other, nor are there any other feasible solutions
which dominate them. Hence, both S1 and A lie on the Pareto front.
28
Figure 2.2: Pareto-optimal front for multi-objective optimization of functions f1
and f2.
The main aim of a multi-objective optimization algorithm is to obtain the Pareto-
optimal set. One of the simplest strategies is to convert the multi-objective
problem into a single objective optimization problem. One method is to use a
weighted sum of all the objectives as the single objective function: *
1 1 2 2
*
1 2
1 2
Where,f is the resultant single objective functionf and f are the objective functionsand w , w are the respective weight
f w f w f
s
= +
(2.13)
By using different weights and performing several single objective optimizations,
different points on the Pareto-front can be obtained. However, a good distribution
of points along the front is not guaranteed.
29
By using evolutionary algorithms (such as GA), one can simultaneously obtain
several points along the entire Pareto-front with an evenly distributed Pareto
points along the front.
2.5.5 Non-dominated Sorting Genetic Algorithm II (NSGA II)
Non-dominated Sorting Genetic Algorithm II (NSGA II) is a multi-objective
evolutionary algorithm based on non-dominated sorting [20]. The algorithm uses
elitist non-dominated sorting along with crowding distance sorting to obtain the
non-dominated set. The algorithm is capable of handling constrained multi-
objective optimization problems with binary coding and real parameters. It uses
the SBX crossover operator and polynomial mutation. The appropriate objective
function in terms of the variables is coded in the algorithm. The algorithm
produces the non-dominated set out of the entire population after a specific
number of generations. Members of Pareto-front belong to the non-dominated set
which is obtained on convergence of the algorithm.
30
Chapter 3 Experimental Set-Up and Procedure 3.1 Experimental Set-Up
3.1.1 EDM Machine
All the experiments have been conducted on a Z numerically controlled (NC) oil
die-sinking EDM Machine, (R50 #ZNC). The EDM Machine is of Elektra,
Electronica Machine Tools India make. In this machine, the Z axis is servo
controlled and can be programmed to follow an NC code which is fed through
the control panel. The servo control feedback is based on the gap voltage
between the tool and the workpiece electrodes. As machining takes place, the
tool is fed into the workpiece to maintain a constant gap voltage, and this
determines the gap distance. The gap distance cannot be independently controlled
on this machine. The X and Y axes are manually controlled. All three axes have
an accuracy of 5μm. The machining time is displayed online during machining
and is updated after every minute. Through an NC code, machining can be
programmed to occur up to a fixed depth of cut. Alternately, sparks can be
stopped manually after the desired time interval of machining has elapsed.
The power supply system produces a DC pulsed power in the frequency range of
0.07 – 300 kHz. The pulse can be represented as shown in Figure 3.1. The pulse
has been idealized by considering the pulse delay time as negligibly small. The
pulse can be defined in terms of the gap voltage (Vg), discharge current (Id),
pulse-on time (Ton) and pulse-off time (Toff). An additional parameter, duty factor
(d) can be represented in terms of the pulse on and off times as:
31
on
on off
TdT T
=+
(3.1)
Figure 3.1: Idealized voltage pulse generated by the EDM machine power supply and the corresponding variation in current with time obtained during machining
The control panel allows independent control of the gap voltage, discharge
current, pulse on time and the duty factor. Corresponding to each Ton value, duty
factor can be set to values between 8% and 96% in steps of 8%, subject to the
maximum and minimum frequency limitations of the power supply. The duty
factor is set by changing the duty factor position (D) on the control panel.
Where:
8%d D= ×
(3.2)
During machining actual (time-average) values of discharge current and gap
voltage can be read on the corresponding analog meters on the control panel.
32
During machining arcing is sensed internally by the control system through an
analysis of the current pulse. Power is switched off during a pulse if arcing is
sensed. Anti-arc sensitivity determines the average percentage of arcing pulses
for which power is switched off. If the anti-arc sensitivity is set to a low value
then power is switched off for a higher fraction of arcing pulses. The range and
least count of various electrical parameters available on the machine are shown
in Table 3.1.
Table 3.1: Range of values available on the ZNC EDM machine on which
experiments have been conducted
Parameter Range In steps of Gap Voltage 20 – 100 V 1 V
Discharge Current 1 – 50 A 1 A
Pulse on time
1 – 2000 μs Available values:
1,2,5,10,20,30,50,75,100,150,200, 300,500,750,1000,2000 μs
Duty factor position 1-12 1 (each step corresponding to 8%) Anti-Arc Sensitivity 1-10 1 (each step corresponding to
10%)
3.1.2 Dry EDM Unit Attachment
To enable performing the dry EDM process on existing EDM machines (which
were originally designed for liquid dielectric only), a dry EDM unit attachment
has been designed and developed. The dry EDM unit along with the ZNC EDM
machine on which it is mounted is shown in Figure 3.2. The unit has been
designed to fulfill the basic requirements of dry EDM: rotating tool and high
velocity gas flow through tubular tool. Additionally, the entire arrangement is in
the form of an independent unit which can be attached to existing EDM machines
to perform dry EDM without any modifications in the existing machines.
The dry EDM unit comprises a hollow spindle shaft supported on the flange of a
cylindrical support through a pair of bearings. The shaft can rotate relative to the
support cylinder. An O-ring sealing is provided at one of end of the shaft and a
tool holder is mounted at the other end for holding tubular tools. The motor for
spindle rotation is mounted on the support cylinder and power is transmitted
33
from the motor through a belt-pulley system. Channel for high pressure gas flow
is made in the support cylinder. A tube transfers this gas from the support
cylinder channel into the shaft-bore through the O-ring seal. The tubular tool
mounted at the shaft end receives this high pressure gas while rotating relative to
the support cylinder.
Various parts of the attachment are shown in Figure 3.3. The dry EDM spindle
can be functionally divided into five units. The functional units are:
a) Main Support Structure
b) Spindle Shaft
c) Gas Inlet Unit
d) Drive Unit
e) Tool Holding Unit
Figure 3.2: Experimental Set-Up showing (a) Dry EDM spindle attachment (b) Machining in progress and (c) ZNC EDM machine
34
Main support structure
The main support structure consists of a cylindrical frame which can be attached
to the machine spindle through bolts. The main body of the dry EDM spindle is
attached separately to this cylindrical structure. The main body consists of the
spindle shaft which is supported axially through a pair of deep groove ball
bearings. The shaft has a passage for gas through it.
Spindle shaft
The spindle shaft is in the form of a hollow cylinder. The shaft is rotated relative
to the main support cylinder frame while high velocity gas is passed through it.
Tubular tool electrode is mounted at the lower end of the shaft.
Figure 3.3: Dry EDM machine unit showing various parts
35
Gas inlet unit
The gas inlet unit ensures that there is a path for continuous supply of high
pressure gas through the shaft during rotation. Gas inlet into the system is
through a channel made in the main support cylinder. At the end of this channel a
gas inlet tube is fitted to the cylinder. The gas inlet tube fits into the end of the
shaft through the O-ring seal. The O-ring groove is designed for rotating shaft
dynamic sealing [21]. This ensures a leak-free gas inlet into the rotating shaft.
Drive unit
Rotation to the shaft is provided by an electric motor. A 200W (at 1800 rpm) DC
motor has been used to allow for continuous speed control from 300 rpm to 2250
rpm. Since the spindle moves along the vertical direction relative to the ground
frame (during machining) due to the feed motion, the motor has to be supported
on the spindle itself. The motor is side mounted on a platform which is joined to
the main support structure, effectively forming a cantilever support frame for the
motor. Power is transmitted from the motor to the spindle through a belt-pulley
arrangement.
Tool holding unit
Tubular electrodes are used as the tool for dry EDM. The tool electrode is held in
a collet chuck. For a leak free entry of gas from the spindle into the tool, an
adapter is used which fits at the end of the shaft passage. One end of the adapter
opens to the passage in the shaft and the other end has a tapered hole. The tool
electrode sits on this tapered end.
3.1.3 Spindle Rotation and High Pressure Air Source
Spindle shaft is rotated by a DC motor which is mounted on the spindle itself.
Continuous speed control in the range 300-2250 rpm is possible on the motor
through a thyristor based control system. A rheostat control is provided on the
motor control unit which can be used to increase or decrease the motor speed by
changing the input voltage to the motor. Before starting with the experiments, the
36
control unit is calibrated and the motor speeds corresponding to various rheostat
positions are marked against it. During calibration, a mechanical tachometer (of
least count 10 rpm) has been used to measure the motor RPM corresponding to a
particular position of the rheostat.
High pressure air is obtained from an ELGI make screw air compressor (E11-7.5)
which has a built-in air drier. The compressor has a rated pressure of 7 kgf/cm2
and a capacity of 1.81 m3/min. At the inlet to the EDM machine a maximum
gauge pressure of 2.5 kgf/cm2 is obtained. At the inlet, an air regulator with a
regulation range of 0-10 bars has been used. A Bourdon tube pressure gauge with
a least count of 0.1 kgf/cm2 is used to monitor the inlet pressure to the dry EDM
unit.
3.1.4 Workpiece and Tool
Experiments are conducted on EN32 mild steel (density 7.8 g/cm3) workpiece
using a copper (density 8.9 g/cm3) tool. The workpiece is in the form of a thin
strip of dimensions 75 mm x 20 mm x 5 mm. Small sized work pieces are used
for ease of weight measurement on the balance. Tool electrode is in the form of a
tube such that high velocity gas flows through it. The tool design is discussed in
detail in the following sections.
Initial Tool Design: Single hole tube
During the exploratory experimental stage, experiments were first conducted
using a thin walled tubular electrode with a centrally located single hole. It is
found that use of such a tool leads to a central core formation during machining.
The tube is shown in figure 3.4. Machining takes place only along the tube walls
and no material is removed from the workpiece regions corresponding to the
tube-central hole.
37
Figure 3.4: Formation of central core. (a) Machining with a centrally located single hole tube electrode (b) Machining with a non-centrally located multi-holed tube electrode For a through hole machining, formation of the central core during machining
does not pose any serious problem because eventually the central core falls off
when the hole-drilling is complete (similar to material removed during the
trepanning operation). However, in such a case it is not possible to get an
accurate MRR value for the process by using the weight measurement MRR
calculation method used here. The material removed as the central core also adds
to the MRR, but this material removal is not purely by the dry EDM process.
Thus, a parametric study done for dry EDM process would not be accurate due to
this “trepanning type material removal” contribution.
When a blind hole is made using a single-hole tube, the central core remains on
the workpiece. Due to its presence it is not possible to take surface roughness
measurements on the bottom surface of the hole. To take measurements of the
bottom surface of the hole it is important to eliminate the central core.
Insert-type multi-hole tool
In order to prevent the formation of a central core, a tube with non-central holes
is used. Due to tube rotation the entire surface is exposed to sparks and no central
core is formed. Due to the difficulty in manufacturing such tubes with high
38
aspect ratio drilled holes, an insert type tool can be used, where a major portion
of the tool (tool shank) consists of a tube with a large central hole and at the end
of this tube, a cylindrical insert with non-central axial holes is fitted. The insert
type tool is shown in figure 3.5.
There are two major problems with the insert type tools. First, if the axes of the
outer cylindrical surface and the central hole in the main tube do not coincide
(i.e. if the central hole is eccentric), then the insert would rotate eccentrically.
Secondly, the gas-sealing at the insert-main tube junction poses a problem. It is
not easy to ensure sealing at the junction without going for elaborate arrangement
such as screw-threading or a proper press fit.
Single tube, multi-hole tool
Similar to the insert type tool, a single tube tool with non-central holes can be
manufactured easily if the length of the non-central holes is small. Small non-
central holes are drilled in a solid cylinder from one end. These holes open into a
larger central hole which is drilled into the cylinder from the other end. The tool
is shown in figure 3.6. This tool design has been selected for conducting the
experiments. The top portion of the tool is made to the size of the holding collet.
The outer diameter of the lower portion is determined by the diameter of the hole
to be drilled.
39
Figure 3.5: Insert-type tool electrode showing the tool shank and the insert
The major problem with a single tube electrode is the large amount of material
and time required for manufacturing the electrodes. It is observed that material is
deposited on the tool during machining. Ideally each EDM operation should be
carried on with a new tool electrode to take care of this effect. With the single
tube design, a large number of electrodes would be required. Making such a tool
requires more time and material than an insert type tool.
To minimize the effect of debris which gets attached on the tool after machining,
the tool face and sides are cleaned using emery cloth before starting a new
experiment. This removes the deposited layer from the surface of the tool.
40
Figure 3.6: Single tube multiple-hole tool electrode with non-central holes
3.2 Experimental Procedure
3.2.1 Conducting Experiments: Standardization
Several controllable parameters such as the gap voltage discharge current, pulse-
on time, duty factor position, air inlet pressure and spindle speed have been
considered for analysis during the project. However, many other parameters
which may have an effect on the output have not been studied. Some of these
may be beyond our control (such as environmental conditions: room temperature
and humidity). However it may be possible to control some of them (such as Z
41
motor sensitivity and anti-arc sensitivity). During the experiments it is essential
to keep such parameters at some preset values so that data obtained from
different runs are comparable. To ensure this, the following minimum standard
has been maintained throughout all the experiments. Wherever necessary (and
possible), extra precaution has been taken. The protocol is explained below:
For setting inlet gas pressure value
(a) The tool is first fixed in the spindle and the workpiece is fixed in the
fixture. The machine zero is then set and values of all electrical parameters are
fed to the control panel.
(b) Motor for spindle rotation is started and the RPM value is approximately
set to the desired value (using the calibration markings on the motor speed
controller).
(c) The inter-electrode gap is set to 2mm. It was observed that the pressure
value (value indicated on pressure gauge) changed on changing the inter-
electrode gap. The pressure value becomes more or less constant when the gap
is more than 2 mm.
(d) Gas inlet valve is then switched on and the desired gas pressure is set
using the regulator.
For making/finding zero gap tool position
(a) First the tool and workpiece are set.
(b) The tool is the brought near the workpiece surface and motor sensitivity
value of ‘2’ is selected. Motor sensitivity value determines the speed of the servo
controlled Z-axis motor during the feed motion of the spindle. The speed of Z-
axis motor is inversely proportional to the motor sensitivity value. Thus for a
value of ‘1’, the speed is low and for a value of ‘10’ the speed is high. During
sparking if the motor speed is too high it leads to instability due to frequent
arcing. Hence the sensitivity value is set to as low as possible. However, it was
observed that sometimes the servo motor was unable to produce enough starting
torque at ‘1’ setting and the spindle did not move along the Z axis. Hence the next
42
higher value (setting ‘2’) was chosen. The motor speed along Z axis is 40
mm/min at this setting.
(c) The ‘APOS’ operation was then selected on the machine control panel to
set the machine zero.
For starting machining operation
(a) First the tool and workpiece are set
(b) Machining zero (zero inter-electrode gap position) is then set
(c) Gas inlet pressure value is then set
(d) Spindle rpm is then verified by using a tachometer
(e) The tool-workpiece gap is then to a preset value (=250 μm) and Z-motor
sensitivity value of ‘2’ is selected. It is important to standardize the initial gap
value since MRR may depend on it. It is found that typically the spark gap in dry
EDM is less than 100 μm. If the starting gap is set to a very high value, the
machine takes a long time before the tool-workpiece gap reduces to spark gap
value and machining starts. On the other hand, a very small value may lead to
arcing or short circuit. Hence the starting gap is set to an intermediate value of
250 μm.
(f) Finally, the ‘SPARK’ operation is selected on the control panel to start
machining.
3.2.2 MRR and TWR Calculation
Material removal rate is calculated by measuring the loss in weight of the
workpiece after machining. The initial and final weights of the workpiece are
measured on Afcoset electronic balance (FX-400) having a resolution of 0.001 g.
The weight material removal rate (MRRg) is then converted into volumetric
material removal rate (MRRv) by knowing the density of the workpiece material.
An alternate method of MRR calculation is by measuring the depth of cut and
then multiplying it with the area of cross-section of the cut. However, such a
method may lead to faulty values if a constant area of cross-section is assumed
since it is expected that the drilled section would be tapered. On the other hand,
43
the weight loss method of MRR calculation gives the actual material removed
during machining. Hence this method has been used for calculating the MRR.
The weight loss method is also used for obtaining the tool wear rate. The tool is
weighed before and after machining on the same balance as that used for the
workpiece. The weight TWR is converted into the volumetric TWR by knowing
the density of tool material.
3.2.3 Surface Roughness measurement
Blind holes have been made by EDM during the experiments and the surface
roughness of the end surface of the holes has been measured. The center line
average (CLA) surface roughness parameter, Ra has been used to quantify the
surface roughness of the machined surface. Ra (JIS 2001 standard) has been
measured using a contact type stylus based surface roughness tester, Mitutoyo
Surftest SJ-301. Gaussian digital filter has been used for surface profile analysis
using the instrument. The cut-off length is 0.8 mm and the evaluation length is 4
mm. Ra is measured along three different lines on the surface and the average
value is considered for further analysis.
44
Chapter 4 Plan of Experiments and Genetic Algorithm (GA) Based Optimization Strategy 4.1 Plan of Experiments
Experiments have been conducted in three stages:
a) Exploratory experiments
b) Parametric Analysis
c) Focused experiments and model verification
Before starting with a systematic set of experiments, some exploratory experiments
were conducted to select suitable parameters for the later stage DOE experiments and
to select appropriate values of other controllable variables. The effect of machining
time and tool geometry on MRR and Ra was also studied during this stage.
Additionally an OVAT (One Variable At a Time) analysis was done to have a
preliminary idea about the effect of machining parameters on MRR and Ra.
A set of designed experiments based on central composite rotatable design (CCD)
was then conducted to systematically study the effect of various process parameters
and their interaction effects on MRR and Ra. Response surface analysis was done
using the experimental data. Along with the response surface analysis, CCD designs
allow for a regression analysis of the parameters up to the second order (including the
quadratic terms). The data obtained from the CCD runs was used to fit a model of
MRR and Ra in terms of the six parameters: gap voltage (Vg), discharge current (Id),
pulse-on time (Ton), duty factor setting (D), inlet gas pressure (P) and spindle
rotational speed (N).
Based on the regression models obtained from the DOE runs, Genetic Algorithm
(GA) based optimization has been done to obtain the optimum machining conditions.
45
First, single objective optimizations were done by separately considering MRR and
Ra as the objective functions. Then, a multi-objective optimization has been done by
considering 1/MRR and Ra as the two objectives (minimization). Real parameter GA
has been used for single objective optimization and NSGA II has been used for multi-
objective optimization.
GA based multi-objective optimization provides a Pareto-Optimal curve. Points lying
on this curve can be considered to be optimum in both the objectives. Out of the
entire curve, the two end-regions are especially important. One end of the curve
represents the rough machining region and the other end represents the finish
machining region as discussed in Section 3.5. Next stage experiments were now
focused only in these two regions. By keeping some of the non-critical parameters at
a constant level, experiments were conducted to verify the optimization results and
the model adequacy specific to the region.
Details of the methodology in each step are discussed in the following sections.
4.2 Exploratory Experiments
4.2.1 Parameter selection and range selection
Out of the several controllable parameters available on the control panel of the
EDM machine, Vg, Id, Ton and D were chosen as the input parameters. The
idealized pulse shown in Figure 3.1 can be completely represented in terms of
these four parameters. The Z-motor sensitivity was set to ‘2’ and the anti-arc
sensitivity was set to 50%. It was found that material removal from workpiece
occurred when a reverse polarity was used (i.e. workpiece as negative terminal
and tool as positive terminal). Hence, all the experiments were conducted with
reverse polarity. In addition to the electrical parameters, air inlet pressure (P) and
spindle rotational rpm (N) were also considered among the input variables. The
upper limit of all the parameters is restricted by the machine capabilities. For
determining the lower limit of the parameters, first an average value of all the
parameters was chosen. Then one variable was considered at a time and it was
reduced until no visible sparks were observed. The existence of sparks could be
verified by the current reading on the control panel. When no sparking takes
46
place, the ammeter on the EDM control panel displays zero current value. The
range of parameter values obtained by this procedure is shown in Table 4.1.
Table 4.1: Range of parameters over which experiments were conducted
Parameter Minimum value
Maximum Value
In steps of
Voltage, Vg (volt) 50 100 1 Current, Id (ampere) 8 50 1 Pulse on time, Ton (μs)
5
2000
Available values: 5,10,20,30,50,75,100,150,200,
300,500,750,1000,2000 μs Duty factor position, D 1 12 1 (each step corresponding to 8%) Gas pressure, P (kgf/cm2) 0.5 2.5 0.1 Spindle speed, N (rpm) 300 2250 Continuous variable
Average parameter values for OVAT Analysis: Vg = 60 V, Id = 26 A, Ton = 500 μs, D = 6, P = 1.5 kgf/cm2, N = 1300 rpm
4.2.2 One Variable At a Time (OVAT)
Initial parametric studies of MRR and Ra have been made by considering one
variable at a time. By keeping all other variables at fixed average values (values
shown in Table 4.1), one variable at a time was varied and its effect on MRR and
Ra studied. Experiments were conducted for five different values of the variable.
Although the OVAT analysis does not give a clear picture of the phenomena over
the entire range of the input parameters, it can highlight some of the important
characteristics. This may be helpful in reducing the number of variables or
restricting the range of the variables in later stage experiments.
4.2.3 Tool face geometry
The effect of tool face geometry on MRR and Ra was investigated and the
optimum values were used for later stage experiments. The tool face geometry is
shown in Figure 4.1. Only two parameters have been changed here: the tool outer
diameter (OD) and the number of holes (n) for air flow. The radial position and
size of the holes was kept constant. All the holes were of 2 mm diameter and
47
made on a pitch circle diameter of 5 mm. First, the tool outer diameter was
changed keeping the number and size of the holes constant (4 holes, 2 mm each).
Best among these was then chosen and experiments were conducted for different
number of holes, keeping the outer diameter constant. Based on the results of
these experiments, the tool face geometry (OD and n) for later stage experiments
was chosen.
Figure 4.1: Tool face showing size and position of the non-central holes for air flow (a) one hole, (b) two holes 180o apart, (c) three holes 120o apart and (d) four holes 90o apart
4.2.4 Depth of cut and Machining time
The depth of cut was measured as the depth of tool penetration into the
workpiece during machining. It is expected that the depth of cut would increase
linearly with time during machining. Experiments were conducted to verify this
and a suitable time interval for machining was chosen such that a linear trend is
observed. However, the MRR is expected to depend on the machining time as the
area of cross-section changes during machining. Experiments were conducted to
select a suitable machining time based on the MRR obtained for different
machining times.
48
4.3 Parametric Analysis
4.3.1 Central Composite Design Coded Variables
In order to conduct a designed experiment based on the Central Composite
Design (CCD), it is necessary to represent the input parameters into the same
range [-1 1]. This is done by a simple linear mapping from the actual values to
the coded values. In the coded space, high level of an input parameter is
represented as +1 and the low level is represented as -1. Hence, the mapping
function is:
( )21
VV LLCV
HL LL−
= −−
(4.1)
Where,
CV=Coded ValueVV=Variable ValueHL=High Level value of variableLL=Low Level value of variable
Apart from the high and low levels, zero level (center point) and ± αd levels
(axial points) are also included in CCD (Section 2.4.3). Value of αd depends on
the number of factors. For six factors, a small practical value of αd =1.56508 was
chosen. The high and low level values of the factors were chosen such that the
± αd values were within the controllable range of the variables. Levels of the
coded variables in CCD and the corresponding parameter values calculated using
the above formula are shown in Table 4.2.
49
Table 4.2: List of calculated parameter values corresponding to the coded levels in CCD
-1.565
-1
0
+1
+1.565
Coded Levels Parameter
Voltage, Vg (volt) 55.09 63 77 91 98.91 Current, Id (ampere) 8.66 16 29 42 49.34 Pulse on time, Ton (μs) 44.6 200 475 750 905.4 Duty factor position, D 1.3 3 6 9 10.7 Gas pressure, P (kgf/cm2) 0.56 0.9 1.5 2.1 2.44 Spindle speed, N (rpm) 296.88 650 1275 1900 2253.12
4.3.2 CCD Modified Variables
Due to machine and hardware constraints on the available ranges and least count
of parameter values, all the parameter values corresponding to the coded levels in
CCD design may not be available. Hence, in case of unavailability of the exact
values, the nearest possible parameter value was used for conducting the
experiments. The parameter values corresponding to the ± 1 level were the true
values. For the axial and center points, the nearest feasible parameter setting was
used. The actual parameter values used for generating the design matrix are
shown in Table 4.3
Table 4.3: List of actual parameter values used corresponding to the coded levels in CCD due to constraints on the available parameter setting values
Modified
-αd
-1
Modified
0
+1
Modified
+αd
Coded Value Parameter
Voltage, Vg (volt) 55 63 77 91 99 Current, Id (ampere) 9 16 29 42 49 Pulse on time, Ton (μs) 50 200 500 750 1000 Duty factor position, D 1 3 6 9 11 Gas pressure, P (kgf/cm2) 0.6 0.9 1.5 2.1 2.5 Spindle speed, N (rpm) 300 650 1275 1900 2250
50
4.3.3 Corrected Table
Using the parameter settings shown in Table 4.3, the design table (in terms of
coded parameter values) for 6 factors, full factorial CCD with 10 central runs is
shown in Table 4.4.
4.3.4 Response Surface and Regression Analysis
Analysis of the experimental results has been done using the Design Expert 7.0.0
software. The software was first used for model fitting. The CCD design is
capable of quadratic model fitting. Hence, first a quadratic fitting of MRR and Ra
was done. Analysis of Variance (ANOVA) based statistical tests were performed
to determine the suitability of the fitted model.
Several models such as linear, linear with first-order interaction terms and
quadratic models could be fitted using the software. Each one of them was tested
to obtain the highest F-value for model significance F-test. Values of various
regression statistics have been compared to select the most suitable model.
Additionally, not all terms in the fitted model may have significant effects. In
such a case, the fitting can be improved by removing some of the terms [17].
This was done by a step wise model fitting. Here, a backward step-wise model
fitting has been used.
Table 4.4: CCD run design table with coded levels of the parameter values used for conducting experiments
Run Order
Vg Id Ton D P N
1 1 -1 -1 1 1 -1 2 -1 1 -1 1 1 1 3 -1 -1 -1 -1 -1 -1 4 1 1 1 -1 1 -1 5 1 -1 -1 1 -1 -1 6 -1 -1 1 1 1 -1 7 -1 -1 1 1 -1 -1 8 0 0 0.091 1.667 0 0
51
Run Order
Vg Id Ton D P N
9 1 1 1 1 -1 -1 10 -1 -1 -1 -1 1 -1 11 1 -1 1 1 -1 1 12 -1.571 0 0.091 0 0 0 13 0 0 0.091 0 0 0 14 1 1 1 -1 -1 -1 15 -1 -1 -1 -1 -1 1 16 -1 -1 -1 -1 1 1 17 -1 1 -1 -1 1 1 18 -1 -1 -1 1 -1 1 19 1 -1 -1 -1 1 -1 20 -1 1 -1 -1 -1 1 21 0 0 0.091 0 0 0 22 -1 1 1 1 1 1 23 -1 1 -1 1 -1 1 24 1 1 -1 1 -1 -1 25 0 1.538 0.091 0 0 0 26 1 1 -1 -1 1 1 27 1 -1 -1 -1 -1 -1 28 1 -1 -1 -1 -1 1 29 -1 1 1 -1 1 1 30 1 1 1 -1 -1 1 31 0 0 -1.545 0 0 0 32 -1 -1 -1 1 -1 -1 33 1 -1 1 -1 1 -1 34 1 1 1 -1 1 1 35 0 0 0.091 0 -1.5 0 36 0 0 0.091 0 0 0 37 -1 -1 -1 1 1 -1 38 -1 1 1 1 -1 1 39 -1 1 -1 1 1 -1 40 1 -1 1 1 1 -1 41 0 0 0.091 0 0 0 42 -1 -1 1 1 -1 1 43 0 0 1.909 0 0 0 44 0 0 0.091 0 0 1.56 45 -1 1 1 1 1 -1 46 1 -1 1 1 -1 -1 47 1 1 -1 -1 -1 -1 48 1 -1 1 -1 -1 1 49 1 -1 -1 1 1 1 50 -1 -1 1 -1 -1 -1 51 0 0 0.091 0 0 0
52
Run Order
Vg Id Ton D P N
52 1 1 -1 -1 1 -1 53 0 -1.538 0.091 0 0 0 54 0 0 0.091 0 0 0 55 -1 1 1 -1 1 -1 56 0 0 0.091 0 0 0 57 1 1 -1 1 1 -1 58 0 0 0.091 0 0 0 59 1 -1 1 -1 -1 -1 60 -1 1 1 -1 -1 -1 61 1 1 -1 1 1 1 62 -1 1 1 1 -1 -1 63 0 0 0.091 0 0 0 64 1 -1 1 1 1 1 65 0 0 0.091 -1.667 0 0 66 1 1 1 1 -1 1 67 1 1 1 1 1 1 68 -1 1 -1 -1 1 -1 69 1.571 0 0.091 0 0 0 70 1 1 1 1 1 -1 71 1 -1 -1 -1 1 1 72 0 0 0.091 0 1.667 0 73 1 -1 1 -1 1 1 74 0 0 0.091 0 0 0 75 -1 1 -1 1 -1 -1 76 -1 1 -1 -1 -1 -1 77 1 -1 -1 1 -1 1 78 0 0 0.091 0 0 -1.56 79 -1 1 1 -1 -1 1 80 1 1 -1 1 -1 1 81 -1 -1 1 -1 1 1 82 1 1 -1 -1 -1 1 83 -1 -1 1 -1 -1 1 84 -1 -1 1 -1 1 -1 85 -1 -1 -1 1 1 1 86 -1 -1 1 1 1 1
4.4 GA Based Optimization
4.4.1 Single Objective Optimization
A real parameter genetic algorithm has been used to obtain the optimum MRR
and the optimum Ra separately. Tournament selection, simulated binary cross-
53
over (SBX) and polynomial mutation have been used as the selection, cross-over
and mutation operators respectively. Source codes available from Prof.
Kalyanmoy Deb’s Kangal laboratory homepage [22] were used. Maximization of
MRR and minimization of Ra were considered as two separate optimization
problems. Regression models obtained from the CCD experimental runs were
used as the objective functions. Variable bounds were taken from the ranges of
parameters used in the CCD runs. It was observed that for some values of
parameters, the MRR model predicts a negative value. Hence the constraint,
MRR>0 was also considered in the optimization problem.
Parameters for GA have been obtained by a series of trial-run tests. As the rule of
thumb suggests the population size to be equal to ten times the number of
variables, GA was run with a safer value of the population size of 100. For the
first set of runs, average values for SBX and polynomial mutation parameter
were taken (2, 10). GA was run 20 times up to 100 generations and the results
were observed to see if converged solution is obtained and whether the
converged solution is same in each run. GA is run for higher generation if no
convergence is observed. Plot of population best with generation was used to
select the generation for subsequent tests. If the same converged solution is not
obtained in all the runs, the SBX and mutation parameters are changed and the
process repeated. Typically, premature convergence suggests decreasing the
mutation parameter in polynomial mutation and increasing the population size. A
highly different value of converged solution among the different runs suggests
increasing the SBX cross-over parameter value.
The program reports the best member among the population and the generation
number when the best member is obtained. Value of the objective function and
the parameter values corresponding to the optimum point are also reported by the
program.
4.4.2 Multi-objective Optimization
By considering MRR and Ra values at the same time a multi-objective
optimization can be done. This was done by using the NSGA II algorithm
54
developed by Deb et al. [20]. Source codes available from Prof. Kalyanmoy
Deb’s Kangal laboratory homepage [22] were used. The NSGA II algorithm
gives the non-dominated points in the population. The program is coded for
minimizing the objective functions. Hence, Ra and 1/MRR were taken as the two
objective functions. Regression models for MRR and Ra were used for
representing the objective functions in terms of the input parameters.
GA parameters for NSGA II were also found by a series of trial-run tests similar
to those done for single objective optimizations. The number of generations is
same as that in the single objective GA runs. Population size is determined by the
number of points desired along the Pareto front. Population size was set to 400
here. The SBX and mutation parameter values were first set to average values
(10, 15). The points on the extremes of the Pareto front were compared to the
results of single objective optimization. If the results do not match, the parameter
values were increased.
4.5 Focused Experiments
4.5.1 Finish machining region
From the results of the multi-objective optimization, separate regions for
finishing and roughing conditions can be identified. The points which lie along
the extreme end on the Pareto front corresponding to the low Ra values form the
finish machining region. Out of the total points forming the Pareto front, 2.5% of
the points starting from the finish machining end have been considered as
forming the finish machining region.
To experimentally confirm the optimization results and to improve upon the
model in the focused finishing region, another set of DOE based experiments
have been conducted. Parameters which have the same value all long the Pareto-
front were kept fixed to those values during the experiments. Additionally, range
of other parameters may be enhanced to the extent allowed by machine
constraints.
55
4.5.2 Rough cutting region
In a manner similar to identification of the finish machining region, the rough
machining region was identified as the region near the Pareto front extreme end
corresponding to high MRR values (low 1/MRR values). 2.5% points starting
from this end were considered to form the roughing region. Experiments similar
to the finish machining region were conducted to verify and improve the
experimental model in the rough machining region.
56
Chapter 5 Results and Discussion 5.1 Exploratory Experiments
Exploratory dry EDM experiments (as discussed in Sections 3.2 and 4.2) were
conducted by drilling blind holes in mild steel workpiece using a rotary cylindrical
copper tube with multiple non-central holes for air flow. Results obtained from the
experiments are discussed in the subsequent sections.
5.1.1 Depth of cut and machining time
For a particular set of input parameters, machining was done and the position of
the tool face was recorded at regular time intervals. The variation of depth of cut
with machining time is shown in Figure 5.1. From the figure it can be seen that
the depth of cut increases linearly with time when sufficient cutting has taken
place. However, for the first few minutes of machining, the depth of cut depends
on the second power of the machining time. Based on the information derived
from this figure it was concluded that experiments must be conducted for at least
8-10 minutes before stable cutting conditions can be achieved. It can also be seen
from the 2nd order polynomial fitting function that the depth of cut
corresponding to t=0 is negative. This negative value of depth of cut denotes the
electrode gap distance at the start of machining.
57
Figure 5.1: Increase in depth of cut with time during machining
The effect of machining time on MRR and Ra is shown in Figure 5.2. Three
experiments were conducted corresponding to each machining time and the
average values of MRR and Ra are shown in the figure. It can be seen that MRR
increases with an increase in the machining time. This effect can be attributed to
the side-cutting taking place along the cylindrical face of the tool. As machining
progresses, material is not only removed from the bottom surface of the hole in
the workpiece but also from the sides of the hole. As machining takes place,
more of the tool penetrates into the hole being machined in the workpiece and the
length over which side-cutting takes place increases. This increases the MRR
with machining time. Additionally, with reference to Figure 5.1, stable
machining conditions are not established during the first few minutes of
machining and the depth of cut increases quadratically with time. This explains
the steep rise in MRR when machining time increases from 5 minutes to 10
minutes. For machining times greater than 10 minutes, the increase in MRR is
less steep. Effect of machining time on Ra values is not as prominent since side-
58
cutting does not significantly affect the surface finish of the bottom surface of the
hole.
Figure 5.2: Effect of machining time on material removal rate and surface finish
Based on the information derived from Figures 5.1 and 5.2, machining time for
later stage experiments was set to 10 minutes. Each experiment was conducted
for 10 minutes and the weight loss after machining was used to calculate the
MRR.
5.1.2 One Variable At a Time (OVAT)
Effect of the input process parameters on the responses was studied by changing
one parameter at a time while all others were held constant. One experiment was
performed at each level of the parameter.
59
Effect of current
The effect of discharge current on MRR and Ra is shown in Figure 5.3. As
expected, MRR was found to increase with an increase in the current. The spark
energy increases with current which leads to higher crater volumes. Thus MRR
increases with current. However, Ra values remain almost constant with increase
in current. For higher currents, the crater volume may increase either due to an
increase in the depth of the crater or the diameter of the crater or due to an
increase in both of these. The Ra value is more sensitive to the crater depth as
compared to the crater diameter. Hence, if with an increase in current, the size of
crater is affected more than the depth of crater then the effect of increased current
would not be observed clearly on the Ra values.
Figure 5.3: Effect of discharge current on MRR and Ra
Effect of voltage
The effect of gap voltage on MRR and Ra is shown in Figure 5.4. Initially MRR
increases with an increase in voltage but an optimum exists and the MRR drops
with further increase in voltage. A similar trend was observed for Ra values which
decrease up to an optimum point and then increase with voltage. Since spark
60
energy is proportional to the gap voltage (Equation 2.2), increase in voltage would
lead to a higher MRR. The decrease in Ra values with an increase in voltage
suggests that larger but shallower craters are formed at higher voltage values.
Discharge takes place when the effective electric field (=gap voltage/inter-
electrode distance) between the electrodes exceeds the dielectric strength of the
medium. Hence, with an increase in the gap voltage the discharge gap distance
increases and the breakdown electric field can now be achieved even at a larger
gap distance. The effective gas velocity at the workpiece surface is lower when
the gap distance is high. Thus, flushing efficiency reduces and the probability of
arcing increases due to the presence of debris in the tool-workpiece gap. Due to
partial removal of debris from the discharge gap, low MRR and a high Ra value
was obtained at very high voltages. Thus an optimum value of voltage exists at
which high MRR and low Ra value was obtained.
Figure 5.4: Effect of gap voltage on MRR and Ra
61
Effect of pulse-on time
The effect of pulse-on time on MRR and Ra is shown in Figure 5.5. It can be
seen that MRR and Ra values both increase with an increase in the pulse-on time.
The spark energy depends on Ton (Equation 2.2). For a higher Ton, the discharge
crater is deeper and more material is removed per spark. This leads to higher Ra
values. Also, Equation 2.3 for spark frequency may not hold true for a rotating
tool as discussed in Section 2.3.1. Hence, in spite of a constant value of duty
factor the MRR increases with Ton. For very large values of Ton the drop in MRR
can be explained by the high values of pulse-off time. Since the duty factor was
held constant during the experiment, a higher Toff value was obtained
corresponding to a higher Ton value. No material removal occurs during the Toff.
Hence, a high value of Toff increases non-cutting time and reduces the MRR. This
non-cutting time however does not have a significant effect on the Ra value.
Figure 5.5: Effect of pulse-on time on MRR and Ra
Effect of pulse-off time
The effect of pulse-off time on MRR and Ra is shown in Figure 5.6. For a very
small value of Toff, the MRR was low but then increased drastically when Toff
62
was increased. The MRR then fell slowly with an increase in Toff. For very short
pulse-off time, the probability of arcing is high because the dielectric in the gap
may not have completely recovered its dielectric strength. Also, the debris
particles may still remain in the discharge gap. This would lead to a low MRR
and high Ra value. When the Toff is sufficiently high, the dielectric regains its
dielectric strength and the debris particles are also flushed away from the gap.
Thus, a drastic increase in MRR and decrease in Ra value is achieved. With
further increase in Toff, MRR decreased slowly because machining does not take
place during the pulse-off time and it only adds to the non-cutting time. Further
advantage due to dielectric strength recovery was not available hence increase in
Toff leads to a decrease in MRR. The effect of increased Toff on Ra values cannot
be explained by the above phenomenon as according to it the Ra values should
have remained unaffected. One of the reasons for the observed trend in Ra values
could be the effect of Toff on the re-solidification of molten workpiece at the
discharge crater. Molten material may re-solidify when long pulse-off times are
used due to continuous supply of high velocity air through the tool. Also, air flow
may distort the distribution of molten material in the crater leading to a poorer
surface finish when the material solidifies. Further experiments are necessary to
clarify this.
63
Figure 5.6: Effect of pulse-off time on MRR and Ra
Effect of inlet air pressure
The effect of inlet air pressure on MRR and Ra is shown in Figure 5.7. The
figure suggests that higher air pressure provides a better performance in terms of
both the MRR and Ra values. Flushing efficiency improves with an increase in
the pressure. A better removal of debris particles from the gap leads to a lower
arcing probability. Arcing leads to surface damage, hence lower values of Ra
were obtained with low arcing probability at high pressures. Also, when arcing is
sensed by the EDM machine during a pulse, it stops power supply throughout the
duration of the pulse. This increases the non-cutting time during machining
leading to a lower MRR. Hence higher MRR was obtained at higher air inlet
pressures.
64
Figure 5.7 Effect of air inlet pressure on MRR and Ra
Effect of spindle speed
The effect of spindle speed on MRR and Ra is shown in Figure 5.8. MRR
initially increased with an increase in the spindle rpm but then saturated to a level
and did not increase with an increase in the spindle rpm. Ra values also followed
a similar trend and decreased with increase in spindle rpm up to a level and then
almost saturated. This behavior can be explained by the effect of spindle rotation
on the discharge phenomenon. Spindle rotation during discharge leads to an
improvement in the flushing efficiency. Due to rotation of the gas as it flows
through the tube, the gas is forced outward away from the center when it comes
out of the tool. This flow of gas takes the debris particles away from the
discharge gap. The outward flow velocity of the gas is proportional to the spindle
rotational speed and increases with it. This leads to an improvement in the
flushing efficiency up to a maximum limit. After this stage, there is no scope for
improvement in the flushing efficiency even on increasing the spindle speed
since almost all the debris particles have been removed from the discharge gap.
Hence, the MRR and Ra values saturated at very high values of the spindle
65
speed. Apart from the flushing efficiency, tool rotation has an impact on the
spark frequency. At high spindle speeds, a discharge may be interrupted even
during the pulse-on time due to movement of the tool. Thus, several short sparks
occur over a single pulse-on time and the spark frequency increases with the
spindle rpm. Since the same pulse energy is now distributed over a number of
sparks, the crater depth is lower. Hence, lower Ra values were observed when the
spindle speed was increased.
Figure 5.8: Effect of spindle speed on MRR and Ra
5.1.3 Tool face geometry
Experiments were conducted for identical input parameters using two tools with
different outer diameters: 11.5 mm and 15 mm. Both the tools had four axial
through-holes for air flow; each hole of 2 mm diameter on a pitch circle of 5 mm
diameter. One experimental run was performed with each tool. The results
obtained are shown in Figure 5.9. The tool with a smaller outer diameter (11.5
mm OD tool) had a higher performance. From the figure it can be seen that the
MRR for 11.5 mm tool was greater than the 15 mm tool. Also, the TWR and Ra
values were lower for the 11.5 mm tool as compared to the 15 mm tool. As the
66
location and size of holes in both the tools was same, difference in the tool OD
affected the flushing efficiency. With a larger tool diameter, it becomes more
difficult to remove debris particles from the discharge gap and this increases the
probability of arcing. Thus, the MRR was reduced and Ra was increased for a
larger tool. Also, for a larger tool the amount of tool material exposed to sparking
increases leading to a higher TWR. This experiment suggests that a smaller tool
provides a better machining performance. However, for tool sizes lower than
11.5 mm it was found that there were problems during measurement of surface
roughness due to interference of the roughness tester probe arm with the side
walls of the machined hole. Hence the tool with an OD of 11.5 mm was selected
for the DOE experiments.
Figure 5.9: Effect of tool electrode outer diameter on MRR, TWR and Ra
Experiments were performed by changing the number of holes (n) for air flow on
the end face of the tools. Tools of the same outer diameter were used and the size
and radial location of the holes was kept constant (2 mm holes on pitch circle of
67
5 mm diameter). Different tools with one, two, three and four holes were used
and three experiments were conducted with each tool for the same set of input
parameters. The results are shown in Figure 5.10. It can be seen that the MRR
increased with increase in the number of holes till n=3 but then decreased as n
increased to 4. A similar trend was observed for the Ra values which decreased
with increasing n till 3 holes but then the Ra increased for a four-hole tool. The
observed trends in MRR and Ra values suggest the existence of an optimum
number of holes. When the number of holes is increased, the flow rate through
the tool has to be increased to maintain a constant air inlet pressure. Hence the
flushing efficiency increases which leads to an improvement in the MRR and the
Ra values. However, the tool area over which sparks can occur reduces when the
number of holes increases. This reduction in area would reduce the number of
sparks per unit time. This would lead to a lower MRR. Also, low frequency
sparks lead to a higher Ra value due to more energy contained in each spark as
compared to high frequency sparks. Thus, an optimum value of number of holes
exists for which the MRR is highest and the Ra value is lowest. This optimum
condition was found to occur for a three-hole tool. Hence a three-hole tube was
selected for the DOE experiments.
68
Figure 5.10: Effect of number of holes in tool electrode on MRR and Ra
5.2 Parametric Analysis
In order to study the effect of the input parameters and the effect of their interactions,
a designed experiment has been conducted as discussed in Section 4.3. The OVAT
analysis shows that effect of none of the factors is linear. Hence, a CCD design has
been conducted which is capable of fitting a second order polynomial function.
5.2.1 CCD Observations
The experimental results obtained from the CCD runs are shown in Table 5.1.
The runs were randomized and experiments were conducted in a single block. It
is interesting to note that although the MRR and Ra values seem to change when
the factors were changed, significant changes in TWR were not obtained. In most
of the runs, the TWR in fact remained in the small range of [-0.02 0.02]
mm3/min.
69
Table 5.1: MRR, Ra and TWR observations of the CCD runs
Run Order
Input Parameters
Output Response
Vg Id Ton D P N MRR Ra TWR V A μs kgf/cm2 rpm mm3/min μm mm3/min
1 91 16 200 9 2.1 650 0.71 3.04 0.04 2 63 42 200 9 2.1 1900 5.68 3.14 -0.03 3 63 16 200 3 0.9 650 0.33 3.22 0.01 4 91 42 750 3 2.1 650 2.28 3.1 -0.02 5 91 16 200 9 0.9 650 0.55 3.46 -0.02 6 63 16 750 9 2.1 650 0.69 2.98 0.03 7 63 16 750 9 0.9 650 0.58 3.76 -0.06 8 77 29 500 11 1.5 1275 2.67 3.31 0.02 9 91 42 750 9 0.9 650 2.31 3.98 0.01 10 63 16 200 3 2.1 650 0.14 2.66 0.03 11 91 16 750 9 0.9 1900 1.03 3.25 -0.02 12 55 29 500 6 1.5 1275 0.87 3.53 0.02 13 77 29 500 6 1.5 1275 1.60 3.26 0.01 14 91 42 750 3 0.9 650 1.33 4.29 -0.01 15 63 16 200 3 0.9 1900 0.17 2.86 0.01 16 63 16 200 3 2.1 1900 0.68 2.4 -0.03 17 63 42 200 3 2.1 1900 2.31 2.46 -0.03 18 63 16 200 9 0.9 1900 0.99 2.96 0.03 19 91 16 200 3 2.1 650 0.47 2.63 0.04 20 63 42 200 3 0.9 1900 1.85 3.33 0.04 21 77 29 500 6 1.5 1275 1.58 3.25 0.01 22 63 42 750 9 2.1 1900 4.67 2.98 0.03 23 63 42 200 9 0.9 1900 5.37 3.11 0.02 24 91 42 200 9 0.9 650 3.19 4.27 0.03 25 77 49 500 6 1.5 1275 4.22 3.94 0.04 26 91 42 200 3 2.1 1900 2.44 3.5 0.02 27 91 16 200 3 0.9 650 0.26 3.42 0.01 28 91 16 200 3 0.9 1900 0.64 2.95 -0.02 29 63 42 750 3 2.1 1900 4.27 2.84 0.03 30 91 42 750 3 0.9 1900 2.86 4.08 0.01 31 77 29 50 6 1.5 1275 0.86 2.87 -0.01 32 63 16 200 9 0.9 650 0.36 3.36 0.02 33 91 16 750 3 2.1 650 0.53 3.01 0.02 34 91 42 750 3 2.1 1900 3.60 3.37 -0.02 35 77 29 500 6 0.6 1275 1.19 3.33 0.01 36 77 29 500 6 1.5 1275 1.82 3.21 0.04 37 63 16 200 9 2.1 650 0.47 2.86 -0.07
70
38 63 42 750 9 0.9 1900 3.31 4.2 0.04 39 63 42 200 9 2.1 650 4.67 3.3 -0.01 40 91 16 750 9 2.1 650 1.03 2.92 0.03 41 77 29 500 6 1.5 1275 2.04 3.35 -0.02 42 63 16 750 9 0.9 1900 0.88 3.7 0.07 43 77 29 1000 6 1.5 1275 2.69 3.13 0.02 44 77 29 500 6 1.5 2250 3.19 3.38 0.01 45 63 42 750 9 2.1 650 2.51 3.29 0.01 46 91 16 750 9 0.9 650 0.51 3.77 -0.02 47 91 42 200 3 0.9 650 1.22 3.4 0.02 48 91 16 750 3 0.9 1900 0.90 3.37 0.02 49 91 16 200 9 2.1 1900 1.14 2.48 0.02 50 63 16 750 3 0.9 650 0.49 3.78 0.02 51 77 29 500 6 1.5 1275 1.92 2.99 0.01 52 91 42 200 3 2.1 650 1.53 2.64 0.03 53 77 9 500 6 1.5 1275 0.51 2.85 0.03 54 77 29 500 6 1.5 1275 1.79 3.18 0.01 55 63 42 750 3 2.1 650 2.04 3.21 0.01 56 77 29 500 6 1.5 1275 1.79 3.3 0.02 57 91 42 200 9 2.1 650 2.69 3.57 0.04 58 77 29 500 6 1.5 1275 1.59 3.79 -0.01 59 91 16 750 3 0.9 650 0.55 3.68 0.02 60 63 42 750 3 0.9 650 1.55 3.89 -0.01 61 91 42 200 9 2.1 1900 4.19 3.34 0.02 62 63 42 750 9 0.9 650 1.94 4.28 0.01 63 77 29 500 6 1.5 1275 1.85 3.6 0.01 64 91 16 750 9 2.1 1900 1.06 3.1 -0.01 65 77 29 500 1 1.5 1275 1.10 3.49 0.03 66 91 42 750 9 0.9 1900 4.06 3.4 0.02 67 91 42 750 9 2.1 1900 4.42 3.28 0.01 68 63 42 200 3 2.1 650 1.81 3.6 0.03 69 99 29 500 6 1.5 1275 1.95 4.28 -0.03 70 91 42 750 9 2.1 650 2.88 3.65 -0.01 71 91 16 200 3 2.1 1900 0.68 2.49 0.02 72 77 29 500 6 2.5 1275 2.14 3.46 0.00 73 91 16 750 3 2.1 1900 0.51 2.75 0.00 74 77 29 500 6 1.5 1275 1.99 3 0.02 75 63 42 200 9 0.9 650 4.19 3.69 -0.03 76 63 42 200 3 0.9 650 1.21 3.07 0.02 77 91 16 200 9 0.9 1900 1.41 3.2 -0.02 78 77 29 500 6 1.5 300 1.00 3.49 0.01 79 63 42 750 3 0.9 1900 2.27 3.42 0.03 80 91 42 200 9 0.9 1900 4.19 3.81 0.01 81 63 16 750 3 2.1 1900 0.27 3.24 0.03 82 91 42 200 3 0.9 1900 1.81 3.08 0.00
71
83 63 16 750 3 0.9 1900 0.44 4.03 0.01 84 63 16 750 3 2.1 650 0.44 2.86 -0.02 85 63 16 200 9 2.1 1900 1.19 2.84 0.02 86 63 16 750 9 2.1 1900 0.79 3.5 0.01
5.2.3 Regression analysis and Model fitting
Regression analysis of the experimental results obtained from the CCD runs has
been done using the software Design Expert 7.0.0. Models with significant factor
effects were obtained for MRR and Ra. But for TWR no suitable model could be
obtained which had a significant effect. The regression analysis for each response
is discussed below.
Regression Analysis for MRR
First of all, ANOVA based sequential sum of squares test was done to select the
most appropriate model to be fitted. The test result is shown in Table 5.2. Linear,
two factor interaction, quadratic and cubic models were compared to see if
addition of extra terms improved the fitting as indicated by the F value in the
Fischer’s F test [17]. The F values can be converted into the p value by using the
F probability distribution curve. The model significance can be tested either by
comparing the F value to a threshold F value or by comparing the corresponding
p value to the threshold p value. The threshold p value depends on the chosen
significance level which was set here to 5%. The highest order polynomial for
which the additional terms were significant and the model was not aliased was
chosen. Based on the test result, the two factor interaction model was chosen for
fitting.
Table 5.2: Sequential Model Sum of Squares for MRR
Source
Sum of Squares
(SS)
Degrees of
Freedom
Mean Square
F Value
p-value Prob > F
Mean vs Total 282.61 1.00 282.60 Linear vs Mean 122.30 6.00 20.38 52.69 < 0.0001 2FI vs Linear 17.92 15.00 1.19 6.05 < 0.0001 Suggested
Quadratic vs 2FI 1.09 6.00 0.18 0.91 0.49 Cubic vs Quadratic 9.66 27.00 0.36 5.85 < 0.0001 Aliased
Residual 1.90 31.00 0.06 Total 435.47 86.00 5.06
72
The regression statistics for the full two factor interaction model are shown in
Table 5.3. The predicted R2 value and the adjusted R2 value were found to be in
close agreement. Adjusted R2 is a measure of the amount of variation about the
mean which is explained by the model. A value of 0.89 indicates that 89% of the
observed variation in the response can be explained by the model. The statistics
‘Adequate precision’ measures the signal to noise ratio of the experiment. A
value greater than 4 is preferable. A ratio of 23.315 indicates an adequate signal
and the model can be used to navigate the design space. When there is a large
difference in the values of predicted R2 the adjusted R2, it indicates that some
non-significant terms have been included in the model and the model would
improve on excluding such terms. To check if the fitting would improve on
dropping some terms, a reduced two factor interaction model was fitted.
Backward step-wise fitting was used for model fitting [17] with term-dropping p
value of 10%. It was found that the difference between the predicted R2 value
and the adjusted R2 value decreased on dropping some of the terms. Hence the
reduced two factor interaction model was chosen.
Table 5.3: Comparison of regression statistics for the full two factor interaction
model and reduced two-factor interaction model for MRR
ModelStatistics
Full 2FI Reduced 2FI
R-Squared 0.917 0.907 Adj R-Squared 0.890 0.892 Pred R-Squared 0.844 0.869 Adeq Precision 23.315 30.130
The ANOVA table for the reduced two factor interaction model is shown in
Table 5.4. The model F-value of 59.39 implies the model is significant. There is
only a 0.01% chance that a "Model F-Value" this large could occur due to noise.
Values of "Prob > F" less than 0.0500 indicate model terms are significant. In
this case Id, D, P, N, VgId, VgTon , IdD, IdP, IdN and TonD were significant model
terms. Values greater than 0.1000 indicate that the model terms are not
73
significant. The "Lack of Fit F-value" of 8.09 implies the "Lack of Fit" is
significant. There is only a 0.10% chance that a "Lack of Fit F-value" this large
could occur due to noise. A significant lack of fit is bad because we want the
model to fit. Where as a whole model test checks if anything in the model is
significant, a lack-of-fit test checks whether anything left out of the model is
significant. If the lack-of-fit test is significant, there is some significant effect
that has been left out of the model, and that effect is a function of the factors
already in the model. It could be a higher order power of a factor or some form of
interaction among the factors. In this case, one of the reasons for the significant
lack of fit could be due to the inability to represent the interaction terms which
inlcude the Toff variable. Since, Toff is not represented directly but in terms of D
(Equations 3.1, 3.2), it is not possible to get the effect of interaction terms of the
form VgToff, …, NToff. If any of these interaction terms are important, then the
current model would not be able to capture it and would show a significant lack
of fit.
Table 5.4: Analysis of variance table for response surface reduced two-factor
interaction model of MRR
Source
Sum of Squares
(SS)
Degrees of
Freedom
Mean Square
F Value
p-value Prob > F
Test result
Model 138.6591 12 11.55492 59.39111 < 0.0001 significant
Vg 0.000119 1 0.000119 0.000612 0.9803 Id 91.85232 1 91.85232 472.1114 < 0.0001
Ton 0.040099 1 0.040099 0.206103 0.6512 D 17.17029 1 17.17029 88.25352 < 0.0001 P 1.9298 1 1.9298 9.918974 0.0024 N 11.42346 1 11.42346 58.71541 < 0.0001
Vg Id 0.921477 1 0.921477 4.736296 0.0328 Vg Ton 0.807586 1 0.807586 4.150907 0.0452 Id D 6.258015 1 6.258015 32.16555 < 0.0001 Id P 1.156314 1 1.156314 5.943336 0.0172 Id N 3.64296 1 3.64296 18.72444 < 0.0001
Ton D 3.573746 1 3.573746 18.36868 < 0.0001
Residual SS 14.20262 73 0.194556
74
Source
Sum of Squares
(SS)
Degrees of
Freedom
Mean Square
F Value
p-value Prob > F
Test result
Lack of Fit 13.96008 64 0.218126 8.094147 0.0010 significantPure Error 0.242538 9 0.026949 Corrected Total SS
152.8617 85
The final regression equation for MRR in terms of the actual parameter values is:
-1.04901 0.00536 0.02829 - 0.00044 0.06911
- 0.22108 - 0.0002 - 0.00066 0.00003
0.00802 0.01723 0.00003 - 0.00029
g d on
g d g on
d d d on
MRR V I T D
P N V I V T
I D I P I N T D
= + + +
+
+ + +
(5.1)
Where, MRR is in mm3/min and Vg in V, Id in A, Ton in μs, D is dimensionless, P
in kgf/cm2 and N in rpm.
Regression Analysis for Ra
ANOVA-based sequential sum of squares test was done to select the most
appropriate model to be fitted. The test result is shown in Table 5.5. A linear
model is suggested. However, the regression statistics shows that the value of
adjusted R2 is low. Hence reduced models were fitted and compared as shown in
Table 5.6. The reduced quadratic model was chosen based on the high value of
adjusted R2. The "Pred R-Squared" of 0.5230 was found to be in reasonable
agreement with the "Adj R-Squared" of 0.5920. Also "Adeq Precision" ratio of
16.396 indicates an adequate signal and the model can be used to navigate the
design space.
75
Table 5.5: Sequential Model Sum of Squares for Ra
Source Sum of Squares
(SS)
Degrees of
Freedom
Mean Square
F Value
p-value Prob > F
Mean vs Total 945.07 1.00 945.07 Linear vs Mean 9.05 6.00 1.51 16.19 < 0.0001 Suggested2FI vs Linear 1.54 15.00 0.10 1.13 0.3510
Quadratic vs 2FI 0.87 6.00 0.14 1.69 0.1386 Cubic vs Quadratic 2.62 27.00 0.10 1.29 0.2462 Aliased
Residual 2.33 31.00 0.08 Total 961.48 86.00 11.18
The ANOVA table for the reduced quadratic model is shown in Table 5.7. The
Model F-value of 13.33 implies the model is significant. There is only a 0.01%
chance that a "Model F-Value" this large could occur due to noise. Values of
"Prob > F" less than 0.0500 indicate model terms are significant. In this case Id,
Ton, D, P, N, Vg2 and Ton
2 were significant model terms. The "Lack of Fit F-
value" of 1.34 implies the Lack of Fit is not significant relative to the pure error.
The final regression equation for Ra in terms of the actual parameter values is:
2 2
7.95767 - 0.13375 - 0.01624 0.00334 0.02655
- 0.20635 - 0.00015 0.00038 - 0.00042
0.00081 - 0.000002
g d on
g d on
g on
Ra V I T D
P N V I T P
V T
= + +
+
+
(5.2)
Where, Ra is in μm and Vg in V, Id in A, Ton in μs, D is dimensionless, P in
kgf/cm2 and N in rpm.
76
Table 5.6: Comparison of regression statistics for the reduced quadratic, reduced
two-factor interaction, reduced linear and linear Ra models
Model Statistics
Reduced Quadratic
Reduced 2FI
Reduced Linear
Linear
R-Squared 0.640 0.589 0.545 0.552 Adj R-Squared 0.592 0.546 0.517 0.517 Pred R-Squared 0.523 0.492 0.479 0.469 Adeq Precision 16.396 17.051 18.531 18.045
Table 5.7: Analysis of variance table for response surface reduced quadratic model of Ra.
Source Sum of Squares
(SS)
Degrees of
Freedom
Mean Square
F Value
p-value Prob > F
Test result
Model 10.500 10 1.049973 13.332 < 0.0001 significant Vg 0.101 1 0.100989 1.282 0.2611 Id 1.997 1 1.997364 25.361 < 0.0001
Ton 1.968 1 1.967931 24.987 < 0.0001 D 0.441 1 0.441253 5.603 0.0205 P 4.085 1 4.084806 51.866 < 0.0001 N 0.586 1 0.585806 7.438 0.0079
Vg Id 0.308 1 0.308025 3.911 0.0516 Ton P 0.306 1 0.306311 3.889 0.0523 Vg
2 0.472 1 0.472464 5.999 0.0166 Ton
2 0.640 1 0.640005 8.126 0.0056
Residual SS 5.907 75 0.078758 Lack of Fit 5.362 66 0.081243 1.342 0.3336 not
significant Pure Error 0.545 9 0.060534 Corrected Total SS
16.407 85
Regression Analysis for TWR
ANOVA-based sequential sum of squares test was done to select the most
appropriate model to be fitted. The test result is shown in Table 5.8. Two factor
interaction model is suggested. On performing ANOVA, it was found that the
predicted R2 was negative. A negative value of predicted R2 implies that the
overall mean is a better predictor of response than the current model. Different
77
models were chosen for fitting and it was found that the predicted R2 was negative
in all the cases. The results are shown in Table 5.9. Hence, instead of using a
regression equation, TWR has been estimated by the mean value:
3 0.01 mm /minTWR =
(5.3)
Table 5.8: Sequential Model Sum of Squares for TWR
Source
Sum of Squares
(SS)
Degrees of
Freedom
Mean Square
F Value
p-value Prob >
F
Mean vs Total 0.73 1.00 0.73 Suggested Linear vs Mean 0.07 6.00 0.01 0.22 0.9694 2FI vs Linear 1.32 15.00 0.09 1.94 0.0355 Suggested
Quadratic vs 2FI 0.22 6.00 0.04 0.78 0.5860 Cubic vs Quadratic 1.34 27.00 0.05 1.14 0.3612 Aliased
Residual 1.35 31.00 0.04 Total 5.02 86.00 0.06
Table 5.9: Comparison of regression statistics for the reduced quadratic, reduced
two-factor interaction and linear TWR models
ModelStatistics
Reduced Quadratic
Reduced 2FI
Linear
R-Squared 0.281 0.281 0.016 Adj R-Squared 0.175 0.175 -0.058 Pred R-Squared -0.001 -0.001 -0.187 Adeq Precision 7.672 7.672 2.133
During the experiments it was found that some debris material was deposited on
the tool face after machining. This material deposition on tool electrode may
explain the near-constant value of TWR. When high MRR conditions exist, large
amount of debris is formed and the amount of material deposited on the tool
increases. At the same time, the amount of actual material removed from the tool
also increases at high MRR conditions. Similarly, for low MRR conditions the
78
amount of debris deposited on tool and amount of actual tool material removed is
also low. Since TWR is calculated by measuring the difference in tool weight
before and after machining, the combined effect of deposition and removal from
tool is included in the measured TWR. The constant value of TWR indicates that
the difference between material removed from tool and material deposited on
tool remains constant even when the process parameters are changed.
5.2.3 Response surface analysis
MRR Response Surface
The response surfaces of MRR were obtained for the interaction terms in the
reduced two-factor interaction model. Response surface of MRR versus gap
voltage and discharge current is shown in Figure 5.11. From the figure it can be
seen that a high current and voltage combination leads to high MRR due to an
increase in the spark energy as given by Equation 2.4. It can be observed from
the figure that at low current values, MRR increases with an increase in voltage
due to increase in the spark energy. However, at high current levels, an increase
in voltage leads to a slight decrease in the MRR. One of the reasons for this could
be the higher amount of debris formation and higher flushing required at high
current levels. Since, discharge gap increases with an increase in voltage (Section
5.1.2); flushing efficiency is reduced at high voltages. The increase in spark
energy is dominated by the reduction in spark efficiency as voltage is increased.
This leads to a reduction in MRR as voltage is increased at high current levels.
The response surface of MRR versus gap voltage and pulse-on time is shown in
Figure 5.12. From the figure it can be seen that the effect of Vg and Ton is not
significant and the MRR values remain almost constant with changes in Vg and
Ton.
79
Figure 5.11: Response surface of MRR versus gap voltage and discharge current
Response surface of MRR versus discharge current and duty factor setting is
shown in Figure 5.13. From the figure it can be observed that MRR increases
with an increase in duty factor and current in accordance with Equation 2.4.
Similarly, from Figure 5.14 and Figure 5.15 it can be observed that high MRR is
obtained at high current and high air inlet pressure combination and high current
and high spindle speed combination. High values of air pressure and spindle
speed lead to a better flushing efficiency which improves the MRR. MRR
increases on increasing any of the five factors (Vg, Id, D, P, N), but it can be seen
Id has the highest effect on MRR.
80
Figure 5.12: Response surface of MRR versus gap voltage and pulse-on time
The effect of pulse-on time is not straightforward as can be seen from the
response surface of MRR versus Ton and D (Figure 5.16). For high values of duty
factor, an increase in Ton leads to a decrease in the MRR where as for low values
of duty factor, an increase in Ton leads to an increase in MRR. A possible reason
for this could be that for high duty factors, the pulse-off time is low. When a high
Ton is used, the amount of material which melts during the spark increases due to
higher spark energy. However, due to extremely low pulse-off times, a
substantial part of the material re-solidifies or remains in the spark gap instead of
being flushed away from the gap. With an increase in Ton, the amount of debris
particles in the spark gap is expected to increase. This leads to a higher arcing
probability and reduces the MRR. On the other hand, high pulse-off time is
obtained at low duty factor and sufficient time for flushing of debris from the gap
is available in between the sparks. Hence, when a high Ton is used more material
is melted and the material is also removed due to flushing. Thus MRR increases
on increasing Ton at low duty factors.
81
Figure 5.13: Response surface of MRR versus discharge current and duty factor setting
Figure 5.14: Response surface of MRR versus discharge current and air inlet pressure
82
Figure 5.15: Response surface of MRR versus discharge current and spindle speed
Figure 5.16: Response surface of MRR versus pulse-on time and duty factor setting
83
Ra Response Surface
The response surfaces of Ra were obtained for the interaction terms in the
reduced quadratic model.
Response surface of Ra versus gap voltage and discharge current is shown in
Figure 5.17. From the Vg-Id response surface it can be seen that the Ra value
decreases with a decrease in the current. However, an optimum exists for voltage.
Also, this optimum point depends on the value of the current. The existence of
optimum voltage can be explained as in the case of OVAT analysis (Section
5.1.2). The optimum voltage shifts towards higher values as the current
decreases. At low currents, the amount of debris formed is lower because of the
lower spark energy. Thus the need for flushing is not as significant at lower
currents as in the case of higher currents. At lower voltage values the flushing
efficiency is reduced due to lower spark gap. Hence for obtaining the same Ra
value at higher current levels, lower voltage values are required. Thus, the
optimum voltage value decreases with an increase in the current value.
Response surface of Ra versus pulse-on time and air inlet pressure is shown in
Figure 5.18. Corresponding to every air pressure, a Ton value exists at which the
Ra value is highest and Ra decreases on either side of this Ton value. For very
low values of Ton, high frequency sparks take place leading to shallower crater
formation. This leads to a low Ra value for very low Ton values. But for very
large values of Ton, the Toff values also increase (since the duty factor is held
constant). Thus, flushing efficiency improves leading to a lower Ra value. The
Ton corresponding to highest Ra value depends on the value of air pressure. High
values of Ton lead to melting of more material per spark requiring better flushing.
Thus at high pressure values (i.e. better flushing conditions), higher Ton values
can be afforded for the same Ra value (as seen on the contour plot in Figure
5.18).
84
Figure 5.17: Response surface of Ra versus gap voltage and discharge current
Figure 5.18: Response surface of Ra versus pulse-on time and air inlet pressure
85
The duty factor does not show interaction effect with any other factor. The effect
of duty factor can be seen from the regression equation 5.2. Ra values increase
on increasing the duty factor. High duty factors lead to more material removal
and higher debris formation (Equation 2.4). This increases the arcing probability
and leads to poorer surface finish.
5.3 GA based Optimization
5.3.1 Single objective optimization
Optimization of MRR
Single objective optimization of MRR and Ra was done separately using the
regression model obtained from the CCD based experiments. Because of the non-
linear nature of the models and the existence of upper and lower limits on parameter
values, GA based optimization has been preferred. The optimization problem is
formulated as:
[ ][ ][ ][ ][ ][ ]
2
Maximize MRRSubject to: MRR>0Where:MRR is given by Equation 5.1
55 99
9 49
50 1000
1 11
0.6 2.5 /
300 2250
g
d
on
V V
I A
T s
D
P kgf cm
N rpm
μ
∈
∈
∈
∈
∈
∈
(5.4)
Real parameter GA was used with a population size of 100 and SBX parameter value
of 2 and polynomial mutation parameter value of 10. The variation in population best
value of MRR and population average with generation is shown in Figure 5.19. It can
be seen that convergence is achieved by the end of 100 generations and the
population average and population best values match closely after 100 generation.
86
GA was run 20 times and the best value in each run was observed. It was found that
in all the runs the same converged best value for MRR was obtained. Hence, the trial
values used for the GA parameter were found to be good enough and no further
parameter tuning was necessary. The optimum value of MRR and the corresponding
parameter values are shown in Table 5.10.
Figure 5.19: Variation in population best and population average with generation for
maximization of MRR
Table 5.10: Values of input parameters and response variables at the operating point
corresponding to maximum MRR obtained through optimization
Input Parameters Values at maximum MRR condition Gap voltage, Vg 55 V Discharge current, Id 49 A Pulse on time, Ton 50 μs Duty factor position, D 11 Gas pressure, P 2.5 kgf/cm2 Spindle speed, N 2250 rpm Response Variables Material removal rate MRR 8.18 mm3/min Ra 2.84 μm
87
From the table it can be seen that the optimum value of MRR is obtained when the
values of current, inlet air pressure and spindle speed are highest. As discussed earlier
in Section 5.1.2, spark energy increases with current and the flushing efficiency is
improved by high air inlet pressure and high spindle speed. Hence, MRR is highest
corresponding to the highest value of these parameters. Also, lower discharge gap is
obtained at low values of gap voltage. Hence flushing efficiency is improved at low
voltage setting. This explains the low value of voltage corresponding to the optimum
MRR setting. It was also found that for optimum MRR, high frequency sparks are
favorable. From Table 5.10, the value of Ton is lowest and value of duty factor is
highest at optimum MRR. High values of duty factor lead to high MRR as given by
Equation 2.4. Also, low values of Toff are favorable for a high MRR as discussed in
Section 5.1.2. From the ANOVA of MRR regression model it can be seen that the
effect of Ton is not significant at 5% significance level. Thus, the low value of Ton for
optimum MRR can be explained by the low value of Toff at optimum MRR.
Independent control of Toff is not available on the EDM machine. Instead, Ton and
duty factor are varied independently for changing Toff. Hence, the lowest Toff value is
obtained for lowest Ton value and highest duty factor value combination. This very
combination was obtained for optimum MRR value through GA.
The optimization problem for minimization of Ra is formulated as:
[ ][ ][ ][ ][ ][ ]
2
Minimize RaSubject to: MRR>0Where:Ra is given by Equation 5.2
:55 99
9 49
50 1000
1 11
0.6 2.5 /
300 2250
g
d
on
AndV V
I A
T s
D
P kgf cm
N rpm
μ
∈
∈
∈
∈
∈
∈
88
(5.5)
The real parameter GA was first run for 100 generations with a trial value of ηc (=2)
and ηp (=10) and a population size of 100. Evolution of population best and
population average is shown in Figure 5.20. The best and average values match
closely by the end of 100 generations. Hence, subsequent GA runs were made for 100
generations each. When the GA was run for 20 times it was found that different
converged Ra values were obtained in different runs. Hence, the GA parameters ηc
and ηp were increased to 25 and 150 respectively and GA was run again. The lowest
converged Ra value from the previous runs was noted and the number of times GA is
successful in obtaining this value was observed. The success rate was found to
increase to 50 % from 10 % on increasing the GA parameters. The population was
then increased to improve the convergence success rate. The variation of success rate
with population size is shown in Figure 5.21. GA was then run with a population size
of 400 and ηc and ηp values of 25 and 150 respectively. The resulting optimum Ra
value and the corresponding input parameter values are shown in Table 5.11.
Figure 5.20: Variation in population best and population average with generation for
minimization of Ra
89
Table 5.11: Values of input parameters and response variables at the operating point
corresponding to minimum Ra obtained through optimization
Input Parameters Values at minimum Ra condition Gap voltage, Vg 80 V Discharge current, Id 9 A Pulse on time, Ton 1000 μs Duty factor position, D 1 Gas pressure, P 2.5 kgf/cm2 Spindle speed, N 2250 rpm Response Variables Material removal rate MRR 0.89 mm3/min Ra 1.86 μm
From Table 5.11 it can be seen that optimum Ra is obtained at low values of
discharge current and duty factor due to a decrease in the spark energy (Equation 2.4).
Also, the values of air pressure and spindle speed are highest for optimum Ra. This
can be explained by the increase in flushing efficiency achieved at high air pressures
and high spindle speeds. GA result shows that an intermediate value of voltage exists
for optimum Ra as can be seen from the Ra response surface in Figure 5.17. High Ton
values are obtained for optimum Ra. It may be argued that high Ton values would lead
to low spark frequency and hence high Ra values should be obtained. However, as
discussed earlier the spark frequency may be reasonably high even for high Ton values
due to tool rotation. The high Ton values at optimum Ra are obtained because the
corresponding Toff values are very large at low duty factors. Since Ra is improved at
high pulse-off time values, a high value of Ton is obtained for optimum Ra.
90
Figure 5.21: Variation of success rate of convergence with population size for
minimization of Ra
5.3.2 Multi-objective optimization
The multi-objective optimization problem for minimization of 1/MRR and Ra is
formulated as:
[ ][ ][ ][ ][ ][ ]
Minimize (1/MRR,Ra)Subject to: MRR>0Where:MRR is given by Equation 5.1Ra is given by Equation 5.2
55 99
9 49
50 1000
1 11
0.6 2.5 / 2
300 2250
g
d
on
V V
I A
T s
D
P kgf cm
N rpm
μ
∈
∈
∈
∈
∈
∈
(5.6)
91
NSGA II was run for 100 generations with a population size of 400 and ηc and ηp
values of 25 and 150 respectively. The non-dominated member solutions
obtained after the GA run are shown in Figure 5.22. NSGA II also gives the
corresponding parameter values for the non-dominated points. The parameter
values corresponding to points shown in Figure 5.22 are provided in Appendix A
in the form of 3D plots. The plot in figure 5.22 represents the Pareto-optimal
front for minimization of the objective functions: 1/MRR and Ra. Ra is plotted
on the x-axis and 1/MRR is plotted on the y-axis. It can be seen that for large
values of Ra, low values of MRR are obtained (high 1/MRR value) and vice-
versa. Any point along the curve is optimum in both the objectives as defined by
the Pareto-optimality criterion (Section 2.5.4). This curve can be used to select an
operating point when a target Ra (or MRR) value is given. Several set of
operating conditions may exist for the same target Ra (or MRR). But the best
possible MRR for a given target Ra and vice-versa can be directly obtained from
the Pareto-optimal front. Performance improvement is obtained by selecting
operating conditions along this curve.
92
Figure 5.22: Pareto-optimal front for minimization of 1/MRR and Ra obtained by plotting
the non-dominated solutions from NSGA II run
The extreme ends on the Pareto curve have special significance. The end at
which the tangent to the curve is perpendicular to the x-axis has the lowest Ra
value (finish machining conditions). And the end at which the tangent to the
curve is perpendicular to the y-axis has the highest MRR value (rough machining
conditions). The Ra value at finish machining end and the MRR value at rough
machining end were compared to the results of single objective optimizations of
Ra and MRR respectively to verify the accuracy of the NSGA II results.
The finish and rough machining regions were obtained as discussed in Section
4.5. The MRR and Ra values along with the parameter values for finish and
rough machining are shown in Table 5.12 and Table 5.13 respectively. It is
interesting to note that for both the regions, high air inlet pressures and high
spindle speeds are favorable. In fact, on inspection of the parameter values of the
Pareto-points it is found that all along the Pareto-front, the air pressure and
spindle speed have constant values (P=2.5 kgf/cm2 and N=2250 rpm) which are
the highest feasible value of the parameters. This shows that a high value of air
93
pressure and spindle speed improves both MRR and Ra. This can be explained
by the improved flushing efficiency at high values of air pressure and spindle
speed.
Table 5.12: MRR, Ra and input parameter values corresponding to the finish
machining region obtained from Pareto-front analysis
MRR Ra Vg Id Ton D P N mm3/min μm V A μs kgf/cm2 rpm
0.886 1.857 79.95 9.01 1000.00 1.00 2.50 2250.000.886 1.857 79.97 9.01 1000.00 1.00 2.50 2250.000.895 1.857 80.27 9.00 1000.00 1.00 2.50 2249.990.897 1.858 80.37 9.00 1000.00 1.01 2.50 2249.570.905 1.858 80.64 9.00 1000.00 1.00 2.50 2250.000.906 1.858 80.67 9.00 1000.00 1.00 2.50 2250.000.910 1.858 80.79 9.00 1000.00 1.00 2.50 2249.580.912 1.858 80.85 9.01 999.98 1.00 2.50 2249.990.914 1.858 80.93 9.01 999.99 1.00 2.50 2249.990.920 1.859 81.16 9.00 1000.00 1.00 2.50 2249.98
Table 5.13: MRR, Ra and input parameter values corresponding to the rough
machining region obtained from Pareto-front analysis
MRR Ra Vg Id Ton D P N mm3/min μm V A μs kgf/cm2 rpm
8.176 2.844 55.27 49.00 50.12 11.00 2.50 2249.99 8.175 2.843 55.30 49.00 50.03 11.00 2.50 2249.99 8.167 2.838 55.53 49.00 50.07 11.00 2.50 2249.72 8.167 2.838 55.53 49.00 50.07 11.00 2.50 2249.72 8.161 2.832 55.73 49.00 50.04 10.99 2.50 2249.89 8.161 2.832 55.73 49.00 50.04 10.99 2.50 2249.89 8.155 2.826 55.99 49.00 50.06 10.99 2.50 2249.57 8.146 2.818 56.31 49.00 50.06 10.99 2.50 2249.57 8.145 2.816 56.42 48.99 50.01 11.00 2.50 2249.88 8.130 2.807 56.81 48.99 50.01 10.99 2.50 2249.84
5.4 Focused Experiments
5.4.1 Finish machining region
In the finish machining region it was found that low value of duty factor and high
values of pulse-on time, inlet air pressure and spindle speed were favorable for
94
obtaining a low Ra value (Table 5.12). The values of these parameters remain
almost constant over the region hence the focused experiments were conducted
keeping the values of these parameters constant. Since an optimum in voltage was
found, a CCD design, capable of 2nd order fitting, was chosen. Gap voltage and
discharge current were varied in a small range around the optimum point. Since
values of current lower than 9 A were available on the EDM machine,
experiments were conducted at lower current values. Voltage was also considered
because the optimum voltage value was found to shift with the current level
(Section 5.2.3). The input parameter values and the output response (MRR and
Ra) for the CCD runs are shown in Table 5.14. Best Ra value of 1.60 μm has been
obtained.
Table 5.14: Experimental observations for CCD runs in the finish machining
region
Run Order Vg Ton MRR Ra V μs mm3/min μm 1 50 30 2.08 3.53 2 50 30 2.82 3.14 3 45 50 5.06 3.71 4 55 10 3.26 3.51 5 45 10 2.56 3.05 6 55 50 6.83 2.97 7 50 30 1.49 3.27
Id=49 A, D=11, P=2.5 kgf/cm2, N=2250 rpm
The experimental Ra and MRR values corresponding to the input parameters
obtained by the GA optimization are highlighted in Table 5.14. It can be seen that
the experimental Ra value (2.21 μm) is higher than the estimated optimum (1.86
μm) by about 15.8%. Also, the corresponding experimental MRR value (0.37
mm3/min) is lower than the estimated optimum (0.89 mm3/min) by about 140.5%.
Thus, a poorer process performance was obtained experimentally for both MRR
and Ra. This indicates that the overall efficiency of the process is less than
estimated by the developed model. One of the reasons for this could be that the
95
effect of high inlet air pressure and high spindle rpm combination has been over-
estimated by the model. High values of pressure and spindle speed lead to a
higher flushing efficiency. However there exists a limiting value of flushing
efficiency (100%), which is achieved when all the debris particles are flushed
away from the gap. Since there is a limit to the flushing efficiency improvement,
it may so happen that the flushing efficiency saturates at values lower than P=2.5
kgf/cm2 and N=2250 rpm due to the combined effect of the two factors. Thus, the
flushing efficiency estimated at the highest pressure and spindle speed
combination is probably greater than 100% and hence not feasible in practice.
Figure 5.23: Effect of gap voltage on Ra in finish machining region
The effect of gap voltage and discharge current on Ra is shown in Figure 5.23 and
Figure 5.24 respectively. It was found that the Ra value decreased with a decrease
in the voltage and current indicating that lower pulse energy leads to a lower Ra
value. The interaction plot (Figure 5.25) shows that there is no significant
interaction effect between voltage and current.
96
Figure 5.24: Effect of discharge current on Ra in finish machining region
Figure 5.25: Interaction plot for Ra in finish machining region
97
5.4.2 Rough machining region
In the rough machining region it was found that low values of gap voltage and
pulse-on time and high values of discharge current, duty factor, inlet air pressure
and spindle speed were favorable for obtaining a high MRR. Since values of gap
voltage lower than 55 V and pulse-on time lower than 50 μs were available on the
EDM machine, experiments were conducted at lower voltage and pulse-on times.
A 22 factorial experiment was conducted with Vg and Ton as the input parameter. 3
center runs were also included to check for curvature effect in the region.
Discharge current, duty factor, inlet air pressure and spindle speed were held
constant during the factorial runs. The input parameter values and the output
response (MRR and Ra) for the factorial runs are shown in Table 5.15. Best MRR
value of 6.83 mm3/min has been obtained.
Table 5.15: Experimental observations for factorial runs in the rough machining
region
Run Order Vg Id MRR Ra V A mm3/min μm 1 82 7 0.26 2.25 2 75 7 0.27 2.15 3 75 4 0.11 1.88 4 75 10 0.45 2.34 5 68 7 0.26 1.60 6 80 9 0.37 2.21 7 75 7 0.24 2.42 8 75 7 0.24 1.79 9 80 5 0.14 1.79 10 75 7 0.22 2.01 11 70 5 0.10 1.75 12 70 9 0.29 1.94 13 75 7 0.21 1.83
Ton=1000 μs , D=1, P=2.5 kgf/cm2, N=2250 rpm
98
The experimental MRR and Ra values corresponding to the input parameters
obtained by the GA optimization are highlighted in Table 5.15. It can be seen that
the experimental MRR value (6.83 mm3/min) is lower than the estimated
optimum (8.18 mm3/min) by about 19.8%. Also, the corresponding experimental
Ra value (2.97 μm) is higher than the estimated optimum (2.84 μm) by about
4.4%. Thus, the model over-estimates the process efficiency even in the rough
machining zone similar to the finish machining zone. However, the extent of
overestimation is lower than in the finishing zone. This could be due to a higher
amount of debris formation during rough machining because of which better
flushing is required in the rough machining zone. Thus, the saturation of flushing
efficiency takes place at higher values of inlet air pressure and spindle speed. At
the highest pressure and spindle speed combination there is indeed an increase in
flushing efficiency as predicted by the model. The model is thus closer to
experimental values in the rough machining region.
Figure 5.26: Effect of gap voltage on MRR in rough machining region
99
Figure 5.27: Effect of pulse-on time on MRR in rough machining region
The effect of gap voltage and pulse-on time on MRR is shown in Figure 5.26 and
Figure 5.27 respectively. It can be seen that the MRR increased when either the
gap voltage or the pulse-on time was increased. However, the central runs indicate
that there is sufficient curvature in the zone. The MRR values of central points lie
much below the MRR values at the ± 1 level. Apart from the curvature effect, one
of the reasons for this could be the effect of changes in the pulse-off time
accompanied by the changes in pulse-on time. Since the duty factor is held
constant during the experiments, the pulse-off time changes with changes in
pulse-on time. To investigate this further, experiments were conducted to observe
the changes in MRR with Toff at a constant value of Ton. The results are shown in
Figure 5.28. It can be seen that for a very low value of Toff, the MRR is low. As
the Toff is increased, MRR increases drastically and then falls down slowly with
further increase in Toff. This behavior is similar to the one obtained for Toff during
the OVAT experiments (Section 5.1.2). It was visually observed that a vigorous
100
sparking takes place for the Toff condition when MRR was high suggesting a
different discharge mechanism. One of the probable causes could be the presence
of an explosive mode discussed by Kunieda et. al. [5] which is active within a
specific Toff band. Spontaneous oxidation reaction takes place in the explosive
mode even during the pulse-off time leading to a relatively high MRR.
Figure 5.28: Effect of pulse-off time on MRR in rough machining region
5.5 Comparison with oil EDM
Experiments were conducted for the same input parameters for dry EDM and oil
EDM. The results are shown in Figure 5.29. It can be seen that the MRR in dry EDM
is much less than in oil EDM indicating a poorer performance in terms of MRR.
However, the TWR and Ra values obtained in dry EDM were much lower than in oil
EDM. This indicates that dry EDM has a better performance for finishing operations
and is also suitable for precision cutting due to the lower tool wear rate.
101
It is difficult to compare the overall process performance of oil EDM and dry EDM
by considering both MRR and Ra values simultaneously. Oil EDM had a higher MRR
where as dry EDM had a better surface finish. It may be argued that the reduction in
Ra value in case of dry EDM is only because of the corresponding reduction in MRR
and a similar Ra value may be achieved in oil EDM by changing the input parameter
values corresponding to a comparable MRR. In order to compare the performance of
the processes, the MRR and Ra values can be scaled by using Equations 2.4 and 2.7.
From Equations 2.4 and 2.7 it can be seen that MRR scales linearly with VgId where
as Ra scales as the cube root of VgId. Hence, the following relation must hold: 3
1 1
2 2
MRR RaMRR Ra
⎛ ⎞= ⎜ ⎟⎝ ⎠
(5.7)
According to this, when MRR for oil EDM reduces to 1.54 mm3/min from 28.97
mm3/min, the Ra should decrease from 18.9 μm to 7.1 μm. But it is found that for dry
EDM, a better value of Ra (3.9 μm) is obtained. Hence it can be concluded that dry
EDM gives a better surface finish than oil EDM for comparable values of MRR.
102
Figure 5.29: Comparison of dry EDM with oil die-sinking EDM
103
Chapter 6 Conclusion In the present work, parametric analysis of the dry EDM process has been done based on
experimental results. Experiments based on the Central Composite Design (CCD) were
conducted to develop empirical models of the process. Process optimization was then
performed using Genetic Algorithms (GA). Following conclusions can be drawn from the
analysis of the results:
a) From the preliminary experiments it was found that EDM with air as the dielectric
is feasible with reverse polarity. However, high velocity gas flow into the inter-
electrode gap through a hollow tubular tool electrode and rotation of the tool are
necessary conditions for obtaining a reasonable material removal rate. Flow
characteristic of the gas in the inter-electrode gap affects the material removal rate
(MRR) and the surface roughness (Ra), as was observed on changing the tool
outer diameter and the number of air-flow holes in the tool.
b) From the designed set of experiments based on CCD it was found that discharge
current, duty factor, air pressure and spindle speed are the significant factors
which affect MRR and MRR increases with an increase in any of these factors.
For MRR, most significant two-factor interaction effects are present among
current and duty factor, current and spindle speed and pulse-on time and duty
factor.
c) From CCD experiments it was found that except for gap voltage all other input
parameters (discharge current, pulse-on time, duty factor, air pressure and spindle
speed) have significant effect on Ra. Ra values decrease with a decrease in the
values of current and duty factor. Also, Ra values decrease with an increase in the
104
values of air pressure and spindle speed. No significant two-factor interactions
were found for Ra. However, Ra was found to have a quadratic dependence on
gap voltage and pulse-on time.
d) Based on the CCD experiments, the tool wear rate (TWR) was found to be very
small (less than 1% of the MRR). It was found that the TWR is independent of the
input parameters.
e) Multi-objective optimization revealed that high air pressure and high spindle
speed combination is favorable for obtaining both a high MRR and a low Ra.
Such a combination of these input parameters leads to a higher flushing
efficiency. Rough machining region (high MRR) was obtained for high current,
low pulse-on time and high duty factor values. Finish machining region (low Ra)
was obtained for low current, high pulse-on time and low duty factor values.
f) Focused experiments conducted in the finish and rough machining regions
revealed the existence of an additional process constraint based on the flushing
efficiency. Flushing efficiency cannot increase indefinitely with an increase in air
pressure and spindle speed since it saturates (theoretically to 100%) beyond some
combination of air pressure and spindle speed.
g) The air pressure and spindle speed values for flushing efficiency saturation
depend on the amount of debris produced during machining and hence depend on
the MRR. Under high MRR conditions, higher pressure and spindle speed values
are required for obtaining the saturation point of flushing efficiency. Thus,
predictions of the optimization model presented here are more close to the
experimental values in the rough machining region than in the finishing region.
h) A comparison of the process performance of dry EDM and oil EDM shows that a
better surface finish is obtained in dry EDM for comparable values of MRR.
Additionally, the TWR in dry EDM is very low. This suggests that the dry EDM
process is more suitable for precision EDM operations.
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Chapter 7 Scope for Future Work Analysis of the results obtained from the current work suggests several feasible
extensions to the research. Some of them are listed below:
a) One of the most relevant extensions would be conducting further experimental
investigations to identify the practical constraints (such as flushing efficiency) as
a function of the input parameters in order to improve the empirical process
models and the process optimization. Apart from that, the current research
establishes fairly well that the material removal rate (MRR) in dry EDM with air
as dielectric is poorer than oil EDM; however the tool wear rate (TWR) and
surface finish are better. Hence, further work may focus more on developing dry
EDM as a precision machining process. For that, it is important to study not only
the surface finish but also other performance variables such as over-cut, process
repeatability and surface integrity.
b) The current work was done using air as dielectric. It would be interesting to
compare the process performance of other gaseous dielectrics. Oxygen, nitrogen,
helium and argon are some of the most promising ones. It is expected that high
MRR would be obtained with oxygen. Nitrogen may be helpful if surface
treatments such as nitriding are required post-machining. Helium has a relatively
very high heat capacity and may provide better performance in terms of precision
of the cut. An optimization similar to the one presented in this work may be
performed and Pareto-fronts from each dielectric may then be superimposed on
the same graph. That would help in selecting the best dielectric-parameter setting
combination for the finish and rough machining conditions. The performance of
various gas-liquid dielectric combinations in near-dry EDM may also be studied.
106
c) In terms of applications, the dry EDM process may be implemented for
micromachining. Not much work has been done in this field so far and it would
require building up a knowledge base for the process at the micro-level to make
dry Electric Discharge Micromachining feasible. Additionally, dry EDM milling
characteristics may be investigated by implementing X-Y table movement.
Complex two or two and a half dimensional parts may be machined using the dry
EDM milling process.
d) Apart from experimental work, ample scope exists for theoretical modeling and
process simulation (such as finite element analysis) in dry EDM. Current
literature is insufficient in this regard. Existing oil EDM theory and simulation
models may be modified to include the effect of the gaseous dielectric. Also,
further computational work is required to fully understand the fluid dynamics of
the dielectric gas flow in the inter-electrode gap and its effect on process
performance. Results from the developed theoretical and computational models
may then be compared with the experimental results reported in this work.
107
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109
Appendix A Parameter Values for Optimum MRR and Ra In addition to the Pareto-front, the parameter values corresponding to the optimum
conditions are also generated by NSGA II. Parameter values corresponding to the
optimum points are shown in the following figures. To get the parameter values for an
optimum MRR and Ra combination (obtained from Figure 5.22), each parameter value
must be read from the corresponding 3D plot of the parameter versus Ra and 1/MRR. For
example, the optimum current value must be obtained from Figure A.1, optimum voltage
from Figure A.2 and so on. It must be noted that not all feasible combinations of MRR
and Ra are optimum. The optimum combinations must be obtained from the Pareto-
optimal curve (Figure 5.22). Only the parameter values corresponding to the optimum
MRR and Ra combinations have been shown in the following figures.
110
Figure A.1: Current values corresponding to optimum MRR and Ra combinations
Figure A.2: Voltage values corresponding to optimum MRR and Ra combinations
111
Figure A.3: Pulse-on time values corresponding to optimum MRR and Ra combinations
Figure A.4: Duty factor setting values corresponding to optimum MRR and Ra combinations
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Figure A.5: Air pressure values corresponding to optimum MRR and Ra combinations
Figure A.6: Spindle speed values corresponding to optimum MRR and Ra combinations
