33

CHAPTER 4

EXPERIMENTAL DETAILS

4.1 RESEARCH METHODOLOGY

The methodology that has been adopted to accomplish the

objectives of this Research work is summarized in the flow chart shown in the

Figure 4.1. Experimental investigation and optimization of machining

conditions of the materials with different thermal properties or advanced

materials, such as Incoloy 800, Titanium alloy and AISI D3 tool steel on

WEDM have been selected as a broad field of research.

WEDM technology has been found to be one of the most recently

developed advanced non-traditional methods used in industry for material

processing with the distinct advantages of no thermal distortion, high

machining versatility, high flexibility, rapid machining and high accuracy of

complex parts. WEDM utilizes a continuously travelling wire electrode made

of thin copper, brass or tungsten of diameter 0.05–0.3 mm, which is capable

of achieving very small corner radii. The wire is kept in tension using a

mechanical tensioning device reducing the tendency of producing inaccurate

parts. During the WEDM process, the material is eroded ahead of the wire

and there is no direct contact between the work piece and the wire, thus,

eliminating the mechanical stresses during machining. In addition, the

WEDM process is able to machine exotic and high strength and temperature

resistive (HSTR) materials and eliminate the geometrical changes that

normally occur in the machining of heat-treated steels (Ho et al 2004).

Furthermore, WEDM is capable of producing a fine, precise, corrosion-

resistant and wear resistant surface.

34

Selection of Material for the

focused area

Design of

Experiment

Selection ofInput andOutput

Parameters

Selection of Research

Area

Machining of Work

Materials by WEDM

Identification ofResearchable problem by

delimation

Extensive LiteratureSurvey

Conclusions and Further Research

Validation of output

Development of

Mathematical Model

Optimization using

Grey-Taguchi method

Result and

Discussions

Microstructure

study

Figure 4.1 Research methodology

35

In wire electrical discharge machining (WEDM), the cost of

machining is rather high due to a high initial investment for the machine and

the cost of the wire which is used as a tool in this process. The WEDM

process is economical if it is used to produce intricate shapes and varying

tapers in all electrically conductive materials irrespective of their hardness

and toughness.

The lack of information in the previous research works in this

domain was identified and used to define the research problem. The thrust

activities in the development of these materials influence the scope of the

research were identified for investigation and subsequently, research

methodology has been designed. Experiments have been conducted by

applying the designed research methodology. The results of the application of

research methodology were analysed and reviewed. Based on the review of

the results, conclusions have been drawn. Finally, the scope for further

research has been projected.

4.2 SELECTION OF WORK MATERIALS

As need for materials with different thermal and mechanical

properties or advanced materials like Incoloy 800, Titanium alloy and AISI

D3 tool Steel, grows in technologically sophisticated industries such as

aerospace, electronics, defence automotive, nuclear, medical, chemical,

structural and tool and die making industries. So machining of these materials

in WEDM process have been identified as the research problem based on

extensive literature.

From the literature review it was observed that the ultimate goal of

the WEDM process is to achieve an accurate and efficient machining

operation without compromising the machining performance and settings for

machining of these work materials have to be further optimized

experimentally.

36

4.2.1 Incoloy 800

Incoloy 800 is one of iron based exotic super alloy or Heat

resistant alloy, mainly used in chemical processing applications such as heat

exchanger, piping, mixing tanks, heat treatment equipment, muffles,

conveyors, baskets and boxes. Also it is widely used in nuclear power

plants(for steam-generator tubing), domestic appliances (for sheathing of

electric heating elements), Thermal processing equipment in industrial

applications( such as baskets, trays, and fixtures), production of paper pulp,

digester-liquor heaters, pumps, valves, Jigs, fixtures, aerospace and jet engine

components. Table 4.1 shows the chemical composition of Incoloy 800.

Table 4.1 Chemical composition of Incoloy 800

Element C Cr Mn Al Mo Ni Fe Ti W V Co

Wt % 0.096 20.096 0.501 0.302 0.335 34.991 42.821 0.304 0.066 0.027 0.07

The important mechanical and physical properties of the Incoloy

800 work material are listed in Table 4.2.

Table 4.2 Properties of Incoloy 800

Properties Values

Melting point(°K) 1658Hardness Brinnell (HB) 179Density (Kg/m3) 7940

Modulus of elasticity(GPa) 198Tensile strength(MPa)) 600Yield strength(MPa) 275

Electrical resistivity m) 0.98Specific Heat capacity(J/Kg°K) 460

Coefficient of Thermal Expansion (/°K , at 20°C) 14.4 x 10-6

Poisson’s ratio 0.34Elongation (annealed) 30%

Thermal conductivity(W/m°K) 11.5

37

Incoloy 800 is generally referred as difficult-to-cut alloy due to its

low thermal conductivity and low heat dissipation quality at elevated

temperatures.

4.2.2 Titanium alloy

Titanium and its alloys have been experiencing extensive

development over the past few decades stimulated by a series of their unique

properties, such as high strength-to weight ratio maintained at elevated

temperature, high hot hardness, high fracture resistance, and exceptional

resistance to corrosion at temperature below 500°C.

Titanium alloy (Ti-6Al-4V) is typical alpha-beta titanium alloy,

which is usually used in the medical, aerospace, automotive, petrochemical,

nuclear and power generation industries. Although titanium alloys have

outstanding mechanical properties, their low thermal conductivity, low

Young’s modulus and high heat capacity may cause difficulties in heat

dissipation during cutting process, which result in high cutting temperatures

concentrated at a narrow region adjacent to the cutting edge, where the

temperature can reach as high as 1,000°C. Another significant characteristic

of titanium alloys is a very high chemical reactivity. As a result, tool wear

progresses rapidly, and then reduces the tool life and machining quality. The

chemical composition of Titanium alloy is presented in Table 4.3.

Table 4.3 Chemical composition of Titanium Alloy

Element Ti Al V Fe O C N H

Wt % 89.464 6.08 4.02 0.22 0.18 0.02 0.01 0.0053

Mechanical and physical properties of the Titanium alloy work

material are listed in Table 4.4.

38

Table 4.4 Properties of Titanium alloy

Properties Values

Melting point(°K) 1933

Density (Kg/m3) 4420

Specific Heat capacity (J/Kg°K) 530

Thermal conductivity(W/m°K) 7.2

Coefficient of Thermal Expansion (/°K , at 20°C) 8.0 x 10-6

Electrical resistivity ( m) 1.78

Tensile strength(MPa) 950

Yield strength(MPa) 880

Hardness, Brinell(HB) 334

Hardness, Rockwell(HRC) 36

Modulus of elasticity(GPa) 114

Poisson’s ratio 0.342

Percentage elongation (annealed) 18

Ti-6Al-4V alloy is an important material in modern industry. Its

exceptional properties, such as high strength-weight ratio, high temperature

stability and outstanding corrosion resistance, make it widely used in the

aerospace, automobile, chemical and biomedical fields. However, poor

machinability using the traditional mechanical cutting process results in high

tooling costs. Therefore, nontraditional machining methods, such as WEDM

have been explored to machine this alloy.

4.2.3 AISI D3 Tool Steel

AISI D3 Tool Steel is a high carbon and high chromium steel

developed for applications requiring high resistance to wear or to abrasion

and for resistance to heavy pressure rather than to sudden shock. Because of

39

these qualities and its non-deforming properties, AISI D3 Tool Steel is

unsurpassed for die work on long production runs. The production from a die

after each grind is consistently uniform. While the impact strength is

comparatively low, by proper adjustment of tool design and heat treatment,

this steel has been used successfully for punches and dies on quite heavy

material. Table 4.5 shows the chemical composition of AISI D3 tool steel.

Table 4.5 Chemical composition of AISI D3 Tool Steel

Elements C Cr Mn S Mo Ni Fe Si W V P

Wt % 2.078 11.125 0.223 0.030 0.060 0.152 85.740 0.395 0.056 0.106 0.031

Important properties of the AISI D3 tool steel are listed in

Table 4.6.

Table 4.6 Properties of AISI D3 tool steel

Properties Values

Melting point(°K) 2590

Hardness, Rockwell (HRC) 62

Hardness, Brinell (HB) 225

Density (Kg/m3) 7700

Modulus of elasticity(GPa) 194

Tensile strength(MPa) 850

Yield strength(MPa) 495

Electrical resistivity m) 0.98

Specific Heat capacity(J/Kg°K) 460

Coefficient of Thermal Expansion (/°K , at 20°C) 11 x 10-6

Poisson’s ratio 0.30

Elongation (annealed) 25%

Thermal conductivity(W/m°K) 20.5

40

4.3 MACHINE TOOL IDENTIFICATION

In this research, experimentations have been performed on Elektra

Ecocut CNC WEDM machine, manufactured by Electronica Machine Tools

Limited, India.

Increasing demands in the field of High precision machine

technology require a higher quality standard of machining systems.

Inaccuracies in conventional machining are a result of inaccuracies in the

quality of the machining systems. Some of the reasons are:

Axial and Radial run out of the machining spindle.

Resolution of the control system.

Resolution of the measurement system.

Inaccuracies in Vibration dampers.

Inaccurate drive elements.

Fluctuations in temperature, air pressure and humidity.

Elektra Ecocut achieves high accuracy in machining by solving

these problems effectively.

The Elektra Ecocut WEDM machine consists of four subsystems :

1. Machine tool

2. Wire movement

3. Power supply

4. Dielectric fluid

Figure 4.2 shows the Photographic view of Elektra Ecocut WEDM

Unit.

41

Figure 4.2 Photographic view of Elektra Ecocut WEDM Unit

4.3.1 Sample Photograph of Ti-6Al-4V Work Material

Rectangular jobs of sizes 5 mm × 5 mm × 8 mm were cut from the

work material as test specimens for every experimental run and sample

photograph of Ti-6Al-4V Work Material is shown in Figure 4.3.

Figure 4.3 Photograph of the sample work material

42

4.3.2 Technical Specifications

The technical specifications of Elektra Ecocut WEDM are tabulated

in Table 4.7 (Manual).

Table 4.7 Technical Specifications

Maximum table size 600 × 370 mm

Maximum work piece height 200 mm

Maximum work piece weight 275 kg

X,Y table traverse 250,350 mm

U,V table traverse 30,30 mm

Vertical traverse (z) 200 mm

Main table feed rate 80 mm/ min

Max. Cutting speed 70 mm2/min.

Maximum Taper angle ± 8° over 50 mm

Wire guide type Diamond closed

Wire electrode diameter 0.25 mm (std), 0.15,0.2,0.3 mm (optional)

Max. wire pool capacity 6 Kg

Input power supply 3 phase, AC 415V, 50 Hz

Dielectric fluid Deionized water

Connected load 7.5 kVA

Servo speed, SF (mm/min) 1 (at no load) normal servo control

Wire tension WT (g) 500

Wire speed WS (mm/min) 12

Flushing pressure WP (bar) 45

Polarity Work piece: Positive

Wire electrode: Negative

Wire electrode Brass (hard brass) wire (Ø 0.25 mm)

43

4.3.3 Wire Electrode

Cutting performance of the WEDM process depends on a

combination of electrical and mechanical characteristics. Surface finish and

tolerance control are strongly related to the quality of the electrode, which

must posses electrical conductivity, close size tolerance, and strength to allow

tensioning to limit bow or taper in a work piece.

Based on the above information, the selection of the right wire to be

used in this study will be more convenient. After considering all the important

criteria, the brass wire of 0.25 mm diameter was used in the experiments as

wire material. This wire will be used for the whole experiments in order to

investigate the surface quality of the machined surface of work materials.

Positive polarity was maintained for workpiece and negative polarity is

maintained for the tool (wire).

4.3.4 Dielectric Fluid

De-ionized water is the dielectric fluid which is generally used for

WEDM. Water was used because it can be flows better into the small slots

than other dielectrics and provides good cooling. Some machines submerge

the work piece, machine arms, and guides in a dielectric bath to control

thermal changes. In some cases, oil was used as a dielectric. Hydrocarbon

dielectrics have been applied in laboratory environments to investigate the

cutting performances during finishing stages. In other cases, air, gas, or plain

water is used. The major advantage of water is formed by its good cooling

qualities, which are needed for the energy transmission during the wire

cutting process.

44

4.4 SELECTION OF MACHINING PARAMETERS

Based on the literature reports, there are twelve machining factors

that are directly involved in WEDM operation. Some of the factors are

significant in influenced the performance characteristics and some are less.

The literatures on the significance affect of these parameters to the machining

process already have been discussed in Chapter 2. Four cutting parameters

have been identified by the aid of previous researches and literature reviews

affecting the work materials machining performance; gap voltage, Pulse on

time, Pulse off time and wire feed and A, B, C and D are the corresponding

notations respectively. The setting of the machining parameters and their

levels are given in Table 4.8.

4.4.1 Gap Voltage

The gap voltage is the nominal voltage in the gap between the wire

and workpiece. Thus, increasing distance between the wire and workpiece

means increasing gap voltage, and vice-versa. Increasing gap voltage also

usually means decreasing cutting speed and will improve the flushing

conditions and helps to stabilize the cut. The WEDM training manual

compares gap voltage to feed of workpiece of a band saw.

4.4.2 Pulse on Time

During WEDM all the work is done during pulse on time (Pulse

duration) and the erosion rates are affected mainly by pulse parameter. Metal

removal is directly proportional to the amount of energy applied during the

pulse on time. The energy applied during the pulse on time controls the peak

amperage and the length of the pulse on time. If the pulse on time is longer,

then more workpiece material will be melted away. Consequently the

resulting craters will be broader and deeper; therefore the surface finish will

45

be rougher. Obviously with shorter duration of sparks the surface finish will

be better.

4.4.3 Pulse off Time

To complete the cycle sufficient Pulse off time is needed before the

next cycle can be started. Other than that, the Pulse off time (Pulse interval)

also affects the speed and the stability of the cut. From theory, the shorter the

interval the faster the machining operation will be. But this will affect the

workpiece material where it will not be swept away by the flow of the

dielectric and as a result the fluid will not be de-ionized. As a result the next

pulse will be unstable and hard to control. This unstable condition will cause

erratic cycling and retraction of the advancing servo and this will slow down

the cutting rate. At the same time, pulse interval must be greater than the

de-ionization time to prevent continued sparking at one point. In addition, the

Pulse off time also provides the time to clear the disintegrated particles from

the gap between the electrode and workpiece for efficient cut removal

(Ho et al 2003).

4.4.4 Wire Feed Rate

Wire feed rate is traverse velocity of the wire as it moves through

the workpiece. It determines rate of material removes from workpiece. It is

important to note that this is not a constant speed, but it can be thought of as

maximum possible speed. The machine reads the actual gap voltage, and

automatically increases or decreases feed rate to maintain constant gap

voltage. This denotes the wire velocity. Its significance on the material

46

removal rate and surface finish is very low. Increase in wire feed rate slightly

increases surface finish.

4.5 SELECTION OF PERFORMANCE CHARACTERISTICS

The performance characteristics (output parameters) are the

dependent variables which are the output of the experiment during machining

operation. Material removal rate, surface roughness and Kerf width are

important features on WEDM since the MRR determines the economics of

machining and rate of production while the surface roughness influences the

performance of machined surface and Kerf width determines the dimensional

accuracy of the finishing part. Hence these performance characteristics have

been selected for this research as output responses based on identification by

the previous researchers as the most significant machining criteria that can

influence the WEDM performance (Mahapatra and Amar Patnaik 2007,

Ahmet Hascalyk et al 2004).

4.5.1 Material Removal Rate

In WEDM operations, material removal rate (MRR) determines the

economics of machining and rate of production. Material removal rate is a

rate at which the material is removed from the work materials in WEDM

machine. The effects of the machining parameters on the MRR have also been

considered as measure of the machining performance. The mean cutting

speed data (Cs) was observed directly from the computer monitor, which was

attached to the machine tool.

MRR ( Tosun et al 2004, Mahapatra and Patnaik 2007) is

calculated by using the following formula (Equation 4.1),

MRR = Kf × t × vc × (4.1)

47

where, MRR - Material Removal Rate (g/min)

Kf - Kerf width (mm)

t - Thickness of work piece (mm)

cv - Cutting speed (mm/min)

- Density of the work piece material (g/mm3)

4.5.2 Surface Roughness

Surface roughness and dimensional accuracy have been important

factors in predicting the machining performances of any machining operation.

Surface roughness plays an important role in many areas and is a factor of

great importance in the evaluation of machining accuracy. Surface roughness

is the surface irregularities of machined surfaces.

The surface roughness parameter used to evaluate surface

roughness in this study is the Roughness average (Ra). This parameter is also

known as the arithmetic mean roughness value, Arithmetic Average (AA), or

Centreline Average (CLA). Within the presented research framework, the

discussion of surface roughness is focused on the universally recognised Ra

(in m). The average roughness is the area between the roughness profile and

its centre line, or the integral of the absolute value of the roughness profile

height over the evaluation length.

The arithmetic surface roughness value (Ra) will be adopted and

measurements will be carried out on work specimens using a contact stylus

surface roughness tester shown in Figure 4.4.

48

Figure 4.4 Surface roughness tester

Conditions for surface roughness measurement:

Cutoff Length 0.8mm

Evaluation Length 4.0mm

Measuring Speed 0.05mm/Sec

Vertical Magnification 10000

Horizontal Magnification 5000

4.5.3 Kerf width

Kerf width is one of the important performance measures in

WEDM. Kerf width is the measure of the amount of the material that is

wasted during machining. It determines the dimensional accuracy of the

finishing part. The internal corner radius to be produced in WEDM operations

are also limited by the Kerf width. The wire-workpiece gap usually ranges

from 0.025 to 0.075mm and is constantly maintained by a computer

controlled positioning system.

49

The Kerf was measured using the Mitutoyo tools makers’

microscope (100 X), is expressed as sum of the wire diameter and twice of

wire-workpiece gap. Kerf width can directly be measured from the slot in the

machined workpiece by using Video Measuring System as shown in

Figure 4.5.

Figure 4.5 Video measuring system

4.6 SCANNING ELECTRON MICROSCOPE

The Scanning Electron Microscope (SEM) is one of the most

versatile and widely used tools of modern science as it allows the study of

both morphology and composition of biological and physical materials. The

poor surface characteristics such as high tensile residual stresses, high surface

roughness, presence of micro-cracks and micro-voids caused by WEDM were

analyzed by Scanning Electron Microscopy (SEM).

50

The JEOL6300F, JEOL Ltd., Japan SEM unit as shown in

Figure 4.6 is used in this research. It uses a field emission gun with cold

cathode. The resolution is 1.5 µm in secondary electron imaging and 3.0 µm

in backscattered electron imaging at 30 kV. The airlock specimen chamber

allows up to a 32 mm diameter sample, and the size can also be up to 150 mm

without the airlock.

Figure 4.6 Scanning electron microscope

4.7 DESIGN OF EXPERIMENT

Design of Experiments (DOE) refers to planning, designing and

analyzing an experiment so that valid and objective conclusions can be drawn

effectively and efficiently. 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. Each factor can take several values during the

51

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 essential to incorporate statistical data analysis methods in the experimental

design in order to draw statistically sound conclusions from the experiment.

Proper experimental design significantly contributes towards the

accurate characterization and optimization of the process. Here, the criterion

for experimental design and analysis is to achieve higher MRR along with

reduction in Kf and reduced Ra. The increase in MRR and reduction in Kf is

required to increase productivity, dimensional stability and improvement in

geometrical trueness.

4.7.1 Selection of an orthogonal array

Before selecting a particular orthogonal array (OA) to be used as a

matrix for conducting the experiments, the following points must first be

considered :

1. The number of variables and interaction of interest

2. The number of levels for the variables of interest

3. Resource and budget availability, and

4. The time constraint

The non-linear behavior, if exist, among the process variables can

only be studied if more than two levels of the variables are used. The number

of Machining parameters (process variables) and their levels with their

notations are identified and selected from the discussion in section 4.4 and

from the manufacturer manual, are presented in Table 4.8. To limit the study,

it was decided not to study the second order interaction among the variables.

52

Table 4.8 Machining parameters and their Levels

Symbol Machining parameters Unit Level 1 Level 2 Level 3

A Gap voltage V 50 60 70

B Pulse on time s 6 8 10

C Pulse off time s 4 6 8

D Wire feed rate mm/min 6 8 10

Each three level parameter has two degree of freedom (DOF) (number

of levels – 1), the total DOF required for four variables each at three levels is

8(i.e.) 4× (3–1). As per Taguchi’s method the total DOF of selected OA must

be greater than or equal to the total DOF required for the experiment (Roy,

2001). So an L9 OA (a standard three-level OA) having 8 DOF was selected

for the present analysis (Table 4.9). The typical L9 orthogonal array layout

with factors is shown in Table 4.10.

Table 4.9 L9 Orthogonal array layout

Exp. No.Machining parameters

A B C D

1 1 1 1 1

2 1 2 2 2

3 1 3 3 3

4 2 1 2 3

5 2 2 3 1

6 2 3 1 2

7 3 1 3 2

8 3 2 1 3

9 3 3 2 1

53

Table 4.10 L9 Orthogonal array layout - with factors

Exp. No.Machining parameters

A B C D

1 50 6 4 6

2 50 8 6 8

3 50 10 8 10

4 60 6 6 10

5 60 8 8 6

6 60 10 4 8

7 70 6 8 8

8 70 8 4 10

9 70 10 6 6

4.8 GREY-TAGUCHI OPTIMIZATION METHOD

Dr.Genichi Taguchi, a Japanese scientist, developed a technique

based on OA of experiments. This technique has been widely used in different

fields of engineering to optimize the process parameters (Taguchi,1986). The

integration of DOE with parametric optimization of process can be achieved

in the Taguchi method. An OA provides a set of well-balanced experiments,

and Taguchi’s signal-to-noise (S/N) ratios, which are logarithmic functions of

the desired output, serve as objective functions for optimization. It helps to

learn the whole parameter space with a small number of experiments. OA and

S/N ratios are used to study the effects of control factors and noise factors and

to determine the best quality characteristics for particular applications. The

optimal process parameters obtained from the Taguchi method are insensitive

to the variation of environmental conditions and other noise factors.

However, originally, Taguchi method was designed to optimize single-

54

performance characteristics (Taguchi 1986). Optimization of multiple

performance characteristics is not straightforward and much more

complicated than that of single-performance characteristics. To solve the

multiple performance characteristics problems, the Taguchi method is

coupled with grey relational analysis.

Any system in nature is not white (full of precise information); on

the other hand, it is not black (complete lack of information) either, and it is

mostly grey (a mixture of black and white). Grey relational analysis (GRA) is

part of grey system theory, which was proposed by Deng (1982) to fulfill the

crucial mathematical criteria for dealing with poor, incomplete, and uncertain

system. When experiments are ambiguous or when the experimental method

cannot be carried out exactly, grey analysis helps to compensate for the

shortcomings in statistical regression (Ross 1996).This grey-based Taguchi

technique is a completely new analysis method applied to solve the

multicriteria problems in diverse fields such as agriculture, ecology, economy,

meteorology, medicine, history, geography, industry, earthquake, geology,

hydrology , irrigation strategy, military affairs, sports, traffic, management,

material science, environment, biological protection, and judicial system etc.,

(Deng 1989).

The Grey-Taguchi method, a powerful experimental design tool,

uses simple, effective, and systematic approach for deriving of the optimal

machining parameters. Further, this approach requires minimum experimental

cost and efficiently reduces the effect of the source of variation. So this

method can be effectively employed for optimizing WEDM parameter.

The GRA procedure is used to combine all the considered

performance characteristics into a single value that can then be used as the

single characteristic in optimization problems. The procedure of the grey-

based Taguchi method is given under the following sections (Yiyo Kuo et al

2008).

55

4.8.1 Experiment Design and Execution

Basically, classical process parameter design is complex and not

easy to use. Many experiments have to be carried out when the number of

process parameters increases. To solve this task, the Taguchi method uses a

special design of orthogonal arrays to study the entire process parameter

space with a small number of experiments. Therefore, the first step of the

proposed procedure of WEDM optimization is to select an appropriate OA as

discussed in section 4.7.1. The experimental runs are then executed by

following the experimental structure of the selected L9 OA.

4.8.2 Signal-to-noise(S/N) Ratio Calculation

Taguchi’s method uses the statistical measure of performance

called signal-to-noise ratios (S/N), which is logarithmic functions of desired

output to serve as objective functions for optimization. The ratio depends on

the quality characteristics of the product/process to be optimized. The three

categories of S/N ratios are (a) higher the better (HB), (b) lower the- better

(LB) and (c) nominal-the best (NB). The parameter level combination that

maximizes the appropriate S/N ratio is the optimal setting.

In WEDM, the higher MRR, the lower Ra nd minimum are the

indication of better performance. Hence, the HB type S/N ratio was applied

for MRR and can be expressed (Kao 2010, Huang and Liao 2003) as

( ) 10 1

n

1

y (4.2)

where = number of replications,

= observed response value of the MRR calculated the th time

and = 1,2,….. ; = 1, 2... .

56

And also, the LB type S/N ratio was applied for Ra and , can be

expressed (Kao 2010, Huang and Liao 2003) as

( ) 10 1

ny (4.3)

4.8.3 Grey Relational Generating

When the units in which performance is measured are different for

different responses, the influence of some responses may be neglected. This

may also happen if some performance responses have a very large range. In

addition, if the goals and directions of these responses are different, this will

cause incorrect results in the analysis (Huang and Liao 2003).

The S/N ratios obtained by Taguchi’s method are normalized in the

range of 0 and 1, and this procedure is known as grey relational generating

(Deng, 1989). As the HB was applied to maximise the MRR, the normalised

result of HB was obtained from the following equation,

== 1,2,…

= 1,2,… = 1,2,… (4 .4)

As the LB was applied to the lower Ra and minimum , the

normalised result of LB was obtained from the following equation,

== 1,2,…

= 1,2,… = 1,2,… (4.5)

where is the value after the grey relational generation,

max ( ,, = 1,2,….. ) is the Largest value of for the th

response ,

min ( ,, = 1,2,….. ) is the Smallest value of for the th

response

57

Basically, the larger normalized S/N ratio corresponds to the better

performance and the best-normalized S/N ratio is equal to unity.

4.8.4 Reference Sequence Definition

After the grey relational generating procedure, all performance

values will be scaled into [0, 1]. For an response of scenario , if the value

that has been processed by grey relational generating is equal to 1, or

nearer to 1 than the value for any other scenario, the performance of scenario

is the best one for response . Therefore, a scenario will be the best choice if

all of its performance values are closest to or equal to 1. However, this kind of

scenario does not usually exist. This article defines the reference sequence

as ( , ,…, , . . . , ) = (1, 1, . . . , 1, . . . , 1), and then aims to

find the scenario whose comparability sequence is the closest to the reference

sequence.

The =1, =1, 2… 9 are the ideal sequence for MRR, SR and

Kerf. The definition of the grey relational grade in the grey relational analysis

is to show the relational degree between the sequences of and

( =1, 2… 9; = 1, 2… 9).

4.8.5 Grey Relational Coefficient Calculation

Next, the Grey relational coefficient is calculated to express the

relationship between the ideal (best) and actual normalized S/N ratio. The

Grey relational coefficient for the th performance characteristic in the th

experiment can be expressed as

( ) ( ) =(k)

(4.6)

j

58

where;

1. = 1,2... ; k = 1,2... , is the number of experimental data

items and is the number of responses.

2. ( ) is the reference sequence ( ( )= 1, = 1,2... );

( ) is the specific comparison sequence.

3. = ( ) ( )

is the ( ) ( )

4. = min min ( ) ( )

( )

5. = max max ( ) ( )

( )

6. denotes the equation’s ‘‘contrast control’’ which is also

known as the distinguishing coefficient and in the range

1. The purpose of the distinguishing coefficient is to

expand or compress the range of the grey relational

coefficient. The value is normally set at 0.5 for the grey

system (Deng 1989, Kao et al 2010).

4.8.6 Grey Relational Grade Calculation

After the grey relational coefficient is derived, it is usual to take the

average value of the grey relational coefficients as the grey relational grade

(Lin and Ho 2003). The grey relational grade is defined as following:

=1

(4.7)

where is the grey relational grade for the th experiment and is the

number of performance characteristics.

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However, in a real engineering system, the importance of various

factors to the system varies. In the real condition of unequal weight being

carried by the various factors, the grey relational grade in Equation (4.6) was

modified and the weighted average grey relational grade defined as follows :

=1

(4.8)

where is the grey relational grade for the th experiment, is the

weighting factor for the th performance characteristics.

4.9 NON-LINEAR REGRESSION ANALYSIS

The purpose of developing the mathematical model relating the

responses and their process parameters was to facilitate the optimization of

machining new and advanced engineering materials, ceramic materials and

MMCs in WEDM and to achieve higher MRR with a desired accuracy and

surface finish. However, the selection of cutting parameters for obtaining

higher cutting efficiency or accuracy in WEDM is still not fully solved, even

with the most up-to date CNC WEDM machine. This is mainly due to the

nature of the complicated stochastic process mechanisms in wire EDM. As a

result, the relationships between the cutting parameters and the process

performance are hard to model accurately.

Many researches have successfully used Regression analysis

method to obtain the mathematical relations between machining outputs and

machining process parameters (Ozdemir et al 2005, Tosun et al 2003). SPSS,

SAS, Mat lab software are used to analysis the regression model. In this

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research, Non-linear regression analysis was used to establish a mathematical

model between the experimentally obtained machining outputs and machining

parameters of WEDM by SPSS software.

Non-linear regression analysis is a collection of mathematical and

statistical techniques that are useful for modeling and analysis of problem in

which a response of interest is influenced by several variables and the

objective is to optimize these responses. Non-linear regression analysis allows

for better understanding of relations between inputs and responses. In case of

WEDM process the inputs refers gap voltage, pulse on time, pulse off time

and wire feed rate and the responses are material removal rate, surface

roughness and Kerf width.