EDM

Study of EDM and Optimization of its machining parameters

Department of Mechanical Engineering M.M.M. Engineering College Gorakhpur

1

Historical Perspective

In 1770, English physicist Joseph Priestley studied the erosive effect of electrical discharges. Furthering Priestley's research, the EDM process was invented by two Russian scientists, Dr. B. R. Lazarenko and Dr. N. I. Lazarenko, in 1943. In their efforts to exploit the destructive effects of an electrical discharge, they developed a controlled process for machining of metals. Their initial process used a spark machining process, named after the succession of sparks (electrical discharges) that took place between two electrical conductors immersed in a dielectric fluid. The discharge generator effect used by this machine, known as the Lazarenko circuit, was used for many years in the construction of generators for electrical discharge.

Additional researchers entered the field and contributed many fundamental characteristics of the machining method we know today. In 1952, the manufacturer Charmilles created the first machine using the spark machining process and was presented for the first time at the European Machine Tool Exhibition in 1955.

In 1969 Agie launched the world's first numerically controlled wire-cut EDM machine. Seibu developed the first CNC wire EDM machine 1972 and the first system manufactured in Japan.

There is clearly a need to understand the process closely.

When Japan began its reconstruction efforts after world war2, it faced an acute shortage of

good quality of raw materials, high quality manufacturing equipment and skilled engineers.

The challenge was to produce high quality products and continue to improve the quality

under those circumstances. The task of developing a methodology to meet the challenge

was assigned to Dr. Genichi Taguchi, who at that time was a manager in Nippon Telephone

& Telegraph Company. Thorough his research in the 1950s and early 1960s Dr. Taguchi

developed the foundations of robust design and validated its basic philosophies by applying

them in the development of many products. In recognition of this contribution, he received

the individual Deming Award in 1962, which is one of the highest recognition in quality field.

The robust design method can be applied a wide variety of problems. The application of the

method in electronics, automotive products, photography, and many others industries have

been an important factor in the rapid industrial growth and the subsequent domination of

international market in these industries by Japan.



2

Introduction

Electric discharge machining (EDM), sometimes colloquially also referred to as spark machining, spark eroding, burning, die sinking or wire erosion, is a manufacturing process whereby a desired shape is obtained using electrical discharges (sparks). Material is removed from the work piece by a series of rapidly recurring current discharges between two electrodes, separated by a dielectric liquid and subject to an electric voltage. One of the electrodes is called the tool-electrode, or simply the ‘tool’ or ‘electrode’, while the other is called the work piece-electrode, or ‘work piece’.

When the distance between the two electrodes is reduced, the intensity of the electric field in the volume between the electrodes becomes greater than the strength of the dielectric (at least in some point(s)), which breaks, allowing current to flow between the two electrodes. This phenomenon is the same as the breakdown of a capacitor (condenser) (see also breakdown voltage). As a result, material is removed from both the electrodes. Once the current flow stops (or it is stopped – depending on the type of generator), new liquid dielectric is usually conveyed into the inter-electrode volume enabling the solid particles (debris) to be carried away and the insulating proprieties of the dielectric to be restored. Adding new liquid dielectric in the inter-electrode volume is commonly referred to as flushing. Also, after a current flow, a difference of potential between the two electrodes is restored to what it was before the breakdown, so that a new liquid dielectric breakdown can occur.



3

Study of Electro Discharge Machining:

Process :

In EDM, a potential difference is applied between the tool and work piece. Both the tool and the work material are to be conductors of electricity. The tool and the work material are immersed in a dielectric medium. Generally kerosene or deionised water is used as the dielectric medium. A gap is maintained between the tool and the work piece. Depending upon the applied potential difference and the gap between the tool and work piece, an electric field would be established. Generally the tool is connected to the negative terminal of the generator and the work piece is connected to positive terminal. As the electric field is established between the tool and the job, the free electrons on the tool are subjected to electrostatic forces. If the work function or the bonding energy of the electrons is less, electrons would be emitted from the tool (assuming it to be connected to the negative terminal). Such emission of electrons are called or termed as cold emission. The “cold emitted” electrons are then accelerated towards the job through the dielectric medium. As they gain velocity and energy, and start moving towards the job, there would be collisions between the electrons and dielectric molecules. Such collision may result in ionisation of the dielectric molecule depending upon the work function or ionisation energy of the dielectric molecule and the energy of the electron. Thus, as the electrons get accelerated, more positive ions and electrons would get generated due to collisions.

This cyclic process would increase the concentration of electrons and ions in the dielectric medium between the tool and the job at the spark gap. The concentration would be so high that the matter existing in that channel could be characterised as “plasma”. The electrical resistance of such plasma channel would be very less. Thus all of a sudden, a large number of electrons will flow from the tool to the job and ions from the job to the tool. This is called avalanche motion of electrons. Such movement of electrons and ions can be visually seen as a spark. Thus the electrical energy is dissipated as the thermal energy of the spark.



4

Process Parameters :

The process parameters in EDM are mainly related to the waveform characteristics.

Fig. 2 shows a general waveform used in EDM.

The waveform is characterised by the

• The open circuit voltage - Vo • The working voltage - Vw • The maximum current - Io • The pulse on time – the duration for which the voltage pulse is applied - ton • The pulse off time - toff • The gap between the work piece and the tool – spark gap - δ • The polarity – straight polarity – tool (-ve) • The dielectric medium • External flushing through the spark gap.



5

Characteristics of EDM

(a) The process can be used to machine any work material if it is electrically conductive

(b) Material removal depends on mainly thermal properties of the work material rather

than its strength, hardness etc.

(c) In EDM there is a physical tool and geometry of the tool is the positive impression of

hole or geometric feature machined.

(d) The tool has to be electrically conductive as well. The tool wear once again depends on

the thermal properties of the tool material

(e) Though the local temperature rise is rather high, still due to very small pulse on time,

there is not enough time for the heat to diffuse and thus almost no increase in bulk

temperature takes place. Thus the heat affected zone is limited to 2 – 4 μm of the spark

crater

(f) However rapid heating and cooling and local high temperature leads to urface hardening

which may be desirable in some applications

(g) Though there is a possibility of taper cut and overcut in EDM, they can be controlled and

compensated.

Dielectric:

In EDM, as has been discussed earlier, material removal mainly occurs due to thermal

evaporation and melting. As thermal processing is required to be carried out in absence of

oxygen so that the process can be controlled and oxidation avoided. Oxidation often leads

to poor surface conductivity (electrical) of the workpiece hindering further machining.

Hence, dielectric fluid should provide an oxygen free machining environment. Further it

should have enough strong dielectric resistance so that it does not breakdown electrically

too easily but at the same time ionise when electrons collide with its molecule. Moreover,

during sparking it should be thermally resistant as well.

Generally kerosene and deionised water is used as dielectric fluid in EDM. Tap water cannot

be used as it ionises too early and thus breakdown due to presence of salts as impurities

occur. Dielectric medium is generally flushed around the spark zone. It is also applied

through the tool to achieve efficient removal of molten material.



6

Equipment:

• Dielectric reservoir, pump and circulation system

• Power generator and control unit

• Working tank with work holding device

• X-y table accommodating the working table

• The tool holder

• The servo system to feed the tool

Modelling of Material Removal and Product Quality

Material removal in EDM mainly occurs due to intense localised heating almost by point

heat source for a rather small time frame. Such heating leads to melting and crater

formation as shown in Fig.

The molten crater can be assumed to be hemispherical in nature with a radius r which forms

due to a single pulse or spark. Hence material removal in a single spark can be expressed as

the energy content of a single spark is given as



7

A part of this spark energy gets lost in heating the dielectric, and rest is distributed between

the impinging electrons and ions. Thus the energy available as heat at the workpiece is given

by

Now it can be logically assumed that material removal in a single spark would be roportional

to the spark energy. Thus

Now material removal rate is the ratio of material removed in a single spark to cycle time.

Thus

The model presented above is a very simplified one and linear relationship is not observed

in practice. But even then such simplified model captures the complexity of EDM in a very

efficient manner. MRR in practice does increase with increase in working voltage, current,

pulse on time and decreases with increase in pulse off time.

Product quality is a very important characteristic of a manufacturing process along with

MRR. The followings are the product quality issues in EDM

• Surface finish

• Overcut

• Tapercut

No two sparks take place side by side. They occur completely randomly so that over time

one gets uniform average material removal over the whole tool cross section. But for the

sake of simplicity, it is assumed that sparks occur side by side as shown in Fig.



8

Thus it may be noted that surface roughness in EDM would increase with increase in spark

energy and surface finish can be improved by decreasing working voltage, working current

and pulse on time.

In EDM, the spark occurs between the two nearest point on the tool and workpiece. Thus

machining may occur on the side surface as well leading to overcut and tapercut as depicted

in Fig. 5. Taper cut can be prevented by suitable insulation of the tool. Overcut cannot be

prevented as it is inherent to the EDM process. But the tool design can be done in such a

way so that same gets compensated.



9

RC type Relaxation Circuit of EDM:

In RC type generator, the capacitor is charged from a DC source. As long as the voltage in

the capacitor is not reaching the breakdown voltage of the dielectric medium under the

prevailing machining condition, capacitor would continue to charge. Once the breakdown

voltage is reached the capacitor would start discharging and a spark would be established

between the tool and work piece leading to machining. Such discharging would continue as

long as the spark can be sustained. Once the voltage becomes too low to sustain the spark,

the charging of the capacitor would continue. Fig. 8 shows the working of RC type EDM

relaxation.

Analytical Results and Formulae:

During charging, at any instant, from circuit theory,

Differential equation:

Solution:

where, Ic = charging current Vo= open circuit voltage Rc= charging resistance C = capacitance Vc= instantaneous capacitor voltage during charging



10

During discharging, the electrical load coming from the EDM may be assumed a totally

resistive and is characterised by a machine resistance of Rm. then the current passing

through the EDM machine is given by:

where, Id = discharge current or current flowing through the machine

Vc= instantaneous capacitor voltage during discharging

Rm= machine resistance



11

Study of Taguchi’s method of Design of experiment using

orthogonal arrays:

Literature Survey: The model quality improvement focuses on the reduction on variability of the manufactured

product. It is more costly to costly the cause of variations than to make a process insensitive

to control the cause of variations than to make a process insensitive to those variations. The

manufacturing variability can never be controlled if checked at the manufacturing and the

inspection stages only. Considerable advantages can be obtained by achieving product

quality at manufacturing process stage (Design stage) instead of controlling quality at

manufacturing process stage or through the inspection of the finished product.

Taguchi method is a powerful tool for the design of high quality system. It provides a simple,

efficient and systemic approach to optimize design of performance, quality and cost. The

methodology is valuable when the design parameters and qualitative or discrete. Taguchi

parameter design can optimize the performance characteristics through the setting of

design parameters and reduce the sensitivity of the system performance to source of

variations. In recent years the rapid growth of interest in the Taguchi method has led to

numerous applications of the method in a world-wide range of industries and nations.

In the present research work, the above methodology is employed to optimize the

machining parameters and to find out the most important factors and their influence on the

quality characteristics, i.e. surface roughness. In order to obtain better surface roughness,

the proper setting of cutting parameters is crucial before the process takes place. As a

starting point for determining cutting parameters, technologists could use the hands on

data tables that are furnished in machining data handbooks. Lin (1994) suggested that a trial

and error approach could be followed in order to obtain the optimal machining conditions

for a particular operation. Consequently, it is a very time consuming process of identifying

the optimum cutting conditions for a particular operation. Recently, a Design of Experiment

(DOE) has been implemented to select manufacturing process parameters that could result

in a better quality product.

The DOE is an effective approach to optimize the throughput in various manufacturing

related processes. In their study, three independent variables, each with three levels, had

total of (33) = 27 experimental runs. Oftentimes, the optimum metal cutting process

required studying more than three factors for the cutting parameters. For example, if a DOE

setup considered 4 or 5 independent variables, each with at least three levels, then (34)=81

runs or (35)=243 runs were required in the experiments. Imagining the total cost of these

experimental runs, one could conclude that it was very costly for the industry. In addition,



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the time of these runs could delay any quality resolving action for the industry. More

industrial technology (IT) graduates are facing challenges to improve the quality of products

and processes with minimum cost and time constraints in their careers. The Taguchi

parameter design techniques has been proved to be successful in the meeting this challenge

over the past 15 years. Therefore, there is a need to not only introduce our IT graduates to

DOE but also Taguchi parameter design.

In the present work, the experiments have been designed using highly fractional factorial

experimental design (Taguchi’s orthogonal array) to determine the influence of various

factors on the response. The experimental findings are used to identify the best

combination of parameters. It has been shown that this method yield the same or even

better results (in term of precision) as a complete factorial experiment. Basically the Taguchi

methodology is valuable when the design parameters are qualitative and discrete. In recent

years, the rapid growth of interest in the Taguchi method has led to numerous applications

of the method in a worldwide range of industries and nations.

Surface finish is one of the important criteria to be considered for proper functioning of

many machined part. It is found from result of metal cutting experiments that machining

variables like peak current, Pulse on Time and feed, and tool geometry have a marked

influence on the quality of surface produced. The roughness is directly dependent on the

peak current. In practice, the machining variables are often adjusted so as to give

dimensional accuracy only and further, if the finish is unsatisfactory, the setup is adjusted

until this difficulty is eliminated. The objective of this investigation is to experimentally

determine the effect of process variables on the surface finish obtainable during the process

and also to identify the parameters affecting the surface roughness

Subject overview:

Design of experiments (DOE) is a powerful statistical technique introduced by R.A Fisher in

England in 1920’s to study the effect of multiple variables simultaneously. In his early

applications, fisher wanted to find out how much rain, water, fertilizer, sunshine etc. are

needed to produce the best crop. Since that time, much development of the technique has

been taken place in the academic environment, but did help generate many applications in

the production floor.

As a researcher in Electronic Control Laboratory in Japan, Dr. Genechi Taguchi carried out

significant research with DOE techniques in the late 1940’s he spent considerable effort to

make his experimental technique more user friendly (easy to apply) and applied it to

improve the quality of manufactured products. Dr. Taguchi’s standardized version of DOE,

popularly known as the Taguchi approach, was introduced in the USA in the early 1980’s.



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Today it is one of the most effective quality building tools used by engineers in all types of

manufacturing activities.

The DOE using Taguchi approach can economically satisfy the needs of problem solving and

product/process design optimization projects. By learning and applying this technique,

engineers, scientists and researchers can significantly reduce the time required for

experimental investigations. DOE can be highly effective when we wish to:

Optimise product and process design, study the effects of multiple factors (i.e.-

variables, parameters, ingredients, etc.) on the performance, and solve production

problems by objectively laying out the investigate experiments. (Overall application

goals).

Study influence of individual factors on the performance and determine which factor

has more influence, which one have one less. We can also find out which factor

should have tighter tolerance and which tolerance should be relaxed. The

information from the experiments will tell us how to allocate quality assurance

resources based onobjective data. It will indicate whether a supplier’s part causes

problems or not(ANOVA data), and how to combine different factors in their proper

settings to get the best results(Specific Objectives).

Further the experimental data will allow us to determine:

How to substitute a less expensive part to get the same performance

How much money we can save the design improvement we propose

How we can determine which factor is causing most variations in the result

How we can set up our process such that it is insensitive to the uncontrollable

factors

Which factors have more influence on the mean performance

What we need to do to reduce performance variation around the target

How we can adjust the factors for a system whose response varies proportional

to signal factor(Dynamic response)

How to combine multiple criteria of evaluation into a single index

How we can adjust factor for overall satisfaction of criteria of evaluations

How the uncontrollable factors affect the performance



14

Taguchi Parameter Design:

In the early 1950s, Dr. Genichi Taguchi, “The father of quality engineering”, introduced the

concept of offline quality control techniques known as Taguchi parameter design. Offline

quality control techniques are those activities performed during the product (or process)

design and development phases. Taguchi parameter design is based on the concept of

fractional factorial design. The two major goals of parameter design are:

1. To minimise the process or product variation

2. To design robust and flexible processes or products those are adaptable to

environmental conditions.

“Robust” means that the process or product performs consistently and is relatively

insensitive to factors that are difficult to control.

Two important tools used in parameter design are orthogonal arrays and signal-to-

noise(S/N) ratios. Orthogonal arrays have a balanced property in which every factor setting

occurs the same number of times for every setting of all other factors in the experiment.

Orthogonal arrays allow researchers or designers to study many design parameters which

can be obtained with minimum time and resources. The signal-to-noise ratio is simply a

quality indicator by which the experimenters and designers can evaluate the effect of

changing a particular design parameter on the performance of the process or product. The

following are the steps of Taguchi parameter design:

1. Select the quality characteristics

2. Select noise factors and control factors

3. Select orthogonal array

4. Conduct the experiments

5. Analyse results; determine optimum factor level combination

6. Predict optimum performance

7. Confirm experimental design



15

Types of Optimization Problems

Taguchi Method treats optimization problems in two categories:

Static Problems

Generally, a process to be optimized has several control factors, which directly decide the

target or desired value of the output. Such a problem is called as a “Static Problem”. This is

best explained using a P-Diagram, which is shown (“P” stands for process or product). Noise

is shown to be present in the process but should have no effect on the output! This is the

primary aim of the Taguchi experiments-to minimize variations in output even though noise

is present in the process. The process is then said to have become ROBUST.

NOISE

OUTPUT

Z

Fig 3.1 P-Diagram for STATIC Problems

Dynamic Problems

If the product to be optimized has a signal input that directly decides the output, the

optimization involves determining the best control factor levels so the “input signal/Output”

ratio is closest to the desired relationship. Such a problem is called as a “Dynamic Problem”.

P-Diagram



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This is best explained by a P-Diagram, which is best shown below. Again the primary aim

of the Taguchi experiments-to minimize in output even though noise is present in the

process- is achieved by getting improved linearity in the input/output relationship.

NOISE

SIGNAL OUTPUT

Z

Fig.3.2 P-Diagram for DYNAMIC problems

8-Steps in Taguchi Methodology

Taguchi method is a scientifically disciplined mechanism for evaluating and implementing

improvements in products, processes, materials, equipment, and facilities.

These improvements are aimed at improving the desired characteristics and

simultaneously reducing the number of defects by studying the key variables controlling the

process and optimizing the procedures or design to yield the best results. The method is

applicable over a wide range of engineering fields that include processes that manufacture

raw materials, sub systems, products for professional and consumer markets.

P-Diagram



17

8-Steps in Taguchi Methodology are:

Identify the main function, side effects, and failure mode

Identify the noise factors, testing conditions and quality characteristics

Identify the objective function to be optimized

Identify the control factors and their levels

Select the orthogonal array matrix experiment

Conduct the matrix experiment

Analyze the data; predict the optimum levels and performance

Perform the verification experiment and plan the future action



18

Taguchi Method and ISO-9000

The ISO-9000 aims at improving the capability of an organization as a whole to manufacture

products to specified technical specification and quality standards and to deliver them to

the customer on time. Taguchi Method, on the other hand, attacks the product design itself.

Through product and process design optimization it improves product quality and reduces

costs drastically. Taguchi Method and ISO-9000 thus complement each other.

Quality Engineering Principles

Though “Quality” can be defined as “conformance to specification” and “fitness for use” etc

in the general concept, these definitions do not cover the entire implied meaning of quality.

The ideal Quality a customer can expect is that the product delivers the target performance

each time the product is used, under all intended operating conditions and throughout its

intended life, with no harmful side effects.

Dr. Taguchi brought the facility in the fraction defective definition for the quality, in which

the number of defectives based on the principle is depicted in Fig. 3.1 was the only concern.

As per his theory, the measure of quality of a product is in terms of the total loss to society

due to functional variation and harmful side effects. Under ideal quality, this loss is equal to

zero. Greater the loss, lower the quality. As per this the total cost of the product is the sum

of the operating cost including maintenance and inventory, the manufacturing cost, the R &

D cost(the time, laboratory charges, resources etc) and the cost incurred by its breakdown

and thereby the losses caused to the society.



19

Quality Loss Function & the Fraction Defective Fallacy

As per the definition, the quality loss function is the total loss incurred by the society due to

failure of the product to deliver the target performance and due to harmful side effects of

the product including its operating cost. According to the primitive concepts of quality, the

product was certified as good quality if measured characteristics were within the

specification & Vice versa. This is shown in Fig. 3.3

Reject Accept Reject

Good Good

Bad Good Good Good

Target- Target Target +

General Trend

Of Quality Definition



20

This means that all products that meet the specifications are equally good. But in reality it is

not so. The product whose response is exactly on target gives the best performance. As the

products performance deviate from the target, the quality becomes progressively worse.

These two quality philosophies are narrated in Fig. 3.4. as in one case, the focus is on

meeting the target and on other case the focus is on meeting tolerance. This is the actual

case study result on SONY TV companies of USA & Japan and demonstrates how the japan

made TVs were branded as high quality products by following the principle of focussing the

target than focussing the tolerance.

From these it can be realized that the true quality measure should not be based on the

step function as shown in Fig. 3.3 but as a quadratic loss function as shown in Fig. 3.4. Here

the quality loss function L(y) is symmetric about the target performance. As the

performance deviate from the target the quality loss correspondingly increases. Also the

cost of replacement or repair and represents the acceptable limit.

Quality loss L(y)

A

Target- Target Target+

Fig. Quality loss as a step function and quadratic function



21

As shown in Fig., with the quadratic loss function the quality loss is given by the relation

L=K(y-m)^2 , where k is constant called Quality Loss Coefficient. When y=m, loss is zero. The

loss L(y) increases slowly in the neighbourhood of m; but as we go further from m, the loss

increases more rapidly. The average quality loss incurred by a customer, who receives a

product with y as a the quality characteristics will be L(y).

L()y

Quality loss

m- m m+

L=K(Y-m)^2

Fig. Quadratic Quality Loss

L=Loss associated with attribute y

m=Specification target

k=constant depending upon the cost and width of the species

Example : The cost of scraping a part is Rs. 100 when it deviates ±0.50mm from a target

nominal of 2 mm.

Rs 100=k(2.5-2)^2

K=Rs. 400 per mm^2

L=400(y-2)^2



22

Different Types of Quality Loss Function

I. Nominal-the best Type

Is applicable where the quality characteristics y has a finite target value, usually

non-zero and the Q loss is symmetric on either side of target. E.g color density of a

TV set . This type is schematically shown in fig. 3.6

L()y

Quality loss

m- m m+ y

Fig. Quality loss function for Nominal the best type

II. Smaller the better type

For quality characteristics that can never take negative values and their

ideal value will be zero and as their value increases, performance becomes

progressively worse.

A

Loss

Fig. Quality Loss for smaller the better type



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Eg. Radiation leakage from a microwave oven , Response time of computer Pollution from

automobile etc.

III. Larger the better type

For Quality characteristics that do not take negative values and zero is their

worst value. As their value becomes larger the performance becomes progressively

smaller. Their ideal value is infinity and that point loss=zero. E.g.: Bond Strengthof

adhesive.

L(y)=k(1/y^2)

loss

A

Fig. 3.8 Quality loss for larger the better type



24

Matrix Experiments using Orthogonal Array

Robust design draws on many ideas from statistical experimental design to plan

experiments for obtaining dependable information about variables involved in making

engineering decisions. Various types of matrices are used for planning experiments to study

several decision variables simultaneously. Among them, robust design makes heavy use of

the orthogonal arrays.

Robust design adds a new dimension to statistical experimental design. It explicitly

addresses the following concerns faced by all product & process designers.

How to reduce economically the variation of a product function in the customer’s

environment. (Note that achieving a product function consistently on target

maximizes customer’s satisfaction )

How to ensure that decisions found to be optimum during laboratory experiments

will prove to be so in manufacturing & in customer environment.

In addressing these concerns, robust design uses the mathematical formalism of statistical

experimental design. A matrix experiment is a set of experiments, where we change the

setting of the various parameters we want to study from one experiment to another. After

conducting a matrix experiment, the data from all experiments in the set taken together are

analyzed to determine the effects of various parameters. The analysis of Means(ANOM) and

the analysis of variance (ANOVA) are used to interpret the data to find the sensitivity of

each parameters of interest.

Conducting the matrix experiments using special matrices called “Orthogonal Arrays” ,

allows the effect of several parameters to be determined efficiently and is an important

technique in robust design. The different levels of the parameters are known as

experimental region or the region of interest.

Orthogonality is interpreted in a combinatory sense -(i.e. ) for any pair of columns, all

combinations of factor levels occurs and they occur on equal number of times. This is called

the balancing property and it implies Orthogonality.

So an Orthogonal Array can be defined as a matrix with the columns representing the

number of parameters to be studied with their different levels in different combinations of

experiments and the number of rows equal to the number of experiments. Standard

orthogonal arrays are designed and are available. Selection of an orthogonal array for a

robust design project is based on the number of degrees of freedom of the experiment in



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such a way that the number of experiments should be greater than or equal to the number

of degrees of freedom.

Each parameter with n levels will have n-1 degrees of freedom and overall mean will have

one degree of freedom. In case of a robust design project with 4 parameters and three

levels, the total degrees of freedom will be 9. So the selected standard orthogonal array

should have at least 9 rows. A L4 array means an orthogonal array with 4 rows and an L8

array have 8 rows. Some of the standard orthogonal arrays are shown here in Table. Here

the otrhogonality is interpreted in a combinatory sense-(i.e.) for any pair of columns all

combinations of factor levels occur and they occur on equal number of times.

The column y1 to y4 in Table below are the different measurements taken on each setting

to capture noise effect. The performance or the responses measured in these matrix

experiments are analyzed using ANOM & ANOVA to find the relative effects of noises on the

response. By this method the optimum values of the control factors for which the sensitivity

of the response to the L9 othogonal array

Column N0.

Y1 y2 y3 y4

* * * *

* * * *

* * * *

* * * *

* * * *

* * * *

* * * *

* * * *

* * * *

Table. L9 Orthogonal array

Trial No. 1 2 3 4

1 1 1 1 1

2 1 2 2 2

3 1 3 3 3

4 5

2 1 2 3 2 2 3 1

6 2 3 1 2

7 3 1 3 2

8 3 2 1 3

9 3 3 2 1



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As mentioned earlier the columns y1 to y4 corresponds to the response measurements to

capture the effects of noises. These measurements should be planned according to the

sources of noises in the given problem. For each trial the average of all these y values are to

be taken.

Typically there are the following two choices regarding noise factors:

Improve the quality without controlling or removing the causes of variation

to make the product robust against noise factors.

Improve the quality by controlling the noise factors , or recommending

certain actions to control the noise factors.

The detailed steps in robust design are illustrated below:

L4 Array L8 Array

Table: L4& L8 orthogonal arrays with two levels.

Expt.

No.

Column

1 2 3

1 1 1 1

2 1 2 2

3 2 1 2

4 2 2 1

Exp

No.

Column

1 2 3 4 5 6 7

1

2

3

4

5

6

7

8

1

1

1

1

2

2

2

2

1

1

2

2

1

1

2

2

1

1

2

2

2

2

1

1

1

2

1

2

1

2

1

2

1

2

1

2

2

1

2

1

1

2

2

1

1

2

2

1

1

2

2

1

2

1

1

2



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Selection of factors levels:

A minimum of two levels is necessary to estimate a factor’s effect.

Continuous factors must be discretised (in preferably equal intervals).

Example: Levels of a length parameters: 1 cm, 1.5 cm and 2.0 cm.

The more levels the more experimental runs that are necessary/.

The number of levels indicates the resolution of effects that can be predicted.

The advantage of taking minimum of three points to capture the second order effect is

demonstrated in Fig. 4.5 and Fig 4.6 more the number of levels means more the capture of

non- linearity, but more the number of experiments and associated efforts. So it is

recommended to consider optimum of three levels. Fig. 4.5 demonstrates how the non-

linearity can be missed if only two levels are taken and in Fig 4.6, it is shown that

considering three levels will help in better representation of actual effect, which can be non-

linear. Even a three level combination wouldn’t capture the exact relationship. So the entire

matrix experimentation may have to be repeated several times to get most robust design.

Factor Assignment:

The selected factors are assigned to the different columns of the specific orthogonal array

as shown below.

The OA system in Table 4.4 is a 3 level, a 4 four parameter and 9 experiment orthogonal

array. The first column represents, starting from 1 to 9. Second to fourth columns are the

levels of each parameter or factors A,B,C and D. This will result in 9 experiments with factor

combinations as given in each row. For example, the first experiment will be conducted with

all the factors A, B, C and D at level 1. For the second experiment factor a will be at level 1 &

all other factors at 2 and so on.

As per this project concern this chapter introduces the techniques of matrix experiments

based on experimental rrays for optimisation of machining parameter to measure surface

roughness. The engineering issues inviolved in planning and conducting matrix experiment

and the technique of constructing orthogonal array are discussed in the following section



28

Table - factor level assignments

Before starting it is very essential to construct the proper orthogonal array for conducting

the experiment in a specific manner.

Trial number Factor A Factor B Factor C Factor 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



29

Selecting a standard orthogonal Array:

Taguchi has tabulated 18 basic orthogonal arrays that were called standard orthogonal

arrays. In many case studies, any of the arrays table 4.5, listed below is available and and

can be used directly to plan a matrix experiment. An array name indicates the number of

rows and columns it has, and also the number of levels in each of columns. Thus array L4

(23) has four rows and three level column ; and seven t3-level columns. Thus there are eight

columns in the L18 (2137). Table 4.5 listed the 18 standard orthogonal arrays along with the

number of columns at different levels:

Orthogonal array

No. of rows

Maximum no. of factors

Maximum no. of columns at these levels

2 3 4 5

L4 L8 L9 L12

4 8 9 12

3 7 4 11

3 7 - 11

- - 4 -

- - - -

- - - -

L16 L’16 L18

L25

16 16 18 25

15 5 8 6

15 - 1 -

- - 7 -

- 5 - -

- - - 6

L27 L32

L’32

L36

L’36

27 32 32 36 36

13 31 10 23 26

- 31 1 11 3

13 - - 12 13

- - 9 - -

- - - - -

L50

L54

L64

L’64

L81

50 54 64 64 81

12 26 63 21 40

1 1 63 - -

- 25 - - 40

- - - 21 -

11 - - - -

2 LEVEL ARRAYS: L4, L8, L12, L16, L32, L64

3 LEVEL ARRAYS: L9, L27, L81.

MIXED 2- AND 3- LEVEL ARRAYS: L18, L36, L’36, L54.

TABLE -4.5 Standard Orthogonal Arrays



30

Example: A case study has only two level factors and we are only interested in main effect

only. Here there are total eight degree of freedom- one of overall mean and seven for the

seven 2 level factor. Thus the smallest array L8 has seven 2- level columns and hence this can

study perfectly each column of array will have one factor assigned to it.

Counting the degree of freedom:

The first step tin constructing the orthogonal array to fit specific case is to count total

degree of freedom that tells the minimum number of experiments that must be performed

to study all the chosen control factors. To begin with one degree of freedom is associated

with the overall mean regardless the no. of experiments to be conducted. And as we have

three 3-level factors, the degree of freedom associated with each factor will be 2 degrees of

freedom. As we want to know the response change when the comparisons are done with

other two factors.

So, the degree of freedom for this project can be calculated as follows.:

Source of DOF DOF

Three 3level factor 3*(3-1)=6

Overall mean 1

Total 7

Since there three level factors in this project, it is preferable to use array from the three

level series because there are sevan degrees of freedom, the array must have 7 or more

rows.

Looking at Table 4.5 we see that the smallest array with the smallest array with at least 7

rows is Ls. but this array has seven 2-level columns. As per uor project, we nrrd 3-level

column. The next larger array is Ls which has four 3-level columns. Here we can assign three

3-Level factors to three of the four 3-level columns, keeping one 3-level column empty.

Keeping one or more column of an array empty lose not lose orthogonality of the matrix

experiment. So Ls is a good choice for this experiment. In a situation like this, we would take

another look at the control factors if there is an additional control factor to be studied which

we may have ignored as less important. If one exist it should assign in the empty column.

Doing this allow us a chance to gain information about this additional factor without

spending any more resources.



31

Linear graph and interaction assignment

Linear graph

Linear graph represent the interaction information graphically and make it easy to assign

and interactions to the various columns of an orthogonal array. In a linear graph dots and

lines represent the column of an array. When two dots are connected by a lines, it means

that the interaction of the two column represented by the dots is contained in column

represented by the line. In a linear graph each dot and each line has distinct column

numbers associated with it. Further every column of the array is represented in its linear

graph once and only once.

One standard linear graph for the array Ls is given in fig 4.7. It has two dots (or nodes)

corresponding to columns 1 and 2. Also it has one lines (or edges) representing column 3and

4. This line corresponds to the interaction between column 1 and 2.

1 2

Fig 4.7 Linear graph

in general, linear graph dose not show the interaction between every pair of columns of the

orthogonal array. That information contained in the interaction table.

Interaction between factors

Two factors (A and B) consider interaction between them one has influence of of the effect

of the other factor respectively.

Consider the factors “Temperature” and “Humidity” and their influence on comfort level. If

the temperature is increased by, say 20 degree F, the comfort level decreased by, say 30%

when humidity is kept at 90 %. On a different day, if the temperature is raised the same

amount at humidity level of 70%, the comfort level is reported to drop only by 10%. In this

case the factors “temperature” and “humidity” are interacting with each other.

Interaction:

Is an effect (output) and does not alter the trial condition.

Can be determined even if no column reserved for it.

Can be fully analysed by keeping appropriate column empty.

Affect the optimum condition and expected result.



32

Interaction table shows in which column the interaction is contained. Thus it can be used to

determined which column of the array should be kept empty in order to estimate particular

interaction.

The L9 orthogonal array has four column and nine rows. As per our project all the factors

that are chosen have three levels. So from the four 3-level column, colimn four is designated

as empty column and factor A through C were assigned respectively 1,2,3.any columns can

be assigned to any factor, exept to the factor that are difficult to change, which should be

assigned to the column toward left.

Expt no Column number and factor assignment

1 A

2 B

3 C

4 E

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

*empty column are identified by E

Table - L9 orthogonal array and Factors assignment



33

The nine rows of the L9 array represent the nine experiment 1 to be conducted at level 1 to

for each of the three next chapter. These labels can be read from table 4.6, which is

mentioned in next chapter. However to make it convenient and to prevent translation error,

the entire matrix of table 4.6 should should be translated using the level definitions in table

4.7 to create the experimenters log sheet.

Expt no Column number and factor assignment

1 A

2 B

3 C

1 8 200 6

2 8 500 12

3 8 750 18

4 10 200 6

5 10 500 12

6 10 750 18

7 12 200 6

8 12 500 12

9 12 750 18

Table – The experimenter’s log



34

Multi-objective optimization:

Generally in industries for every product and process there are always more than one

responses that are of manufacturing and quality interest. While varying the input

parameters to change the output the values of responses change and sometimes in a

completely independent manner. From the quality point of view it can’t be allowed for one

response to be of very high quality and other to be of very low. Therefore, the multi –

optimization problem solving requires finding out a perfect balance between the values of

different responses so that the overall quality can be maximized. In modern industry the

goal is to manufacture low cost, high quality products in a short time.

Furthermore, during the problem solving the experimentation is to be done. For

experimentation the input parameters are to be selected to study their effect on responses.

The responses chosen to be studied upon should be of quality importance. This implies that

the responses selected should be such that the quality depends on them highly. Selection of

parameters is whole new task.

After the selection of parameters and responses different levels of input parameter are

decided. Then the combinations of these parameter levels are made and experiment are

conducted. Observations show the variation of response at every different combination of

input parameters. After this the multi-response analysis techniques are used to analyse the

data and find out the best combination.

Here in this study the experiments are planned through the Taguchi method which generally

quite successfully implemented in process optimization. Therefore the study intends to

apply the Taguchi method to plan the experiments on the EDM operation. After the

planning of experiments, the study is to investigate the optimization of EDM operation

parameters using the Grey Relational Analysis method to obtain the best combination or

optimum parameters to obtain the best multi response i.e. surface finish, tool wear rate,

and material removal rate. Here we shall employ statistical methods to EDM operation.

There are a lot of different parameters affecting surface finish, tool wear rate, and material

removal rate are peak current, applied voltage, pulse on time, pulse off time, dielectric flow

rate etc. The surface properties, average roughness, electrode wear rate, and material

removal rate (MRR) are selected quality targets or the response variables.

The controlling parameters that are chosen for the study purpose are peak current, pulse on

time, and duty cycle. An optimal parameter combination of the turning operation will be

found out via the Grey Relational Analysis. By analysing the Grey relational matrix, the

degree of influence for each controllable factor onto each quality target can also be

ascertained.



35

Grey Relational Analysis :

Grey Relational Analysis. The Grey System Theory that was developed by Deng (1982) is

mainly utilized to study system models uncertainty, analyse relations between systems,

establish models, and forecast and makes decisions (Deng, 1984). Grey Relational Analysis is

utilized to probe the extent of connections between two digits by applying the methodology

of departing and scattering measurement to the actual measurement of distance. Grey

Relational Analysis is an effective means of analysing the relationship between two series.

This study applies grey relational analysis to measure the similarity between the series.

1. Data Pre-processing

Grey data processing must be performed before Grey correlation coefficients can be

calculated. A series of various units must be transformed to be dimensionless. Usually, each

series is normalized by dividing the data in the original series by their average. Let the

original reference sequence and sequence for comparison be represented as xo(k) and xi(k),

i=1, 2, . . .,m; k=1,2, . . ., n, respectively, where m is the total number of experiment to be

considered, and n is the total number of observation data. Data pre-processing converts the

original sequence to a comparable sequence. Several methodologies of pre-processing data

can be used in Grey relation analysis, depending on the characteristics of the original

sequence.

If the target value of the original sequence is “the-larger-the-better”, then the original

sequence is normalized as follows:

If the purpose is “the-smaller-the-better”, then the original sequence is normalized as

follows:



36

However, if there is “a specific target value”, then the original sequence is normalized using,

2. Grey Relational Coefficients:. Following the data pre-processing, a Grey relational

coefficient can be calculated using the pre-processed sequences. The Grey relational

coefficients are calculated to express the relationship between the ideal (best =1) and the

actual experimental results. The grey relational coefficient δij can be expressed as follows:

Where xio

is the ideal normalized results for the ith performance characteristics and δ is the

distinguishing coefficient which is defined in the range 0 ≤ ξ ≤ 1. ξ is also called

environmental factor.

Computing the Grey Relational Grades:

A Grey relational grade is a weighted sum of the Grey Relational Coefficients. The Grey

relational grade corresponding to each performance characteristic is to be computed and

the overall evaluation of the multi response characteristic is based on the Grey relational

grade, which is given by:

GRG =

,

Here, the Grey relational grade represents the level of correlation between the reference

and comparability sequences. If the two sequences are identical, then the value of the Grey



37

relational grade equals to one. The Grey relational grade also indicates the degree of

influence exerted by the comparability sequence on the reference sequence. Consequently,

if a particular comparability sequence is more important to the reference sequence than

other comparability sequences, the Grey relational grade for that comparability sequence

and the reference sequence will exceed that for other Grey relational grades. The Grey

relational analysis is actually a measurement of the absolute value of data difference

between the sequences, and can be used to approximate the correlation between the

sequences.



38

EXPERIMENTAL DESIGN, SET-UP AND ANALYSYS:

Principle of operation: Electrical discharge machining

In the precision engineering the electrical discharge machining is very important method of

manufacturing. In this electrical sparks cause the metal removal and MRR is measured due

to heat produced. Work piece and tool both are conductive material. Spark is generated

between tool and work piece and that’s why the electricity is generated and heat is

produced all these happens within micro seconds. The frequency of sparking may be

thousands of sparks in a second the area over which he spark is effective is very small. And a

very high temperature is developed. Partly melting and partly vaporizing material from a

localised area on the both of electrodes i. e. work piece and tool is found.

The material is removed in the form of craters which spreads over the entire surface of the

work piece. Finally the cavity produced in the work piece is approximately the replica of the

tool. To have machined cavity as replica of the tool wear should be zero. The tool wear is

minimised by Taguchi’s method.

Fig.

The above figure shows the experimental set-up with basic components of z- axis controlled

electrical discharge machine. The schematic diagram of machining operation through

electrical discharge machining shown in the fig. The EDM used for our experiment has been

manufactured by electronica machine Tools Ltd.



39

Specification of the EDM machine used for experimentation

Value of current density varies with the tool material used.

1. For copper maximum current density is 5 to 7 amp/ cm2.

2. For graphite maximum current density varies from 7 to 10 amp/cm2

3. For Tungsten – Copper maximum current density varies from 12 to 15 amp/cm2

Pluse on- time: Range 0.5 to 4000 micro seconds

The following discrete value can be taken with this EDM in the process.

Pulse on time values: 0.5, 0.75, 1.5, 2, 3, 4, 5, 7, 5, 10, 15, 20, 30, 40, 50, 75, 100, 150,

200, 300, 400, 500, 750, 1000, 1500, 2000, 3000, and 4000.

Pulse duty factor: Range 1 to 12 in the steps of 1.

Gap voltage: 50 V

Flushing Pressure: 0.1 kg/cm2

Electrode: copper

Electrode polarity: positive

Dielectric: kerosene (EDM oil)

Flushing condition: Side pressure flushing

Mains voltage: 3Ф, 415 V

Peak current: Range 0 to 50 ampere in steps of 0.5.

Surface Roughness Measurement: Sutronic 10.



40

Factors to be optimized:

The most important factor to be optimized is surface roughness since cost and life of

a component depends upon its surface roughness. The S/N to be used for surface

roughness is smaller the better.

The factor of concern is Material removal rate. Higher the material removal rate,

higher will be the production. The S/N ratio to be used for MRR is larger the better.

To have the exact machined cavity replica of the tool the wear should be as small as

possible. Therefore, the S/N ratio for this case will be smaller the better.

Selection of the control factors:

In case of EDM the control factor i.e. the factors which can be easily controlled and affects

the response are:

Duty cycle

Pulse on time Ton

Peak current

PULSE ON TIME: During this period the voltage is applied across the tool and the work

piece.

DUTY CYCLE: it is the ratio of on time and of time of EDM. Duty cycle control the amount of

time the pulse should apply the energy.

PEAK CURRENT: it is the maximum current obtained in the process.

Selection of the factor levels:

More the numbers of the factor levels mean more the capture of linearity but more the

number of experiments and associated effort. Three factor levels are considered optimum in

this experiment to reach any conclusion.

Duty cycle: (Range: 1 to 12 in the steps of 1)

Low 8

Medium 10

High 12



41

Current: (Range: 0 to 50 amp in steps of 0.5)

Low 6 Amp

Medium 12 Amp

High 18 Amp

Pulse on time Ton: (Range 0 to 400 μs)

Low 200 μs

Medium 500 μs

High 750 μs

Selection of orthogonal array:

Out of 18 basic tabulated orthogonal arrays to select an appropriate orthogonal array

degree of freedom is defined as the no. of comparisons between the design parameter to be

made to determine which level is better and specifically by how much.

Once the degree of freedom is known, the next step is to select an appropriate orthogonal

array. Here the degree of freedom associated with each parameter is two, as the there are

three levels and one degree of freedom is associated with mean of the parameters

regardless the no. of parameters. Therefore, the degree of freedom is 3*2 + 1= 7. The

Taguchi’s design suggests that:

DOF of Orthogonal Array => Total degree of freedom

Thus, the orthogonal array that will be satisfying this condition is L9 array (its degree of

freedom is 8). This array has nine rows that represent the trial conditions for the factor

levels indicated by the no. of rows. The vertical column corresponds to the factors specified

in the study and each contains a total of nine conditions for the factor assigned to that

column. Each column has nine conditions (1,1), (1,2), (1,3),(2.1),(2,2), (2,3), (3,1), (3,2), (3,3).

Note that any two columns have same no. of combinations. So, all four columns are said to

be balanced, orthogonal, and statistically independent of each other. The experimental

layout for the orthogonal array is shown in table. Since the orthogonal array has four

column it has one column empty for the error of experiment.

Orthogonality is not lost by one empty column. The input parameters are put in the column

and there outputs are MRR, SR, and TW.



42

The experiments were performed in similar sequence as mentioned in the table. Data

obtained for the response through the experiments were performed in the similar sequence

as mentioned in the table. During the experiments the data obtained as response is noted.

ORTHOGONAL ARRAY OF THE FACTORS

S. no. Duty cycle (T)

Ton(μs) Peak current (Ampere)

E(error)

1. 8 200 6 1

2. 8 500 12 2

3. 8 750 18 3

4. 10 200 12 3

5. 10 500 18 1

6. 10 750 6 2

7. 12 200 18 2

8. 12 500 6 3

9. 12 750 12 1



43

The above sequence when was executed on the machine the following observations were

obtained:

Table 1:

Tool Wear Rate

S. NO. Weight in gm. (before

machining)

Weight in gm. (after machining)

Difference

1. 160.484 160.435 0.049

2. 158.625 158.406 0.219

3. 160.172 159.345 0.827

4. 160.389 159.981 0.408

5. 159.345 158.017 1.328

6. 160.435 160.416 0.019

7. 158.406 157.159 1.247

8. 159.981 159.951 0.03

9. 160.345 159.903 0.451



44

Table 2:

Material Removal Rate

S. no.

Before machining After machining Weight difference

Weight (gm.)

Avg. surface roughness(μs)

Weight (gm.)

Avg. surface roughness(μs)

1. 83.628 39.4 82.737 19.1 0.891

2. 80.432 36.7 76.807 28.65 3.625

3. 83.63 35.2 80.665 28.5 3.018

4. 79.119 31.2 76.413 19.125 2.706

5. 84.203 29.8 80.854 26.25 3.349

6. 84.149 29.6 83.531 15.98 0.618

7. 85.184 31.4 81.844 26.00 3.34

8. 83.779 30.7 82.984 18.55 0.795

9. 89.169 31.7 86.326 24.30 2.843



45

S.no. Duty cycle

Ton P.I. E Surface roughness Avg. S.R.

MRR TWR

1 2 3 4

1. 8 200 6 1 20.7 21.1 17 17.9 19.1 74.25 4.08

2. 8 500 12 2 29.6 25.8 28.8 30.4 28.65 302.08 18.25

3. 8 750 18 3 2.6 34.3 30.7 26.4 28.5 251.5 68.92

4. 10 200 12 3 11.9 20.6 20.3 31.7 19.125 225.5 34

5. 10 500 18 1 32.9 22.5 20.8 28.8 26.25 279.04 110.06

6. 10 750 6 2 10.9 18 15.3 19.7 15.8 51.50 1.58

7. 12 200 18 2 24.5 23.7 28.5 26.3 26 278.33 103.92

8. 12 500 6 3 12.7 27.8 25.0 8.7 18.55 66.25 2.50

9. 12 750 12 1 34.7 20.9 13.2 28.3 24.3 236.92 37.58



46

ANALYSIS OF RESULTS:

Grey relational analysis of collected data:

Step 1: Normalization of response data:

Normalized response table:

Formula used:

Where: xi*(k) is the normalized response, and xi(k) is the orignal response

Avg. S.R.

Normalized Avg. S.R.

MRR Normalized MRR

TWR Normalized TWR

19.1 0.7537 74.25 0.09 4.08 0.9769

28.65 0.0 302.08 1.00 18.25 0.8463

28.5 0.0118 251.5 0.798 68.92 0.3792

19.125 0.7517 225.5 0.694 34 0.701

26.25 0.1894 279.04 0.908 110.06 0.00

15.8 1.00 51.50 0.00 1.58 1

26 0.20915 278.33 0.905 103.92 0.0566

18.55 0.797 66.25 0.0588 2.50 0.99

24.3 0.3433 236.92 0.7399 37.58 0.668



47

Step 2: Calculation of Grey relational Coefficients (GRC) and

Grade (GRD).

Formula used: (γi(k) is GRC)

& GRD=

GRC (Avg. S.R.) GRC (MRR) GRC (TWR) GRD

0.6699 0.3546 0.9608 0.6617

0.33 1.0 0.7648 0.6994

0.3359 0.7122 0.4461 0.4981

0.6681 0.6203 0.6258 0.6088

0.3815 0.8446 0.3333 0.5198

1.00 0.3333 1.000 0.7777

0.373 0.8403 0.3464 0.52467

0.7112 0.3469 0.9 0.6793

0.4322 0.6578 0.6 0.5033

As shown in the table that the greatest value of grey relational grade is .7777 therefore the

combination of the parameters in the experiment will have the best possible compromise

between the responses and the optimized machining parameters.



48

Regression analysis of the experimental data:

Regression analysis: Surface roughness vs x1, x2, and x3The Regression

analysis was performed by MINITAB software to find out the interaction of Duty cycle (x1),

Pulse on time Ton (x2), and Peak Current (x3) on the average surface roughness (SR), and

Material removal rate (MRR). The regression equation obtained is given below:

regression equation obtained is given as:

Different values of surface roughness is obtained by keeping two values constant and

varying any one of the value. Three lines are plotted in one graph showing change in nature

of one factor by varying the other. This shows the interaction one factor with other.



49

S.R

.

D.C.

Ton=200

Ton=500

Ton=750

1. Effect of Duty cycle on surface roughness with varying pulse on time

Surface roughness is decreasing with increase in pulse n time. Higher is the duty cycle lower

is the surface roughness. However variation in Pulse On Time effects the nature of graph of

Duty Cycle. With the increase in Pulse On Time the curve the curve become almost flat i.e,

there is very slight change in surface roughness.



50

S.R

.

D.C.

I.P.=6

I.P.=12

I.P.=18

2. Effect of Duty Cycle on surface roughness with varying peak current

All the three lines in the graph almost coincide with each other. This shows that peak

current feebly affects the nature of graph of duty cycle vs surface roughness. Higher value of

surface should be selected to minimize surface roughness.



51

Ton

S.R

.

I.P.=6

I.P.=12

I.P.=18

3. Effect of Pulse ON Time on Surface Roughness with varying Peak

Current

nature of the graph is changing wiyh varying peak current. It shows that peak current and

pulse on time interacts with each other in the manner shown in the graph.



52

Ton

S.R

.

D.C. 8 D.C. 10 D.C. 12

4. Effect of pulse on time on Surface Roughness with duty cycle varying

Pulse on time has very less effect on surface roughness at low duty cycle but this effect

becomes significant at higher value of duty cycle. Surface roughness starts increasing with

pulse on time at higher value of duty cycle.



53

I.P.

S.R

. D.C. 8

D.C. 10

D.C. 12

5. Effect of Peak Current on Surface Ruoghness with Duty Cycle

With the increase in peak current the surface roughness increases. As the lines obtained are

parallel it shows that with increase in pulse on time the surface roughness increases but the

nature of the graph remains unaffected.



54

I.P.

S.R

.

6. Effect of Peack Current on Surface Roughness wih varying

Pulse on Time

Since all the three lines almost coincide with each other, it shows that effect of these two

factors on surface roughness are almost independent of each other.

Ton 200 μs

Ton 500 μs

Ton 750 μs



55

Regression analysis MRR vs. x1, x2, x3

Similar as obtained for surface roughness different values of maerial rate is obtained by

keeping two values constant and varying any one of the value three lines are plotted in one

graph showing change in nature of one factor by varying the other this shows the

interaction of one factor with other.

1. Effect of duty cycle on MRR with varying Pulse on Time

MRR decreases with increase in Duty cycle. With increase in Ton the curve shifts downwards.



56

2. Effect of duty cycle on mrrr with varying peak current

With increases in duty cycle mrr decreases, but the nature of the curve remains same. It can

be seen that the changes are not very high.

3. Effect of Pulse on Time on MRR with varying Duty Cycle

With increase in TON the MRR decreases. At lower duty cycle the curve is shifted high but as

d.c. increases the MRR decreases. At high peak current the MRR increases with increase in

duty cycle.



57

4. Effect of Pulse on time on MRR with varying peak current

With increase in Pulse on Time the MRR decreases. The magnitude of MRR increases but the

nature remains same.

5. Effect of Peak Current on MRR with varying Duty Cycle

MRR increases with increasing Peak current. The nature of the curve remains same .



58

6. Effect of peak current on MRR with varying Pulse on Time

MRR increases with increasing peak current. The nature of the curve remains same. With

increasing Ton MRR decreases.

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