Optimization of cutting parameters for cnc plasma cutting machine alfhatech maxpro 200

Kurdistan Region
Salahaddin University-Erbil
College of Engineering
Mechanical Engineering Department
Optimization of cutting parameters for
CNC plasma cutting machine alfhatech
MAXPRO 200
A Project Submitted to the Mechanical Engineering Department
University of Salahaddin-Erbil
in the Partial Fulfillment of the Requirement for the Degree of Bachelor of Science
in Mechanical Engineering
Prepare By:
Kosar Faruq
Mazyar Taha
Hawre Tofiq Ali
Hogr Mohammed
Supervisor:
Dr. Abulkader Kadauw
2016 - 2017

ii
Abstract
In last forty years there is tremendous research in machining and
development in technology. With increase in competition in market and to
attain high accuracy now a days the nonconventional machining are become
lifeline of any industry. One of the most important non-conventional
machining methods is Plasma Arc Machining. Its high accuracy, finishing,
ability of machining any hard materials and to produce intricate shape
increases its demand in market.
This project work focuses on finding out the optimum parameters in plasma
arc cutting for machining of Steel. With the use of plasma arc cutting
machine the cutting is possible by using different process parameters as
cutting speed, arc current, gas pressure, arc gap, kerf, etc. and gets the
changes in response variables like surface roughness and material removal
rate.
To optimization of all these parameters with multi responses characteristics
based on the Grey Relational Analysis. By analyzing grey relational grade,
it is observed that which parameter has more effect on responses of process
parameters to the response variables. Our team has used three process
parameters (cutting speed, arc current, gas pressure) and two response
variables (surface roughness, material removal rate).
Also from grey relational analysis it concludes that 10th
experiment give
multi-performance characteristics of the plasma arc cutting process among
the 18 experiments. From grey relational analysis it will also conclude that
the optimum parameter level for cutting speed, arc current and gas pressure
are (3800 mm/min), (130 amp) and (60 Psi) respectively. The results shows
its better surface roughness and material removal rate prediction capabilities
and applicability to such industrial plasma arc cutting leading to effective
selection of machining parameter for better qualitative cutting

iii
Acknowledgement
First and foremost, we wish to express my sincere appreciation to our project
guide Dr. Abulkader Kadauw , Department of Mechanical engineering,
Salahaddin University-Erbil, a decent and disciplined personality, keep
interest, giving immense encouragement, inspiring guidance, constructive
criticism and fruitful suggestions, throughout the course of our studies and
completion of this manuscript.
We would also like to acknowledge with much appreciation the essential role
of Mr.Azwar A. Hussein and Mr. Fakhir A. Rozhbiany, providing the
facilities to perform the experiment work.
We are thankful to all teaching and non-teaching faculty members of
Mechanical engineering department, and all staff members of College of
Engineering, for providing help me directly or indirectly in bringing of this
piece of work successful completion.
We like to thanks Abdulla jawhar Company which support us through
giving some plate sheet for the work.

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Supervisor’s Certificate
I certify that the engineering project titled "Optimization of cutting
parameters for CNC- plasma cutting machine alfhatech MAXPRO 200”
was done under my supervision at the Mechanical Engineering Department,
College of Engineering - Salahaddin University–Erbil. In the partial
fulfillment of the requirement for the degree of Bachelor of Science in
Mechanical Engineering.
Supervisor
Signature:
Name: Assist. Prof. Dr.
Date: / /

v
List of Contents
Abstract .........................................................................................................ii
Acknowledgement........................................................................................iii
Supervisor’s Certificate................................................................................iv
List of Contents.............................................................................................v
List of Figures ..............................................................................................ix
List of Tables................................................................................................xi
Nomenclature ..............................................................................................xii
1 Introduction ............................................................................................1
1.1 Overview...........................................................................................1
1.2 What is a Plasma? .............................................................................2
1.3 Introduction to CNC plasma cutting machine ..................................3
1.4 How plasma cuts through metal?......................................................4
1.5 Sequence of operating plasma cutter ................................................5
1.6 Shielding and cutting gases for plasma cutting ................................7
1.7 Plasma gas selection .........................................................................8
1.7.1 Air plasma ..............................................................................8
1.7.2 Nitrogen Plasma .....................................................................8
1.7.3 Argon/Hydrogen Plasma........................................................9
1.7.4 Oxygen Plasma.......................................................................9
1.8 Secondary gas selection for plasma cutting......................................9
1.8.1 Air secondary .........................................................................9
1.8.2 CO2 secondary .......................................................................9
2 Devices ...................................................................................................11
2.1 System.............................................................................................11
2.1.1 Control panel (CNC) ............................................................12
2.1.2 Power supply ........................................................................12
2.1.3 Compressor...........................................................................13

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2.1.4 Torch 13
2.1.5 Torch Consumable ...............................................................14
2.1.5.1 Electrode.................................................................14
2.1.5.2 Swirl ring ................................................................15
2.1.5.3 Nozzle.....................................................................15
2.2 Operating system Software.............................................................16
2.2.1 Operating the CNC...............................................................16
2.2.2 Operator Console..................................................................16
2.2.3 Touch Screen LCD...............................................................16
2.2.4 Shape Library .......................................................................17
3 Design of Experiments .........................................................................18
3.1 Introduction.....................................................................................18
3.2 Design factors .................................................................................19
3.2.1 Process parameters ...............................................................19
3.2.1.1 Cutting speed..........................................................19
3.2.1.2 Arc Current.............................................................19
3.2.1.3 Gas pressure............................................................20
3.2.2 Response variables ...............................................................20
3.2.2.1 Surface roughness...................................................20
3.2.2.2 Material removal rate .............................................21
3.3 Design of experiments ....................................................................22
3.3.1 Introduction ..........................................................................22
3.3.2 Methods of DOE ..................................................................22
3.3.2.1 Factorial method.....................................................23
3.3.2.2 Response surface method .......................................23
3.3.2.3 Taguchi method......................................................24
3.3.3 Selection of work sample .....................................................24
3.3.3.1 Material selection ...................................................24
3.3.3.2 Shape and size selection .........................................25

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3.3.4 Selection of process parameters ...........................................26
 Process parameters..................................................26
 Process parameters with levels value .....................26
 Fixed variables........................................................26
3.3.5 Experimental design.............................................................27
3.4 Summary .........................................................................................27
4 Experimental Measurement and Results...........................................28
4.1 Measuring surface roughness and Material Removal Rate ............28
4.1.1 Surface roughness Measurement..........................................28
4.1.2 Material Removal Rate Measurement..................................29
4.2 Experimental Results ......................................................................31
4.3 Analysis...........................................................................................32
4.3.1 Analysis of variance.............................................................32
4.3.1.1 Introduction ............................................................32
4.3.1.2 Analysis of variance (ANOVA) terms & Notations
32
4.3.1.3 Analysis of Variance for surface Roughness .........34
4.3.1.4 Analysis of Variance for Material Removal Rate..38
4.3.2 Multi response optimization.................................................42
4.3.2.1 Grey relation Analysis for Multi Object Optimization
42
4.3.2.2 Data pre-processing................................................43
4.3.2.3 Grey relational coefficient and grey relational grade
44
4.3.2.4 Process steps for multi response optimization .......45
4.3.2.5 Normalization of experimental result.....................46
4.3.2.6 Calculation of deviation sequence..........................47
4.3.2.7 Calculation of grey relational coefficient and grey
relational grade .......................................................48

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4.4 Analysis and discussion of experimental results ............................51
4.4.1 Graph for grey relational grades...........................................51
4.4.2 Main effect plot for grey relational grade ............................52
4.5 Summary .........................................................................................54
5 Results and Conclusion........................................................................55
5.1 Main Effect Plot for Process Parameters v/s Response Variables..55
5.2 Conclusion ......................................................................................60
References ...................................................................................................62

ix
List of Figures
Figure 1.1 Generation of plasma...................................................................2
Figure 1.2 CNC plasma cutting machine (ALFHATECH MAXPRO 200). 3
Figure 1.3 CNC while the metal to be cut (workpiece) is connected directly
to positive. Gas flows through the nozzle and exits out the orifice. There is
no arc at this time as there is no current path for the DC voltage.................5
Figure 1.4 in such a way that the gas must pass through this arc before exiting
the nozzle.......................................................................................................6
Figure 1.5Current flow to the workpiece is sensed electronically at the power
supply. As this current flow is sensed, the high frequency is disabled and the
pilot arc relay is opened. Gas ionization is maintained with energy from the
main DC arc. .................................................................................................6
Figure 1.6 At this time, torch motion is initiated and the cutting process
begins. ...........................................................................................................7
Figure 1.7 plasma cutting gasses...................................................................7
Figure 2.1 plasma cutting machine system. ................................................11
Figure 2.2 alphateach CNC.........................................................................12
Figure 2.3 Hypertherm MAXPRO200 power supply.................................12
Figure 2.4 torch. ..........................................................................................14
Figure 2.5 Electrode....................................................................................14
Figure 2.6 Swirl ring ...................................................................................15
Figure 2.7 Nozzle........................................................................................15
Figure 2.8 The EDGE Pro operator console. ..............................................16
Figure 2.9 Touch Screen Display................................................................17
Figure 2.10 shape library.............................................................................17
Figure 3.1 shape and dimension..................................................................25
Figure 4.1 TYLOR-HOBSON Instrument for Measuring Surface
Roughness. ..................................................................................................28

x
Figure 4.2 graph for grey relational grades.................................................51
Figure 4.3 Graph of grey relational grade v/s Cutting Speed (mm/min)...52
Figure 4.4 Graph of grey relational grade v/s Arc Current (amp). ............53
Figure 4.5 Graph of grey relational grade v/s Gas Pressure (Psi)..............53
Figure 5.1 Graph of main effect plot for surface roughness.......................56
Figure 5.2 Graph of main effect plot for material remove rate...................57
Figure 5.3 Graph of main effect plot for grey relational grade...................58

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List of Tables
Table 1.1 summary table for gas selection..................................................10
Table 3.1 Process parameters and response variables.................................18
Table 3.2 Fixed variables. ...........................................................................18
Table 3.3 Process parameters with levels value..........................................26
Table 3.4 Fixed variables value. .................................................................26
Table 3.5 process parameters levels and range...........................................27
Table 4.1 MRR Calculation Sheet ..............................................................30
Table 4.2 Result of Surface roughness and material removal rate obtain from
experimental work.......................................................................................31
Table 4.3 Summery of ANOVA calculation for surface roughness...........37
Table 4.4 Summery of ANOVA calculation for MRR...............................41
Table 4.5 Quality characteristics of the machining performance. ..............42
Table 4.6 Data Pre-Normalization. .............................................................46
Table 4.7 Deviation sequences....................................................................47
Table 4.8 Calculation of grey relational coefficient and grey relational grade.
.....................................................................................................................48
Table 4.9 Response table for gray relational grade.....................................50

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Nomenclature
List of abbreviation
Symbol Description
PAC Plasma Arc Cutting
CNC Computer Numerical Controlled
WRW Work piece Removal Weight
WRV Work piece Removal Volume
SR Surface roughness
MRR Material removal rate
GRA Grey relational analysis
GRC Grey relational coefficient
GRG Grey relational grade

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Chapter One
1 Introduction
1.1 Overview
The topic for the thesis writing is Optimization of cutting parameters for
CNC plasma cutting machine alfhatech MAXPRO 200. The focus on this
project is to obtain an optimum condition (setting) to obtain maximum MRR
and minimum the surface roughness (SR).
The fourth state of matter, plasma, looks and behaves like a high temperature
gas, but with an important difference; it conducts electricity. The plasma arc
is the result of the electrical arcs heating of any gas to a very high temperature
so that its atoms are ionized (an electrically charged gas due to an unequal
number of electrons to protons) and enabling it to conduct electricity. The
major difference between a neutral gas and plasma is that the particles in
plasma can exert electromagnetic forces on one another.
A plasma cutter will cut through any metal that is electrically conductive.
That means that one unit will cut steel, stainless steel, aluminum, copper,
bronze, and brass, etc.

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1.2 What is a Plasma?
One common description of plasma is that it is the fourth state of matter. We
normally think of the three states of matter as solid, liquid and gas. For the
most commonly known substance, water, these states are ice, water and
steam. If you add heat energy, the ice will change from a solid to a liquid,
and if more heat is added, it will change to a gas (steam). When substantial
heat is added to a gas, it will change from gas to plasma, the fourth state of
matter. As shown in figure1.1 the temperature of ice cubes is 0 ˚C, the energy
or heat is applied at about 100 ˚C and it convert in to liquid. The more energy
is applied to liquid at above 100 ˚C it converts in to gas. The more energy
applied to gas at about 10,000 ˚C it converts in to plasma state.
Figure 1.1 Generation of plasma.

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1.3 Introduction to CNC plasma cutting machine
Plasma cutting technology is one in which argon, nitrogen and compressed
air are used to produce a plasma jet and then they are used to cut nonferrous
metal, stainless steel and black metal by the high temperature of the highly
compressed plasma arc and the mechanical erosion of the first plasma jet.
This technology has developed since this its introduction in the 1990s to
complete with flame cutting process for thick plates and lesser cutting
technology for thin plates. It has recently been used widely for process of
irregular cutting, rough machining and structure component stocking in
shipbuilding industry, machine manufacturing industry and so on. The CNC
plasma cutting machine is shown in figure1.2
Figure 1.2 CNC plasma cutting machine (ALFHATECH MAXPRO 200).

4
1.4 How plasma cuts through metal?
The plasma cutting process, as used in the cutting of electrically conductive
metals, utilizes this electrically conductive gas to transfer energy from an
electrical power source through a plasma cutting torch to the material being
cut.
The basic plasma arc cutting system consists of a power supply, an arc
starting circuit and a torch. These system components provide the electrical
energy, ionization capability and process control that is necessary to produce
high quality, highly productive cuts on a variety of different materials.
The power supply is a constant current DC power source. The open circuit
voltage is typically in the range of 240 to 400 VDC. The output current
(amperage) of the power supply determines the speed and cut thickness
capability of the system. The main function of the power supply is to provide
the correct energy to maintain the plasma arc after ionization.
The arc starting circuit is a high frequency generator circuit that produces an
AC voltage of 5,000 to 10,000 volts at approximately 2MHz. This voltage is
used to create a high intensity arc inside the torch to ionize the gas, thereby
producing the plasma.
The Torch serves as the holder for the consumable nozzle and electrode, and
provides cooling (either gas or water) to these parts. The nozzle and electrode
constrict and maintain the plasma jet.

5
1.5 Sequence of operating plasma cutter
The power source and arc starter circuit are connected to the torch via
interconnecting leads and cables. These leads and cables supply the proper
gas flow, electrical current flow and high frequency to the torch to start and
maintain the process.
A start input signal is sent to the power supply. This simultaneously activates
the open circuit voltage and the gas flow to the torch (see Figure1.3).
Figure 1.3 CNC while the metal to be cut (workpiece) is connected directly
to positive. Gas flows through the nozzle and exits out the orifice. There is
no arc at this time as there is no current path for the DC voltage.
Open circuit voltage can be measured from the electrode (-) to the nozzle
(+). Notice that the nozzle is connected to positive in the power supply
through a resistor and a relay (pilot arc relay),
After the gas flow stabilizes, the high frequency circuit is activated. The high
frequency breaks down between the electrode and nozzle inside the torch

6
Figure 1.4 in such a way that the gas must pass through this arc before
exiting the nozzle.
Energy transferred from the high frequency arc to the gas causes the gas to
become ionized, therefore electrically conductive. This electrically
conductive gas creates a current path between the electrode and the nozzle,
and a resulting plasma arc is formed. The flow of the gas forces this arc
through the nozzle orifice, creating a pilot arc.
Assuming that the nozzle is within close proximity to the workpiece, the pilot
arc will attach to the workpiece, as the current path to positive (at the power
supply) is not restricted by a resistance as the positive nozzle.
Figure 1.5Current flow to the workpiece is sensed electronically at the
power supply. As this current flow is sensed, the high frequency is disabled
and the pilot arc relay is opened. Gas ionization is maintained with energy
from the main DC arc.

7
The temperature of the plasma arc melts the metal, pierces through the
workpiece and the high velocity gas flow removes the molten material from
the bottom of the cut kerf.
Figure 1.6 At this time, torch motion is initiated and the cutting process
begins.
1.6 Shielding and cutting gases for plasma cutting
Inert gases such as argon, helium, and nitrogen (except at elevated
temperatures) are used with tungsten electrodes. Air may be used for the
cutting gas when special electrodes made from water-cooled copper with
inserts of metals such as hafnium are used. Recently, PAC units shielded by
compressed air have been developed to cut thin-gauge materials.
Figure 1.7 plasma cutting gasses.

8
Almost all plasma cutting of mild steel is done with one of three gas types:
1. Nitrogen with carbon dioxide shielding or water injection
(mechanized)
2. Nitrogen-oxygen or air
3. Argon-hydrogen and nitrogen-hydrogen mixtures
The first two have become standard for high-speed mechanized applications.
Argon hydrogen and nitrogen-hydrogen (20 to 35 percent hydrogen) are
occasionally used for manual cutting, but the formation of dross, a tenacious
deposit of resolidifide metal attached at the bottom of the cut, is a problem
with the argon blend. A possible explanation for the heavier, more tenacious
dross formed with argon is the greater surface tension of the molten metal.
1.7 Plasma gas selection
1.7.1 Air plasma
 Mostly used on ferrous or carbon based materials to obtain good
quality a faster cutting speeds.
 Only clan, dry air is recommended to use as plasma gas. Any oil
or moisture in the air supply will substantially reduce torch parts
life.
 Air Plasma is normally used with air secondary.
1.7.2 Nitrogen Plasma
 Your words can be used in place of air plasma with air secondary.
 Provides much better parts life than air Provides better cut
quality on non-ferrous materials such as stainless steel and
aluminum.
 A good clean welding grade nitrogen should be used.

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1.7.3 Argon/Hydrogen Plasma
 A 65% argon 35% hydrogen mixture should be used.
 Recommended use on 19 mm and thicker stainless steel.
Recommended for 12 mm and thicker non-ferrous material.
 Ar/H2 is not normally used for thinner non-ferrous material because
less expensive gases can achieve similar cut quality.
 Provides faster cutting speeds and high cut quality on thicker
material to offset the higher cost of the gas.
 Poor quality on ferrous materials.
1.7.4 Oxygen Plasma
 Oxygen is recommended for cutting ferrous metals.
 Provides faster cutting speeds.
 Provides very smooth finishes and minimizes nitride build-up on
cut surface (nitride build-up can cause difficulties in producing
high quality welds if not removed).
1.8 Secondary gas selection for plasma cutting
1.8.1 Air secondary
 Air secondary is normally used when operating with air plasma
and occasionally with nitrogen plasma.
 Inexpensive - reduces operating costs.
 Improves cut quality on some ferrous materials.
1.8.2 CO2 secondary
 CO2 secondary is used with nitrogen or Ar/H2 plasma.
 Provides good cooling and maximizes torch parts life.
 Usable on any ferrous or non-ferrous material.
 May reduce smoke when used with Ar/H2 plasma.

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Table 1.1 summary table for gas selection.
GAS
MATERIAL
THICKNESS
MATERIAL
CARBON
STEEL
STAINLESS
STEEL
ALUMINIUM
Air Plasma Gage Good/Excelle
nt
Good/Excellent Good/Excellent
Air
Secondary
Gage to 12 mm Excellent Good Good
12 mm and Up Excellent Fair Fair
Nitrogen
Plasma
Gage Good/Excelle
nt
Air
Secondary
or CO2
Secondary
Gage to 12 mm Good/Excelle
nt
12 mm and Up Good/Excelle
nt
Ar/H2
Plasma
Gage to 6 mm NR NR NR
N2 or
CO2
Secondary
6 mm to 30 mm NR Good Excellent
12 mm and Up NR Good/Excellent Excellent

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Chapter Two
2 Devices
2.1 System
Plasma arc cutting can increase the speed and efficiency of both sheet and
plate metal cutting operations. Manufacturers of transportation and
agricultural equipment, heavy machinery, aircraft components, air handling
equipment, and many other products have discovered its benefits. Basically
Plasma Arc Cutter comprises of five major parts such as air compressor,
power supply, Control (CNC part), plasma torch and work piece. The plasma
arc cutting system shown in figure2.1.
Figure 2.1 plasma cutting machine system.

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2.1.1 Control panel (CNC)
This part is work as the brain of CNC plasma machine which control the
torch and change the voltage, and control the movement of cutter.
Figure 2.2 alphateach CNC.
2.1.2 Power supply
This part is produce constant current pure DC output, and houses the control
circuity for the proper sequencing of the entire system, houses of the cooling
system for the torch, we have Hypertherm MAXPRO200 that’s shown in the
figure.
Figure 2.3 Hypertherm MAXPRO200 power supply.

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2.1.3 Compressor
This devise is used to compressing air for both primary and secondary gases.
2.1.4 Torch
The Plasma cutting process is used with mechanically mounted torch. There
are several types and sizes of each, depending on the thickness of metal to
be cut. Some torches can be dragged along in direct contact with the work
piece, while others require that a standoff be maintained between the tip of
the torch and work piece.
Mechanized torches can be mounted either on a tractor or a on a computer-
controlled cutting machine or robot. Usually a standoff is maintained
between the torch tip and work piece for best- cut quality. The standoff
distance must be maintained with fairly close tolerances to achieve uniform
results.
The timely replacement of consumable parts is required to achieve good
quality cuts. Modern plasma torches have self-aligning and self-adjusting
consumable parts. As long as they are assembled in accordance with the
manufacturer’s instructions, the torch should require no further adjustment
for proper operation.
Other torch parts such as shield cups, insulators, seals etc. may also require
periodic inspection and replacement if they are worn or damaged.

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2.1.5 Torch Consumable
The plasma torch is designed to generate and focus the plasma cutting arc.
In machine torches, the parts are used: an electrode to carry the current form
the power source, a swirl ring to spin the compressed air, a nozzle that
constricts and focuses the cutting arc, and a shield and retaining ring to
protect the torch. Torch consumables are shown in figure.
Figure 2.4 torch.
2.1.5.1 Electrode
The purpose of the electrode is to provide a path for the electricity from the
power source and generate the cutting arc. The electrode is typically made
of copper with an insert made of hafnium. The Hafnium alloyed electrodes
have good wear life when clean, dry compressed air or nitrogen is used
(although, electrode consumption may be greater with air plasma than with
nitrogen). The electrode is shown in figure.
Figure 2.5 Electrode

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2.1.5.2 Swirl ring
The swirl ring is designed to spin the cutting gas in a vortex. The swirl ring
is made of a high temperature plastic with angled holes that cause the gas
to spin. Spinning the gas centers the arc on the electrode and helps to control
and constrict the arc as it passes through the nozzle.
The swirl ring for hypertherm HSD/HyPro2000 torch is shown in figure.
Figure 2.6 Swirl ring
2.1.5.3 Nozzle
The purpose of the torch nozzle is to constrict and focus the plasma arc.
Constricting the arc increases the energy density and velocity. The nozzle
is made of copper, with a specifically sized hole or orifice in the center of
the nozzle. Nozzle is sized according to the amperage rating of the torch
that they are to be used in. Nozzle use in plasma cutting machine is shown
in figure.
Figure 2.7 Nozzle

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2.2 Operating system Software
2.2.1 Operating the CNC
Phoenix software runs on the Hypertherm computer numerical controls
(CNCs) including the EDGE® Pro and MicroEDGE® Pro, and EDGE®Pro
Ti. Phoenix supports either a touch screen or LCD display with a USB-
connected keyboard and mouse for entering information and navigating the
software.
2.2.2 Operator Console
An optional operator console provided by Hypertherm, an OEM, or a system
integrator powers up the CNC and controls machine motion such as station
selection, raising or lowering the cutting tool, and positioning the cutting tool
before starting a part program.
The EDGE Pro operator console is shown below. The operator console on
your CNC may look different and have other controls than those shown here.
Figure 2.8 The EDGE Pro operator console.
2.2.3 Touch Screen LCD
The Phoenix software is designed for 38 cm (15 inch) touch screens with1024
x 768 or higher resolution is shown in figure2.9. When your CNC is equipped
with a touch screen, you can enter data into the software by touching the
window controls and fields.
Any field that requires data input automatically displays an onscreen keypad
when you touch it.

17
Figure 2.9 Touch Screen Display.
2.2.4 Shape Library
The CNC contains a built-in Shape Library with more than 68 commonly
used shapes. These shapes are parametric, that is, shapes whose size or
geometry you can edit. The shapes in the library are color-coded from
simplest (green) to most complex (black).
Figure 2.10 shape library.

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Chapter Three
3 Design of Experiments
3.1 Introduction
In this project work process parameters considered for plasma arc cutting are
cutting speed, arc current and gas pressure and response variables considered
which to be measures are surface roughness and material removal rate. These
are shown in Table 3.1.
Table 3.1 Process parameters and response variables.
Process Parameters Response Variables
Cutting Speed (mm/min) Surface roughness (µm)
Arc Current (amp) Material removal rate (gms/sec)
Gas Pressure (psi) -
There are some fix variables in plasma arc cutting process, which is shown
in Table 3.2.
Table 3.2 Fixed variables.
Sr. No. Fixed Variables
1 Work material (STEEL)
2 Sample Dimensions (200mm × 200 mm × 6 mm)
3 Kerf (5mm)

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3.2 Design factors
Design of Experiments technique has been utilized to obtain the best
combination of design factors to achieve optimum performance measures.
Plasma Arc Cutting involves several input parameters to be considered
during machining process. In this thesis, the combination factors such as
Cutting Speed [mm/min], Current Flow Rate [amp] and Gas Pressure [Psi]
are considered. These factors are the most important to have the best value
for Surface Roughness (Ra) and Material Removal Rate (MRR) when cutting
material like Steel.
3.2.1 Process parameters
3.2.1.1 Cutting speed
The best way to judge cutting speed is to look at the arc as it exits the bottom
of the work piece. Observe the angle of the cutting arc through the proper
welding lens. If cutting with air, the arc should be vertical straight down, or
zero degrees as it exits the bottom side of the cut. If cutting with nitrogen or
argon/hydrogen, then the correct cutting speed will produce a trailing arc
(that is, an exit arc that is opposite to the direction of torch travel).
The torch speed needs to be adjusted to get a good-quality cut. A cutting
speed that is too slow or too fast will cause cut quality problems. In most
metals there is a window between these two extremes that will give straight,
clean, dross free cuts.
For this project work cutting speed is considered the range between 3000-
4200 mm/min.
3.2.1.2 Arc Current
Arc Current is the value of current given during cutting process. The cause
of the burn- through was the increase in the cutting current or the decrease
in the cutting speed. When the cutting current increases or the cutting speed
decreases, the stable state of the keyhole changes accordingly. If the cutting
current and the flow rate of the plasma gas are increased and/or the cutting

20
speed is decreased, the process will withstand larger variations in the
cutting parameters.
For this project work Arc Current is considered the range between 50amp
and 130amp.
3.2.1.3 Gas pressure
According to Larry Jeffus, “Principle and Application of Welding” Sixth
Addition, almost any gas or gas mixture can be used today for the PAC
process. Normally Nitrogen or Argon with 0-35% Hydrogen is used for
cutting Stainless Steel material. We used O2 for our experiment purpose.
It is important to have the correct gas flow rate for the size tip, metal type
and thickness. Too low a gas flow will result in a cut having excessive
dross and sharply beveled sides. Too high a gas flow will produce a
poor cut because of turbulence in the plasma stream and waste gas.
Controlling the pressure is one way of controlling gas flow.
For this project work gas pressure is considered the range between 60-100
Psi.
3.2.2 Response variables
3.2.2.1 Surface roughness
Roughness is a measure of the texture of a surface. It is quantified by the
vertical deviations of a real surface from its ideal form. If these deviations
are large, the surface is rough; if they are small the surface is smooth.
Roughness is typically considered to be the high frequency, short wavelength
component of a measured surface. Surface roughness normally measured.
Roughness plays an important role in determining how a real object will
interact with its environment. Rough surfaces usually wear more quickly and
have higher friction coefficients than smooth surfaces (see tribology).
Roughness is often a good predictor of the performance of a mechanical

21
component, since irregularities in the surface may form nucleation sites for
cracks or corrosion.
In this thesis, the average surface roughness is measured and calculated.
Surface roughness will be measures by surface roughness tester.
3.2.2.2 Material removal rate
The material removal rate, MRR, can be defined as the volume of material
removed divided by the machining time. Material Removal Rate (MRR) is
defined by:
MRR = WRW/T [gms/sec]
Where,
WRW: work piece removal weight (gms)
T: cutting time (sec)
WRW is the weight different between before and after work piece cutting.
The volume different can be calculated when information regarding material
density available.
The relation between WRW and WRV is given as follow:
WRV = WRW/ρ
Where,
ρ: Work piece density (gms/ mm3
)

22
3.3 Design of experiments
3.3.1 Introduction
In industry, designed experiments can be used to systematically investigate
the process or the product variables that influence the product quality. In
design of experiments, the experimenter is often interested in the effect of
some process or investigation. Increasing productivity and improving quality
are important goal in any business. The method for determining how to
increase productivity and improving quality are evolving. The design of
experiments (DOE) is an efficient procedure for planning experiments
so that the obtained data can be analyzed to yield valid and objective
conclusions. DOE begins with determining the objectives of an experiment
and selecting the process factors for the study. An Experimental Design is
the laying out of a detailed experimental plan in advance of doing the
experiment.
The purpose of design of experiment is to plan, design and analyze the
experiment so that the valid and objective conclusions can be drawn
effectively and efficiently.
3.3.2 Methods of DOE
Following methods are used in design of experiment.
1. Factorial method
2. Response surface method
3. Taguchi method

23
3.3.2.1 Factorial method
Factorial design allows simultaneous study of effect that several factors may
have on a process. When performing an experiment, varying the level of
factor simultaneously rather than one at a time is efficient in terms of time
and cost, and also allow for the study of interaction between the factors.
Interaction is the driving force in many times processes. Without the use of
factorial experiments, important interaction remains undetected. However,
factorial design can only give relative values, and to achieve actual numerical
values the math becomes difficult, as regressions (which require minimizing
a sum of values) need to be performed. Regardless, factorial design is a
useful method to design experiments in both laboratory and industrial
settings.
3.3.2.2 Response surface method
Factorial design allows simultaneous study of effect that several factors may
have on a process. When performing an experiment, varying the level of
factor simultaneously rather than one at a time is efficient in terms of time
and cost, and also allow for the study of interaction between the factors.
Interaction is the driving force in many times processes. Without the use of
factorial experiments, important interaction remains undetected. However,
factorial design can only give relative values, and to achieve actual numerical
values the math becomes difficult, as regressions (which require minimizing
a sum of values) need to be performed. Regardless, factorial design is a
useful method to design experiments in both laboratory and industrial
settings.

24
3.3.2.3 Taguchi method
This experiment design proposed by Taguchi involves using orthogonal
array to organize the parameters affecting the process and the levels at which
they should be varied; it allows for the collection of the necessary data to
determine which factor most affect product quality with a minimum amount
of experimentation, thus saving time and resources.
3.3.3 Selection of work sample
3.3.3.1 Material selection
Material selection for this project work is Steel. A high strength structural
steel supplied in quenched and tempered condition. The steel is designed to
provide excellent welding and bending properties and it offers substantial
possibilities for savings in material costs, processing and handling. Due to
its high strength, it enables design of lighter, more durable and efficient
products and structures.
Applications:
 Machine building,
 Lifting and mobile equipment,
 Vehicles and transport equipment,
 Steel constructions,
 Framework structures,
 Construction of bridges,
 Containers Pylons and other architectural structures

25
3.3.3.2 Shape and size selection
Select one of shapes from shape library and change dimension to suitable
value, as shown in figure 3.1.
Figure 3.1 shape and dimension.

26
3.3.4 Selection of process parameters
Most researchers identified plasma arc cutting process parameters that
greatly affect response parameters. Process parameters like cutting speed,
arc current, gas pressure, arc gap, kerf are most frequently used parameters
for research work. Thus taking Cutting Speed [mm/min], Current Flow Rate
[amp] and Gas Pressure [Psi] for research works and analyze for Surface
Roughness (μm) and Material Removal Rate for plasma arc Cutting process.
As Table 3.3 shows, the level value is determined by its operation according
to the correlated processing parameter of mechanical equipment.
 Process parameters
 Factor A: Cutting Speed (mm/min)
 Factor B: Arc Current (amp)
 Factor C: Gas Pressure (Psi)
 Process parameters with levels value
Table 3.3 Process parameters with levels value.
Sr.
No.
Factors Level 1 Level 2 Level 3
1 Cutting Speed (mm/min) 3000 3800 4200
2 Arc Current (amp) 50 130 -
3 Gas Pressure (Psi) 60 80 100
 Fixed variables
Table 3.4 Fixed variables value.
Sr. No. Fixed Variables Set Value
1 Work material Steel
2 Sample Dimensions (200mm × 200 mm × 6 mm)
3 Kerf 5 mm

27
3.3.5 Experimental design
Experimental design of three process parameters with their range and levels
Table 3.5 process parameters levels and range
Level
Cutting Speed
(mm/min)
Arc Current
(amp) Gas Pressure (Psi)
1 3000 50 60
2 3000 50 80
3 3000 50 100
4 3000 130 60
5 3000 130 80
6 3000 130 100
7 3800 50 60
8 3800 50 80
9 3800 50 100
10 3800 130 60
11 3800 130 80
12 3800 130 100
13 4200 50 60
14 4200 50 80
15 4200 50 100
16 4200 130 60
17 4200 130 80
18 4200 130 100
3.4 Summary
In this chapter we have discussed about the selected process parameters,
response variables and fixed variables for the experiment. We have also
discussed about the procedure for the design of experiment, DOE table and
briefly discussed about Design expert software. In next chapter we will
discuss on experimental work for machine and its specification, material
specification and also discussed about measurement of response variables.

28
Chapter Four
4 Experimental Measurement and Results
4.1 Measuring surface roughness and Material Removal Rate
4.1.1 Surface roughness Measurement
Surface roughness values of finished work pieces were measured by
TAYLOR-HOBSON instrument it is shown in figure. This device has two
ways of reading the surface roughness, first is reading the surface roughness
(SR) directly from the gage, and second is drawing the surface texture
profile. The range of device is reading from (0.01µm to 5µm), and the range
of drawing the profile is from (0.04µm to 60µm).
Figure 4.1 TYLOR-HOBSON Instrument for Measuring Surface
Roughness.

29
4.1.2 Material Removal Rate Measurement
The material removal rate, MRR, can be defined as the volume of material
removed divided by the machining time. Material Removal Rate (MRR) is
defined by:
MRR = WRW/T [gms/sec]
Where,
WRW: work piece removal weight (gms)
T: cutting time (sec)
WRW is the weight different between before and after work piece cutting.
The volume different can be calculated when information regarding material
density available.
The relation between WRW and WRV is given as follow:
WRV = WRW/ρ
Where,
ρ: Work piece density (gms/ mm3)
MRR calculation sheet is shown in Table 4.1.

30
Table 4.1 MRR Calculation Sheet
Sr. No.
Mass 1
(before
cutting)
Mass 2
(after
cutting)
∆m
(gms)
Time(T)
(sec)
MRR=∆m/T
(gms/sec)
1 1025 986 39 11.97 3.2584
2 1025 978 47 12.87 3.6515
3 1025 983 42 12.165 3.4524
4 1025 985 40 11.97 3.34168
5 1025 985 40 12.03 3.32502
6 1030 985 45 11.63 3.8693
7 1020 983 37 10.74 3.444
8 1025 990 35 10.24 3.4177
9 1015 984 31 9.61 3.2271
10 1030 990 40 9.18 4.35729
11 1025 958 40 8.95 4.46927
12 1020 985 35 8.92 3.92376
13 1025 985 40 11.09 3.6058
14 1030 992 38 10.40 3.6538
15 1015 980 35 11.74 2.9796
16 1015 980 35 8.06 4.39243
17 1020 985 35 8.92 3.92376
18 1020 980 40 8.74 4.57665

31
4.2 Experimental Results
From the measurements of surface roughness and material removal rate
obtain results are shown in Table 4.2.
Table 4.2 Result of Surface roughness and material removal rate obtain
from experimental work.
Exp.
No.
Process Parameters Response Variables
Cutting
Speed
(mm/min
)
Arc
Current
(amp)
Gas
Pressure
(Psi)
Surface
Roughness
(µm)
Material
Removal rate
(gms/sec)
1 3000 50 60 0.57 3.2584
2 3000 50 80 0.63 3.6515
3 3000 50 100 0.95 3.4524
4 3000 130 60 0.5 3.34168
5 3000 130 80 0.83 3.32502
6 3000 130 100 1.1 3.8693
7 3800 50 60 0.385 3.444
8 3800 50 80 0.58 3.4177
9 3800 50 100 0.75 3.2271
10 3800 130 60 0.215 4.35729
11 3800 130 80 0.45 4.46927
12 3800 130 100 0.7 3.92376
13 4200 50 60 0.52 3.6058
14 4200 50 80 0.68 3.6538
15 4200 50 100 0.83 2.9796
16 4200 130 60 0.26 4.39243
17 4200 130 80 0.685 3.92376
18 4200 130 100 0.91 4.57665

32
4.3 Analysis
4.3.1 Analysis of variance
4.3.1.1 Introduction
The analysis of variance (ANOVA) is the statistical treatment most
commonly applied to the results of the experiments to determine the
percentage contribution of each factors. Study of ANOVA table for a given
analysis helps to determine which of the factors need control and which do
not. Once the optimum condition is determined, it is usually good practice to
run a confirmation experiments. In case of fractional factorial some of the
tests of full factorial are conducted. The analysis of the partial experiment
must include an analysis of confidence that can be placed in the results. So
analysis of variance is used to provide a measure of confidence.
Analysis provides the variance of controllable and noise factors. By
understanding the source and magnitude of variance, robust operating
condition can be predicted
4.3.1.2 Analysis of variance (ANOVA) terms & Notations
n = Number of trials C.F. = Correction factor
E = Error P = Percentage contribution
F = Variance ratio T = Total of results
𝑓 = Degree of freedom S = sum of squares
𝑓E = Degree of freedom of error V = Mean squares (variance)
𝑓T = total degree of freedom

33
Total number of trials
The total number of trial is the sum of numbers of trials at each level.
Degree of freedom
It is a measure of amount of information that can be uniquely determined
from a given set of data. DOF for data concerning a factor equals one less
than the number of levels.
Sum of squares
The sum of squares is the measure of the deviation of the experimental data
from the mean value of the data.
Variance
Variance measures the distribution of the data about the mean of the data.
Variance ratio
Variance ratio is the ratio of variance due to the effect of a factor and variance
due to the error term. This ratio is used to measure the significance of the
factor under investigation with respect to the variance of all the factors
included in the error term. The F value obtained in the analysis is compared
with a value from standard F – tables for a given level of significance. When
the computed value is less than the value determined from the F tables at the
selected level of significance, the factor does not contribute to the sum of
squares within the confidence level.

34
4.3.1.3 Analysis of Variance for surface Roughness
Total no of runs (n) = 18
Total degree of freedom 𝑓T = n - 1 = 17
Three factors and their levels:
Cutting Speed A: A1, A2, A3
Arc Current B: B1, B2
Gas Pressure C: C1, C2, C3
Degree of freedom:
Factor A – Number of level of factor A - 1 = 𝑓A = 2
Factor B – Number of level of factor B - 1 = 𝑓B = 1
Factor C – Number of level of factor C - 1 = 𝑓C = 2
For error 𝑓E = 𝑓T – 𝑓A – 𝑓B – 𝑓C = 17 – 2 – 1 – 2 = 𝑓E = 12
T = Total of all SR value results = 11.545
Correction factor C.F. = (T2
/ n) = (11.5452
/ 18) = 7.4048

35
Total sum of squares:
𝑆 𝑇 = ∑ 𝑦𝑖2
𝑛
𝑖=1
− 𝐶. 𝐹. = 8.3456 − 7.4048 = 0.9408
The total contribution of each factor level:
A1 = 0.570 + 0.630 + 0.950 + 0.500 + 0.830 + 1.100
= 4.58
A2 = 0.385 + 0.580 + 0.750 + 0.215 + 0.450 + 0.700
= 3.08
A3 = 0.520 + 0.680 + 0.830 + 0.260 + 0.685 + 0.910
= 3.885
B1 = 0.570 + 0.630 + 0.950 + 0.385 + 0.580 + 0.750 + 0.520 + 0.680 + 0.830
= 5.895
B2 = 0.500 + 0.830 + 1.100 + 0.215 + 0.450 + 0.700 + 0.260 + 0.685 + 0.910
= 5.650
C1 = 0.570+ 0.500 + 0.385 + 0.215 + 0.520 + 0.260
= 2.450
C2 = 0.630 + 0.830 + 0.580 + 0.750 + 0.680 + 0.685
= 4.155
C3 = 0.950 + 1.100 + 0.450 + 0.700 + 0.830 + 0.910
= 4.940

36
Factor sum of squares:
SA = 𝐴1
2
/NA1 + 𝐴2
2
/NA2 + 𝐴3
2
/NA3 – C.F.
= (4.58)2
/6 + (3.08)2
/6 + (3.885)2
/6 – 7.4048
= 0.1788
SB = 𝐵1
2
/NB1 + 𝐵2
2
/NB2 – C.F.
= (5.895)2
/9 + (5.650)2
/9 – 7.4048
= 0.0034
SC = 𝐶1
2
/NC1 + 𝐶2
2
/NC2 + 𝐶3
2
/NC3 – C.F.
= (2.450)2
/6 + (4.155)2
/6 + (4.940)2
/6 – 7.4048
= 0.5402
SE = ST – (SA + SB + SC)
= 0.9408 – (0.1788+ 0.0034+ 0.5402)
= 0.2184
Mean square (variance):
VA = SA / 𝑓A = 0.1788/ 2 = 0.08940
VB = SB / 𝑓B = 0.0034/ 1 = 0.00340
VC = SC / 𝑓C = 0.5402/ 2 = 0.27010
VE = SE / 𝑓E = 0.2184/ 12 = 0.01820

37
Variance ratio F:
FA = VA / VE = 0.08940 / 0.01820= 4.9120
FB = VB / VE = 0.00340 / 0.01820= 0.1868
FC = VC / VE = 0.27010/ 0.01820= 14.8406
FE = VE / VE = 0.01820/ 0.01820= 1
Percentage contribution:
PA = SA / ST = 0.1788/ 0.9408 = 19.00
PB = SB / ST = 0.0034 / 0.9408 = 0.370
PC = SC / ST = 0.5402/ 0.9408 = 57.42
PE = SE / ST = 0.2184/ 0.9408 = 23.21
Table 4.3 shows the summary of analysis of variance for surface roughness.
Table 4.3 Summery of ANOVA calculation for surface roughness.
Source of
variation
𝑓
Sum of
squares
Variance
(Mean
square)
Variance
ratio F
Percentage
contribution
Factor-A,
Cutting Speed
2 0.1788 0.08940 4.9120 19.00
Factor-B,
Arc Current
1 0.0034 0.00340 0.1868 0.370
Factor-C,
Gas Pressure
2 0.5402 0.27010 14.8406 57.42
Error – E 12 0.2184 0.01820 1 23.21
Total 17 0.9408

38
4.3.1.4 Analysis of Variance for Material Removal Rate
Total no of runs (n) = 18
Total degree of freedom 𝑓T = n - 1 = 17
Three factors and their levels:
Cutting Speed A: A1, A2, A3,
Arc Current B: B1, B2
Gas Pressure C: C1, C2, C3
Degree of freedom:
Factor A – Number of level of factor A - 1 = 𝑓A = 2
Factor B – Number of level of factor B - 1 = 𝑓B = 1
Factor C – Number of level of factor C - 1 = 𝑓C = 2
For error 𝑓E = 𝑓T – 𝑓A – 𝑓B – 𝑓C = 17 – 2 – 1 – 2 = 𝑓E = 12
T = Total of all depth value results = 66.8694
Correction factor C.F. = (T2
/ n) = (66.86942
/ 18) = 248.4175
Total sum of squares:
𝑆 𝑇 = ∑ 𝑦𝑖2
𝑛
𝑖=1
− 𝐶. 𝐹. = 252.2411 − 248.4175 = 3.8236

39
The total contribution of each factor level:
A1 = 3.25840 + 3.65150 + 3.45240 + 3.34168+ 3.32502 + 3.86930
= 20.8983
A2 = 3.44400 + 3.41770 + 3.22710 + 4.35729 + 4.46927 + 4.9376
= 22.83912
A3 = 3.60580 + 3.65380 + 2.97960 + 4.39243 + 3.92376 + 4.57665
= 23.13204
B1 = 3.25840 + 3.65150 + 3.45240 + 3.34168 + 3.32502 + 3.8693 + 3.44400
+ 3.41770 + 3.22710
= 30.98710
B2 = 4.35729 + 4.46927 + 3.92376 + 3.6058 + 3.6538 + 2.9796 + 4.39243
+ 3.92376 + 4.57665
= 35.88236
C1 = 3.2584 + 3.6515 + 3.444 + 3.4177 + 3.6058 + 3.6538
=21.0312
C2 = 3.4524 + 3.34168 + 3.2271 + 4.35729 + 2.9796 + 4.39243
=21.7505
C3 = 3.32502 + 3.8693 + 4.46927 + 3.92376 + 3.92376 + 4.57665
=24.08776

40
Factor sum of squares:
SA = 𝐴1
2
/NA1 + 𝐴2
2
/NA2 + 𝐴3
2
/NA3 – C.F.
= (20.8983)2
/6 + (22.83912)2
/6 + (23.13204)2
/6 – 248.4175
=0.49177
SB = 𝐵1
2
/NB1 + 𝐵2
2
/NB2 – C.F.
= (30.98710)2
/9 + (35.88236)2
/9– 248.4175
= 1.33260
SC = 𝐶1
2
/NC1 + 𝐶2
2
/NC2 + 𝐶3
2
/NC3 – C.F.
= (21.0312)2
/6 + (21.7505)2
/6 + (24.08776)2
/6 – 248.4175
= 0.85180
SE = ST – (SA + SB + SC)
= 3.8236 – (0.49177+ 1.3326+ 0.85180)
= 1.14743
Mean square (variance):
VA = SA / 𝑓A = 0.49177/ 2 = 0.24588
VB = SB / 𝑓B = 1.3326 / 1 = 1.03326
VC = SC / 𝑓C = 0.85180/ 2 = 0.42590
VE = SE / 𝑓E = 1.14743/ 12 = 0.09561
Variance ratio F:
FA = VA / VE = 0.24588 / 0.09561= 2.57169
FB = VB / VE = 1.03326 / 0.09561= 10.80702
FC = VC / VE = 0.42590 / 0.09561= 4.45455
FE = VE / VE = 0.09561/ 0.09561= 1

41
Percentage contribution:
PA = SA / ST = 0.49177/ 3.8236 = 12.86
PB = SB / ST = 1.33260/ 3.8236 = 34.85
PC = SC / ST = 0.85180/ 3.8236 = 22.27
PE = SE / ST = 1.14743 / 3.8236 = 30.02
Table 4.4 shows the summary of analysis of variance for depth
Table 4.4 Summery of ANOVA calculation for MRR.
Source of variation
𝑓
Sum of
squares
Variance
(Mean
square)
Variance
ratio F
Percentage
contribution
Factor-A,
Cutting Speed
2 0.49177 0.24588 2.57169 12.86
Factor-B,
Arc Current
1 1.33260 1.03326 10.80702 34.85
Factor-C,
Gas Pressure
2 0.85180 0.42590
4.45455
22.27
Error – E 12 1.14743 0.09561 1 30.02
Total 17 3.82360
From the above ANOVA analysis we can conclude that,
1) For surface roughness percentage contribution of cutting speed 19 %, arc
current 0.37 %, gas pressure 57.42 %, error 23.21 %,
2) For material removal rate percentage contribution of cutting speed 12.86
%, arc current 34.85%, gas pressure 22.27 %, and error 30.0.2 %. This error
is due to machine vibration.

42
4.3.2 Multi response optimization
4.3.2.1 Grey relation Analysis for Multi Object Optimization
The grey relational analysis (GRA) is one of the powerful and effective soft-
tool to analyse various processes having multiple performance
characteristics Grey relational Analysis (GRA) Technique is used to solve
the problems of the systems that are complex and multivariate. Generally,
GRA is carried out for solving complicated problems which have
interrelationships among the designated performance characteristics. The
purpose of grey relational analysis the multi-objective problem has been
converted into single objective optimization using GRA technique. GRA is
alternate method for traditional statistical methods which deals with the
small sample size and uncertainty conditions and can be applied in
optimization of multiple quality characteristics. GRA is normalization based
evolution technique in which the quality characteristics of the measured data
are first normalized ranging from 0 to 1. Therefore one has to pre-process
the data which are related to a group of sequence ,which is called “grey
relational generation “data preprocessing is a process of transferring the
original sequence to a comparable sequence for this purpose the
experimental result are normalized in the range between zero and one.
Table 4.5 Quality characteristics of the machining performance.
Sr. No. Machine Characteristic Quality Characteristic
1 SR (Surface Roughness) Minimum
2 MRR (Material Removal Rate) Maximum

43
4.3.2.2 Data pre-processing
Normalize the measured values of Surface roughness and Material removal
rate ranging from zero to one. This process is known as Grey relational
normalization.
If the target value of original sequence is infinite, then it has a characteristic
of “the larger the better” than the original sequence can be normalized as
follows:
𝑥𝑖( 𝑘) =
𝑦𝑖( 𝑘) − 𝑚𝑖𝑛𝑦𝑖( 𝑘)
𝑚𝑎𝑥 𝑦𝑖( 𝑘) − 𝑚𝑖𝑛 𝑦𝑖( 𝑘)
… … … . . (4.1)
If the expectancy is “the smaller the better” than the original sequence should
be normalized as follows:
𝑥𝑖( 𝑘) =
𝑚𝑎𝑥 𝑦𝑖( 𝑘) − 𝑦𝑖( 𝑘)
𝑚𝑎𝑥 𝑦𝑖( 𝑘) − 𝑚𝑖𝑛 𝑦𝑖( 𝑘)
… … … . . (4.2)
Here X (k) i is the value after grey relational generation, min y(k)i is the
smallest value of y (k) i for the kth response, and max y (k) i is the largest
value of y (k) i for the kth response. An ideal sequence is (1, 2, 3..., 18) 0 x
k, k = for the responses. The definition of grey relational grade in the course
of grey relational analysis is to reveal the degree of relation between the 30
sequences, (1, 2, 3..., 18) 0 x k and x k, k = i.

44
4.3.2.3 Grey relational coefficient and grey relational grade
Following data pre-processing, a grey relational coefficient is calculated to
express the relationship between the ideal and actual normalized
experimental results. The Grey relation coefficient can be express as follows:
ζ𝑖(𝑘) =
∆𝑚𝑖𝑛 + 𝜓Δ𝑚𝑎𝑥
Δ0𝑖(𝑘) + 𝜓Δ𝑚𝑎𝑥
… … … (4.3)
Where (k) is the deviation sequence of the reference sequence xi(k) and the
comparability
sequence.ᴪ = distinguishing or identification coefficient in between zero and
one. GRC is calculated by selecting proper distinguishing coefficient
generally ᴪ = 0.5 is accepted .In the present study same was considered.
is distinguishing or identification coefficient: [0,1], is generally
used.
After obtaining the Grey relation coefficient, its average is calculated to
obtain the Grey relation grade.
The Grey relation grade is defined as follows:
𝛾𝑖 =
1
𝑛
∑ 𝜉𝑖(𝑘)
𝑛
𝑘=1
… … … . .4.7
Where n is the no of process responses, ζi is the grey rational grade for the
kth experiment.

45
The GRG is used to analyse the relational degree of multiple response
characteristics. Higher the grey relational grade represent a stronger
relational degree between the ideal normalized value xok and the given
sequences xik.
In Grey relation analysis, the grey relation grade is used to show the
relationship among the sequences. The Grey relation grade also indicates
the degree of influence that the comparability sequence could exert over the
reference sequence. Therefore, if a particular comparability sequence is
more important than the other comparability sequence to reference
sequence will be higher than other grey relation grades. In this study, the
importance of both the comparability sequence and reference sequence is
treated as equal.
4.3.2.4 Process steps for multi response optimization
The basic process steps for multi-response optimization are given below:
a). Normalization of experimental results for all performance characteristics.
b). Calculation of grey relational coefficient (GRC).
c). Calculation of grey relational grade (GRG) using weighing factor
for performance characteristics.
d). Analysis of experimental results using GRG.
e). Selection of optimal levels of process parameters.
f). Conducting confirmation experiment to verify optimal process parameter
settings.

46
4.3.2.5 Normalization of experimental result
In this research work, normalization of surface roughness and material
removal rate is done between 0 and 1. Here for surface roughness and
material removal rate, normalization equation smaller-the-better, larger-the-
better is used is shown in Table 4.6.
Table 4.6 Data Pre-Normalization.
Exp. No.
Data Pre-Normalization
S
R
MRR
1 0.59887 0.174572
2 0.531073 0.420713
3 0.169492 0.296046
4 0.677966 0.226718
5 0.305085 0.216286
6 0 0.55709
7 0.80791 0.290786
8 0.587571 0.274318
9 0.39548 0.154973
10 1 0.862647
11 0.734463 0.932764
12 0.451977 0.59119
13 0.655367 0.392098
14 0.474576 0.422153
15 0.305085 0
16 0.949153 0.88465
17 0.468927 0.59119
18 0.214689 1

47
4.3.2.6 Calculation of deviation sequence
In this work, to find out grey relation coefficient, one has to calculate
deviation sequence using equation (4.4) shown in table 4.7. The deviation
sequences ∆0i, ∆max(k), and ∆min(k) for i=1- 30 and k=1-2 can be calculated
as follows:
∆01 (1) =|x0 (1) – x1 (1)| = |1.0000 – 0.59887| = 0.40113
∆01 (2) =|x0 (2) – x1 (2)| = |1.0000 – 0.531073| = 0.468927
∆01 (3) =|x0 (3) – x1 (3)| = |1.0000 – 0.169492| = 0.830508
Table 4.7 Deviation sequences.
Exp. No.
Deviation Sequence
∆0i (1) ∆0i (2)
1 0.40113 0.825428
2 0.468927 0.579287
3 0.830508 0.703954
4 0.322034 0.773282
5 0.694915 0.783714
6 1 0.44291
7 0.19209 0.709214
8 0.412429 0.725682
9 0.60452 0.845027
10 0 0.137353
11 0.265537 0.067236
12 0.548023 0.40881
13 0.344633 0.607902
14 0.525424 0.577847
15 0.694915 1
16 0.050847 0.11535
17 0.531073 0.40881
18 0.785311 0
Using Table 4.7, ∆max and ∆min can be found as follows:
∆max = ∆06 (1) =∆15 (2) = 1.0000
∆min = ∆10 (1) = ∆18 (2) = 0.0000

48
4.3.2.7 Calculation of grey relational coefficient and grey relational
grade
The grey relational coefficient is use to express the relationship between the
ideal (best) and actual normalized experimental results. Table 4.8 list the
grey relational coefficient and grey relational grade for each experiment by
applying Eqe.4.3, 4.7.
Table 4.8 Calculation of grey relational coefficient and grey relational
grade.
Esp. No:
Grey Relation Coefficients Grey Relational
Grade
OrdersSR MRR
1 0.554859 0.377237 0.466048 13
2 0.516035 0.463269 0.489652 10
3 0.375796 0.415298 0.395547 18
4 0.608247 0.392686 0.500467 9
5 0.41844 0.389495 0.403967 16
6 0.333333 0.530273 0.431803 14
7 0.722449 0.413492 0.56797 5
8 0.547988 0.407936 0.477962 11
9 0.452685 0.37174 0.412213 15
10 1 0.784494 0.892247 1
11 0.653137 0.881467 0.767302 3
12 0.477089 0.55017 0.513629 8
13 0.591973 0.451303 0.521638 6
14 0.487603 0.463888 0.475746 12
15 0.41844 0.333333 0.375887 18
16 0.907692 0.812545 0.860119 2
17 0.484932 0.55017 0.517551 7
18 0.389011 1 0.694505 4

49
In grey relational analysis total performance of multi objective optimization
is depending on value of grey relational grade. According to performed
experiment design, it is clearly observed from Table 6.8 that the „plasma arc
cutting process parameters‟ setting of experiment no. 10 has the highest grey
relation grade. Thus, the 10th
experiment gives the best multi-performance
characteristics among the 18 experiments.
To find out the optimum level of plasma arc cutting process parameters,
calculate the average grey relational grade for each factor level. For example,
the grey relational grades for factors A, B and C at level 1 can be calculated
as follows:
γA1 =1/6 (0.466047766 + 0.489651937 + 0.39554719 + 0.500466707 +
0.403967328 + 0.431803215)
= 0.447914
γB1 =1/9 (0.466047766 + 0.489651937 + 0.39554719 + 0.500466707 +
0.403967328 + 0.431803215 + 0.567970383 + 0.47796193 + 0.412212618)
= 0.460625
γC1 =1/6 (0.466047766 + 0.500466707 + 0.567970383 + 0.89224716 +
0.521638335 + 0.86011889)
= 0.634748

50
The same way we calculate for factors A, B, C at level 2 and level 3. Result
Table 4.9 Response table for gray relational grade.
Machining
parameters
Average grey relational grade by
factor level
Level 1 Level 2 Level 3
Cutting Speed
(mm/min)
0.447914 0.605221* 0.574241
Arc Current (amp) 0.460625 0.624292* -
Gas Pressure (Psi) 0.634748* 0.52203 0.470597
Table 4.9 shows average grey relational grade by factor level. From this
table, one has concluded optimum parameter levels which are indicated by
“*”. In this table, higher grey relational grade from each level of factor
indicates the optimum level. From this table it is concluded that the optimum
parameter level for Cutting Speed, Arc Current, Gas Pressure is (3800
mm/min), (130 amp) and (60 Psi) respectively.

51
4.4 Analysis and discussion of experimental results
Optimal parameter combination on the Steel 200mm × 200mm × 6mm work-
piece for surface roughness and material removal rate with different
combinations of plasma arc cutting process parameter of 18 experimental
runs.
4.4.1 Graph for grey relational grades
Figure 4.2 graph for grey relational grades.
According to performed experimental design, it is clearly observed from
Table 4.8 and the Grey relational grade graph (Figure 4.2) which shows the
change in the response when the factors go from one level to other that the
laser engraving process parameters setting of experiment no. 10 has highest
grey relation grade. Thus, the 10th experiment gives the best multi-
performance characteristics of the plasma arc cutting process among the 18
experiments.

52
4.4.2 Main effect plot for grey relational grade
Figure 4.3 Graph of grey relational grade v/s Cutting Speed (mm/min).
Figure 4.3 shows the effect of cutting speed on grey relational grade. From
this graph we conclude that at 3800 mm/min cutting speed, grey relational
grade is higher compare to 3000 mm/min, and 4200 mm/min cutting speed.
So, 3800 mm/min is optimum parameter level from three level of cutting
speed.
Figure 4.3 shows the effect of Arc Current on grey relational grade. From
this graph we conclude that at 130 amp arc current, grey relational grade is
higher compare to 50 amp arc current. So, 130 amp is optimum parameter
level from two level of arc current.

53
Figure 4.4 Graph of grey relational grade v/s Arc Current (amp).
Figure 4.5 Graph of grey relational grade v/s Gas Pressure (Psi).

54
Figure 4.5 shows the effect of gas pressure on grey relational grade. From
this graph we conclude that at 60 Psi gas pressure, grey relational grade is
higher compare to 80 Psi and 100 Psi gas pressure. So, 60 psi is optimum
parameter level from three level of gas pressure.
4.5 Summary
In this chapter we have discussed about the introduction of ANOVA and
mathematical step for find out the percentage contribution of each process
parameters on response variables, and discussed about the basics of grey
relational analysis and procedure for implementation of grey relational
analysis for our experimental work.

55
Chapter Five
5 Results and Conclusion
In previous chapter we have discussed about ANOVA and grey relational
technique, and we have done normalization of experimental results and then
calculate deviation sequence to find out grey relational coefficient and grey
relational grade. After performing the experiment for all 18 runs and
measuring response variables like surface roughness, material removal rate
for plasma arc cutting of Steel, whatever results generated are discussed in
this chapter.
5.1 Main Effect Plot for Process Parameters v/s Response Variables
In this topic it covered main effect plot for surface roughness, material
removal rate and grey relational grade. These three main effect plots are
combined with three process parameters cutting speed, arc current, and gas
pressure.

56
Figure 5.1 Graph of main effect plot for surface roughness.
Figure 5.1 shows the main effect plot for surface roughness. From figure 5.1
it is clearly shown that from 3000 mm/min to 3800 mm/min cutting speed,
surface roughness is decrease and from 3800 mm/min to 4200 mm/min
cutting speed, surface roughness is increase. So it concludes that for achieve
good surface quality, cutting speed must be required less.
Now concentrate on effect of arc current on surface roughness. From figure
5.1 it is clearly shown that with increase in arc current, surface roughness is
decrease. So it concludes that for achieve good surface quality, arc current
required must be more.
Now concentrate on effect of gas pressure on surface roughness. From figure
5.1 it is clearly shown that with increase in gas pressure, surface roughness
is increase. So it concludes that for achieve good surface quality, gas pressure
must be required less.

57
Figure 5.2 Graph of main effect plot for material remove rate.
Figure 5.2 shows the main effect plot for material removal rate. From figure
5.2 it is clearly shown that with increase in cutting speed, material removal
rate is increase too. So it concludes that for achieve good material removal
rate, cutting speed must be required more.
Now concentrate on effect of arc current on material removal rate. From
figure 5.2 it is clearly shown that with increase in arc current, material
removal rate is increase. So it concludes that for achieve good material
removal rate, arc current must be required more.
Now talk about effect of gas pressure on material removal rate. From figure
5.2 it is clearly shown that from 60 Psi to 80 Psi gas pressure, material
removal rate is increase and from 80 Psi to 100 Psi gas pressure, material

58
removal rate is decrease. So it concludes that for achieve good material
removal rate, gas pressure must be near 80 Psi.
Figure 5.3 Graph of main effect plot for grey relational grade.
Figure 5.3 shows that main effect plot for grey relational grade to individual
process parameters.
From figure 5.3 it is clearly shown that it is clearly shown that from 3000
mm/min to 3800 mm/min cutting speed, grey relational grade is increase and
from 3800 mm/min to 4200 mm/min cutting speed, grey relational grade is
decrease. So, highest grey relational grade is achieved at 3800 mm/min
cutting speed amongst three level of cutting speed.

59
Now concentrate on effect of pulse frequency on grey relational grade. From
figure 5.3 it is clearly shown that with increase in arc current, grey relational
grade is increase. So, highest grey relational grade is achieved at 130 amp
arc current amongst two level of arc current.
Now concentrate on effect of scanning speed on grey relational grade. From
figure 5.3 it is clearly shown that for increasing gas pressure, grey relational
grade is decrease. So, highest grey relational grade is achieved at 60 Psi gas
pressure amongst three level of gas pressure.

60
5.2 Conclusion
In the presented work, experiment are carried out for response variables are
surface roughness and material removal rate with process parameters as
cutting speed, arc current and gas pressure. There are 18 experimental
readings taken for all variables to conduct the parametric study.
For experimental work it will be considered three, two and three levels for
process parameters respectively. Cutting speed is 3000, 3800, 4200 mm/min,
Arc current is 50, 130 amp and Gas pressure is 60, 80, 100 Psi.
Experimental result shows that from 3000 mm/min to 3800 mm/min cutting
speed, surface roughness is decrease and from 3800 mm/min to 4200
mm/min cutting speed, surface roughness is increase. So it concludes that for
achieve good surface quality, cutting speed must be required less. Now
concentrate on effect of arc current on surface roughness, it concludes that
with increase in arc current, surface roughness is decrease. So it concludes
that for achieve good surface quality, arc current required must be more.
Now concentrate on effect of gas pressure on surface roughness, it concludes
that with increase in gas pressure, surface roughness is increase. So it
concludes that for achieve good surface quality, gas pressure must be
required less.
Experimental result shows that for material removal rate with increase in
cutting speed, material removal rate is increase. So it concludes that for
achieve good material removal rate, cutting speed must be required more.
Now concentrate on effect of arc current on material removal rate, it
concludes that with increase in arc current, material removal rate is increase.

61
So it concludes that for achieve good material removal rate, arc current must
be required more. Now talk about effect of gas pressure on material removal
rate, it shows that from 60 Psi to 80 Psi gas pressure, material removal rate
is increase and from 80 Psi to 100 Psi gas pressure, material removal rate is
decrease. So it concludes that for achieve good material removal rate, gas
pressure must be near 80 Psi.
From the experimental results for ANOVA analysis it conclude that for
surface roughness percentage contribution of gas pressure is more in three
response variables compare to other two process parameters and for material
removal rate percentage contribution of arc current is more in three response
variables compare to other two process parameters.
In grey relational analysis total performance of multi objective optimization
is depending on value of grey relational grade. According to performed
experiment design, it observed that the ‘plasma arc cutting process
parameters’ setting of experiment no. 10 has the highest grey relation grade.
Thus, the 10th
experiment gives the best multi-performance characteristics
among the 18 experiments. From the grey relational analysis it also conclude
that the optimum parameter level for Cutting Speed, Arc Current, Gas
Pressure is (3800 mm/min), (130 amp) and (60 Psi) respectively.
The results shows its better surface roughness and material removal rate
prediction capabilities and applicability to such industrial plasma arc cutting
leading to effective selection of machining parameter for better qualitative
cutting.

62
References
[1] Fundamentals_of_Modern_Manufacturing_4th_Edition_
By_Mikell_P.Groover
[2] http://www.omni-cnc.com/
[3] www.hypertherm.com
[4] Hypertherm
2016 torch and consumables catalog For mechanized plasma
systems
[5] www.alfatekmakina.com.tr
[6] Facts about plasma technology and plasma cutting
[7] Analysis Of Process Parameters Of Plasma Arc Cutting Using
Design Of Experiment by Vivek Singh (2011)
[8] Study of Process Parameters in Plasma Arc Machining Process
by Nishant Sharma (2011)
[9] Analysis of process parameters of Plasma arc cutting using design
of Experiment
By: VIVEK SINGH
[10] Rudolf N. Cardinal, “ANOVA in practice and complex ANOVA
design”.
[11] Phonex® software V9.75.0 Operator manual By Hypertherm
[12] Microsoft office Excle2016, for calculating data
[13] Minitab 15 software for creating curves and charts

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