ANALYSIS AND PARAMETRIC OPTIMIZATION OF PAC WITH

ANALYSIS AND PARAMETRIC OPTIMIZATION OF PAC

WITH MATHEMATICAL MODELING 2013-14

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Chapter:-1 Introduction



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1.1 Project background:-

• Because of the growing need for manufacturing functional metallic parts, rapid

Manufacturing processes have become the focus of increasing research and

development.

• Manufacturing processes based on material removal (i.e., drilling, milling, turning,

and Cutting) have been used for many years.

• The recent advancements in manufacturing technology have enabled Manufacturers to

make parts and products faster, with better quality, and more Complexibility.

• The process of plasma cutting was introduced in 1950. Since then, the Manufacturing

industries are using this process extensively because of its wide Applications.

1.2 Problem statement:-

In plasma arc cutting (PAC) process, there are many problems found. The main problems

are listed below:

• Plasma arc cutting can be characterized in terms of two different speeds.

• At cutting speeds above, the plasma jet does not cut through metal plate.

• At speeds below, the molten metal from the kerf sticks to the bottom of the plate. So,

we have to optimize proper parameters (gas pressure, currents, cutting speed, and arc

gap) for plasma arc cutting of AISI H11 alloy steel material.

1.3 Project Objective:-

This project was developed to study about the plasma arc cutting parameter in smooth cutting

using straight polarity process. The main purposes of this project are listed below:

• To reduce the hazardous effect during cutting process.

• To study about the influence of Plasma Arc Cutting Parameters on Suitable material.



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• To design a series of experiment using the help of Design of Experiments (DOE)

layout in order to study about Plasma Arc Cutting (PAC).

• To study about the best combination of solution for optimum condition (setting)

parameters.

• To improve the productivity.

• To increase the effectiveness of product.

• To reduce the time consumption.

• To reduce the material waste during cutting process.

1.4 Scope of project:-

Based on this work many improvements can be made and the scope can also be winded

Following are suggestion for future work:

• Study for manual calculation for other method in DOE to improve knowledge and

skills.

• Using Plasma Arc Cutting system, add the parameter such as current, material

dimension, and change advance material such as brass and bronze then compare the

result obtained.

• Also side clearance and thermal effect on material and work piece like Heat Affected

Zone (HAZ) can also be considered to study the effect on properties of work piece.

• This project focuses on the optimization of cutting parameters of Plasma Arc Cutting

(PAC).

• The material used to cut was hot die tool steel of specification AISI H11 alloy steel.

• Design of Experiments (DOE) layout will be used for testing and analyzing with

Taguchi Method.

• All of data was analyzed by using Minitab 15 Software to produce the best

combination setting in plasma cutting for die tool Steel.



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Chapter:-2 Literature review



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In this chapter definition of plasma, principle of plasma arc cutting, plasma cutting

construction and quality of plasma cutting process will be describe and select machining

parameter for experimental set up.

2.1 Definition of plasma

Figure 2.1 Structure of the plasma cutting system [1]

In figure 2.1 the structure of plasma cutting system will be shown in which the construction

of nozzle is described. Plasma is typically an ionized gas. Plasma is considered to be a

distinct state of matter, apart from gases, because of its unique properties. Ionized refers to

presence of one or more free electrons, which are not bound to an atom or molecule. The

free electric charges make the plasma electrically conductive so that it responds strongly to

electromagnetic fields [3].

The Arc type uses a two cycle approach to producing plasma. First, a high-voltage, low

current circuit is used to initialize a very small high intensity spark within the torch body,

thereby generating a small pocket of plasma gas. This is referred to as the pilot arc. The pilot

arc has a return electrical path built into the torch head. The pilot arc will maintain until it is

brought into proximity of the work piece where it ignites the main plasma cutting arc.

Plasma arcs are extremely hot and are in the range of 15,000 degrees Celsius.[3]



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2.2 Plasma cutting

Plasma cutting is a process that is used to cut steel and other metal of different thickness

using a plasma torch. In this process, an inert gas is blown at high speed out of a nozzle; at

the same time an electrical arc is formed through that gas form the nozzle to the surface

being cut, turning some of that gas to plasma. The plasma is sufficiently hot to melt the

metal being cut and moves sufficiently fast to blow molten metal away from the cut. Plasma

cutting proved to be an effective process for cutting nonferrous metals, but it would to

compete with oxy fuel cutting on mild steel only if it took advantage of the reaction between

iron and oxygen. Plasma cutting is typically easier for the novice to master, and on thinner

materials, plasma cutting is much faster than oxy fuel cutting. However, for heavy sections

of steel (1inch and greater), oxy fuel is still preferred since oxy fuel is typically faster and,

for heavier plate applications, very high capacity power supplies are required for plasma

cutting applications [4] .

2.3 Working principle of plasma cutting machine

Figure. 2.2 The principle of the plasma cutting [2]



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In this figure 2.2 working principle of plasma arc cutting is described. In this process

electrode act as negative charge and workpiece act as positive charge. Cutting gas like n2,

O2, air, etc are used around electrode. High voltage charges apply to the electrode. Cutting

gas gets ionized and converts into plasma, and generate arc. Heavy gas like Ar, Ne used as

shielding gas which protect arc from atmospheric condition. In this process uses a

concentrated electrical arc which melts the material through a high-temperature plasma

beam. All conductive materials can be cut. Plasma cutting units with cutting currents from

20 to 1000 amperes to cut plates with inert gas, 5 to 160 mm thicknesses. Plasma gases are

compressed air, nitrogen, oxygen or argon/ hydrogen to cut mild and high alloy steels,

aluminum, copper and other metals and alloys [4].

For the cutting process first of all a pilot arc ignition by high voltage between nozzle and

cathode takes place. This low- energy pilot arc prepares by ionization in parts the way

between plasma torch and work piece. When the pilot arc touches the work piece (flying

cutting, flying piercing), the main arc will start by an automatic increase in power. [4]

The basic principle is that the arc formed between the electrode and the work piece is

constricted by a fine bore, copper nozzle. This increases the temperature and velocity of the

plasma emanating from the nozzle. The temperature of the plasma is in excess of 20 000°C

and the velocity can approach the speed of sound. When used for cutting, the plasma gas

flow is increased so that the deeply penetrating plasma jet cuts through the material and

molten material is removed in the efflux plasma. [4]

2.4 Plasma machine construction

In this figure 2.3 explains that basic plasma cutting use electricity to superheat air into

plasma, which is then blown through the metal to be cut. Plasma cutters are extremely

simple and require only a compressed air supply and AC power outlet to operate. A

complete plasma cutter consists of a power supply and an AC power outlet to operate. A

complete plasma cutter consist of a power supply, a good clamp, and a hand torch, the main

function of the power supply is to convert the AC line voltage into a user-adjustable



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regulated DC current. The hand torch contains a trigger for controlling the cutting, a nozzle

through which the compressed air blows. An electrode is also mounted inside the hand torch,

behind the nozzle.[2]

Figure 2.3 Plasma cutting machine construction [2]

2.4.1 Plasma power supply

The power source required for the plasma arc process must have a drooping characteristic

and a high voltage. Although the operating voltage to sustain the plasma is typically 100 to

160V, the open circuit voltage needed to initiate the arc can be up to 400V DC. On

initiation, the pilot arc is formed within the body of the torch between the electrode and the

nozzle. For cutting, the arc must be transferred to the work piece in the so-called 'transferred'

arc mode. The electrode has a negative polarity and the work piece a positive polarity so that

the majority of the arc energy (approximately two thirds) is used for cutting.[5]

2.4.2 Plasma burner electrode and nozzle

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. [6]



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The swirl ring is designed to spin the cutting gas in a vortex. The swirling is made of a high

temperature plastic with angled holes that cause the gas to spin. The purpose of the torch tip

is to constrict and focus the plasma arc. Constricting the arc increases the energy density and

velocity. The tips are made of copper, with a specifically sized hole or orifice in the center

of the tip.[6]

2.4.3 Plasma torch

The Plasma cutting process is used with either a handheld torch or a 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.

PAC torches operate at extremely high temperatures, and various parts of the torch must be

considered to be consumable. The tip and electrode are the most vulnerable to wear during

cutting, and cutting performance usually deteriorates as they wear. 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 [19].

2.4.4 Work piece

In plasma cutting with transferred plasma arc, the material to be cut has to be electrically

conductive since the work piece is a part of an electric circuit. The ground of the connected

work piece must be designed to permit a continuous flow of current [3].

2.4.5 Gas supply

Plasma cutting system operates with the following gases: inert, reduced- reactivity, low-

reactivity, active, and mixture of any of these.[3]



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2.4.5.1 Plasma Gas Selection

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. [3]

Nitrogen Plasma

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.

Good clean welding grade nitrogen should be used.[3]

Argon/Hydrogen Plasma

A 65% argon/35% hydrogen mixture should be used.

Recommended use on 19mm and thicker stainless steel. Recommended for 12mm 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. [3]

Oxygen Plasma

Oxygen is recommended for cutting ferrous metals.

Provides faster cutting speeds.



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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). [3]

2.4.5.2 Secondary Gas Selection

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 [3]

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.[3]

2.4.6 Coolant circulation system

Due to high thermal loads, plasma cutting requires effective cooling. A distinction is made

between integrated and external water circulation cooling and gas cooling. Burners of

approx. 100 amps or more are generally water-cooled [4].

2.4.7 Cutting bench and exhaust system

Cutting benches serve as a stable device for positioning metal sheet to be cut. The

dimensions of the bench depend on the size, thickness and weight of the metal plate.

Emissions released during the cutting process can be significantly reduced by using a plasma

cutter in combination with an exhaust system for smoke and dust or with a water basin.

Oxygen is used as a plasma gas for cutting non-alloy and low-alloy steels. When oxygen



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mixes with the melt, the viscosity of the melt decreases, causing it to become more fluid.

This generally permits burr-free edges and top edges that are not rounded. Owing to the high

cutting speed, the width of the heat affected zone is very small and the mechanical properties

of the cut metal do not deteriorate. The high cutting speed is due to the chemical reaction of

the oxygen with the material.[4]

2.5 Arc constriction

The action greatly increases the resistive heating of the arc so that both the arc temperature

and the voltage are raised. After passing through the nozzle, the arc exist in the form of a

high velocity, well collimated and intensely hot plasma jet as shown below[5].

A plasma jet can either be operated in the transferred mode, where the power supply is

connected between the electrode and the work piece or in the non-transfer mode where the

power supply is connected between the electrode and nozzle. Both modes of operation are

illustrated in figure 2.4 and 2.5.

Figure. 2.4 Temperature Differences of arcs [5]

Figure. 2.5 Two Basic Types of Constricted Arcs [5]



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The characteristics of the plasma jet can be altered greatly by changing the gas type, gas

flow rate, are current, and nozzle size. In this paper only the plasma cutting process- the use

of a plasma arc developed under condition of high gas flow and high current [5].

The plasma cutting arc is considerably hotter than the example described above in Figure 2.5

Greater temperatures are possible because the high gas flow forms a relatively cool

boundary layer of unionized gas inside the nozzle bore, thereby allowing a higher degree of

arc constriction. The thickness of this boundary layer can be further increased by swirling

the cutting gas. The swirling action forces the cool, unionized gas to move radially outward

and form a thicker boundary layer. Most mechanized plasma cutting torches swirl the cutting

gas to attain maximum arc constriction.[5]

2.6 Gas supply for plasma cutting machines

Plasma cutting machines operate with one or several different gases. The required supply

pressure and throughput depends on the type of equipment being used. The manufacturer’s

specifications should always be complied with. The gas can be supplied in various forms,

such as in cylinders, in cylinder packs or in liquid state in tanks.

The form in which the required gases are delivered – in gaseous or liquefied state –

primarily depends on how much of the gases are needed. The same holds true for the size

and type of the gas storage unit.

However, economic factors also have to be considered in terms of the design of the gas

supply system for plasma cutting. The amount of plasma and secondary gases required

depends on various factors such as the plasma nozzle diameter, gas pressure and cutting

current and can lie anywhere between 20–100 l/min. Under these conditions, depending on

the job(s) at hand, anything from individual gas cylinders to stationary tanks may be required

to supply sufficient gas.

If gas utilization is 200–300 m3/week, the gas is delivered in its gaseous form; for quantities

above that amount, it comes in liquid state. If the gas flows in plasma cutting system falls



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below the value specified by the manufacturer, the burner can be seriously damaged. To

avoid this, it is paramount that the pressure be set to the value specified by the manufacturer.

At least 12 bars of pressure should be available.[6]

2.7 Quality of plasma cutting process

The standard applies to materials suitable for oxy-fuel cutting, plasma cutting and laser

cutting and should be used for oxy-fuel cuts from 3 to 300 mm, plasma cuts from 1 to 150

mm, and laser cuts from 0.5 to 40 mm. This standard contains the geometric product

specifications and dimensional (quality) tolerances.

It is important to determine the correct quality for every product to be cut. This section

explains the most important quality parameters [6].

2.8 Machining parameter

2.8.1 Input parameters

2.8.1.1 Current Flow

Current flow 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 speed is decreased, the process will withstand larger variations in the

cutting parameters.[12]

2.8.1.2 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



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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.[12]

2.8.1.3 Arc Gap

Arc gap is the gap between the plasma arc cutter torch and welding electrodes with the work

piece [12].

2.8.2 Response parameters

There are two Plasma Arc Cutting responses measured in this study, known as:

Surface Roughness (Ra)

Kerf width

2.8.2.1 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. Roughness is often a good predictor of the performance of

a mechanical component, since irregularities in the surface may form nucleation sites for

cracks or corrosion.[2]



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2.8.2.2 Kerf width

Kerf is defined as the width of material that is removed by a cutting process. It was

originally used to describe how much wood was removed by a saw, because the teeth on a

saw are bent to the side, so that they remove more material than the width of the saw blade

itself, preventing the blade from getting stuck in the wood.

Each cutting process removes a different amount of material, or kerf. The more precise

processes, like water jet and laser, remove a smaller amount of kerf, which is one of the

reasons they can be more precise! A typical example shown here is for 1/2” thick mild steel.

Literature review provides the scope for the present study. It works as guide to run this

analysis. This chapter will play a part to get the information about plasma cutting machine

and will give idea to operate the test. From the early stage of the project, various literature

studies have been done. Research journals, books, printed or online conference article were

the main sources of guidance and used as a supporting material in the project. This chapter

includes almost the whole operation including the test, history, machining properties and

results. Literature review section works as reference, to give information and guidance based

on journal and other source in the media.[2]

AbdulkadirGullu et al.(2005), Have been investigated the effect of material thickness,

cutting speed, cutting gas, current and voltage to improve the hardness of material like

AISI 304 and St 52 steels. In this study, AISI 304 stainless steel and St 52 carbon steel have

been cut by plasma arc and the variations of structural specifications occurred after cutting

has been investigated. According to the experimental results, it has been seen that burning of

particulars and distribution amount were increased when the cutting was performed using

the speeds which are upper or lower limits of the ideal cutting speeds proposed by the

manufacturer of the machine tool. It have been found that after cutting, in the areas near to

outer surface of the part hardness increased, around 250–350 HV, and it decreased towards

to the core of the material. The amount of material removed from cutting area is proportional

to thickness [9].



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ArsenNarimanyan (2007), Have been investigated the effect of temperature distribution in

the work piece and the geometry of the cut front during the plasma cutting. The weak

formulation of the model is discussed in the framework of vibrational inequalities and level-

set theory. Using the adaptive finite elements method, numerical results are obtained and

illustrated in the manuscript. As a result they conclude following results- Description of

thermal plasma cutting process and physical modeling of different effects taking place in the

work piece during the cutting. Mathematical modeling of the metal piece cut with plasma

via Stefan–Signorini moving-boundary approach. Reformulation of the classical model into

a weak model using the concepts of theories on variation inequalities and level sets

Mathematical analysis of the weak model, establishment of existence and uniqueness results.

Numerical results and computer simulations. The model allows us to get several qualitative

results on the process, but is still open for further modifications. We would like to mention

that the temperature field analysis and computation of the geometry of the cut pieces is the

first step on the way of the modeling of the whole plasma cutting process. Further steps

include the determination of thermoplastic, thermoplastic deformations as well as the

deformations due to phase transformations [8].

W. J. Xu et al.(2002), Have been investigated the effect of current, pressure, voltage and

flow rate on the Al2O3 ceramic plate to reduce kerf width and to improve kerf quality. By

experiments and analysis, the characteristics of the hydro-magnetically confined plasma arc

were explored and the effect of secondary confinement on cutting quality, arc properties,

and optimal process parameters were determined, the authors achieved better cutting quality

and higher cutting speeds When nozzle diameter is 3 mm, the kerf width of Al2O3 ceramic

plate of 6 mm thickness is less than 4.3 mm, while the cutting speed reaches to 0.9- 1.2

m/min. It have been found that the hydro-magnetic constriction of plasma arc forms a three

dimensional constriction with improved shape and uniformity of the arc column, narrower

kerfs, minimum beveling of cuts and higher dross-free cutting speed and is capable of

improving arc stability, which is reflected by the higher arc voltage at arc extinction, than

that under any single constriction [10].



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E. Gariboldi et al.(2004), Have been investigated the effect cutting speed, nozzle diameter,

cutting gas and feed rate of a 5mm commercially pure titanium sheet to improve kerf width

by use of high tolerance plasma arc cutting process. It have been found that due to the

reduced interaction with the plasma-beam related to higher feed rates when oxygen was

used, the geometrical features (unevenness and kerf width, measured on both sides of the

cutting edges due to their asymmetry) revealed a better quality for this set of cuts. the quality

features of the cutting edge of HTPAC of commercially pure titanium from a geometrical

point of view need to be integrated with the considerations on the functional requirements

for the cutting edge and on economic considerations that are partially correlated to micro-

structural modifications occurred at the cutting edge [11].

B.M. Colosimo et al.(2007), Have been investigated the effect of arc voltage , cutting

speed, plasma gas flow rate, shield gas flow rate of mild steel material to reduce the cutting

speed by a 200A high tolerance plasma arc cutting system(HTPAC). It has been found that

the arc voltage is the main parameter and it influences all the aspects related with the cut

quality. Rather than the effect on the arc power, its proportionality with the standoff distance

seems to be the true responsible for its importance. on the other hand, by reducing the arc

voltage, i.e. the standoff distance, the thermal stress on the torch components, especially the

electrode and the nozzle, increases, thus accelerating their wear. Beyond the arc voltage, the

cutting speed showed a noticeable effect. In particular, results obtained in the last

experimental stage allowed one to observe that unevenness can be reduced by reducing the

cutting speed [12].

Jia Deli et al.(2010), Have been investigated the effect of Arc voltage, Cutting current,

Cutting speed , Thickness of plate , Gas pressure and Torch height of low carbon steel to

improving the comprehensive characteristics of incision. In the model, the controller

neglects the effects of the equivalent resistance on control in the arc initiation process and

assumes the equivalent plasma load to be the resistance load. Adopting digital inverted

plasma arc cutting power as a platform and focusing on its strong nonlinearity and time-

varying property. this paper puts forward a variable interval fuzzy-PI quantification

algorithm with a self-adjustable factor in the full domain. It have been found that the



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conventional constant current closed-loop control makes the finish worse and the ripples

deeper. If the system only advances response speed, then the ripples will be uneven and the

cutting precision cannot improve and also the cutting effect and the simulation that the

control strategy proposed in this paper has great practical significance for optimizing cutting

control and improving the process effect [13].

Daniel J. Thomas (2011), Have been investigated the effect of power, current, and cutting

speed of hot rolled steel to improving the cutting speed. The durability of steel components

produced for service as Yellow Goods vehicle applications, are primarily influenced by the

condition of their thermal cut-edges. The chassis structures of such demanding applications

are manufactured with laser and plasma cut-edges left exposed after final fabrication. It has

been found that Laser cut-edges were observed to have a greater incidence of overlap

striations present at lower traverse cutting speeds. These features became less apparent and

reduced in size as the traverse cutting speed was increased [14].

M. Boutinguiza et al.(2001), Have been investigated the effect of various gases to increase

the cutting speed. Slate is a natural stone which has the characteristic that shows a well-

developed defoliation plane, allowing to easily split it in plates parallel to that plane which

are particularly used as tiles for roof building. It have been found that the use of oxygen as

assist gas leads to a slight increase of the cutting velocity compared with the use of inert

gases and also Slate tiles of different thickness up to 13mm can be cut with an acceptable

cutting speed using a CO2 laser delivering no more than 1200W and the use of a supersonic

nozzle leads to an increase in the maximum cutting speed with respect to the use of a conical

one [15].

Jiayou Wang et al.(2010), Have been investigated the effect of Arc current, Cutting speed,

Thickness, Flow rates and Pressure to improving kerf width by using metallic material. It

have been found that with a decrease of arc current and an increase of cutting speed, kerf

widths decrease, and the bevel angle and the straightness increase while as the oxygen

content of the operating gas decreases, kerf widths decrease and the dross increases, while

the bevel angle varies slightly on the high speed side of the cut. For the pure oxygen and



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pure air processes, the bevel angle on the low speed side and the straightness of cut surface

are the smallest, but the pure oxygen cut surface is the roughest due to the occurrence of a

saw-like kerf [16].

Vivek Singh, Have been investigated the effect of Gas pressure , Current flow rate, Cutting

speed, Arc gap to improve material removal rate(MRR) and surface roughness(Ra).It have

been found that the Optimum levels of parameters for maximizing MRR are Gas Pressure(5

Bar), Current(150 A), Cutting Speed(600 mm/min), and Arc Gap(4mm) while The optimum

levels of parameters for minimizing Surface Roughness (Ra)are Gas Pressure: 6 Bar

Current(150 A), Cutting Speed(400 mm/min),and Arc Gap( 2 mm) [2].

2.9 Patent search:

Kjellberg Elektroden [97F[LIX(2)],129G[XXXV]; 1967] “improvements in or relating to a

method of plasma arc cutting or welding” the invention relates to a method of plasma arc

cutting and welding with very high emission velocity of the plasma stream and with mixing

of the working gas and the additional gas in the arc plasma torch, and to the arrangement for

use in carrying out the method.

Roberts J Tevorog P [CN202411644 (U) ― 2012-09-05; 2010] “Spray nozzle, spray nozzle

maintaining cap, cutting torch head and vortex ring for plasma arc cutting torch” The

utility model discloses a spray nozzle, a spray nozzle maintaining cap, a cutting torch head

and a vortex ring for a plasma arc cutting torch, wherein the spray nozzle for the plasma arc

cutting torch comprises a first end and a second end. The spray nozzle also comprises a

plasma outlet hole positioned a first end of a body. A flange is positioned at a second end of

the body. The flange is suitable to be in close fit with a corresponding consumable

component. The flange is configured to selectively block at least one gas passage on the

corresponding consumable component, so as to establish a gas flow opposite to the body of

the sprayNozzle. According to the spray nozzle, the spray nozzle maintaining cap, the

cutting torch head and the vortex ring, due to the generality of the consumable component,

the time used for a user to determine which combination of the consumable component is



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correct aiming at the specific parameter of the plasma cutting torch can be reduced.

Moreover, the operation total expense of the plasma cutting torch can be also reduced, as the

premature failure or the underperforming initiated due to the wrong matching of the

consumable component can be reduced since the single consumable component can be used

for a plurality of parameters of the cutting torch.

Yuehong YIN [CN] et al [CN101364101 (A); 2009] “Numerical control plasma cutting machine

trepanning modular system” The invention relates to a numerically-controlled (NC)

intersection-line cutting machine nest system used in the field of NC cutting. The system

comprises a NC file processing module, a parameter-setting module, a tube-laying module, a

data management module and a display module. The NC file processing module reads a NC

file to be processed from a computer hard disk or a mobile memory and generates a new NC

file that is stored in the computer hard disk or a mobile memory. The parameter-setting

module lists the tube-laying parameters which are required for the tube-laying operation and

need to be reset or modified to allow a user to reset or modify. The data management

module transmits the data to other modules. The tube-laying module receives the tube-laying

parameters and the original steel tube processing data of the tubes and performs the tube-

laying, and optimizes the arrangement of the tube nest by adjusting the position of the

intersection-line track of each tube. The display module displays the data that are required to

be viewed by the user during the tube-laying process. The NC intersection-line cutting

machine nest system can not only maximize the utilization rate of the blank material but also

greatly increase the time efficiency of the user.

Warren Joseph Valerious [US] et al. [US6274842 (B1); 2001] “Method of cutting a work piece

along an accurate path with a plasma arc torch” A method of cutting a work piece along

a cutting path that is accurate or that has one or more accurate portions includes the step of

determining a control parameter that is proportional to the angular velocity of the torch. The

arc current supplied to the torch is regulated based on the control parameter and the linear

advance rate of the torch, which in turn is a function of the material type and thickness of the

work piece. In one embodiment of the invention suitable for the cutting of holes, the control

parameter is the diameter of the hole to be cut, which for a specified linear advance rate is



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inversely proportional to the angular velocity of the torch. The current is increased above a

nominal current when the hole diameter is less than or equal to a predetermined limiting

diameter, and otherwise is set at the nominal current. In other embodiments of the invention

suitable for cutting holes or other shapes, the control parameter is the radius of curvature of

the cutting path. Alternatively, the angular velocity can be used as the control parameter.

Increasing the current at higher angular velocities and/or when cutting holes of small

diameter tends to reduce the problem of the arc not following the desired cutting path and

creating cut surfaces that do not conform to the desired cut surfaces.

Joseph Allen Daniel [208231; 2007] “A plasma arc installation and a method for retracting

a cutting arc of said installation” An arc retract circuit for use in a plasma arc system with

a torch having an electrode and a nozzle, a power supply for providing a D.C. current, a

power circuit for connecting the power supply across said electrode and a work piece to be

cut, a power switch for connecting the nozzle to the power supply when in a closed

condition defining a pilot arc mode of operation and for disconnecting the nozzle from the

work piece when in an open condition defining a cut mode of operation, amplifier means for

regulating said power supply to a first set current when in the pilot - arc mode and a second

set current when in the cut mode, and an arc retract circuit for shifting the power switch

from the open condition to the closed condition, which arc retract circuit includes current

sensing means for creating a first signal representing the actual current applied by the power

supply to the power circuit, means for creating a second signal representative of a current

level below the second set current, and switch operations means for closing the power

switch when the first signal is substantially equal to the second signal.

Orszagh Peter [SK] [SK99598 (A3); 2000] “Method for controlling plasma cutting process

with aim to secure constant distance of a cutting torch from cut material” The invention

relates to a method of controlling plasma cutting process with aim to secure constant

distance of a cutting torch from cut material, especially in the process of plasma cutting with

air and oxygen atmosphere, which method can be characterized in that electric resistance of

the cutting circuit, or the part thereof, is a controllable parameter. During the process of

cutting a real value and the deviation of said controllable parameter from desired values, or



SRPEC [ME] Page 23

the intervals thereof, is measured, thus indicating that a correction of the position between

the torch and material to be cut needs attention.

Schmidt KLAUS-P [DE] [DE19522369 (A1); 1997] “Rectifier-power pack e.g. for welding or

plasma-cutting apparatus” rectifier for welding or plasma-cutting apparatus is a full-wave

one (1) with a capacitative support circuit (4) and a step-up converter (3). The latter has a

control unit 913) receiving as input parameters the link current and input and output

voltages, as well as a set point for the converter output voltage. The output voltage

parameter is fed to the control unit via a band-limiting filter unit (18) which damps the

alternating components generated by the capacitative support circuit. The filter unit is a low-

pass filter and its base frequency is chosen so that the doubled mains frequency lies within

the damping region.

Yuehong Yin [CN] et al [CN101364101 (A); 2012] “Numerical control plasma cutting machine

trepanning modular system” The invention relates to a numerically-controlled (NC)

intersection-line cutting machine nest system used in the field of NC cutting. The system

comprises a NC file processing module, a parameter-setting module, a tube-laying module, a

data management module and a display module. The NC file processing module reads a NC

file to be processed from a computer hard disk or a mobile memory and generates a new NC

file that is stored in the computer hard disk or a mobile memory. The parameter-setting

module lists the tube-laying parameters which are required for the tube-laying operation and

need to be reset or modified to allow a user to reset or modify. The data management

module transmits the data to other modules. The tube-laying module receives the tube-laying

parameters and the original steel tube processing data of the tubes and performs the tube-

laying, and optimizes the arrangement of the tube nest by adjusting the position of the

intersection-line track of each tube. The display module displays the data that are required to

be viewed by the user during the tube-laying process. The NC intersection-line cutting

machine nest system can not only maximize the utilization rate of the blank material but also

greatly increase the time efficiency of the user.



SRPEC [ME] Page 24

Twarog peter J [US] et al [US2008237202 (A1); 2009] “Plasma Arc Torch Having an Electrode

With Internal Passages” An electrode for a plasma arc cutting torch which minimizes the

deposition of high emissivity material on the nozzle, reduces electrode wear, and improves

cut quality. The electrode has a body having a first end, a second end in a spaced

relationship relative to the first end, and an outer surface extending from the first end to the

second end. The body has an end face disposed at the second end. The electrode also

includes at least one passage extending from a first opening in the body to a second opening

in the end face. A controller can control the electrode gas flow through the passages as a

function of a plasma arc torch parameter. Methods for operating the plasma arc cutting torch

with the electrode are disclosed.

Wayen Staniey Severance [US6274842 (B1); 2008] “Method and apparatus for low voltage

plasma arc cutting” The field of cutting and welding metals comprises a number of

techniques, of which three of the most prominent are the oxygen-acetylene, electric-arc, and

plasma arc techniques. In oxygen-acetylene (or "oxyacetylene") welding, a high temperature

flame is generated by the combustion of acetylene in oxygen and then used to melt and weld

metals. In electric-arc ("arc") welding, an electric potential is established between a metal

work piece and an electrode which are maintained in sufficiently close proximity for an

electric arc to form between the electrode and the work piece. The heat generated by the arc

welds the metals. Typically, the arc and the metal are shielded from the surrounding

atmosphere--which would otherwise tend to contaminate the weld--by the flow of an "inert"

gas that is maintained adjacent the arc.

DU Changfu [US2008237202 (A1); 2001] “Plasma cutting machine capable of outputting arc

strike signals” The utility model relates to the field of plasma cutting machines, in

particular to a plasma cutting machine capable of outputting arc strike signals. The plasma

cutting machine capable of outputting arc strike signals comprises a control unit, an air

pump, a power supply and a cutting lance. The control unit is a logic control module. The

logic control module comprises a CPU (central processing unit) chip. The CPU chip is

provided with an AD (analog-digital) conversion end and an arc strike result output end. The

plasma cutting machine further comprises a current detection circuit, an OC (open collector)



SRPEC [ME] Page 25

driver and a control output interface. The current detection circuit comprises a sensor. After

the cutting lance strikes arc successfully, the current detection circuit may monitor great

increase in output current of the power supply through the sensor. After the current rises to

preset start current, the CPU chip of the logic control module can analyze and determine the

result of arc strike. Current output and voltage output can be reasonably controlled through

real-time accurate monitoring data, and accordingly arc striking impact is effectively

reduced for the cutting lance.

Makoto Komatsu Research Laboratory Lnove, et al [EP 0390998 A1; 2008] “Method of

working a plate in a plasma cutting machine and plasma torch” In a method of cutting

metals or non-metals with high precision, a plasma cutter is widely used. An example of the

structure of a conventional plasma torch used in a plasma cutter is shown in Fig. 5. A disc or

cylindrical material 21 (hereinafter referred to as an electrode material) for resisting wear at

high temperature Composed of hafnium, tungsten or the like is buried in the front end of

water cooling type copper-bar electrode 20. In this example of a swirl flow type plasma

cutter, the front end of a nozzle 22 is formed in the form of a funnel. This arrangement is a

simple means for fixing an arc to the electrode material 21 on the arc axis center in a case

where the front end shape of the electrode 20 is flat. A swirl air flow 24 is generated by the

funnel-like nozzle 22. An arc column 25 which causes a powerful thermal pinch effect is

formed and the directivity of a plasma arc is maintained, thus cutting a work piece 26. The

smaller a nozzle diameter d is, the greater the thermal pinch effect will become. Further,

since a pressure several times greater than the atmospheric pressure is distributed inside the

arc column 25, this acts to return the pressure to the same pressure as the atmospheric

pressure after it is emitted from the nozzle 22. As a result, the arc column 25 has a tendency

to be diffused rather than converged.

Yoshihiro Yamaguchi [CN202780198 U; 1990] “Controlling working gas flow rate and arc

current level in plasma arc cutting machine” A plasma arc cutting machine which utilizes

oxygen as a working gas is controlled to provide: a long electrode life without serious

electrode wear even if the starting operation of the arc is repeated frequently; a smooth

transition from a pilot arc to a main arc even when a thin plate is cut; and a low noise



SRPEC [ME] Page 26

characteristic. A first stop valve (4) is connected in parallel with a serially connected second

stop valve (7) and a gas flow regulating means (6) between a supply of working gas and a

plasma torch (1). In response to a start signal S.sub. T, the second stop valve (7) is opened

so as to supply the working gas at a small flow rate Q.sub. P to the plasma torch (1) via the

gas flow regulating means (6). After a pilot arc is started, the first stop valve (4) is gradually

opened so as to gradually increase the flow rate of the working gas from the small flow rate

Q.sub. P up to a normal flow rate Q.sub. M, and at the same time, the pilot current is

gradually increased from an initial pilot current level I.sub .S to a pilot current level I.sub. P,

corresponding to the gradual increase in the flow rate of the working gas up to the normal

flow rate Q.sub. M. I.

Seigo Hagiwary, Kazoo Kimato [US 5424507 A; 2013] “Plasma cutting machine capable of

outputting arc strike signals” The present invention relates to an arc welding machine and

a plasma cutting machine wherein an arc is generated between an electrode and a base metal

in contactless fashion and so electric wave interference is reduced to drastically improve the

arc start characteristic when an extension cable is used. Conventionally, in an inconsumable

electrode arc welding machine and a plasma cutting machine, high frequency voltage is

applied across an electrode and a base metal only upon arc start to effect arc start in

contactless fashion According to the present invention there is provided an arc welding

machine and a plasma cutting machine each including a first power supply unit for

supplying power across an electrode and a base metal, and a second DC power supply unit

connected to a circuit fed by said first power supply unit to apply a high voltage across said

electrode and said base metal during starting of the arc, characterized in that said second DC

power supply unit is of the descending characteristic type and each of said machines

comprises means for applying the high voltage from said second DC power supply unit

across said electrode and said base metal during arc start and after generation of an arc

stopping the application of the high voltage from said second DC power supply unit to cause

said first power supply unit to feed power.



SRPEC [ME] Page 27

In this chapter, studying about project related literature reviews and patent search improve

skills about project. In next chapter methodology and work preparation for next procedure in

project.



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Chapter:-3 Methodology and work

preparation



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3.1 Methodology

Fig 3.1 Methodology

literature review

find out CNC plasma cutting machine

selaction of material & specification preparation

selaction of process parameter and DOE

experimental work and measurment

analysis

optimization

mathematical modelling

conformation test

Conclusion writting

report writting

End



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In methodology ,from the literature reviews find out CNC plasma cutting machine and then

prepare an experimental set up and done analysis on Hot Die Tool Steel(AISI H11 Alloy

Steel) material through ANOVA analysis and create mathematical modeling.

3.2 Work preparation

In work preparation, select Hot Die Tool Steel (H11 Alloy Steel) as an experimental

material because of its properties like longer life of machine and higher design accuracy and

its chemical composition and its applications which are listed below and Select dimension of

material.

3.2.1 Composition of AISI H11 steel

Table 3.1 Composition of AISI H11 steel

Element Weight %

C 0.33-0.43

Mn 0.20-0.50

Si 0.80-1.20

Cr 4.75-5.50

Ni < 0.3

Mo 1.10-1.60

V 0.3-0.6

Cu <0.25

P <0.03

S <0.03

3.2.2 Properties of H11

Machinability

The machinability rate of H11 tool steels is nearly 75% of that of the W group tool

steels.



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Forming

H11 tool steels are formed by using conventional methods, machining and forging.

Welding

H11 tool steels can be readily welded by conventional methods.

Heat Treatment

H11 tool steels are preheated to 816°C (1500°F). Then the steels are directly heated

by increasing the temperature to 1010°C (1850°F) followed by holding for 15 to 40

mins. The steels are then air-quenched.

Forging

H11 tool steels are forged at 1121°C (2050°F). For this type of steels, forging below

899°C (1650°F) is not preferable.

Cold Working

Cold working may be carried out on H11 tool steels using conventional methods.

Annealing

H11 tool steels are annealed at 871°C (1600°F) and slowly cooled at 4°C (40°F) in

the furnace.

Tempering

Tempering is carried out on H11 tool steels at temperature ranging from 538 to 649°C

(1000 to 1200°F) to obtain Rockwell C hardness of 54 to 38. Double tempering can

also be performed in these steels every one hour at the preferred tempering

temperature.



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3.2.3 Application of H11

hot-work forging

extrusion dies

helicopter rotor blades

For longer life of machine

To get higher design accuracy

3.2.4 Material dimension

Figure 3.2 Material dimension

Work piece Specification

Dimension : 300 mm*80 mm*25 mm

Quantity : 3 plates

In this chapter, complete methodology of this project will be planned and work preparation

will be done in which select hot die tool steel (AISI H11 Alloy Steel) material for

experimental result. For this material chemical composition, properties and application will

be described.



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Chapter:-4 Design of Experiments



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In this chapter design of experiment will be explained and generate orthogonal arrayL27

using taguchi method of DOE and also assign parameter. ANOVA analysis of variance and

various formulas for ANOVA will be explained.

4.1 Design of experiment

4.1.1 Introduction

DOE is an essential piece of the reliability program piece.it plays an important role in design

for reliability (DFR) programs, allowing the simultaneous investigation of the effects of

various factors and thereby designs optimization. This article introduces the concept of

DOE.

The objective of this research work is to study for Surface roughness and Arc gap, the

Design variables can be summarized as follows:

Table 4.1 DOE table

Parameters Level 1 Level 2 Level 3 DOF

Current flow

rate(A)

180 200 260 2

Cutting speed

(mm/min)

575 700 850 2

Arc gap (mm) 5 5.5 6 2

For conducting the experiments, it has been decided to follow the Taguchi method of

Experimental design and an appropriate orthogonal array is to be selected after taking into

consideration the above design variables. Out of the above listed design Variables, the

orthogonal array was to be selected for four design variables (namely Gas Pressure, Current,

Cutting Speed and Arc gap) which would constitute the L27 Orthogonal array.

The two most important outputs are Surface Roughness and Arc gap the same have been

selected as response parameters for this research work also. The effect of the variation in



SRPEC [ME] Page 35

input process parameter will be studied on these two response parameters and the

experimental data will be analyzed as per Taguchi method to find out the optimum

machining condition and percentage contribution of each factor.

4.1.2 Stages of DOE

Designed experiments are usually carried out in five stages planning, screening,

optimization, robustness testing and verification.

Planning

A few of the considerations to keep in mind at this stage are a through and precise objective

identifying the need to conduct the investigation, assessment of time and resources available

to achieve the objective and integration of prior knowledge to the experimentation

procedure. A team composed of individuals from different disciplines related to the product

or process should be used to identify possible factors to investigate and the most appropriate

response(s) to measure.

Screening

Screening experiments are used to identify the important factors that affect the process under

investigation out of the large pool of potential factors. These eliminate unimportant factors

and focus attention on the key factors that require further detailed analyses. Screening

experiments are usually efficient designs requiring few executions, where the focus is not on

interactions but on identifying the vital few factors.[8]

Optimization

After you identified the important variable by screening, you need to determine the best or

optimal value for these experimental factors. Optimal factor values depend on the process

objective. This objective may be to either increase yield or decrease variability or to find

settings that achieve both at same time.[8]



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Robustness testing

Once the optimal settings of the factors have been determined, it is important to make the

product or process insensitive to variations that are likely to be experienced in the

application environment.

These variables result from changes in factors that affect the process but are beyond the

control of the analyst.

It is important to identify such sources of variation and take measures to ensure that the

product or process is made insensitive (or robust) to these factors.[8]

Verification

This final stage involves validation of the best settings by conducting a few follow up

experimental runs to confirm that process functions as desired and all objectives are met.[8]

4.1.3 Different techniques of DOE

Factorial design

Factorial design allows simultaneously 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 the time and cost, and also allow for the study of

interaction between the factors.[10]

Response surface method

Response surface methods are used to examine the relationship between one or more

response variables and a set of quantitative experimental variables or factors. These methods

are often employed after you have identified the important controllable factors you want to

find factor setting that optimizes the response.[10]



SRPEC [ME] Page 37

Mixture experiments

Mixture experiments are special class of response surface experiment in which the product

under investigation is made up of several components or ingredients. Design for these

experiments is useful because many product design and development activities in industrial

situation involve formulation or mixtures. In this situation, the response is a function of the

properties of the different ingredients in the mixture.[10]

Taguchi design

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.[10]

4.1.4 Taguchi design of experiment

Dr. Genichi Taguchi is regarded as the foremost proponent of robust parameter Design, high

is an engineering method for product or process design that focuses on minimizing variation

and/or sensitivity to noise. When used properly, Taguchi Designs provide a powerful and

efficient method for designing products that operate consistently and optimally over a

variety of conditions.[10]

In robust parameter design, the primary goal is to find factor settings that minimize response

variation, while adjusting (or keeping) the process on target. After we determine which

factors affect variation, we can try to find settings for controllable factors that will either

reduce the variation, make the product insensitive to changes in uncontrollable (noise)

factors, or both. A process designed with this goal will produce more consistent output. A

product designed with this goal will deliver more consistent performance regardless of the

environment in which it is used.[10]



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Engineering knowledge should guide the selection of factors and responses. When

interactions among control factors are likely or not well understood, we should choose a

design that is capable of estimating those interactions. Minitab can help us to select a

Taguchi design that does not confound interactions of interest with each other or with main

effects.[10]

Noise factors for the outer array should also be carefully selected and may require

preliminary experimentation. The noise levels selected should reflect the range of conditions

under which the response variable should remain robust. Robust parameter design uses

Taguchi designs (orthogonal arrays), which allow us to analyze many factors with few runs.

Taguchi designs are balanced, that is, no factor is weighted more or less in an experiment,

thus allowing factors to be analyzed independently of each other Minitab provides both static

and dynamic response experiments.[10]

In a static response experiment, the quality characteristic of interest has a fixed level. In a

dynamic response experiment, the quality characteristic operates over a range of values and

the goal is to improve the relationship between an input signal and an output response.

An example of a dynamic response experiment is an automotive acceleration experiment

where the input signal is the amount of pressure on the gas pedal and the output response is

vehicle speed. We can create a dynamic response experiment by adding a signal factor to a

design − see Creating a dynamic response experiment. The goal of robust experimentation is

to find an optimal combination of control factor settings that achieve robustness against

(insensitivity to) noise factors. Minitab calculates response tables, linear model results, and

generates main effects and interaction plots for:

signal-to-noise ratios (S/N ratios, which provide a measure of robustness) vs. the control

factors

means (static design) or slopes (dynamic design) vs. the control factors

standard deviations vs. the control factors

natural log of the standard deviations vs. the control factors



SRPEC [ME] Page 39

Use the results and plots to determine what factors and interactions are important and

evaluate how they affect responses. To get a complete understanding of factor effects it is

advisable to evaluate S/N ratios, means (static design), slopes (dynamic design), and

standard deviations.[10]

4.1.4.1 What is taguchi design?

A Taguchi design, or an orthogonal array, is a method of designing experiments that usually

requires only a fraction of the full factorial combinations. An orthogonal array means the

design is balanced so that factor levels are weighted equally. Because of this, each factor can

be evaluated independently of all the other factors, so the effect of one factor does not

influence the estimation of another factor.[10]

In robust parameter design, we first choose control factors and their levels and choose an

orthogonal array appropriate for these control factors. The control factors comprise the inner

array. At the same time, we determine a set of noise factors, along with an experimental

design for this set of factors. The noise factors comprise the outer array.

The experiment is carried out by running the complete set of noise factor settings at each

combination of control factor settings (at each run). The response data from each run of the

noise factors in the outer array are usually aligned in a row, next to the factors settings for

that run of the control factors in the inner array.

Each column in the orthogonal array represents a specific factor with two or more levels.

Each row represents a run; the cell values indicate the factor settings for the run. By default,

Minitab's orthogonal array designs use the integers 1, 2, 3... To represent factor levels. If we

enter factor levels, the integers 1, 2, 3... Will be the coded levels for the design.[10]



SRPEC [ME] Page 40

4.2 Selection of orthogonal array and parameter assignment

In this experiment, there are 3 parameters at 3 levels each. The degree of freedom (DOF) of

a three level parameter is 2(Number of Levels minus 1), hence total DOF for the experiment

is 27 and generate L27 array for experimental setup By Full Factorial Method in MINITAB

15

Table 4.2 L27 array for experimental setup

EX. NO Current Flow (Amp.) Cutting Speed(mm/sec) Arc Gap(mm)

1 180 575 5

2 180 700 5.5

3 180 850 6

4 180 575 5.5

5 180 575 6

6 180 700 5

7 180 700 6

8 180 850 5

9 180 850 5.5

10 260 575 5

11 260 575 5.5

12 260 575 6

13 260 700 5

14 260 700 5.5

15 260 700 6

16 260 850 5

17 260 850 5.5

18 260 850 6

19 200 575 5

20 200 575 5.5

21 200 575 6

22 200 700 5

23 200 700 5.5

24 200 700 6

25 200 850 5

26 200 850 5.5

27 200 850 6



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4.3 ANOVA (Analysis of Variance)

The purpose of the statistical analysis of variance (ANOVA) is to investigate which design

parameter significantly affects the material removal rate and surface roughness. Based on

the ANOVA, the relative importance of the machining parameters with respect to material

removal rate and surface roughness is investigated to determine more accurately the

optimum combination of the machining parameters.

Two types of variations are present in experimental data:

Within treatment variability

Observation to observation variability

So ANOVA helps us to compare variability within experimental data. In my thesis ANOVA

table is made with help of MINITAB 16 software. When performance varies one determines

the average loss by statistically averaging the quadratic loss. The average loss is proportional

to the mean squared error of Y about its target T. The initial techniques of the analysis of

variance were developed by the statistician and geneticist R. A. Fisher in the 1920s and

1930s, and are sometimes known as Fisher's ANOVA or Fisher's analysis of variance, due to

the use of Fisher's Distribution as part of the test of statistical significance.[11]

4.4 Various formulas for ANOVA

4.4.1 Degree of freedom (DOF)

Indicates the number of independent elements in the sum of squares. The degrees of freedom

for each component of the model are:

DF (Factor) = r-1

DF (Error) = nT – r

Total = nT – 1



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Where, nT = the total number of observations and

r = the number of factor levels. [12]

4.4.2 Sum of squares (SS)

The sum of squared distances. SS Total is the total variation in the data. SS (Factor) is the

deviation of the estimated factor level mean around the overall mean. It is also known as the

sum of squares between treatments. SS Error is the deviation of an observation from its

corresponding factor level mean. It is also known as error within treatments. The

calculations are:

SS (Factor) = S ni (yi. - y..)2

SS Error = Si Sj (yij - yi. )2

SS Total = Si Sj (yij - y..)2

Where yi.= mean of the observations at the ith factor level,

y.. = mean of all observations and

yij = value of the jth observation at the ith factor level.[12]

4.4.3 Pure sum of square

SS’ (Factor) = SS (Factor) – DF (Factor) * MS (Error)

4.4.4 Mean Square (MS)

The calculations for the mean square for the factor and error are:

MS (Factor) = SS (Factor)/ DF (Factor)

MS (Error) = SS (Error)/ DF (Error)

F VALUE



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A test to determine whether the factor means are equal or not. The formula is:

F = MS (Factor)/ MS (Error)

The degrees of freedom for the numerator are r - 1 and for the denominator are nT - r. Larger

values of F support rejecting the null hypothesis that the means are equal.

In this chapter generate level table and orthogonal array for selected parameter for

experimental set up. in next chapter, taking experimental data of other related project for

case study to improve skills and knowledge of ANOVA analysis.



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Chapter:-5 Experimental Setup



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In this chapter, experiments are performed on hyperformance HPR260XD Plasma cutting

machine at AMMANN APOLLO, the specification and details of these machine illustrated

below and selection of nozzle will be done according to selected parameters and than

experiment data sheet is made.

5.1 Machine specification

HyPerformance HPR260XD

Figure 5.1 plasma cutting machine (HPR260XD)



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Figure 5.2 Machine Specification

Figure 5.3 Nozzle Selection



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Table 5.1 Fixed parameter

Fixed parameter Set value

material H11

Gas pressure 8 bar

Cutting Gas N2

Shielding gas Air

Table 5.2 Final measurement data sheet

.

EX.

NO

Current

Flow

(Amp.)

Cutting

Speed(mm/sec)

Arc

Gap(mm)

SR (µm) KW (mm)

A B C mean

SR A B C

mean

KW

1 180 575 5 2.09 2.39 2.55 2.34 3.26 3.24 3.27 3.26

2 180 700 5.5 2.67 2.12 2.25 2.35 3.24 3.50 3.30 3.35

3 180 850 6 2.27 2.72 1.56 2.18 3.42 3.50 3.42 3.45

4 180 575 5.5 1.57 2.09 2.02 1.89 3.37 3.36 3.13 3.29

5 180 575 6 1.56 1.67 1.55 1.59 3.70 3.78 3.68 3.72

6 180 700 5 1.67 1.78 2.12 1.86 3.45 3.39 3.46 3.43

7 180 700 6 1.35 1.27 1.55 1.39 3.67 3.84 3.63 3.71

8 180 850 5 1.19 1.73 1.98 1.63 3.46 3.45 3.19 3.37

9 180 850 5.5 1.35 1.03 1.00 1.13 3.31 3.31 3.37 3.33

10 260 575 5 1.38 2.16 2.33 1.96 4.35 4.35 4.24 4.31

11 260 575 5.5 1.68 1.99 1.79 1.82 4.43 4.53 4.57 4.51

12 260 575 6 1.48 2.43 2.74 2.22 4.70 4.68 4.68 4.69

13 260 700 5 2.25 1.60 1.46 1.77 4.29 4.48 4.57 4.45

14 260 700 5.5 1.45 1.28 1.27 1.33 4.69 4.41 4.48 4.53

15 260 700 6 2.14 1.26 1.59 1.66 4.25 4.68 4.70 4.54

16 260 850 5 2.29 2.20 2.45 2.31 4.38 4.37 4.28 4.34

17 260 850 5.5 2.12 2.36 2.45 2.31 4.26 4.48 4.26 4.33

18 260 850 6 2.49 2.98 2.73 2.73 4.50 4.48 4.36 4.45

19 200 575 5 2.81 2.73 2.12 2.55 4.02 4.48 4.53 4.34

20 200 575 5.5 1.24 2.01 2.74 2.00 4.39 4.48 4.33 4.40

21 200 575 6 2.10 1.24 2.04 1.79 4.26 4.20 4.19 4.22

22 200 700 5 2.05 1.86 1.24 1.72 4.10 4.52 4.22 4.28

23 200 700 5.5 1.56 1.98 1.18 1.57 4.39 4.55 4.29 4.41

24 200 700 6 1.27 1.14 1.33 1.25 4.35 4.25 4.13 4.24

25 200 850 5 2.48 1.36 1.24 1.69 4.20 4.25 4.48 4.31

26 200 850 5.5 1.18 1.12 1.14 1.15 4.77 4.48 4.53 4.59

27 200 850 6 1.48 1.66 1.24 1.46 4.72 4.92 4.82 4.82



SRPEC [ME] Page 48

Here, Total number of runs, n = 27

Total degree of freedom fT = n-1 = 26

three factors and their levels:

Current flow, A – A1, A2, A3

Cutting speed, B – B1, B2, B3

Arc gap, C – C1, C2, C3

Degree of freedom:

Factor A – Number of level of factors, fA= A - 1 = 2

Factor B – Number of level of factors, fB = B - 1 = 2

Factor C – Number of level of factors, fC = C - 1 = 2

For error, Fe = fT – fA – fB – fC

= 26 – 2 – 2 – 2

=20

This chapter put focus on the observations made during the experiments and corresponding

results obtained. In the next chapter the analysis of result obtained with ANOVA analysis.



SRPEC [ME] Page 49

Chapter:-6 ANOVA Analysis



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In this chapter ANOVA analysis carried out based on experimental data sheet and total

percentage contribution of factors to the response parameter are calculated according to

math model and compared with software analysis.

6.1 Analysis of variance for H11:

6.1.1 Response 1: Surface Roughness (Reference: table 5.2)

T = Totals of all results of surface roughness = 49.663333

Correction factor C.F. = (T2 / n) = (49.663333)2 27 = 91.349877

Total sum of squares, 2 .

1

nS y C FT i

i

= 96.1081– 91.349877

= 4.7582008

1. THE TOTAL CONTRIBUTION OF EACH FACTOR LEVEL

A1 = 2.3433+2.3467+2.1833+1.8933+1.5933+1.8567+1.3900+1.6333+1.1267

= 16.36666 (All SR reading total at 180Amp.)

A2 = 1.9567+1.8200+2.2167+1.7700+1.3333+1.6633+2.3133+2.3100+2.7333

= 18.116667 (All SR reading total at 260 Amp.)

A3 = 2.5533+1.9967+1.7933+1.7167+1.5733+1.2467+1.6933+1.1467+1.4600

= 15.18 (All SR reading total at 200 Amp.)



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B1 = 2.3433+1.8933+1.5933+1.9567+1.8200+2.2167+2.5533+1.9967+1.7933

= 19.21 (All SR reading total at 575 mm/s)

B2 = 2.3467+1.8567+1.3900+1.7700+1.3333+1.6633+1.7167+1.5733+1.2467


B3 = 2.1833+1.6633+1.1267+2.3133+2.3100+2.7333+1.6933+1.1467+1.4600


C1 = 2.3433+1.8567+1.6333+1.9567+1.7700+2.3133+2.5533+1.7167+1.6933

= 18.766667 (All SR reading total at 5 mm)

C2 = 2.3467+1.8933+1.1267+1.8200+1.3333+2.3100+1.9967+1.5733+1.1467

= 15.636667 (All SR reading total at 5.5 mm)

C3 = 2.1833+1.5933+1.3900+2.2167+1.6633+2.7333+1.7933+1.2467+1.4600

= 15.26 (All SR reading total at 6 mm)

2. FACTOR SUM OF SQUARES

𝑆𝐴 = (𝐴1²

𝑁𝐴1+

𝐴2²

𝑁𝐴2+

𝐴3²

𝑁𝐴3) − 𝐶. 𝐹

= 0.48499

𝑆𝐵 = (𝐵1²

𝑁𝐵1+

𝐵2²

𝑁𝐵2+

𝐵3²

𝑁𝐵3) − 𝐶. 𝐹

= 1.25008



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𝑆𝐶 = (𝐶1²

𝑁𝐶1+

𝐶2²

𝑁𝐶2+

𝐶3²

𝑁𝐶3) − 𝐶. 𝐹

= 0.82354

𝑆𝑂 = 𝑆𝑇 − (𝑆𝐴 + 𝑆𝐵 + 𝑆𝐶)

= 4.7582008 – (0.48499 + 1.25008 + 0.82354)

=2.1995

3. MEAN SQUARE (VARIANCE)

0.484990.24249

2

AA

A

SV

f

1.250080.62504

2

BB

B

SV

f

0.823540.41177

2

CC

C

SV

f

2.199590.15711

14

OO

O

SV

f

4. VARIANCE RATIO

0.411772.62083

0.15711

CC

O

VF

V

0.625043.97828

0.15711

BB

O

VF

V



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0.157111

0.15711

OO

O

VF

V

5. PERCENTAGE CONTRIBUTION

0.484990.10193 10.19%

4.7582008

AA

T

SP

S

1.250080.26272 26.27%

4.7582008

BB

T

SP

S

0.823540.1731 17.31%

4.7582008

CC

T

SP

S

2.199590.46227 46.23%

4.7582008

OO

T

SP

S

Above analysis shows the percentage contribution of individual parameters on SR.The

percentage contribution of current flow 10.19%, cutting speed is 26.27%, arc

gap is 17.31%, Parametric analysis is carried out for the quality of the sample. i.e. SR

Thisparametric analysis (ANOVA) shows the percentage contribution of parameters indivi

dualy shown in table :

Table 6.1 Percentage contribution of process parameter for Surface Roughness

Source Of

Variation

D.O.F

Sum

Of Squares

Percentage

Contribution

(P)%

Factor A 2 0.4850 10.19%

Factor B 2 0.5944 26.27%

Factor C 2 0.3039 17.31%

Error O 20 3.3749 46.23%

Total 26 4.7582 100%



SRPEC [ME] Page 54

The calculated value in table 6.1 is also found out with the use of our developed software

ANOVA analyzer, so by using this software; the value is as same as calculated value as

shown in figure 6.1



SRPEC [ME] Page 55

Figure 6.1 Print screen of ANOVA analyzer software for Surface Roughness



SRPEC [ME] Page 56

6.1.2 Response 2: KW (reference: table 4.1)

T = Totals of all results of KW = 110.66667

Correction factor C.F. = (T2 / n) = (110.66667)2 27 = 453.59671

Total sum of squares, 2 .

1T

nS y C F

ii

= 460.241 – 453.59671

= 6.6442033

1. THE TOTAL CONTRIBUTION OF EACH FACTOR LEVEL

A1 = 3.2567+3.3467+3.4467+3.2867+3.7200+3.4333+3.7133+3.3667+3.3300

= 30.9 (All KW reading total at 180 Amp.)

A2 = 4.3133+4.5100+4.6867+4.4467+4.5267+4.5433+4.3433+4.3333+4.4467


A3 = 4.3433+4.4000+4.2167+4.2800+4.4100+4.2433+4.3100+4.5933+4.8200


B1 = 3.2567+3.2867+3.7200+4.3133+4.5100+4.6867+4.3433+4.4000+4.2167

= 36.52 (All KW reading total at 575 mm/s)

B2 = 3.3467+3.4333+3.7133+4.4467+4.5267+4.5433+4.2800+4.4100+4.2433

= 36.89(All KW reading total at 700 mm/s)



SRPEC [ME] Page 57

B3 = 3.4467+3.3667+3.3300+3.3433+3.3333+3.4467+4.3100+4.5933+4.8200

= 37.256667(All KW reading total at 850 mm/s)

C1 = 3.2567+3.4333+3.3667+4.3133+4.4467+4.3433+4.3433+4.2800+4.3100

= 36.106667(All KW reading total at 5 mm)

C2 = 3.3467+3.2867+3.3300+4.5100+4.5267+4.3333+4.4000+4.4100+4.5933

= 37.673333(All KW reading total at 5.5 mm)

C3 = 3.4467+3.7200+3.7133+4.6867+4.5433+4.4467+4.2167+4.2433+4.8200

= 36.886667 (All KW reading total at 6 mm)

2. FACTOR SUM OF SQUARES

22 2

31 2

1 2 3

.A

A A A

AA AS C F

N N N

5.99360

22 2

31 2

1 2 3

.B

A A A

BB BS C F

N N N

0.03015

22 2

31 2

1 2 3

.C

A A A

CC CS C F

N N N

0.13636

S O S T ( S A S B S C )

S O = 6.6442033 - (5.99360 + 0.03015 + 0.13636)

= 0.48409



SRPEC [ME] Page 58

3. MEAN SQUARE (VARIANCE)

5.993602.99680

2

AA

A

SV

f

0.030150.01507

2

BB

B

SV

f

0.136360.06818

2

CC

C

SV

f

0.484090.03458

14

OO

O

SV

f

4. VARIANCE RATIO

2.9968086.66736

0.03458

AA

O

VF

V

0.015070.43595

0.03458

BB

O

VF

V

0.068181.97175

0.03458

CC

O

VF

V

0.034581

0.03458

OO

O

VF

V



SRPEC [ME] Page 59

5. PERCENTAGE CONTRIBUTION

5.993600.90208 90.21%

6.6442033

AA

T

SP

S

0.030150.00454 0.45%

6.6442033

BB

T

SP

S

0.136360.02052 2.05%

6.6442033

CC

T

SP

S

0.484090.07286 7.29%

6.6442033

OO

T

SP

S

Above analysis shows the percentage contribution of individual parameters on KW. The

percentage contribution of Current flow is 90.21%, cutting speed is 0.45%, and arc gap is

2.05%. Parametric analysis is carried out for the quality of the sample. i.e. KW. This

parametric analysis (ANOVA) shows the percentage contribution of parameters individually

as shown in table 6.2.

Table 6.2 Percentage Contribution of Process Parameter for Kw

Source Of

Variation

D.O.F

Sum

Of Squares

Percentage

Contribution (P)

Factor A 2 5.9936 90.21%

Factor B 2 0.0042 0.45%

Factor C 2 0.1727 2.05%

Error 20 0.4738 7.29%

Total 26 6.6442 100.00%

The calculated value in table 6.2 is also found out with the use of our developed software

ANOVA analyzer, so by using this software; the value is as same as calculated value as

shown in figure 6.2.



SRPEC [ME] Page 60

Figure 6.2 Print screen of ANOVA analyzer software for Kerf Width



SRPEC [ME] Page 61

6.2 Data Calculation with Minitab15

In this project ,manual calculation are compare with minitab15 data and both are same.

6.2.1 Factorial Analysis: SR versus A, B, C:-

Table 6.3 Delta Rank Of SR

LEVEL CF CS AG

1 -5.04337 -6.15183 -5.97887

2 -6.00002 -4.32676 -4.54613

3 -4.48415 -5.04895 -5.00254

Delta -1.51588 -1.82507 -0.45641

Rank 2 3 1

If value of Delta rank is higher than the percentage contribution of this factor will be more

and effect to response parameter will be higher than other factor. So analyses that Arc Gap

will more effect on Surface Roughness.

Table 6.4 Percentage Contribution of Process Parameter for SR

Source Of

Variation

D.O.F

Sum

Of Squares

Percentage

Contribution

(P)%

Factor A 2 0.4850 10.19%

Factor B 2 0.5944 26.27%

Factor C 2 0.3039 17.31%

Error O 20 3.3749 46.23%

Total 26 4.7582 100%

R-sq = 29.07 %

In above analysis error find to be more so to reduce error interaction of input parameter will

be taken and same analysis will be done again.



SRPEC [ME] Page 62

Table 6.5 General Linear Model: SR versus Interaction of current flow, cutting speed,

arc gap

Source Df Seq SS Percentage contribution

current flow 2 0.48499 10.20%

cutting speed 2 0.59440 12.50%

arc gap 2 0.30389 06.40%

current flow*cutting speed 4 1.49799 31.50%

current flow*arc gap 4 0.41038 08.60%

cutting speed*arc gap 4 0.78046 16.40%

Error 8 0.68580

Total 26 4.75820

R-sq = 85.89%

Table 6.5 indicates the percentage contribution of input parameters and its interaction to SR

and Model error will be minimized and R-sq. value will be increased.

Graph 6.1 Main plot for Means for SR



SRPEC [ME] Page 63

In Graph 6.1 shows effect of different factor on the Surface roughness ,if increasing value of

current flow than value of SR will be decrease and suddenly increasing, by increasing value

of cutting speed than SR will be little decrease and then increase , by increasing value of arc

gap than value SR will decrease and then increase.

6.2.2 Factorial Analysis: KW versus A, B, C:-

Table 6.6 Delta Rank Of KW

LEVEL CF CS AG

1 -10.7071 -12.1493 -12.0039

2 -12.9883 -12.2147 -12.1372

3 -12.8692 -12.2007 -12.4235

Delta -0.11909 0.065389 -0.28622

Rank 2 1 3

If value of Delta rank is higher than the percentage contribution of this factor will be more

and effect to response parameter will be higher than other factor. So analyses Cutting Speed

will more effect on Kerf Width.

Table 6.7 Percentage Contribution of Process Parameter For KW

Source Of

Variation

D.O.F

Sum

Of Squares

Percentage

Contribution (P)

Factor A 2 5.9936 90.20%

Factor B 2 0.0042 00.26%

Factor C 2 0.1727 02.59%

Error 20 0.4738 07.12%

Total 26 6.6442

R-sq= 92.87%

In above analysis error find to be more so to reduce error interaction of input parameter will

be taken and same analysis will be done again.



SRPEC [ME] Page 64

Table 6.8 General Linear Model: KW versus Interaction of current flow, cutting speed,

arc gap

Source Df Seq SS Percentage contribution

current flow 2 5.99630 90.20%

cutting speed 2 0.00415 00.06%

arc gap 2 0.17271 02.60%

current flow*cutting speed 4 0.18491 02.78%

current flow*arc gap 4 0.09141 01.37%

cutting speed*arc gap 4 0.01501 00.22%

Error 8 0.18242 2.75%

Total 26 6.64420

R-sq= 97.25 %

Table 6.8 indicates that the percentage contribution of input parameters and its interaction to

KW and model error will be minimized and R-sq value will be increased.



SRPEC [ME] Page 65

Graph 6.2 Main plot for Means for KW

In Graph 6.2 shows effect of different factor on the kerf width ,if increasing value of current

flow than value of KW will be increasing, by increasing value of cutting speed than no

larger change found in the value of KW, by increasing value of arc gap than value KW will

increasing.

In this chapter, studied about ANOVA analysis for above case and analyzed that error in

above study is more. So in this project, trying to improve accuracy of analysis and minimize

error as possible.



SRPEC [ME] Page 66

6.3 Mathematical modeling

6.3.1 Introduction to regression analysis

The term multiple regression literally means stepping back toward the average. It was use by

British mathematician Sir Francis Galton .Regression analysis is a mathematical measure of

the average relationship between two or more variables in terms of the original units of the

data. In regression analysis there are two types of variables. The value whose value is

influenced or is to be predicted is called dependent variable and the variable which

influences the values or is to be used for prediction is called independent variable.

Regression analysis can be done in two ways;

Bivariate regression

Multiple regression

6.3.2 Bivariate regression:

Two variables X and Y may be related to each other or inexactly. In physical sciences,

variables frequently have an exact relationship to each other. The simplest relationship can

be expressed by

Y=a+bX

Where the values of the coefficient, a and b, determine respectively the precise height and

steepness of the line. Thus coefficient a represent to as the intercept or constant, and

coefficient b referred to as the slope.

In contrast, relationship between variables in social sciences is almost always inexact.

The equation for a linear relationship between two social science variables would be written

as:

Y = a+bX+e



SRPEC [ME] Page 67

Where e represents the presence of error

6.3.3 The least squares principle

In postulating relationship among social science variables, we commonly assume linearity.

Of course this assumption is not always correct. Least square principle tells us or identified

best line which can fit the model for example. The question arises out of all possible line we

should choose. From the scatter plot we will calculated prediction error is calculated as:

Prediction error = observed error - predicted

Summing the prediction error for all observation would yield a total prediction error (TPE).

2

( )( )

( )

t t

t

x x y yb

x x

a Y bX

These values of a and b are our least square estimates. As we know Multiple Regression

Analysis is use when more than two parameters are used .in my thesis there are 4 parameters

so I will consider multiple regression analysis. In multiple regressions analysis linear

equation is given by:

1 2 3....y a bx cx NX

Where b, c etc. are called partial slope .Some terms which are considered in multiple

regressions are discussed below:



SRPEC [ME] Page 68

6.3.4 Residual

The difference between an observed value (y) and its corresponding fitted value (ŷ) is called

residual. Residual values are especially useful in regression and ANOVA procedures

because they indicate the extent to which a model accounts for the variation in the observed

data.

6.3.5 Sampling error

When estimating a population parameter from a sample it is important not only to derive a

specific value but also estimate the effect of the sampling error on the estimate. To

accomplish this it is necessary to consider the concept of a sampling distribution for a

regression coefficient.

This could be easily understood as the distribution of estimates of the regression coefficient

that would be result if sample of given size were drawn repeatedly from the population and

coefficient calculated from each sample .Because coefficient estimated from random

samples will deviate from populations values by varying amounts, the estimates , the

estimates of the coefficient from a series of random samples of population will not be

identical but instead will distribute themselves around a mean. the estimated standard

deviation of the sampling distribution of a regression coefficients is known as a standard

error and is denoted by ‘s’.

6.3.6 Coefficient of determination R2

This is called coefficient of determination indicates explanatory power of any regression

model. Its value lies between +1 and 0. It can also been shown that R –sq is the correlation

between actual and predicted value. It will reach maximum value when dependent variable

is perfectly predicted by regression equation.



SRPEC [ME] Page 69

6.3.7 Multicollinearity

Multicollinearity means that none of that independent variable or linear variable is perfectly

correlated with another independent variable or linear combination of other independent

variable .In multiple regression if there is linearity among variables, then regression surface

not even define (because in multiple regression instead of two plane we will consider

multiple plain) as there are infinite number of surface that fit the observation equally well

and therefore it is impossible to drive unique estimates of the intercepts and partial slope

coefficient for the regression.

6.4 First order linear model for SR

With the help of Minitab 15 Software, developed first order linear model and ANOVA

Table.

The regression equation is

SR = 2.53 + 0.00312 current flow(A) - 0.000571 cutting speed(mm/s)- 0.173 arc gap(mm)

R-Sq = 11.6%

Table 6.9 Analysis of variance for SR

exp.

No

current

flow

cutting

speed

arc

gap SR

predicted

SR

1 180 575 5 2.3433 1.898275

2 180 700 5.5 2.3467 1.7404

3 180 850 6 2.1833 1.56825

4 180 575 5.5 1.8933 1.811775

5 180 575 6 1.5933 1.725275

6 180 700 5 1.8567 1.8269

7 180 700 6 1.3900 1.6539

8 180 850 5 1.6333 1.74125

9 180 850 5.5 1.1267 1.65475

10 260 575 5 1.9567 2.147875

11 260 575 5.5 1.8200 2.061375



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12 260 575 6 2.2167 1.974875

13 260 700 5 1.7700 2.0765

14 260 700 5.5 1.3333 1.99

15 260 700 6 1.6633 1.9035

16 260 850 5 2.3133 1.99085

17 260 850 5.5 2.3100 1.90435

18 260 850 6 2.7333 1.81785

19 200 575 5 2.5533 1.960675

20 200 575 5.5 1.9967 1.874175

21 200 575 6 1.7933 1.787675

22 200 700 5 1.7167 1.8893

23 200 700 5.5 1.5733 1.8028

24 200 700 6 1.2467 1.7163

25 200 850 5 1.6933 1.80365

26 200 850 5.5 1.1467 1.71715

27 200 850 6 1.4600 1.63065

Graph 6.3 Variance of predicted SR and Actual SR

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

3.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

interaction of SR and predicted SR

SR predicted SR



SRPEC [ME] Page 71

Model Adequacy Check: The coefficient of determination (R-Sq) which indicates the

goodness of fit for the model so the value of R-Sq = 11.6% which indicate the less

significance of the model.

6.5 First order linear model for KW

With the help of Minitab 15 Software, I developed first order linear model and ANOVA

Table.

The regression equation is

KW = 0.80 + 0.0101 current flow(A) + 0.000101 cutting speed(mm/s) + 0.194 arc gap(mm)

R-Sq = 50.6%

Table 6.10 Analysis of variance for KW

exp.

No

current

flow

cutting

speed

arc

gap KW

predicted

KW

1 180 575 5 3.2567 3.646075

2 180 700 5.5 3.3467 3.7557

3 180 850 6 3.4467 3.86785

4 180 575 5.5 3.2867 3.743075

5 180 575 6 3.7200 3.840075

6 180 700 5 3.4333 3.6587

7 180 700 6 3.7133 3.8527

8 180 850 5 3.3667 3.67385

9 180 850 5.5 3.3300 3.77085

10 260 575 5 4.3133 4.454075

11 260 575 5.5 4.5100 4.551075

12 260 575 6 4.6867 4.648075

13 260 700 5 4.4467 4.4667

14 260 700 5.5 4.5267 4.5637

15 260 700 6 4.5433 4.6607

16 260 850 5 4.3433 4.48185

17 260 850 5.5 4.3333 4.57885

18 260 850 6 4.4467 4.67585



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19 200 575 5 4.3433 3.848075

20 200 575 5.5 4.4000 3.945075

21 200 575 6 4.2167 4.042075

22 200 700 5 4.2800 3.8607

23 200 700 5.5 4.4100 3.9577

24 200 700 6 4.2433 4.0547

25 200 850 5 4.3100 3.87585

26 200 850 5.5 4.5933 3.97285

27 200 850 6 4.8200 4.06985

Graph 6.4 Variance of predicted KW and Actual KW

Model Adequacy Check: The coefficient of determination (R-Sq) which indicates the

goodness of fit for the model so the value of R-Sq =50.6% which indicate the less

significance of the model.

0.0000

1.0000

2.0000

3.0000

4.0000

5.0000

6.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

interaction of KW and predicted KW

KW predicted KW



SRPEC [ME] Page 73

In this chapter based on ANOVA analysis the percentage contribution is generated and it

shows the effect of input parameters on plasma arc cutting machine then creating a excel

based software for percentage contribution and compare with analysis, generate regression

equation and based on these find predicted values.



SRPEC [ME] Page 74

Chapter:-7 Optimization



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In this chapter optimization will be done with grey relational analysis method and taguchi

method will be used.

7.1 Grey Relational Analysis Method

The integrated Grey based Taguchi method combines the algorithm of Taguchi method and

grey relational analysis to determine the optimum process parameters with multiple

performance characteristics.

7.1.1Taguchi method

The significance of the Taguchi method is to Find controllable factors and levels during

product design or process improvement Acquire the best factor level combination through

orthogonal array design and Reduce quality loss and costs.

The concept of the Taguchi method is that the parameter design is performed to reduce the

sources of variation on the quality [22,23]. Taguchi recommends the use of the loss function

to measure the performance characteristic deviating from the desired value. This is further

converted to S/N ratio.

The loss function Lij for higher the better

2

1

11/

n

ij ijkL Y k

n

n - number of repetition; K – number of tests; Yijk – experimental value of the ith

performance in the jth experiment at the kth tests.

1

1²

n

ij ijkL Y k

n

The S/N ratio for both LB and HB is given by

log( )ij ijL



SRPEC [ME] Page 76

The S/N ratio value can be considered for the optimization of single response problems.

However, optimization of multiple performance characteristics it cannot be used straight

away as in the case of single performance[24].The normalization of S/N values can be done

by the following equation

1

ij

n

iji

NSN

In the grey relational analysis, experimental results (CVm%, tenacity and number of hair per

meter) were first normalized and then the grey relational coefficient was calculated from the

normalized experimental data to express the relationship between the desired and actual

experimental data. Then, the grey relational grade was computed by averaging the grey

relational coefficient corresponding to each process response (3 responses). The overall

evaluation of the multiple process responses is based on the grey relational grade.

As a result, optimization of the complicated multiple process responses can be converted

into optimization of a single grey relational grade. In other words, the grey relational grade

can be treated as the overall evaluation of experimental data for the multi response process.

Optimization of a factor is the level with the highest grey relational grade.

Data Pre-Processing is normally required, since the range and unit in one data sequence may

differ from others. It is also necessary when the sequence scatter range is too large, or when

the directions of the target in the sequences are different.[21]

In the study, a linear data preprocessing method for the yarn tenacity is the higher-the-better

and is expressed as:

( ) min ( )( )

max ( ) min ( )

i ii

i i

y k y Kx k

y k y k



SRPEC [ME] Page 77

Yarn unevenness indexes (CVm%) and hair number of yarn per meter, which are the lower-

the-better can be expressed as:

( ) min ( )( )

max ( ) min ( )

i ii

i i

y k y Kx k

y k y k

where xi (k) is the value after the grey relational generation, min yi (k) is the smallest value

of yi (k) for the k th response, and max yi(k) is the largest value of yi(k) for the kth response.

An ideal sequence is x 0(k) (k=1, 2, 3) for three responses. The definition of the grey

relational grade in the grey relational analysis is to show the relational degree between the

twenty-seven sequences (x0(k) and xi(k), i=1, 2, . . . , 27; k=1, 2, 3). The grey relational

coefficient ξi(k) can be calculated as:

min max( )

( ) maxi

i

ko k

Where ( ) ( ) ( )oi k Xo k Xi k is the difference of absolute value between x0(k) and

xi(k); ϛ = distinguishing coefficient (0_1); ∆min, smallest value of ∆0i; and ∆max, largest value

of ∆0i.. After averaging the grey relational coefficients, the grey relational grade Ύi can be

obtained as:

1

1( ) ( )

n

i ikk k

n

where n is the number of process responses. The higher value of the grey relational grade

represents the stronger relational degree between the reference sequence x0(k) and the given

sequence xi(k). As mentioned before, the reference sequence x0(k) is the best process

response in the experimental layout. The higher value of the grey relational grade means that

the corresponding cutting parameter is closer to optimal.[21] In other words, optimization of

the complicated multiple process responses is converted into optimization of a single grey

relational grade.[20]



SRPEC [ME] Page 78

Figure. 7.1 Print Screen of Grey relational coefficient for SR



SRPEC [ME] Page 79

Figure. 7.2 Print Screen of Delta rank of GRC (SR)



SRPEC [ME] Page 80

Figure. 7.3 Print Screen of Grey relational coefficient for KW



SRPEC [ME] Page 81

Figure. 7.4 Print Screen of Delta rank of GRC (KW)



SRPEC [ME] Page 82

Figure 7.5 Print Screen of Grey relational Grade (GRG)



SRPEC [ME] Page 83

Graph 7.1 Grey relational grade plot

Graph 7.1 indicates the GRG values according to Experiment no. which optimized by Grey

Relational Method to decide the optimum parameter, Higher value of GRG will give

optimum parametric setting for experiment



SRPEC [ME] Page 84

Figure 7.6 Print Screen of Parametric optimization



SRPEC [ME] Page 85

7.1.2 RESULTS AND DISCUSSIONS

Table 7.1 Optimum Parametric Combination for PAC of H11

Table 7.1 shows the optimum parametric setting for PAC of H11 material.This analysis is

based on combining the data associated with each level for each factor. The difference in the

average results for the highest and lowest average response is the measure of the effect of

that factor. The greatest value of GRG is related to the largest effects of that particular

factors. Data preprocessing of each performance characteristic and the experimental results

for the grey relational according to formulas of Grey Relational Optimization with Taguchi

Design.

In this chapter Grey Relational Analysis method used to find Optimum Parametric setting

for PAC of H11. GRC and GRG value of experiment will find and its higher value of GRG

value shows the optimum Setting ,on the based summery of all above chaper conclusion will

given below.

Current flow(Amp)

Cutting speed(mm/s)

Arc gap

(mm)

Surface roughness(µm)

Kerf width (mm)

180 850 5.5 1.12667 3.33



SRPEC [ME] Page 86

Conclusion

ANOVA analysis carried out based on experimental data sheet and total percentage

contribution of factors to the response parameter are calculated according to math

model and compared with software analysis,

the percentage contribution of current flow 10.19%, cutting speed is 26.27%, arc gap

is 17.31% affects on SR.The percentage contribution of Current flow is 90.21%,

cutting speed is 0.45%, and arc gap is 2.05% affects on KW

value of Delta rank is higher than the percentage contribution of this factor will be

more and effect to response parameter will be higher than other factor. So analyses

that Arc Gap will more effect on Surface Roughness.

value of Delta rank is higher than the percentage contribution of this factor will be

more and effect to response parameter will be higher than other factor. So analyses

Cutting Speed will more effect on Kerf Width.

In above analysis error find to be more so to reduce error, interaction of input

parameter will be taken and same analysis will be done again its shows that the

percentage contribution of input parameters and its interaction to SR and Model error

will be minimized and R-sq. value will be increased upto 85.89%.

Analysis for KW its indicates that the percentage contribution of input parameters

and its interaction to KW and model error will be minimized and R-sq value will be

increased 97.25 %.

Main effect Plots of different factor on the Surface roughness ,if increasing value of

current flow than value of SR will be decrease and suddenly increasing, by

increasing value of cutting speed than SR will be little decrease and then increase ,

by increasing value of arc gap than value SR will decrease and then increase.

Main effect Plots of different factor on the kerf width ,if increasing value of current

flow than value of KW will be increasing, by increasing value of cutting speed than

no larger change found in the value of KW, by increasing value of arc gap than value

KW will increasing.



SRPEC [ME] Page 87

Grey Relational Analysis method used to find Optimum Parametric setting for PAC

of H11. GRC and GRG value of experiment will find and its higher value of GRG

shows that the optimum Setting will be the exp. no-9 and its parametric setting will

be listed below:

Current flow(Amp)

Cutting speed(mm/s)

Arc gap

(mm)

Surface roughness(µm)

Kerf width (mm)

180 850 5.5 1.12667 3.33



SRPEC [ME] Page 88

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ANALYSIS AND PARAMETRIC OPTIMIZATION OF PAC WITH