this pdf explains how we can optimise the machining parameters by using different optimising tools.

1. 1
VIKRAM SARABHAI SPACE CENTRE (VSSC)
PROFILE
VSSC is the lead centre for development of satellite launch vehicles and
associated technologies. The centre pursues active research and development in a host
of distinct technology domains like aeronautic, avionics, composites etc… with a view
to achieve self-reliance in the high tech realm of launch vehicle technology.
VSSC has its origin in the Thumba Equatorial Rocket Launching Station
(TERLS). TERLS became operational on November 21, 1963 with the successful
launching of a two-stage sounding rocket, ‘Nike-Apache’. After the death of
Dr Vikram Sarabhai, on December 30, 1971, the whole complex at
Thiruvananthapuram was renamed as “Vikram Sarabhai Space Centre”.
Major programmes of VSSC include Polar Satellite Launch Vehicle (PSLV),
Geosynchronous Satellite Launch Vehicle (GSLV), Rohini Sounding Rocket, Space
Capsule Recovery Experiment, Reusable Launch Vehicles and Air Breathing
Propulsion.
VSSC made significant contribution to India’s maiden mission to the Moon.
Chandrayaan-1. VSSC R&D efforts have included solid propellant formulations.
Another focus area has been navigation systems, the ISRO Inertial Systems Unit (IISU)
established at Vattiyoorkavu is a part of VSSC. VSSC involved in the development of
air-breathing vehicles. A reusable launch vehicle technology demonstrator is under
development, which will be tested soon.

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CHAPTER 1
INTRODUCTION
INCONEL 625 is a nickel based super alloy which is widely used in aerospace
industry. Inconel 625 is a nickel chromium molybdenum solid solution strengthened,
high strength alloy, which retains strength at high temperatures. It is used from
cryogenic temperatures to 980°C. Fatigue strength is outstanding, particularly as the
bellows grade, Inconel 625 LCF, where carbon, silicon and nitrogen are controlled to
low levels. The alloys have good oxidation resistance and resist corrosion in any
corrosive media. When exposed to high temperature for long periods, Inconel 625 will
age hardened due to the niobium, titanium and aluminium additions. When aged there is
an increase in strength and some loss of ductility and toughness. These materials are
referred to as “difficult to machine” since they possess rapid work hardening during
machining which will reduce further metal cutting. Machining of these materials in the
optimum range is required so as to have maximum material removal rate at minimum
surface roughness.
At present ISRO is diversifying its research activities and re-usable launch
vehicle technology is one of them. This diversification equally effects in product
realisation also which demands for realisation of products in super alloy materials like
INCONEL 625. The project is on the theme on optimisation of machining parameters
on Inconel component by addressing the machining difficulties discussed above. For
this attempt Taguchi method, grey relational analysis are used for better result. Hence a
set of optimised parameters is aimed to obtain for immediate application in the
component for better result.

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CHAPTER 2
LITERATURE SURVEY
Lalit Kumar, R Venkataramani, M.Sundararaman, P. Mukhopadhyay and
S.P.Garg [1] investigated the oxidation behaviour of Inconel 625 in 2000 during the
early stages been studied at oxygen pressure of 0.12kPa and 101.3kPa in the
temperature range of 1323K to 1523K by using TGA and between 873 and 1523K by
using XPS,AES and EDS. The results of XPS and AES analysis suggested that two
distinctly different oxidation mechanisms operate, depending on the temperature of
oxidisation.
Kamran Mumtaz, Neil Hopkinson [2] investigated about the top surface and side
roughness of Inconel 625 in 2000 parts processed using selective laser melting and
showed that higher peak powers tended to reduce top surface roughness and reduce side
roughness as recoil pressures flatten out the melt pool and reduce balling formation by
increasing wettability of the melt.
Chen Hong, Donghua Dai, Moritz Alkhayat [3] conducted the study on High-
temperature oxidation performance and its mechanism of TiC/Inconel 625 composites
in 2001 prepared by laser metal deposition additive manufacturing and revealed that
The incorporation of TiC reinforcement in Inconel 625 matrix improved the oxidation
resistance of the LMD-processed parts. For the LMD-processed TiC/Inconel 625
composites, the oxidized layers on the surface were composed of Cr2O 3 and TiO2.
T.E. Abioye, J. Folkes, A.T. Clare [4] Conducted a parametric study of Inconel 625
wire laser deposition in 2003 and found out that Energy per unit length of track and
wire deposition volume per unit length of track significantly influence both the
deposition process characteristics and the track geometrical characteristics. Excessively
low and high wire deposition volume per unit of track for a given energy per unit length
of track resulted in wire dripping and wire stubbing respectively.
Taiwo Ebenezer Abioye [5] conducted an experiment on Laser Deposition of Inconel
625/Tungsten Carbide Composite Coatings by Powder and Wire Feedstock in 2005 and
revealed the fact that the life span of stainless steel components can be extended in
chloride ion rich corrosive environment (e.g. oil and gas environments) by coating them

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with Inconel 625 laser coatings. However, using Inconel 625 wire coatings is more
advantageous because of better process economy and improved corrosion resistance.
Rodge M.K, Sarpate S.S, Sharma S.B [6] investigated on process response and
parameters in wire electrical discharge machining of Inconel 625 in 2007 and concluded
that pulse-on time has the highest rank ‘1’. Therefore, it has the most significant effect
on kerf width. As pulse-on time increase the kerf width increases significantly.
Guru Prasad Dinda, Ashish Dasgupta, Jyoti Mazunder [7] investigated about
Microstructural studies on Inconel 625 components fabricated by laser aid metal
deposition in 2008 and concluded that a variety of different phases can be produced in
Inconel 625 during solidification and during thermal processing.
Abhishek Jivrag, Shashikant Pople [8] studied Erosion Wear Behaviour of Inconel
625 Plasma Transferred Arc Weld (PTAW) Deposits using Air Jet Erosion Tester in
2008 and revealed that the wear rate is maximum at 30°, sharply decreases at 60° and is
minimum at 90°. Thus rate of wear goes on decreasing from 30° to 90°. This provides
the evidence that Inconel 625 despite having hardness value around 350 VHN follows
the wear trend of ductile material and not of hard material as expected from its hardness
value.
E.Pavithran, V.S.Senthil Kumar [9] conducted experimental investigation and
performance evaluation of hydro formed tubular bellows in Inconel 625 alloy in 2010
and summarized that the Inconel 625 bellows exhibits better performance as a material
that can be suitable to construct the bellows.

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CHAPTER 3
PROBLEM DESCRIPTION
Inconel 625 is a nickel based super alloy. These alloys have very important
advantages at the same time it has the drawback of difficult to machine. These have
very high strength to weight ratio. They are highly heat resistant and corrosion resistant.
So it has very useful application in different industrial sectors, aircraft, marine systems
etc... So want to reduce the difficulties involved in the machining of these alloy.
In this project we try to improve the machinability of Inconel 625 alloy by
taking three machining parameters cutting velocity, feed rate and depth of cut. Any
metal can be machined in any values of feed, velocity and depth of cut. But maximum
output is obtained only when optimum ranges of cutting velocity, feed and depth of cut
are used. In this project we aims to find out the optimum value of machining parameters
for machining Inconel 625 by using Taguchi method of optimisation along with grey
relational analysis and ANOVA.

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CHAPTER 4
THEORETICAL STUDY
4.1 SUPER ALLOYS
Super alloys are unique high temperature materials used in gas turbine engines,
which display excellent resistance to mechanical and chemical degradation. Single
crystal super alloys are commonly used as blade materials for aircraft turbines. These
alloys are also called high performance alloys. They are high temperature heat resistant
alloys that can retain their strength at high temperature. Alloying increases the strength
and temperature capabilities but decreases the processability. These alloys exhibits
excellent mechanical strength and creep resistance at high temperature, good surface
stability, corrosion and oxidation resistance. It have a matrix with austenitic face
centred cubic crystal structure. A super alloy’s base alloying elements are Nickel,
Cobalt and Nickel-iron. These also contains lesser amounts of Tungsten, Molybdenum,
Tantalum, Niobium, Titanium, and Aluminium. Examples of super alloys are Hastelloy,
Inconel, Waspaloy, Rene alloys, Haynes alloys, Incoloy, MP98T, TMS alloy and
CMSX single crystal alloys. Effect of different alloying elements are shown below
Fig 4.1 Effects of different alloying elements

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4.2 CLASSIFICATION OF SUPER ALLOYS
a) Iron-base super alloys:
Iron-base super alloys are those alloys that have iron as the major
constituents, with significant amounts of chromium and nickel and lesser
amounts of molybdenum or tungsten. They are also strengthened by a carbide or
inter metallic precipitate and solid solution. The inter metallic precipitate is
usually of the Niȝ (Al,Ti) γ΄ type. They differ from stainless steel in their
chromium-nickel ratios and strengthening mechanisms
.
b) Cobalt-base super alloys:
Cobalt-base super alloys are those alloys that have cobalt as the major
constituent, with significant amount of nickel, chromium and tungsten and lesser
amount of molybdenum, niobium, tantalum, titanium, lanthanum and Iron on
occasion. They are strengthened by solid solution and carbide phases. Cobalt
solid solution alloys can be classified into three groups on the basis of use
a) Alloys for use primarily at temperatures from 650 to 1150 ºC including
Haynes 25, Haynes 188, Umco-50 and S-816.
b) Fastener alloys MP-35N and MP-159 for use about 650ºC.
c) Wear resistant stellite-6B.
c) Nickel-base super alloys:
Nickel-base super alloys are defined as those alloys that have nickel as
the major constituent, with significant amounts of chromium. They may contain
cobalt, iron, tungsten, molybdenum and tantalum as major alloying elements.
They are strengthened by solid solution and second phase inter metallic
precipitation. Many nickel base alloys contain small amounts of aluminium,
titanium, niobium, molybdenum and tungsten to enhance either strength or
corrosion resistance. The combination of nickel and chromium gives these alloys
outstanding corrosion resistance.

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4.3 APPLICATIONS
 Aircraft and industrial turbines: Disks, bolts, shafts, cases, blades, vanes,
burner cans, afterburners, and thrust reverses.
 Steam turbine power plants: Bolts, blades and stack gas reheaters.
 Space vehicles: Aerodynamically heated skins and rocket engine parts.
 Reciprocating engines: Turbochargers exhaust valve, hot plugs, pre combustion
cups and valve seat inserts.
 Metal processing: Hot work tool and dies.
 Heat treating equipment: Trays, fixtures and conveyer belts.
 Nuclear power systems: Control-rod drive mechanism, valve stems, springs and
ducting.
 Chemical and petrochemical industries: Bolts, reaction vessels, valves, piping
and pumps.
4.4 NICKEL-BASE SUPER ALLOYS
Nickel is the fifth most abundant element on earth. The atomic number is 28,
and it in the first row of the d block of transition metals, alongside iron and cobalt. The
atomic weight is 58.71, the weighted average of the five stable isotopes 58, 60, 61, 62
and 64, which are found with probabilities 67.7%, 26.2%, 1.25%, 3.66% and 1.16%,
respectively. The crystal structure is face-centred cubic from ambient conditions to the
melting point, 1455 ◦C, which represents an absolute limit for the temperature capability
of the nickel-based super alloys. The density under ambient conditions is 8907 kg/m³.
Thus, compared with other metals used for aerospace applications, for example, Ti
(4508 kg/m³) and Al (2698 kg/m³), Ni is rather dense. This is a consequence of a small
interatomic distance, arising from the strong cohesion provided by the outer d electrons
– a characteristic of the transition metals.
Nickel based super alloys are austenitic and derive their strength from
precipitation hardening during heat treatment (solution treatment and ageing). Most of
the alloys contain significant amounts of chromium, cobalt, aluminium and titanium.
Small amounts of boron, zirconium and carbon are often included. Other elements that
are added, but not to all alloys, include rhenium, tungsten, tantalum and hafnium, from

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the 5d block of transition metals, and ruthenium, molybdenum, niobium and zirconium
from the 4d block. Certain super alloys, such as IN718 and IN706, contain significant
proportions of iron, and should be referred to as nickel–iron super alloys. Thus, most of
the alloying elements of nickel are taken from the d block of transition metals. To avoid
possible crucible contamination and to obtain clean alloy, these are melted in vacuum
induction or arc furnace. Boron and iridium are added to increase rupture life. These
alloys are very important in industries because of their wide varieties of severe
operating conditions and corroding environments, high temperature, high stress and
combination of these cases.
4.4.1 PROPERTIES
I. Physical properties:
a) FCC lattice structure till the melting point lattice constant= 0.31567nm at
20ºC.
b) Density at 25ºC 8.902gm/cc and at melting point= 7099gm/cc.
c) Boiling point= 2730ºC.
II. Thermal properties:
a) Co-efficient of thermal expansion= 13.3µ m/Mk at 0 to 100ºC.
b) Recrystallization temperature= 370ºC.
c) Thermal conductivity= 82.9w/m at 100ºC.
III. Electrical properties:
a) Electrical resistance of pure nickel is negligible at extremely low
temperature but increases with increase in temperature, ρ= 68.4Ω.
IV. Magnetic properties:
a) It is one of the three metals that are highly ferromagnetic.
b) µ max= 1240 at B= 1900G.
c) corelic force 167A/m at H= 4.
d) Saturation magnetisation= 0.616T at 20ºC.
e) Residual induction= 0.0300T.

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V. Mechanical properties:
a) Tensile strength= 317Mpa.
b) O.2% offset yield strength= 53Mpa.
c) Elongation in 50mm= 30%.
d) Hardness value= 64HV for annealed high purity nickel.
4.5 INCONEL-625
INCONEL® nickel-chromium alloy 625 (UNSN06625/W.Nr. 2.4856) is used
for its high strength, excellent fabricability (including joining), and outstanding
corrosion resistance. Strength of INCONEL alloy 625 is derived from the stiffening
effect of molybdenum and niobium on its nickel-chromium matrix; thus precipitation
hardening treatments are not required. This combination of elements also is responsible
for superior resistance to a wide range of corrosive environments of unusual severity as
well as to high-temperature effects such as oxidation and carburization.
Alloy 625 is a nonmagnetic, corrosion and oxidation resistant alloy. Its
outstanding strength and toughness in the temperature range cryogenic to 2000ºF are
derived primarily from the solid solution effects of the refractory metals, columbium
and molybdenum, in a nickel chromium matrix. The alloy has excellent fatigue strength
and stress corrosion cracking resistance to chloride iron.
The outstanding and versatile corrosion resistance of INCONEL alloy 625 under
a wide range of temperatures and pressures is a primary reason for its wide acceptance
in the chemical processing field. Because of its ease of fabrication, it is made into a
variety of components for plant equipment. Its high strength enables it to be used, for
example, in thinner-walled vessels or tubing than possible with other materials, thus
improving heat transfer and saving weight. Some applications requiring the combination
of strength and corrosion resistance offered by INCONEL alloy 625 are bubble caps,
tubing, reaction vessels, distillation columns, heat exchangers, transfer piping, and
valves.

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4.5.1 Chemical composition
TABLE 4.1 Chemical composition of INCONEL 625
COMPOSITION WEIGHT% COMPOSITION WEIGHT%
Nickel 58 min carbon 0.10
Chromium 20 min- 23 max manganese 0.50
Molybdenum 8 min- 10 max silicon 0.50
Iron 5 phosphorous 0.015
Niobium+ tantalum 3.15 min- 4.15max sulphur 0.40
Titanium 0.40 cobalt 1.0
4.5.2 Properties of Inconel 625
a) Physical constants and thermal properties
TABLE 4.2 Physical constants and thermal properties of INCONEL 625
Density 8.44g/cm³
Melting range 1290ºC to 1350ºC
Coefficient of expansion(20-100ºC) 12.8µm/mºC
Thermal conductivity(at 38ºC) 10.1w/mºC
Electrical resistivity (at 38ºC) 130µΩ-cm
Specific heat(at 21ºC) 410 J/kgºC
Permeability at 200 oersted 1.0006
Curie temperature -196ºC

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b) Mechanical properties of annealed Inconel 625
TABLE 4.3 Mechanical properties of INCONEL 625
Tensile strength 827-1034Mpa
Yield strength 414-655Mpa
Elongation 60-30%
Reduction of area 60-40%
Hardness brinell 145-220
Modulus of elasticity 205.8kN/mm²
Modulus of rigidity 79kN/mm²
c) Aqueous Corrosion
The high alloy content enables it to withstand a wide variety of severe
corrosive environments like the atmosphere, fresh and sea water, neutral salts,
and alkaline media. Combination of nickel and chromium provides resistance to
oxidizing chemicals, whereas the high nickel and molybdenum contents supply
resistance to non-oxidizing environments, pitting and crevice corrosion, and
niobium prevents intergranular cracking.
d) High temperature oxidation resistance
It has good resistance to oxidation and scaling at high temperature. It has
the ability to retain a protective oxide coating under drastic cyclic conditions.
e) Workability
i. Hot working:
It may be done at 1149ºC maximum furnace temperature. It
becomes very stiff below 1010ºC so that it may be reheated. Uniform
reductions are recommended to avoid the formation of a duplex grain
structure.
ii. Cold forming:
Alloy 625 can be cold formed by standard methods. When the
material becomes too stiff annealing can be done for retaining ductility.

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iii. Machinability:
Low cutting speeds. Rigid tool and workpiece, heavy equipment,
ample coolant and positive feeds are general recommendations.
iv. Weldability:
Welding can be done by gas shielded processes using a tungsten
electrode or a consumable electrode. Post weld heat treatment of the
weld are not necessary to maintain corrosion resistance.
4.5.3 Motives behind the use in aerospace
INCONEL 625 super alloy provides higher strength to width ratio compared to
steels. The use of Inconel 625 in such aggressive environments hinges on the face that it
maintains high resistance to corrosion, mechanical & thermal fatique, thermal shock and
creep at elevated temperature. Most of the aerospace parts requires high temperature
resistant metals to withstand high temperature as used in reusable launch vehicle. This
property makes it most preferable in aerospace industry.
4.5.4 Applications
 Aerospace Components: bellows and expansion joints, ducting systems, jet
engine exhaust systems, engine thrust-reversers, turbine shroud rings, aircraft
ducting systems, resistance-welded honeycomb structures for housing engine
controls, fuel and hydraulic line tubing, spray bars, heat exchanger tubing in
environmental control systems, combustion system transition liners, turbine
seals, compressor vanes, and thrust-chamber tubing for rocket motors.
 Air Pollution Control: chimney liners, dampers, flue gas desulfurization (FGD)
components.
 Chemical Processing: equipment handling both oxidizing and reducing acids,
super-phosphoric acid production.
 Sea water applications (Marine Service): steam line bellows, Navy ship
exhaust systems, submarine auxiliary propulsion systems, wire rope for mooring
cables, propeller blades for motor patrol gunboats, submarine quick-disconnect
fittings, sheathing for undersea communication cables, submarine transducer
controls.

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 Nuclear Industry: reactor core and control rod components, waste reprocessing
equipment.
 Offshore Oil and Gas Production: waste flare gas stacks, piping systems, riser
sheathing, sour gas piping and tubing.
 Petroleum Refining: waste flare gas stacks.
 Waste Treatment: waste incineration components.
4.5.5 Advantages
 High strength to width ratio.
 Excellent fabricability (including joining), and outstanding corrosion resistance.
 Resistance to chloride-ion stress-corrosion cracking.
 High tensile, creep, and rupture strength; outstanding fatigue and thermal-fatigue
strength and excellent weldability and brazeability.
 Resistance to post weld age cracking.
 High temperature resistance.
 Age hardening with unique properties of slow aging response that permits
heating and cooling during annealing without danger of cracking.

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CHAPTER 5
MACHINING AND ITS ASPECTS IN HRSA
5.1 MACHINABILITY
Machinability is defined as the ease with which material can be removed from a
metal. The most machinable metal is the one which will permit the fastest removal of
the largest amount of material per grind of tool with satisfactory finish. Machining is
any of the various processes in which a piece of raw material is cut into a desired final
shape and size by a controlled material removal process. Machining is influence by
machine variables, tool variables, cutting conditions, work material variables.
Different factors affecting the machinability of metals are the type of the work
piece, type of tool material, size and shape of tool, type of machining operation, size,
shape and velocity of cut, type and quality of machine used, quality of lubricant used
during machining operation, coefficient of friction between chip and tool.
Machinability index gives a quantitative measurement of machinability. It is
used to compare the machinability of different material. Machinability index of free
cutting steel is taken as 100. It is expressed as ratio of cutting speed of material for 20
min tool life to cutting speed of standard steel for 20 min tool life.
5.2 MACHINABILITY ASSESSMENT
Machinability of a material may be assessed by one or more of the following
criteria:
1) Tool life for a given cutting speed and tool geometry.
2) Ratio of material removal.
3) Magnitude of cutting forces.
4) Quality of surface finish.
5) Dimensional stability of finished work.
6) Heat generated during cutting.
7) Ease of chip disposal.
8) Chip hardness.
9) Shape and size of chip.
10) Power consumption per unit volume of material removed.

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5.3 MACHINING DIFFICULTY OF INCONEL 625
INCONEL 625 is often referred to as “difficult to cut material”. These materials
now a days causing greater challenges for manufacturing engineers. The high pressure
produced during machining causes a hardening effect which prevents further machining.
The main challenges in machining Inconel 625 are as follows
 The high strength of Inconel 625 at cutting temperatures causes high cutting forces,
generates more heat at the tool tip and limits their speed capability.
 The presence of hard, abrasive intermetallic compounds and carbides in these alloys
causes severe abrasive wear on the tool tip.
 The high capacity for work hardening in Inconel 625 causes depth-of-cut notching
on the tool, which can lead to burr formation on the work piece.
 The chip produced during machining is tough and continuous, therefore requiring
acceptable chip breaker geometry.
 High-Temperature Alloys have a low thermal conductivity, meaning heat generated
during machining is neither transferred to the chip nor the work piece, but is heavily
concentrated in the cutting edge area.
 These temperatures can be as high as 1100°C to 1300°C, and can cause crater wear
and severe plastic deformation of the cutting tool edge, thereby increasing the
cutting forces.
 The chemical reactivity of these alloys facilitates formation of Built Up Edge
(BUE) and coating delamination, leading to poor tool life.
 Heat generated during machining can alter the alloy microstructure, potentially
inducing residual stress that can degrade the fatigue life of the component.
Difficulty of machining will shortens tool life and reduces surface finish of the
metal. Extreme care must be taken to ensure the surface integrity of the component
during machining. Most of the major parameters includes the choice of tool life and
coating materials, tool geometry, machining methods, cutting speed, feed rate, depth of
cut, lubrication must be controlled in order to achieve better surface finish.

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CHAPTER 6
MILLING AND ITS ASPECTS IN HRSA
6.1 MILLING
Milling is the most important form of machining, a material removal process,
which can create a variety of features on a part by cutting away the unwanted material.
It is the process of cutting away material by feeding a work piece past a rotating
multiple tooth cutter. The cutting action of many teeth around the milling cutter
provides the fastest method of cutting. The milling process requires a milling machine,
work piece, fixture and cutter. The work piece is a piece of pre-shaped material that is
secured to the fixture, which itself is attached to the platform inside the milling
machine. The cutter is a cutting tool with sharp teeth that is also secured in the milling
machine and rotates at high speeds. By feeding the work piece into the rotating cutter,
material is cut away from the work piece in the form of small chips to create the desired
shape.
Slab milling is one of the most widely used material cutting operation. In slot
milling we will get 100% tool engagement so it can be used as a method of optimisation
of machining parameters.
6.2 TYPES OF MILLING OPERATIONS
A. On the basis of rotational direction of cutter
Table 6.1 Classification based on direction of rotation of cutter
TYPES DESCRIPTION
Up milling In this case movement of cutter teeth is
opposite to the direction of feed motion.
Down milling In this case direction of cutter motion is
the same as that of direction of feed
motion.

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B. On the basis of application
Table 6.2 Classification based on application
TYPES DESCRIPTION
Slab milling In this the cutter width extends beyond
the work piece on both the sides
Slot milling It is used to make slot in the work piece.
Straddle milling In this cutting takes place simultaneously
on both sides of the work piece.
Conventional Face milling In this milling cutter remains overhanging
on both sides of the work piece.
Partial face milling In this case the milling cutter overhangs
only to one side of the work piece.
End milling In this thin cutter are used as compared to
work piece width.
Profile milling It cover multi-axis milling of convex and
concave shapes in two and three
dimensions.
Pocket milling This is a selective portion milling on the
flat surface of work piece used to make
shallow packets there.

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6.3 GENERAL ASPECTS IN HRSA MILLING
 Milling of high temperature alloys often requires more rigid and powerful
equipment than the milling of carbon steel.
 Cutter accuracy in both radial and axial direction is essential to maintain a constant
tooth load and a smooth operation and to prevent premature failure of individual
cutting teeth.
 Cutting edge must be sharp with an optimised edge-rounding, to prevent chip
adherence at the point where the edge exits the cut.
 The number of cutting teeth actually in cut during the milling cycle must be as high
as possible. This will give good productivity provided that the stability is good
enough.
 Cutting speeds for super alloys are generally low. Common practice is to employ a
fairly low cutting speed in combination with a moderately high feed per tooth, to
produce a chip thickness not less than 0.1mm which prevents work hardening of the
material.
 Coolant should be applied in generous quantities around the cutting edge when the
cutting speeds are low, inorder to reduce chip adhesion. Coolant supplied through
the machine tool spindle is recommended for HRSA materials. High pressure
coolant (HPC) will give better tool life.
 Down milling (climb milling) should be used, to obtain the smallest chip thickness
where the edge exits cut and reduce any chip adherence.
6.4 CUTTING TOOL MATERIALS USED FOR MACHINING
In machining Ni-based super alloys tooling related technologies are treated
seriously. The appropriate consideration for these technologies can lead to optimum
production output, consistency of machined product and value added activities. Inorder
to produce good quality and economic parts a cutting tool must have
 Good wear resistance & High hot hardness
 High strength and toughness
 Good thermal shock properties.
 Adequate chemical stability at elevated temperatures.

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1. Cemented carbide tool :
Carbide tools are the oldest amongst the hard cutting tool materials.
These tools are used to machine Ni based super alloys in the range of 10-
30m/min. these materials are composed of carbide of tungsten, titanium,
tantalum, or some combination of these sintered or cemented in a matrix binder
usually cobalt. The carbide tools can be of two types:
a) Uncoated carbide tools :
The uncoated cemented carbides are commonly used at lower cutting
speeds in the range of 10-30m/min and it gives better performance than that
of coated carbide tools in the lower speed range
b) Coated carbide tools:
Coatings improves the performance of the carbide tools. Coatings are
hard materials and therefore provides a good abrasion resistance. The good
lubricating properties of coating minimize the friction at the tool-chip and
tool-work piece interfaces, thus lowering the cutting temperatures. By using
these cutting tools high speeds can be achieved. Both PVD and CVD coated
carbides are employed. Typical coating materials used includes TiC, TiN,
TiAlN, TiCN, TiZrN and diamond coatings. Multi coated carbide perform
better, in terms of tool life than that of single layer coated carbides. TiAlN
coating is the best for machining Inconel 625.
2. Ceramic tools:
Ceramics are non-metallic materials. The application of ceramic cutting
tool is limited because of their extreme brittleness. The transverse rupture
strength is very low. This means that they will fracture easily when making
heavy interrupted cuts. However the strength of ceramics under compression is
much higher than HSS and carbide tools. Proper tool geometry and edge
preparation play an important role in the application of ceramic tools and help to
overcome their weakness. Some of the advantages of ceramic tools are
 High strength for light cuts on very hard work materials.
 Extremely high resistance to abrasive wear and crater wear.
 Capability of running at high speeds.
 Extremely high hot hardness and Low thermal conductivity.

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3. CUBIC BORON NITRIDE
CBN is the hardest material available after diamond, and doesn’t occur in
nature. The synthesis of polycrystalline CBN is composed of about 50-90% of
CBN and ceramic binders such as titanium carbide and titanium nitride. A high
CBN content is better in cutting super alloy. Higher CBN content was better
because of their hardness. The hardness increases almost linearly with the CBN
content. Compared to ceramics, CBN has a better hardness and resistance to
fracture but poor chemical resistance. These are recommended to machine
Inconel 625 in a speed range of 120-240m/min.
6.5 MILLING PARAMETERS
There are three major cutting parameters to be controlled in any milling operation.
These three parameters are cutting speed, feed rate and depth of cut. By optimising
these parameters better results can be obtained in milling Inconel 625. These parameters
are described below:
1. Cutting velocity
Cutting speed of a milling cutter is its peripheral linear speed resulting from
operation. It is expressed in m/min. The cutting speed can be derived from the
below formula. Spindle speed of the milling machine is selected to give the desired
peripheral speed of the cutter.
V=
𝛱𝑑𝑁
1000 (6.1)
Where, V= linear cutting speed in m/min
d= diameter of milling cutter in mm
n= cutter speed in rev/min
2. Feed rate
It is the rate with which the work piece under process advances under the
revolving milling cutter. It is known that revolving cutter remains stationary and
feed is given to the work piece through worktable. Generally feed is expressed in
three ways:

22. 22
a Feed per tooth(ƒt)
It is the distance travelled by the work piece between engagements by the
two successive teeth expressed as mm/tooth.
b Feed per revolution(ƒrev)
Travel of work piece during one revolution of milling cutter expressed as
mm/rev.
c Feed per unit of time(ƒm)
It is the distance advances by the work piece in unit time expressed as
feed/min or feed/sec.
Above described three feed rates are mutually convertible:
ƒm=n*ƒrev=z*n*ƒt (6.2)
Where, n= rpm of the cutter
z= number of teeth in the milling cutter
3. Depth of cut
Depth of cut in milling operation is the measure of penetration of cutter into the
work piece. It is the thickness of the material removed in one pairs of the cutter
under process. One pairs of cutter means when the cutter completes the milling
operation from one end of the work piece to the other end. In other words it is the
perpendicular distance measured between the original and final surface of work
piece measure in mm.
4. Material removal rate(MRR)
It is the volume of the metal removed in unit time.
MRR=
𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑚𝑒𝑡𝑎𝑙 𝑟𝑒𝑚𝑜𝑣𝑒𝑑(𝑚𝑚³)
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛(min)
(6.3)

23. 23
CHAPTER 7
METHODOLOGY
7.1 PROJECT DESCRIPTION
RPFF (rocket payload fabrication facility) is a section of VSSC where machining
of different aerospace parts are done. Presently machining is carried out on parts for
reusable launching vehicle. Inconel 625 is widely used in different parts in many
aerospace application. Inconel 625 has wide application in reusable launching vehicles
because of the property to withstand high temperature. Inconel 625 is very difficult to
machine and as all aerospace parts should have high surface quality, better machining
possibilities should be investigated. This project investigates in optimising the
machining parameters of slot milling of Inconel 625 super alloy to have better surface
quality and less production time which could be benefited for milling operations.

24. 24
7.2 SCOPE OF THE PROJECT
LITERATURE SURVEY
SELECTION OF MATERIAL
SELECTION OF TOOL INSERT
MACHINING
PROCESS
OPTIMISATION
TECHNIQUE
SELECTION OF
SPEED, FEED &
DEPTH OF CUT
TAGUCHI BASED
GREY
RELATIONAL
ANALYSIS
CNC MILLING OPTIMISATION
ANOVA
CONCLUSION
RESULT

25. 25
7.3 WORK PIECE MATERIAL
The work piece material used in the machining test was Inconel 625. Three
samples of Inconel 625 each of length 160mm, width 53mm, and thickness 40mm were
taken for the experiment.
7.4 CUTTING CONDITIONS
Cutting condition is created by appropriate selection of cutting parameter values
corresponding to cutting speed, feed, axial and radial depth of cut. The ranges of cutting
parameters are determined using Sandvik coromant tool catalogue. In this study slot
milling operation is carried out. In slot milling operation 100% cutter engagement is
possible. Therefore we can assess the conditions on any engagement from the result
obtained from the experiment. The milling operation is carried out in a wet condition. A
6% soluble oil through coolant system at 1 bar pressure and 12 litre/minute flow rate.
7.5 CUTTING TOOL
The cutting tool used in the machining test was Sandvik bull nose end mill cutter
(25mm diameter, 2 flute) with a PVD coated cemented carbide insert. The insert used
was PVD coated cemented carbide round insert (S30T grade). It has high edge strength
and bulk toughness. It has well resistant to micro chipping and keeps the cutting edge
line intact longer. The grade focuses on high performance at elevated cutting speed.

26. 26
 Specification of Cutting tool and tool insert
Table 7.1 Specification of cutting tool and tool insert
Cutting tool Bull nose end mill cutter
Insert holder Seco tools
Insert RCKT10T3MO-PM
Insert engagement 100%
Insert grade YBG302
Chip breaker Through type
Insert grade description nc-TiAlN nano PVD
coating on high
toughness carbide, a
Nano Coating grade
Insert work piece
material
P25-P40, M25-M40
 Specification of tool and tool holder
Table 7.2 Specification of tool and tool holder
Tool diameter 25mm
Tool holder KENAMETAL ISOBT50
Holder taper BT50
Made Kennel metal
7.6 MACHINE TOOL
The machine tool used in the cutting test was Jyoti EXF 1680 which is a three
axis CNC machine. The machine configuration is of fixed bed moving column and its
spindle is delivering a maximum torque of 472-712Nm depending upon the load
condition. With its high torque motor and gearbox the table size of machine is
2000mm*800mm and its working volume is 1600mm*800mm*800mm. the machine is
installed with Siemens 840D-SL controller with updated machining cycles. This
machine complies with VDI/DGQ 3447 standard and maintain its positional uncertainty

27. 27
within 0.001mm and repeatability within 0.005mm. shopmill software is installed in the
machine.
7.7 PROCEDURE
The experiment was conducted as per the details in Jyoti CNC machine. Nine
experiments are done according to taguchi method in three sample (three experiments
on each sample). The samples were fixed properly by suitable mechanical clamping.
Correct values of spindle speed, feed and depth of cut was provided on the program
software in the CNC machine. After attaining all the precautions experiment was
started. Time for cutting each slot was noted by using a stop watch. The machined
surface of nine samples were inspected for surface roughnes (Ra) using Talysurf
measuring instrument. Material removal rate is used as another performance parameter
to evaluate the machining performance. Material removal rate is expressed as the
amount of material removed under a period of machining time and is expressed as
mm³/min. experimental setup is shown in the figure.
Fig 7.1 Experimental setup

28. 28
CHAPTER 8
DESIGN OF EXPERIMENT
8.1 PLAN OF EXPERIMENT
Dr Genichi Taguchi is a Japanese quality management consultant who has
developed and promoted a philosophy and methodology for continuous quality
improvement in product and process. The methodology of Taguchi which combine the
experiment design theory and the quality loss function concept have been used in
developing robust designs of products and processes.
The degrees of freedom for three parameters in each of three levels were
calculated as follows:
Degree of Freedom (DOF) = number of levels -1
For each factor, DOF equal to:
For (Vc); DOF = 3 – 1 = 2
For (f); DOF = 3 – 1 = 2
For (d); DOF = 3 – 1 = 2
In this project nine experiments were conducted at different parameters. For this
Taguchi L9 orthogonal array was used, which has nine rows corresponding to the
number of tests, with three columns at three levels. L9 orthogonal array has eight DOF,
in which 6 were assigned to three factors (each one 2 DOF) and 2 DOF was assigned to
the error. For the purpose of observing the degree of influence of the process parameters
in machining. The process parameters and their levels are given in the table below:
Table 8.1 Process parameters and their levels
PARAMETERS UNIT LEVEL1 LEVEL 2 LEVEL3
Cutting velocity m/min 30 35 40
Feed rate Mm/tooth 0.1 0.15 0.2
Depth of cut mm 1 2 3

29. 29
8.2 TAGUCHI EXPERIMENTAL RESULT
By using Taguchi plan of experiment and by using the procedures explained in
the previous chapters 9 experiments were conducted 3 on each samples (total 3
samples). The figure showing the slots prepared is shown below:
Fig 8.1 Slots prepared on the samples

30. 30
In this work, L9 Orthogonal Array design matrix is used to set the control
parameters to evaluate the process performance. The design matrix used in this work
and the corresponding results of surface roughness and material removal rate are shown
in the table below.
Table 8.2 Results obtained from the experiment
EXP NO PARAMETER COMBINATIONS SURFACE
ROUGHNESS
(microns)
MRR
(mm³/s)V f d
1 1 1 1 0.3084 17.09
2 1 2 2 0.4161 55.06
3 1 3 3 1.5312 42.97
4 2 1 2 0.4290 35.33
5 2 2 3 0.5277 96.36
6 2 3 1 0.5110 42.4
7 3 1 3 0.2659 49.68
8 3 2 1 0.4773 27.17
9 3 3 2 0.7504 84.8
8.3 OPTIMISATION OF MACHINING PARAMETERS
In this project optimisation of machining parameters are done by using two
statistical tools. They are Grey relational analysis and Analysis of variance. Each
methods are discussed in detail in the following sections.
8.3.1 GREY RELATIONAL ANALYSIS (GRA)
The grey relational analysis (GRA) associated with the Taguchi method
represents a rather new approach to optimisation developed by Deng in 1989. The grey
theory is based on the random uncertainty of small samples which develop into an
evaluation technique to solve certain problems of system that are complex and having
incomplete information. The grey relational analysis (GRA) is one of the powerful and
effective soft-tool to analyse various processes having multiple performance
characteristics.

31. 31
8.3.1.1 Steps in GRA
1. Normalization of experimental results in GRA
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 directions of the
target in the sequences are different. Normalization is the process in which
transformation of input data takes place to an evenly distributed data in a scale
range between 0 and 1. In this project a linear normalization of the raw data for
surface roughness and MRR were performed in the range between 0 and 1 which is
also called grey relational generation.
 Normalization of Ra
Surface roughness values should be minimised to 0. So we take smaller
the better equation for normalising the Ra values.
xі(k) =
max 𝑦і(𝑘)−𝑦і(𝑘)
max 𝑦і(𝑘)−min 𝑦і(𝑘)
(8.1)
where, yi(k)→ value after grey relational generation
min yi(k)→ smallest value of yi(k) for the kth response
max yi(k)→ largest value of yi(k) for the kth response
 Normalization of MRR
Normalization of MRR is based on larger the better criterion because
MRR should be maximised.
xj(k)=
𝑦ј(𝑘)−min 𝑦і(𝑘)
max 𝑦і(𝑘)−min 𝑦і(𝑘)
(8.2)
Where yi(k)→ value after grey relational generation
min yi(k)→ smallest value of yi(k) for the kth response
max yi(k)→ largest value of yi(k) for the kth response

32. 32
2. Grey relational coefficient
Based on normalized experimental data, grey relational coefficient is
calculated to represent the correlation between the desired and actual
experimental data.ᵢ
ɸі(k)=
∆min + Ψ∆max
∆ₒі+ 𝛹∆𝑚𝑎𝑥
(8.3)
Where Δₒi→ difference between absolute value xₒ(k)and xi(k)
Ψ→ distinguishing coefficient 0<=ψ<=1
Δmin→ the smallest value of oi
Δmax→ largest value of oi
3. Grey relational grade
Grey relational grade is the weighted sum of the grey relational coefficients
for a particular experiment. The higher value of grey relational grade corresponds
to intense relational degree between the reference sequence xₒ(k) and the given
sequence xi(k). The reference sequence x0 (k) represents the best process
sequence. Therefore, higher grey relational grade means that the corresponding
parameter combination is closer to the optimal.
ᵞі=
1
𝑛
⅀ɸі(𝑘) (8.4)
Where n→ number of process response
Φi(k)→ grey relational coefficient

33. 33
The below table shows the normalized value, grey relational coefficient
and grey relational grade for each experiment. Higher grey relational
coefficient better the product quality.
Table 8.3 Table for calculating grey relational grade
EXP
NO
NORMALIZED
VALUES
GREY
COEFFICIENT
GREY GRADE
SR MRR SR MRR GREY
GRADE
RANK
1 0.9665 0.0000 0.9372 0.3333 0.6352 5
2 0.8813 0.4790 0.8081 0.4897 0.6489 4
3 0.0000 0.3265 0.3333 0.4261 0.3797 9
4 0.8711 0.2301 0.7950 0.3937 0.5944 6
5 0.7931 1.0000 0.7073 1.0000 0.8537 1
6 0.8063 0.3193 0.7208 0.4235 0.5722 7
7 1.0000 0.4111 1.0000 0.4592 0.7296 2
8 0.8329 0.1272 0.7495 0.3642 0.5569 8
9 0.6171 0.8542 0.5663 0.7742 0.6703 3
4. Find out the response table for grey relational grade
The mean of the grey relational grade for each level of parameter and the total
mean of the grey relational grade for the 9 experiments were calculated and
tabulated as shown below:
Table 8.4 Response table for grey relational grade
PROCESS
PARAMETERS
GREY RELATIONAL GRADE
LEVEL 1 LEVEL 2 LEVEL 3 MAX-
MIN
RANK
Cutting velocity 0.5546 0.6734* 0.6523 0.1188 2
Feed rate 0.6531 0.6865* 0.5407 0.1458 1
Depth of cut 0.5881 0.6379 0.6543* 0.0662 3
Total mean value of grey grade = 0.6268
*Optimum levels

34. 34
8.3.2 ANALYSIS OF VARIANCE (ANOVA)
The purpose of analysis of variance (ANOVA) is to investigate which of the
process parameters significantly affect the performance characteristics. This is
accomplished by separating the total variability of the grey relational grades, which is
measured by the sum of the squared deviation from the total mean of the grey relational
grade into contributions by each machining parameter and the error. The analysis of
variance (ANOVA) test establishes the relative significance of the individual factors
and their interaction effects.
The total sum of squared deviation SSt= total sum of squared deviation by each
parameters (SSf) + sum of squared deviation by error (SSe)
8.3.2.1 Steps for ANOVA calculations
1. Calculate degrees of freedom of each parameters (DF)
It is a measure of the amount of information that can be uniquely determined
from a given set of data. DOF for data concerning a factor equals one less than the
number of levels .The degrees of freedom for three parameters in each of three
levels were calculated as follows:
Degree of Freedom (DOF) = number of levels-1 (8.5)
2. Calculate the sum of squares of each parameters (SS)
Sum of squares of each parameters is given by
Sum of squares due to factor A= [(no: of experiments at level Aı)*(mAı-m) ²] +
[(no: of experiments at level A2)*(mA2-m) ²] +
[(no: of experiments at level Aȝ)*(mAȝ-m) ²](8.6)
Sum of squares of error SSe= SSt-SSf (8.7)

35. 35
3. Variance for each factors (MS)
It measures the distribution of the data about the mean of the data .Variance of
each factor is given by
Variance for each factor=
𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑜𝑓 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑓𝑎𝑐𝑡𝑜𝑟
𝑑𝑜𝑓
(8.8)
4. F ratio of each factor (F)
It is the ratio of variance due to the effect of a factor and variance due to the
error term. This ratio is used to measure the significance of the factor under
investigation on the performance characteristics with respect to the variance of all
the factors included in the error term.
F ratio for each factor=
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
𝑒𝑟𝑟𝑜𝑟 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒
(8.9)
5. Contribution of each factors (C)
It is obtained by dividing the sum of square of the factor by total sum of square
and multiplied by 100. It is denoted by C and can be calculated using the following
equation:
Contribution of each parameters=
𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟𝑠
𝑡𝑜𝑡𝑎𝑙 𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠
*100. (8.10)
Table 8.5 Results of ANOVA
Source DOF SS MS F % C
Vc 2 0.0241 0.01205 0.3532 17.93
f 2 0.0350 0.0175 0.513 26.03
d 2 0.007131 0.003566 0.1045 5.30
Error 2 0.06821 0.03411 50.736
Total 2 0.13444 100

36. 36
8.4 CONFIRMATION EXPERIMENT
After evaluating the optimal parameter settings, the next step is to predict and verify
enhancement of the quality characteristics using optimal parametric combination. The
estimated grey relational grade
γʹʹ=γm+∑ (γi-γm) (8.11)
Where γm= total mean grey relational grade
γi=mean grey relational grade at the optimum level
Fig 8.2 Specimen with confirmation slot

37. 37
Table 8.6 Results of confirmation experiment
Initial machining
parameter
Optimal machining parameters
prediction Experiment
Setting level V₂f₂d₃ V₂f₂d₃ V₂f₂d₃
Surface roughness 0.5277 0.562
MRR 96.36 100.64
Grey grade 0.8537 0.7606
Improvement in
grey grade
0.0931

38. 38
CHAPTER 9
CALCULATIONS
9.1 CALCULATION FOR TABLE 8.1
All the values in the table 8.1 are chosen from the catalogue book of Sandvick
coromant.
9.2 CALCULATION FOR TABLE 8.2(SET NO:1)
Average response values
1. Surface roughness
Surface roughness values are obtained from talysurf measuring instrument.
For set no: 1 Ra= 0.3044/0.3123
Average Ra=
0.3044+0.3123
2
= 0.3084microns (9.1)
2. Material removal rate
Material removal rate is obtained by calculating the volume of metal removed
from the specimen and the time taken for preparing the slot.
Length of the slot=53mm
Breadth of the slot=25mm
Height of the slot=1mm
Time taken=77.53s
Volume= length of the slot*breadth of the slot*height
= 53*25*1
=1325mm³
MRR=
1325
77.53
= 17.09mm³/s (9.2)

39. 39
9.3 CALCULATION FOR TABLE 8.3(SET NO: 1)
1. Normalized values
a Surface roughness
xі(k) =
max 𝑦і(𝑘)−𝑦і(𝑘)
max 𝑦і(𝑘)−min 𝑦і(𝑘)
(9.3)
max yi(k)=1.5312microns
min yi(k)=0.2652microns
yi(k)=0.30835microns
x1=
1.5312−0.30835
1.5312−0.2652
=0.9665
b Material removal rate
xј(k)=
𝑦ј(𝑘)−min 𝑦і(𝑘)
max 𝑦і(𝑘)−min 𝑦і(𝑘)
(9.4)
min yi(k)=17.09mm³/s
max yi(k)=96.36mm³/s
yi(k)=17.09
x1=
17.09−17.09
96.36−17.09
=0.0000
2. Grey relational coefficients
a Surface roughness
ɸі(k)=
∆min + Ψ∆max
∆ₒі+ 𝛹∆𝑚𝑎𝑥
(9.5)

40. 40
Consider the following table
Table 9.1 Table for calculating Δ values
SLNO 1- NORMALIZED Ra 1-NORMALIZED MRR
1 1-0.9665=0.0335 1-0.0000=1.0000
2 0.1187 0.5210
3 1.0000 0.6735
4 0.1289 0.7699
5 0.2069 0.0000
6 0.1937 0.6807
7 0.0000 0.5889
8 0.1671 0.8728
9 0.3829 0.1458
From above table,
Δmin=0.0000
Δmax=1.0000
Ψ=0.5 (assume)
Δₒi=0.0335 (respective values from the above table)
Δ1=
0+(0.5∗1)
0.0335+(0.5∗1)
=0.9372
b Material removal rate
Considering the same above equation and table
Δmin=0.0000
Δmax=1.0000
Ψ=0.5
Δₒi=1.0000
Δ1=
0+(0.5∗1)
1.0000+(0.5∗1)
=0.3333
3. Grey relational grade
a Grey grade
Φ1=0.9372
Φ2=0.3333

41. 41
n=2
ᵞі=
1
𝑛
⅀ɸі(𝑘) (9.6)
=
0.9372+0.3333
2
=0.6353
b Rank
Ranks are provided according to the decreasing order of grey grades for
all experiments. 1st
rank corresponds to highest value of grey grade among 9
values.
9.4 CALCULATIONS FOR TABLE 8.4 (PARAMETER: Vc)
a Level 1
Consider Taguchi’s parameter combination, in that level 1 of cutting speed is
used in 1, 2 and 3rd
experiment. Take the average value of grey grades of the 3
experiment.
Level 1=
0.6353+0.6489+0.3797
3
=0.5546
b Level 2
Level 2 of cutting speed is used in 4, 5 and 6th
experiment. Take the average
value of grey grades of the 3 experiment.
Level 2=
0.5944+0.8537+0.5722
3
=0.6734
c Level 3
Level 3 of cutting speed is used in 7, 8 and 9th
experiment. Take the average
value of grey grades of the 3 experiment.
Level 3=
0.7296+0.5569+0.6703
3
=0.6523

42. 42
d Max-Min
Max=0.6734
Min=0.5546
Max-Min=0.6734-0.5546=0.1188
e Rank
Ranks are provided according to the decreasing order of Max-Min values for each
parameter.
f Mean value of grey relational grade
Mean=
0.6353+0.6489+0.3797+0.5944+0.8537+0.5722+0.7296+0.5569+0.6703
9
=0.6268
9.5 CALCULATIONS FOR TABLE 8.5 (SOURCE: Vc)
a Degree of freedom (DOF)
Degree of Freedom (DOF) = number of levels -1 (9.7)
= 3 – 1 = 2.
b Sum of squares (SS)
Sum of squares due to factor A= [(no: of experiments at level Aı)*(mAı-m) ²] +
[(no: of experiments at level A2)*(mA2-m) ²]+
[(no: of experiments at level Aȝ)*(mAȝ-m) ²]. (9.8)
= [3*(0.5546-0.6268)2
] + [3*(0.6734-0.6268)2
] +
[3*(0.6523-0.6268)
=0.0241
Where mA1= respective values of Vc from response table
m= mean value of grey grade
no: of experiments at each level=3
c Variance of each factor (MS)
Variance for each factor=
𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑜𝑓 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑓𝑎𝑐𝑡𝑜𝑟
𝑑𝑜𝑓
(9.9)
=
0.0241
2
=0.01205

43. 43
d F ratio
F ratio for each factor=
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
𝑒𝑟𝑟𝑜𝑟 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒
. (9.10)
=
0.01205
0.03411
=0.35
e % contribution
Contribution of each parameters=
𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟𝑠
𝑡𝑜𝑡𝑎𝑙 𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠
*100. (9.11)
=
0.0241∗100
0.13444
=17.93%
9.6 CALCULATIONS FOR TABLE 8.6
Optimum value of grey relational grade
γ’’= γm+∑ (γi-γm) (9.12)
=0.6268+ [(0.6734-0.6268) + (0.6865-0.6268) + (0.6543-0.6268)]
=0.7606.
Improvement in grey grade=0.8537-0.7606
=0.0931.

44. 44
CHAPTER 10
RESULT
The nine experiments were conducted on 3 samples (3 experiments on each sample)
according to Taguchi L9 combination set.
The minimum surface roughness was 0.2659microns and corresponding material
removal rate was 49.68mm³/min.
The maximum surface roughness was 1.5312microns and the corresponding
material removal rate was 42.97mm³/min.
According to grey relational analysis, the optimum value of machining parameter is
found out to be set 223. i.e. Vc=35m/min, f=0.15mm/tooth and d=3mm.
From analysis of variance, most significant parameter is feed rate with highest
contribution on performance characteristics followed by cutting velocity and depth
of cut.
The confirmation experiment was done after optimising the parameters using
Taguchi based grey relational analysis.
Optimised result gave a surface roughness value of 0.562microns and corresponding
material removal rate was 100.64mm³/min.

45. 45
CHAPTER 10
CONCLUSION
It has been established that Taguchi based grey relational analysis is an effective
optimisation tool for determining the optimum machining parameters for machining of
Inconel 625 super alloy in slot milling . It has been found that according to grey
relational analysis, the optimum value of machining parameter are Vc=35m/min,
f=0.15mm/tooth and d=3mm. After comparing the confirmation result it has been found
that there is an increase in material removal rate. Analysis of variance shows that feed
rate is the most significant machining parameters followed by cutting velocity and depth
of cut.

46. 46
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