EXPERIMENTAL WORK - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/8182/13/13_chapter 04.pdf · Hardness test Hardness test was carried out on Brinnell cum Rockwell Hardness

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CHAPTER-4

EXPERIMENTAL WORK

Process of Fabrication and techniques for characterization of 7075 Al alloy and AA7075/

wt % SiC Particles, composites with various weight fractions and particle size have been

explained. Pilot experiments were carried out to find suitable range of cutting process

parameters.

4.1 MATERIALS

The chemical composition of 7075 Al alloy is as shown in Table 4.1.

Table 4.1 Chemical composition (wt %) of 7075 Al alloy

Material Zn Mg Cu Cr Si Fe Al

Wt % 5.62 2.52 1.63 0.22 0.06 0.18 balance

The following composites were fabricated by stir casting process.

AA7075/10 wt % SiC Particles (10 to 20 µm). Composite-1

AA7075/15 wt % SiC Particles (10 to 20µm). Composite-2

AA7075/10 wt % SiC Particles (20 to 40 µm). Composite-3

AA7075/15 wt % SiC Particles (20 to 40µm). Composite-4

4.2 PROCESSING OF MMC

4.2.1 Stir Casting Technique

Schematic diagram of stir caster is shown in figure 4.1. The stir casting furnace is

mounted on ground. Electrical resistance furnace of 50 KW is used for melting and

49

casting upto 100 Kg weight. Solid state temperature controller and 02 K type mineral

insulated thermocouple with accuracy of ±2 ºC are used for temperature control and

measurement. One thermocouple provides the control input to temperature controller.

This thermocouple is placed near the coil. The other thermocouple is used to measure the

temperature of melt.

Figure 4.1: Experimental set up of Stir casting process

4.2.2 Fabrication of Aluminium Alloy-SiC Composites

Composite was prepared using an electrically heated furnace. Aluminium alloy was

placed in crucible and heated. The flux was added in molten metal in the furnace.

Degassing of molten metal was carried out by passing dry nitrogen gas in the molten

metal. Dross was taken out from the molten metal with a perforated flat spoon. The

temperature of molten metal was maintained at 800 ºC for 15 minutes. 10 wt % SiC

50

particles of size 20 to 40 μm, preheated to 650ºC, were added in the molten metal.

Stirring was done by using a mechanical stirrer. It was continued for 10 minutes in order

to have better distribution of SiC particles in the molten metal. Test specimen castings in

the shape of cylindrical rods (diameter 40 mm; length 120 mm) were prepared by pouring

the molten metal into cast iron permanent mould. Same process was used to fabricate 15

wt % SiC composites with particles of size 20 to 40 μm and 10 to 20 μm. Cylindrical rods

were sectioned to produce samples for metallographic examination. Conventional

grinding and polishing techniques were used for grinding and polishing the samples.

4.3 CHARICTRIZATION OF MMC

Characterization of AA7075/10 wt% SiC (particle size10-20µm), AA7075/15 wt% SiC

(particle size10-20µm), AA7075/10 wt% SiC (particle size 20-40µm) and AA7075/15wt

% SiC (particle size20-40µm) was done by carrying out the following tests.

Energy Dispersive X-Ray Analyses (EDAX)

The samples were examined using scanning electron microscopy (SEM)

QUANTA 200FEG, FEI Netherland equipped with energy dispersive X-ray analyses

(EDAX). This machine is shown in figure 4.2.

Electron Probe Microscopic Analysis (EPMA)

An electron probe micro-analyzer (EPMA) is a microbeam instrument and is used

primarily for the in situ nondestructive chemical analysis of minute solid samples. This

instrument is shown in figure 4.2. It is an analytical technique that is used to establish the

composition of small areas of the specimen. This analysis was carried out on CAMECA

SX 100 machine. Column Conditions were taken as 15 keV 20nA. Electron beam size

51

was maintained at 20 µm. Signal(s) used for analysis are Mg Ka, Al Ka, Si Ka, Cr Ka,

Fe Ka, Cu Ka, Zn Ka.

Figure 4.2 Scanning Electron Microscope interfaced with EDAX

Figure 4.3: Electron Probe Microscopic Analyzer

52

Differential Thermal Analysis (DTA)

Thermal decomposition of the samples was carried out in Perkin Elemer Pyr‘s

Diamond TG/DTA thermogravimetric / Differential thermal analyzer (figure 4.4),

capable of recording the thermogravimetric (TG), derivative thermogravimetric (DTG)

and differential thermal analysis (DTA) curves simultaneously. Differential thermal

analysis (DTA) is carried out to confirm the onset temperature of reactions. DTA, DTG

and TG of 7075 Al alloy, 7075 Al alloy reinforced with 10 wt % and 15 wt% SiC

particles were carried out from room temperature to 1500 ºC in the atmosphere of argon

at the rate of 50 ºC/min.

Figure 4.4: Perkin Elemer Pyr‘s Analyzer

X Ray Diffraction Analysis (XRD)

X-ray diffraction (XRD) measurements were performed using a Bruker ASX D-8 X-

ray diffractometer. It is shown in figure 4.5. X-ray diffraction was carried out at a

53

scanning rate of 0.01º 2θ/sec using Cu k (α) radiation. The source voltage and current

were maintained at 40 kV and 40 mA. Peaks obtained in the diagram were analyzed.

Figure 4.5: Bruker ASX D-8 X-ray diffractometer.

Figure 4.6: Thermo Mechanical Analyser

54

Thermo Mechanical Analysis (TMA)

TMA (figure 4.6) is used to find coefficient of thermal expansion (CTE). It was

carried out on LINSESIS TMA 1000 machine. Quartz was taken as standard material. A

force of 5 Newton was applied. Test was carried out in argon gas atmosphere in order to

prevent oxidation. Heating rate was set at 2ºC/hour and end temperature at 400ºC.

Young’s Modulus and Peak Frequency

Young‘s Modulus was found by Dynamic Elastic Property Analyzer (DEPA).

DEPA is based on Impulse Excitation Technique (IET). This technique is a non

destructive method that uses natural frequency, dimensions and mass of the test piece to

determine young‘s modulus and peak frequency.

Tensile test

Tensile test were carried out on Universal Testing Machine (UTM) of 50 KN

capacities. It is shown in figure 4.7. Load was increased in the steps of 5 KN. Samples

were homonised. Sample dimensions were taken as 40 mm in gauge length, 50 mm in

parallel length and 10 mm in diameter.

Figure 4.7: Universal Testing Machine

55

Figure 4.8: Brinnell cum Rockwell Hardness testing machine

Hardness test

Hardness test was carried out on Brinnell cum Rockwell Hardness testing

machine. It is shown in figure 4.8. Samples were homonised for test. Samples were

prepared metallographically and polished. Tungsten carbide ball indenter of 20 mm in

diameter with a test tip of 3 mm in diameter was used for brinnell hardness test.

4.4 MACHINING

4.4.1 Computer Numerical Control Turning Machine

The basic objective behind the use of CNC turning machine is the reduction of cost of

production and improvement in product quality. Machining by CNC turning can be done

to very precise limits, which normally is very difficult by a conventional Lathe. Also, a

range of cutting speed, feed and depth of cut can be selected on CNC turning machine.

56

Any combination of cutting speed, feed and depth of cut is possible on CNC turning

machine, whereas on conventional lathe only a particular combination of cutting speed,

feed and depth of cut is possible. CNC Turning Machine (Model TC 20) was used for

experiments. The Machine parameters are given in Table 4.2. Machine is shown in figure

4.9.

Figure 4.9: CNC Turning Machine

Table 4.2 Parameters of CNC Turning Machine

Parameter Specifications

Distance between centers 575 mm

Swing over telescopic cover 500 mm

Spindle speed range 40 -4000rpm

Positioning Accuracy

X-axis

Z-axis

+/- 0.005 mm

+/- 0.0075 mm

Main motor 7.5 KW

Control panel

Hydraaulic Chuck

cCCChuck

Tool Holder

SiC

57

4.4.2 Turning inserts

Since the machining of 7075 Al alloy/SiC composites is very difficult, the properties of

available tools were compared with properties of Al alloy/SiC composite with the

objectives to minimize the tool wear. Hardness of SiC is 2300 -2600 HV where as

hardness of TiCN is 4400 to 4600 HV. So TiCN will provide better resistance against

wear. Based on this property TiCN (Titanium carbo nitride) coated carbide tool was

selected. Cuboid shape of insert offers better resistance to shocks as compared to

triangular shape. Negative rake, because of its strength, offers greater advantage during

roughing, interrupted, scaly and hard spot cuts. Details of tool holders and inserts used

for turning are shown in Table 4.3.

Table 4.3 Details of inserts and tool holders

Turning

Tool

Holder

Type of

Insert

Clearance

Angle

(degree)

Back

rake

Angle

(degree)

Nose

radius (r)

mm

Feed (f)

mm/rev

Depth of

cut (mm)

PCLNL

2525

M12 KT

809

Carbide

insert

CNMG

120404EM

120408EM

120412EM

grade 6615

0º 7º

0.4

0.8

1.2

fmin= 0.15

fmax =0.60

apmin = 1.0

apmax = 6.0

A tool was fabricated locally by brazing carbide insert on mild steel rod. It is indicated in

figure 4.10.It was used in initial turning for removing material from cast cylindrical rods.

Figure 4.10: locally fabricated tool

4.4.3 Dynamometer

Piezoelectric dynamometer was used to measure three components of cutting force i.e

tangential force, feed force, and radial force in turning operation. It is shown in figure

4.11.

58

4.4.4 Surface roughness tester

After turning, the surface roughness was measured using the Gippan SRT -6210, a

portable surface roughness instrument. It is shown in figure 4.12. The cut-off and

sampling lengths for each measurement were taken as 0.8 and 4 mm, respectively.

Driving speed of stylus was taken as 0.5 mm/rev. ISO 4287 standard was followed during

measurement.

Figure 4.11: Three component Dynamometer

Figure 4.12: Surface roughness tester

59

4.4.5 Selection of process parameters and their ranges

The process parameters that may affect the machining characteristics of parts machined

by CNC turning machine have been identified based on literature review. The identified

process parameters are:

Cutting tool related parameters: tool material, tool geometry, type of

coating, grade and insert condition.

Machining parameters: cutting speed, feed, depth of cut and nose radius.

The ranges of process parameters for the experiment were decided on the basis of

literature survey and the results of pilot experiments conducted using one parameter at a

time approach.

4.4.6 Effect of process parameters

The experimental work carried out at Shri Mata Vaishno Devi University, Katra, J&K, on

a CNC Turning Machine (Model TC 20).7075 Al alloy/15 wt% SiC (particle size 20-40

µm) composites (30 mm diameter and 110 mm length) were used for experimentation.

Insert CNMG 120408 grade 6615 was used for external turning. A customized

dynamometer was applied to measure the three component of cutting force, namely

tangential force (Fz), feed force (Fx) and radial force (Fy).Surface roughness was

measured using surface roughness measurement instrument. Power consumption was

measured using a set of wattmeters. Machining was done under dry machining

conditions.

4.4.6.1 Effect of cutting speed

The experimental data of cutting force, power consumption and surface roughness for

varying cutting speed keeping feed and depth of cut constant are indicated in table 4.4.

60

The effect of cutting speed on tangential force, feed force, radial force, surface roughness

and power consumption are shown in figure 4.13 to 4.17 respectively.

Table 4.4 Experimental Data of Dependent Parameters for Varying Cutting Speed

(Feed= 0.2mm/rev & Depth of Cut= 0.8 mm)

Sr

No

Cutting

speed

(m/min)

Tangential

force (Fz)

N

Feed

force

(Fx) N

Radial

force(Fy)

N

Power

consumption

(watt)

Average

Surface

Roughness

Ra (μm)

1 60 150 49 83 1230 3.987

2 90 146 47 82 1251 3.850

3 120 145 43 76 1326 3.78

4 150 141 41 74 1350 3.702

5 180 136 40 73 1450 3.652

6 210 132 38 70 1540 3.509

7 240 130 38 70 1560 3.586

Figure 4.13: Effect of Cutting speed on Tangential force

Figure 4.14: Effect of Cutting speed on Feed force

120

125

130

135

140

145

150

155

60 90 120 150 180 210 240

Tang

entia

l for

ce (N

)

Cutting speed (m/min)

35

40

45

50

60 90 120 150 180 210 240

Feed

forc

e (N

)


61

Figure 4.15: Effect of Cutting speed on Radial force

Cutting forces decreases gradually due to increase of cutting speed. Thermal softening of

composite with increasing cutting speed accounts for the progressive fall in force

components. These findings are in agreement with those of Manna and

Bhattacharayya[2003], Varada Rajan et al[2006].

Figure 4.16: Effect of Cutting speed on Power consumption

Figure 4.16 shows that with increase in cutting speed from 60 to 240 m/min, power

consumption increases linearly. It may be due to the fact that amount of power used in

machining operation is generally proportional to cutting speed as the rate of metal removal

is proportional to speed.

1100

1200

1300

1400

1500

1600

1700

60 90 120 150 180 210 240

Pow

er c

onsu

mpt

ion

(wat

t)


65

70

75

80

85

60 90 120 150 180 210 240

Rad

ial f

orce

(N)


62

Figure 4.17: Effect of Cutting speed on Surface roughness

Figure 4.17 indicates that the Surface roughness decreases with increase of cutting speed.

4.4.6.2 Effect of Feed rate

The experimental data of cutting force, power consumption and surface roughness for

varying feed rate keeping cutting speed and depth of cut constant are shown in Table 4.5.

Table 4.5 Experimental Data of Dependent Parameters for Varying Feed

(Cutting speed = 150 m/min & Depth of Cut= 0.8 mm)

Sr

No

Feed

(mm/rev)

Tangential

force (Fz) N

Feed force

(Fx) N

Radial

force(Fy) N

Power

consumption

(watt)

Average

Surface

Roughness

Ra (μm)

1 0.05 152 46 75 1190 2.212

2 0.10 164 52 78 1250 2.646

3 0.15 172 53 80 1264 2.762

4 0.20 198 57 87 1302 2.973

5 0.25 210 60 91 1365 3.048

6 0.30 214 61 92 1370 3.056

7 0.35 220 64 94 1390 3.077

The effect of feed rate on tangential force, feed force, radial force, surface roughness and

power consumption are shown in figure 4.18, to 4.22 respectively.

3.400

3.500

3.600

3.700

3.800

3.900

4.000

60 90 120 150 180 210 240

Sur

face

roug

hnes

s (m

icro

ns)


63

Figure 4.18: Effect of Feed rate on Tangential force

Figure 4.19: Effect of Feed rate on Feed force

Figure 4.20: Effect of Feed rate on Radial force

It is clear from the figures 4.18, 4.19 and 4.20 that all the component of the cutting force

increase with increase in feed rate.

140

160

180

200

220

240

260

280

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Tang

enti

al fo

rce

(N)

Feed (mm/rev)

40

45

50

55

60

65

70

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Feed

forc

e (N

)

Feed (mm/rev)

70

80

90

100

110

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Rad

ial f

orc

e (N

)

Feed (mm/rev)

64

Figure 4.21: Effect of Feed rate on Power Consumption

It is inferred from figure 4.21 that power consumption increases with increase in feed

rate.

Figure 4.22 depict that the surface roughness is showing an increasing trend with increase

in feed rate and best value is found in the feed range of 0.15 to 0.25 mm/rev. These results

are in agreement with those of Manna, and Bhattacharayya [2004].

Figure 4.22: Effect of Feed rate on surface roughness

1100

1150

1200

1250

1300

1350

1400

1450

1500

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Po

wer

co

nsu

mp

tio

n (w

att

)

Feed (mm/rev)

2.100

2.300

2.500

2.700

2.900

3.100

3.300

3.500

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Su

rfac

e ro

ug

hn

ess

(mic

ron

s)

Feed (mm/rev)

65

4.4.6.3 Effect of Depth of cut

The experimental data of cutting force, surface roughness and power consumption for

varying depth of cut keeping cutting speed and feed rate constant are shown in Table 4. 6.

The effect of depth of cut on tangential force, feed force, radial force, power consumption

and surface roughness are shown in figure 4.23 to 4.27 respectively.

Table 4.6 Experimental Data of Dependent Parameters for Varying Depth of cut

(Feed= 0.2mm/rev & Cutting speed = 150 m/min

Sr

No

Depth of

Cut (mm)

Tangential

force (Fz) N

Feed force

(Fx) N

Radial

force(Fy) N

Power

consumption

(watts)

Average

Surface

Roughness

Ra (μm)

1 0.2 175 61 97 981 2.3

2 0.4 203 65 102 1260 2.514

3 0.6 238 69 107 1376 2.707

4 0.8 240 70 107 1400 2.778

5 1.0 257 72 109 1511 3.098

6 1.2 270 81 118 1560 3.124

7 1.4 275 83 122 1580 3.537

Figure 4.23 Effect of Depth of cut on Tangential force

150

170

190

210

230

250

270

290

0.2 0.4 0.6 0.8 1 1.2 1.4

Tan

gen

tial

forc

e (N

)

Depth of cut (mm)

66

Figure 4.24: Effect of Depth of cut on Feed force

Figure 4.25: Effect of Depth of cut on Radial force

Figure 4.26: Effect of Depth of cut on Power consumption

55

60

65

70

75

80

85

90

0.2 0.4 0.6 0.8 1 1.2 1.4

Fee

d fo

rce

(N)

Depth of cut (mm)

90

100

110

120

130

140

0.2 0.4 0.6 0.8 1 1.2 1.4

Rad

ial f

orc

e (N

)

Depth of cut (mm)

950

1050

1150

1250

1350

1450

1550

1650

1750

1850

0.2 0.4 0.6 0.8 1 1.2 1.4

Po

wer

co

nsu

mp

tio

n (w

att)

Depth of cut (mm)

67

It is inferred that depths of cut have strong influence on cutting force as apparent from

figures 4.23, 4.24 and 4.25. The various components of the cutting force increase

significantly with increase in depth of cut. These findings tally with those of Manna, and

Bhattacharayya [2004], Palanikumar and Karthikeyan [2007].

The total power required in the turning process is the sum of power required for turning

the workpiece against the tool and that required to feed the tool in axial direction. This

indicates that only the Tangential force and Feed force are used for the assessment of

power consumption. The radial component does not contribute to power required in the

process. Figure 4.26 shows that the power consumption substantially increases with

increase in depth of cut. Figure 4.27 show that variation in surface roughness is the

minimum in the depth of cut range of 0.2 to 0.6 mm and thereafter, it increases.

Figure 4.27 Effect of Depth of cut on Surface roughness

2.100

2.300

2.500

2.700

2.900

3.100

3.300

3.500

3.700

3.900

4.100

0.2 0.4 0.6 0.8 1 1.2 1.4

Su

rface r

ou

gh

ness (m

icro

ns)

Depth of cut (mm)

68

4.4.7 Selection of the Range of Parameters Based On Preliminary Investigation

The analysis of the results show that the high cutting speed, low feed and low depth of cut

are desirable settings of process parameters resulting in minimum values of three

component of cutting force while machining 7075 Al alloy/ SiC composite with TiN coated

carbide inserts on CNC turning center. The similar setting of process variable results in

reduction of surface roughness. The power consumption increases almost in direct

proportion to the increase in cutting speed, feed rate and depth of cut. These results were

utilized for obtaining the range of parameters for cutting speed, feed and depth of cut for

conducting design of experiments in CNC turning of 7075 Al alloy/ SiC composite as

depicted in table 4.7. Based on literature survey and availability, cutting inserts of three

different nose radius were chosen.

Table 4.7 Process parameters with their values at three levels

Factors Process parameters Level 1 Level 2 Level 3

A Cutting speed (m/min) 90 150 210

B Feed (mm/rev) 0.15 0.2 0.25

C Depth of Cut (mm) 0.2 0.4 0.6

D Nose radius (mm) 0.4 0.8 1.2

4.5 DESIGNS OF EXPERIMENTS

Designs of experiments are considered as very useful strategy for deriving clear and

accurate conclusions from the experimental observations. In this phase of

experimentation a design of experimentation technique viz Response Surface

Methodology (RSM) has been used for studying the influence of four process parameters

(cutting speed, feed, depth of cut and nose radius) on eight different responses in

69

machining of 7075 Al alloy SiC composites. Face centered central composite design was

preferred in this case. Experiments were performed at three different levels. Thirty

experiments were performed.

4.6 RESPONSE SURFACE METHODOLOGY

Box and Wilson [1951] have proposed response surface methodology for the

optimization of experiments. The RSM is an empirical modeling approach for the

determination of relationship between various process parameters and responses with the

various desired criteria and searching the significance of these process parameters on the

coupled response [Myers and Montgomery, 1995]. It is a sequential experimentation

strategy for building and optimizing the model. Therefore RSM is a collection of

mathematical and statistical procedures that are useful for the modeling and analysis of

problems in which response of demand is affected by several parameters and objective is

to optimize this response [Grum and Slab 2004, Ozecelik and Erzurmlu 2005, Kansal

et.al. 2005, Oktem et. al.2005]. By using the design of experiments and applying

regression analysis, the modeling of the desired response to several independent input

variables could be gained. In the RSM, the quantitative form of relationship between

desired response and independent input parameters could be represented as

[Montgomery, 1990].

y = f ( x1, x2, x3………….xn) ± er

where y is the desired response, f is the response function (or response surface), x1, x2,

x3………….xn are independent input parameters, and er is fitting error.

The appearance of response function is a surface as plotting the expected response of f.

The identification of suitable approximation of f will determine whether the application

70

of RSM will be successful or not. In this study, the approximation of f will be proposed

using the fitted second order polynomial regression model, called the quadratic model.

The quadratic model of f can be written as following [Montgomery and Peck, 1992]

Y= bo+ rjiij

k

i

i

k

i

i eXXbbiiXbiX1

2

1

4.1

Where Y is the corresponding response and Xi are the values of the ith

machining process

parameters. The terms b…. are the regression coefficients and the residual e measures the

experimental error of the observations.

This assumed surface Y contains linear, squared and cross product terms of parameters

Xi‘s. In order to estimate the regression coefficients a number of experimental design

techniques are available. Box and Hunter [1957] have proposed that scheme based on

central composite rotatable design fits the second order response surface very accurately.

4.6.1 Central Composite Second Order Rotatable Design

In this design standard error remains the same at all the points which are equidistance

from the centre of design. These criteria of rotatability can be explained as follows. Let

the points (0, 0,…….0) represent the centre of the region in which the relation between Y

and X is under investigation. From the result of any experiment the standard error, er of Y

can be computed at any point on the fitted surface. This standard error will be a function

of the co-ordinates Xi‘s of the point. Due to rotatability condition this standard error is

same at all equidistance points with the distance ρ from the centre of the region i.e. for all

points for which [Cochran and Cox 1962, Montgomery 2001]:

X12+X2

2+…………. +Xk

2= ρ

2= constant 4.2

Central composite rotatable design is subdivided into three parts:

71

Points related to 2k design, where k is the number of parameters and 2 is the

number of levels at which the parameters is kept during experimentation.

Extra points called star points positioned on the co-ordinate axes to form a central

composite design with a star arm of size γ.

Few more points added at the centre to give roughly equal precision for response

Y with a circle of radius one.

The components of Central Composite Second Order Rotatable Design for different

number of variables are shown in table 4.8. Figure shows the central composite rotatable

design in 3-X variables [Cochran and Cox, 1962].

Table 4. 8 Components of Central Composite Second Order Rotatable Design

Number of

Variables

Number of

Factorial

points

Star Points Center

Points

Total Value of

k 2k

2k N N γ

3 8 6 6 20 1.682

4 16 8 6 30 2

5 16*

10 6 32 2

6 32*

12 9 53 2.378

*- Half replication, γ-Distance of Star Points fron the centre, k- number of parameters

Figure 4.28: Central Composite Rotatable Design in 3X –Variables

72

The factor γ is the radius of the circle or sphere on which the star points lie. With k≥5 the

experiment size is reduced by using a half replication of 2k factorial design. With half

replication γ becomes 2(k-1)/4

.Also no replication is needed to find error mean square,

since this can be found out by replicating the centre points [Hines and Montgomery

1990].

4.6.2 Face Centered Central Composite Design

A face-centered CCD, is used whenever the region of operability encompasses the full

region of interest as described by the variable ranges or when non allowable operating

conditions exist at only one of the extremes of the design region. The face-centered CCD

requires only three levels of each experiment variable, making it the simplest variety of

CCD to carry out as well as the least prone to corruption due to sources of experimental

error associated with setup and operation [Montgomery, 2001].

4.6.3 Estimation of the Coefficients

As stated earlier the regression equation representing second order response surface has

been assumed as [Montgomery and Peck 1992] (Equation 1).

Y= bo+ rjiij

k

i

i

k

i

i eXXbbiiXbiX1

2

1

Where Y is the corresponding response and Xi are the values of the ith

machining process

parameters. The terms b…. are the regression coefficients and the residual e measures the

experimental error of the observations. The method of least squares may be used to

estimate the regression coefficients [Hines and Montgomery 1990]. Let Xqi denote the qth

73

observation of variables Xi and N the total number of observations. The data for N

observations in terms of various variables will appear as shown below:

Y X1 X2 . . . . XK X12

X22

XK2

X1X2

XK-1 XK

Y1 X11 X12 X1K X112

X122 X1K

2 X11 X12

X1 K-I X1K

Y2 X21 X22 X2K X21 2 X22

2 X2K

2 X21X22 X2K-1 X2K

. . .

. . .

. . .

YN XN1 XN2 XNK XN1 2 XN2

2 XNK

2 XN1XN2 XNK-1 XNK

In terms of qth

observation the equation 1 can be written as:

Yq= bo+ qqjiqij

k

iiq

k

iiq eXXbbiiXbiX

1

2

1

4.3

Where q = 1,2 ………..N

The least square function is, L= N

q

qe1

2 4.4

Hence from equation (3)

L= ][2

2

11

0

1

qjqi

k

ji

ijqi

k

i

iiqi

k

i

i

N

q

q XXbXbXbbY

2 4.5

This function L is to be minimized with respect to b0, b1 . . . . ..These least square

estimates of b0, bi, bii and bij must satisfy the following set of equations:

0b

L= -2 ][

2

2

11

0

1

qjqi

k

ji

ijqi

k

i

iiqi

k

i

i

N

q

q XXbXbXbbY

Xqi=0 4.6

ib

L= -2 ][

2

2

11

0

1

qjqi

k

ji

ijqi

k

i

iiqi

k

i

i

N

q

q XXbXbXbbY

Xqi=0 4.7

74

ijb

L= -2 ][

2

2

11

0

1

qjqi

k

ji

ijqi

k

i

iiqi

k

i

i

N

q

q XXbXbXbbY

Xqi2=0 4.8

ijb

L= -2 ][

2

2

11

0

1

qjqi

k

ji

ijqi

k

i

iiqi

k

i

i

N

q

q XXbXbXbbY

XqiXqj=0 4.9

There are P= k+1 normal equations, one for each unknown regression equation

coefficient. Hence by solving the above equations, the coefficient of regression can be

obtained.

It is simpler to solve the normal equations if they are expressed in matrix form. The

second order response surface in matrix form may be written as:

Y=Xβ+ er 4.10

Where Y =

NY

Y

Y

2

1

X=

NNNkNNN

K

K

XXXXXX

XXXXXX

XXXXXX

21

2

121

2212

2

1222212

2111

2

1112111

.............................1

.

.

.

..................................1

...................................1

β=

1

1

0

.

.

.

Pb

b

b

er =

Ne

e

e

.

.

.

2

1

N= Total number of experiments

75

P= Total number of coefficients

Y is an (N×1) vector of observations, X is an (N×P) matrix of the level of the

independent variables, β is a (P×1) vector of regression coefficients, and er is a (N×1)

vector of random errors. The least square estimator is

L=N

q

re1

2= er/er = (Y-Xβ)/ (Y-Xβ) 4.11

This may be expressed as

L= Y/Y - β

/X

/Y- Y

/X β + β

/X

/X β 4.12

Since β/X

/Y is a (1×1) matrix and its transpose will also be a (1×1) matrix. Then

(β/ X

/Y)

/= β XY

/

Hence equation 12 can be written as:

L= Y/Y - 2β

/X

/Y + β

/X

/X β 4.13

The least square estimate must satisfy

Lβ = -2XY +2 X X β=0 4.14

Wich on simplification yields the values of different coefficient of regression equation

(Peng 1967).

X/X β =X

/Y 4.15

Β=(X/ X)

-1 X

/ Y 4.16

4.6.4 Analysis of Variance

For the analysis of variance, total sum of squares may be divided into four parts:

i. The contribution due to first order terms.

ii. The contribution due o second order terms.

76

iii. A lack of component which measures the deviation of the response from the fitted

surface.

iv. Experimental error which is obtained from the centre points.

The general formulae for the sum of squares are given in the Table 4.9 [Steel & torrie

1986], where N is the total number of experimental points, no,Ys,

_

oY represent total

number of observations, Sth

response value and mean value of response respectively at

the centre point of experimental region.

Table 4.9 Analysis of Variance (Peng 1967)

Source Sum of Squares Degree of

Freedom

1.First order

terms

2.Second order

terms

3.Lack of fit

4.Experimental

Error

5.Total

N

q

qiq

k

i

i YXb11

bo

2

1

11

2

11 N

Y

YXXbYXbY

N

q

q

qjqiq

k

i

ij

N

q

qiq

k

i

ii

N

q

q

Found by subtraction

2

1

_on

x

os YY

N

Y

Y

N

q

qN

q

q

2

1

2

1

k

2

)1(kk

N-no-

2

)3(kk

no-1

N-1

77

The experimentation was done in three stages using face centered central composite

design. Four input parameters were varied i.e cutting speed, feed, depth of cut and nose

radius. Thirty numbers of experiments were performed as per face centered central

composite for four variables at three levels as depicted in Table 4.7.

4.6.5 Planning of Experimentation

Stage I [AA7075/10 wt% SiC (particle size 10-20µm)] Composite 1

In this stage machining of AA7075/10 wt% SiC (particle size10-20µm) was

carried out by carbide insert on CNC turning machine. Values of responses viz surface

roughness, tangential force, feed force, radial force, power consumption, flank wear,

crater wear and tool life were measured. Adequate model was selected for these

responses. Analysis of variance (ANOVA) was performed in order to statistically analyze

the results. Significant process parameters were identified. Interaction effects of process

parameters were studied.

Stage II [AA7075/15 wt% SiC (particle size 10-20µm)] Composite 2

AA7075/15 wt% SiC (particle size10-20µm) was machined by carbide insert on

CNC turning machine. Values of responses viz surface roughness, tangential force, feed

force, radial force, power consumption, flank wear, crater wear and tool life were

measured. Adequate model was selected for these responses. ANOVA was performed in

order to statistically analyze the results. Significant process parameters were identified

and their interaction effects were studied.

78

Stage III [AA7075/10 wt% SiC (particle size 20-40µm)] Composite 3

CNC turning machine was used for machining of AA7075/10 wt% SiC (particle

size 20-40µm) by carbide insert. Responses values viz surface roughness, tangential

force, feed force, radial force, power consumption, flank wear, crater wear and tool life

were measured. Adequate model was selected for these responses. ANOVA was

conducted in order to statistically analyze the results and thus significant process

parameters were identified. Further to interaction effects of process parameters were

studied.

Stage IV [AA7075/15 wt% SiC (particle size 20-40µm)] Composite 4

In this machining of AA7075/15 wt% SiC (particle size 20-40µm) was carried out

on CNC turning machine by carbide insert. Values of responses viz surface roughness,

tangential force, feed force, radial force, power consumption, flank wear, crater wear and

tool life were measured. Adequate model was selected for these responses. ANOVA was

performed in order to statistically analyze the results. Significant process parameters were

identified and their interaction effects were studied.

Experimental results for Composite 1, Composite 2, Composite 3 and Composite 4 are

tabulated in Tables 4.11, 4.12, 4.13 and 4.14 respectively. Which are the average values

of three readings.

79

Table 4.10 Face centered central composite design for four variables at three levels

Std Run Block Cuttingspeed(A)

m/min

Feed(B)

mm/rev

Depthof

Cut(C)

mm

Nose

radius(D)

mm 1 28 Block 1 90 0.15 0.20 0.40

2 14 Block 1 210 0.15 0.20 0.40 3 10 Block 1 90 0.25 0.20 0.40

4 13 Block 1 210 0.25 0.20 0.40 5 30 Block 1 90 0.15 0.60 0.40

6 27 Block 1 210 0.15 0.60 0.40 7 20 Block 1 90 0.25 0.60 0.40 8 7 Block 1 210 0.25 0.60 0.40

9 24 Block 1 90 0.15 0.20 1.20 10 22 Block 1 210 0.15 0.20 1.20

11 17 Block 1 90 0.25 0.20 1.20 12 2 Block 1 210 0.25 0.20 1.20


16 8 Block 1 210 0.25 0.60 1.20 17 29 Block 1 90 0.20 0.40 0.80

18 5 Block 1 210 0.20 0.40 0.80 19 11 Block 1 150 0.15 0.40 0.80

20 19 Block 1 150 0.25 0.40 0.80 21 26 Block 1 150 0.20 0.20 0.80 22 1 Block 1 150 0.20 0.60 0.80 23 3 Block 1 150 0.20 0.40 0.40

24 4 Block 1 150 0.20 0.40 1.20 25 12 Block 1 150 0.20 0.40 0.80

26 23 Block 1 150 0.20 0.40 0.80 27 21 Block 1 150 0.20 0.40 0.80


80

Table 4.11 Experimental Results –Composite 1 [AA7075/10 wt %SiC (10-20µm)]

A= Cutting speed(m/min) R1=Surface roughness (µm) R5= Power consumption(watt)

B= Feed(mm/rev) R2= Tangential force(N) R6= Flank wear(mm)

C= Depth of Cut(mm) R3= Feed force(N) R7= Crater wear(mm)

D= Nose radius(mm) R4= Radial force (N) R8= Tool life(min)

Ex A B C D

R1 R2 R3 R4 R5 R6 R7 R8

1 90 0.15 0.20 0.40 1.499 60 19 43 525 0.16 0.22 8.1

2 210 0.15 0.20 0.40 1.284 54 15 38 690 0.22 0.25 7.2

3 90 0.25 0.20 0.40 1.562 79 22 51 566 0.27 0.31 6.4

4 210 0.25 0.20 0.40 1.338 70 17 28 820 0.42 0.45 4.3

5 90 0.15 0.60 0.40 2.269 98 54 81 690 0.31 0.36 5.8

6 210 0.15 0.60 0.40 1.923 86 45 71 926 0.49 0.44 3.6

7 90 0.25 0.60 0.40 2.412 114 69 98 717 0.36 0.42 5.1

8 210 0.25 0.60 0.40 2.189 99 60 85 1025 0.54 0.68 3.1

9 90 0.15 0.20 1.20 1.251 123 39 75 542 0.28 0.31 6.3

10 210 0.15 0.20 1.20 1.071 108 35 66 727 0.41 0.47 4.4

11 90 0.25 0.20 1.20 1.302 132 56 88 603 0.32 0.58 5.7

12 210 0.25 0.20 1.20 1.115 117 47 78 862 0.54 0.77 3.1

13 90 0.15 0.60 1.20 1.826 185 111 142 714 0.41 0.49 4.4

14 210 0.15 0.60 1.20 1.569 163 101 126 1010 0.51 0.69 3.4

15 90 0.25 0.60 1.20 1.999 202

144 171 788 0.42 0.68 4.3

16 210 0.25 0.60 1.20 1.732 176 136 151 1108 0.64 0.86 2.1

17 90 0.20 0.40 0.80 1.913 149 80 109 689 0.32 0.36 5.7

18 210 0.20 0.40 0.80 1.688 131 73 97 911 0.36 0.39 5.1

19 150 0.15 0.40 0.80 1.797 135 63 88 714 0.38 0.40 4.8

20 150 0.25 0.40 0.80 1.862 148 74 106 813 0.41 0.82 4.2

21 150 0.20 0.20 0.80 1.461 81 37 55 652 0.42 0.54 4.3

22 150 0.20 0.60 0.80 1.991 161 98 130 825 0.53 0.64 3.2

23 150 0.20 0.40 0.40 2.064 76 34 67 766 0.24 0.31 6.8

24 150 0.20 0.40 1.20 1.698 168 89 118 803 0.36 0.54 5.1

25 150 0.20 0.40 0.80 1.879 136 73 93 788 0.26 0.51 6.6

26 150 0.20 0.40 0.80 1.851 138 72 94 788 0.27 0.50 6.5

27 150 0.20 0.40 0.80 1.848 145 72 98 763 0.27 0.51 6.4

28 150 0.20 0.40 0.80 1.824 138 73 96 775 0.31 0.54 5.9

29 150 0.20 0.40 0.80 1.821 146 76 98 776 0.32 0.57 5.7

30 150 0.20 0.40 0.80 1.802 149 76 100 763 0.33 0.61 5.6

81






Ex A B C D

R1 R2 R3 R4 R5 R6 R7 R8

1 90 0.15 0.20 0.40 1.651 66 21 47 567 0.17 0.23 8.8

2 210 0.15 0.20 0.40 1.414 59 17 42 745 0.22 0.31 8.1

3 90 0.25 0.20 0.40 1.712 87 25 56 611 0.29 0.35 6.1

4 210 0.25 0.20 0.40 1.465 77 19 31 885 0.45 0.48 3.4

5 90 0.15 0.60 0.40 2.487 108 59 89 745 0.36 0.42 5.7

6 210 0.15 0.60 0.40 2.123 94 50 78 1002 0.58 0.63 1.8

7 90 0.25 0.60 0.40 2.652 125 76 108 774 0.43 0.49 4.6

8 210 0.25 0.60 0.40 2.397 109 66 93 1107 0.65 0.78 1.1

9 90 0.15 0.20 1.20 1.371 135 43 82 585 0.31 0.37 6.0

10 210 0.15 0.20 1.20 1.193 119 38 73 785 0.44 0.58 3.4

11 90 0.25 0.20 1.20 1.432 145 62 96 651 0.3 0.68 4.7

12 210 0.25 0.20 1.20 1.226 129 52 86 930 0.47 0.79 3.5

13 90 0.15 0.60 1.20 1.904 204 122 156 771 0.43 0.75 3.6

14 210 0.15 0.60 1.20 1.718 179 111 139 1091 0.57 0.85 1.5

15 90 0.25 0.60 1.20 2.199 222 158 198 851 0.49 0.91 3.1

16 210 0.25 0.60 1.20 1.902 194 150 166 1196 0.66 0.96 0.8

17 90 0.20 0.40 0.80 2.113 164 88 120 744 0.39 0.43 6.0

18 210 0.20 0.40 0.80 1.848 144 80 107 983 0.42 0.47 5.1

19 150 0.15 0.40 0.80 1.967 148 69 97 771 0.39 0.51 4.5

20 150 0.25 0.40 0.80 2.046 163 81 116 878 0.49 0.82 2.8

21 150 0.20 0.20 0.80 1.64 89 41 60 704 0.42 0.63 2.9

22 150 0.20 0.60 0.80 2.181 177 108 143 891 0.59 0.68 1.6

23 150 0.20 0.40 0.40 2.264 83 37 73 827 0.29 0.36 7.3

24 150 0.20 0.40 1.20 1.858 185 98 130 867 0.43 0.63 4.2

25 150 0.20 0.40 0.80 2.071 149 70 102 851 0.32 0.65 6.0

26 150 0.20 0.40 0.80 2.052 152 79 103 851 0.33 0.64 5.9

27 150 0.20 0.40 0.80 2.038 160 79 108 824 0.34 0.54 5.8

28 150 0.20 0.40 0.80 2.021 152 80 105 837 0.37 0.58 5.0

29 150 0.20 0.40 0.80 2.012 160 83 108 838 0.38 0.56 4.7

30 150 0.20 0.40 0.80 2.003 164 92 110 824 0.39 0.57 4.7

82






Ex A B C D

R1 R2 R3 R4 R5 R6 R7 R8

1 90 0.15 0.20 0.40 1.764 72 26 54 757 0.21 0.24 7.3

2 210 0.15 0.20 0.40 1.511 65 20 48 985 0.27 0.31 6.4

3 90 0.25 0.20 0.40 1.838 91 30 64 809 0.15 0.37 5.5

4 210 0.25 0.20 0.40 1.574 80 24 35 1214 0.53 0.48 3.2

5 90 0.15 0.60 0.40 2.905 118 74 101 1003 0.41 0.44 4.4

6 210 0.15 0.60 0.40 2.498 103 62 89 1337 0.62 0.54 2.3

7 90 0.25 0.60 0.40 3.073 134 95 122 1038 0.46 0.51 3.9

8 210 0.25 0.60 0.40 2.634 116 82 106 1478 0.69 0.81 1.6

9 90 0.15 0.20 1.20 1.471 147 54 94 774 0.36 0.38 5.1

10 210 0.15 0.20 1.20 1.259 130 48 82 1038 0.52 0.58 3.3

11 90 0.25 0.20 1.20 1.532 155 76 110 862 0.4 0.71 4.5

12 210 0.25 0.20 1.20 1.312 138 65 97 1232 0.55 0.81 3.1

13 90 0.15 0.60 1.20 2.384 222 152 178 1020 0.50 0.78 3.5

14 210 0.15 0.60 1.20 2.082 197 139 158 1443 0.60 0.85 2.5

15 90 0.25 0.60 1.20 2.588 240 197 214 1126 0.48 0.90 3.7

16 210 0.25 0.60 1.20 2.273 210 186 189 1584 0.70 0.96 1.5

17 90 0.20 0.40 0.80 2.251 175 109 134 985 0.41 0.42 4.2

18 210 0.20 0.40 0.80 1.977 154 100 119 1302 0.45 0.56 4.1

19 150 0.15 0.40 0.80 2.106 161 86 107 1020 0.42 0.57 4.3

20 150 0.25 0.40 0.80 2.191 174 101 130 1161 0.52 1.1 3.3

21 150 0.20 0.20 0.80 1.719 95 50 69 932 0.51 0.66 3.4

22 150 0.20 0.60 0.80 2.578 189 134 162 1179 0.63 0.71 2.2

23 150 0.20 0.40 0.40 2.428 85 46 79 1108 0.31 0.37 5.5

24 150 0.20 0.40 1.20 1.998 202 122 145 1148 0.46 0.68 3.9

25 150 0.20 0.40 0.80 2.189 160 100 114 1126 0.35 0.62 5.4

26 150 0.20 0.40 0.80 2.178 162 99 115 1126 0.34 0.61 5.3

27 150 0.20 0.40 0.80 2.175 171 99 120 1091 0.33 0.63 5.1

28 150 0.20 0.40 0.80 2.146 162 100 117 1108 0.39 0.68 4.7

29 150 0.20 0.40 0.80 2.143 172 104 119 1108 0.41 0.71 4.5

30 150 0.20 0.40 0.80 2.121 175 104 124 1091 0.42 0.73 4.4

83






Ex A B C D

R1 R2 R3 R4 R5 R6 R7 R8

1 90 0.15 0.20 0.40 2.916 125 27 85 1112 0.24 0.28 6.5

2 210 0.15 0.20 0.40 2.256 138 30 75 1334 0.32 0.35 6.0

3 90 0.25 0.20 0.40 3.208 173 43 99 1098 0.41 0.42 4.5

4 210 0.25 0.20 0.40 2.706 152 38 88 1640 0.62 0.55 2.5

5 90 0.15 0.60 0.40 3.996 227 91 161 1338 0.45 0.51 4.2

6 210 0.15 0.60 0.40 3.302 199 81 131 1790 0.73 0.62 1.3

7 90 0.25 0.60 0.40 4.754 250 118 192 1390 0.70 0.65 1.5

8 210 0.25 0.60 0.40 3.747 220 109 158 1976 0.81 0.92 0.8

9 90 0.15 0.20 1.20 2.607 285 70 147 1046 0.42 0.44 4.4

10 210 0.15 0.20 1.20 2.113 250 61 129 1406 0.61 0.67 2.5

11 90 0.25 0.20 1.20 3.334 295 93 173 1176 0.47 0.82 3.5

12 210 0.25 0.20 1.20 2.847 263 82 153 1680 0.65 0.93 1.5

13 90 0.15 0.60 1.20 3.261 422 197 280 1382 0.54 0.90 2.7

14 210 0.15 0.60 1.20 2.759 374 176 243 1948 0.71 0.98 1.1

15 90 0.25 0.60 1.20 3.923 443 256 339 1488 0.56 1.21 2.3

16 210 0.25 0.60 1.20 3.176 392 238 290 2160 0.82 1.1 0.6

17 90 0.20 0.40 0.80 3.278 332 145 216 1344 0.48 0.32 4.5

18 210 0.20 0.40 0.80 2.707 294 132 183 1776 0.53 0.41 3.8

19 150 0.15 0.40 0.80 2.988 310 114 173 1372 0.49 0.61 3.3

20 150 0.25 0.40 0.80 3.421 330 133 210 1584 0.61 1.16 2.1

21 150 0.20 0.20 0.80 2.353 185 48 110 1272 0.59 0.76 2.4

22 150 0.20 0.60 0.80 3.052 359 177 250 1608 0.74 0.82 1.2

23 150 0.20 0.40 0.40 2.999 180 65 135 1492 0.36 0.43 5.4

24 150 0.20 0.40 1.20 2.299 375 185 243 1512 0.54 0.76 3.1

25 150 0.20 0.40 0.80 2.633 310 118 182 1536 0.41 0.7 4.4

26 150 0.20 0.40 0.80 2.648 313 121 186 1536 0.41 0.71 4.3

27 150 0.20 0.40 0.80 2.825 320 127 194 1488 0.43 0.72 4.1

28 150 0.20 0.40 0.80 2.869 333 130 190 1512 0.46 0.77 3.7

29 150 0.20 0.40 0.80 2.773 332 132 194 1512 0.48 0.83 3.7

30 150 0.20 0.40 0.80 2.818 334 134 199 1488 0.49 0.83 3.6

Documents

EXPERIMENTAL WORK - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/8182/13/13_chapter 04.pdf · Hardness test Hardness test was carried out on Brinnell cum Rockwell Hardness