design of experiments.ppt
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About This Presentation
Experimental methods are widely used in industrial settings and research activities. In industrial settings, the main goal is to extract the maximum amount of unbiased information regarding the factors affecting production process form few observations, whereas in research, ANOVA techniques are used...
Slide Content
Design of Experiments
Jatinder kapoor
Professor
Mechanical Engineering Department
GNE, College ,Ludhiana
Selection of Significant Parameters for
Experimentation…..
Jatinder kapoor
Professor
Mechanical Engineering Department
GNE, College ,Ludhiana
Selection of Significant Parameters for
Experimentation…..
Design of experiments
•It is important to obtain maximum realistic information
with the minimum number of well designed experiments.
•An experimental program recognizes the major “factors”
that affect the outcome of the experiment.
•The factors may be identified by looking at all the
quantities that may affect the outcome of the experiment.
•The most important among these may be identified using:
–a few exploratory experiments or
–From past experience or
–based on some underlying theory or hypothesis.
This Selection Process is known as
Design of Experiments.
•It is important to obtain maximum realistic information
with the minimum number of well designed experiments.
•An experimental program recognizes the major “factors”
that affect the outcome of the experiment.
•The factors may be identified by looking at all the
quantities that may affect the outcome of the experiment.
•The most important among these may be identified using:
–a few exploratory experiments or
–From past experience or
–based on some underlying theory or hypothesis.
This Selection Process is known as
Design of Experiments.
Special Terminology : Design of Experiments
•Response variable
–Measured output value
•Factors
–Input variables that can be changed
•Levels
–Specific values of factors (inputs)
•Continuous or discrete
•Replication
–Completely re-run experiment with same input levels
–Used to determine impact of measurement error
•Interaction
–Effectof one input factor depends on levelof another input
factor
•Response variable
–Measured output value
•Factors
–Input variables that can be changed
•Levels
–Specific values of factors (inputs)
•Continuous or discrete
•Replication
–Completely re-run experiment with same input levels
–Used to determine impact of measurement error
•Interaction
–Effectof one input factor depends on levelof another input
factor
Design of Experiments (DOE)
–A statistics-based approach to design experiments
–A methodology to achieve a predictive knowledge of a
complex, multi-variable process with the fewest acceptable
trials.
–An optimization of the experimental process itself
–A statistics-based approach to design experiments
–A methodology to achieve a predictive knowledge of a
complex, multi-variable process with the fewest acceptable
trials.
–An optimization of the experimental process itself
Major Approaches to DOE
•Factorial Design
•Taguchi Method
•Response Surface Design
•Factorial Design
•Taguchi Method
•Response Surface Design
Factorial Design : Full factorial design
•A full factorial design of experiments consists of the following:
•Vary one factor at a time
•Perform experiments for all levels of all factors
•Hence perform a large number of experiments that are needed!
•All interactions are captured.
•Consider a simple design for the following case:
•Let the number of factors = k
•Let the number of levels for the i
th
factor = n
i
•The total number of experiments (N) that need to be performed is
K
i
i
nN
1
•A full factorial design of experiments consists of the following:
•Vary one factor at a time
•Perform experiments for all levels of all factors
•Hence perform a large number of experiments that are needed!
•All interactions are captured.
•Consider a simple design for the following case:
•Let the number of factors = k
•Let the number of levels for the i
th
factor = n
i
•The total number of experiments (N) that need to be performed is
K
i
i
nN
1
•Many factors/inputs/variables must be taken into consideration
when making a product especially a brand new one
•The Taguchi method is a structured approach for determining
the ”best” combination of inputs to produce a product or service
•Based on a Design of Experiments (DOE) methodology for
determining parameter levels
•DOE is an important tool for designing processes and products
•A method for quantitatively identifying the right inputs and
parameter levels for making a high quality product or service
•Taguchi approaches design from a robust design perspective
Taguchi Design of Experiments
when making a product especially a brand new one
•The Taguchi method is a structured approach for determining
the ”best” combination of inputs to produce a product or service
•Based on a Design of Experiments (DOE) methodology for
determining parameter levels
•DOE is an important tool for designing processes and products
•A method for quantitatively identifying the right inputs and
parameter levels for making a high quality product or service
•Taguchi approaches design from a robust design perspective
Taguchi Design of Experiments
Taguchi method
•Traditional Design of Experiments focused on how
different design factors affect the average result level
•In Taguchi’s DOE(robust design), variation is more
interesting to study than the average
•Robust design: An experimental method to achieve product
and process quality through designing in an insensitivity to
noise based on statistical principles.
•The Taguchi method is best used when there are an
intermediate number of variables (3 to 50), few
interactions between variables, and when only a few
variables contribute significantly.
•Traditional Design of Experiments focused on how
different design factors affect the average result level
•In Taguchi’s DOE(robust design), variation is more
interesting to study than the average
•Robust design: An experimental method to achieve product
and process quality through designing in an insensitivity to
noise based on statistical principles.
•The Taguchi method is best used when there are an
intermediate number of variables (3 to 50), few
interactions between variables, and when only a few
variables contribute significantly.
Taguchi Method
•Dr. Taguchi of Nippon Telephones and Telegraph
Company, Japan has developed a method based on "
ORTHOGONAL ARRAY " experiments.
•This gives much reduced " variance " for the
experiment with " optimum settings " of control
parameters.
•"Orthogonal Arrays" (OA) provide a set of well
balanced (minimum) experiments serve as objective
functions for optimization.
•Dr. Taguchi of Nippon Telephones and Telegraph
Company, Japan has developed a method based on "
ORTHOGONAL ARRAY " experiments.
•This gives much reduced " variance " for the
experiment with " optimum settings " of control
parameters.
•"Orthogonal Arrays" (OA) provide a set of well
balanced (minimum) experiments serve as objective
functions for optimization.
Experimentalmethodsarewidelyusedinindustrial
settingsandresearchactivities.Inindustrialsettings,the
maingoalistoextractthemaximumamountofunbiased
informationregardingthefactorsaffectingproduction
processformfewobservations,whereasinresearch,
ANOVAtechniquesareusedtorevealthereality.Drawing
inferencesfromtheexperimentalresultisanimportant
stepindesignprocessofproduct.Therefore,proper
planningofexperimentationisthepreconditionfor
accurateconclusiondrawnfromtheexperimentalfindings.
Designofexperimentispowerfulstatisticaltoolintroduced
byR.A.FisherinEnglandintheearly1920tostudythe
effectofdifferentparametersaffectingthemeanand
varianceofaprocessperformancecharacteristics
settingsandresearchactivities.Inindustrialsettings,the
maingoalistoextractthemaximumamountofunbiased
informationregardingthefactorsaffectingproduction
processformfewobservations,whereasinresearch,
ANOVAtechniquesareusedtorevealthereality.Drawing
inferencesfromtheexperimentalresultisanimportant
stepindesignprocessofproduct.Therefore,proper
planningofexperimentationisthepreconditionfor
accurateconclusiondrawnfromtheexperimentalfindings.
Designofexperimentispowerfulstatisticaltoolintroduced
byR.A.FisherinEnglandintheearly1920tostudythe
effectofdifferentparametersaffectingthemeanand
varianceofaprocessperformancecharacteristics
2
k
factorial design
•Used as a Preliminary Experimentation !!!
•Each of the k factors is assigned only two levels.
•The levels are usually High = 1 and Low = -1.
•Scheme is useful as a preliminary experimental program
before a more ambitious study is undertaken.
•The outcome of the 2
k
factorial experiment will help
identify the relative importance of factors and also will
offer some knowledge about the interaction effects.
k
factorial design
•Used as a Preliminary Experimentation !!!
•Each of the k factors is assigned only two levels.
•The levels are usually High = 1 and Low = -1.
•Scheme is useful as a preliminary experimental program
before a more ambitious study is undertaken.
•The outcome of the 2
k
factorial experiment will help
identify the relative importance of factors and also will
offer some knowledge about the interaction effects.
DOE -Factorial Designs -2
3
Trial A B C
1 Lo Lo Lo
2 Lo Lo Hi
3 Lo Hi Lo
4 Lo Hi Hi
5 Hi Lo Lo
6 Hi Lo Hi
7 Hi Hi Lo
8 Hi Hi Hi
3
Trial A B C
1 Lo Lo Lo
2 Lo Lo Hi
3 Lo Hi Lo
4 Lo Hi Hi
5 Hi Lo Lo
6 Hi Lo Hi
7 Hi Hi Lo
8 Hi Hi Hi
DOE -Factorial Designs -2
3
Trial A B C
1 -1 -1 -1
2 -1 -1 +1
3 -1 +1 -1
4 -1 +1 +1
5 +1 -1 -1
6 +1 -1 +1
7 +1 +1 -1
8 +1 +1 +1
3
Trial A B C
1 -1 -1 -1
2 -1 -1 +1
3 -1 +1 -1
4 -1 +1 +1
5 +1 -1 -1
6 +1 -1 +1
7 +1 +1 -1
8 +1 +1 +1
Output Matrix
•Let us represent the outcome of each experiment to be a
quantity y.
•Thus y
1will represent the outcome of experiment number
1 with all three factors having their “LOW” values,
•y
2will represent the outcome of the experiment number 2
with the factors A & B having the “Low” values and the
factor C having the “High” value and so on.
•Let us represent the outcome of each experiment to be a
quantity y.
•Thus y
1will represent the outcome of experiment number
1 with all three factors having their “LOW” values,
•y
2will represent the outcome of the experiment number 2
with the factors A & B having the “Low” values and the
factor C having the “High” value and so on.
The advantages of DOE are summarized as:
• Number of trail experiment are significantly reduced
• The important decision variables are easily identified
• Optimal setting of process parameters
• Experimental errors are significantly reduced
• Number of trail experiment are significantly reduced
• The important decision variables are easily identified
• Optimal setting of process parameters
• Experimental errors are significantly reduced
•A statistical / engineering methodology that aim at reducing
the performance “variation” of a system.
•The input variables are divided into two board categories.
•Control factor: the design parameters in product or process
design.
•Noise factor: factors whoes values are hard-to-control
during normal process or use conditions
Robust Design
the performance “variation” of a system.
•The input variables are divided into two board categories.
•Control factor: the design parameters in product or process
design.
•Noise factor: factors whoes values are hard-to-control
during normal process or use conditions
Robust Design
Taguchi Method : When to Select a ‘larger’ OA
to perform “Factorial Experiments”
•We always ‘think’ about ‘reducing’ the number of
experiments (to minimize the ‘resources’ –equipment,
materials, manpower and time)
•However, doing ALL / Factorial experiments is a good
idea if
–Conducting experiments is ‘cheap/quick’but
measurements are ‘expensive/take too long’
–The experimental facility will NOTbe available later to
conduct the ‘verification’ experiment
–We do NOTwish to conduct separateexperiments for
studying interactions between Factors
to perform “Factorial Experiments”
•We always ‘think’ about ‘reducing’ the number of
experiments (to minimize the ‘resources’ –equipment,
materials, manpower and time)
•However, doing ALL / Factorial experiments is a good
idea if
–Conducting experiments is ‘cheap/quick’but
measurements are ‘expensive/take too long’
–The experimental facility will NOTbe available later to
conduct the ‘verification’ experiment
–We do NOTwish to conduct separateexperiments for
studying interactions between Factors
Taguchi Method Design of Experiments
•The general steps involved in the Taguchi Method are as follows:
•1. Define the process objective, or more specifically, a target value
for a performance measure of the process.
•2. Determine the design parameters affecting the process.
•The number of levels that the parameters should be varied at must
be specified.
•3. Create orthogonal arrays for the parameter design indicating the
number of and conditions for each experiment.
•The selection of orthogonal arrays is based on the number of
parameters and the levels of variation for each parameter, and will
be expounded below.
•4. Conduct the experiments indicated in the completed array to
collect data on the effect on the performance measure.
•5. Complete data analysis to determine the effect of the different
parameters on the performance measure.
•The general steps involved in the Taguchi Method are as follows:
•1. Define the process objective, or more specifically, a target value
for a performance measure of the process.
•2. Determine the design parameters affecting the process.
•The number of levels that the parameters should be varied at must
be specified.
•3. Create orthogonal arrays for the parameter design indicating the
number of and conditions for each experiment.
•The selection of orthogonal arrays is based on the number of
parameters and the levels of variation for each parameter, and will
be expounded below.
•4. Conduct the experiments indicated in the completed array to
collect data on the effect on the performance measure.
•5. Complete data analysis to determine the effect of the different
parameters on the performance measure.
Taguchi's Orthogonal Arrays
•Taguchi's orthogonal arrays are highly fractional
orthogonal designs. These designs can be used to estimate
main effects using only a few experimental runs.
•Consider the L4 array shown in the next Figure. The L4
array is denoted as L4(2^3).
•L4 means the array requires 4 runs. 2^3 indicates that the
design estimates up to three main effects at 2 levels each.
The L4 array can be used to estimate three main effects
using four runs provided that the two factor and three
factor interactions can be ignored.
•Taguchi's orthogonal arrays are highly fractional
orthogonal designs. These designs can be used to estimate
main effects using only a few experimental runs.
•Consider the L4 array shown in the next Figure. The L4
array is denoted as L4(2^3).
•L4 means the array requires 4 runs. 2^3 indicates that the
design estimates up to three main effects at 2 levels each.
The L4 array can be used to estimate three main effects
using four runs provided that the two factor and three
factor interactions can be ignored.
Taguchi's Orthogonal Arrays
L4(2^3)
2
III
3-1
I = -ABC
L4(2^3)
2
III
3-1
I = -ABC
Taguchi’s Two Level Designs-Examples
L8 (2^7)
L4 (2^3)
L8 (2^7)
L4 (2^3)
Taguchi’s Three Level Designs-
Example
L9 (3^4)
Example
L9 (3^4)
The full factorial randomized block (ANOVA)
Source Degree of
freedom
Sun of
squares
Mean square (MS)F-ratio
A r-1 SS
A MS
A= SS
A/(r-1)F
A= MS
A/MS
E
B s-1 SS
B MS
B= SS
B/(s-1)F
B= MS
B/MS
E
C t-1 SS
C MS
C= SS
A/(t-1)F
C= MS
C/MS
E
AB (r-1) (s-1) SS
AB MS
AB= SS
A/(r-1)
(s-1)
F
AB= MS
AB/MS
E
BC (s-1) (t-1) SS
BC MS
BC= SS
A/(s-1)
(t-1)
F
BC= MS
AB/MS
E
AC (r-1) (t-1) SS
AC MS
AC= SS
A/(r-1)
(t-1)
F
AC= MS
Ac/MS
E
Blocks (p-1) (rs-1)
(st-1) (rt-1)
SS
bl MS = SS
bl/(p-1) F
A= MS
bl/MS
E
Error p-1 SS
E MS
E= SS
E/(rs-1)
(p-1) (st-1) (rt-1)
Total rstp-1 SS
T MS
A= SS
A/(r
A, B, C are factors having r, s and t their respective levels. L is the number of
blocks
Source Degree of
freedom
Sun of
squares
Mean square (MS)F-ratio
A r-1 SS
A MS
A= SS
A/(r-1)F
A= MS
A/MS
E
B s-1 SS
B MS
B= SS
B/(s-1)F
B= MS
B/MS
E
C t-1 SS
C MS
C= SS
A/(t-1)F
C= MS
C/MS
E
AB (r-1) (s-1) SS
AB MS
AB= SS
A/(r-1)
(s-1)
F
AB= MS
AB/MS
E
BC (s-1) (t-1) SS
BC MS
BC= SS
A/(s-1)
(t-1)
F
BC= MS
AB/MS
E
AC (r-1) (t-1) SS
AC MS
AC= SS
A/(r-1)
(t-1)
F
AC= MS
Ac/MS
E
Blocks (p-1) (rs-1)
(st-1) (rt-1)
SS
bl MS = SS
bl/(p-1) F
A= MS
bl/MS
E
Error p-1 SS
E MS
E= SS
E/(rs-1)
(p-1) (st-1) (rt-1)
Total rstp-1 SS
T MS
A= SS
A/(r
A, B, C are factors having r, s and t their respective levels. L is the number of
blocks
Analyzing Experimental Data
•To determine the effect each variable has on the output, the
signal-to-noise ratio, or the SN number, needs to be
calculated for each experiment conducted.
•yi is the mean value and si is the variance. yi is the value of
the performance characteristic for a given experiment.
•To determine the effect each variable has on the output, the
signal-to-noise ratio, or the SN number, needs to be
calculated for each experiment conducted.
•yi is the mean value and si is the variance. yi is the value of
the performance characteristic for a given experiment.
signal-to-noise ratio
TheS/Nratioprovidesameasureoftheimpactofnoise
factorsontheperformance.ThelargertheS/Nratio,the
morerobosttheproductisagainstthenoise.Threetypesof
theS/Nratiosareemployedinpracticedependinguponthe
experimentalobjectiveandthetypeofresponse.).The
signaltonoiseratios(S/N)intermsoflargerthebetter(LB),
smallerthebetter(SB)andnominalthebest(NB)are
calculatedbyusingthefollowingequations
LB:S/NRatio=-10log
10[(1/N)
*∑(1/Y
i
2
)]
SB:S/NRatio=-10log
10[(1/N)
*∑(Y
i
2
)]
NB:S/NRatio=-10log
10[Mean
2
/variance]
Where Y
iis the performance characteristic and N is the
number of observations for each trail.
TheS/Nratioprovidesameasureoftheimpactofnoise
factorsontheperformance.ThelargertheS/Nratio,the
morerobosttheproductisagainstthenoise.Threetypesof
theS/Nratiosareemployedinpracticedependinguponthe
experimentalobjectiveandthetypeofresponse.).The
signaltonoiseratios(S/N)intermsoflargerthebetter(LB),
smallerthebetter(SB)andnominalthebest(NB)are
calculatedbyusingthefollowingequations
LB:S/NRatio=-10log
10[(1/N)
*∑(1/Y
i
2
)]
SB:S/NRatio=-10log
10[(1/N)
*∑(Y
i
2
)]
NB:S/NRatio=-10log
10[Mean
2
/variance]
Where Y
iis the performance characteristic and N is the
number of observations for each trail.
Worked out Example
Control ParametersRange Designation Levels
L 1 L2 L3
Type of wire electrode- A Untreated
brass wire
Cryogenic treated
(-110
0
C) brass wire
Cryogenic treated
(-184
0
C) brass wire
Pulse width(μs) 0.4-1.2 B 0.4 0.8 1.2
Wire tension (daN)0.6-2.0 C 0.6 1.3 2.0
Fixed Parameters
Time between two pulses 10 μs
Servo reference voltage 35 V
Short pulse time 0.2 μs
Wire feed rate 8m/min
Size of wire 0.25mm
Thickness of workpiece 11 mm
Angle of cut Straight
Cutting voltage(V ) -80
Max feed rate 15mm/min
Ignition pulse current 8
Injection pressure 4bar
Response Characteristics
1.MRR
2.SR
3.WWR
Control ParametersRange Designation Levels
L 1 L2 L3
Type of wire electrode- A Untreated
brass wire
Cryogenic treated
(-110
0
C) brass wire
Cryogenic treated
(-184
0
C) brass wire
Pulse width(μs) 0.4-1.2 B 0.4 0.8 1.2
Wire tension (daN)0.6-2.0 C 0.6 1.3 2.0
Fixed Parameters
Time between two pulses 10 μs
Servo reference voltage 35 V
Short pulse time 0.2 μs
Wire feed rate 8m/min
Size of wire 0.25mm
Thickness of workpiece 11 mm
Angle of cut Straight
Cutting voltage(V ) -80
Max feed rate 15mm/min
Ignition pulse current 8
Injection pressure 4bar
Response Characteristics
1.MRR
2.SR
3.WWR
The experimental trail conditions for full factorial
Exp. No. Run Order A B C Response
1 12 1 1 1 Y
11 Y
12Y
13
2 15 1 1 2 --
3 10 1 1 3 --
4 2 1 2 1 --
5 13 1 2 2 --
6 22 1 2 3 --
7 11 1 3 1 --
8 25 1 3 2 --
9 9 1 3 3 --
10 1 2 1 1 --
11 26 2 1 2 --
12 21 2 1 3 --
13 14 2 2 1 --
14 4 2 2 2 --
15 8 2 2 3 --
16 18 2 3 1 --
17 19 2 3 2 --
18 27 2 3 3 --
19 24 3 1 1 --
20 5 3 1 2 --
21 23 3 1 3 --
22 20 3 2 1 --
23 7 3 2 2 --
24 3 3 2 3 --
25 16 3 3 1 --
26 6 3 3 2 --
27 17 3 3 3 Y
27 1 Y
27 2Y
27 3
A –Type of wire
B –Pulse width
C –Wire tension
Exp. No. Run Order A B C Response
1 12 1 1 1 Y
11 Y
12Y
13
2 15 1 1 2 --
3 10 1 1 3 --
4 2 1 2 1 --
5 13 1 2 2 --
6 22 1 2 3 --
7 11 1 3 1 --
8 25 1 3 2 --
9 9 1 3 3 --
10 1 2 1 1 --
11 26 2 1 2 --
12 21 2 1 3 --
13 14 2 2 1 --
14 4 2 2 2 --
15 8 2 2 3 --
16 18 2 3 1 --
17 19 2 3 2 --
18 27 2 3 3 --
19 24 3 1 1 --
20 5 3 1 2 --
21 23 3 1 3 --
22 20 3 2 1 --
23 7 3 2 2 --
24 3 3 2 3 --
25 16 3 3 1 --
26 6 3 3 2 --
27 17 3 3 3 Y
27 1 Y
27 2Y
27 3
A –Type of wire
B –Pulse width
C –Wire tension
DCTWEUTWE
60
50
40
30
1.20.80.4 16104
2.01.30.6
60
50
40
30
503520
Type of wire(A)
M
e
a
n
o
f
M
e
a
n
s
Pulse width (B) Time between two pulses (C)
Wire tension(D) Servo reference mean voltage(E)
Main Effects Plot for Means (MRR)
Data Means DCTWEUTWE
34
32
30
28
1.20.80.4 16104
2.01.30.6
34
32
30
28
503520
Type of wire(A)
M
e
a
n
o
f
S
N
r
a
t
io
s
Pulse width (B) Time between two pulses (C)
Wire tension(D) Servo reference mean voltage(E)
Main Effects Plot for SN ratios (MRR)
Data Means
Signal-to-noise: Larger is better
60
50
40
30
1.20.80.4 16104
2.01.30.6
60
50
40
30
503520
Type of wire(A)
M
e
a
n
o
f
M
e
a
n
s
Pulse width (B) Time between two pulses (C)
Wire tension(D) Servo reference mean voltage(E)
Main Effects Plot for Means (MRR)
Data Means DCTWEUTWE
34
32
30
28
1.20.80.4 16104
2.01.30.6
34
32
30
28
503520
Type of wire(A)
M
e
a
n
o
f
S
N
r
a
t
io
s
Pulse width (B) Time between two pulses (C)
Wire tension(D) Servo reference mean voltage(E)
Main Effects Plot for SN ratios (MRR)
Data Means
Signal-to-noise: Larger is better
1.20.80.4 6.02.01.3
50
35
20
50
35
20
Type of wire(A)
Pulse width(B)
Wire tension(C)
DCTWE
SCTWE
UTWE
wire(A)
Type of
0.4
0.8
1.2
width(B)
Pulse
Interaction Plot for MRR (mm3/min)
Data Means
50
35
20
50
35
20
Type of wire(A)
Pulse width(B)
Wire tension(C)
DCTWE
SCTWE
UTWE
wire(A)
Type of
0.4
0.8
1.2
width(B)
Pulse
Interaction Plot for MRR (mm3/min)
Data Means
Taguchi Method
Experimentation was designed to study the effect of process
parameters on response characteristics of WEDM with untreated
and cryogenic treated wire electrode. Taguchi parametric
methodology was adopted for the optimal setting of process
parameters. The experimental findings were validated with the
help of confirmation experiments. The parameters were grouped
into two groups and experiments were conducted by using
appropriate orthogonal array.
Experimentation was designed to study the effect of process
parameters on response characteristics of WEDM with untreated
and cryogenic treated wire electrode. Taguchi parametric
methodology was adopted for the optimal setting of process
parameters. The experimental findings were validated with the
help of confirmation experiments. The parameters were grouped
into two groups and experiments were conducted by using
appropriate orthogonal array.
Process parameters and their Values at Different
Levels
Parameters Designation Levels
*
L 1 L2 L3
Type of wire A Untreated
brass wire
electrode
Deep Cryogenic treated
(-184
0
C) brass wire electrode
-
Pulse Width(μs) B 0.4 0.8 1.2
Time between two
pulses (μs)
C 4 10 16
Wire Tension
(daN(Kg))
D 0.6 1.3 2.0
Servo Reference
Voltage (V)
E 20 35 50
*
L represents levels
Constant Parameters
Short pulse time 0.2 μs
Wire feed rate 8m/min
Size of wire 0.25mm
Thickness of workpiece 11 mm
Angle of cut Straight
Cutting voltage(V ) -80
Max feed rate 15mm/min
Ignition pulse current 8
Injection pressure 4bar
Response characteristics
MRR
SR
WWR
Levels
Parameters Designation Levels
*
L 1 L2 L3
Type of wire A Untreated
brass wire
electrode
Deep Cryogenic treated
(-184
0
C) brass wire electrode
-
Pulse Width(μs) B 0.4 0.8 1.2
Time between two
pulses (μs)
C 4 10 16
Wire Tension
(daN(Kg))
D 0.6 1.3 2.0
Servo Reference
Voltage (V)
E 20 35 50
*
L represents levels
Constant Parameters
Short pulse time 0.2 μs
Wire feed rate 8m/min
Size of wire 0.25mm
Thickness of workpiece 11 mm
Angle of cut Straight
Cutting voltage(V ) -80
Max feed rate 15mm/min
Ignition pulse current 8
Injection pressure 4bar
Response characteristics
MRR
SR
WWR
The L
18 (2
1
x3
7
) Orthogonal array design matrix
Exp.
No.
Run
Order
1 2 3 4 5 6 78 Response
A B C D E F GH R
1 R
2 R
3
1 4 1 1 1 1 1 1 1 1Y
11Y
12Y
13
2 17 1 1 2 2 2 2 2 2-- -- --
3 1 1 1 3 3 3 3 3 3-- -- --
4 13 1 2 1 1 2 2 3 3-- -- --
5 6 1 2 2 2 3 3 1 1-- -- --
6 15 1 2 3 3 1 1 2 2-- -- --
7 8 1 3 1 2 1 3 2 3-- -- --
8 12 1 3 2 3 2 1 3 1-- -- --
9 9 1 3 3 1 3 2 1 2-- -- --
10 11 2 1 1 3 3 2 2 1-- -- --
11 18 2 1 2 1 1 3 3 2-- -- --
12 14 2 1 3 2 2 1 1 3-- -- --
13 16 2 2 1 2 3 1 3 2-- -- --
14 2 2 2 2 3 1 2 1 3-- -- --
15 7 2 2 3 1 2 3 2 1-- -- --
16 5 2 3 1 3 2 3 1 2-- -- --
17 3 2 3 2 1 3 1 2 3-- -- --
18 10 2 3 3 2 1 2 3 1Y
18 1Y
18 2Y
18 3
Note: The 1, 2,3 are the levels of the parameters. R
1, R
2, R
3 represent repetitions. Y
ijare the
measured values of the response characteristic.
A.Type of wire , B-Pulse width, C –Time between two pulses, D-Wire tension, E-Servo
reference mean voltage
Three columns(6, 7, 8) are ignored because only five parameters have been taken for the study
18 (2
1
x3
7
) Orthogonal array design matrix
Exp.
No.
Run
Order
1 2 3 4 5 6 78 Response
A B C D E F GH R
1 R
2 R
3
1 4 1 1 1 1 1 1 1 1Y
11Y
12Y
13
2 17 1 1 2 2 2 2 2 2-- -- --
3 1 1 1 3 3 3 3 3 3-- -- --
4 13 1 2 1 1 2 2 3 3-- -- --
5 6 1 2 2 2 3 3 1 1-- -- --
6 15 1 2 3 3 1 1 2 2-- -- --
7 8 1 3 1 2 1 3 2 3-- -- --
8 12 1 3 2 3 2 1 3 1-- -- --
9 9 1 3 3 1 3 2 1 2-- -- --
10 11 2 1 1 3 3 2 2 1-- -- --
11 18 2 1 2 1 1 3 3 2-- -- --
12 14 2 1 3 2 2 1 1 3-- -- --
13 16 2 2 1 2 3 1 3 2-- -- --
14 2 2 2 2 3 1 2 1 3-- -- --
15 7 2 2 3 1 2 3 2 1-- -- --
16 5 2 3 1 3 2 3 1 2-- -- --
17 3 2 3 2 1 3 1 2 3-- -- --
18 10 2 3 3 2 1 2 3 1Y
18 1Y
18 2Y
18 3
Note: The 1, 2,3 are the levels of the parameters. R
1, R
2, R
3 represent repetitions. Y
ijare the
measured values of the response characteristic.
A.Type of wire , B-Pulse width, C –Time between two pulses, D-Wire tension, E-Servo
reference mean voltage
Three columns(6, 7, 8) are ignored because only five parameters have been taken for the study
DCTWEUTWE
60
50
40
30
1.20.80.4 16104
2.01.30.6
60
50
40
30
503520
Type of wire(A)
M
e
a
n
o
f
M
e
a
n
s
Pulse width (B) Time between two pulses (C)
Wire tension(D) Servo reference mean voltage(E)
Main Effects Plot for Means (MRR)
Data Means DCTWEUTWE
34
32
30
28
1.20.80.4 16104
2.01.30.6
34
32
30
28
503520
Type of wire(A)
M
e
a
n
o
f
S
N
r
a
t
io
s
Pulse width (B) Time between two pulses (C)
Wire tension(D) Servo reference mean voltage(E)
Main Effects Plot for SN ratios (MRR)
Data Means
Signal-to-noise: Larger is better
60
50
40
30
1.20.80.4 16104
2.01.30.6
60
50
40
30
503520
Type of wire(A)
M
e
a
n
o
f
M
e
a
n
s
Pulse width (B) Time between two pulses (C)
Wire tension(D) Servo reference mean voltage(E)
Main Effects Plot for Means (MRR)
Data Means DCTWEUTWE
34
32
30
28
1.20.80.4 16104
2.01.30.6
34
32
30
28
503520
Type of wire(A)
M
e
a
n
o
f
S
N
r
a
t
io
s
Pulse width (B) Time between two pulses (C)
Wire tension(D) Servo reference mean voltage(E)
Main Effects Plot for SN ratios (MRR)
Data Means
Signal-to-noise: Larger is better
SourceDF Seq SSAdj SSAdj MSF P
A 1 293.30 293.30 293.30 19.79 0.004*
B 2 2912.29 2912.29 1456.15 98.26 0.000*
C 2 459.17 459.17 229.58 15.49 0.004*
D 2 156.88 269.51 134.75 9.09 0.015*
E 2 16.44 40.09 20.04 1.35 0.327
A*C 2 156.56 156.56 78.28 5.28 0.048*
Residual
Error
6 88.92 88.92 14.82
Total 17 4083.56
Type of wire, B-Pulse width, C-Time between two pulses,
D-wire tension, E-Servo reference mean voltage
*-significant at 95% confidence level
SourceDF Seq SSAdjSS Adj MSF P
A 1 13.438 13.438 13.438 15.89 0.007*
B 2 180.577 180.577 90.2884 106.76 0.000*
C 2 37.860 37.860 18.9298 22.38 0.002*
D 2 12.720 33.579 16.7895 19.85 0.002*
E 2 1.321 17.191 8.5954 10.16 0.012*
A*C 2 22.669 22.669 11.3343 13.40 0.006*
Residual
Error
6 5.074 5.074 0.8457
Total 17 273.658
Type of wire, B-Pulse width, C-Time between two pulses,
D-wire tension, E-Servo reference mean voltage
*-significant at 95% confidence level
A 1 293.30 293.30 293.30 19.79 0.004*
B 2 2912.29 2912.29 1456.15 98.26 0.000*
C 2 459.17 459.17 229.58 15.49 0.004*
D 2 156.88 269.51 134.75 9.09 0.015*
E 2 16.44 40.09 20.04 1.35 0.327
A*C 2 156.56 156.56 78.28 5.28 0.048*
Residual
Error
6 88.92 88.92 14.82
Total 17 4083.56
Type of wire, B-Pulse width, C-Time between two pulses,
D-wire tension, E-Servo reference mean voltage
*-significant at 95% confidence level
SourceDF Seq SSAdjSS Adj MSF P
A 1 13.438 13.438 13.438 15.89 0.007*
B 2 180.577 180.577 90.2884 106.76 0.000*
C 2 37.860 37.860 18.9298 22.38 0.002*
D 2 12.720 33.579 16.7895 19.85 0.002*
E 2 1.321 17.191 8.5954 10.16 0.012*
A*C 2 22.669 22.669 11.3343 13.40 0.006*
Residual
Error
6 5.074 5.074 0.8457
Total 17 273.658
Type of wire, B-Pulse width, C-Time between two pulses,
D-wire tension, E-Servo reference mean voltage
*-significant at 95% confidence level
ESTIMATION OF OPTIMUM RESPONSE
CHARACTERISTICS
The significant process parameters affecting the MRR and their optimal levels are:
Significant parameters: A, B, C, D
Optimal levels; A2, B3, C1, D1, E1
= 47.83 The average value of MRR (From Table C1, Appendix C) at:
2
nd
Level of type of wire (A2)
3
rd
Level of pulse duration (B3) = 55.67
1
st
Level of time between two pulses(C1) = 47.74
1
st
Level of wire tension (D1) = 46.98
The overall mean of MRR (Ť
MMR) = 43.79
The predicted optimal value of η
MMRhas been calculated as:
η
MMR = A2+B3+C1+D1-3 Ť
MMR = 66.85
CHARACTERISTICS
The significant process parameters affecting the MRR and their optimal levels are:
Significant parameters: A, B, C, D
Optimal levels; A2, B3, C1, D1, E1
= 47.83 The average value of MRR (From Table C1, Appendix C) at:
2
nd
Level of type of wire (A2)
3
rd
Level of pulse duration (B3) = 55.67
1
st
Level of time between two pulses(C1) = 47.74
1
st
Level of wire tension (D1) = 46.98
The overall mean of MRR (Ť
MMR) = 43.79
The predicted optimal value of η
MMRhas been calculated as:
η
MMR = A2+B3+C1+D1-3 Ť
MMR = 66.85
•The 95% confidence intervals for the mean of the population (CI
POPand CI
CE)
and three confirmation experiments have been calculated as
•N= 18x3= 54(treatment = 18, R (repetitions) = 3); f
e(Error degree of freedom)
= (17-9)= 8 V
e(Error variance) = 13.17
•F
0.05 (1, 8) = 5.32 (Tabulated F value)
•
POPand CI
CE)
and three confirmation experiments have been calculated as
•N= 18x3= 54(treatment = 18, R (repetitions) = 3); f
e(Error degree of freedom)
= (17-9)= 8 V
e(Error variance) = 13.17
•F
0.05 (1, 8) = 5.32 (Tabulated F value)
•
Thanks…..
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