CHAPTER-4 ANOVA was first described by Sir Ronald

 

 

CHAPTER-4

EXPERIMENTAL DESIGN

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4.1 INTRODUCTION

To
investigate the tribological behavior of     metal
matrix composites based on Taguchi method and Grey Relation Analysis (GRA) were
used to investigate the influence of control factor and optimal combination of
the testing parameter was also determined. Furthermore, the analysis of
variance (ANOVA) is employed to determine the most significant control factor
and their interactions. 

4.2 TAGUCHI METHOD

A
large number of experiments have to be carried out when the no of the process
parameter increases. To solve the problem, the Taguchi method used a special
design of orthogonal arrays that helps to study the entire parameter space with
only a small no of experiments. Taguchi’s techniques consist of an experimental
plan to obtain information about the behavior of a process. The treatment of
experimental result in this work is based on ANOVA. The experimental plan was
set by a technique based on the Taguchi techniques, cornering different
variables at different levels, like load, sliding speed, sliding distance,
percentage of reinforcement and particle size of the reinforcement.

4.3 ANALYSIS OF VARIANCE

ANOVA
was first described by Sir Ronald Fisher a British Statistician. Analysis of
variance is a method of partitioning variability into identifiable source of
variation and the associated degrees of freedom in experiment. The F-test is
simply a ratio of sample variances. Comparing the F-ratio of a source with the
tabulated F-ratio is called the F-test.

 

When
analysis of variance has been performed on a set of data and respective sums of
squares have been calculated, it is possible to use this information to
distribute the correct sums of squares to the appropriate factors. Comparing
this value with the total sum of square gives the percent of contribution of
each factor. The percent contribution due to error provides an estimate of the
adequacy of the experiment. Since ‘error’ refers to unknown and that cannot be
controlled factors, the percent contribution due to error suggests that if the
sufficiency due to error is low (15% or less), then it can be assumed that no
important factors have been omitted from the experiment.

4.4 GREY RELATIONAL ANALYSIS (GRA)

Optimizations
of multiple performance characteristics like wear rate, specific wear rate and
coefficient of friction is much more complicated than single performance characteristics
like only wear loss.  Taguchi method
coupled with grey relational analysis was used to solve the multiple performances
characteristics in tribological area. Grey theory forwarded by Prof. Deng
Julong from China (Deng 1982 and 1989) was a theory and the method applicable
was the study of unascertained problems with few a data but poor information.
Grey theory works on unascertained but partially known as well as unknown information
by drawing out variable information by producing and developing the partially
known information. In this theory ‘Black’ is to represent unknown information
and ‘White’ is for known information , besides grey is for that information
that is partially known and partially unknown and the producer for grey
relational analysis as follows.

4.4.1 Data Pre-processing

According
to Grey relational analysis, the data pre-processing means transforming of
original sequence into comparable sequence. During data pre-processing the
experimental results (wear rate, specific wear rate and coefficient of
friction) are normalized in the range between two and one. Grey Relational
Analysis is depends on the quality characteristics of a data sequence.

 

Various
methods of data pre-processing are available (Tosun 2006). For higher the
better characteristic, the original sequence is normalized as follows:         

   

     
– (4.1)                               

In
case of lower-the-better characteristic, the original sequence is normalized as
follows:

                         

     
– (4.2)

For
instance, for nominal-the-better characteristic, the original sequence is
normalized as follows:

 

      – (4.3)

Or,
the values of original sequence are divided by the first value of the sequence:

 

     
– (4.4)

Where
i=1,…,m; k=1,…n. m is the no of experimental data items and n is the no of
parameters. 

 denotes the original sequence,

 the sequence after the data pre-processing,
max

 the largest value of

 ,
min

 the smallest value of

 and

 is
the preferred value.

4.4.2 Grey Relational Coefficient and
Grey Relational Grade

After
pre-processing, the grey relation coefficient

 for the

 performance characteristics in the

 experiment can be calculated as:

 

      
– (4.5)

 

 

Whereas,

 is
the deviation sequence of the reference sequence and the comparability
sequence.

                        0

;

 

  

;

                                        

 

                         

  

                                        

 denotes both the reference sequence and
guishing coefficient so,  ? is taken as
0.5. After the grey relational coefficient is calculation, the average value of
the grey relational coefficient is taken grey relational grade. Therefore, the
grey relational grade is defined as follows:

                                      

     
– (4.6)

The
grey relational grade

 represents the level of correlation between
the reference sequence and the comparability sequence, in the case of higher
grey relational grade the corresponding experimental result is closer to the
ideally normalized value.

 

4.5 METHODOLOGY FOR STUDY THE DRY SLIDING
WEAR BEHAVIOUR OF AMMCs

The
selection of independent variables for dry sliding wear of the composites can
be attempted based on an understanding of the process well as from the
available literature. Again, from the preliminary investigation it was thought
that three independent variables, load, sliding speed and sliding distance of
silicon carbide (SiC) as well as alumina (

) in the composite material, could
influence the magnitude of dry sliding. Applied load (L), sliding speed (S) and
sliding distance (D) predominately govern the tribological parameter like wear
rate, specific wear rate and coefficient of friction. To study the effect of
factors interactions, Taguchi’s parameter design approach is
employed for modelling and analysing the influence of control factors on
performance output. The level of these factors chosen for the experimentation
is given in the Table 4.1. The response variables to be studied were the
friction coefficient and the wear rate. The experimental plan consisted of 9
tests as given in Table 4.2. The chosen array was the L9, with 9 rows in
agreement to the number of tests (8 degrees of freedom) and at three levels.

Table 4.1 design factors along and
their levels for dry sliding wear of Aluminium MMCs

Level
 

Factors

Applied load, L (N)

Sliding speed, S (m/s)

Sliding distance, D (m)

1

10

2

1000

2

20

3

1750

3

30

4

2500

 

Table 4.2 Dry sliding wear test
parameters

Parameters

Values

Applied load

10, 20 and 30

Sliding distance

Up to 2000 m

Sliding speed

2 m/s

Disk speed

700-800 rpm

Test duration

20-25 min.

Temperature

Room temp.

Surrounding Atmosphere

Laboratory air

 

 

Table 4.3 Experimental layout of L9
orthogonal array

Expt. No.

Factors

L

S

D

1

1

1

1

2

1

2

2

3

1

3

3

4

2

1

2

5

2

2

3

6

2

3

1

7

3

1

3

8

3

2

1

9

3

3

2

 

On
L9 orthogonal array with design factors are assigned is shown in Table 4.2. The
response variables are selected for this study is wear rate and coefficient of
friction of composites.

The
sliding experiments were conducted in the room temperature in a pin-on-disc
wear testing machine. The test parameters are listed in table 4.3. The wear
test on composite specimen were carried out under dry sliding condition with
different applied load of 10 N, 20 N and 30 N for a sliding distance up to 200
m at a constant sliding speed of 2m/s for all sample. The test duration was 20
minute at a constant disk speed of 764 rpm for all tests.

In
this study silicon carbide particulate (SiCp) was reinforced in different
weight percentage (5%, 10%, 15%, 20%, 25%, 30%, 35% & 40%) and mesh size
(150 and 600) in Al6061 metal matrix composites.

 

 

 

4.6 METHODOLOGY FOR STUDY THE DRY
SLIDING WAER BEHAVIOUR OF HYBRID MMCs

The
following parameters are considered for wear performances of hybrid MMCs are
applied load, sliding speed and sliding distance. Details of the design factors
and their levels shown in table 4.4.

Table 4.4 design factors along with
their levels for dry sliding wear of Aluminium Hybrid MMCs

Level
 

Factors

Applied load, L (N)

Sliding speed, S (m/s)

Sliding distance, D (m)

1

25

2.0

1000

2

30

2.25

1500

3

35

2.50

2000

 

The
experimental plan consisted of 27 tests as given in table 4.5 .The chosen array
was the L27 (313), with 27 rows in agreement to the number of tests
(26 degrees of freedom) and 13 columns at three levels (Ross 1988).

Each
variable and the corresponding interactions were assigned to a column defined
by Taguchi’s method, the first Column being assigned to the applied load (L)
and the second column to sliding speed(S), the fifth column to the sliding
distance(D), and the remaining column 
were assigned to their interactions.

The
results obtained from tribological tests allowed the evaluation of the load,
sliding speed and sliding distance on the friction and wear behaviour of hybrid
composites.

 

 

 

Table 4.5 Standard L27 orthogonal
array

Expt.
No.

Factors

1

2

3

4

5

6

7

8

9

10

11

12

13

(L)

(S)

(L×S)

(L×S)

(D)

(L×D)

(L×D)

(S×D)

(S×D)

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

1

1

1

1

2

2

2

2

2

2

2

2

2

3

1

1

1

1

3

3

3

3

3

3

3

3

3

4

1

2

2

2

1

1

1

2

2

2

3

3

3

5

1

2

2

2

2

2

2

3

3

3

1

1

1

6

1

2

2

2

3

3

3

1

1

1

2

2

2

7

1

3

3

3

1

1

1

3

3

3

2

2

2

8

1

3

3

3

2

2

2

1

1

1

3

3

3

9

1

3

3

3

3

3

3

2

2

2

1

1

1

10

2

1

2

3

1

2

3

1

2

3

1

2

3

11

2

1

2

3

2

3

1

2

3

1

2

3

1

12

2

1

2

3

3

1

2

3

1

2

3

1

2

13

2

2

3

1

1

2

3

2

3

1

3

1

2

14

2

2

3

1

2

3

1

3

1

2

1

2

3

15

2

2

3

1

3

1

2

1

2

3

2

3

1

16

2

3

1

2

1

2

3

3

1

2

2

3

1

17

2

3

1

2

2

3

1

1

2

3

3

1

2

18

2

3

1

2

3

1

2

2

3

1

1

2

3

19

3

1

3

2

1

3

2

1

3

2

1

3

2

20

3

1

3

2

2

1

3

2

1

3

2

1

3

21

3

1

3

2

3

2

1

3

2

1

3

2

1

22

3

2

1

3

1

3

2

2

1

3

3

2

1

23

3

2

1

3

2

1

3

3

2

1

1

3

2

24

3

2

1

3

3

2

1

1

3

2

2

1

3

25

3

3

2

1

1

3

2

3

2

1

2

1

3

26

3

3

2

1

2

1

3

1

3

2

3

2

1

27

3

3

2

1

3

2

1

2

1

3

1

3

2

 

 

 

 

 

 

4.8
SUMMARY

Wear
processes in composites are complex phenomena involving a number of process
parameters and it is essential to understand how the wear characteristics of
the composites are affected by these parameters. Selecting the correct
operating conditions is always a major concern as traditional experiment design
would require many experimental runs to achieve satisfactory results. In any
process, the desired testing parameters are either determined based on the
experience or by use of a data books. However, it does not provide optimal
testing parameters for a particular situation. An approach based on design of
Experiments (DOE) technique was adopted to obtain maximum possible information
with minimum number of experiments. Grey relational analysis was used to obtain
optimum conditions for wear testing. ANOVA was used to obtain the significant
parameters influencing the wear behaviour of metal matrix composites.

 

 

 

 

 

 

 

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