# CHAPTER-4 ANOVA was first described by Sir Ronald

CHAPTER-4

EXPERIMENTAL DESIGN

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.