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# Chapter-4 obtain information about the behavior of a

CHAPTER-4EXPERIMENTAL DESIGN4. 1 INTRODUCTIONToinvestigate the tribological behavior of     metalmatrix composites based on Taguchi method and Grey Relation Analysis (GRA) wereused to investigate the influence of control factor and optimal combination ofthe testing parameter was also determined. Furthermore, the analysis ofvariance (ANOVA) is employed to determine the most significant control factorand their interactions.  4. 2 TAGUCHI METHODAlarge number of experiments have to be carried out when the no of the processparameter increases. To solve the problem, the Taguchi method used a specialdesign of orthogonal arrays that helps to study the entire parameter space withonly a small no of experiments. Taguchi’s techniques consist of an experimentalplan to obtain information about the behavior of a process.

The treatment ofexperimental result in this work is based on ANOVA. The experimental plan wasset by a technique based on the Taguchi techniques, cornering differentvariables at different levels, like load, sliding speed, sliding distance, percentage of reinforcement and particle size of the reinforcement. 4. 3 ANALYSIS OF VARIANCEANOVAwas first described by Sir Ronald Fisher a British Statistician. Analysis ofvariance is a method of partitioning variability into identifiable source ofvariation and the associated degrees of freedom in experiment.

The F-test issimply a ratio of sample variances. Comparing the F-ratio of a source with thetabulated F-ratio is called the F-test.  Whenanalysis of variance has been performed on a set of data and respective sums ofsquares have been calculated, it is possible to use this information todistribute the correct sums of squares to the appropriate factors.

Comparingthis value with the total sum of square gives the percent of contribution ofeach factor. The percent contribution due to error provides an estimate of theadequacy of the experiment. Since ‘ error’ refers to unknown and that cannot becontrolled factors, the percent contribution due to error suggests that if thesufficiency due to error is low (15% or less), then it can be assumed that noimportant factors have been omitted from the experiment. 4. 4 GREY RELATIONAL ANALYSIS (GRA)Optimizationsof multiple performance characteristics like wear rate, specific wear rate andcoefficient of friction is much more complicated than single performance characteristicslike only wear loss.  Taguchi methodcoupled with grey relational analysis was used to solve the multiple performancescharacteristics in tribological area. Grey theory forwarded by Prof.

DengJulong from China (Deng 1982 and 1989) was a theory and the method applicablewas the study of unascertained problems with few a data but poor information. Grey theory works on unascertained but partially known as well as unknown informationby drawing out variable information by producing and developing the partiallyknown information. In this theory ‘ Black’ is to represent unknown informationand ‘ White’ is for known information , besides grey is for that informationthat is partially known and partially unknown and the producer for greyrelational analysis as follows. 4. 4. 1 Data Pre-processingAccordingto Grey relational analysis, the data pre-processing means transforming oforiginal sequence into comparable sequence. During data pre-processing theexperimental results (wear rate, specific wear rate and coefficient offriction) are normalized in the range between two and one.

Grey RelationalAnalysis is depends on the quality characteristics of a data sequence.  Variousmethods of data pre-processing are available (Tosun 2006). For higher thebetter characteristic, the original sequence is normalized as follows:                   – (4. 1)                                Incase of lower-the-better characteristic, the original sequence is normalized asfollows:                               – (4. 2)Forinstance, for nominal-the-better characteristic, the original sequence isnormalized as follows:        – (4.

3)Or, the values of original sequence are divided by the first value of the sequence:       – (4. 4)Wherei= 1,…, m; k= 1,…n. m is the no of experimental data items and n is the no ofparameters.   denotes the original sequence,  the sequence after the data pre-processing, max  the largest value of  , min  the smallest value of  and  isthe preferred value. 4.

4. 2 Grey Relational Coefficient andGrey Relational GradeAfterpre-processing, the grey relation coefficient  for the  performance characteristics in the  experiment can be calculated as:        – (4. 5)  Whereas,  isthe deviation sequence of the reference sequence and the comparabilitysequence.                        0 ;     ;                                                                                                                 denotes both the reference sequence andguishing coefficient so,  ? is taken as0. 5. After the grey relational coefficient is calculation, the average value ofthe grey relational coefficient is taken grey relational grade. Therefore, thegrey relational grade is defined as follows:                                            – (4.

6)Thegrey relational grade  represents the level of correlation betweenthe reference sequence and the comparability sequence, in the case of highergrey relational grade the corresponding experimental result is closer to theideally normalized value.  4. 5 METHODOLOGY FOR STUDY THE DRY SLIDINGWEAR BEHAVIOUR OF AMMCsTheselection of independent variables for dry sliding wear of the composites canbe attempted based on an understanding of the process well as from theavailable literature. Again, from the preliminary investigation it was thoughtthat three independent variables, load, sliding speed and sliding distance ofsilicon carbide (SiC) as well as alumina ( ) in the composite material, couldinfluence the magnitude of dry sliding. Applied load (L), sliding speed (S) andsliding distance (D) predominately govern the tribological parameter like wearrate, specific wear rate and coefficient of friction. To study the effect offactors interactions, Taguchi’s parameter design approach isemployed for modelling and analysing the influence of control factors onperformance output. The level of these factors chosen for the experimentationis given in the Table 4. 1.

The response variables to be studied were thefriction coefficient and the wear rate. The experimental plan consisted of 9tests as given in Table 4. 2. The chosen array was the L9, with 9 rows inagreement to the number of tests (8 degrees of freedom) and at three levels. Table 4.

1 design factors along andtheir 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 testparameters 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 L9orthogonal 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  OnL9 orthogonal array with design factors are assigned is shown in Table 4.

2. Theresponse variables are selected for this study is wear rate and coefficient offriction of composites. Thesliding experiments were conducted in the room temperature in a pin-on-discwear testing machine. The test parameters are listed in table 4. 3. The weartest on composite specimen were carried out under dry sliding condition withdifferent applied load of 10 N, 20 N and 30 N for a sliding distance up to 200m at a constant sliding speed of 2m/s for all sample. The test duration was 20minute at a constant disk speed of 764 rpm for all tests. Inthis study silicon carbide particulate (SiCp) was reinforced in differentweight 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 DRYSLIDING WAER BEHAVIOUR OF HYBRID MMCsThefollowing parameters are considered for wear performances of hybrid MMCs areapplied load, sliding speed and sliding distance. Details of the design factorsand their levels shown in table 4. 4. Table 4. 4 design factors along withtheir 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  Theexperimental plan consisted of 27 tests as given in table 4. 5 . The chosen arraywas 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).

Eachvariable and the corresponding interactions were assigned to a column definedby 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 slidingdistance(D), and the remaining column were assigned to their interactions. Theresults obtained from tribological tests allowed the evaluation of the load, sliding speed and sliding distance on the friction and wear behaviour of hybridcomposites.   Table 4.

5 Standard L27 orthogonalarray 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. 8SUMMARYWearprocesses in composites are complex phenomena involving a number of processparameters and it is essential to understand how the wear characteristics ofthe composites are affected by these parameters. Selecting the correctoperating conditions is always a major concern as traditional experiment designwould require many experimental runs to achieve satisfactory results. In anyprocess, the desired testing parameters are either determined based on theexperience or by use of a data books.

However, it does not provide optimaltesting parameters for a particular situation. An approach based on design ofExperiments (DOE) technique was adopted to obtain maximum possible informationwith minimum number of experiments. Grey relational analysis was used to obtainoptimum conditions for wear testing. ANOVA was used to obtain the significantparameters influencing the wear behaviour of metal matrix composites.

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