
International Journal of ChemTech Research CODEN (USA): IJCRGG ISSN: 09744290 Vol.8, No.12 pp 292303, 2015

Analysis in Drilling of Al6061/20%SiCp Composites using Grey Taguchi based TOPSIS (GTTOPSIS)
H.Ravikumar, P.L.Arun, S.Thileepan
Department of Mechanical Engineering, Saveetha Engineering College,
Chennai602105, Tamilnadu, India
Abstract: Drilling is an important metal removal process for the final fabrication stage particularly in cases of components joined by mechanical fasteners. The selection of drilling parameters like drill bit speed, feed and the cutting point angle is vital, while drilling holes in ceramic based composites. The objective of research work is to perform drilling on Al6061/20%SiCp compositeand observe the responses like surface finish and drilling induced thrust force. Taguchi’s L9orthogonal arrayis used to conduct the machining trials and a new integrated approach of the grey Taguchi based technique for order performance by similarity to ideal solution (GTTOPSIS) is disclosed to predict the optimal drilling conditions. The confirmation experiment is conducted at the best input setting identified by the proposed algorithm for demonstrating the accuracy of the approach.Feed rate is identified as the prime factor affecting the quality of drilled holes.
Keywords: Al/SiCp composite;Optimization; Drilling; Grey relational analysis;TOPSIS; Taguchi; Surface finish.
1 Introduction
Aluminium based composites find wide applications in the aerospace and automotive partsand particularly those reinforced with ceramic particles offer many advantages, exhibitingan isotropic mechanical behaviour. The growing industrial application demands a structured study of their drilling characteristics, as it is an important metal removal process for the final fabrication stage prior to application. However the presence of a secondary ceramic phase like silicon carbide increases the difficulty in machining,causing an excessive tool wear [1]. Wide spread applications of these composites are practically impossible without solution to the drilling problems. Hence a drilling database with optimal input parameters becomes essential to find a solution to multi criteria decision making (MCDM) problem involving responses like tool wear, cutting forces and surface finish.
While turning Al/SiC composites tool wear was observed to be higher at the elevated cutting speed and feed rate [2]. The effect of various input parameters could be clearly seen in the quality of machined surfaces [3]. Taguchi’s optimization approach was used to obtain the optimal parameters for better quality characteristics in different manufacturing processes [4,5]. However the method was effective only in single response optimization,while a practical situation demands simultaneous optimization of multiple responses. An approach based on Taguchi design and ANN was used to form a model. It was further optimized using genetic algorithm in machining of Al/SiC composites [6]. During the drilling of aluminium based composites,carbide tipped drills were observed to show acceptable levels of drill forces and hole quality in dry conditions. It was found that the feed rate and cutting point angle play an important role in affecting the responses. It was also found that the
HSS tools are not so effective in handling aluminium based composites as the tool wear was found to be more, along with poor finish of the machined surfaces [7, 8]. Taguchi based simulated annealing could be used for parameter design to achieve better responses [9].
A deterministic decision making approach adopted to study the drilling operations on the CNC machines had proved that a global solution was possible with a clearly defined approach [10]. The response surface methodology (RSM) based on grey theory was used tominimize the surface roughness in nontraditional cutting processes,but it was observed that the method losses its power in irregular regions and requires tedious computational efforts as well [11, 12]. A hybrid model of artificial neural networksimulated annealing (ANNSA) and artificial neural networkgenetic algorithm (ANNGA) could predict as well as optimize the machining characteristics. However training of back propagation network was found to be difficult and it was also observed that GA cannot scale well with complexity [13, 14].
Hence many methods were suggested for multi response optimization including grey relational analysis (GRA), principal component analysis (PCA), data envelopment analysis and neural networks [15]. Technique for order performance by similarity to ideal solution(TOPSIS) was used for ranking the responses with respect to several criteria parameters and was found to be effective in multi response optimization [16, 17]. Itwas a MCDM technique with fewest rank reversals, which can be successfully applied to solve selection problems with a finite number of options. Its intuitive nature allows easy understanding and implementation [18]. GRA was applied for optimizing the input parameters in a pure format or in an integrated format with other techniques and was found to improve the quality characteristics significantly [19, 20]. A hybrid approach for optimization using GRA and PCA was found to take the advantages of the techniques adopted and could predict an optimal solution [21].Taguchi’s experimental design and further analysis using desirability method or RSM was observed to be economical because of a reduced number of experimentations [2224].
From the available literature, it was understood that not enough work has been done on decision making associated with the drilling of composites. Hence the present work is focussed towards developing a new methodology (GTTOPSIS), which combines the merits of Grey Taguchi and TOPSIS to identify the optimal drilling condition for the Al/SiCp composites.
2 Experimental Design and Observation
Table 1 Drillingparameters and their levels
Symbol 
Input Parameters 
unit 
Level 1 
Level 2 
Level 3 
A 
Feed rate 
mm/rev 
0.12 
0.16 
0.20 
B 
Spindle speed 
rpm 
900 
1120 
1330 
C

Cutting Point angle

deg 
90

118

135

Table 2 L9 array showing the combination of process parameters and the responses obtained
Trial 
Parameters and their levels 
Responses 

A 
B 
C 
Ra (μm) 
FT(N) 

1 
1 
1 
1 
2.42 
281.31 
2 
1 
2 
2 
2.12 
129.33 
3 
1 
3 
3 
1.79 
182.11 
4 
2 
1 
2 
2.94 
330.31 
5 
2 
2 
3 
2.85 
235.64 
6 
2 
3 
1 
1.91 
401.32 
7 
3 
1 
3 
3.01 
675.77 
8 
3 
2 
1 
2.96 
458.61 
9 
3 
3 
2 
2.05 
535.97 
3 Methodology of Grey Taguchi based TOPSIS (GTTOPSIS)
In grey relational analysis, black represents a state with no information and white represents astate with all the data. A grey system has a level of information between the two [19]. GRA helps in compensating the shortcoming of statistical regression and identifies the relations between the elements based on the degree of similarity or difference of development trends among those elements. The measure of performance in the grey theory is the signaltonoise ratio (S/N ratio), according to which each performance characteristic would have a target value. The algorithm for the GTTOPSISwas discussed in two phases (section 3.1 and section 3.2).
Step 1: Calculate the S/N ratio (yij) for the responses using the appropriate formula based on the quality characteristic [27]. A quality characteristic is one which determines the outcome of a process and will have a target which may be smallerthebetter or largerthebetter.
Smallerthebetter
The target of smallerthebetter characteristic is 0 (zero). Minimization of such a characteristic is desired in the smallerthebetter type problems. The S/N ratio (yij) for such a characteristic is calculated by usingEquation(1).
(1)
Where
r = number of replications, yij = observed response values, i = 1,2,3… r and
j = 1,2,…m, m is the number of trials.
Largerthebetter
A largerthebetter characteristic has a target of infinity and the maximization of such a quality characteristic is achieved by finding the S/N ratio using Equation(2). (2)
Step 2: Calculate the normalized S/N ratio (Zij) using Equation(3) to avoid the effect of variability among the S/N ratio [19, 20]. The normalized S/N ratio varies as 0Zij1.
(3)
Step 3: Compute the grey relational coefficient (GRC (γ))to express the relationship between the best and the actual normalized experimental results from normalized S/N ratio using Equation(4).
(4)
is the absolute value of the difference between and, is the reference sequence (=1; i=1,2,…,n), is the specific comparison sequence, is the smallest value of , is the largest value of and ξ is the distinguishing coefficient, whose value is taken to be 0.5 for analysis.
TOPSIS is an attractive ranking technique requiring a limited subjective input [25,26].The advantage of TOPSIS lies in its ability to identify the best alternative faster. The grey coefficients are used to form the decision making matrix in TOPSIS which is further analysed as follows.
Step 4:Establish the matrix [A]for multiple attribute decision making [26].
Where n is the number of variables and is the value of GRC.
Step 5:Normalize the matrix [A] to form matrix AN [25].This is done to transform the various attribute dimensions into nondimensional attributes, allowing for the comparison across the attributes.
Where (5) is the normalized valueof the GRC ().
Step 6:Determine the distance of the jth alternative from the ideal and negativeideal solutions.The distance of jth alternative from ideal solution (separation measure I) is calculated using Equation(6).
, for i=1, 2… n (6)
The distance of jth alternative from negativeideal solution (separation measure II) is calculated using Equation(7).
, for i=1, 2… n (7)
Where
Step 7: Calculate the relative closeness of various alternatives to ideal solution[26] using Equation(8).It is considered as the multiattribute performance index (MAPI). The MAPI value lies between 0 and 1.
(8)
Step 8:Determine the optimal level of the parameters based on MAPI. The main effect (εi) of the control factors was calculated using Equation(9) to determine the optimal level.
(9)
The best level j* of the controllable factor ‘i’ is selected asj* = max (MAPIij)
Step 9: Calculate the predicted S/N ratio () at the selected optimal levelsof the parameter using Equation(10).
(10)
Where = Average S/N ratio,f = Number of control factors and = Average S/N ratio corresponding to the ith factor on the fth level.
Step 10: Perform ANOVA to predict the significant parameters and their contribution. Conduct the confirmation experiment at the identified optimal process parameters setting for validation.
4. Results and Discussion
A linear normalization of the experimental results was performed for the responses (Ra and FT) and the grey relational coefficients (GRC) were calculated using Equation(4). These values are listed in Table 3. The Raand FTweretreated as the smallerthebetter characteristics with the target for them remaining to be zero. The S/N ratio was taken as themeasure of performance in the grey theory and a higher value of S/N ratio was desired, irrespective of the nature of quality characteristic [24].
Table 3 S/N ratio, normalized S/N ratio and GRC of responses
Trial 
S/N ratio 
Normalized S/N ratio 
GRC (matrix A) 

Ra 
FT 
Ra 
FT 
Ra 
FT 

1 
7.676 
48.984 
0.420 
0.530 
0.463 
0.515 
2 
6.527 
42.234 
0.674 
1.000 
0.606 
1.000 
3 
5.057 
45.207 
1.000 
0.793 
1.000 
0.707 
4 
9.367 
50.378 
0.045 
0.433 
0.344 
0.469 
5 
9.097 
47.445 
0.105 
0.637 
0.358 
0.579 
6 
5.621 
52.070 
0.875 
0.315 
0.800 
0.422 
7 
9.571 
56.596 
0.000 
0.000 
0.333 
0.333 
8 
9.426 
53.229 
0.032 
0.234 
0.341 
0.395 
9 
6.235 
54.583 
0.739 
0.140 
0.657 
0.368 
4.2. Effect of parameters on responses
After calculating the S/N ratio corresponding to each experimental trial, the parameter effect at any level can be found out by taking the average of all S/N ratios at the same level. A graphical representation of the effect of various parameters at different levels isshown in Figure (24)for the various responses. The level corresponding to a maximum average S/N ratio for a parameter could produce better responses [24].It was seen that lesser value of feed rate (0.12 mm/rev) is desired for minimal thrust forces and roughness(Figure 2). The improvement in finish could be attributed to lower wear rate and lesser distortion of the carbide tip. From Figure3, it was observed that an increase in spindle speed produces better finish of the surface, while a moderate value of spindle speed (1120 rpm) was desired for keeping the drilling induced thrust forces at a minimal level. From Figure4, it was found that the variation in S/N ratio (for surface roughness) at different levels of cutting point angle was less.However the thrust forces were observed to be lesser at a point angle of 118o.
Figure2 Effect of feed rate on the responses
Figure3 Effect of spindle speed on the responses
Figure4 Effect of cutting point angleon the responses
4.3 Calculation of MAPI
The normalized matrix (AN)and the separation measure matrix were formed and the relative closeness of various alternatives to the ideal solution, considered as a function of MAPI value is listed in Table 4.
Table 4 Separation measure matrix and MAPI values.
Trial 
Normalized matrix (AN) 
Separation measure I II 
MAPI 

Ra 
FT 



1 
0.2618 
0.3026 
0.416 
0.130 
0.2375 
2 
0.3425 
0.5870 
0.223 
0.421 
0.6535 
3 
0.5655 
0.4152 
0.172 
0.436 
0.7174 
4 
0.1944 
0.2751 
0.485 
0.080 
0.1410 
5 
0.2027 
0.3402 
0.439 
0.145 
0.2486 
6 
0.4525 
0.2477 
0.358 
0.269 
0.4294 
7 
0.1885 
0.1957 
0.543 
0.000 
0.0000 
8 
0.1926 
0.2319 
0.515 
0.036 
0.0662 
9 
0.3716 
0.2159 
0.419 
0.184 
0.3055 
The MAPI values represent an overall quality measure for the two responses. The MAPI values plotted for the various trials is shown in Figure5. Higher values of MAPI indicate that the combination of factors in the corresponding trial would produce better responses. The parameter combination close to trial number 3 was found to have higher MAPI value (Figure5). However the effect of the factor levels on the MAPI should be observed (Figure6), before arriving at the optimal setting.
Figure5 Variation of MAPI values for the various trials
Figure6 Effect of parameter levels on MAPI
The main effect of the various input parameters on the MAPI for each level was calculated and shown in Table5. The best level of each input parameter was identified as the one having the maximum value of average MAPI among the different levels. From Figure 6 and Table 5, the optimal parameter level was identified as A1B3C2.
Table 5 Effect of the drilling parameters on MAPI
Parameters 
Level 1 
Level 2 
Level 3 
MaxMin 
A 
0.5361* 
0.2730 
0.1239 
0.4122 
B 
0.1262 
0.3228 
0.4841* 
0.3579 
C 
0.2443 
0.3667* 
0.3220 
0.1223 
*Best level of each input parameter.
4.4 Results of ANOVA
Using ANOVA (analysis of variance), the significant input parameters for multi response performance and their percentage contribution to the total variation was found out. ANOVA was performed on the MAPI values and the results are listed in Table 6. A pictorial representation of the contribution of various factors is shown in Figure7.
Table 6 Result of ANOVA onMAPI
Source of variation 
Sum of square 
Degrees of freedom 
Mean sum of square 
Fratio 
% Contribution 
A 
0.2614 
2 
0.1307 
18.44 
53.21 
B 
0.1928 
2 
0.0964 
13.60 
39.23 
C 
0.0230 
2 
0.0115 
1.62 
4.68 
Error 
0.0142 
2 
0.0071 

2.89 
Total 
0.4913 
8 


100 
Figure7Contribution chart for the various parameters based on MAPI
The predicted values of S/N ratio () for the responses were calculated using Equation(10).After obtaining the optimal level of the drillingparameters using the hybrid approach of GTTOPSIS,the confirmation test was conducted to verify the improvement in the performance characteristics. The results of the confirmation experiment conducted with the optimal parameter setting were compared with those obtained with the initial setting of parameters (Table 7).Consequentlythese confirmatory tests gave satisfactory resultsand a significant improvement in the response values was observed.
Table 7 Comparison between the outcome of initial parameter setting and the optimal parameter setting
Responses 
Initial parameter Setting 
Optimal parameter (GTTOPSIS)setting 
Improvement 

Observed S/N ratio 
Response value 
Predicted S/N ratio 
Response value 
S/N ratio 
Response value 

Ra (μm) 
5.0571 
1.79 
4.1946 
1.63 
0.8625 
0.16 
FT(N) 
45.2067 
182.11 
44.9985 
172.65 
0.2082 
9.46 
parameter settings 
A1B3C3 
A1B3C2 

5 Conclusion and Future Research
An effective optimization strategy for multi criteria optimization problems is still a challenging task.This paper has presented a new integrated methodology of GTTOPSIS for predicting the optimal conditions in drilling of Al/SiCp composites. The following conclusions can be drawn.
In future, a suitable metaheuristic algorithms can be identified for MCDM problems, either in an individual or in a combined format and the results of this study may be comparedwith the results of other fuzzy based methods.
Acknowledgement
The authors are grateful to ‘CNC Center of Excellence for Advanced Manufacturing’, Saveetha Engineering College, Chennai, India for extending the facilities to carry out the investigation.
References
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