Optimization of end milling on Al–SiCfly ash metal matrix composite using Topsis and fuzzy logic
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Abstract
Metal matrix composites are extensively used in aerospace, automobile and other engineering applications as an alternative to a wide range of elements. High strength–weight ratio, durability and high corrosion resistance are benefits of metal matrix composites. The study that exhibits adopts optimal cutting parameters (speed, feed and depth of cut). The initial study is to explore end milling process of alumina (AA6082 with SiC 3% and fly ash 2%) molted metal matrix composite. The technique for order preference by similarity to ideal solution and fuzzy logic for optimizing the cutting parameter values has been utilized in the MMC. The response surface methodology is being used to develop the numerical model between output responses and machining parameters. The secondorder regression models are studied through analysis of variance. The experimental investigation exhibits that feed rate is the important factor on response variables.
Keywords
Milling Alumina Optimum Machining Composites Fuzzy logic1 Introduction
Metal matrix composites (MMCs) have a rare mechanical property. Reinforced aluminum MMC has a notable design property. These materials have been recognized as hardtomachine materials, due to their durability and abrasive nature of support components like silicon carbide particles [1]. The MMCs are most generally used in aviation and automotive industries [2]. End milling is one of the primary machining activities used in modern industries due to its ability to produce geometric surfaces, accuracy and surface finish. The surface roughness (SR) of the component highly depends on the exclusive cutting parameters. SR is the major parameter, used for assurance and the estimation of the quality characteristics. SR and material removal rate (MRR) are the measures of the quality of a product and have a significant impact on the product cost.
Although destruction has been used in this article, technique for order preference by similarity to ideal solution (Topsis) presented by Hwang and Yoon [3] has been utilized for evaluation of the alternatives. Vinodh et al. [4] have built up a tool with integrated fuzzy, analytical hierarchy process (AHP) and Topsis for doing execution assessment and distinguishing the best strategy for the reuse of plastics. Nayak and Mahapatra [5] utilized AHP with Topsis method for the optimization of various responses like MRR, surface finish and kerf angle. Dewangan et al. [6] examined the impact of different electrodischarge machining (EDM) parameters on the distinctive parts of surface integrity. A response surface methodology (RSM)based design of experiment was treated in their research. Awasthi et al. [7] proposed a crossbreed approach in the light of the service quality model and fuzzy logic (Fl)—Topsis for assessing the administration nature of urban transportation frame works. Fuzzy with Topsis is used to resolve the relative weights of decision criteria [8]. A fuzzyTopsisbased system for appraisal and decision of vertical computer numerical control machining centers for an assembling unit is studied by Onut et al. [9]. Yurdalul and Lc [10] evaluate the advantages of utilizing fuzzy numbers instead of crisp numbers in a Topsis method based on instrument choice model. The conclusion was that fuzzy numbers should be preferred instead of crisp in the decisionmaking issues.
Sidhu et al. [11] investigated the effect of EDM process parameters on the surface properties of variant Al/SiC composites. Their result shows that microhardness of the machined surface is directly proportional to the concentration of reinforced (SiC) particulates. Gadakh [12] applied Topsis for taking care of various criteria enhancement issues in the wireEDM procedure. Yurdakul and Cogun [13] have proposed a determination strategy for nontraditional machining processes (NTMPs) in the light of a gathering of AHP and Topsis techniques. Temucin et al. [14] built up a fuzzybased choice help for demonstrating NTMPs choice through application of Topsis and fuzzyTopsis strategies. Shivakoti et al. [15] used the triangular fuzzy member for ascertain the weight performance criteria, and fuzzyTopsis. Kumar et al. [16] applied the Taguchi and Topsis techniques in the EDM machining process with conventional electrodes on M2 tool steel with aluminum power and without aluminum powder.
Sidhu et al. [17] studied the surface modification of three different types of metal matrix composite using powder mixed electrical discharge machining process and reported that microhardness increased primarily with increase in the density of reinforced particles in the matrix. Shunmugesh and Paneerselvam [18] studied the drilling parameter with carbon fiber reinforced polymer. The result shows that multiobjective technique has good agreement with Topsis technique. Arif Gok [19] studied the SR expectation dependent on the cutting parameters in turning operation. Tamiloli et al. [20] dealt with improvement in cutting parameters for end milling process dependent on grayfuzzy logic for SR and MRR. The statistical methods of signaltonoise ratio and analysis of variance are applied in their investigation. Sidhu and Yazdani [21] used lexicographic goal programming for investigating the better EDM machining parameters to optimize conflicting objectives such as induced residual stresses on the machined surface, tool wear rate and material removal rate. Makadia [22] studied the machining parameters and output response (SR). The outcomes revealed the feed rate is the main influencing factor of the machining parameter.
Sidhu [23] reports the optimal process conditions for machining of three different types of MMC’s: 65 vol% SiC/A356.2; 10 vol% SiC5 vol% quartz/Al; and 30 vol% SiC/A359 using powder mixed electric discharge machining process. MRR, TWR, SR and surface integrity were identified. The four responses were then collectively optimized using Topsis, and optimal process conditions were identified for each type of MMC. Roy and Dutta [24] studied about the multiobjective optimization of electrical discharge machining using integrated fuzzy AHP and fuzzyTopsis method. A fuzzyTopsis method was used [25] to optimize multiple responses, viz. SR, MRR and tool wear rate, in EDM based on various process parameters. Recast layer thickness and SR were optimized [26] using Taguchibased fuzzy logic technique. This technique significantly improved multiple responses in WEDM. Topsis is a wellknown application in many areas [27, 28, 29, 30, 31] and given a choice network and a basic leadership strategy.
Topsis finds an ideal choice elective that is at the closest partition to the positive ideal solution (PIS) and most remote division to the negative ideal solution (NIS). PIS is an ideal arrangement wail, and NIS is the most perceptibly horrendous game plan that is not of any interest. Based on the multiregression analysis, a suitable mathematical model of the responses has been established. The prime objective of this research is to minimize the surface roughness and normal cutting force simultaneously. Thus, this case of an inconsistent condition requires multiobjective optimization tool for an optimum solution. In the second phase of analysis, the multioptimization techniques such as technique for order preference by similarity to ideal solution and fuzzy logic have been adopted to optimal solution.
2 Materials and methods
Chemical composition of aluminum, silicon carbide and fly ash
Materials  Chemical compositions 

AA6082T6  Si (0.7–1%), Fe (0.5%), Cu (0.1%), Mn (0.4–1%), Mg (0.6–1.20%), Cr (0.25%), Zn (0.20%), Ti (0.1%) and aluminum (remaining) 
Silicon carbide  Sic (98.7%), Si (0.3%), Sio_{2} (0.4%), Fe (0.08%), Al (0.1%) and C (0.3%) 
Fly ash  SiO_{2} (52.78%), Al_{2}O_{3} (24.48%), Fe_{2}O_{3} (6.25%), CaO (11.08%), MgO (2.58%), SO_{3} (1.31%) and loss of ignition 1.3% by weight 
Property of the workpiece
Peak stress (MPa)  Peak load (KN)  Hardness (BHN) (100 Kgf)  Modulus (GPa)  Flexural stress (MPa) 

119.6  4.3  537  49.797  229.1 
2.1 Process variables with their limits
Process variables with their limits
Parameters  Unit  Level 1  Level 2  Level 3 

Spindle speed (A)  rpm  500  710  1000 
Feed (B)  mm/min  40  63  100 
Depth of cut (C)  mm  0.5  0.75  1.0 
2.2 Evaluation of surface roughness (SR) (R _{a}) and cutting force (F _{z})
Results of surface roughness and cutting force using L27 orthogonal array
S. no.  Speed (rpm)  Feed (mm/min)  Doc (mm)  SR R_{a} (µm)  F_{z} (N) 

1  500  40  0.5  4.416  144.000 
2  500  40  0.75  4.525  144.149 
3  500  40  1  4.108  125.766 
4  500  63  0.5  5.301  182.156 
5  500  63  0.75  4.830  160.300 
6  500  63  1  4.467  145.390 
7  500  100  0.5  5.878  213.725 
8  500  100  0.75  5.461  195.341 
9  500  100  1  5.831  156.200 
10  710  40  0.5  5.548  169.442 
11  710  40  0.75  4.908  150.200 
12  710  40  1  4.714  132.675 
13  710  63  0.5  5.907  189.065 
14  710  63  0.75  5.490  170.682 
15  710  63  1  5.639  170.700 
16  710  100  0.5  6.484  277.200 
17  710  100  0.75  6.067  202.250 
18  710  100  1  5.650  183.867 
19  1000  40  0.5  6.385  178.983 
20  1000  40  0.75  5.968  160.599 
21  1000  40  1  6.610  164.100 
22  1000  63  0.5  7.643  180.100 
23  1000  63  0.75  6.327  180.223 
24  1000  63  1  5.910  161.84 
25  1000  100  0.5  7.321  230.175 
26  1000  100  0.75  6.904  197.600 
27  1000  100  1  6.487  193.408 
2.3 Topsis steps
Normalized decision matrix, weighted normalized values, separation measures, average, fuzzy reasoning grade (FRG) and rank
S. no.  Normalized decision matrix  Weighted normalized values  Separation measures  Average  Rank  FRG  Rank  

R _{a}  F _{z}  R _{a}  F _{z}  R _{a}  F _{z}  
1  0.1465  0.1555  0.073  0.078  0.011  0.090  0.890  3  0.888  2 
2  0.1502  0.1556  0.075  0.078  0.012  0.089  0.880  4  0.878  3 
3  0.1363  0.1358  0.068  0.068  0.000  0.101  1.000  1  0.950  1 
4  0.1759  0.1967  0.088  0.098  0.036  0.064  0.639  14  0.629  14 
5  0.1603  0.1731  0.080  0.087  0.022  0.078  0.780  7  0.781  7 
6  0.1482  0.1570  0.074  0.078  0.012  0.089  0.879  5  0.875  5 
7  0.1951  0.2308  0.098  0115  0.056  0.045  0.447  24  0.437  25 
8  0.1812  0.2109  0.091  0.105  0.044  0.057  0.566  17  0.572  19 
9  0.1935  0.1686  0.097  0.084  0.033  0.072  0.686  8  0.750  8 
10  0.1841  0.1829  0.092  0.091  0.034  0.068  0.669  10  0.680  10 
11  0.1628  0.1622  0.081  0.081  0.019  0.082  0.815  6  0.878  3 
12  0.1564  0.1432  0.078  0.072  0.011  0.092  0.896  2  0.875  5 
13  0.1960  0.2041  0.098  0.102  0.045  0.056  0.551  18  0.583  17 
14  0.1822  0.1843  0.091  0.092  0.033  0.068  0.670  9  0.657  11 
15  0.1871  0.1843  0.094  0.092  0.030  0.066  0.654  13  0.719  9 
16  0.2152  0.2993  0.108  0.150  0.091  0.019  0.175  27  0.333  27 
17  0.2013  0.2184  0.101  0.109  0.053  0.048  0.478  22  0.469  24 
18  0.1875  0.1985  0.094  0.099  0.040  0.060  0.598  15  0.572  19 
19  0.2119  0.1932  0.106  0.097  0.047  0.057  0.546  20  0.583  17 
20  0.1980  0.1734  0.099  0.087  0.036  0.069  0.656  12  0.643  12 
21  0.2193  0.1772  0.110  0.089  0.046  0.063  0.578  16  0.625  15 
22  0.2536  0.1945  0.127  0.097  0.066  0.052  0.444  25  0.513  22 
23  0.2100  0.1946  0.105  0.097  0.047  0.057  0.546  19  0.531  21 
24  0.1961  0.1747  0.098  0.087  0.036  0.069  0.658  11  0.631  13 
25  0.2429  0.2485  0.121  0.124  0.078  0.026  0.251  26  0.354  26 
26  0.2291  0.1918  0.115  0.096  0.054  0.055  0.504  21  0.593  16 
27  0.2153  0.2088  0.108  0.104  0.054  0.049  0.477  23  0.500  23 
2.4 Fuzzy rulebased modeling
During this analysis, the multiobjective responses were changed to single objective optimization utilizing the Topsis technique. The uncertainties in the output were condensed further by Fl. The criteria acknowledged as the best executions with machining aluminum composites need aid for lower surface roughness and normal feed force.
Utilizing the Topsis technique, the original sequence data were converted into normalized decision matrix. After that all the machining parameters are manipulated. A more significant value of the average was indicative of the good performance characteristic equal to one. The parametric condition was corresponding to the highest cutting force and SR. However, there is a tendency of a certain level of a particular degree about the controversial matter to bring about shortage.
Uncertainties emerged mainly due to the imprecision and absence of the majority of the data. The Fl approach appeared to offer a compelling result for controlling these averages. As a result, fuzzy thinking about various execution qualities was formed and suggest to the fuzzy thinking evaluation. The steps in the Fl approach include fuzzification of input data, principle induction for more defuzzification procedure [22].

The extended parameters may be determined, and a suitable orthogonal show adjusted for leading examinations.

Responses such as SR and F_{z} were considered for each trial. These responses were initially normalized during data preprocessing. Following this, normalized decision matrix weighted normalized values and separation measures, average and FRG determined are listed in Table 3. The input parameters and output values were normalized with help of Topsis.

Fuzzy multireactions output (normal) μD0(η) is figured with the maximum and minimum interface tasks. The inferential outcome in a fuzzy set with a participation work for the multireaction output η can be expressed as:

Fuzzy reasoning grade η_{0} is considered from fuzzy multiresponses output μD_{0}(η) with the accompanying equation:

Optimum level of parameters was resolved for the utilization of the data found in the response table and after that assessed.

The results were obtained based on the confirmation test carried out for the optimum level of machining parameters.

Selection of the input parameters and their levels.

To perform the experiments, values utilize a L_{27} design.

Calculation of SR and F_{z}, ξ_{i} (k) for every response by utilizing Eqs. (1), (2) was utilized for the generation of the overall fuzzy reasoning grade γ_{i}.

Fuzzification of the SR and F_{z} was obtained from every response and fuzzification of the general FRG by utilizing the membership function. Likewise, the rules in a linguistic form relating to SR, F_{z} and overall FRG were built up.

Calculation of the fuzzy multiresponse output μD_{0}(η) utilizing the max–min interface operation (Eq. 3) was trailed by employment of centroid defuzzification and by computation of a fuzzy reasoning grade η_{0}.

Selection of the optimum combination of parameters found in the response table and the graph. Interaction effects were determined with help of ANOVA for finding the contribution of each parameter.

Finally, a confirmation test was conducted in the outcomes.
3 Results and discussion
3.1 Effect of surface roughness
Average values of surface roughness
S. no  L1  L2  L3 

1  4.980  5.601  6.617 
2  5.242  5.724  6.231 
3  6.098  5.609  5.491 
ANOVA for surface roughness
Parameters  DOF  SS  MSS  F _{cal}  % contribution 

A  2  12.302  6.151  41.631  59.083 
B  2  4.403  2.201  14.899  21.145 
C  2  1.867  0.933  6.318  8.967 
AB  4  0.555  0.139  0.939  2.664 
BC  4  0.328  0.082  0.555  1.576 
AC  4  0.185  0.046  0.313  0.889 
Error  8  1.182  0.148  5.677  
Total  26  20.821  0.801  100 
3.2 Effect of cutting force
Optimal values of cutting force
S. no  L1  L2  L3 

1  163.003  182.898  183.003 
2  152.213  171.162  205.530 
3  196.094  173.483  159.327 
ANOVA for cutting force
Parameters  DOF  SS  MSS  Fcal  % contribution 

A  2  2387.466  1193.733  9.669  9.146 
B  2  13148.711  6574.355  53.250  50.373 
C  2  6190.301  3095.150  25.070  23.715 
AB  4  917.900  229.475  1.859  3.516 
BC  4  1621.516  405.379  3.283  6.212 
AC  4  849.083  212.271  1.719  3.253 
Error  8  987.699  123.462  3.784  
Total  26  26102.676  1003.949  100 
3.3 Technique for order preference by similarity to ideal solution
Average of Topsis optimal values
S. no  L1  L2  L3 

1  0.751  0.612  0.518 
2  0.770  0.647  0.596 
3  0.512  0.655  0.714 
ANOVA for average Topsis values
Parameters  DOF  SS  MSS  F  % contribution 

A  2  0.250  0.125  36.115  25.664 
B  2  0.424  0.212  61.266  43.537 
C  2  0.194  0.097  27.970  19.876 
AB  4  0.035  0.009  2.545  3.617 
BC  4  0.027  0.007  1.950  2.772 
AC  4  0.016  0.004  1.190  1.691 
Error  8  0.028  0.003  2.842  
Total  26  0.974  0.037  100 
3.4 Fuzzy logic
Fuzzy input and output variables and ranges
variables  Parameters  Fuzzy set  Range 

Input  Speed  L, M, H  500–1000 
Feed  L, M, H  40–100  
Depth of cut  L, M, H  0.5–1  
Output  Average Topsis values  EL, VVL, VL, L, M, H, VH, VVH, EH  0–1 
Optimal values of fuzzy
S. no  L1  L2  L3 

1  0.751  0.641  0.553 
2  0.778  0.658  0.596 
3  0.556  0.667  0.722 
ANOVA for fuzzy logic
Parameters  DOF  SS  MSS  F  % contribution 

A  2  0.178  0.089  27.544  24.333 
B  2  0.327  0.163  50.492  44.605 
C  2  0.129  0.065  19.984  17.654 
AB  4  0.042  0.010  3.208  5.669 
BC  4  0.016  0.004  1.270  2.244 
AC  4  0.014  0.004  1.110  1.961 
ERROR  8  0.026  0.003  3.534  
TOTAL  26  0.732  0.028  100 
3.5 Response surface methodology (RSM)
4 Confirmation experiment
Confirmation test results
Process  Initial (A1–B1–C1)  Predicted (A1–B1–C3)  Experimental  Variation  % improvement 

SR (µm)  4.416  –  4.108  0.308  6.97 
Force (N)  144  –  125.766  18.234  12.66 
Topsis  0.890  0.981  1.000  0.11  12.36 
Fuzzy  0.888  0.955  0.950  0.062  6.98 
Improvement in Topsis is 12.36% 
5 Conclusions

The mathematical study of the influence of individual parameters demonstrates that speed (59.083%) is the important parameter which influences the SR, where the feed (50.373%) influences the cutting force.

The ANOVA demonstrated the most influence factor for both Topsis and Fl. This analysis indicates that the speed and feed rate are the dominant factors for surface roughness and cutting force.

Topsis is used to reveal the effect of parameters influencing both R_{a} and F_{z}. Feed is found as the transcendent parameter that influences both R_{a} and F_{z}. Topsis is used to identify the optimum machining parameters such as cutting speed of 500 rpm, the feed rate of 40 mm/min and DOC of 1 mm from the third experiment.

The relative closeness values of fuzzy logic are used to find the optimal levels in the experiments. The most extreme fuzzy reasoning grade is identified in the third experiment (A1–B1–C3). The optimal level found in the Topsis and Fl is the same.

According to Topsis and Fl, the smallest values of speed, feed and depth of cut lead to R_{a} and F_{z} values as shown in Table 4.

The response surface methodology is effectively used to create the numerical model between machining parameters.

From the quadratic polynomial model, the obtained correlation coefficient R^{2} values are 93.69% and 90.83%. The value indicates that the generated model can be used to predict R_{a} and F_{z} in milling operation.

The total number of experiments in milling operations is reduced by using Topsis and Fl for determining the optimum cutting conditions. The results acquired in this research would be useful in manufacturing sectors.
The methodology offered experimentally and statically during this study is often viewed as an applicable method for the improvement in milling processes.
Notes
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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