#### Abstract

Optimization is an essential action to select the effective input parameters for the responses obtained from machining. In this work, the combination of six sigma techniques and grey relational optimization are used for the corresponding input parameters, namely, spindle speed, feed rate, and drill diameter. The responses recorded are torque, thrust force, surface roughness, temperature, and ovality. Smaller the better response is preferred for all the output responses. Taguchi design of L27 array is preferred, and based on 27 combinations of input parameters, output responses are recorded. The thrust force and torque values are obtained in the graphical form during drilling process by the vertical machining center. After the drilling process the surface roughness of the hole is measured using profilometer. The probe in the profilometer is moved along the surface of the hole and the corresponding surface roughness values are noted for twenty-seven holes. The roundness of the hole is measured using a profile projector. The roundness of the hole is expanding due to the heat generated during the machining process. The expanded diameter of the hole is measured along the vertical and horizontal axes using the projector. Six sigma techniques are used to analyze the input parameters such as spindle speed, feed rate, and drill diameter. The optimization technique is used to determine the optimized parameters.

#### 1. Introduction

Composites have the high specific strength and so the automobile and airplanes move at high speed with better fuel efficiency. Hybrid metal matrix composite is more advantageous compared to metal matrix composites since it is having the combined effect of improved mechanical properties, high wear resistance, and less wear of the tool while machining. Aluminium–Silicon-based metal matrix composites have major applications in automobile brakes and clutches. The orthogonal array, analysis of variance, and signal-to-noise ratio analyzed the machining parameters, and it also derived the optimal combination of input parameters. It is also proved that the Taguchi method derived the solution with minimum number of trials compared to the full factorial design [1]. Giasin and Ayvar-Soberanis measured the ovality error and burr height as the output responses in the drilling process. It was proved that the burr height at the exit is maximum than at the entry of the work piece. The ovality error and burr height is reduced at the minimum feed rate [2]. Fernandez-Perez et al. analyzed the output responses such as hole quality and tool wear. The influence of input parameters in drilling the output responses tool wear and hole quality was analyzed. The analytical study revealed that the input parameters, speed and feed, greatly influenced the output responses. The higher values of speed and feed resulted in less tool wear [3].

##### 1.1. Literature on Machining of Metal Matrix Composites

Ekici et al. proved the reinforcement of solid lubricant graphite as a third element to the aluminum and boron carbide composites reduced the thrust force value to 25% compared to aluminum-boron carbide. The surface roughness value is greatly influenced by the percentage of graphite added with the aluminum-boron carbide composites [4]. The percentage of error between the predicted and validated values is 4.5 for the aluminum alloy reinforced with aluminum nitride so the optimization prediction is liable. The optimum condition for minimum surface roughness is uncoated carbide drills 320 m/min cutting speed, 0.4 mm/tooth feed rate, axial depth 0.4 mm, and 10% of reinforcement [5]. The optimal machining parameters while machining hybrid metal matrix composites LM 6/fly ash/silicon carbide particle is 175 m/min cutting speed, 0.25 mm depth of cut, and 0.1 mm/rev feed [6]. A review was made on machining hybrid metal matrix composites and concluded that the addition of third reinforcement with SiCp reduced the cutting force and improved the tool life and surface texture. In optimizing multiple responses, grey relational analysis is termed by the preferable technique by the researcher due to its simplicity [7]. Better hole quality and minimum surface roughness are achieved at maximum grey relational code value (GRC). The maximum value of GRC indicates the optimum input parameters and the maximum spindle speed; the minimum feed is termed as optimized values [8].

Priyadarshi and Sharma proved the reinforcement of nanosized silicon carbide particle in an aluminum alloy requires large cutting force (43 N) than hybrid reinforcement of nanosized silicon carbide particle and graphite requires less force (38 N). The optimization revealed that the hybrid reinforcement is better than individual reinforcement, and the confirmation test is within the acceptable limit of 5% [9]. The cutting speed influenced the surface roughness at the greater rate followed by feed and depth of cut. The error obtained is less than 5% between the modeled and experimental values [10]. Aluminum composites reinforced with silicon carbide particle with different mesh size reinforcements such as 220 and 600 using the machining process. The output response cutting force is greatly influenced by the feed and the depth of cut whereas surface roughness is influenced by feed and preheating temperature. Minimum cutting force is obtained at 80°C and 100°C, and a good surface finish is obtained at 60°C [11]. With the addition of the third element in metal matrix composites, it increased the wear and friction resistance. The optimum input parameters to obtain the minimum friction and wear are 15 N load and 3.25 m/sec sliding speed [12]. The grey relational code is maximum at 0.2 mm the depth of cut, 0.4 mm/rev feed, and 930 rpm speed. These optimal inputs reduced the surface roughness and tool temperature and maximize the material removal rate [13]. The material structure is the most significant factor for surface roughness, and the feed rate is the dominant factor that influences the thrust force in machining the aluminum alloy reinforced with alumina. The surface texture is increased by the addition of milled alumina with the aluminum alloy [14]. The optimized input parameters for better surface finish are cutting speed 900 rpm, feed rate 0.25 mm/rev, and depth of cut 0.5 mm. The feed has the major contribution of 82.6% followed by the depth of 6.8% and then cutting speed 6.43% [15]. The feed rate greatly influenced the thrust force and burr height in drilling hybrid metal matrix composites (Al/15%SiC/4%graphite). The spindle speed is less influenced compared to the feed rate. At the lowest spindle speed of 1000 rpm and at a maximum feed rate of 1.5 mm/rev, the thrust force is 220 N [16].

Chaudhary et al. optimized aluminum silicate composite with spindle speed, feed rate, and drill diameter and output responses such as cylindricity, circularity, and surface finish, and various conclusions are made. The dimensional deviation is reduced with minimum drill bit diameter (6 mm). Circularity deviation is avoided at a minimum cutting speed (360 rpm) and minimum feed rate (0.095 mm/rev). Good surface finish is obtained by high cutting speed (680 rpm) and low feed rate (0.095 mm/rev). Cylindricity deviation is avoided with low spindle speed (680 rpm) and high feed rate (0.285 mm/rev) [17]. Confirmation test in optimizing A 356 reinforced with silicon carbide and boron carbide during machining operation revealed that the thrust force and surface roughness has 95% of the confidence interval. The analysis of variance deals with the influence of depth of cut and feed rate influence more with the cutting force and the surface roughness [18]. The best performance is obtained using uncoated carbide tool, the lower cutting speed of 119.2 m/min, and medium depth of cut 0.15 mm, and the corresponding grey relational grade value is 0.8084 [19]. The increased surface roughness (0.988 microns) is observed at high cutting speed (m/min) and high feed rate (mm/rev) at the higher percentage of reinforcement (15%) [20]. The feed greatly influenced the uncut fiber factor followed by drill diameter and spindle speed. The uncut fiber factor is reduced by increasing the drill diameter [21]. The addition of graphite in the mixture of aluminum and silicon carbide particle improved the machinability and increased the tribological properties. The confirmation test during optimization showed improvement from 0.619 to 0.891 percentage [22]. Ganesh and Chandrasekaran proved in their experiment that the thrust force values increased to a maximum of 200 N at a higher feed rate and at low speed of 500 rpm. When the speed rose to 1000 rpm, the thrust force decreased [23, 24].

The literature reviewed above explain the fabrication of composites and machining of the prepared specimen. It also includes the influence of input parameters with the output response using various analyzing tools. These research results in the greater influenced by feed and drill diameter on the output responses. In this paper, HMMCs (LM25/treated SiCp with MWCNT) are subjected to drilling process and the influence of input parameters are analyzed using mathematical modeling technique.

##### 1.2. Scope and Objective

To perform the drilling operation on the specimen using the L_{27} orthogonal array. The drilling operation is done by considering the spindle speed, feed rate, and drill diameter as input parameter, and the output responses observed are thrust force, surface roughness, and ovality, to conduct wear test using the pin on disc device with inputs load, velocity, and percentage of reinforcement, to analyze the outputs responses using the statistical tool, and to optimize the input parameters using grey relational grade (GRG).

##### 1.3. Methodology

The drilling process performed in the product with improved mechanical properties. The input parameters in drilling process are spindle speed, feed rate, and drill diameters of three different ranges, and the output responses recorded during machining process are torque, thrust force, surface roughness, ovality, and temperature. The effect of input parameters on the output responses is analyzed using response surface methodology and six sigma techniques. The results are analyzed using analysis of variance. The input parameters are optimized. The optimized values of output responses are obtained using grey relational analysis (GRA). The wear test conducted on the fabricated product with input parameters load, sliding speed, and percentage of reinforcement. The wear rate of the tool observed before and after drilling to study the wear rate of the tool after machining the hybrid metal matrix composite, and it is compared with the wear rate of the tool after machining the metal matrix composites. Figure 1 explains the experimental set up from machining of hybrid metal matrix composites and measurement of output responses such as torque, thrust forces, ovality, surface roughness, and temperature, the analysis of output responses using six sigma techniques, and optimization of input parameters using grey relational analysis.

#### 2. Analyze the Output Response Using Six Sigma Techniques and Response Surface Methodology

##### 2.1. Analysis of Torque

Torque is measured using dynamometer connected to the vertical machining center. Torque is measured using a graphical form. The measured torque is analyzed using six sigma technique. Figures 2(a) and 2(b) show the main effect plot for means and signal-to-noise ratio.

**(a) Main effect plot for means**

**(b) Main effect plot for signal-to-noise ratio**

**(c) Interaction plot for means**

**(d) Interaction plot for signal-to-noise ratio**

**(e) Normal plot of residuals**

**(f) Probability plot of torque**

**(g) Histogram of torque with respect to frequency**

**(h) Empirical CDF of torque**

**(i) Torque with respect to and feed**

**(j) Torque with respect to feed**

**(k) Torque with respect to drill diameter**

In mean plot, the input parameter speed increased to a maximum value, and then, it reduced and in signal-to-noise ratio, the minimum speed is obtained at 1230 rpm, and then, it increased. The feed rate is maximum at 25 mm/min for mean plot whereas for signal-to-noise ratio, the feed rate is minimum at 25 mm/min. In mean plot, the drill diameter is maximum at 12 mm drill diameter, and in signal-to-noise plot, the minimum value is obtained at 12 mm drill diameter. Figures 2(c) and 2(d) explain the interaction plot of means and signal-to-noise ratio in which each parameter is plotted in two different ways for better understanding. Figures 2(e) and 2(f) show the normal probability plot. Residuals are closer to diagonal line which represents ideal normal distribution, and the data is normally distributed. Figure 2(g) represents the histogram of torque with respect to frequency. The data values are in same interval size; at 10 Nm, the frequency level is 4; for 20 Nm, the graph shows the highest frequency of 7. The addition of all frequency values gives the normal frequency value of 27. Figure 2(h) shows empirical cumulative distribution function (CDF). CDF is the integral of probability distribution function. Figures 2(f), 2(i), and 2(j) explained the variation of output response torque with respect to speed, feed, and drill diameter. The -square value in the table represent the percentage of data closer to the regression line.

The response of torque is listed in Table 1. This table displays the three levels of input parameters, and it influenced output response. Torque values are influenced by drill diameter with rank 1, and it is followed by speed with rank 2 and finally feed rate with rank 3. Analysis of variance (ANOVA) is the group of statistical models, and it is used to analyze the difference between the groups and among the groups. Mean square value in ANOVA is obtained by dividing sum of squares (SS) by degrees of freedom (DF). The value is the ratio between the variance of group means and mean of within group variances. The value is used to determine the smallest level of significance by avoiding the null hypothesis (Table 2).

##### 2.2. Analysis of Thrust Force

Thrust force on a surface is normal and perpendicular to the normal reaction on the surface. Thrust force is measured using dynamometer in a vertical machining center in a graphical form. It is revealed that the thrust force is minimum at the entry and exit of tool, and it is maximum during the drilling process [25]. Figures 3(a) and 3(b) show the mean and signal-to-noise ratio, and they are opposite to each other. Main effect plot for means shows the peak point at 600 rpm, 75 mm/min of feed rate, and at 12 mm drill diameter and the corresponding speed, feed rate, and drill diameter are least in signal-to-noise ratio. Figures 3(c) and 3(d) explained the interaction plot for both means and signal-to-noise ratio, and it explained that each factor is plotted in two different ways. Figure 3(e) shows the histogram plot of thrust force in equal intervals with respect to frequency. Figure 3(f) shows the empirical CDF of thrust force in terms of percentage. Figures 3(e)–3(g) explain the 3D surface plot of thrust force with respect to the combination of two input parameters. Thrust force increased to the largest with feed compared to the speed. Similarly, thrust force increased to the largest with drill diameter compared to speed. The percentage of thrust force closer to the regression line is about 96.78%. Tables 3 and 4 describe response table and ANOVA table for thrust force.

**(a) Main effect plot for means**

**(b) Main effect plot for signal-to-noise ratio**

**(c) Interaction plot for means**

**(d) Interaction plot for signal-to-noise ratio**

**(e) Histogram of thrust force with respect to frequency**

**(f) Empirical CDF of thrust force**

**(g) 3D surface plot of thrust force with the combination of feed and speed**

**(h) 3D surface plot of thrust force with the combination of drill diameter and speed**

**(i) 3D surface plot of thrust force with the combination of drill diameter and feed**

##### 2.3. Analysis of Surface Roughness

Surface roughness of the drilled hole is measured using a profilometer by moving the probe of the profilometer along the drilled surface, and the corresponding values are obtained in the graphical form. Figures 4(a) and 4(b) represent main effect plot for means and signal-to-noise ratio, and the minimum surface roughness is obtained at 1860 rpm, 25 mm/min of feed rate, and 4 mm drill diameter for means, and the values are entirely conflicted with the signal-to-noise ratio. Figures 4(c) and 4(d) represent the interaction plot for means and signal-to-noise ratio, and it displayed the two different models in which each parameter is plotted. Figure 4(e) shows the histogram of surface plot, and it is used to derive normal residual plot as well as probability plot. Figure 4(f) displays the empirical cumulative distribution, and it represents the integral of probability distribution function. Figure 4(g) represents 3D surface plot in which surface roughness increased with the increased combination of feed and drill diameter. Figure 4(h) proved the closeness of predicted value with the actual values. 92.4% of surface roughness values are accumulated closer to regression line, and it is represented as the -square value. Response table of surface roughness indicates the influence of each input parameters on the output response surface roughness. The three levels of input parameters are listed in Table 5. Feed rate is influenced more on surface roughness with rank 1, and then drill diameter placed the next rank followed by spindle speed. ANOVA table for surface roughness is shown in Table 6. It explained the sum of square and mean square of linear form of input parameters, square values of input parameters, and interaction values of input parameters and their corresponding and values.

**(a) Main effect plot for means**

**(b) Main effect plot for signal-to-noise ratio**

**(c) Interaction plot for means**

**(d) Interaction plot for signal-to-noise ratio**

**(e) Histogram of surface plot with respect to frequency**

**(f) Empirical CDF of surface roughness**

**(g) 3D surface plot of surface roughness with respect drill diameter and feed rate**

**(h) Predicted value vs. actual value**

##### 2.4. Analysis of Ovality

Ovality is the dimensional change along its diameter, horizontally and vertically. Ovality is measured by the profile projector. The drilled hole is projected on the screen with cross wires; then, the readings are noted using micrometers in the projector. Ovality occurred due to the heat generated during drilling operation. Figures 5(a) and 5(b) show the main effects plot for means and signal-to-noise ratio, and it describes variation of input parameters speed, feed rate, and drill diameter. Figures 5(c) and 5(d) display the interaction plot for means and signal-to-noise ratio. Figure 5(e) elaborates the histogram plot of ovality in terms of frequency in equal intervals; this histogram graph is related to normal probability distribution plot. Figure 5(f) represents empirical CDF of ovality in percentage. Figures 5(g)–5(i) describe the 3D surface plot of ovality in the combination of speed, feed rate, and drill diameter. This graph explains there is a drastic increase in ovality with the increasing range of feed rate and drill diameter. Figure 5(j) shows the graph plotted between the actual value and predicted value, and the actual values are accumulated along the regression line. 89.95% of data gradually gathered along the regression line and it is denoted as square.

**(a) Main effect plot for means**

**(b) Main effect plot for signal-to-noise ratio**

**(c) Interaction plot for means**

**(d) Interaction plot for signal-to-noise ratio**

**(e) Histogram of ovality with respect to frequency**

**(f) Empirical CDF of ovality**

**(g) 3D surface plot of ovality with respect to feed and speed**

**(h) 3D surface plot of ovality with respect to drill diameter and speed**

**(i) 3D surface plot with respect to drill diameter and feed**

**(j) Predicted value vs. actual values**

Table 7 shows the response table for means (ovality) listed the three different levels of input parameters. The influence of feed rate on ovality is more since it is assigned to rank 1 followed by drill diameter which holds the second rank and with lower influence on ovality is spindle speed and it is assigned with the rank 3. ANOVA (Table 8) shows the analysis of variance such as speed, feed rate, and the drill diameter.

##### 2.5. Analysis of Temperature

The temperature for each hole is determined by pointing the infrared temperature indicator in a position while the tool performs the drilling operation, and it indicates the specific temperature. Figures 6(a) and 6(b) represent the main effects plot for means as well as signal-to-noise ratio. In means plot, the maximum value is obtained at 600 rpm and minimum value is obtained at 1230 rpm, and it reverses in the signal-to-noise ratio. Figures 6(c) and 6(d) show the interaction plot for means and signal-to-noise ratio, and it explains the input parameters are plotted in two different ways. Figures 6(e)–6(g) are related to each other; the normalization plot is obtained from histogram of temperature in terms of frequency. The empirical CDF is obtained from the integral of probability distribution function. This normal residual plot shows the closest distribution of temperature data towards the regression line. Figures 6(h)–6(j) explain that, as the diameter increase the temperature increased, similarly when the feed rate increases the temperature increased and the value of temperature decreased as the speed increased. -square value represent the accumulation of temperature data along the regression line of about 71.86%. Response table for temperature represents that the influence of feed rate is more on temperature which is assigned to be rank 1; then, the percentage of influence of speed on temperature plays the second role and then the spindle speed (Table 9 (a)). Table 9(b) displays the analysis of variance table for temperature which listed the sum of squares; mean squares; value and value for linear form of input parameters of input parameters speed, feed rate, and drill diameter; square form of speed, feed rate, and drill diameters; and the interaction between the input parameters.

**(a) Main effect plot for means**

**(b) Main effect plot for signal-to-noise ratio**

**(c) Interaction plot for means**

**(d) Interaction plot for signal-to-noise ratio**

**(e) Histogram of temperature with respect to frequency**

**(f) Empirical CDF of temperature**

**(g) Normal plot of residuals**

**(h) Temperature plot with respect to speed**

**(i) Temperature plot with respect to feed rate**

**(j) Temperature plot with respect to drill diameter**

#### 3. Optimize the Input Parameters Using Grey Relational Analysis (GRA) Techniques

GRA is one of the measurements in a grey system which briefs the correlation between the main factor and all other factors. It is an effective tool for multiresponse optimization. GRA used to evaluate and describe the relation of two or more things to the others when their direction of development is either varied or similar. Optimization is an essential action to select the effective input parameters for the responses obtained from machining. In this work, grey relational optimization is used. In this case, the output responses are listed in Table 10. For the corresponding input parameters, namely, spindle speed, feed rate, and drill diameter, the responses recorded are torque, thrust force, surface roughness, ovality and temperature, and smaller the better response is preferred for all the output responses.

##### 3.1. Calculation of Signal-to-Noise Ratio and Normalization

The data obtained from the experiments are converted into signal-to-noise (S/N) ratio, and normalization values by the formula are listed in Table 11. The value obtained is negative since smaller the better concept is chosen, and the analysis is done to reduce the output response. Normalized the output responses as using the formula: , where is the number of experiments and is the number of responses.

##### 3.2. Calculation of Grey Relational Code

Grey relational coefficient (GRC) for the responses are calculated using the formula , where is the minimum value, is the maximum value, and ranges from 0 to 1; then, the corresponding data are listed in Table 12. Grey relation grade (GRG) is calculated using the formula . and is the number of responses The optimized input parameters are obtained from the response table for GRC. The highest value is termed as rank 1, and its corresponding parameters are optimized inputs. Spindle speed of 600 rpm in level 1, 75 mm/min of feed rate in level 3, and 12 mm of diameter in level 3 are the optimized input values. Figure 7(a) shows the main effect plot of grey relational grade (GRG). The maximum value of speed is obtained at 600 rpm, 75 mm/min, and 12 mm of drill diameter. A1B3C3 is the initial design where represents spindle speed, feed rate, and drill diameter. Figure 7(b) displays the normal probability plot, fits, and histogram; all the four graphs are related to each other. In normal plot, the accumulation of data towards the regression lines indicate the less deviation, and this normal probability plot is derived from the histogram of residuals or GRG in terms of frequency. Response table for grey relational grade is displayed in Table 13. The input process parameters is listed in three levels in which the optimized value is chosen to be maximum. According to the spindle speed, level 3 is maximum compared to level 2 and 1. Feed rate and drill diameter level 3 are the maximum value compared to the other levels, so the predicted value is termed as A3B2C1, which is the predicted design, where represents spindle speed, represents feed rate, and represents drill diameter. Table 14 is the analysis of variance which listed sequential sum of squares, mean sum of squares, value, and value. The optimal condition is set, and the selected experiments are carried out. The confirmation test is the final step to analyze the result obtained from the experiment. The average results obtained from the experiment is compared with the predicted average values. The optimal condition is set, and the selected experiments are carried out. The confirmation test is displayed in Table 15, and it shows the percentage is approximately equal.

**(a) Main effect plot for means (GRG)**

**(b) Residuals plots for GRG**

#### 4. Conclusion

Response surface methodology is used to generate the -square value of the output responses which reveals the percentage of data accumulated along the regression line. Six sigma techniques are used to analyze the output responses using nominal probability plot, histogram plot, and main effect plot for means and noise-to-signal ratio while drilling hybrid metal matrix composites. The input parameter of feed rate and drill diameter greatly influenced the thrust force than the spindle speed.

##### 4.1. The Data Are Analyzed Using Six Sigma and Response Surface Methodology

(a)Drill diameter and speed values greatly influenced the torque compared to spindle speed during drilling process(b)Among the input parameters, the feed rate value is greatly influenced the thrust force and the corresponding -square value is 96.78%(c)The surface roughness is raising along with the feed rate, and it declines as the spindle speed increased and the corresponding -square value is 92.4%(d)In the output response, ovality is obtained using the optical projector and analyzed and the response is highly affected by feed rate and drill diameter. As the feed rate increases, the ovality increased and it decreased as the spindle speed increased and the accumulation of date along the regression line is 89.95%.(e)The output response, temperature, is mainly dependent on federate and spindle speed compared to drill diameter, and the -square value is 71.86%.

##### 4.2. The Optimized Input Parameters Are Obtained Using Grey Relational Analysis

The optimized input parameters are obtained using grey coefficient grade. The level of optimized input parameters is A1B3C3. The corresponding optimized values of input parameters are spindle speed of 600 rpm (), feed rate value of 75 mm/min (), and drill diameter of 12 mm (), and the confirmation test reveals that the predicted and experimental values are approximately equal, and hence, the design is significant.

#### Data Availability

The data used for the study is used in the manuscript itself.

#### Conflicts of Interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.