Prediction and Modelling with Taguchi, ANN and ANFIS of Optimum Machining Parameters in Drilling of Al 6082-T6 Alloy

Abstract

In this study, the drilling of an Al 6082-T6 alloy and the effects of cutting tool coating and cutting parameters on surface roughness, cutting temperature, hole diameter, circularity, and cylindrical variations was investigated. In addition, the prediction accuracy of Taguchi, artificial neural networks (ANNs), and adaptive neuro-fuzzy inference system (ANFIS) methods was compared using both experimental results and Signal/Noise (S/N) ratios derived from the experimental results. The experimental design was prepared according to Taguchi L27 orthogonal indexing. As a result, it was observed that increasing the cutting speed and feed rate increases the cutting temperature hole error, circularity error and cylindricity error. Increasing the cutting speed positively affected the surface roughness, while increasing the feed rate led to an increase in the surface roughness. The lowest surface roughness, cutting temperature, hole diameter error and hole circularity error values were measured for the uncoated cutting tool. The minimum cylindricity variation was measured for drilling with TiAlN-coated cutting tools. The optimum cutting parameters were A1B1C3 (Uncoated, 0.11 mm/rev, 200 m/min) for surface roughness, A1B1C1 (Uncoated, 0.11 mm/rev, 120 m/min) for cutting temperature, hole error, circularity error and cylindricity error. In the estimation of the output parameters with Taguchi, ANNs and ANFIS, it was observed that the estimates made by converting the experimental values into S/N ratios were more accurate than the estimates made with the experimental results. The reliability coefficient and prediction ability of the ANN model were found to be higher than Taguchi and ANFIS models in estimating the output parameters.

1. Introduction

In recent years, aluminum alloys have been preferred in many engineering applications due to their lightweight and higher energy absorption in crash tests than steel with similar mechanical properties [1]. In particular, the Al 6082-T6 alloy, a member of the Al–Mg–Si family, is widely preferred in the fields of aerospace technology, the automotive sector, the nuclear industry and rail transportation due to its low density, high strength, excellent corrosion resistance, relatively low cost, good formability and machinability [2,3,4,5,6,7]. Despite the important properties of Al alloys, several challenges are encountered during their machining. For example, the combination of a high coefficient of thermal expansion and high thermal conductivity significantly reduces the machinability in dry processing environments [8]. In addition, the high chemical affinity of Al alloys to most cutting tool coatings causes Al alloys to adhere to cutting tools, resulting in the formation of a Built-Up Edge (BUE) and a Built-Up Layer (BUL) at the cutting tool tip [9]. The variables affecting the output parameters in the dry drilling of Al alloys have been reported in studies conducted through the National Centre for Manufacturing Sciences (NCMS) as important variables that can improve the performance of output parameters in tool coating drilling [10].

For this reason, different studies in the literature have been conducted in which the effects of cutting parameters, cutting tool coating, cutting tool geometry and cooling/lubrication on the output parameters have been evaluated experimentally and statistically in the drilling of engineering materials. Roy et al. [11] investigated the effects of tool material and coating on the output parameters in the machining of aluminum and Al–Si alloys with uncoated, TiC, TiN, Al₂O₃, AlON, TiB₂ and diamond tools at constant cutting parameters. It was reported that surface roughness and cutting force increased due to the increase in flank wear and BUE in TiC, TiN, TiB₂, Al₂O₃ and AlON-coated tools compared to uncoated tools. They also stated that BUE formation decreased in the diamond tool compared to the uncoated tool. Braga et al. [12] reported that when the Al–Si alloy was drilled with coated and uncoated tools at high feed rates with different cooling/lubrication methods, the life of the coated tool showed a significant improvement. Masooth and Jayakumar in their study [13] they investigated the effects of cutting tool coating on surface roughness and cylindricity when drilling Al 5052 alloy with uncoated, TiN, AlCrN and TiAlN coated drills. The TiAlN coated drill was found to have less tool wear, excellent surface finish and minimum cylindricity error. Mohan et al. [14], using a 10 mm solid carbide drill and different cutting parameters, aimed to predict the thrust force by using a machine learning model in the drilling of glass laminated aluminum reinforced epoxy composites. They found that the combined use of low cutting speed and low feed rate minimized the thrust forces in drilling GLARE composites. They also reported that the provided machine learning-based linear regression model can be used to accurately predict the thrust force when drilling GLARE composites. Al-Tameemi et al. [15] investigated the effect on surface quality, surface form and dimensional tolerances when drilling an Al 6061 alloy at different cutting parameters and with different coatings (TiN/TiAlN, TiAlN and TiN). They achieved the best surface roughness with a TiN-coated tool. They reported that the hole diameters exceeded the nominal value at all cutting parameters and coatings. While lower circularity and higher cylindricity were obtained at the hole entrance with TiN-coated tools, they reported that increasing the cutting speed was effective in reducing the hole properties in drilling operations with TiN/TiAlN- and TiAlN-coated tools. In the literature, it is seen that there are different studies in which researchers have experimentally and statistically investigated the effects of cutting parameters, cutting tool coating and cooling/lubrication methods on output parameters in drilling different aluminum alloys [16,17,18,19,20]. As seen in the literature analysis, there are a limited number of studies in which the effects of different cutting parameters and different drill coating types are evaluated in terms of their effect on surface roughness, cutting temperature, hole diameter error, hole circularity error and hole cylindricity error in drilling Al 6082-T6 alloys under dry cutting conditions, both experimentally and statistically. Therefore, this study aims to contribute to the elimination of this deficiency.

In addition, the experimental results and the S/N ratios derived from these experimental results were used separately to create models for estimating the output parameters using Taguchi, ANN and ANFIS methods. It was decided whether the experimental results or the S/N ratios provided the more accurate results regarding the created models’ predictive ability.

2. Materials and Methods

2.1. Workpiece, Cutting Tool, Machine Tool and Experimental Measurements

In the study, Al 6082-T6 alloy (Seykoç Aluminum Marketing and Industry, Çayırova/Kocaeli, Turkey) with dimensions of 25 × 90 × 190 mm was used as the workpiece and its chemical composition is given in

Table 1. Chemical composition of Al 6082-T6 alloy used as workpiece in this research.

	Elements
	Si	Fe	Cu	Mn	Mg	Cr	Zn	Ti	Al
Wt%	0.96	0.38	0.03	0.69	0.94	0.002	0.03	0.023	Bal.

.

Three different drills with uncoated carbide, TiAlN and TiSiN coatings were selected for drilling operations. The diameter of the helical drills, whose geometry is given in Figure 1, is 10 mm and the tip angle is 140°. A new drill was used in the drilling operations for each combination of drilling experiments. Drilling operations were carried out on a YCM MV 106A CNC (Yeong Chin Machinery Industries, Taichung, Taiwan) vertical machining center with 15 KW power and 10,000 rpm output and a Fanuc MXP-200i control unit. Roughness measurements of the holes were made using the Time brand TR200 model surface roughness measuring device. The average surface roughness values were determined by the arithmetic mean of the measurements taken from four points perpendicular to the hole axis. Fluke Ti9 infrared thermal camera was used to measure the temperature in the cutting zone during drilling. The temperature measurement of the infrared thermal camera used in the measurements is between −20 and 250 °C. The thermal imager was positioned 250 mm from the cutting zone and at a 45° angle for temperature measurements. The diameter, circularity and cylindrical deviation of the holes on the workpiece were measured using Mitutoya CRYSTA-Apex V 9106 (Mitutoyo Corporation, Kawasaki, Japan) series three-dimensional CMM device. The wear mechanisms on the cutting tools were analyzed using Insize brand ISM-PM200SA (Insize Corporation, Suzhou, China) model digital polarizing microscope with 1600 × 1200 resolution and up to 200× magnification and Quanta FEG 250 (FEI, Warendorf, Germany) scanning electron microscope (SEM). The experimental setup is shown in Figure 1.

2.2. Experimental Design

The experimental combination to be used in drilling operations was prepared according to the Taguchi L27 orthogonal index. Cutting tool coating (CTC), cutting speed (Vc) and feed rate (f) were selected as input parameters. The selected cutting parameters and their levels are shown in

Table 2. Drilling parameters and levels.

Symbols	Cutting Parameters	Units	Levels
			Level 1	Level 2	Level 3
A	Cutting Tool Coating, (CTC)	-	Uncoated	TiAlN	TiSiN
B	Feed Rate, (f)	mm/rev	0.11	0.15	0.19
C	Cutting Speed, (Vc)	m/min	120	160	200

. Surface roughness (Ra), cutting temperature (T), hole diameter error (Hd), hole circularity error (Hc) and hole cylindricity error (Hcy) were measured as output parameters in each experimental combination. The measured values were converted to Signal to Noise (S/N) ratios with Minitab 19 software using the “lower-the-better” approach given in Equation (1). Then, each output parameter was modeled with Taguchi, ANN and ANFIS methods using experimental results and S/N ratios. In this context, experimental results and predicted values were compared. Minitab 19 software was used to estimate the values with Taguchi and Matlab R2023a software was used to estimate the values with ANN and ANFIS. Finally, the obtained prediction results are compared according to MAD, MSE, RMSE and R² performance criteria. The data flow diagram used for this section is given in Figure 2.

2.3. Calculating S/N Ratios

Especially in experimental studies on machinability, it has been observed that there are many papers using Taguchi method in modeling and optimization of input parameters to find the best values of output parameters [21,22,23,24]. The Taguchi method uses a loss function to determine the deviation between the experimental and desired results. This loss function is then converted to the S/N ratio. The Taguchi method is used to check the efficiency of the operation by converting the output parameters into S/N ratios. There are three types of quality attributes for the calculation of S/N ratios, namely “smaller is better”, “the nominal is the best” and “larger is better”. In this study, since the smallest values of the output parameters are desired, the “Smallest Best” approach given in Equation (1) is chosen [25,26].

$$S/N=-10log\left(1/n\sum _{i=1}^n{y}_i^2\right)$$

(1)

The results of the output parameters (Ra, T, Hd, Hc and Hcy) and the calculated S/N ratios in each experimental combination of the experimental design prepared using the Taguchi method for the drilling process are given in

Table 3. Experimental results and S/N ratios.

Test No	Drilling Parameters			Test Results and S/N Ratio for Test Results
	CTC	f (mm/rev)	Vc (m/min)	Ra (µm)	Ra (dB)	T (°C)	T (dB)	Hd (mm)	Hd (dB)	Hc (mm)	Hc (dB)	Hcy (mm)	Hcy (dB)
1	UNC	0.11	120	1.42	−3.05	27.9	−28.91	10.0062	−20.0054	0.0029	50.7520	0.007	43.098
2	UNC	0.11	160	1.19	−1.51	28.1	−28.97	10.0087	−20.0076	0.0037	48.6360	0.015	36.478
3	UNC	0.11	200	1.07	−0.59	30.7	−29.74	10.0117	−20.0102	0.0044	47.1309	0.022	33.152
4	UNC	0.15	120	1.79	−5.06	31.1	−29.86	10.0091	−20.0079	0.0035	49.1186	0.021	33.556
5	UNC	0.15	160	1.57	−3.92	33.2	−30.42	10.0123	−20.0107	0.0041	47.7443	0.028	31.057
6	UNC	0.15	200	1.44	−3.17	35.7	−31.05	10.0164	−20.0142	0.0057	44.8825	0.038	28.404
7	UNC	0.19	120	2.06	−6.28	35.2	−30.93	10.0176	−20.0153	0.0049	46.1961	0.041	27.744
8	UNC	0.19	160	1.86	−5.39	36.6	−31.27	10.0203	−20.0176	0.0056	45.0362	0.051	25.849
9	UNC	0.19	200	1.72	−4.71	39.6	−31.95	10.0231	−20.0200	0.0069	43.2230	0.064	23.876
10	TiAlN	0.11	120	1.58	−3.97	31.7	−30.02	10.0084	−20.0073	0.0034	49.3704	0.008	41.938
11	TiAlN	0.11	160	1.36	−2.67	33.6	−30.53	10.0122	−20.0106	0.0043	47.3306	0.017	35.391
12	TiAlN	0.11	200	1.21	−1.66	35.8	−31.08	10.0156	−20.0135	0.0051	45.8486	0.024	32.396
13	TiAlN	0.15	120	1.99	−5.98	36.3	−31.20	10.0124	−20.0108	0.0046	46.7448	0.026	31.701
14	TiAlN	0.15	160	1.74	−4.81	38.1	−31.62	10.0148	−20.0128	0.005	46.0206	0.029	30.752
15	TiAlN	0.15	200	1.59	−4.03	39.8	−32.00	10.0187	−20.0162	0.0065	43.7417	0.042	27.535
16	TiAlN	0.19	120	2.28	−7.16	39.7	−31.98	10.0206	−20.0179	0.0058	44.7314	0.044	27.131
17	TiAlN	0.19	160	2.07	−6.32	42.2	−32.51	10.0235	−20.0204	0.0064	43.8764	0.053	25.514
18	TiAlN	0.19	200	1.88	−5.48	44.7	−33.01	10.0269	−20.0233	0.0079	42.0475	0.065	23.742
19	TiSiN	0.11	120	1.71	−4.66	36.2	−31.17	10.0091	−20.0079	0.0035	49.1186	0.009	40.915
20	TiSiN	0.11	160	1.54	−3.75	37.5	−31.48	10.0130	−20.0113	0.0045	46.9357	0.018	34.895
21	TiSiN	0.11	200	1.34	−2.54	40.3	−32.11	10.0174	−20.0151	0.0054	45.3521	0.025	32.041
22	TiSiN	0.15	120	2.18	−6.77	40.4	−32.13	10.0134	−20.0116	0.0047	46.5580	0.027	31.373
23	TiSiN	0.15	160	1.98	−5.93	41.9	−32.44	10.0154	−20.0134	0.0052	45.6799	0.032	29.897
24	TiSiN	0.15	200	1.75	−4.86	45.2	−33.10	10.0192	−20.0167	0.0066	43.6091	0.043	27.331
25	TiSiN	0.19	120	2.42	−7.68	45.4	−33.14	10.0215	−20.0187	0.0059	44.5830	0.046	26.745
26	TiSiN	0.19	160	2.32	−7.31	46.8	−33.40	10.0244	−20.0212	0.0065	43.7417	0.055	25.193
27	TiSiN	0.19	200	2.07	−6.32	48.2	−33.66	10.0276	−20.0239	0.0082	41.7237	0.067	23.479

.

3. Results and Discussions

3.1. Surface Roughness

It is known that the surface roughness of parts produced using machining methods is one of the most important output parameters in terms of machinability as it affects the quality and service life of the part. One of the biggest problems, especially in drilling operations, is the evacuation of chips from the drilled holes during the drilling process. During the evacuation of chips from the holes, the adhesion of the chips to the hole and the cutting tool causes deterioration of the quality of the drilled surface, wear of the cutting tool and even breakage of the cutting tool [27]. In experiments using different cutting tool coatings and cutting parameters, it is vital to reduce the surface roughness by removing the chips from the cutting zone. Therefore, in this study, the surface roughness changes obtained by drilling an Al 6082-T6 alloy with different cutting tool coatings and different cutting parameters are given in Figure 3.

The Ra values ranged between 1.07 and 2.42 µm when the 6082-T6 alloy was drilled with different cutting tool coatings at different cutting parameters. The lowest surface roughness value was 1.07 µm with the uncoated tool at 200 m/min cutting speed and 0.11 mm/rev feed rate. The highest surface roughness value was 2.42 µm with the TiSiN-coated tool at 120 m/min cutting speed and 0.19 mm/rev feed rate. In general, the experiments with the uncoated, TiAlN- and TiSiN-coated tools showed that the surface roughness values increased significantly with increasing feed rate. Increasing the feed rate leads to an increase in the chip cross-section removed per unit time. Therefore, it was reported that increasing the chip cross-sectional area will increase the drilling forces and the increase in the vibrations in parallel with this increase will negatively affect the surface roughness [15,28]. In the experiments with the uncoated tool, TiAlN and TiSiN, the surface roughness values showed a decreasing trend when increasing the cutting speed from 120 m/min to 200 m/min. Surface roughness values generally improve with an increasing cutting speed. It was stated that with the increase in cutting speed, the tool–chip contact surface decreases and the friction decreases, thus reducing the yield strength of the workpiece and reducing the surface roughness [29,30]. Figure 4 also shows that BUE and BUL are formed on the cutting tool at low cutting speeds. The decreasing surface roughness with increasing cutting speed can be easily explained by the decreasing tendency of BUE and BUL formation.

Figure 3 shows the changes in the surface roughness values of the coating in the experiments with the uncoated, TiAlN- and TiSiN-coated tools at constant cutting speeds and feed rates. It is seen that the surface roughness values are generally better than TiAlN- and TiSiN-coated tools in the experiments performed with uncoated tools at constant cutting speed and feed rates. This is thought to be due to the higher chemical affinity of aluminum for the coating material in the continuous release of silicon elements that are caused as a result of the analysis, such as deformation in the dry machining of ductile materials like aluminum. The cutting tool SEM examinations shown in Figure 4a–d and the EDX analysis results given in

Table 4. EDX analysis of cutting tools at: (a) TiSiN, 120 m/min and 0.19 mm/rev, (b) TiAlN, 120 m/min and 0.19 mm/rev, and (c) UNC, 120 m/min and 0.19 mm/rev.

EDS Spot	Element Weights (%)
	C	O	Mg	Al	Si	Ti	Cr	Mn	Fe	Cu	Zn
1	26.82	4.1	1.46	29.25	16.58	0.38	0.73	0.67	0.74	2.64	16.63
2	22.29	5.8	2.58	26.64	18.41	0.42	1.08	0.82	0.78	3.11	18.07
3	24.69	4.61	1.82	28.38	17.53	0.31	0.81	0.76	0.69	2.78	17.62

confirm this. It is also stated that this situation will increase the cutting forces and cause an increase in surface roughness values [11]. It was reported that machining with tools using aluminum-based coatings will create some disadvantages when using such coatings, as the workpiece is plastered to the tool surface, increasing the surface roughness [16].

In the experiments with the TiAlN-coated tool, it was observed that the surface roughness values were generally better than those of the TiSiN-coated tool. This is because the coefficient of friction of the TiSiN coating material is higher than that of the TiAlN coating material. For this reason, the lower coefficient of friction causes the cutting forces to decrease and the surface roughness values to improve accordingly [31,32]. For these reasons, the surface roughness of the uncoated tool was on average 9% and 16.6% lower than the TiAlN- and TiSiN-coated tools, respectively. For this reason, it seems that it would be more appropriate to use the uncoated cutting tool for this material in order to reduce the production cost.

3.2. Cutting Temperature

Cutting temperature is one of the most important parameters that directly affects the roughness quality of the workpiece and tool wear in machining operations. Especially in operations that take place in a closed environment such as drilling operations, it is even more important to examine the cutting temperature. For this reason, the jamming of the chips formed in drilling operations, sticking to the tool and the increase in tool wear mechanisms cause the temperature in the cutting zone to increase. Controlling the cutting temperature in the drilling process is vital for drilling operations. For this reason, the cutting temperature variation depending on the cutting tool coating and cutting parameters in the drilling of an Al 6082-T6 alloy is shown in Figure 5.

The drilling of an Al 6082-T6 alloy with tools with different coatings at different cutting parameters shows that the cutting temperature varies between 27.9 °C and 48.2 °C. At a 120 m/min cutting speed, different feed rates and different coatings, the average cutting temperature was 33.12 °C. By increasing the cutting speed to 160 m/min and 200 m/min, the average cutting temperatures increased by 14.7% and 28.11%, respectively. At 0.11 mm/rev feed rate, at different cutting speeds and with tools with different coatings, the average cutting temperature was 33.53 °C. It was observed that by increasing the feed rate to 0.15 m/min and 0.19 m/min, the cutting temperatures increased by 13.22% and 25.38%, respectively. The reason for this problem is that increasing the cutting speed and feed rate increases the volume of chips removed per unit of time and the friction between the tool and the workpiece, resulting in an increase in the heat generated in the cutting zone [33,34,35]. In addition, in the drilling of ductile materials such as aluminum, it is thought that the inability to remove the chips from the cutting zone by stacking them from the helical channels at high feed rates is another reason for the temperature increase.

The average cutting temperature of the uncoated drill at different feed rates and different cutting speeds was 36 °C. It was found that the drill coatings TiAlN and TiSiN increased the average cutting temperatures by 4.35% and 11.15%, respectively. The cutting temperatures measured in drilling operations with coated tools are higher than the cutting temperatures measured in drilling operations with uncoated tools. As a result of the experiments, the highest cutting temperatures were measured with the TiSiN-coated drill. The reason for this problem is that the coating types have different coefficients of friction. The average friction coefficients of the coating materials used in the experiments are TiSiN > TiAlN > UCN, respectively. This increased the friction between the tool and the workpiece during drilling operations, resulting in the highest cutting temperatures being measured for TiSiN-, TiAlN- and UCN-coated tools, respectively [36,37].

3.3. Hole Diameter Error

Keeping the hole diameter size within the desired dimensional tolerances after drilling is one of the difficult processes in the production sector [27]. Therefore, it is very important to maintain accuracy in hole diameter variation in drilling operations. Especially in assembly parts with oversized or undersized holes, undesirable stresses, cracks, loosening and bearing failures are caused [38]. Therefore, the hole diameter error variation depending on the cutting tool coating and the cutting parameters in drilling a Al 6082-T6 alloy is given in Figure 6.

When Figure 6 is examined, it is seen that all holes are above the nominal diameter (Ø 10 mm) in the hole diameter measurements after drilling. As a result of the drilling operation of an Al 6082-T6 alloy using tools with different coatings and different cutting parameters, the hole diameters ranged between 10.0062 mm and 10.0276 mm. At a 120 m/min cutting speed, with different feed rates and tools with different coatings, the average hole diameter was 10.0131 mm. By increasing the cutting speed to 160 m/min and 200 m/min, the average hole diameter error increased by 22.2% and 49%, respectively. At 0.11 mm/rev feed rate, the average hole diameter was 10.0114 mm in the drilling process performed at different cutting speeds and with tools with different coatings. By increasing the feed rate to 0.15 m/min and 0.19 m/min, the average hole diameter error increased by 29% and 100%, respectively. It is known that the increase in cutting speed is an important parameter in increasing vibration. Increased vibration during drilling is another important factor that negatively affects the hole quality. It is seen that the change in feed rate is effective on the change in hole diameter error. It is generally observed that increasing the feed rate leads to an increase in hole diameters. It is stated that the increase in cutting forces with increasing feed rate increases the axial loads on the cutting tool and causes the hole diameter to enlarge [39,40,41]. The data obtained as a result of the studies coincide with the studies of Niinomi [42], Antonialli et al. [43], Astakhov [44], Çiçek [22], and Hanif [45].

The average hole diameter was 10.0140 mm in drilling at different feed rates and different cutting speeds with an uncoated drill. It was determined that the average hole diameters increased by 25% and 26% in the case of the TiAlN and the TiSiN coating of the drill, respectively. In addition, the average hole diameter error in drilling operations with TiAlN-coated drills was 1% larger than the average hole diameter error in drilling operations with TiSiN-coated drills. In general, it was observed that the decrease in the coefficient of friction of the drills contributed to the minimum hole diameters. It is also seen that increasing the feed rate by 0.19 mm/rev causes the hole diameters to exhibit unstable behavior at three cutting speeds.

3.4. Hole Circularity Error

In drilling operations, failure to select the appropriate cutting tool, cutting parameters and cooling/lubrication results in high cutting force, cutting temperature, vibration and tool wear. In this case, the hole circularity error increases. For this reason, the results of the hole circularity error depending on the cutting tool coating and cutting parameters in the drilling of the Al 6082-T6 alloy are given in Figure 7.

As a result of drilling the Al 6082-T6 alloy with drills with different coatings at different cutting parameters, the circularity error deviation values vary between 0.0029 mm and 0.0082 mm. The lowest circularity error value of 0.0029 mm was measured at 120 m/min cutting speed, 0.11 mm/rev feed rate and using the uncoated drill. The highest circularity error value was 0.0082 mm at 200 m/min cutting speed, 0.19 mm/rev feed rate and drilling with the TiAlN-coated drill. When the cutting speed was increased from 120 m/min to 160 m/min and 200 m/min, the circularity error tended to increase by 15.56% and 44.64%, respectively. In addition, it was observed that by increasing the feed rate from 0.11 mm/rev to 0.15 mm/rev and 0.19 mm/rev, the circularity error increased by 23.39% and 56.18%, respectively. In the experiments, increasing the cutting speed and feed rate generally tends to increase the circularity error values. This situation is similar to the hole diameter error results in Figure 6 of the circularity error values given in Figure 7. These two output parameters are similar to the cutting temperature results shown in Figure 5. This shows us that higher cutting temperature values cause hole diameter error and circularity error deviation values. In addition, the literature has stated that increasing cutting temperature with increasing cutting speed and feed rate negatively affects the deviation from circularity error values as it causes thermal distortion in the holes obtained by the drilling process [46]. In general, it was observed that the deviation from circularity error increased more when increasing the feed rate than with the cutting speed. It is reported that this situation can be explained by the increase in drill runout parallel to the increase in feed rate, which leads to an increase in hole diameter error and circularity error [27]. Figure 7 shows the circularity error deviation variations depending on the cutting tool coating at constant cutting speed and feed rate. The average circularity error deviation was 0.0046 mm for drilling with uncoated drill at different cutting speeds and feed rates. Drilling with TiAlN- and TiSiN-coated drills tended to increase the average circularity error deviation by 19.66% and 18.94%, respectively, compared to the uncoated tool. This problem is because the coating types have different coefficients of friction.

3.5. Hole Cylindricity Error

The cylindricity of holes can be defined as the distance of all hole surfaces from a common center. Therefore, the cylindricity deviation of the holes after drilling is an important quality control tolerance to be controlled for the holes. In this study, the cylindricity error variations of the holes formed by drilling the Al 6082-T6 alloy with drills with different cutting parameters and different coatings are shown in Figure 8.

Cylindricity error values ranged between 0.007 mm and 0.067 mm when drilling the Al 6082-T6 alloy using tools with different coatings and cutting parameters.

The average cylindricity error value was 0.024 mm in drilling at 120 m/min cutting speed with different feed rates and tools with different coatings. By increasing the cutting speed to 160 m/min and 200 m/min, the average cylindricity error values in the holes increased by 35.45% and 77.27%, respectively. The average cylindricity error value of 0.016 mm was measured in the drilling process performed at 0.11 mm/rev feed rate with tools with different cutting speeds and different coatings. When the feed rate was increased by 0.15 m/min and 0.19 m/min, the average deviation from the cylindricity error of the holes increased by 96.53% and 234%, respectively. It was stated that the reason for the increase in cylindricity error values due to the increase in cutting parameters is the high thrust and moment values that occur during drilling operations. It is reported that high cutting temperatures due to the increase in cutting speed will cause an increase in cylindricity errors by disrupting the dimensional stability of the cutting tool and workpiece. In addition, it is reported that the increase in thrust forces due to the increase in feed rate will increase the axial runout. In parallel, the cylindricity error deviation values will increase [27,46].

Figure 8 shows the deviation from cylindricity error at different cutting tool coatings, constant cutting speed and feed rate. The average deviation from cylindricity error was 0.033 mm for drilling with uncoated drills at different cutting speeds and feed rates. When drilling with TiAlN- and TiSiN-coated drills, the cylindricity error increased by 5.41% and 1.4%, respectively, compared to the experiments with uncoated drills.

3.6. Statistical Analysis

The sine qua non of the machining industry is efficiency. For this, optimum input parameters should be determined for optimum output parameters. It is possible to reach these optimum results with different statistical analyses. The most widely used of these methods is the Taguchi method. In the Taguchi method, output parameters and S/N ratios are used for optimization and prediction. In addition, artificial intelligence techniques such as ANN and ANFIS are used for optimization and prediction. In artificial intelligence techniques such as ANN and ANFIS, the output parameters are either used directly or normalized. Optimizations and predictions using normalized output values give closer results to the actual values.

3.7. Determination of Optimum Cutting Parameters Using Taguchi

In order to improve the quality of the workpiece and reduce the production cost, it is very important to reach the smallest values of the output parameters. The S/N response values obtained for Ra, T, Hd, Hc and Hcy as a result of the analysis are shown in

Table 5. S/N response table for Ra, T, Hd, Hc and Hcy output parameters.

Symbol	S/N Ratios
	Level 1	Level 2	Level 3	Delta	Rank
Ra
CTC	−3.741	−4.675	−5.536	1.795	3
f	−2.711	−4.947	−6.294	3.583	1
Vc	−5.622	−4.624	−3.706	1.916	2
T
CTC	−30.35	−31.55	−32.52	2.17	1
f	−30.45	−31.54	−32.43	1.98	2
Vc	−31.04	−31.41	−31.97	0.93	3
Hd
CTC	−20.012	−20.015	−20.016	0.003	3
f	−20.010	−20.013	−20.020	0.010	1
Vc	−20.011	−20.014	−20.017	0.006	2
Hc
CTC	46.97	45.52	45.26	1.71	3
f	47.83	46.01	43.91	3.92	1
Vc	47.46	46.11	44.17	3.29	2
Hcy
CTC	31.47	30.68	30.21	1.26	3
f	36.7	30.18	25.47	11.23	1
Vc	33.8	30.56	28	5.81	2

. In Table 5, the optimum input parameters and levels are determined for the smallest values of the output parameters. The magnitude of the delta value in Table 5 represents the effect of the input parameters on the output parameters. For the output parameter Ra, the effect of the input parameters is f, Vc and CTC, respectively, while for the output parameters T, Hd, Hc and Hcy it is CTC, f and Vc, respectively. The best level for each cutting parameter was calculated according to the highest S/N ratio for that cutting parameter. Accordingly, the best Ra value (1.07 µm) was achieved at UNC, 0.11 mm/rev feed rate and 200 m/min cutting speed. This ranking was obtained for the best values of T, Hd, Hc and Hcy (27.9 °C, 10.0062 mm, 0.0029 mm and 0.007 mm) at UNC, 0.11 mm/rev feed rate and 120 m/min cutting speed.

3.8. Determination of Optimum Cutting Parameters by Taguchi

It was observed that the studies comparing prediction modeling methods based on output parameters and S/N ratios in the drilling of Al 6082-T6 alloy are limited in the literature. In this study, prediction models were created with Taguchi, ANN and ANFIS according to the output parameters and S/N ratios. The error percentages of the results obtained for each experimental and prediction output parameter were calculated with the average percentage error (APE) given in Equation (2).

$$APE=\left[{\displaystyle \frac{\left|Exp-Pre\right|}{Exp}}\right]\times 100$$

(2)

3.9. Estimation with Taguchi Method

First, the experimental results and S/N ratios were determined according to the experimental design prepared using the Taguchi method. Separate models were created for each of the output parameters and all output parameters and S/N ratios were estimated. In the estimation of the experimental results and the S/N ratios using the Taguchi method, “Linear + interactions” were used. The percentage errors of the estimated output parameters and S/N ratios calculated using the obtained models are given in

Table 6. Error values of experimental and S/N ratios for the Taguchi model.

Ra (µm)				T (°C)				Hd (mm)				Hc (mm)				Hcy (mm)
Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios
Pred µm	APE %	Pred dB	APE %	Pred °C	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %
1.41	0.5	−2.98	2.2	27.44	1.7	−28.79	0.4	10.0076	0.006	−20.0028	0.003	0.0028	3.19	50.9286	0.35	0.006	11.64	43.175	0.18
1.21	1.7	−1.54	1.3	28.24	0.5	−29.03	0.2	10.0088	0.001	−20.0077	0.001	0.0037	0.80	48.6180	0.04	0.016	3.46	36.349	0.35
1.08	0.6	−0.62	6.3	31.03	1.1	−29.81	0.2	10.0122	0.005	−20.0106	0.002	0.0045	1.43	46.9724	0.34	0.022	1.35	33.204	0.16
1.80	0.7	−5.12	0.5	31.44	1.1	−29.95	0.3	10.0098	0.007	−20.0085	0.003	0.0036	3.07	48.8837	0.48	0.022	2.47	33.352	0.61
1.56	0.5	−3.88	1.0	32.90	0.9	−30.34	0.3	10.0122	0.001	−20.0106	0.001	0.0041	0.72	47.6938	0.11	0.027	2.91	31.282	0.72
1.47	2.1	−3.14	0.7	35.66	0.1	−31.03	0.1	10.0159	0.005	−20.0138	0.002	0.0056	2.40	45.1680	0.64	0.038	0.78	28.383	0.08
2.05	0.3	−6.28	0.1	35.33	0.4	−30.96	0.1	10.0176	0.000	−20.0152	0.000	0.0049	0.30	46.2545	0.13	0.041	0.72	27.871	0.46
1.87	0.4	−5.40	0.1	36.76	0.4	−31.29	0.1	10.0203	0.000	−20.0176	0.000	0.0055	1.06	45.1048	0.15	0.051	0.58	25.753	0.37
1.72	0.1	−4.70	0.3	39.31	0.7	−31.90	0.2	10.0232	0.001	−20.0201	0.000	0.0070	1.07	43.0961	0.29	0.063	0.93	23.846	0.13
1.59	0.5	−4.01	0.8	31.87	0.5	−30.08	0.2	10.0085	0.001	−20.0074	0.001	0.0034	0.87	49.3107	0.12	0.009	6.48	41.755	0.44
1.35	0.4	−2.65	0.7	33.50	0.3	−30.49	0.1	10.0120	0.002	−20.0104	0.001	0.0043	0.34	47.3439	0.03	0.017	2.83	35.563	0.49
1.21	0.2	−1.64	0.8	35.73	0.2	−31.05	0.1	10.0156	0.000	−20.0136	0.000	0.0051	0.29	45.8951	0.10	0.024	0.15	32.407	0.03
2.08	4.5	−5.98	0.1	35.80	1.4	−31.08	0.4	10.0122	0.002	−20.0106	0.001	0.0046	0.81	46.8429	0.21	0.026	1.85	31.924	0.70
1.74	0.2	−4.83	0.4	38.10	0.0	−31.63	0.0	10.0149	0.001	−20.0129	0.000	0.0050	0.37	45.9967	0.05	0.030	2.94	30.487	0.86
1.58	0.4	−4.00	0.6	40.29	1.2	−32.10	0.3	10.0188	0.001	−20.0163	0.000	0.0065	0.28	43.6676	0.17	0.042	0.88	27.577	0.15
2.27	0.5	−7.12	0.1	40.03	0.8	−32.03	0.2	10.0207	0.001	−20.0179	0.000	0.0058	0.13	44.6931	0.09	0.044	0.08	27.091	0.15
2.14	3.4	−6.32	0.0	42.29	0.2	−32.53	0.1	10.0236	0.001	−20.0205	0.000	0.0064	0.06	43.8871	0.02	0.053	0.70	25.607	0.36
1.89	0.5	−5.52	0.1	44.28	0.9	−32.92	0.2	10.0267	0.002	−20.0232	0.001	0.0079	0.05	42.0751	0.07	0.065	0.63	23.689	0.22
1.71	0.1	−4.69	0.2	36.49	0.8	−31.24	0.2	10.0096	0.005	−20.0083	0.002	0.0036	1.80	49.0018	0.24	0.009	3.29	41.022	0.26
1.55	0.4	−3.74	0.3	37.46	0.1	−31.46	0.1	10.0130	0.000	−20.0113	0.000	0.0045	0.33	46.9405	0.01	0.018	0.21	34.851	0.12
1.34	0.3	−2.52	0.9	40.05	0.6	−32.06	0.1	10.0169	0.005	−20.0146	0.002	0.0054	0.89	45.4642	0.25	0.025	1.04	31.978	0.20
2.16	0.7	−6.70	0.1	40.56	0.4	−32.15	0.1	10.0129	0.005	−20.0112	0.002	0.0046	1.50	46.6950	0.29	0.027	0.14	31.353	0.06
2.04	3.0	−5.95	0.3	42.19	0.7	−32.51	0.2	10.0155	0.001	−20.0134	0.000	0.0052	0.93	45.7544	0.16	0.032	0.12	29.937	0.13
1.76	0.6	−4.91	0.2	44.75	1.0	−33.02	0.3	10.0196	0.004	−20.0170	0.002	0.0067	1.80	43.3978	0.48	0.043	0.17	27.311	0.07
2.44	0.7	−7.71	0.4	44.95	1.0	−33.05	0.3	10.0215	0.000	−20.0186	0.000	0.0059	0.13	44.5629	0.05	0.046	0.56	26.659	0.32
2.31	0.4	−7.30	0.1	46.55	0.5	−33.36	0.1	10.0243	0.001	−20.0211	0.000	0.0066	0.97	43.6625	0.18	0.055	0.13	25.196	0.01
2.06	0.3	−6.30	0.4	48.90	1.5	−33.79	0.4	10.0277	0.001	−20.0240	0.000	0.0081	0.86	41.8230	0.24	0.067	0.28	23.562	0.35
	0.9		0.7		0.7		0.2		0.002		0.001		0.98		0.20		1.75		0.30

. According to the results of the experiment and analysis, the mean absolute percentage error (MAPE) was calculated as 0.9%, 0.7%, 0.002%, 0.98% and 1.75% for Ra, T, Hd, Hc and Hcy, respectively. The MAPE for the S/N ratios of Ra, T, Hd, Hc and Hcy were 0.7%, 0.2%, 0.001%, 0.2% and 0.3%, respectively. It was observed that better results were obtained by converting the output parameters into S/N ratios instead of estimating them using the Taguchi method. Figure 9 shows the MAPE values obtained according to the Taguchi estimation models for Ra, T, Hd, Hc and Hcy. When Figure 9 is analyzed, it is seen that the prediction ability of the Taguchi model for Ra, T, Hd, Hc and Hcy has increased significantly. Using S/N ratios instead of the experimental results reduced the MAPE by 22%, 71%, 50%, 80% and 93% for Ra, T, Hd, Hc and Hcy, respectively.

3.10. Prediction with ANN Method

The small number of experiments in engineering applications and the estimation of output parameters for different input parameters are of vital importance. For this reason, artificial neural network (ANN) is frequently used in engineering applications for modeling and estimation algorithms of output parameters according to input parameters [47]. ANN has been used in versatile applications because they can handle information flows in complex and nonlinear systems [48]. In the study, the 3-15-7-1 structure given in Figure 10 was determined as the most ideal network structure by changing the number of hidden layers and neurons for Ra, T, Hd, Hc and Hcy prediction. In studies with ANN, some of the data are used for training and some of the data are used for testing. For this, 67% of the data were used for training (18) and 33% for testing (9). The Levenberg–Marquardt (trainlm) algorithm and the performance function mean square error (MSE) were chosen for training the data. The prediction values and errors obtained with ANN as a result of the analysis are given in

Table 7. Error values of experimental and S/N ratios for the ANN model.

Ra (µm)				T (°C)				Hd (mm)				Hc (mm)				Hcy (mm)
Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios
Pred µm	APE %	Pred dB	APE %	Pred °C	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %
1.42	0.2	−3.06	0.3	28.08	0.64	−28.94	0.1	10.0108	0.0262	−20.0054	0.0001	0.0030	3.448	50.7495	0.005	0.007	0.000	43.095	0.007
1.18	0.5	−1.64	1.3	28.05	0.19	−29.02	0.2	10.0127	0.0002	−20.0076	0.0002	0.0036	2.703	48.6360	0.000	0.015	0.000	36.476	0.005
1.11	3.3	−0.58	1.7	30.66	0.12	−29.75	0.0	10.0148	0.0007	−20.0102	0.0002	0.0044	0.000	47.1309	0.000	0.022	0.000	33.124	0.084
1.69	5.7	−5.05	0.2	30.98	0.39	−29.83	0.1	10.0100	0.0024	−20.0079	0.0000	0.0035	0.000	49.1178	0.002	0.021	0.000	33.558	0.006
1.50	4.6	−3.92	0.0	33.11	0.27	−30.39	0.1	10.0167	0.0064	−20.0107	0.0001	0.0041	0.000	47.7443	0.000	0.028	0.000	31.056	0.003
1.44	0.2	−3.22	0.3	35.75	0.14	−31.05	0.0	10.0172	0.0034	−20.0142	0.0002	0.0057	0.000	44.8825	0.000	0.038	0.000	28.431	0.095
2.05	0.3	−6.29	0.2	35.21	0.04	−30.81	0.4	10.0177	0.005	−20.0153	0.0001	0.0049	0.000	46.1843	0.026	0.041	0.000	27.747	0.011
1.89	1.4	−5.38	0.2	36.55	0.14	−31.25	0.1	10.0235	0.0118	−20.0176	0.0001	0.0057	1.786	45.0362	0.000	0.052	1.961	25.848	0.004
1.72	0.0	−4.56	0.6	39.60	0.00	−31.95	0.0	10.0227	0.0101	−20.0200	0.0002	0.0069	0.000	43.2230	0.000	0.064	0.000	23.869	0.029
1.57	0.4	−3.98	0.3	29.01	8.49	−29.99	0.1	10.0141	0.007	−20.0073	0.0000	0.0033	2.941	49.3748	0.009	0.007	12.500	41.918	0.048
1.36	0.0	−2.54	0.4	33.60	0.01	−30.57	0.1	10.0145	0.0075	−20.0106	0.0000	0.0043	0.000	47.3306	0.000	0.017	0.000	35.329	0.175
1.21	0.4	−1.71	0.6	35.85	0.14	−31.09	0.1	10.0196	0.0000	−20.0135	0.0002	0.0051	0.000	45.8486	0.000	0.024	0.000	32.392	0.012
1.98	0.6	−5.96	0.3	36.21	0.24	−31.16	0.1	10.0129	0.002	−20.0108	0.0002	0.0045	2.174	46.7448	0.000	0.026	0.000	31.751	0.158
1.73	0.7	−4.81	0.0	37.99	0.29	−31.57	0.2	10.0147	0.0075	−20.0128	0.0002	0.0050	0.000	46.0233	0.006	0.031	6.897	30.752	0.000
1.42	10.7	−4.04	0.3	39.82	0.04	−32.02	0.1	10.0193	0.0009	−20.0162	0.0001	0.0065	0.000	43.7417	0.000	0.042	0.000	27.479	0.203
2.29	0.4	−7.18	0.3	39.65	0.12	−31.97	0.0	10.0224	0.0021	−20.0179	0.0001	0.0057	1.724	44.7314	0.000	0.043	2.273	27.131	0.000
2.06	0.4	−6.3	0.3	42.99	1.87	−32.48	0.1	10.0287	0.0124	−20.0204	0.0001	0.0065	1.562	43.8759	0.001	0.052	1.887	25.514	0.000
1.7	9.4	−5.48	0.0	44.56	0.32	−32.98	0.1	10.0295	0.0039	−20.0233	0.0002	0.0079	0.000	42.0475	0.000	0.064	1.538	23.742	0.000
1.69	1.1	−4.64	0.4	36.17	0.07	−31.15	0.1	10.0095	0.0029	−20.0079	0.0000	0.0036	2.857	49.1186	0.000	0.008	11.111	40.876	0.095
1.53	0.4	−3.90	0.3	36.88	1.65	−31.51	0.1	10.018	0.0002	−20.0113	0.0001	0.0044	2.222	46.9357	0.000	0.018	0.000	34.895	0.000
1.34	0.0	−2.55	0.4	40.58	0.69	−32.11	0.0	10.0179	0.0000	−20.0151	0.0000	0.0054	0.000	45.3521	0.000	0.025	0.000	32.040	0.003
2.26	3.6	−6.85	1.2	40.45	0.14	−32.12	0.0	10.0142	0.0016	−20.0116	0.0002	0.0047	0.000	46.5580	0.000	0.027	0.000	31.372	0.003
1.96	1.0	−5.91	0.3	41.76	0.34	−32.47	0.1	10.0173	0.0007	−20.0134	0.0002	0.0052	0.000	45.6799	0.000	0.032	0.000	29.897	0.000
1.84	5.4	−4.87	0.2	45.24	0.09	−33.06	0.1	10.0238	0.0043	−20.0167	0.0002	0.0066	0.000	43.6091	0.000	0.043	0.000	27.331	0.000
2.36	2.3	−7.65	0.4	45.36	0.08	−33.15	0.0	10.0221	0.0005	−20.0187	0.0002	0.0058	1.695	44.5722	0.024	0.046	0.000	26.688	0.213
2.34	1.0	−7.43	0.1	46.14	1.41	−33.33	0.2	10.0278	0.0039	−20.0212	0.0002	0.0065	0.000	43.7417	0.000	0.056	1.818	25.193	0.000
2.06	0.5	−6.31	0.2	46.05	4.46	−33.57	0.3	10.0306	0.0100	−20.0239	0.0002	0.0081	1.220	41.7178	0.014	0.067	0.000	23.479	0.000
	2.0		0.4		0.83		0.1		0.005		0.0001		0.901		0.003		1.481		0.043

. The mean absolute percentage error (MAPE) for the obtained experimental results (Ra, T, Hd, Hc and Hcy) were calculated as 2%, 0.83%, 0.005%, 0.901% and 1.481%, respectively. These values were 0.4%, 0.1%, 0.0001%, 0.003% and 0.043% for the S/N ratios, respectively. It was observed that using the data converted to an S/N ratio in the prediction process with ANN yielded better results than using the experimental results. Figure 11 shows that using S/N ratios instead of experimental results reduced MAPE by 80%, 88%, 98%, 100% and 97% for Ra, T, Hd, Hc and Hcy, respectively.

3.11. ANFIS-Based Estimation Method

Adaptive network-based fuzzy inference system (ANFIS) is a hybrid model that coordinates the versatile prospective and subjective procedures of ANN and fuzzy logic. Moreover, ANFIS utilizes the capabilities of ANN and fuzzy logic and eliminates their disadvantages [49,50]. It is widely used in solving complex problems by combining the learning capabilities of different neural networks with the inference capabilities of fuzzy logic [51]. In the study, 67% of the experimental data were randomly selected as the training set and 33% as the test data. The ANFIS model was created by utilizing the fuzzy logic toolbox of Matlab software. Tool coating, cutting speed and feed rate were determined as input parameters of the model. Ra, Ra-S/N, T, T-S/N, Hd, Hd-S/N, Hc, Hc-S/N, Hcy and Hcy-S/N were accepted as output parameters in the model. According to the output parameters, the optimum output parameters were estimated by creating 18 rules in the IF-THEN structure. The ANFIS structure for each output is given in Figure 12. Fuzzy inference system (FIS) parameters, training data set and test data set were determined by trial and error. The prediction results, prediction errors and average errors obtained with the ANFIS model for the input parameters (Ra, Ra-S/N, T, T-S/N, Hd, Hd-S/N, Hc, Hc-S/N, Hcy and Hcy-S/N) are given in

Table 8. Error values of experimental and S/N ratios for the ANFIS model.

Ra (µm)				T (°C)				Hd (mm)				Hc (mm)				Hcy (mm)
Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios		Exp.		S/N Ratios
Pred µm	APE %	Pred dB	APE %	Pred °C	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %	Pred mm	APE %	Pred dB	APE %
1.42	0.0	−3.05	0.14	27.90	0.0	−28.91	0.0	10.0072	0.010	−20.0044	0.005	0.0029	0.000	50.7520	0.000	0.007	0.00	43.098	0.00
1.19	0.0	−1.51	0.06	28.10	0.0	−28.97	0.0	10.0137	0.050	−20.0026	0.025	0.0037	0.000	48.6359	0.000	0.015	0.00	36.478	0.00
0.96	10.3	−0.59	3.01	28.30	7.8	−29.03	2.4	10.0132	0.015	−20.0077	0.012	0.0045	2.272	46.5198	1.297	0.021	4.55	33.154	0.01
1.79	0.0	−5.06	0.06	31.10	0.0	−29.86	0.0	10.0151	0.060	−20.0019	0.030	0.0035	0.000	49.1186	0.000	0.021	0.00	33.556	0.00
1.61	2.9	−3.92	2.48	33.40	0.6	−30.45	0.1	10.0167	0.044	−20.0070	0.018	0.0046	12.195	47.0005	1.558	0.029	3.57	31.064	0.02
1.44	0.0	−3.17	0.09	35.70	0.0	−31.05	0.0	10.0166	0.002	−20.0140	0.001	0.0057	0.000	44.8825	0.000	0.038	0.00	28.404	0.00
2.00	2.9	−6.28	1.71	33.80	4.0	−30.59	1.1	10.0153	0.023	−20.0125	0.014	0.0044	10.204	47.3558	2.510	0.039	4.88	27.480	0.95
1.86	0.0	−5.39	2.05	35.20	3.8	−30.93	1.1	10.0186	0.017	−20.0143	0.017	0.0052	7.143	46.1960	2.575	0.050	1.96	25.852	0.01
1.72	0.0	−4.71	0.44	36.60	7.6	−31.27	2.1	10.0208	0.023	−20.0171	0.014	0.0063	8.696	45.0362	4.195	0.061	4.69	23.886	0.04
1.58	0.0	−3.97	0.08	31.70	0.0	−30.02	0.0	10.0144	0.060	−20.0013	0.030	0.0034	0.000	49.3704	0.000	0.008	0.00	41.938	0.00
1.39	2.6	−2.67	1.66	33.75	0.4	−30.55	0.1	10.0160	0.038	−20.0064	0.021	0.0042	1.163	47.6095	0.589	0.018	3.02	35.491	0.28
1.21	0.0	−1.66	0.26	35.80	0.0	−31.08	0.0	10.0158	0.002	−20.0133	0.001	0.0051	0.000	45.8486	0.000	0.024	0.00	32.396	0.00
1.89	5.0	−5.98	0.22	36.40	0.3	−31.24	0.1	10.0113	0.011	−20.0089	0.009	0.0041	10.870	48.2993	3.326	0.024	7.69	31.781	0.25
1.74	0.0	−4.81	0.02	38.10	0.0	−31.62	0.0	10.0158	0.010	−20.0118	0.005	0.0050	0.000	46.0205	0.000	0.029	0.00	30.752	0.00
1.59	0.0	−4.03	0.05	39.80	0.0	−32.00	0.0	10.0237	0.050	−20.0112	0.025	0.0065	0.000	43.7417	0.000	0.042	0.00	27.535	0.00
2.28	0.0	−7.16	0.02	39.70	0.0	−31.98	0.0	10.0226	0.020	−20.0159	0.010	0.0058	0.000	44.7314	0.000	0.044	0.00	27.131	0.00
2.07	0.0	−6.32	0.01	42.20	0.0	−32.51	0.0	10.0237	0.002	−20.0202	0.001	0.0064	0.000	43.8763	0.000	0.053	0.00	25.514	0.00
1.86	1.1	−5.48	0.06	44.70	0.0	−33.04	0.1	10.0268	0.001	−20.0224	0.004	0.0074	6.329	43.0212	2.316	0.062	4.62	23.788	0.19
1.74	1.8	−4.66	6.44	34.70	4.1	−30.85	1.0	10.0096	0.005	−20.0064	0.007	0.0036	2.857	48.5191	1.221	0.009	0.00	40.825	0.22
1.54	0.0	−3.75	0.01	37.50	0.0	−31.48	0.0	10.0135	0.005	−20.0108	0.003	0.0045	0.000	46.9356	0.000	0.018	0.00	34.895	0.00
1.34	0.0	−2.54	0.08	40.30	0.0	−32.11	0.0	10.0234	0.060	−20.0091	0.030	0.0054	0.000	45.3521	0.000	0.025	0.00	32.041	0.00
2.18	0.0	−6.77	0.01	40.40	0.0	−32.13	0.0	10.0174	0.040	−20.0076	0.020	0.0047	0.000	46.5580	0.000	0.027	0.00	31.373	0.00
1.98	0.0	−5.93	0.06	41.90	0.0	−32.44	0.0	10.0164	0.010	−20.0124	0.005	0.0052	0.000	45.6798	0.000	0.032	0.00	29.897	0.00
1.78	1.7	−4.86	4.72	43.40	4.0	−32.75	1.1	10.0179	0.013	−20.0146	0.010	0.0063	4.545	44.8016	2.735	0.041	4.65	28.321	3.62
2.42	0.0	−7.68	0.05	45.40	0.0	−33.14	0.0	10.0275	0.060	−20.0127	0.030	0.0059	0.000	44.5830	0.000	0.046	0.00	26.745	0.00
2.24	3.2	−7.31	4.24	46.80	0.0	−33.40	0.0	10.0275	0.031	−20.0183	0.015	0.0070	8.461	43.1533	1.345	0.058	6.34	25.165	0.11
2.07	0.0	−6.32	0.01	48.20	0.0	−33.66	0.0	10.0316	0.040	−20.0199	0.020	0.0082	0.000	41.7237	0.000	0.067	0.00	23.479	0.00
	1.2		1.04		1.2		0.3		0.026		0.014		2.768		0.877		1.70		0.21

. According to the experimental results, MAPE was calculated as 1.2%, 1.2%, 0.026%, 2.768% and 1.7% for Ra, T, Hd, Hc and Hcy, respectively. MAPE for Ra-S/N, T-S/N, Hd-S/N, Hc-S/N, and Hcy-S/N ratios were 1.04%, 0.3%, 0.014%, 0.877%, and 0.21%, respectively. According to the calculations, it is seen that using S/N ratios instead of experimental results for the predictions provides better results. Figure 13 shows that MAPE Ra, T, Hd, Hc and Hcy decreased by 13.33%, 75%, 46.15%, 68.32% and 87.65%, respectively, when the S/N ratios were used instead of the experimental results.

3.12. Comparison of Estimation Methods

In order to reach the best values of output parameters such as Ra, T, Hd, Hc and Hcy, which affect product quality and production cost in the drilling process, and have a significant place in the operations in the manufacturing industry, the optimization of input parameters is required. Therefore, modeling methods such as Taguchi, ANN and ANFIS are used in the optimization of the input parameters to obtain the best results for the output parameters. Therefore, CTC, Vc and f were determined as the input parameters in the study. The effects of the determined input parameters on the output parameters (Ra, Ra-S/N, T, T-S/N, Hd, Hd-S/N, Hc, Hc-S/N, Hcy and Hcy-S/N) were investigated and modeled. The accuracies of the estimated values of the models obtained for the S/N ratios according to the experimental results were calculated with Equation (3).

$$Accuracy={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left[1-{\displaystyle \frac{\left|Exp\left(i\right)-Pre\left(i\right)\right|}{Exp\left(i\right)}}\right]\times 100$$

(3)

The calculated accuracy values for the Taguchi, ANN and ANFIS models are given in

Table 9. Accuracy estimation for Ra, Ra-S/N, T, T-S/N, Hd, Hd-S/N, Hc, Hc-S/N, Hcy and Hcy-S/N of Taguchi, ANN and ANFIS models.

Model	Ra		T		Hd		Hc		Hcy
	Exp.	S/N Ratios	Exp.	S/N Ratios	Exp.	S/N Ratios	Exp.	S/N Ratios	Exp.	S/N Ratios
Taguchi	99.11	99.12	99.24	99.80	99.976	99.988	99.021	99.805	98.248	99.704
ANN	97.97	99.60	99.17	99.91	99.986	99.999	99.098	99.997	98.519	99.957
ANFIS	98.84	98.96	98.79	99.65	99.974	99.986	97.232	99.123	98.298	99.788

. It is seen in Table 9 that the estimated values produced with the developed models have higher accuracy for ANN and S/N ratios. Accordingly, it can be said that estimating with the models created by converting the experimental results to S/N ratios will provide higher estimation accuracy. Especially with the ANN model data, 99.6%, 99.91%, 99.999%, 99.997% and 99.957% accuracy rates were achieved in the estimation of Ra, T, Hd, Hc and Hcy.

For the estimates of Ra, T, Hd, Hc and Hcy, MAD, MSE, RMSE and R² values were calculated using Equations (4)–(7) given below. The MAD, MSE, RMSE and R² values calculated for the estimates of Ra, T, Hd, Hc and Hcy are shown in

Table 10. Comparison of Taguchi, ANN and ANFIS methods for Ra, T, Hd, Hc and Hcy.

	Experimental			S/N Ratios
	Taguchi	ANN	ANFIS	Taguchi	ANN	ANFIS
Ra Error
MAD	0.011	0.020	0.016	0.0104	0.0081	0.0115
MSE	0.0002	0.0014	0.0007	0.000148	0.000141	0.00035
RMSE	0.0115	0.0196	0.159	0.01037	0.00815	0.011481
R2	0.997	0.998	0.994	0.99956	0.999958	0.999895
T Error
MAD	0.010	0.008	0.011	0.0452	0.0048	0.0519
MSE	0.00015	0.00014	0.00035	0.00272	0.00009	0.01060
RMSE	0.0104	0.0081	0.0115	0.045	0.004	0.052
R2	0.99996	0.99999	0.99989	0.998	0.999	0.993
Hd Error
MAD	0.00023	0.00010	0.00011	0.000181	0.000063	0.000115
MSE	0.00000012	0.00000006	0.00000007	0.000000064	0.000000007	0.000000048
RMSE	0.00024	0.00010	0.00011	0.000181	0.000063	0.000115
R2	0.9966	0.9982	0.9979	0.996	0.999	0.997
Hc Error
MAD	0.00028	0.00017	0.00069	0.0002	0.0001	0.0914
MSE	0.00000013	0.00000005	0.00000056	0.00000027	0.00000022	0.01355134
RMSE	0.0003	0.0002	0.0007	0.0003	0.0001	0.0914
R2	0.928	0.974	0.819	0.99947	0.99957	0.997318
Hcy Error
MAD	0.00248	0.00237	0.00085	0.0015	0.0005	0.2288
MSE	0.0000137	0.0000078	0.0000019	0.00004129	0.00000089	0.09132296
RMSE	0.0025	0.0024	0.0009	0.00152	0.00052	0.22882
R2	0.954	0.994	0.974	0.999998	0.999999	0.996799

. As can be understood from Table 10, the most accurate model with the S/N ratios is produced and estimated with ANN.

$$MAD={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|Exp\left(i\right)-Pre\left(i\right)\right|$$

(4)

$$MSE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left(Exp\left(i\right)-Pre\left(i\right)\right)$$

(5)

$$RMS=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left[Exp\left(i\right)-Pre\left(i\right)\right]}^2}$$

(6)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left(Exp\left(i\right)-Pre\left(i\right)\right)}^2}{{\sum }_{i=1}^n{\left(Exp\left(i\right)-AverageExp\right)}^2}}$$

(7)

In the equations, n is the number of tests, Exp (i) is the experimental result, Pre (i) is the value predicted by the model, and AverageExp is the average of the experimental data. The comparison of the values predicted by Taguchi, ANN, ANFIS with the experimental results and S/N ratios for the study performed is shown in Figure 14 for Ra, T, Hd, Hc and Hcy, respectively. When Figure 14 is examined in general, the APE results for the models created with the S/N ratios of Ra, T, Hd, Hc and Hcy have decreased significantly compared to the APE results created with the experimental results of Ra, T, Hd, Hc and Hcy. In general, the MAD, MSE, and RMSE values of the models prepared with ANN were minimal compared to the MAD, MSE, and RMSE values of the models prepared with Taguchi and ANFIS, while this situation was maximum for R². This shows us that the reliability coefficient and prediction ability of the ANN model are higher than the Taguchi and ANFIS models.

4. Conclusions

In the study, the effects of the input parameters of cutting tool coating, cutting speed and feed rate on surface roughness, cutting temperature, hole diameter error, hole circularity error and hole cylindricity error in the drilling of the Al 6082-T6 alloy were investigated. In addition, the S/N ratios of the output parameters were calculated using the Taguchi method and it was compared whether the experimental results or the S/N ratios gave better results in estimating the output parameters using the Taguchi, ANN and ANFIS methods. The results obtained in the study are listed below.

• In the experiments conducted with all cutting tool coatings, it was observed that increasing the cutting speed and feed rate increased the cutting temperature, hole diameter error, hole circularity error and hole cylindricity error. While increasing the cutting speed had a positive effect on the surface roughness, increasing the feed rate caused the surface roughness to increase.
• In drilling operations performed with all cutting tool coatings, BUE and BUL formations were observed in cutting tools at a low cutting speed and a high feed rate.
• In the drilling experiments, the lowest surface roughness and cutting temperature values were measured in the coated cutting tool. The maximum surface roughness and cutting temperature occurred in the TiSiN-coated cutting tool.
• The lowest values for hole diameter error and hole circularity error occurred in the drilling process performed with the uncoated cutting tool. The maximum hole diameter error and cylindricity error were measured in the drilling process performed with the TiAlN-coated cutting tool.
• It was observed that minimum hole circularity error values were obtained in drilling operations performed with TiAlN-coated cutting tools, while maximum cylindricity values were obtained in drilling operations performed with uncoated cutting tools.
• As a result of the analysis, it was determined that the optimum cutting parameters were A1B1C3 (Uncoated, 0.11 mm/rev, 200 m/min) for surface roughness, A1B1C1 (Uncoated, 0.11 mm/rev, 120 m/min) for cutting temperature, hole diameter error, hole circularity error and hole cylindricity error.
• It was observed that the accuracy percentage of the estimations made by converting the values to S/N ratios in the estimation of the output parameters with Taguchi, ANN and ANFIS is higher than the estimations made with the experimental results.
• It shows that the reliability coefficient and prediction ability of the ANN model are higher than the Taguchi and ANFIS models in estimating the output parameters.