MQL Strategies Applied in Ti-6Al-4V Alloy Milling—Comparative Analysis between Experimental Design and Artificial Neural Networks

This paper presents a study of the Ti-6Al-4V alloy milling under different lubrication conditions, using the minimum quantity lubrication approach. The chosen material is widely used in the industry due to its properties, although they present difficulties in terms of their machinability. A minimum quantity lubrication (MQL) prototype valve was built for this purpose, and machining followed a previously defined experimental design with three lubrication strategies. Speed, feed rate, and the depth of cut were considered as independent variables. As design-dependent variables, cutting forces, torque, and roughness were considered. The desirability optimization function was used in order to obtain the best input data indications, in order to minimize cutting and roughness efforts. Supervised artificial neural networks of the multilayer perceptron type were created and tested, and their responses were compared statistically to the results of the factorial design. It was noted that the variables that most influenced the machining-dependent variables were the feed rate and the depth of cut. A lower roughness value was achieved with MQL only with the use of cutting fluid with graphite. Statistical analysis demonstrated that artificial neural network and the experimental design predict similar results.


Introduction
Machining processes, such as turning, boring, drilling, and milling, are some of the most important techniques used in industries [1]. In these processes, the material is separated from the original body by the chips, creating a new shape, and it is estimated that it contributes to approximately 5% of the results. In a turning paper, DOE was employed to select factor levels that benefit network prediction skills, concluding that the DOE methodology constitutes a better approach to the design of RBF networks for roughness prediction than most trial and error approaches. However, a frequently cited ANN disadvantage is the lack of a systematic way to design high-performance networks [35]. Another study deals with AISI 1040 steel machining. Response surface and ANN approaches were used. According to the authors, both approaches predict surface roughness accurately [42]. The authors in [43] reviewed several publications dealing with modeling and roughness by ANNs in machining processes. The review showed that most of the paper had a roughness (R a ) average prediction, and that little attention was given to the efficiency of the training. Researchers point out the definition of the ideal network topology as the main problem in roughness modeling. Optimization efforts are detected in a small number of publications, and comparisons between topology definition approaches are hardly found. Moreover, with regard to validation, most publications neglect or make this ability unclear. The use of the third validation data set can be found in only a few studies. The use of statistical evaluation to compare trained networks can be found in only one fifth of the peer-reviewed papers, in addition to the lack of a statistical evaluation comparing ANN-based models and models obtained by other methods. According to authors, the ANNs models´accuracy are points that require more attention and many papers are presented only in graphic forms, thus lacking information as to the results' reproduction. There is no standard procedure for choosing more appropriate ANN settings, thus becoming a difficult task that depends on many variables. The trial and error method is the procedure most commonly used to identify the best settings [44]. Based on the peer-reviewed literature, some areas of improvement are suggested, such as the no need to transform or change data, that reveal non-regular periodic movement. In addition, papers focus on network characteristics in a specification phase, with tests being performed to determine errors and R oscillations, and to validate a performance optimization model [45].
The objective of this paper is to evaluate the application of different MQL strategies in Ti-6Al-4V alloy machining, and to study whether the prediction of results between the ANNs approaches and factorial design describe similar values. The classical DOE approach and its comparison with a high number of different neural network architectures have not yet been studied. The number of comparative analysis studies between the DOE and ANN approaches is still limited. This paper includes training and testing of 15,000 artificial neural networks to minimize a systematic trial and error in the top milling of a Ti-6Al-4V alloy. An MQL valve was built for this purpose.

Materials and Methods
This was divided into two analyses: the first uses a factorial planning and its statistical correlations, and the second analysis uses artificial neural networks. Milling tests were performed using three different strategies. As results of the experimental planning, the influence of the independent variables on force and roughness parameters was verified by Pareto graphs. Statistical predictions were made using the generated response surfaces. The measured cutting and roughness data served to feed the artificial neural networks, and the predictions obtained by the two approaches were compared by means of a variance analysis. The desirability optimization function was used to seek optimal results aiming at lower roughness and lower cutting efforts. Figure 1 shows the experiment overview. The strategies and materials utilized to manufacture the MQL valve, milling trials, and training of the ANNs are described in this section. A commercial Ti-6Al-4V (Grade 5) titanium alloy bar of 500 mm × 50 mm × 17 mm with an average hardness of 32.4 Hardness Rockwell C was used in this study. Figure 2 illustrates the material with the machining tests performed. Table 1 shows the respective chemical composition.   The strategies and materials utilized to manufacture the MQL valve, milling trials, and training of the ANNs are described in this section. A commercial Ti-6Al-4V (Grade 5) titanium alloy bar of 500 mm × 50 mm × 17 mm with an average hardness of 32.4 Hardness Rockwell C was used in this study. Figure 2 illustrates the material with the machining tests performed. Table 1 shows the respective chemical composition. The strategies and materials utilized to manufacture the MQL valve, milling trials, and training of the ANNs are described in this section. A commercial Ti-6Al-4V (Grade 5) titanium alloy bar of 500 mm × 50 mm × 17 mm with an average hardness of 32.4 Hardness Rockwell C was used in this study. Figure 2 illustrates the material with the machining tests performed. Table 1 shows the respective chemical composition.

Experimental Design and Machining
An experimental design of three factors and two levels (2 3 ) with two central points was used, as shown in Table 2. A replication was performed for each cutting condition, totaling 60 tests. From these, the respective averages were calculated. The data adopted for the cutting speed (v c ), feed rate (f), and depth of cut (a p ) were recommended by the insert manufacturer. The procedure for using each cutting insert was used up to a wear of 0.1 mm. The speed, feed rate, and depth of cut were considered as independent variables. As dependent variables, cutting force (F c ), feed force (F f ), penetration force (F p ), torque (M z ), root mean square height of the surface (S q ), Skewness of height distribution (S sk ) and Kurtosis of height distribution (S ku ) were considered. Response surfaces were generated, and the desirability function was used to optimize the results of each strategy employed. Three different conditions were stipulated for the trials: (a) using no lubrication, called Strategy 1, (b) applying the designed mixing valve and adopting the MQL approach with oil (Strategy 2), and (c) using the MQL approach with the addition of 30% commercial graphite (Strategy 3). The trials were carried out according to Table 3. For the MQL approach, the Superfluid 3 lubricating oil from Quimatic/Tapmatic was applied. Its characteristics are listed in Table 4. The fluid was driven by a Magneti Marelli MAM00103 electric automotive pump (Mauá, Brazil), with a working pressure of 3 bar and a flow rate of 110 L/h connected to a 20 L fuel tank, and with an oil return circuit to the tank. The flow regulation was performed by a manual control valve set to 110 mL/h. The compressed air pressure was maintained at 6 bar. Table 3. Lubrication strategies used (dry/oil/oil + graphite).

Strategy
Cooling and Lubrication Condition 1 Dry (only compressed air) 2 Oil (minimum quantity lubrication (MQL)) 3 Oil + Graphite (MQL) The ROMI D600 machining center (Santa Bárbara d'Oeste, Brazil) with the SIEMENS 840-D CNC control (Figure 3a), a 20 hp motor, and total installed power of 30 kVA was used for milling tests. The insert BDMT 11 03 02 ER-JS (CVD) with grade CA6535 from KYOCERA (Sorocaba, Brazil) was chosen for milling ( Figure 3b). The ROMI D600 machining center (Santa Bárbara d'Oeste, Brazil) with the SIEMENS 840-D CNC control (Figure 3a), a 20 hp motor, and total installed power of 30 kVA was used for milling tests. The insert BDMT 11 03 02 ER-JS (CVD) with grade CA6535 from KYOCERA (Sorocaba, Brazil) was chosen for milling ( Figure 3b). The MQL valve circuit (Sao Caetano do Sul, Brazil) is illustrated in Figure 4. The needle is connected to the bottom part of hydraulic equal cross coupling through a hose, and directs the flow of the mixture. The needle and jet of fluid can be seen in Figure 5. The CAD design and the assembled valve can be seen in Figure 6. The valve was attached to a lubrication hose that was adequate to the machining center.    The needle and jet of fluid can be seen in Figure 5. The CAD design and the assembled valve can be seen in Figure 6. The valve was attached to a lubrication hose that was adequate to the machining center. The needle and jet of fluid can be seen in Figure 5. The CAD design and the assembled valve can be seen in Figure 6. The valve was attached to a lubrication hose that was adequate to the machining center.

Measurements
For the measurement of forces during machining, a KISTLER 9123C rotary dynamometer (Sao Caetano do Sul, Brazil) with 5223B signal conditioner (Sao Paulo, Brazil) was used. Figure 7a shows the dynamometer mounted on the machine, and Figure 7b shows the tool and the mounted valve. The acquisition of the signals was carried out by the PCI 4472 card (Sao Caetano do Sul, Brazil), together with the Labview Signal Express 2.5 software from National Instruments. The frequency for data acquisition was 100 kHz. A Leica S6D microscope (Sao Paulo, Brazil) was used to check the wear after each machining, guaranteeing a Vb flank wear of up to 0.2 mm. Figure 8 shows the measurement of an insert.

Measurements
For the measurement of forces during machining, a KISTLER 9123C rotary dynamometer (Sao Caetano do Sul, Brazil) with 5223B signal conditioner (Sao Paulo, Brazil) was used. Figure 7a shows the dynamometer mounted on the machine, and Figure 7b shows the tool and the mounted valve. The acquisition of the signals was carried out by the PCI 4472 card (Sao Caetano do Sul, Brazil), together with the Labview Signal Express 2.5 software from National Instruments. The frequency for data acquisition was 100 kHz. A Leica S6D microscope (Sao Paulo, Brazil) was used to check the wear after each machining, guaranteeing a Vb flank wear of up to 0.2 mm. Figure 8 shows the measurement of an insert.

Measurements
For the measurement of forces during machining, a KISTLER 9123C rotary dynamometer (Sao Caetano do Sul, Brazil) with 5223B signal conditioner (Sao Paulo, Brazil) was used. Figure 7a shows the dynamometer mounted on the machine, and Figure 7b shows the tool and the mounted valve. The acquisition of the signals was carried out by the PCI 4472 card (Sao Caetano do Sul, Brazil), together with the Labview Signal Express 2.5 software from National Instruments. The frequency for data acquisition was 100 kHz. A Leica S6D microscope (Sao Paulo, Brazil) was used to check the wear after each machining, guaranteeing a V b flank wear of up to 0.2 mm. Figure 8 shows the measurement of an insert.

Measurements
For the measurement of forces during machining, a KISTLER 9123C rotary dynamometer (Sao Caetano do Sul, Brazil) with 5223B signal conditioner (Sao Paulo, Brazil) was used. Figure 7a shows the dynamometer mounted on the machine, and Figure 7b shows the tool and the mounted valve. The acquisition of the signals was carried out by the PCI 4472 card (Sao Caetano do Sul, Brazil), together with the Labview Signal Express 2.5 software from National Instruments. The frequency for data acquisition was 100 kHz. A Leica S6D microscope (Sao Paulo, Brazil) was used to check the wear after each machining, guaranteeing a Vb flank wear of up to 0.2 mm. Figure 8 shows the measurement of an insert.  The Talysurf CCI Lite white light interferometer (Sao Paulo, Brazil) was used for surface measurement. The surface roughness parameters generated using the software TalyMap Gold v. 6.2 and considered in this work were: Sq (root mean square height of the surface), Ssk (skewness of height distribution) and Sku (kurtosis of height distribution). The measuring area was 4.3mm 2 with used 0.8mm cut-off. Figure 9 illustrates the measurement procedure.  The Talysurf CCI Lite white light interferometer (Sao Paulo, Brazil) was used for surface measurement. The surface roughness parameters generated using the software TalyMap Gold v. 6.2 and considered in this work were: S q (root mean square height of the surface), S sk (skewness of height distribution) and S ku (kurtosis of height distribution). The measuring area was 4.3 mm 2 with used 0.8 mm cut-off. Figure 9 illustrates the measurement procedure. The Talysurf CCI Lite white light interferometer (Sao Paulo, Brazil) was used for surface measurement. The surface roughness parameters generated using the software TalyMap Gold v. 6.2 and considered in this work were: Sq (root mean square height of the surface), Ssk (skewness of height distribution) and Sku (kurtosis of height distribution). The measuring area was 4.3mm 2 with used 0.8mm cut-off. Figure 9 illustrates the measurement procedure.

Artificial Neural Networks
From the machining data obtained by the experimental design and measurements, artificial neural networks were created for each cutting condition. With the "Automated Neural Network" workbench from Statistica software (version 13.5), multilayer perceptron networks (MLP) in three independent variables as input were created, and with the machining forces and roughness measured as the "target." Table 5 indicates the independent and dependent variables' selection of the networks used. Table 5. Select variables for analysis.

Train, Test and Validation-ANNs Variables
Continuous inputs v c , f, a p Continuous targets F c , F f , F p , M z , S q , S sk , S ku The MLP architecture has a feedforward characteristic, with a one-way sequence between layers. Neurons have activation functions that use input signals of the anterior layer in a mathematical function, and the choice of activation function influences the behavior of the neural network. The most commonly used ANN type is feedforward, with input, hidden, and output layers. Network data are entered through the input layer and each neuron in this layer relates to each input variable. Hidden layers transmit input data to output layers by accurately simulating the function of the original system. The output layer is related to the results of the network, based on the predicted results errors and the weights of the connections values between neurons. The function of each neuron contains synapses, sums function, and transfer function. Through connections, neurons communicate, multiplying the input value with weight coefficients. These signals are transformed by an activation function, generating the network output result [46]. For each machining strategy, 5000 networks were trained, using various combinations of neuron numbers, activation functions and number of layers, until they reached satisfactory values. Table 6 shows the values used for the training, testing, and validation data for each chosen strategy. Various training and tests were carried out using the test averages to validate the networks' efficiency. Among the averages, three samples were randomly chosen for the tests, and seven samples were used for training. They were replicated 15 times, totaling 112 samples for training. The networks chosen were the ones that obtained the best results in training and testing, as exemplified in Figure 10.
The minimum and maximum number of neurons in the hidden layer were 3 and 25, respectively. The error function chosen was the sum of squares (SOS), due to the fact that it is one of the most used in training of artificial neural networks in regression tasks. The weight decay factor was stipulated between 0.0001 and 0.001. All available activation functions (identity, logistic, tanh, exponential and sine) were used for training.
Various training and tests were carried out using the test averages to validate the networks' efficiency. Among the averages, three samples were randomly chosen for the tests, and seven samples were used for training. They were replicated 15 times, totaling 112 samples for training. The networks chosen were the ones that obtained the best results in training and testing, as exemplified in Figure  10.

Comparative Analysis
With the tabulated data, statistical tests were performed to verify the homogeneity of variances and to compare the pairs of averages. At the end of any experimental design, it should be checked whether the mathematical model obtained is valid [47]. Statistical tests were used to determine whether the two prediction strategies combined with the measurement produce equivalent estimates, i.e., to determine if there is a difference between the averages of results of the artificial neural networks and the experimental design. Analysis of variance was used, and therefore it can be seen if there are statistical differences between the predictions.
In addition, the desirability optimization function was used, in order to obtain optimal values for the three cutting conditions. The approach used in the desirability optimization consists of converting each response of the experimental design y i into a function d i , varying between 0 and 1. If the answer is the desired one, a value of d i = 1 is accepted, otherwise, d i = 0 [47]. In this way, the independent variables are chosen to maximize the global desirability function. In this work, d i = 1 was chosen as the lowest value for machining forces and roughness.

Results and Discussion
This topic provides the experimental design used, and the results of the average measurements of the machining forces and roughness and of the influence of the machining parameters, in relation to the dependent variables. The architectures of the ANNs are demonstrated, and a comparison of the treatments used is made.

Statistical Results of Surface Roughness Measurements
For every cutting condition, the maximum and minimum conditions of the parameters used were analyzed. The S q parameter corresponds to the standard deviation of the distribution curve [48]. The S ku parameter is always presented with the S sk parameter, describing the shape of a topographic surface and its roughness distribution. Mathematically, the parameters skewness and kurtosis measure the symmetry and histogram deviation of all peaks and valleys heights of a machined surface in relation to the Gaussian distribution. The skewness roughness parameter can monitor machined surfaces' wear and tear in service. A surface with a Gaussian distribution, which is symmetrically distributed, has the S sk parameter equal to zero. Positive S sk values indicate the predominance of high peaks, and negative values indicate the prevalence of valleys. On the other hand, S ku parameter measures the degree of flattening or thinning of a topographic distribution of a peak´s roughness profile. On a surface with normal symmetric distribution, the S ku parameter is equal to three. In practical terms, S ku > 3 indicates the presence of acute peaks, while S ku < 3 indicates surface texture free of disproportionately sharp peaks [49,50]. In this work, the lowest S q value was obtained by the number 2 assay used in strategy 3 (0.39 µm). The maximum condition occurred in test 10 strategy 1 (1.57 µm). For the S sk parameter, the minimum value occurred in test 1 strategy 3 (−1.05), and the maximum condition occurred in test 1 strategy 2 (0.49). As for the S ku parameter, the minimum and maximum results are respectively found in test 2 strategy 1 (2.68) and test 1 strategy 3 (15.30). The statistical results are shown in Table 7. Based on statistical analysis results, the minimum and maximum topography surface values measured for each S q , S sk , S ku parameter are shown in Figure 11.

Results and Analysis of Factorial Design
The use of experimental design resulted in measurements of the dependent variables for the three lubrication conditions. The data can be viewed in Table 8. The analysis of the feed rate, cutting, and penetration machining forces for the three tests, as illustrated in the following items, showed that these forces are dominated by the feed rate and the penetration depth variables. It is known that the greater these parameters are, the greater the chip removal forces are and, consequently, the greater the forces generated to remove them are. It has been noted that the cutting force decreases strongly in applications with oil and oil + graphite in relation to the cut without using fluid, due to the fluid emulsivity, minimizing friction, and temperature, acting directly on the flank of the cutting insert. The type of base fluid has a strong effect on the components of the cutting force. Consequently, the force is significantly reduced [1]. For the roughness parameter, the main factors that influence it are the feed rate, the cutting speed, the depth of cut, the vibrations of the cutting tools, the lubricant conditions, and the tool specifications [19]. In this study, it was found that the feed rate and a p were the variables that most influenced roughness.

Trial without Lubrication
Based on the Pareto graphs, it was observed that, for a 95% confidence interval, the cutting speed, advancing and forces were not influenced by the dependent variables. The roughness parameters also did not show any influence on the confidence interval adopted, although the ap and f are the variables with the greatest influence. Analyzing the illustration in Figure 12, the torque was influenced by the feed rate f and the depth of cut a p . parameters also did not show any influence on the confidence interval adopted, although the ap and f are the variables with the greatest influence. Analyzing the illustration in Figure 12, the torque was influenced by the feed rate f and the depth of cut ap. In analyzing the response surfaces obtained by the factorial design of the test without lubrication illustrated in Figure 13, it can be seen that the minimum torque values occur with lower feeds, and lower depths of cut. The analysis process discards the statistical value of vc, since it does not influence the torque in the studied confidence interval. The lowest values of cutting forces, feed rate force, penetration force, and torque occur in smaller feeds, smaller depths of cut, and lower cutting speeds. The contributions of ap and f are striking, indicating that they are possibly responsible for the mechanism regulating the machining forces of this test condition. The area of the section of cut that is defined by the product of the feed by the depth of cut increases with the increase of the feed and the depth of cut, causing an increase in the forces in question.  In analyzing the response surfaces obtained by the factorial design of the test without lubrication illustrated in Figure 13, it can be seen that the minimum torque values occur with lower feeds, and lower depths of cut. The analysis process discards the statistical value of v c , since it does not influence the torque in the studied confidence interval. The lowest values of cutting forces, feed rate force, penetration force, and torque occur in smaller feeds, smaller depths of cut, and lower cutting speeds. The contributions of a p and f are striking, indicating that they are possibly responsible for the mechanism regulating the machining forces of this test condition. The area of the section of cut that is defined by the product of the feed by the depth of cut increases with the increase of the feed and the depth of cut, causing an increase in the forces in question. parameters also did not show any influence on the confidence interval adopted, although the ap and f are the variables with the greatest influence. Analyzing the illustration in Figure 12, the torque was influenced by the feed rate f and the depth of cut ap. In analyzing the response surfaces obtained by the factorial design of the test without lubrication illustrated in Figure 13, it can be seen that the minimum torque values occur with lower feeds, and lower depths of cut. The analysis process discards the statistical value of vc, since it does not influence the torque in the studied confidence interval. The lowest values of cutting forces, feed rate force, penetration force, and torque occur in smaller feeds, smaller depths of cut, and lower cutting speeds. The contributions of ap and f are striking, indicating that they are possibly responsible for the mechanism regulating the machining forces of this test condition. The area of the section of cut that is defined by the product of the feed by the depth of cut increases with the increase of the feed and the depth of cut, causing an increase in the forces in question.

Trial with Oil
Based on the Pareto graphs illustrated in Figure 14, it was observed that the variable a p , the advance f, and the interaction a p and f demonstrated an influence on the cutting force. The variables a p and f demonstrated an influence on the advance force for the 95% confidence interval.

Trial with Oil
Based on the Pareto graphs illustrated in Figure 14, it was observed that the variable ap, the advance f, and the interaction ap and f demonstrated an influence on the cutting force. The variables ap and f demonstrated an influence on the advance force for the 95% confidence interval.
For the same confidence interval, the penetration force was not influenced by the independent variables. Advancement was the most influential variable when a lower confidence interval was adopted.
The torque was influenced by the depth of cut and the feed. For the studied interval, the roughness Sq was influenced by interaction ap and f. The Ssk parameter was influenced by the cutting speed, the feed rate and the interactions between vc and f and vc and ap.  For the same confidence interval, the penetration force was not influenced by the independent variables. Advancement was the most influential variable when a lower confidence interval was adopted.
The torque was influenced by the depth of cut and the feed. For the studied interval, the roughness S q was influenced by interaction ap and f. The S sk parameter was influenced by the cutting speed, the feed rate and the interactions between v c and f and v c and a p .
Analyzing the response surfaces obtained by the test´s factorial with lubrication, it can be seen that the minimum S q values also occur for lower f and higher a p .
The lowest values of cutting forces and torque, illustrated in Figure 15, occur with smaller feed rates and smaller depths of penetration-discarding the cutting speed since it does not influence the approached parameter. The smallest feed rate forces, penetration forces, and torque occur with smaller depths of cut and smaller feed rates. Analyzing the response surfaces obtained by the test´s factorial with lubrication, it can be seen that the minimum Sq values also occur for lower f and higher ap.
The lowest values of cutting forces and torque, illustrated in Figure 15, occur with smaller feed rates and smaller depths of penetration-discarding the cutting speed since it does not influence the approached parameter. The smallest feed rate forces, penetration forces, and torque occur with smaller depths of cut and smaller feed rates.

Trial with Graphite
Based on the Pareto graphs illustrated in Figure 16, it was observed that the variable ap and the feed rate showed an influence on the cutting force. The ap variable showed an influence on the feed rate force, and for a 95% confidence interval, the penetration force was not influenced by the independent variables. The depth of cut was the variable of greatest influence for the penetration force. The torque was influenced by the depth of penetration and the feed rate. For the confidence interval adopted, the Sq roughness was influenced by the feed rate.
Analyzing the response surfaces obtained by the factorial design of the trial with oil and graphite illustrated in Figure 17, it can be seen that the minimum roughness values occur with lower feed rates and smaller depths of cut. The lower values of the cutting forces, feed rate forces, penetration forces, and torque occur with smaller feed rates, smaller depths of penetration, and lower cutting speeds.

Trial with Graphite
Based on the Pareto graphs illustrated in Figure 16, it was observed that the variable a p and the feed rate showed an influence on the cutting force. The a p variable showed an influence on the feed rate force, and for a 95% confidence interval, the penetration force was not influenced by the independent variables. The depth of cut was the variable of greatest influence for the penetration force. The torque was influenced by the depth of penetration and the feed rate. For the confidence interval adopted, the S q roughness was influenced by the feed rate.
Analyzing the response surfaces obtained by the factorial design of the trial with oil and graphite illustrated in Figure 17, it can be seen that the minimum roughness values occur with lower feed rates and smaller depths of cut. The lower values of the cutting forces, feed rate forces, penetration forces, and torque occur with smaller feed rates, smaller depths of penetration, and lower cutting speeds.      Table 9 lists the functions of the responses of the variables F c , F f , F p , M z , S sk , S ku and S q , obtained by the application of the factorial plan in this work. Table 9. Statistical functions for the prediction of dependent variables-Mathematical Function.

Dry MathematicalFunction
In tests with no lubrication, it can be perceived that the machining forces (F c , F f , F p ) are not statistically influenced by the independent variables. Only torque was influenced by the parameters f and a p in the confidence interval studied. In the tests with lubrication, both with oil and graphite, it is apparent that machining forces and torque are significantly influenced by the parameters a p and f. The S q roughness was influenced by the interaction between a p and f in the oil assay, while in the graphite assay, only the f parameter showed significant influence.
The roughness increased with higher feed rates. With the cut depth and feed increase, the cutting area in the tool is increased and, with this, the cutting effort is increased. In the oil strategy, the minimum Ssk values occur with higher cutting speeds and greater feed rates. This is due to a reduction in plastic deformation in the cutting zone incurred by a higher cutting speed. The surface defect is smaller, with a lower overall roughness value. Surface roughness decreases with increased cutting speed due to lower plastic deformation in the cutting zone associated with high speeds [51]. With the increase of the cutting speed, the temperature is increased, and the force is minimized by heating the material, helping its removal, and reducing roughness that, in turn, depends on feed rates. Oil application contributes to this process, minimizes temperature and favors tool life. Tool wear and coolant use generally influence surface finish [52]. This can be seen with the lowest roughness values in the strategies using oil and graphite-added oil. Lower cutting forces and lower feed rates provided lower roughness values. The analysis infers that the cutting force corroborates the surface roughness analysis [52].

Machined Surface Roughness Analysis
Roughness parameters were shown to be governed by the independent variables a p and f. The variable v c is only noted in this work influencing S sk in Strategy 2. To verify the roughness parameters behavior studied, the study of the lowest and highest values of the cut-off conditions was adopted as a premise. Thus, tests 1 and 8 of each experimental planning strategy are analyzed. Figure 18 shows the isometric surfaces and contour maps of the tests for the dry strategy. An increase of S q in 99.8% was perceived due to the increase in a p and f causing greater irregularities of the roughness profile. The negative S sk parameter for both conditions indicates the prevalence of valleys. The positive S ku parameter indicates that the peaks of the machined surface are sharp. The negative Ssk parameter for both conditions indicates the prevalence of valleys. The positive Sku parameter indicates that the peaks of the machined surface are sharp.  Figure 19 shows the isometric surfaces and contour maps of superfluid tests. The Ssk parameter, positive for the minimum cut-off condition, indicates the prevalence of peaks, which does not occur for the maximum values. The positive Sku parameter indicates that the peaks of the machined surface are sharp. It is observed that the increase in feed and cutting speed accentuated the milling marks.  Figure 19 shows the isometric surfaces and contour maps of superfluid tests. The S sk parameter, positive for the minimum cut-off condition, indicates the prevalence of peaks, which does not occur for the maximum values. The positive S ku parameter indicates that the peaks of the machined surface are sharp. It is observed that the increase in feed and cutting speed accentuated the milling marks.

Desirability Function
Once you have the answer functions for all variables dependent on the research, an optimization bringing together all the variables allows you to show the best values for the application of the independent variables. The desirability function is used in single and multiple objective functions. Unlike other strategies, this optimization function avoids a conflict of responses. The variation of the input parameters must be planned to allow for working within the specified experimental design interval [17]. Using the Statistica software, optimal values were sought using the desirability function for each dependent variable. Table 10 and Figure 21 illustrate the results.

Desirability Function
Once you have the answer functions for all variables dependent on the research, an optimization bringing together all the variables allows you to show the best values for the application of the independent variables. The desirability function is used in single and multiple objective functions. Unlike other strategies, this optimization function avoids a conflict of responses. The variation of the input parameters must be planned to allow for working within the specified experimental design interval [17]. Using the Statistica software, optimal values were sought using the desirability function for each dependent variable. Table 10 and Figure 21 illustrate the results.

Prediction of Results by Artificial Neural Networks
With the data obtained by measuring the machining forces and roughness, different training standards and trials of the artificial neural networks were performed. Trainings were performed for different lubrication conditions with an average of 10 samples, creating supervised networks with three input variables (v c , f, and a p ). As the target, the dependent samples F f , F c , F p , M z , and R a were selected.
For the execution of the training and tests, the Automated Neural Network tool of the Statistica software was used. The tests represent the result of the simulation of the previously trained networks. For a future test to validate the training, three samples were randomly reserved. The remaining 7 samples were replicated 15 times, totaling 112 samples for training. Table 11 shows the variables chosen randomly for the validation tests. Table 12 contains information on the architectures of the artificial neural networks used to predict. The test results can be seen in Tables 13 and 14. The measured values and the results of the ANNs are listed respectively as output. There is a good approximation between the values.

Comparative Analysis of Predictions
To verify whether the prediction strategies used in this work produce similar responses, a statistical test was carried out to verify the equality of treatment averages (ANOVA). It was found, as shown in Figure 22, that there were no global differences between prediction strategies (p-value > 0.05). In these graphs, the numbers 1, 2, and 3 represent the measured values, the results of the experimental design using the equations, and the results of the ANNs, respectively.

Comparative Analysis of Predictions
To verify whether the prediction strategies used in this work produce similar responses, a statistical test was carried out to verify the equality of treatment averages (ANOVA). It was found, as shown in Figure 22, that there were no global differences between prediction strategies (p-value > 0.05). In these graphs, the numbers 1, 2, and 3 represent the measured values, the results of the experimental design using the equations, and the results of the ANNs, respectively. Future research can use statistical tests such as Duncan, Bonferroni, Tukey, and the validation in the case of differences in averages that they indicate, can be verified by the Levene test. The inclusion of other percentages of graphite and its comparison with other lubrication strategies, such as liquid nitrogen under dripping, would be interesting.

Conclusions
The design of the MQL mixing valve made it possible to study and analyze different lubrication conditions. The assembled circuit was based on commercial parts. It was found that the independent variables that most influenced the cutting forces and roughness were the depth of cut and feed rate. The cutting forces were significantly reduced with the use of the MQL approach, probably allowing for heat reduction in the cutting flank of the insert, due to the fluid emulsivity. The lowest average of the Sq roughness was achieved by using the MQL practice with cutting fluid and graphite. The desirability function provided the optimized search for the lowest cutting forces and for a lower Future research can use statistical tests such as Duncan, Bonferroni, Tukey, and the validation in the case of differences in averages that they indicate, can be verified by the Levene test. The inclusion of other percentages of graphite and its comparison with other lubrication strategies, such as liquid nitrogen under dripping, would be interesting.

Conclusions
The design of the MQL mixing valve made it possible to study and analyze different lubrication conditions. The assembled circuit was based on commercial parts. It was found that the independent variables that most influenced the cutting forces and roughness were the depth of cut and feed rate. The cutting forces were significantly reduced with the use of the MQL approach, probably allowing for heat reduction in the cutting flank of the insert, due to the fluid emulsivity. The lowest average of the S q roughness was achieved by using the MQL practice with cutting fluid and graphite. The desirability function provided the optimized search for the lowest cutting forces and for a lower roughness value, aiming at the surface finish. In tests with no lubrication, it can be perceived that the machining forces (F c , F f , F p ) are not statistically influenced by the independent variables. Only torque was influenced by the parameters f and a p in the confidence interval studied. In the tests with lubrication, both with oil and graphite, it is apparent that machining forces and torque are significantly influenced by the parameters a p and f. The S q roughness was influenced by the interaction between a p and f in the oil assay, while in the graphite assay, only the f parameter showed significant influence. Lower cutting forces and lower feed rates provided lower roughness values. The paper took into account surface finishing cutting conditions. In the lowest feed rate and depth cut, it can be perceived that statistically, for the confidence interval adopted, that the forces had lower statistical influences than variables a p and f. It has been observed that variables a p and f define the cutting geometry, ergo being responsible for the roughness. The S sk values showed values close to zero in most tests, indicating a symmetry between peaks and valleys. Negative values, however, indicate a trend of valley predominance and a concentration of material near the surface. All S ku parameters measured demonstrated positive values, showing that the tests presented centralized acute peaks. With sharp peaks, there is the possibility of premature wear and tear in contact with another surface. The statistical comparison between the experimental design adopted and the artificial neural networks provided similar responses. Acknowledgments: SENAI-SP and Instituto Mauá de Tecnologia are acknowledged for making their laboratories available for the execution of the tests.

Conflicts of Interest:
The authors declare no conflict of interest. Flank wear (mm) 2(**) two levels