Regression model-based parametric analysis of drilling of multi-walled carbon nanotubes-added glass fiber composite laminates

Multi-walled carbon nanotubes (MCNTs)-enhanced glass fiber composite (GFC) laminates are among the most promising materials for fulfilling various structural and non-structural requirements. They have also shown exceptional functional applications as excellent electrical and thermal conductors, as well as electromagnetic interference shielding materials. The present work primarily focuses on developing regression models for the drilling process of 0.3 wt% MCNTs-GFC laminates. For experimentation, three different coated drills—carbide, TiCN-coated, and TiAlN-coated—are used under both dry and chilled air cutting environments. The lowest thrust force, torque, and delamination factor were observed at a feed rate of 10 mm min−1 and a speed of 1500 RPM using a TiCN-coated drill in a chilled air environment. Regression analysis reveals that feed rate significantly influences thrust force, as justified by the R2 value, which is above 90% for the selected cutting conditions. The corresponding t and F statistics values indicate the statistical significance of the relevant explanatory factors. The efficiency of the developed models is further validated by considering the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values, which are 136.9 and 144.7, respectively. These values indicate a good regression fit and likelihood of the models for data prediction. Additionally, there is a strong correlation (coefficient > 0.85) between thrust force and delamination factor under the selected cutting environments. Concurrently, the developed regression models are simulated and evaluated for random experiments (Nos. 87, 125, 187, 243, 244, and 399), and the predicted responses closely match the experimental values.


Introduction
In the realm of engineering, especially in industries like automobile, aerospace, construction, and sports, there is a constant demand for materials that blend low density with superior strength [1,2].This quest has led to the rise of composite materials, particularly those enhanced by the integration of nano-fillers [3].Nano-fillers, when added to the matrix component of composites, significantly elevate the material's strength without affecting its density [4].One standout example in this category is the multi-walled carbon nanotubes (MCNTs).When incorporated into epoxy-based glass fiber composites (GFCs), MCNTs have been found to be exceptionally effective, rendering the composites suitable for a wide range of structural and non-structural purposes [5].
In these composites, the role of reinforcement, typically in the form of fibers such as carbon, glass, or aramid, is critical for bearing the applied load.The addition of nano-fillers like MCNTs to these fiber-reinforced composites has been observed to yield materials with optimal strength and lower density.However, the process of drilling, which is essential for assembling these composite materials, poses several challenges.Due to the heterogeneous composition of composites, drilling often leads to various types of material damages, such as delamination, matrix cracks, and reinforcement breakage.Delamination, primarily resulting from fiber-ply failure, is particularly noteworthy for its significant impact.
The drilling properties of MCNTs-filled epoxy/glass fabric nano-composites have been the subject of various studies.For instance, Ponnuvel et al [6] explored these properties using different drill geometries, such as twist and split type.Despite the breadth of this research, the application of coolants during drilling, especially chilled air, has not been extensively considered.This gap in research is notable, as coolants can significantly influence drilling performance.Li et al [7] demonstrated this through their work showing how microwave curing could reduce delamination and thermal damage in the drilling of carbon nanotube/carbon fiber reinforced epoxy composites.Similarly, Kanu [8] examined the degradation of ply stiffness due to matrix fracture and the interactions of Lamb waves with matrix fractures, providing insights into the structural integrity of these composites during drilling.
Singh and Kumar [9] delved into the effects of varying MCNT weight percentages in epoxy/glass fabric composites on the drilling outcomes of GFRP nanocomposites.They discovered that higher MCNT weight percentages led to a reduction in delamination and surface roughness of the drilled holes.However, they also noted a critical observation: both delamination and surface roughness tended to increase with the feed rate under the specified cutting conditions.This highlights the delicate balance required in the drilling process of these advanced materials.In a similar vein, the work of Nor Khairusshima and Sharifah [10] focused on the use of chilled air as a means to mitigate tool wear during the milling of carbon fiber reinforced polymers (CFRPs).Their findings emphasized the benefits of maintaining lower temperatures in the cutting zone, which in turn enhances drilling efficiency by reducing thrust force and the delamination factor.This is further corroborated by the studies of Abish et al [11], who also employed chilled air to minimize material damage and cutting force during CFRP drilling.These studies collectively underline the significance of temperature control in drilling processes involving advanced composites.Kharwar and Verma [12] conducted a comprehensive analysis of the impacts of various drilling parameters on the delamination factor, thrust force, and surface roughness of MCNT/epoxy nano-composites.Their findings contribute significantly to the understanding of how different drilling conditions affect the quality and integrity of the drilled holes in these materials.
The literature on composite drilling, as evidenced by these studies, has primarily focused on optimizing the drilling process to minimize damage and enhance cutting efficiency.This optimization is crucial, considering the sensitive nature of applications involving these materials.Different machining parameters, as noted in these studies, can have contrasting effects on various responses.For example, an increase in feed rate might facilitate quicker material removal but could lead to poorer surface quality.This complex interplay necessitates the development of detailed regression models to accurately map the relationships between drilling parameters and their outcomes [13][14][15][16][17].
In this light, Venkateshwaran and Perumal [13] employed multivariate regression analysis to draw correlations between feed rate, speed, and delamination during the drilling of natural fiber composites.Their ANOVA results indicated the predominant influence of feed rate over speed on delamination.Expanding on this, Srinivasan et al [14] used quadratic regression models to assess how feed, speed, and drill diameter affected exit delamination in drilling glass fiber-reinforced polypropylene (GFR-PP) composite laminates.This type of modeling provides a more nuanced understanding of the drilling process, enabling better optimization of the machining parameters for desired outcomes.Anand et al [15] ventured into optimizing the drilling operation of hybrid GFR nano-composites by applying grey relational analysis (GRA).They considered variables like spindle speed, feed rate, and drill diameter, and measured responses such as delamination, thrust force, and torque.Their approach underscores the effectiveness of combining multiple criteria decision-making techniques with experimental data to optimize drilling processes.Further exploring the potential of statistical methodologies, Seretis et al [16] utilized the Taguchi methodology, Poisson regression, and a genetic algorithm to identify the best curing conditions for glass fiber reinforced polymer (GFRP) composites.This multifaceted approach demonstrates the versatility of statistical tools in enhancing the quality of machining processes.Agwa and Megahed [17] took a novel approach by employing a sequential quadratic programming algorithm based on newly developed multiple nonlinear regression models.Their focus was on optimizing cutting parameters to minimize delamination in the drilling of glass fiber-reinforced epoxy laminates.Their findings, suggesting that high spindle speed and low feed rate lead to superior drilling performance, provide valuable insights into the intricate dynamics of composite material drilling.
Yusuf Fedai [18] explored the use of various MCDM approaches to evaluate the impact of process factors on output responses like cutting forces, delamination, and surface roughness in GFRP nanocomposites drilling.His study concluded that the Fuzzy AHP-GRA or Fuzzy AHP-WASPAS MCDM approaches are most effective in optimizing the drilling conditions.
Kaybal et al [19] investigated the effects of boron nitride nanoparticles on the machinability properties of carbon fiber epoxy nano-composites, focusing on responses such as thrust force and delamination factor.This study adds to the understanding of how different nano-fillers influence the drilling process of composite materials.Similarly, Mudhukrishnan et al [20] developed multivariate regression models to decipher the influences of cutting parameters on thrust force and delamination factor during the drilling of GFRP-PP composites.Their work contributes to the growing field of research that uses statistical modeling to predict and optimize machining outcomes in composite materials.
The extensive research in this field, as evidenced by studies such as those conducted by Bayraktar and Turgut [21], Kastabha et al [22], Raja et al [23], Mohan Kumar et al [24], and others [25][26][27][28][29][30][31], highlights the critical importance of understanding the effects of various drilling parameters.These studies have collectively advanced the knowledge of how factors like feed rate, cutting speed, drill geometry, and material composition influence drilling outcomes such as delamination, thrust force, surface roughness, and hole quality.
The present work aims to build upon these findings by developing second-order regression equations for drilling 0.3 wt% MCNTs-GFC laminates.The objective is to predict output responses like thrust force, torque, and delamination factor under varying cutting conditions, optimizing the drilling process for manufacturing defect-free holes.The regression models' efficiency will be validated through statistical analyses, offering a comprehensive solution to the challenges faced in drilling composite materials.The rest of the paper is organized as follows: section 2 details the experimental procedure, including the fabrication of MCNTs-GFC laminates and conducting drilling trials.Section 3 presents the corresponding statistical analysis.Results and discussion are provided in section 4, with conclusions in section 5.

Experimental procedure 2.1. Fabrication of MCNTs-GFC laminates
Fabrication of MCNTs-GFC laminates has been accomplished utilizing a conventional hand-layup precedure [32].Table 1 shows the specifications of MCNTs-GFC laminates.The material testing procedures, like tensile and flexural tests, have been performed in accordance with the ASTM standards.The testing results have reported that 0.3 wt% MCNTs-GFC laminates have the optimal combination of tensile and flexural properties.Thus, all the drilling experiments have been subsequenlty perfomned on 0.3 wt% MCNTs-GFC laminates.Table 2 depicts the material properties of the fabricated composites.Figure 1 illustrates the methodology used for the current work.

Drilling study
A CNC vertical milling center is employed for generating through holes in MCNTs-GFC laminates.Figure 2 exhibits the experimental setup, and table 3 enlists the operating levels of the considered drilling parameters.Three different twist drills (carbide, TiCN-coated and TiAlN-coated) are used during the experiments under two cutting environments, i.e. drill and chilled air.Table 4 shows the geometrical details of the twist drill.A universally accepted fixture has been fabricated to hold the MCNTs-GFC laminates during the drilling experiments.A Kistler 9257B dynamometer has been employed for simultaneous measurement of both thrust force and torque.Dry (ambient) and chilled air (3 o C) environments have been considered to explore the effects of the drilling parameters on the responses under consideration.A traditional pencil test has been conducted to calibrate the drilling setup before starting each experiment, and also to check the connectivity between the sensor and the workpiece.Each experiment has been performed three times and the corresponding response values have been averaged.After each experiment, hole consistencies have been inspected using a digital microscope (Model: AM4113T Dino-Lite Premier, resolution: 1.3 M pixels, magnification rate: 20-50X and frame rate: up to 30 fps), and the derived results have been anlayzed for finding out the corresponding values of delamination factor.Table 5 shows the experimetal data for the drilling operation on 0.3 wt% MCNTs-GFC laminates.In addition to conducting drilling experiments on 0.3 wt% MCNTs-GFC laminates, another set of experiments was performed on 0.2 wt% MCNTs-GFC laminates in order to investigate the material behavior and corresponding output responses.The observed data exhibits in table 6.

Thrust force and torque
A pictorial representation showing variations of thrust force and torque with respect to machining time under dry drilling condition and using TiAlN drill, is provided in figure 3. When drilling starts, the primary contact of the chisel edge of the drill bit with the laminate generates a small amount of cutting force due to frictional rubbing action.On further transfer, the twist drill experiences a thrust force in the axial direction and torque in the peripheral or circumferential direction.Thrust force generation during drilling of MCNTs-GFC laminates takes place in three phases, as shown in figure 3(a).During the increasing phase, the thrust force rises with a steep slope.This cutting action may be attributed to the alternative engagement of matrix and fiber layers with the drill cutting edges.In the second phase, the thrust force increases constantly, resulting in the cutting action of MCNTs-GFC laminates.At the end, the drill goes to the bottom ply, causing severe material damage due to higher thrust force.In the last phase, a sharp decline is noticed when the drill tip exits the laminate, whereupon the thrust force becomes zero or negative.Figure 3(b) shows variation of torque with respect to machining time.At first, the torque is very near to zero; but, as the drill cutting edges go closer to the interior of the laminate, the torque begins to progressively increase until it reaches its maximum value once the laminate has been completely engaged.When the drill bit leaves the laminate, there is an immediate and dramatic decrease in the torque to a low value (close to zero).Thus, the changes in both thrust force and torque with respect to machining time remain almost same during the said drilling operation of MCNTs-GFC laminates.

Drilling induced delamination
As mentioned earlier, a digital microscope has been employed for inspecting delamination factor of the drilled holes.The microscopic images have provided diameters of the damaged holes (D max ).On the other hand, D o denotes the initial (true) hole diameter.Finally, the ratio D max /D o calculates the corresponding delamination  factor.Figure 4 exhibits the photograph of the Dino-Lite digital microscope setup for delamination damage measurement.

Statistical analysis
A comprehensive set of explanatory variables (drilling parameters) and responses is essential to evaluate the cutting performance during drilling of MCNTs-GFC laminates.Moreover, selecting and defining those explanatory variables leading to development of the corresponding multivariate regression models to optimize the drilling conditions and analyze their impacts on the responses is a challenging task.In this paper, feed rate, spindle speed and drill type are treated as the explanatory variables, and thrust force, torque and delamination factor are the responses.In regression analysis, there are three basic least-square methods (LSMs), i.e., ordinary LSM, weighted LSM and generalized LSM available for training, testing and predicting unknown responses for given sets of explanatory variables with high accuracy [33][34][35].Among them, ordinary or weighted LSM is mostly adopted to model simple linear regression equations in conjunction with dummy variable coding and dataset alteration [34].The generalized LSM is an extension of ordinary LSM, and is specifically used for continuous categorical predictors [35].In this paper, various regression models have been tested to determine the best fit between the explanatory and response variables, and it is noticed that a second-order regression model would provide the most suitable resolution for the current problem.A second-order bivariate regression model can be represented using equation (1).
where y is the dependant (unknown) variable, x 1 and x 2 are the two explanatory (independent) variables, and a 0 , a 1 , a 2 , a 11 , a 22 and a 12 are the model coefficients.Therefore, in this paper, nine second-order regression models are developed for each cutting environment (dry and chilled air).There are three regression models for each of the response variables (thrust force, torque and delamination) for three different drill types.In addition to the regression models, a unique code in Python is also developed to identify the combination of drilling parameters for any given experiment number and predict the corresponding response values for the considered drilling operation on MCNTs-GFC laminates.However, it should be noted that the equations (2)-( 19) is valid for 10 < f <40 and 500 < N < 1500.(a) Dry cutting condition: Accuracy of the developed regression models is assessed using values of coefficient of determination (R 2 ), Fstatistic and t-statistic.To understand effects of the explanatory variables, such as feed rate and spindle speed on a particular response (thrust force), equation (12) is taken here for subsequent analysis.Table 7 shows the generalized LSM-based results of thrust force using TiCN drill under chilled air cutting condition (representation of equation ( 12)).In general, the regression results provide information with respect to standard error, t-statistic, probability of t-statistic and percentage influence of the explanatory variables on the response under consideration.As shown in table 7, the calculated R 2 value is acceptable (above 0.9) and the related standard error is also low.These results indicate good fit of the model, and excellent agreement between the experimental and predicted values.F-statistic is a representation of joint variable comparison and its higher value (56.30) is an evidence of statistical significance of the developed model.Similarly, higher t-values for feed and feed×feed indicate that the corresponding null hypothesis can be rejected, and the explanatory variables are significant, proving influence of feed rate on thrust force.On the contrary, spindle speed and drill type are not statistically significant.Practically, thrust force increases with increase in feed rate and decreases with higher values of spindle speed.At higher feed rate, the drill bit pushes the material in axial direction instead of shearing, resulting in higher thrust force.But, an increase in spindle speed cuts the material in a better way without ploughing, resulting in decreased thrust force.
Additionally, efficiency of the developed model is validated using residual analysis.In this connection, values of AIC and BIC help in estimating the likelihood of the model with respect to its prediction performance.The AIC is one of the mathematical formulations used for model selection and assessment of parsimony in the model structure.On the other hand, BIC measures the trade-off between model fit and model complexity.Their lower values (AIC = 136.9and BIC= 144.7) in table 7 symbolize good regression fit.Similarly, skewness indicates the degree of assyemtry of a given distribution, and its value usually ranges between −1 and +1.On the other hand, kurtosis provides information with respect to degree of peakedness of a distribution, and its value lies betweem −3 and +3.In table 7, both the derived values of skewness and kurtosis are satisfactory.The JB is a two-sided goodness-of-fit test adopted when a fully specified null distribution is unknown and its parameters must be estimated.Its value would always be greater than or equal to zero.The DW is an autocorrelation test in the residuals from a regression analysis.The DW statistic should have a value ranging between 0 and 4, and its value of 2.0 would denote no autocorrelation in the sample [34].In table 7, both the JB and DW statistics have their values within the specified ranges, validating goodness-of-fit in the developed regression model and absence of autocorrelation in the residuals.
Likewise, other regression models for the remaining responses for different drill types in both the dry and chilled air cutting environments are also developed (not shown here due to paucity of space), and their goodness-of-fit and prediction capability are validated.It is interestingly noticed that the effects of the considered explanatory variables on torque and delamination are the same as that on thrust force under the selected cutting environments.
In table 8, the prediction performance of the developed regression models is tested using the already conducted experiments for both the cutting enviornments.In this table, the actual (experimetal) response values (thrust force, torque and delamination) at a given combination of feed rate and spindle speed, and varying drill types are compared with the predicted values at the same parametric intermix.It shows excellent prediction perfomance of the regression models for all the combinations of the drilling parameters and cutting enviornments.
Similarly, simulation runs are conducted to envisage the response values for any combination of the explanatory variables.When a random experiment number is provided as the input to the developed Python code, it first attempts to match the given experiment number with the already conducted trials and single out the corresponding intermix of the considered drilling parameters.Table 9 depicts the predicted response values for six randomly selected experiment numbers (87, 125, 187, 243, 244 and 399), again validating superior performance of the developed models having minimum prediction error.For all the random experiment numbers, the predicted responses are nearer to their experimental values.Figure 5 shows error bars that show the difference between the experimental and predicted results for random experiment numbers.

Confirmation tests
With a new set of parameters, an experiment was carried out to make sure that the regression models were correct.Multiple response values were found and compared to the values that were predicted through the models.Table 10 shows the parameter levels tested when confirming the built models.It also shows the experimental results along with predicted values of the output responses, which are the thrust force, torque, and delamination factor of the hole in the drilling of MCNTs-GFC laminates.Error percentages of validation data are shown in figures 6 and 7 (dry and chilled air plots respectively); each drill type was tested three times with varying parameter sets and cutting environments.Figure 7 shows smaller error percentages than figure 6, indicating high accuracy in the models, with only a tiny difference between experimental and predicted results.

Results and discussion
4.1.Influences of feed rate, spindle speed and drill type on thrust force and torque The effects of the drilling parameters (feed rate and spindle speed) on thrust force are presented for each drill type in figure 8, for two distinct cutting environments.When the feed rate is increased from 10 to 40 mm min −1 for any given drill type, an increase in thrust force is noticed.This phenomenon is consistent across all the possible spindle speeds.The influences of feed rate and spindle speed on thrust force for carbide drill are shown in figure 8(a).In dry condition, when the feed rate is increased from 10 to 40 mm min −1 , the reported increment in thrust force is 83%, while in chilled air environment, the corresponding increment is 55%.The relevant reported higher thrust force values for dry and chilled air environments are 53.84N and 42.41 N respectively at 40 mm min −1 and 500 rpm.Based on these findings, it can be stated that a dry cutting environment has a higher thrust force than a chilled air environment.This is due to the fact that the composite laminates have decreased resistance to deformation under ambient cutting conditions.Prior research studies on the mechanical properties of fiber-reinforced composites have shown that both their modulus of elasticity and tensile strength  increase with decrement in temperature.Concurrently, an decrease in thrust force is observed at increasing spindle speeds (from 500 to 1500 rpm), resulting in 28% and 66% decrements in its value for dry and chilled air conditions respectively.The relevant reported lower thrust force values for dry and chilled air environments are 25.45 N and 19.61 N respectively at 10 mm min −1 and 1500 rpm.
Many researchers [6,7,[10][11][12] have also experimentally noticed that as spindle speed would increase, thrust force would go down.At higher spindle speed and dry environment, the matrix material is destroyed by the heat generated which builds up around the drill chisel edge and stays there.In contrast, when chilled air is employed, the cool air around the tool absorbs the heat, making the composite laminates more flexible and softer.It signifies that less force is now required to move the tool with less damage to the composite laminates.
For the same cutting conditions, the thrust force generated by TiCN-coated (figure 8(b)) and TiAlN-coated (figure 8(c)) carbide drills exhibits the same trend as noticed for uncoated carbide drill.As the feed rate rises to 40 mm min −1 , increase in thrust force is 33% (50.77N at 1500 rpm) with TiCN drill at dry condition and 29% (41.21 N at 1500 rpm) at chilled air condition.On the contrary, when the spindle speed increases to 1500 rpm, thrust force goes down by 28% (23.04 N at 10 mm min −1 ) at dry and 134% (12.61 N at 10 mm min −1 ) at chilled air environments.The main reason for lower cutting force at higher spindle speed is due to less frictional force and frictional moment between the tool and the laminate.For the selected cutting conditions, variations in thrust force for TiAlN drill are almost the same as those of TiCN drill.With higher feed rates and lower spindle speeds, cutting force would go on increasing.The identified increase in thrust force is 72% (53.21 N at 40 mm min −1 ) for dry and 40% (44.95 N at 40 mm min −1 ) for chilled air environments respectively.Thus, drilling of MCNTs-GFC laminates is noticed to be more stable at lower feed rate and higher spindle speed.
The effects of the drilling parameters on torque are almost the same as those of thrust force.The experimental studies show that torque would continue to increase as feed rate goes up in dry cutting environment.At ambient temperature, increased twisting force is mostly caused by the increased tool edge force.Hence, different actions of shear and compression forces at the tool-chip interface cause higher torque generation.The highest amount of torque is noticed as 0.556 N-m and 0.406 at 40 mm/min feed rate and 500 rpm spindle speed in dry and chilled air conditions respectively using solid carbide drill.On the other hand, torque goes down as spindle speed increases from 500 to 1500 rpm.However, using chilled air at the cutting zone results in lower torque than in dry environment at the same parametric levels.It indicates that supply of chilled air lowers the coefficient of friction and makes the cutting action smoother at the tool-chip interface [11].In the same way, higher refractoriness of the coated drills at lower cutting temperatures decreases the cutting energy, resulting in less torque.The lowest torque values are reported as 0.194 N-m and 0.152 N-m with TiCN coated drill under dry and chilled air cutting conditions respectively.
Thus, according to the results of the present study, both thrust force and torque decrease with decreasing feed rate and increasing spindle speed in two different cutting conditions.Each of the three drill types has almost consistent cutting force across its edges.Significant differences in thrust force and torque are observed regardless of the considered drilling parameters because of the wide range of cutting environments.It may be deduced that a TiCN-coated drill aids in reducing both thrust force and torque during drilling of MCNTs-GFC laminates to a greater extent than a carbide or TiAlN-coated drill.

Effects of of feed rate, spindle speed and drill type on delamination
Figure 9 shows the effects of feed rate, spindle speed and drill type on exit delamination of the drilled hole in two different cutting environments.The delamination factor goes up with higher feed rates at different spindle speeds under consideration.At higher feed rate, the cutting edge needs more power to crush the alternate layers of MCNTs-GFC laminates, causing severe material damage.On the contrary, higher spindle speed reduces delamination damage in both the cutting environments.Higher spindle speed causes the cutting zone to get hotter, leading to smooth internal surface of the drilled hole resulting in limited delamination damage [12].However, the results of this study show that feed rate has a significant impact on the amount of delamination damage, regardless of the spindle speed.The reason for this behavior may be due to heterogeneous nature of the composite laminates.At the same time, exploring the use of coated drills is crucial for reducing the amount of damage caused by delamination.
The effect of carbide drill on exit delamination is illustrated in figure 9(a), in two distinct cutting environments.In both the cutting conditions, its value increases rapidly at higher feed rate (40 mm min −1 ) and for all the spindle speeds.The reported thrust force is also higher under the same drilling conditions (see section 4.1), which results in higher delamination factor.The possible reason may be attributed to inter-laminar fracturing of the nano-composites accompanied by significant fiber breakage [20].Hence, in case of carbide drill, the maximum delamination at exit side of the hole is recorded as 1.105 when the drilling operation is conducted at feed rate of 40 mm min −1 and spindle speed of 1500 rpm in dry environment.On the contrary, the delamination factor is low (1.031) at 10 mm/min feed rate and 1500 rpm spindle speed in chilled air environment.
Figure 9(b) depicts impact of TiCN drill on exit delamination in two different cutting environments.A TiCN drill exhibits less delamination damage under the same cutting conditions as compared to a carbide drill.The potential reason may be due to superior heat absorption and heat transfer capabilities of the TiCN-coated drill within the cutting zone.Additionally, provision of chilled air effectively absorbs heat from the cutting zone, hence, reducing friction between the tool and MCNTs-GFC laminates.This reduction in friction leads to decrement in delamination damage of the drilled hole.In this study, the lowest delamination factor for the TiCN-coated drill is noticed to be 1.078 and 1.025 respectively, in the dry and chilled air cutting environments, at a feed rate of 10 mm min −1 and spindle speed of 1500 rpm.
Figure 9(c) shows the infleunce of TiAlN drill on delamination factor for variable feed rates and spindle speeds in two distinct cutting environments.While using the TiAlN-coated drill, the delamination factor also increases with increasing feed rate (from 10 to 40 mm min −1 ) for all spindle speeds.The maximum delamination factor is recored as 1.104 at 40 mm/min feed rate and 1500 rpm spindle speed in dry cutting condition.On the other hand, the delamination factor is minimum (1.029) at feed rate of 10 mm min −1 and spindle speed of 1500 rpm, in chilled air cutting environment.So, the TiCN-coated drill is better for drilling of MCNTs-GFC laminates than carbide and TiAlN-coated drills.Between the two different cutting environments, chilled air condition has lower delamination factors at exit side of the drilled holes.Based on these discussions, the lowest delamination factor at exit (1.025) is achieved at lower feed rate (10 mm min −1 ) and higher spindle speed (1500 rpm) while employing a TiCN-coated drill in chilled air cutting environment.becomes evident that thrust force has a significant relationship with delamination factor for a particular set of cutting conditions.It is thus advised that during MCNTs-GFC laminate drilling, proper monitoring and control of thrust force would eventually result in lower delamination damage of the machined laminates.

Conclusions
In this paper, an attempt is put forward to perform regression model-based parametric analysis of drilling of 0.3 wt% MCNTs-GFC laminates in two different cutting environments, considering feed rate, spindle rate and type of the drill as the input parameters, and thrust force, torque and delamination as the responses.The followings are the key conclusions derived from this paper: (a) Excellent values of coefficient of determination (R 2 ) in the regression models developed for different drill types and cutting conditions suggest higher proportion of variations that can be explained for the responses by the explanatory variables.
(b) Satisfactory values of both F-and t-statistics justify statistical significance of the explanatory variables under consideration.
(c) The developed models' prediction efficiency is also checked using residual analysis.Lower values of both AIC and BIC respectively indicate good regression fit and likelihood of the models with respect to data prediction.
(d) A strong correlation exists between thrust force and delamination for both the cutting conditions.
(e) The prediction accuracy of the developed models is validated at random experimental trials, showing excellent results.(f) Thus, for drilling of 0.3 wt% MCNTs-GFC laminates, lower feed rate, higher spindle speed, TiCN-coated carbide drill and chilled air environment are recommended for simultaneous minimization of thrust force, torque and exit delamination.
This regression model-based parametric study can also be carried out for other machining processes for analyzing effects of different input parameters on the responses, leading to process optimization.Besides thrust force, torque and delamination, other quality metrics, like circularity, cylindricity, taper and surface roughness of the drilled holes may be considered for further analysis.Effects of varying drill diameters and cryogenic environment on the drilling performance of MCNTs-GFC laminates may also be explored.Applications of Gaussian process regression, support vector regressor, genetic programming and artificial neural networks may be considered to explore the relationships between the explanatory and response variables during drilling of composite laminates.

Figure 3 .
Figure 3. Variations of (a) thrust force and (b) torque against drilling time (at feed rate = 10 mm min −1 and spindle speed = 500 rpm) using TiAlN drill in dry cutting environment.

Figure 5 .
Figure 5. Error bar representation of an experimental and predicted results for random experiment numbers.

Figure 6 .
Figure 6.Error percentages of validation data (Dry cutting condition).

Figure 7 .
Figure 7. Error percentages of validation data (chilled air cutting condition).

Figure 10
portrays the relationships between thrust force, torque and delamination factor in chilled air environments.It shows that thrust force is directly proportional to delamination, and the generated residuals are very close to the fitted curve.The correlation between thrust force and delamination is illustrated in figure10(a), and it is observed to be smaller with a coefficient of correlation 0.94.Figures10(b) and (c) similarly depict the relationship between thrust force & torque and torque & delamination factor, respectively.When compared to figures 10(b) and (c), the linear regression fit in figure 10(a) is better indicative of the true relationship between the variables.Under a dry cutting environment, the same correlation is attempted with the same output responses, but the coefficient of correlation is lower than under a chilled air cutting environment.Therefore, it

Figure 8 .
Figure 8. Variations of thrust force in different drilling environments using (a) carbide drill (b) TiCN drill and (c) TiAlN drill.

Figure 9 .
Figure 9. Variations of delamination factor in dry and chilled air conditions using (a) carbide (b) TiCN and (c) TiAlN drills.

Table 7 .
Generalized LSM results for thrust force using TiCN drill in chilled air cutting condition.

Table 8 .
Comparison of the experimental and predicted responses in different cutting environments.

Table 9 .
Comparison of the response values for random experiment numbers.