Surface roughness analysis in finishing end milling of Hardox® 450 steel using multilayer graphene-based nanofluid

Hardox® 450 is a structural steel commonly used in the mining and agricultural sectors due to its hardness and toughness combined with high abrasion wear resistance. It is widely known that good surface quality minimizes the occurrence of cracks generating higher fatigue resistance. However, the characteristics of this steel make it difficult to cut, resulting in greater complexity in the choice of process parameters. Additionally, the general industry concern for clean machining encourages the use of lubricooling conditions with less environmental impact. In order to address these difficulties, the paper aims to investigate the performance of multilayer graphene-based nanofluid applied in reduced quantity (NF-RQL) on surface roughness generated by finishing end milling of Hardox® 450 when compared to dry and flood machining. The cutting parameters at three levels were combined, randomized and analyzed via Box–Behnken design. The experimental results showed that the lowest roughness on average values was obtained with NF-RQL (Ra = 0.207 μm), followed by flood machining (Ra = 0.326 μm). The Abbott–Firestone and amplitude probability distribution statistical analysis indicated a greater uniformity of peaks and valleys in the roughness profile obtained by NF-RQL milling than in the other lubricooling environments. All prediction models demonstrated an excellent ability to estimate the roughness values (R-squared > 85%). After the multivariate optimization, NF-RQL and flood conditions generated similar average roughness values (respectively, 0.106 μm and 0.115 μm). However, the material removal rate with NF-RQL (2315 mm3/min) is about 83% higher than flood (1266 mm3/min), justifying its better performance.


Introduction
Materials with high abrasion resistance have been widely used in the industrial sector to increase the useful life of components [1]. Notably, there is the application of Har-dox® 450, which has a nominal hardness of 450 HB and a specific yield point of 1250 MPa [2]. Its tempered martensite microstructure provides high hardness and wear resistance, as well as high tenacity and ductility [3]. These properties reduce the machinability of Hardox® 450 compared to conventional carbon steels [4]. The high hardness and work-hardening rate result in a higher specific cutting pressure, which increases cutting force and power. Higher tensile strength (≈ 1500 MPa) and lower thermal conductivity (≈ 40 W/m⋅K) generate more heat in the cutting zone, increasing the temperature and intensifying the tool failure mechanisms (abrasion, diffusion, oxidation and thermal fatigue) [5]. Therefore, it is typical to apply cutting fluids in machining to increase productivity, as they reduce friction at the tool-chip and tool-workpiece interfaces, decreasing the temperature in the cutting zone and favoring the chip breakage and removal [6,7]. Nevertheless, the upward concern about the environmental impact generated using the machining process has brought the challenge of applying lubricooling methods less aggressive to nature that maintain the established productivity requirements [8]. The demand for renewable or biodegradable lubricants and machining methods with lower environmental and user health impacts has increased recently. In many cases, the search for clean machining involves the reduction (or elimination) of cutting fluids and the consequent reduction in the waste disposal [9][10][11]. Despite the advantages of applying cutting fluid, the conventional "flood" method is often ineffective because it uses too much liquid, which is sometimes unable to reach the cutting zone efficiently. However, dry milling is a better environmentally friendly alternative since it eliminates the cutting fluid. Moreover, this condition can enhance the tool life because an incorrect fluid application in the interrupted cutting can produce thermal fatigue and induce cracks and chipping on the cutting edge. Thus, the dry conditions can provide a long tool life in finishing milling at a high cutting speed [10].
Several alternative lubricooling techniques have been developed in the last decades to improve the overall effectiveness of the process. One of them is the application of reduced quantity lubricant (RQL). Unlike the well-established method for applying the minimum quantity lubricant (MQL) that typically involves a flow rate of 50-500 mL/h (below 50 mL/h generally results in near-dry machining), RQL works at a flow from 0.5 to 5.0 L/h [12]. In the RQL technique, the mineral-, synthetic-or vegetable-based oil is mixed with compressed air at a pressure of 300-600 kPa, producing a mist and introducing droplets into the cutting area. This process significantly reduces the environmental impact, as the droplets are vaporized by extracting latent heat from the cutting zone [13]. Applying MQL or RQL consumes less energy, reducing overall cost and environmental impact. Additionally, the chips generated are almost dry and easy to recycle [8]. Another alternative lubricooling technique involves the application of nanofluids (NF), in which metallic and/or nonmetallic particles of nanometer size (up to 100 nm) are added to a conventional cutting fluid to form a colloidal mixture. Adding specific nanoparticles can significantly improve tribological (friction reduction) and thermophysical (heat transfer) properties of fluids. NFs are not suitable for use in abundance because of their high cost. However, its application in MQL or RQL makes it a viable alternative [14][15][16]. When considering the addition of multilayer graphene platelets (MLG) on the cutting fluid aiming to form a nanofluid, MLG can improve the effect of RQL since it has great thermal dissipation and excellent lubrication performance due to the slip between its layers, in addition to high oxidation and corrosion resistance [11].
Different order deviations are superimposed to form the roughness profile and can characterize the quality of the machined surface. In this case, surface roughness refers to microgeometric errors caused by irregularities, such as small peaks and valleys, which make up the roughness profile [17]. The roughness parameters are representative values that assess the cause of imperfections inherent to the machining process variables such as cutting parameters, tool wear and lubricooling environments [12,18]. The amplitude parameter most used often to evaluate the surface roughness in the industry is R a (average roughness). Nevertheless, due to the limitations of the R a in representing the roughness profile and being little influenced due to random effects, it should not be considered singly [18,19]. Therefore, R z (average maximum height) can complement the analysis since this parameter contemplates the average of the vertical amplitudes. R z is more sensitive to machining process variations than R a because the maximum peak-to-valley profile heights at each sampling length, not their averages, are compared and analyzed [5,19].
However, statistical parameters have a better scientific basis than arithmetic parameters (R a and R z ) and can better characterize the machined surface. For example, the skewness of distribution allows us to assess the symmetry deviation of a roughness profile, and kurtosis describes its degree of flatness [20]. Alternatively, the Abbott-Firestone curve (AFC) makes it possible to represent the statistical roughness profile through a cumulative probability function that indicates how much a reference line will be above or below the profile [21]. Thus, AFC is usually used to analyze flaws in technical surfaces such as topographies (peak-to-valley ratio), lubricating action (oil holding capacity) in sliding parts and load capacity in bearings [22]. Additionally, the amplitude probability distribution (APD) represents the distribution that the set of measured values has about the smallest value, describing the roughness profile [20].
In some cases, the heat generated in the cutting zone can also influence the roughness profile of the machined surface since there is an ideal temperature range for each material where chip shearing is facilitated due to the reduction in its hardness [23]. Furthermore, the abrasion resistance of Hardox® 450 makes it difficult to remove material without lubricating, and this inhibits the choice of a suitable method [1]. Considering the technical hindrances related to Hardox® 450 machining and the hazardous implications of conventional flood machining, the optimization of machining parameters becomes an essential tool to ensure the functional characteristics with the desired quality and high productivity [24].
Response surface methodology (RSM) is a set of mathematical and statistical techniques useful for modeling and analyzing problems in which several input parameters influence the response variable, and the objective is the optimization of this response [25]. Design of experiments (DOE) forms the basis of RSM. Box-Behnken design (BBD) is a statistical optimization of an analytical method to obtain the best combination of parameters that influence a given process. An advantage of BBD is that it does not contain combinations in which all factors are simultaneously at their highest or lowest levels, which avoids extreme conditions and possible unsatisfactory results. BBD also allows determining the variable response using different input variables with a small number of runs. It also permits finding optimal responses for diverse combinations of process parameters [26].
Duc et al. [27] investigated the use of NF-Al 2 O 3 at different concentrations during the milling of Hardox® 500 by evaluating the machining forces using RSM and BBD. The main results were the strong influence of feed rate and low effect of cutting speed, but the investigation was limited to the evaluation of the forces and did not address the quality of the machined surface. Moayyedian et al. [28] evaluated the effects of cutting parameters on surface roughness during dry milling of Hardox® 600 using the Taguchi optimization method. The study showed that the lowest depth of cut, feed per tooth and cutting speed provided the best results. However, there was no comparison between different lubricooling conditions to establish suitable machining conditions. Other modern optimization techniques were observed in recent literature as the multi-response performance index (MRPI) using the gray relational analysis (GRA) in electrochemical micromachining [29] and multi-criteria learning-based optimization (MTLBO) combined with BBD to achieve simultaneous optimization of lower roughness and higher material removal rate (MMR) in the milling process [30].
This work aims to evaluate the surface finish generated by Hardox® 450 milling. Three levels of each cutting parameter (cutting speed, depth of cut and feed per tooth) are tested in three lubricooling techniques (dry, flood and NF-RQL) to verify its effectiveness in minimizing surface roughness (R a and R z values) after the cutting process. In this context, the multilayer graphene-based nanofluid (NF-MLG) applied in the milling of Hardox® 450 steel has still been poorly documented. Thus, the main novelties of this work are mapping the relationship between machined surface finish, lubricooling conditions (especially the NF-MLG in RQL) and cutting parameters for finishing end milling.

Materials and methods
Material properties, machine tool specification, milling cutter characteristics and lubricooling conditions were previously defined before machining. Table 1 shows the chemical composition of Hardox® 450 measured by the SPECTROMAXx™ LMX06 arc/spark optical emission spectrometry analyzer and the manufacturer normalized values (SSAB), Certificate Nr. 850210068 (May 2019). Figure 1 shows the microstructure of Hardox® 450, which is characterized by the tempered martensite. The added alloy elements (Mn, Cr, Mo, Ni and Si) provide high wear resistance, high tenacity and high ductility [3], which reduces machinability compared to conventional carbon steels. About alloy elements, manganese promotes increased tensile strength and favors the formation of martensite; chromium increases hardenability; molybdenum prevents the steel from weakening during quenching; nickel reduces the austenitization temperature without affecting the quenching processes; and silicon increases yield strength, tensile strength and hardness through substitutional solid solution hardening [31]. Figure 2 shows the experimental setup. The ROMI Discovery 308 machining center with a maximum power of 5.5 kW and maximum rotation of 4000 rpm was used for end milling specimens of Hardox® 450 with 100 × 90 x 6.35 mm. In each specimen, six runs of 34 mm length were executed using a Walter Tools Xtra-tec end mill cutter (F4042R.W20.02) with a 20 mm diameter and 35 mm maximum projection length for two Walter Tools PVD (TiAlN + Al 2 O 3 )-coated carbide inserts, grade WSM35, with 0.8 mm tool-tip radius (r ε ). A preliminary study showed that WKP35S CVD (TiCN + Al 2 O 3 )-coated carbide inserts (specified by SSAB [2]) with r ε = 0.4 mm were ineffective in the machining of Hardox® 450 due to premature tool wear [4]. The run-out error (δ) when fixing the milling cutter in the machine tool was verified through the Mitutoyo dial gauge with a resolution of 1.0 μm. The values found were δ ≤ 10 μm. A pair of cutting edges and a lubricooling strategy were used in each experiment.
The oil-free bio-lubricant Bondmann BD-Fluid B90 with 5% dilution on water was used as the cutting fluid in flood condition at 540 L/h. For NF-RQL, the nanofluid consists of the integral water-based synthetic fluid Quimatic® Q-Jet with the addition of multilayer graphene platelets (MLG) with an area of 1-10 µm 2 and a thickness of 1-20 nm at a concentration of 0.05%. The MLG platelets, developed by the Laboratory of Thin Films and Plasma Processes (LFFPP) of the Federal University of Triângulo Mineiro (UFTM), are obtained by exfoliation of natural graphite thermally expanded at high temperature with acids, previously using an ultrasonic process for mechanical exfoliation. The dispersion of MLG in Q-Jet was performed with an ultrasonic homogenizer at LFFPP-UFTM; however, after NF homogenization, simple stirring is sufficient. The NF was applied using a Tapmatic® Nebulizer IV with a flow rate of 2.0 L/h and a pressure of 300 kPa.
After machining, the amplitude roughness parameters R a and R z were measured using the Mitutoyo Surftest SJ-201P (0.01 μm resolution). A sampling length l e = 0.8 mm and an evaluation length l m = 5⋅l e = 4.0 mm were assumed according to DIN EN ISO 4288 (0.1 < R a ≤ 2.0 μm and 0.5 < R z ≤ 10 μm). The mean value of three measurements randomly distributed in the transverse region of the machined profile was considered in the analysis. Additionally, the images of the machined surfaces were collected using the Dino-Lite AM 413ZT USB digital microscope at 50 × magnification. Then, the response variables (R a and R z ) were analyzed through Box-Behnken design of experiment (BBD) based on three controllable factors (cutting speed "v c ," axial depth of cut "a p " and feed per tooth "f z "), each with three levels ( Table 2). The selection of a p values considered the tool-tip radius at 0.5⋅r ε , 1.0⋅r ε and 1.5⋅r ε , while the levels for v c and f z were recommended by the Har-dox® 450 manufacturer [2].
Statistical analyses were performed using Minitab® software, in which the BBD was applied to randomize 15 runs in each experiment (Table 3). Among these runs, three were performed with parameters at the medium level (central point) to test the repeatability of the investigation. Each run had controllable factors that varied according to the preselected levels; however, any run presented the three parameters simultaneously at maximum or minimum levels. Moreover, the ANOVA evaluated the contribution of each controllable input factor (v c , f z , a p ) and their interactions with the response variables (R a , R z ) of the finishing end milling. Additionally, contour plots were used to evaluate the influence and behavior of input factors on the response variables. Finally, a multivariate optimization was carried out to obtain the improved cutting parameters combination that simultaneously resulted in lower R a and R z roughness values. Furthermore, MATLAB® software was used to generate the AFC and APD curves by using the most regular roughness profiles in each experiment in the evaluation length (l m ). Table 3 and Fig. 3 present the roughness values generated in end milling under different lubricooling conditions. Each R a and R z value obtained represents the arithmetic mean of three measurements performed in the stable region of the machined surface (disregarding the sections corresponding to the entrance and exit of the milling cutter) in each sample. Besides, runs 3*, 8* and 13* refer to the controllable input variables at the central point that allows trends to be evaluated during the process. The results show that, on mean values, each lubricooling method provided different ISO categories of surface finish. The dry cutting (R a = 0.426 μm) presented class N6 (0.4 < R a ≤ 0.8 μm), flood condition (R a = 0.326 μm) generated class N5 (0.2 < R a ≤ 0.4 μm) and NF-RQL (R a = 0.207 μm) resulted in a value very close to found R a = 0.47 μm in dry cutting and R a = 0.41 μm under flood condition after the grinding of Hardox® 500. In this case, the roughness values produced by grinding are higher than those generated by milling due to the resulting plowing effects from abrasive machining of this wear-resistant steel. The direct comparison of results obtained in the experiments shows a significant gain in using NF-RQL over the others, resulting in lower values of R a and R z in most runs. The average reduction of R a values was 51.4% compared with dry milling and 36.5% with flood milling. For R z values, the decreases were 44.0% and 33.8%, respectively. Sharma et al. [33]   these runs can be considered the most severe conditions of the experiment. Besides, run 14 generated the highest roughness in dry milling because it combines the critical combination with the absence of a lubricooling environment, thus justifying the high values obtained of R a and R z .

Results and discussions
Alternatively, runs 7 and 15 had the lowest roughness values. In these runs, despite v c7 = 80 m/min and v c15 = 120 m/ min, both used the low level of f z and middle a p . According to Klocke [5], the situation a p = r ε ensures better end milling stability, with slighter variations in cutting force resulting in a more uniform machined surface. Notably, run 7 with flood and NF-RQL produced the lowest surface roughness without significant differences between the values obtained under both lubricooling conditions, probably due to the high significance of feed per tooth in milling hardened steels. According to Chinchanikar et al. [35], the lower f z results in minor cutting force and slight surface roughness. Another significant factor is a p and its interaction with f z , which present ideal combinations according to the cutting parameters used, while v c does not contribute significantly [36]. This result explains the similarity of the results obtained with run 15 since the other parameters are identical.
Aiming to verify statistically whether any random variables affected the process stability and the machined surface finish, Table 4 shows the variance (s 2 ) of the nine values of R a and R z measured in the runs performed at the central points. The greater variation in R z shows that this parameter is more susceptible to random variables inherent in the process (chip formation, cutting temperature, tool wear, etc.). Furthermore, NF-RQL was more stable for R a and flood condition for R z . Then, the results show that the experiments occurred under stable conditions. Figure 4 shows the roughness profile and surface image produced by run 7 (lower roughness values) in each lubricooling method. The differences were well known. According to Wojciechowski et al. [37], the surface profiles have well-defined peaks and valleys when the feed movement of the cutting tool in the milling process is stable. However, these profiles can be affected by possible difficulties with the chip shearing. These difficulties may have influenced the surface profile under flood milling by plastically deforming the material due to its work-hardening rate. The flood condition tends to generate lower temperatures in the cutting zone than the other conditions, resulting in significant variations in its texture. The profile obtained by dry milling has a well-defined distribution, but presents greater amplitudes of peaks and valleys than the others. The NF-RQL profile pattern is similar to the dry condition, but shows a lower amplitude. Majerik and Barenyi [38] point out that temperatures above 250 ºC can cause microstructural changes in Hardox and degradation in mechanical properties (mainly tensile strength and hardness). In the cooling conditions, plastic deformation may have been facilitated, improving the surface finish by machining. Therefore, NF-RQL offers better tribological characteristics than the other conditions. Figure 5 shows the statistical analysis of the Abbott-Firestone curve (AFC) and amplitude probability distribution (APD) for the three lubricooling strategies in run 7. NF-RQL presents good performance since the AFC has a lower slope than the others, in addition to an APD with a higher concentration of values around the mean, i.e., a leptokurtic distribution (positive kurtosis). This result indicates that the profile has low roughness values and slight variation in its peaks and valleys compared to other lubricooling environments, which can be highly desirable in several industrial applications. However, the most significant variation was in dry milling, in which the AFC displayed greater inclination and the APD considerable dispersion, i.e., a platykurtic distribution (negative kurtosis). Policena et al. [18] observe similar variations in the distributions of the AFC and APD curves in their study of surface roughness analysis in finish milling of duplex stainless steel, showing the difference in the roughness profiles of the machined surface, which in their study vary with the cutting parameters used. Sharma et al. [39] explain that the coefficient of friction produced by dry milling is significantly higher than when using cutting fluid, resulting in higher cutting forces and roughness values. Thus, the effects of lubricooling conditions on the surface finish tend to be positive, which justifies the similarity between flood and NF-RQL results in specific runs.
Aiming to investigate the controllable factors and their interactions, the ANOVA was applied, allowing the evaluation of their effects on each response variable. Input factors with a 95% confidence interval (p value ≤ 0.05) were taken into account as significant parameters, while a 0.05 < p value ≤ 0.10 (confidence interval between 90 and 95%), the factors were considered partially significant. Table 5 presents the p values obtained for R a values under each cutting condition, followed by their respective contributions. Analogously, Table 6 shows the ANOVA for R z .
In Table 5, the linear effect of feed per tooth (f z ) is the most significant parameter on the average surface roughness (R a ) under all lubricooling conditions. It was also verified that the cutting speed (v c ) and its interactions are not significant. This result can be observed by comparing runs 2 and 10 and between runs 7 and 15, in which there are no significant differences in the R a values with the increment of v c for the same feed per tooth (f z ) values and axial depth of cut (a p ). When NF-RQL and flood are applied in the milling of Hardox® 450, the linear and quadratic effects of a p become significant. Besides, the interaction f z x a p partially affects R a only in the dry condition. The contribution of a p may be related to the reduction in the friction coefficient due to the formation of an oxide film layer at the tool/machined surface interface provided by the fluid [39]. Thus, the influence of f z is reduced with this tribological improvement, spreading with the increase of a p . Another possible explanation is the reduced hardness of the machined material due to the higher temperature in the cutting zone in dry machining, which favors the chip formation, making the a p less significant for the process [23]. On the other hand, fluid-assisted milling attempts to keep the lower temperature in the cutting zone, resulting in the conservation and increase in the hardness during the chip shearing, indicating the significant contribution of a p to surface roughness [40]. In Table 6, the linear effects of f z and a p are the factors most significantly affecting R z in all lubricooling techniques evaluated. However, the quadratic effect of a p is significant only when NF-RQL or flood is applied. Again, only in dry  condition does the interaction f z x a p partially affect R z . The results obtained for R z are similar to those obtained for R a since the main factors that affect the significance of a p in dry milling compared with NF-RQL or flood milling are possibly due to the same phenomenon. Unlike R a , the parameter R z is sensitive to v c in the NF-RQL condition, in which the interaction v c x a p was significant; in this case, such a change may be related to the greater sensitivity of R z in the detection of roughness peaks since this condition generates a better finish compared to the other lubricooling states, making slight variations between peaks and valleys more representative to R z parameter [18]. According to Hsu et al. [40], the increase in v c can influence the roughness and temperatures in the machining region. However, Dixit et al. [10] mention that in techniques such as MQL and RQL, high temperatures can cause fluid vaporization, influencing the quality of the lubricooling effect and the machined surface finish. The empirical model representing the two responses (Y) can be described as functions of controllable input factors (v c , a p , f z ) and expressed as in Eq. (1).
The coefficient values for the estimation models of R a and R z under different lubricooling environments are shown in Table 7. The comparison plots of the experimental results obtained compared with those predicted by the model are shown in Fig. 6. The excellent approximation of the values estimated by the model for those measured experimentally demonstrates the ability of the respective second-order polynomials to predict the results since all determination coefficients (R-squared) stood above 85%.
The contour plots for each lubricooling condition are shown in Fig. 7, with the lowest level of feed per tooth (f z = 0.05 mm/tooth) being found to be the most significant parameter by ANOVA and indicating higher surface quality as its value decreases. In dry cutting, the lowest R a and R z values are obtained with cutting speed (v c ) at a low level (80 m/min) and axial depth of cut (a p ) close to 1.0 mm. For NF-RQL, the region of lower R a is divided into two zones: one appears with medium/high a p and low v c (i.e., for a p = 1.2 mm, v c ≤ 85 m/min; for a p = 0.8 mm, v c ≤ 102.7 m/ min) while the other appears with high v c (120 m/min) and low a p (0.4 mm). In the case of R z , the lowest values are found in a region that encompasses the parameter ranges for the lowest R a ; however, the range is less wide-ranging for R z . For the flood condition, the contour curves tend to present a pattern for the smallest R a values from the approximate relationship v c < 240 -200⋅a p , indicating little influence of the variation of v c on the process, while the lowest R a is observed with a p < 0.63 mm for any v c . Again, the smallest R z are in a region that covers the parameter ranges for the slightest R a values. Due to the pattern observed in several studies on the milling of hardened materials, this trend is expected. Under different lubricooling conditions, the main factors that affect the surface finish are f z and a p , with v c having little influence and only making significant contributions in exceptional cases [27,28,40].
Based on ANOVA and contour plots that present the conditions that provide better surface finishes, it is noticed that there is a correspondence between the R a and R z behaviors in regions with lower roughness values. This behavior suggests the possibility of simultaneously reaching the lowest values for such parameters. Thus, a multi-objective optimization for surface roughness was performed. Figure 8 presents the composite desirability function for multi-response optimization results for dry, NF-RQL and flood conditions. For all lubricooling strategies, the composite desirability (D) equal to 1.0 was reached. According to Ferreira et al. [26], D = 1.0 presents the optimal maximum or minimum, resulting from the geometric mean of the individual desirability (d) of each analysis parameter. The summarized results are shown in Table 8.
The values of R a and R z obtained using the multivariate optimization are slightly smaller than those obtained with run 7, which presents a similar combination of parameters, changing only the a p level (0.8 mm). Such results are consistent with ANOVA and contour plots parameterized for f z = 0.05 mm/tooth. When comparing the optimized parameters for NF-RQL and flood, in addition to the ecological aspects associated with fluid disposal, the material removal rate (MRR) is higher for NF-RQL (2315 mm 3 /min) compared to flood (1266 mm 3 /min) for similar roughness values. Patil et al. [30] emphasize the industrial importance of the highest possible MRR in combination with a good surface finish since a higher MRR means higher productivity in  milling. In the case of economic aspects, other factors need to be evaluated, such as the cost and consumption of NF-MLG in RQL compared with BD-Fluid B90 in abundance.

Conclusions
This work investigated the performance of multilayer graphene-based nanofluid in reduced quantity (NF-RQL) • NF-RQL produced a better surface finish than dry and flood conditions. The average R a and R z roughness values were at least 33% lower than the others. Dry milling had the worst performance. • NF-RQL resulted in a surface profile with the smallest amplitudes and the greatest homogeneity of peaks and valleys. The AFC and APD analyses confirmed this performance. • ANOVA showed the significant influence of f z over R a and R z regardless of the lubricooling condition. • The estimated values by regression models showed excellent approximation compared to the measured experimental values (R-squared > 85%). • The multivariate optimization resulted in the lowest levels for v c and f z , with different a p levels for each lubricooling condition, which generated the lowest roughness values.  • NF-RQL and flood conditions generated similar R a and R z values using the optimized parameters, whereas the change in the a p level, NF-RQL produced a MRR 82.9% higher than the flood condition, thus resulting in higher productivity. • NF-RQL presents advantages regarding productivity, consumption of lubricooling fluid and environmental impact. However, a more in-depth study must be carried out to demonstrate a significant cost reduction in the process.