Tribological Behavior of Reduced Graphene Oxide–Al2O3 Nanofluid: Interaction among Testing Force, Rotational Speed and Nanoparticle Concentration

The tribological properties of nanofluids are influenced by multiple factors, and the interrelationships among the factors are deserving of further attention. In this paper, response surface methodology (RSM) was used to study the tribological behavior of reduced graphene oxide–Al2O3 (rGO-Al2O3) nanofluid. The interaction effects of testing force, rotational speed and nanoparticle concentration on the friction coefficient (μ), wear rate (Wr) and surface roughness (Ra) of steel disks were investigated via the analysis of variance. It was confirmed that all the three input variables were significant for μ and Wr values, while testing force, nanoparticle concentration and its interaction with testing force and rotational speed were identified as significant parameters for Ra value. According to regression quadratic models, the optimized response values were 0.088, 2.35 × 10−7 mm3·N−1·m−1 and 0.832 μm for μ, Wr and Ra, which were in good agreement with the actual validation experiment values. The tribological results show that 0.20% was the optimum mass concentration which exhibited excellent lubrication performance. Compared to the base fluid, μ, Wr and Ra values had a reduction of approximately 45.6%, 90.3% and 56.0%. Tribochemical reactions occurred during the friction process, and a tribofilm with a thickness of approximately 20 nm was generated on the worn surface, consisting of nanoparticle fragments (rGO and Al2O3) and metal oxides (Fe2O3 and FeO) with self-lubrication properties.


Introduction
During material manufacturing and processing, appropriate lubrication techniques are required to reduce friction and wear. Lubricants are critical for cutting [1], rolling [2], forging [3] and other metal forming processes to provide antiwear, cooling and cleaning effects. The application of lubrication can decrease energy consumption, increase productivity and improve the surface quality of products [4,5].
In recent years, with the development of nanotechnology, nanofluids with excellent thermal conductivity, chemical stability and lubricating properties have attracted extensive attention and investigation [6]. For example, thermal transport was significantly enhanced by adding Fe 3 O 4 -CuO [7] and TiO 2 [8] nanoparticles to water-based fluids. Imran [9] and Muhammad et al. [10] numerically investigated the two-dimensional flow and nonlinear thermal radiation of nanoparticles to reveal the interrelationship between temperature distribution and heat transport mechanisms. It has been documented that reduced graphene (rGO) and aluminum oxide (Al 2 O 3 ) nanoparticles as lubricant additives exhibit favorable friction-reducing and antiwear properties under various conditions [11,12]. Gupta et al. [13]

Preparation of Nanofluids
In our preliminary study [16], rGO-Al 2 O 3 nanocomposite was synthesized through a hydrothermal method. Briefly, 0.1 g of GO powder was added to 49.9 g of deionized water and stirred for 1 h. Then, 0.2 g of AI was added to 49.8 g of deionized water, heated to 90 • C and homogeneously stirred. The two aqueous solutions were blended and regulated to be weakly alkaline (pH = 8) using TEA. Next, the mixing solutions were transferred to a reactor, heated to 210 • C and maintained for 12 h to acquire a black colloid. The obtained colloid was freeze-dried after several centrifugations, filtration and rinsing. Finally, the rGO-Al 2 O 3 nanocomposite was fabricated using a heat treatment at 500 • C for 8 h. rGO-Al 2 O 3 nanofluids with different nanoparticle concentrations (0.1, 0.2 and 0.3 wt.%) were prepared by adding rGO-Al 2 O 3 nanocomposite, 2.5 wt.% OM, 2.5 wt.% glycerol, 2.0 wt.% TEA and 0.3 wt.% SDBS in deionized water. OM was used as an extreme pressure agent to improve the load-bearing capacity of the nanofluids. Glycerol and TEA were used as a lubrication additive and pH regulator, respectively. SDBS was used as a dispersant and surfactant to improve the dispersion stability of nanofluids. In addition, base fluid was prepared without the rGO-Al 2 O 3 nanocomposite as the control group, and the physicochemical properties of the base fluid are listed in Table 2. This paper mainly investigated the influence of nanoparticles on tribological behavior. Therefore, the composition and content of the base fluid remained constant, and all nanofluids differed only in the concentration of nanoparticles, to avoid the influence of important factors such as rheological properties, viscosity, fluid film and the surface separation of nanofluids on tribological properties.

Experimental Design
The tribological behavior of rGO-Al 2 O 3 nanofluids were assessed using an MM-W1A pin-on-disk, and the schematic diagram is illustrated in Figure 1. The pin and disk were made of 1045 steel, and the relevant chemical compositions are listed in Table 3. The steel disk had strict machining accuracy requirements (the upper surface roughness needed to be 0.4 µm), and a uniform polishing process was performed before the tests. According to ASTM G99-2016, the friction coefficient (µ) of the steel/steel friction pairs was obtained at the speed of 200-400 rpm and the load of 100-300 N. Our original intention in designing this experiment was to analogize it to the rolling process. In our previous study [16], the rolling force of steel cold rolling was in the range of 50-200 kN, and the contact surface between the strip and roll was 355.59-377.97 mm 2 , so the contact pressure was in the range of 132-562 MPa. In addition, during the pin-on-disk friction process, the contact surface between the pin and disk was about 0.442 mm 2 . To simulate the pressure of the actual rolling process, the test force should in the range of 58-248 N. As a result, the pin was loaded at 100 N, 200 N and 300 N in our study. Similarly, the test speed was also chosen considering the actual material processing. We used an experimental mill with a speed of 30-60 rpm and a radius of 130 mm. In order to keep the linear speed consistent with the tribological experiments, the speed of the pin-on-disk tribotester was kept at 163-325 rpm. The experimental time was set to 30 min, and each group of tests was performed three times to minimize experimental error. During the tribological experiments, the temperature and other factors were kept as stable as possible to ensure the reliability of the data. Ra value was the most commonly discussed of all roughness parameters and was applied to describe the quality of the worn surface [21]. Surface topography and roughness of the wear track on disks were characterized using a laser scanning confocal microscope (LSCM, Olympus LEXTOLS 4100, Tokyo, Japan).The wear rate (W r ) of the disk was established using the weight-loss method and specified as [22]: where ∆m, ρ, F and l represent the wear weight loss, density of the disk, normal force and total wear stroke. ASTM G99-2016, the friction coefficient (μ) of the steel/steel friction pairs was obtained at the speed of 200-400 rpm and the load of 100-300 N. Our original intention in designing this experiment was to analogize it to the rolling process. In our previous study [16], the rolling force of steel cold rolling was in the range of 50-200 kN, and the contact surface between the strip and roll was 355.59-377.97 mm 2 , so the contact pressure was in the range of 132-562 MPa. In addition, during the pin-on-disk friction process, the contact surface between the pin and disk was about 0.442 mm 2 . To simulate the pressure of the actual rolling process, the test force should in the range of 58-248 N. As a result, the pin was loaded at 100 N, 200 N and 300 N in our study. Similarly, the test speed was also chosen considering the actual material processing. We used an experimental mill with a speed of 30-60 rpm and a radius of 130 mm. In order to keep the linear speed consistent with the tribological experiments, the speed of the pin-on-disk tribotester was kept at 163-325 rpm. The experimental time was set to 30 min, and each group of tests was performed three times to minimize experimental error. During the tribological experiments, the temperature and other factors were kept as stable as possible to ensure the reliability of the data. Ra value was the most commonly discussed of all roughness parameters and was applied to describe the quality of the worn surface [21]. Surface topography and roughness of the wear track on disks were characterized using a laser scanning confocal microscope (LSCM, Olympus LEXTOLS 4100, Tokyo, Japan).The wear rate (Wr) of the disk was established using the weight-loss method and specified as [22]: where ∆ , , F and l represent the wear weight loss, density of the disk, normal force and total wear stroke.  In order to investigate the effect of independent variables, the testing force (F), rotational speed of the disk (V) and nanoparticle concentration (Nc) on tribological performance, a mathematical model based on response surface methodology (RSM) was developed. The μ value of fluids and the Wr and Ra values of wear track on steel disks were chosen as responses in this study. Three levels were defined for each variable using the Box-Behnken design as shown in Table 4. A total of 15 trials were conducted according to the design. All the tests were carried out in triplicate, and the average values were employed as response. A quadratic model was used to establish the relationship between these three variables and responses, which can be defined as Equation (2).  In order to investigate the effect of independent variables, the testing force (F), rotational speed of the disk (V) and nanoparticle concentration (N c ) on tribological performance, a mathematical model based on response surface methodology (RSM) was developed. The µ value of fluids and the W r and R a values of wear track on steel disks were chosen as responses in this study. Three levels were defined for each variable using the Box-Behnken design as shown in Table 4. A total of 15 trials were conducted according to the design. All the tests were carried out in triplicate, and the average values were employed as response. A quadratic model was used to establish the relationship between these three variables and responses, which can be defined as Equation (2). where Y is the desired response; A 0 is a constant; and A i , A j and A ij are coefficients of linear, quadratic and cross-product terms, respectively. X i represents the input variables corresponding to the friction process. Design Expert software (version 13.0, Beijing, China) was employed for the regression, fitting process, the acquirement of 3D response surface and optimal response. The analysis of variance (ANOVA), the coefficient of determination (R 2 ) and adjusted R 2 were applied to verify the goodness of fit for the obtained models through the significance of regression and individual model coefficient.

Sample Characterization and Analysis of Worn Surface
Transmission electron microscopy (TEM, JEOL JEM-2010, Tokyo, Japan) was adopted to study the morphology and structure of different nanoparticles. The crystal structure and chemical composition of the rGO-Al 2 O 3 nanoparticle were characterized using X-ray photoelectron spectroscopy (XPS, Kratos AXIS Ultra, Manchester, UK). X-ray powder diffraction (XRD, Rigaku Ultima IV, Tokyo, Japan) was conducted at 2θ range of 10~60 • . The wear morphologies on the steel disk surface were observed using a laser scanning confocal microscope (LSCM, Olympus LEXT OLS4100, Tokyo, Japan). The worn surface of the steel disk was investigated using a scanning electron microscope (SEM, ZEISS Sigma 500, Oberkochen, Germany) with an energy dispersive spectrometer (EDS). The cross section of the steel disk was acquired using a focused ion beam microscope (FIB, Helios NanoLab 600i, Hillsboro, OR, USA). Subsequently, the morphology and chemical composition of the tribofilm were further characterized through TEM and XPS, to propose the lubrication mechanism of the rGO-Al 2 O 3 nanofluid.

Microstructure and Composition of rGO-Al 2 O 3 Nanoparticle
The morphologies of rGO, Al 2 O 3 and rGO-Al 2 O 3 nanoparticles were characterized using TEM, as presented in Figure 2. In Figure 2a, the rGO nanoparticle consisting of several stacked lamellae, exhibited a smooth surface and large lateral dimensions. Whereas the Al 2 O 3 nanoparticle was easily agglomerated and freely associated with other Al 2 O 3 nanoparticles, thereby enhancing the particle size. For the synthesized Al 2 O 3 nanoparticle, as shown in Figure 2c, it was clearly seen that the Al 2 O 3 nanoparticle was randomly distributed on the lamellae of rGO. The diameter of nano-Al 2 O 3 was less than 20 nm, and there was no obvious agglomeration, although the edges of the rGO nanosheet appeared to be slightly folded. The XPS spectra in Figure 3 were employed to investigate the compositions and chemical states of the rGO-Al2O3 nanoparticle. The C 1s peaks in Figure 3a were located at 284.6 eV, 284.6 eV, 284.6 eV and 284.6 eV, corresponding to the C=C, C-C, C-OH and C=O function groups [16]. The intensities of C-OH and C=O were weaker than those of  The XPS spectra in Figure 3 were employed to investigate the compositions and chemical states of the rGO-Al 2 O 3 nanoparticle. The C 1s peaks in Figure 3a were located at 284.6 eV, 284.6 eV, 284.6 eV and 284.6 eV, corresponding to the C=C, C-C, C-OH and C=O function groups [16]. The intensities of C-OH and C=O were weaker than those of C=C and C-C, demonstrating that GO was reduced in the hydrothermal reaction [15]. The O 1s spectrum was divided into three peaks at 530.  The XPS spectra in Figure 3 were employed to investigate the compositions and chemical states of the rGO-Al2O3 nanoparticle. The C 1s peaks in Figure 3a were located at 284.6 eV, 284.6 eV, 284.6 eV and 284.6 eV, corresponding to the C=C, C-C, C-OH and C=O function groups [16]. The intensities of C-OH and C=O were weaker than those of C=C and C-C, demonstrating that GO was reduced in the hydrothermal reaction [15]. The O 1s spectrum was divided into three peaks at 530.  (119) planes of α-Al2O3 (JCPDS card No.10-0173). These diffraction peaks were also found in the rGO-Al2O3 nanocomposite. It is noteworthy that the sharp peak (001) of GO was absent in the rGO-Al2O3 nanocomposite, while a new diffraction peak (corresponding to the (002) plane of rGO) was observed at the position of 24.4°. This was sufficient to demonstrate that GO was reduced to rGO and combined with Al2O3. Associated with the results of XPS and XRD, the successful synthesis of the rGO-Al2O3 nanocomposite was evidenced.

Experimental Results
The pin-on-disk tribological tests of rGO-Al2O3 nanofluids were conducted as per the design illustrated in Table 5, and the output in terms of the three response values were listed. The obtained friction coefficient (μ), wear rate (Wr, calculated by Equation (1)) and

Experimental Results
The pin-on-disk tribological tests of rGO-Al 2 O 3 nanofluids were conducted as per the design illustrated in Table 5, and the output in terms of the three response values were listed. The obtained friction coefficient (µ), wear rate (W r , calculated by Equation (1)) and surface roughness (R a ) were imported into the Design Expert 13.0 software for the subsequent data analysis. The analysis of the variance (ANOVA) of response results was carried out with the objective of analyzing the influence of test conditions and nanoparticle concentration on the obtained results. Tables 6-8 show the ANOVA results of µ, W r and Ra values, respectively. These analyses were carried out at the significance level of 5% meaning that when the p-values were less than 0.05 (or 95% confidence), the corresponding factors were considered to be statistically significant to the response value. Tables 6 and 7 show that all three factors had significant influence on the µ and W r values of the nanofluids. Testing force (F), nanoparticle concentration (N c ) and its interaction with speed (V) were significant to the Ra value of the steel disk, as illustrated in Table 8.  The images in Figure 4 are externally studentized residuals of the three response values. It was obvious that all the data closely followed a straight line, which indicated that the data distribution law was normal [23]. It further demonstrated that the models proposed were adequate and reasonable. In addition, this judgement can also be derived from Tables 6-8 as the lack of fit items was not significant. The images in Figure 4 are externally studentized residuals of the three response values. It was obvious that all the data closely followed a straight line, which indicated that the data distribution law was normal [23]. It further demonstrated that the models proposed were adequate and reasonable. In addition, this judgement can also be derived from Tables 6-8 as the lack of fit items was not significant.

Quadratic Models and Response Surface Analysis
The initial analysis of the response values obtained from RSM included all input variables and their interactions. The regression models obtained according to the quadratic

Quadratic Models and Response Surface Analysis
The initial analysis of the response values obtained from RSM included all input variables and their interactions. The regression models obtained according to the quadratic model for the µ, W r and R a response values are given in Equations (3)-(5). According to Equation (3), the coefficient of F was positive and the coefficient of V and N c was negative, indicating that the µ value increased with the increase in testing force and decreased with the increase in nanoparticle concentration and speed. Whereas the coefficient of the secondary term N c 2 , which also had a significant influence, was positive, indicating that the µ value decreased first and then increased with the increase in concentration. As a result, there was a value of optimal concentration in the range of 0.1~0.3 wt.%. Similarly, according to Equations (4) and (5), the influence of concentration on W r and R a was consistent with its relationship with the µ value. With regards to the influencing factors of wear rate, the primary term (F, V and N c ) and the quadratic term (F 2 , V 2 and N c 2 ) were significant; however, the positive and negative values of the coefficients (in the primary term and the quadratic term) were completely opposite. Therefore, the influence of these factors on W r need to be further analyzed using the 3D response surface plots. The coefficient of determination (R 2 ) and adjusted R 2 of these three values were 0.9937, 0.9908, 0.9975 and 0.9824, 0.9743, 0.9930, respectively. These values are much higher than the results of the previous studies by Bouacha [23] and Sharma et al. [17]. Furthermore, Figure 5 shows the parity plots between the actual and predicted values, and the points clustered near to the diagonal line of the plot indicate that the predicted data by models were very close to the actual test results [24]. Hence, it was concluded that these quadratic mathematical models are highly accurate and persuasive and can be used to analyze the effect of input variables on response results to obtain optimal solutions.
model for the μ, Wr and Ra response values are given in Equations (3)-(5). According to Equation (3), the coefficient of F was positive and the coefficient of V and Nc was negative, indicating that the μ value increased with the increase in testing force and decreased with the increase in nanoparticle concentration and speed. Whereas the coefficient of the secondary term Nc 2 , which also had a significant influence, was positive, indicating that the μ value decreased first and then increased with the increase in concentration. As a result, there was a value of optimal concentration in the range of 0.1~0.3 wt.%. Similarly, according to Equations (4) and (5), the influence of concentration on Wr and Ra was consistent with its relationship with the μ value. With regards to the influencing factors of wear rate, the primary term (F, V and Nc) and the quadratic term (F 2 , V 2 and Nc 2 ) were significant; however, the positive and negative values of the coefficients (in the primary term and the quadratic term) were completely opposite. Therefore, the influence of these factors on Wr need to be further analyzed using the 3D response surface plots. The coefficient of determination (R 2 ) and adjusted R 2 of these three values were 0.9937, 0.9908, 0.9975 and 0.9824, 0.9743, 0.9930, respectively. These values are much higher than the results of the previous studies by Bouacha [23] and Sharma et al. [17]. Furthermore, Figure 5 shows the parity plots between the actual and predicted values, and the points clustered near to the diagonal line of the plot indicate that the predicted data by models were very close to the actual test results [24]. Hence, it was concluded that these quadratic mathematical models are highly accurate and persuasive and can be used to analyze the effect of input variables on response results to obtain optimal solutions. = 0.469 + 0.0002 · − 0.000342 · − 2.55292 · − 6.25 × 10 · · + 0.0002 · · + 0.000925 · · − 4.33 × 10 · + 1.42 × 10 · + 5.31667 · (3) = 5.89 × 10 − 5.44 × 10 · − 1.52 × 10 · − 0.000033 · − 1.61 × 10 · · − 1.26 × 10 · · − 6.70 × 10 · · + 5.37 × 10 · + 3.00 × 10 · + 0.000094 · (mm 3 ·N −1 ·m −1 ) (4) = 1.55313 + 0.002041 · + 0.002786 · − 13.535 · + 1.70 × 10 · · − 0.007025 · · − 0.008175 · · + 5.08 × 10 · − 2.58 × 10 · + 44.35 · (μm) (5) To intuitively investigate the interaction effects of experimental variables including A-F, B-V and C-Nc with the response values (μ, Wr and Ra), 3D response surface plots with contour lines were obtained as shown in Figure 6. At one time, two of them were flexible within the experimental ranges, while the others were kept constant at the middle level. The change in the shape of the surface plots reflects the interaction between input variables. It can be seen from Figure 6a-c that a higher testing force and rotation speed contributed to lower μ value. For the purpose of reducing friction coefficient, the optimal concentration of rGO-Al2O3 nanofluid was about 0.20 wt.%. From Figure 6d-f, the lowest Wr value was obtained using the combination of the lowest testing force and the appropriate speed (about 350 rpm) at the optimal concentration of about 0.19 wt.%. Regarding surface roughness, it can be deduced from Figure 6g-i that the lowest Ra value was achieved with To intuitively investigate the interaction effects of experimental variables including A-F, B-V and C-N c with the response values (µ, W r and R a ), 3D response surface plots with contour lines were obtained as shown in Figure 6. At one time, two of them were flexible within the experimental ranges, while the others were kept constant at the middle level. The change in the shape of the surface plots reflects the interaction between input variables. It can be seen from Figure 6a-c that a higher testing force and rotation speed contributed to lower µ value. For the purpose of reducing friction coefficient, the optimal concentration of rGO-Al 2 O 3 nanofluid was about 0.20 wt.%. From Figure 6d-f, the lowest W r value was obtained using the combination of the lowest testing force and the appropriate speed (about 350 rpm) at the optimal concentration of about 0.19 wt.%. Regarding surface roughness, it can be deduced from Figure 6g-i that the lowest R a value was achieved with the lowest testing force and an optimum concentration of about 0.20 wt.%. In the studies of Du [25] and He et al. [26], the best tribological performance was achieved when the nanofluid concentration was 0.5 wt.% and 2.0 wt.%, respectively. In contrast, in our study, the optimum tribological performance was obtained by only adding 0.2 wt.% of rGO-Al 2 O 3 nanoparticles, which had a significant advantage. the lowest testing force and an optimum concentration of about 0.20 wt.%. In the studies of Du [25] and He et al. [26], the best tribological performance was achieved when the nanofluid concentration was 0.5 wt.% and 2.0 wt.%, respectively. In contrast, in our study, the optimum tribological performance was obtained by only adding 0.2 wt.% of rGO-Al2O3 nanoparticles, which had a significant advantage. Through the analysis and discussion above, it is worth mentioning that as the nanoparticle concentration increased above 0.20 wt.%, the μ, Wr and Ra values all became higher, which indicated that the antiwear and antifriction performance of nanofluids were weakened. The general reasons for this phenomenon are as follows. As the nanoparticle concentration increased, the stability of the nanofluids in the process of friction was destroyed, so the nanoparticles were more likely to agglomerate and therefore the μ value rose. This was consistent with the results of our previous study [16]. At the same time, the defect degree of nanoparticles increased after friction, which was also one of the reasons for the deterioration of the lubrication effect with the progress of the friction process. In addition, the abrasive wear caused by agglomerated large-size nanoparticles led to the sharp rise in Wr and Ra values [27]. Furthermore, for the μ and Wr values, the change in testing force had a contrasting opposite effect. The friction coefficient was negatively correlated with the testing force, which is contrary to the conventional tribological lubrication process [28]. This is mainly due to the fact that with the increase in pressure during friction, the rolling effect, interlayer sliding effect and polishing effect became stronger, as did the antifriction effect of the nanofluids. This was based on our conclusions derived from simulating the motion of nanoparticles using nonequilibrium molecular dynamics [29]. The movement form of MoS2-Al2O3 nanoparticles during the friction process was reproduced, and it was found that layered MoS2 and spherical Al2O3 occurred during interlayer sliding and rolling, transferring the friction of the Fe surface to the internal friction of nanoparticles, thus playing the role of antifriction [29]. However, the increase in force Through the analysis and discussion above, it is worth mentioning that as the nanoparticle concentration increased above 0.20 wt.%, the µ, W r and R a values all became higher, which indicated that the antiwear and antifriction performance of nanofluids were weakened. The general reasons for this phenomenon are as follows. As the nanoparticle concentration increased, the stability of the nanofluids in the process of friction was destroyed, so the nanoparticles were more likely to agglomerate and therefore the µ value rose. This was consistent with the results of our previous study [16]. At the same time, the defect degree of nanoparticles increased after friction, which was also one of the reasons for the deterioration of the lubrication effect with the progress of the friction process. In addition, the abrasive wear caused by agglomerated large-size nanoparticles led to the sharp rise in W r and R a values [27]. Furthermore, for the µ and W r values, the change in testing force had a contrasting opposite effect. The friction coefficient was negatively correlated with the testing force, which is contrary to the conventional tribological lubrication process [28]. This is mainly due to the fact that with the increase in pressure during friction, the rolling effect, interlayer sliding effect and polishing effect became stronger, as did the antifriction effect of the nanofluids. This was based on our conclusions derived from simulating the motion of nanoparticles using nonequilibrium molecular dynamics [29]. The movement form of MoS 2 -Al 2 O 3 nanoparticles during the friction process was reproduced, and it was found that layered MoS 2 and spherical Al 2 O 3 occurred during interlayer sliding and rolling, transferring the friction of the Fe surface to the internal friction of nanoparticles, thus playing the role of antifriction [29]. However, the increase in force can increase the wear rate, thus the W r value was positively correlated with the testing force. However, it was difficult to control conditions such as velocity and force to achieve the optimal tribological performance in the actual metalworking processes, which creates challenges for the application of the research results. In the early stages of our research, we tried our best to control the force and velocity conditions to keep them close to the actual parameters, hoping to provide theoretical guidance for the actual production process.

Response Optimization
Response surface optimization was helpful to identify the combination of input variables (pin-on-disk test parameters and nanoparticle concentration) that jointly optimize the µ, W r and R a values to a minimum during the friction process. RSM optimization results with predicted and validation results for different response parameters are shown in Table 9. The desirability on a range from 0 to 1 is used to measure the optimization achievement, and the closer this parameter is to 1, the better and more ideal the optimization result [30]. Every validation test was conducted three times. As shown in Table 9, the differences between the validation and predicted values were only 1.1%, 4.7% and 2.2% for µ, W r and R a values, respectively. Hence, it revealed that the quadratic models of RSM analysis were reliable for predicting experimental results.

Pin-on-Disk Tribological Behavior of Nanofluids
The friction coefficient-time curves, average friction coefficient and wear rate of the disk lubricated with base fluid and 0.20 wt.% rGO-Al 2 O 3 nanofluid are presented in Figure 7. Compared to the base fluid, the average friction coefficient and wear rate of 0.20 wt.% rGO-Al 2 O 3 nanofluid decreased by about 45.6% and 90.3%, respectively. It appears that the introduction of nanoparticles into the base fluid was effective to reinforce the antiwear and antifriction behavior of lubricants. As seen in Figure 7a, the friction coefficient-time curves of 0.20 wt.% rGO-Al 2 O 3 nanofluid were relatively smooth and steady without an obvious rise. The curve kept rising and fluctuating for the base fluid: it was zigzagging and unstable throughout the test. The reduction and stability of the friction coefficient was considered to be attributed to the tribofilm formed by nanoparticles [26]. Furthermore, the addition of rGO-Al 2 O 3 in the base fluid improved the tribofilm stability and strength generated on the surface of friction pairs. This is consistent with the results of previous studies [16,25]. In tribological experiments, the lubrication state of nanofluids generally belongs to boundary lubrication. In the friction contact area, some additives and water were extruded, and nanoparticles mainly played the lubrication role, which was similar to solid lubrication. However, the variation of tribological properties caused by the rheological properties of nanofluids with different concentrations should not be ignored as well.  Figure 8 shows the 2D optical images, 3D topographies and cross-section depth profile of wear tracks to evaluate the lubrication effect of the rGO-Al2O3 nanofluid. As evident in Figure 8a, the worn surface of the steel disk lubricated with base fluid presented with deep furrows and asperities accompanied by dense pits, demonstrating that serious wear  Figure 8 shows the 2D optical images, 3D topographies and cross-section depth profile of wear tracks to evaluate the lubrication effect of the rGO-Al 2 O 3 nanofluid. As evident in Figure 8a, the worn surface of the steel disk lubricated with base fluid presented with deep furrows and asperities accompanied by dense pits, demonstrating that serious wear occurred. Such phenomenon can be ascribed to the severe abrasive wear and corrosion wear during the sliding process. After the addition of rGO-Al 2 O 3 nanoparticles to the base fluid, the friction scratches and furrows on the wear scar became shallower with noticeably sparser pits. Meanwhile, large areas of smooth zones were observed on the surface. The flattening and smoothing of the worn surface reflected the polishing effect of nanoparticles [31], especially the high hardness nano-Al 2 O 3 . The surface roughness values along the diameter of the wear track perpendicular to the grinding marks are listed in Table 10. R a , R p and R v are, respectively, the average roughness value, the maximum peak height and the maximum valley depth of the contour center line [32]. It is clear that when lubricated with base fluid, serious furrows and scratches were generated on the large area of wear track. In striking contrast, with respect to the lubrication with the optimal 0.20 wt.% nanofluid, the wear track width was significantly reduced. The worn surface became quite smooth, and the R a , R p and R v decreased by about 56.0%, 61.1% and 65.3%, respectively. This was due to the deposition and formation of a protective film by the nanoparticles, which effectively isolated the direct contact of friction pairs, and as a result, the asperities and valleys on the worn surface decreased. As a result, the surface quality was improved, and the roughness obviously decreased.  Figure 8 shows the 2D optical images, 3D topographies and cross-section depth profile of wear tracks to evaluate the lubrication effect of the rGO-Al2O3 nanofluid. As evident in Figure 8a, the worn surface of the steel disk lubricated with base fluid presented with deep furrows and asperities accompanied by dense pits, demonstrating that serious wear occurred. Such phenomenon can be ascribed to the severe abrasive wear and corrosion wear during the sliding process. After the addition of rGO-Al2O3 nanoparticles to the base fluid, the friction scratches and furrows on the wear scar became shallower with noticeably sparser pits. Meanwhile, large areas of smooth zones were observed on the surface. The flattening and smoothing of the worn surface reflected the polishing effect of nanoparticles [31], especially the high hardness nano-Al2O3. The surface roughness values along the diameter of the wear track perpendicular to the grinding marks are listed in Table 10. Ra, Rp and Rv are, respectively, the average roughness value, the maximum peak height and the maximum valley depth of the contour center line [32]. It is clear that when lubricated with base fluid, serious furrows and scratches were generated on the large area of wear track. In striking contrast, with respect to the lubrication with the optimal 0.20 wt.% nanofluid, the wear track width was significantly reduced. The worn surface became quite smooth, and the Ra, Rp and Rv decreased by about 56.0%, 61.1% and 65.3%, respectively. This was due to the deposition and formation of a protective film by the nanoparticles, which effectively isolated the direct contact of friction pairs, and as a result, the asperities and valleys on the worn surface decreased. As a result, the surface quality was improved, and the roughness obviously decreased.

Lubrication Mechanism of rGO-Al 2 O 3 Nanofluid
The typical SEM images and relevant EDS map scanning results of wear track on the disk lubricated with 0.20 wt.% rGO-Al 2 O 3 nanofluid are shown in Figure 9. It can be seen in Figure 9 that there were plentiful rGO, Al 2 O 3 and Fe debris adsorbed on the worn surface, which was related to their high surface energy and film-forming capability [33,34]. rGO and Al 2 O 3 nanoparticles were easy to deposit in furrows to improve the surface quality. This is known by relevant scholars as the mending effect of nanoparticles [35]. Interestingly, the distribution of C and Al elements on the worn surface was rather distinct. It suggests that the majority of the rGO-Al 2 O 3 nanocomposites were disintegrated during the friction process due to the local high temperature and pressure. It is noteworthy that a small number of large particles (>5 µm in diameter) formed through the soft-agglomeration of nanoparticles due to van der Waals and Coulomb forces [27]. These attractive interaction forces were susceptible to disruption during the friction process, and the effect on the tribological properties of the nanofluid was probably restricted. As the EDS map scanning results in Figure 9 show, a protective tribofilm formed on the friction surface by means of the nanoparticles, and as a result, tribo-oxidation and corrosion were significantly suppressed. In addition, if the sheer force during the friction process is large enough to overcome the van der Waals force, there would be sliding between the rGO layers to further reduce friction force, and this creates the interlayer sliding effect of nanoparticles [36]. Regarding spherical Al 2 O 3 particles, they can act as bearings between the surface of friction pairs to exhibit antiwear and antifriction effects, which is called the rolling effect [31,37].
The typical SEM images and relevant EDS map scanning results of wear track on the disk lubricated with 0.20 wt.% rGO-Al2O3 nanofluid are shown in Figure 9. It can be seen in Figure 9 that there were plentiful rGO, Al2O3 and Fe debris adsorbed on the worn surface, which was related to their high surface energy and film-forming capability [33,34]. rGO and Al2O3 nanoparticles were easy to deposit in furrows to improve the surface quality. This is known by relevant scholars as the mending effect of nanoparticles [35]. Interestingly, the distribution of C and Al elements on the worn surface was rather distinct. It suggests that the majority of the rGO-Al2O3 nanocomposites were disintegrated during the friction process due to the local high temperature and pressure. It is noteworthy that a small number of large particles (>5 μm in diameter) formed through the soft-agglomeration of nanoparticles due to van der Waals and Coulomb forces [27]. These attractive interaction forces were susceptible to disruption during the friction process, and the effect on the tribological properties of the nanofluid was probably restricted. As the EDS map scanning results in Figure 9 show, a protective tribofilm formed on the friction surface by means of the nanoparticles, and as a result, tribo-oxidation and corrosion were significantly suppressed. In addition, if the sheer force during the friction process is large enough to overcome the van der Waals force, there would be sliding between the rGO layers to further reduce friction force, and this creates the interlayer sliding effect of nanoparticles [36]. Regarding spherical Al2O3 particles, they can act as bearings between the surface of friction pairs to exhibit antiwear and antifriction effects, which is called the rolling effect [31,37]. To provide insights into the lubrication mechanism of the rGO-Al2O3 nanofluid in the friction process, the worn surface of the steel disk was further characterized using TEM and XPS spectroscopy, as presented in Figure 10. In Figure 10a, the thickness of the tribofilm was about 20 nm, which was formed by tribo-sintering under the joint action of high pressure and frictional heat, thus reducing wear and friction [38]. The specific composition of the tribofilm was investigated using XPS analysis. For the Fe 2p spectrum in Figure 10b, peaks at the binding energy of 707.2 eV, 711.3 eV and 725.1 eV were assigned to the FeO, Fe 2p1/2 and Fe 2p3/2 of Fe2O3, respectively. The four peaks of O 1s at 529.5 eV, 530.3 eV, 531.8 eV and 532.6 eV were associated with the Fe2O3, FeO, Al2O3 and C-O bond. As for the Al 2p spectrum, the binding energy of 74.5 eV was related to Al2O3. Based To provide insights into the lubrication mechanism of the rGO-Al 2 O 3 nanofluid in the friction process, the worn surface of the steel disk was further characterized using TEM and XPS spectroscopy, as presented in Figure 10. In Figure 10a, the thickness of the tribofilm was about 20 nm, which was formed by tribo-sintering under the joint action of high pressure and frictional heat, thus reducing wear and friction [38]. The specific composition of the tribofilm was investigated using XPS analysis. For the Fe 2p spectrum in Figure 10b, peaks at the binding energy of 707.2 eV, 711.3 eV and 725.1 eV were assigned to the FeO, Fe 2p1/2 and Fe 2p3/2 of Fe 2 O 3 , respectively. The four peaks of O 1s at 529.5 eV, 530.3 eV, 531.8 eV and 532.6 eV were associated with the Fe 2 O 3 , FeO, Al 2 O 3 and C-O bond. As for the Al 2p spectrum, the binding energy of 74.5 eV was related to Al 2 O 3 . Based on the above results, Fe 2 O 3 and FeO were generated on the worn surface due to the tribochemical reaction, as described in Equations (6)- (8), while the appearance of Al 2 O 3 and C-O bond was attributable to the fragmentation of rGO-Al 2 O 3 nanoparticles during the friction process and their adsorption on the metal surface. It has been revealed that metal oxides contributed to the formation of low-friction tribofilm for excellent selflubrication and antiwear properties [39]. Combined with the easy-to-shear property of rGO, the lubrication performance of the rGO-Al 2 O 3 nanofluid was further promoted.

Conclusions
The interaction of testing force, rotational speed and nanoparticle concentration on tribological performance was investigated through pin-on-disk experiments via RSM. The lubrication mechanism of rGO-Al2O3 nanofluid was proposed. The following conclusions were drawn from this study.
(1) According to ANOVA analysis, the quadratic models for all μ, Wr and Ra values were significant. All three variables were significant for μ and Wr values, while testing force, nanoparticle concentration and its interaction with testing force and rotational speed were identified as significant parameters for Ra value. The optimized response values according to regression models were 0.088, 2.35 × 10 −7 mm 3 ·N −1 ·m −1 and 0.832 μm for μ, Wr and Ra values. In addition, the experimental results were in good agreement with predicted values.
(2) During pin-on-disk friction tests, 0.20 wt.% rGO-Al2O3 nanofluid exhibited the optimum lubrication performance. Compared to the base fluid, the μ, Wr and Ra values were reduced by 45.6%, 90.3% and 56.0%, respectively. The worn surface lubricated by 0.20 wt.% rGO-Al2O3 nanofluid was smoother and flatter with fewer furrows and scratches. Based on the mathematical model and 3D response results, higher speed and

Conclusions
The interaction of testing force, rotational speed and nanoparticle concentration on tribological performance was investigated through pin-on-disk experiments via RSM. The lubrication mechanism of rGO-Al 2 O 3 nanofluid was proposed. The following conclusions were drawn from this study.
(1) According to ANOVA analysis, the quadratic models for all µ, W r and R a values were significant. All three variables were significant for µ and W r values, while testing force, nanoparticle concentration and its interaction with testing force and rotational speed were identified as significant parameters for R a value. The optimized response values according to regression models were 0.088, 2.35 × 10 −7 mm 3 ·N −1 ·m −1 and 0.832 µm for µ, W r and R a values. In addition, the experimental results were in good agreement with predicted values.
(2) During pin-on-disk friction tests, 0.20 wt.% rGO-Al 2 O 3 nanofluid exhibited the optimum lubrication performance. Compared to the base fluid, the µ, W r and R a values were reduced by 45.6%, 90.3% and 56.0%, respectively. The worn surface lubricated by 0.20 wt.% rGO-Al 2 O 3 nanofluid was smoother and flatter with fewer furrows and scratches. Based on the mathematical model and 3D response results, higher speed and lower force can reduce the friction and wear rate, which provided theoretical guidance for the parameter setting of metal processing in the future.
(3) C, O and Al elements were found on the worn surface, which indicated the formation of tribofilm (~20 nm) due to the tribochemical reaction and physical absorption. The metal oxides (Fe 2 O 3 , FeO and Al 2 O 3 ) and nanoparticle debris (Al 2 O 3 and rGO) were the main components of the tribofilm. The lubrication action of rGO-Al 2 O 3 nanofluid can be attributed to the polishing effect, mending effect, rolling effect and interlayer sliding effect of nanoparticles.