## 3 Results
### Effect of Lubricants on the Lubrication Regime, Friction, and Wear
#### 3.2.2 Effect of Lubricants on Friction and Wear  
The effect of lubricants on the kinetic friction coefficient (\(\mu_{k}\)) is graphed in Figure 5. In general, it can be seen that the bio-based lubricants produced the lowest friction coefficients; friction was reduced up to 82.2% with the neat Castor oil compared to the highest value achieved with water (L1) as a lubricant (\(\mu_{k}=0.45\)). It can be observed that the water-based lubricants (L1, L2, and L3) caused the highest friction of the system. This behavior was expected since the water-based lubricants were estimated to operate in boundary lubrication and to achieve the lowest film thicknesses. This caused a higher number of asperities to come into contact, and, therefore, the force necessary to allow the sliding was greater. The synthetic oil (L4), despite having higher viscosity and lubricant film thickness, produced a higher friction coefficient than the lubricant made of water with graphite nanoparticles (L3) and the mineral oil (L5). Even though mineral oil (L5) worked under boundary conditions, it was observed to generate similar friction to the bio-based lubricant with synthetic esters (L7) and even less than that with mineral oil (L6). Figure 6 exhibits optical micrographs of the worn surfaces and the wear track profiles of the steel samples tested with each lubricant. It can be noticed that the samples lubricated with water-based lubricants (L1 and L2) experienced very similar abrasive wear, presenting different wear phenomena like grooves, burnishes, and micro-pitting, mainly. Moreover, their wear track profiles exhibited accumulated material at the ends of the wear track (pile-up). However, on the sample lubricated with graphite nanoparticles in water (L3), bumps and some grooves characteristics of adhesive and abrasive wear can be observed. Practically speaking, the steel samples lubricated with the synthetic lubricant (L4) were the most affected. They suffered abrasive wear that generated scratches and wedge-like wear, and, according to the wear profile, there was also adhered material at the center of the wear track. Figure 5: Effect of lubricants on the average kinetic friction coefficient (\(\mu_{k}\)). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lubricant** & **U** & \(\mathbf{a_{p}}\) **(Pa-1)** & **G** & \(\mathbf{h_{min}}\) **(nm)** & \(\mathbf{A_{min}}\) & **Lubrication Regime** \\ \hline L1 & \(2.81\times 10^{-14}\) & \(2.32\times 10^{-8}\) & 6135 & 0.6 & 0.01 & Boundary \\ L2 & \(3.08\times 10^{-14}\) & \(2.10\times 10^{-8}\) & 5542 & 0.6 & 0.01 & Boundary \\ L3 & \(1.67\times 10^{-12}\) & \(2.57\times 10^{-8}\) & 6777 & 10.3 & 0.21 & Boundary \\ L4 & \(3.45\times 10^{-11}\) & \(0.91\times 10^{-8}\) & 2392 & 48.5 & 0.97 & Boundary \\ L5 & \(8.20\times 10^{-12}\) & \(1.81\times 10^{-8}\) & 4787 & 25.7 & 0.51 & Boundary \\ L6 & \(2.52\times 10^{-11}\) & \(4.30\times 10^{-8}\) & 11369 & 84.1 & 1.68 & Mixed \\ L7 & \(2.79\times 10^{-11}\) & \(3.63\times 10^{-8}\) & 9587 & 82.9 & 1.66 & Mixed \\ L8 & \(2.18\times 10^{-11}\) & \(3.86\times 10^{-8}\) & 10193 & 72.2 & 1.44 & Mixed \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimation of the lubrication regime for the different lubricated systems. On the other hand, the mineral (L5) and bio-based lubricants (L6, L7, and L8) generated the lowest wear of the steel samples principally by abrasion. The optical micrographs of these samples exhibited burnishing, scratching, and polishing marks, while the profiles confirmed a slight plowing effect. The observed damage of the steel was corroborated by computing the wear rate (see Figure 7). It can be seen in Figure 7 that the lowest wear rate values were achieved with all the bio-based lubricants (L6, L7, and L8). The wear rate obtained with L8 was up to 99.8% lower than that found with the synthetic lubricant L4 (\(K=2.3\times 10^{-5}\) mm\({}^{3}\)/Nm). Figure 6: Worn surfaces micrographs at 500X (**up**) and wear track profiles (**down**) of the steel samples.