## 3 Material and Methods
### Computational Model
In summary, the operating conditions of the computational model can be seen in Tables 5 and 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Steps** & **Solid Part** & **Fluid Part** & **Rigid Plan Part** \\ \hline Initial & \(V_{x,y,z}=0\) mm/s & \(V_{x,y,z}=0\) mm/s & \(V_{x,y,z}=0\) mm/s \\ \hline Second & \(V_{x,y,z}=0\) mm/s & \(V_{x,y,z}=0\) mm/s & \(V_{y}=-3\) mm/s \\  & \(p_{1}-p_{2}=110-109.99\) MPa \({}^{2}\) & \(V_{x,z}=0\) mm/s \\ \hline Third & \(V_{x}=6.3\) mm/s \({}^{1}\) & \(V_{x,y,z}=0\) mm/s & \(V_{x,y,z}=0\) mm/s \\  & \(V_{y,z}=0\) mm/s & \(p_{1}-p_{2}=110-109.99\) MPa & \(V_{x,y,z}=0\) mm/s \\ \hline \end{tabular} \({}^{1}\) [PERSON] et al. [24]\({}^{2}\) [PERSON] et al. [17]  
\end{table} 
Table 6: Operating conditions for both lubrication regimes. Figure 10: Boundary conditions of the computational model. (**a**) Solid part. (**b**) Fluid part. (**c**) Rigid part. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Lubrication** & **Film Thickness** & **Reynolds** & **Temperature** & **Roughness** \\
**Regimes** & **(\(\mu\)m)** & **Number** & **R\({}_{a}\)/R\({}_{q}\) (\(\mu\)m)** \\ \hline HD Lubrication & 3 & order of \(10^{-6}\) & 24 \({}^{\circ}\)C & 1.159/0.949 \\ Mixed & 1 & order of \(10^{-6}\) & 24 \({}^{\circ}\)C & 1.159/0.949 \\ Lubrication & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The operating conditions. In summary, in search of expressing more clearly the conditions of operations in the modeling proposed in this paper, the following simplifying assumptions were considered:  
* Incompressible and Newtonian viscous fluid. * Fluid flow is laminar. * Dynamic viscosity is constant. * Pressure, temperature, and density are constant. * Adhesion effects are not considered. * Isotropic linear elastic solid for roughness part. * No cavitation is modeled. * Rigid plane was modeled as a non-deformable material without roughness. * The effects of vibrations, temperature, and material properties on shock responses are neglected. * Quasi-static regime with a constant sliding velocity. To calculate the coefficient of friction and evaluate its behavior on the contact surfaces subjected to lubrication regimes, a procedure for homogenizing the results in terms of normal and tangential force was applied. The coefficient of friction was obtained from the ratio between the resisting force (tangential force) and the normal forces acting on the body. In this work, a simple but efficient homogenization implementation procedure is presented. This procedure consists, firstly, before simulation, of generating a surface set containing all the elements in contact with the fluid and the other surface. Secondly, define the history of variables (normal force, tangential force) necessary to calculate the coefficient of friction per mesh element using the surface set created earlier. Thirdly, after the simulation, you need to access the output database where the variables are available and save them in a graphical format to obtain the values at each mesh element in time. In the fourth step, it is necessary to use specific tools to calculate the sum of the variables, obtaining the resulting forces acting on the surface. Finally, calculate the ratio between tangential and normal resultant forces to obtain the homogenized friction coefficient.