## 3 Results and Discussion  
In this section, the proposed methodology is used to assess the effect of DLC and WC-C coatings on the tribological performance of a single cam-tappet conjunction shown in Figure 4. The single valvetrain case study is outlined in the methodology section in detail. As explained above, an experimental characterisation of surfaces is required to inform the numerical models with input values for boundary friction calculations. The summary of the combined topographical characteristics obtained through post-processing of measured data is presented in Table 4. These data are directly used in the boundary interaction model of Section 2.5. The boundary interaction model assumes a Gaussian of surface asperity heights. This can be verified using experimentally obtained surface topographies. Figure 7 shows the real asperity height distributions for steel, DLC and WC-C surfaces. The results reveal that there is a reasonable conformity to a Gaussian distribution. Hence, the application of statistical functions for boundary interaction, assuming this distribution, is justified. \begin{table}
\begin{tabular}{c c} \hline \hline
**Uncoated Tappet** & \\ \hline Asperity Density per unit Area, \(\zeta\) & \(8.3\times 10^{9}\) m\({}^{-2}\) \\ Composite RMS Surface Roughness, \(\sigma_{12}\) & 0.408 \(\upmu\)m \\ Mean Composite Radius of Curvature of Asperity Peaks, \(\beta_{12}\) & 0.669 \(\upmu\)m \\ \hline DLC-Coated Tappet & \\ \hline Asperity Density per unit Area, \(\zeta\) & \(3.8\times 10^{9}\) m\({}^{-2}\) \\ Composite RMS Surface Roughness, \(\sigma_{12}\) & 0.358 \(\upmu\)m \\ Mean Composite Radius of Curvature of Asperity Peaks, \(\beta_{12}\) & 0.332 \(\upmu\)m \\ \hline WC-C-Coated Tappet & \\ \hline Asperity Density per unit Area, \(\zeta\) & \(2.7\times 10^{9}\) m\({}^{-2}\) \\ Composite RMS Surface Roughness, \(\sigma_{12}\) & 0.347 \(\upmu\)m \\ Mean Composite Radius of Curvature of Asperity Peaks, \(\beta_{12}\) & 0.217 \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Combined surface characteristics. Figure 7: _Cont._  
The rheological properties used throughout the investigation can be found in Table 5, which correspond to a standard SAE 5W-20 lubricant. These properties were kept constant for all simulations performed. Other material properties necessary for the formulation can be found in Table 6. The pressure coefficient of boundary shear strength of asperities is required for boundary friction calculation. It is the asperity level equivalent of the coefficient of friction which is expanded to macro-level (conjunction level) using the Greenwood and Tripp approach presented in Section 2.5. The values of this coefficient for surfaces of this study are investigated and obtained using an Atomic Force Microscope (AFM) by [PERSON] et al. [33]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Dynamic Viscosity** & **0.055 Pa. s** \\ \hline Limiting Shear Strength Coefficient & 0.08 \\ Eyring Shear Stress & 2 MPa \\ Pressure–Viscosity Coefficient & \(1.05\times 10^{-8}\) Pa\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Lubricant rheological properties. Figure 7: Surface asperity height distribution for (**a**) steel, (**b**) DLC and (**c**) WC-C and their comparison against Gaussian distribution [28]. (Each vertical axis represents the height distribution.) The simulations performed are representative of a four-stroke engine at a speed of 3000 RPM and evaluate the behaviour of the system over two complete engine cycles. Since the simulation algorithm assumes a fully flooded cam-tappet conjunction as an initial condition, only the second engine cycle (720 to 1440 degrees) is presented, where the solution is considered to be settled after removing all transient effects. Simulation conditions are shown in Table 7.  
As the first step, the validity of using a full numerical EHL contact explicitly is investigated. For this purpose, two versions of multi-body dynamic model are simulated.