# On the Effect of DLC and WCC Coatings on the Efficiency of Manual Transmission Gear Pairs
## 3 Results  
### Experimental Validation  
The friction coefficient of the contacting surfaces, measured at asperity level using AFM measurements and expanded to conjunction level using the provided numerical methodology, was compared to experimental tests using a pin-on-disc machine which directly obtains the conjunction level friction. The test rig is presented in Figure 8. The purpose of this experiment is to validate the presented numerical model from asperity level to conjunction level by comparing the friction coefficient value, since the model will be used for friction calculation of conjunctions in loaded gear. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **DLC** & \multicolumn{2}{c}{**WCC**} \\ \hline \(\zeta\)**—Dry** & \(\zeta\)**—Wet** & \(\zeta\)**—Dry** & \(\zeta\)**—Wet** \\ \hline
0.6531 & 0.0475 & 0.585 & 0.14 \\
0.6233 & 0.033 & 0.5463 & 0.1486 \\
0.4215 & 0.0428 & 0.3438 & 0.1273 \\
0.3229 & 0.0415 & 0.385 & 0.1364 \\
0.2913 & 0.0432 & 0.926 & 0.127 \\
0.519 & 0.0725 & 0.587 & 0.0742 \\
0.4288 & 0.0607 & 0.625 & 0.0752 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Friction coefficient and \(\zeta\) measurements of coatings. Figure 8: Pin-on-disc tribometer. The machine comprises a cantilever that applies the chosen contact force on the sample disc, which is rotating with a chosen speed so as to replicate the sliding speed of the gear teeth contact. Additionally, a strain gauge that is instrumented on the cantilever is used to measure the generated friction. The presence of the lubricant in the contact should not be neglected either, since the contacts in an automotive transmission are not dry. It should be pointed that a lubricant level roller is also essential for the setup in order to allow for the creation of a full thin film on the contact. Finally, a heating device is placed under the rolling plane and a K-type thermocouple is positioned under the heating enclosure to verify the temperature of the lubricant so that the effect of the varying viscosity can also be taken into account [28]. Since the pin-on-disc measurements are destructive for the surface, it was decided that measurements are conducted taking into consideration that the range of operating conditions to be tested should be identified as the most common operating conditions of the RDE cycle (as well as some high load cases). Additionally, different temperatures were chosen for the six sets of measurements conducted with sliding distance of 999 m so that the effect of temperature is captured as well. The setup of the pin-on-disc allows only for the control of the applied load on the surface, the radius on the sample disc were the load is applied and its rotational speed. Consequently, the next step prior to the actual measurement is to translate the pressure and sliding velocity that is assumed for the contact based on the operating conditions that were shown in Table 3 into representative load, speed and radius on the machine. To be more precise, the pressure in the contact as calculated by gear model simulations for the examined operating conditions, has to be transformed into load on the pin to experimentally capture the same pressure. Equation (27) was used to obtain the values of the pin load as shown in Table 4, employing the Hertzian theory for point contacts [23]:  
\[Pressure=\left( \begin{array}{l}6\ Load\ E_{r}^{2}\\ \hline\pi^{3}\ R_{pin}^{2}\end{array} \right)^{1/3} \tag{27}\]  
Additionally, for verifying the simulation-calculated sliding speed in the gear teeth contact it is necessary to calculate the rotational speed of the disc based on the radius where the pin is touching the disc. This is achieved by Equation (28). \[\omega_{disc}=\ \frac{u_{sl}\ 60}{R_{disc}\ 2\ \pi} \tag{28}\]  
In Table 4, the results of the experiments in comparison with the model simulations are also presented. It has to be noted that the experiment was repeated six times for each test condition (1 to 6 as presented in Table 3).