3.1. 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.
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. Τhe 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]:
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).
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). The results were post processed using the Cronbach Alpha statistical method (described in
Section 2.5). The values of the alpha parameter are: 0.96 for test 1, 0.97 for test 2, 0.89 for test 3, 0.91 for test 4, 0.73 for test 5, and 0.76 for test 6. Due to all alpha values being higher than 0.7, the results are statistically meaningful in order to validate the proposed model.
Table 4 shows that the model can accurately calculate the friction coefficient of the contacting surfaces when the coating layer is taken into account, verifying that the numerical approach taken is representative of the performance of the coated contacts and can be used to calculate the generated friction in the contact of coated gear teeth.
3.2. Simulation Results
For this research project, a six-speed manual transmission was examined. This type of transmission is used in small to medium passenger cars. The characteristics and dimensions of the gear pairs of the transmission are presented in
Table 5a whereas in
Table 5b the main material characteristics for the coated and uncoated surfaces are shown.
The properties of the lubricant used are provided in
Table 6. The effect of temperature on the lubricant dynamic viscosity value has been considered for the temperature range that the examined gearbox operates. The change of the lubricant viscosity due to temperature change was experimentally measured. The lubricant was heated using a hot plate and a thermocouple was used for tracing the temperature. The temperature was traced in the whole volume of the lubricant to verify that the measurement is consistent. Then, with the use of a viscometer the dynamic viscosity was measured. Multiple measurements were conducted, and the mean value of the dynamic viscosity was used during the simulations.
The input conditions of the model simulations are obtained from the RDE driving cycle, which is presented in
Figure 9. Snapshots of the cycle were used for the tests (represented by the red dots in the Figure). Two scenarios were examined for each gear as presented in
Table 7. In order to track the effect of the coatings, it was decided to track the friction of engaged gears since they have the biggest contribution on frictional losses. For each case, it was also assumed that only the wheel of each gear pair was coated as is common practice in industry. The characteristics of the coatings are as presented in the previous section.
The results are presented as power losses due to the direct relation with efficiency:
Figure 10 presents the results of the simulations for the operating conditions of scenario 1, when all gears are considered uncoated. It has to be noted that the uncoated gear model has been validated experimentally at system level, as presented in [
29]. For each gear, as described in
Table 7, different operating conditions apply. Hence, even though the results are presented on the same figure, for each gear they refer to different snapshot of the RDE cycle and the time shown on the x axis refers to the duration of the simulation at the corresponding RDE time snapshot. As mentioned before, the power gain by using coated gears is traced for the engaged gear pair of the transmission only due to the fact that engaged gears have the highest values of power losses. Consequently, for each gear that is shown in the following figures the gear is considered engaged and performing under the operating conditions of
Table 7. In the following figures, the oscillation of power losses at each instant of time due to the varying meshing stiffness can also be observed. Similarly to
Figure 10, the same rules apply for
Figure 11, which shows the power losses of each gear for the same operating conditions of the first scenario considering DLC coating.
The results of
Figure 11 reveal that the use of DLC coatings leads to power loss reduction for all gears under certain working conditions. Even though the coating type used for all gears is the same, the effect is different since the performance is affected by the operating conditions and the gear geometry, as discussed in the methodology section. For the operating conditions of scenario 1, the lesser effect on power loss is found on the first gear of the transmission where the power gain is around 6%. The power gain in the middle gear pairs is around 10–15%.
The use of WCC coating has a similar effect, as presented in
Figure 12 for the same operating conditions of scenario 1. Since the surface properties of the two coatings differ as measured experimentally, a different effect on the power loss change was expected. However, it should be noted that the power loss was reduced in all coated gears. In order to further verify the effects of each coating type, both coatings were tested under different operating conditions, described as scenario 2 (see
Table 7).
For the case of uncoated gears operating under the conditions of scenario 2, the power losses are shown in
Figure 13. The power losses when using DLC and WCC coatings are presented in
Figure 14 and
Figure 15, respectively, for the operating conditions of scenario 2.
Based on the results obtained for scenario 2, it is obvious that for this case as well, the use of either type of coating can lead to improvement of the gearbox efficiency. Even though for this scenario the effect of each coating is similar as well, it is clear that the WCC shows a slightly better performance especially on the higher gear pair power losses. However, the range of power loss gain for all gears is between 12% and 60%. The change on total frictional losses on boundary friction especially is mostly influenced by the pressure coefficient of asperity contacts, which was experimentally measured using the AFM. For both coatings this value can be considered to be of similar magnitude. However, there are other parameters that indirectly can contribute to this difference. The topographical values obtained from Alicona measurement also contribute to the amount of asperity interaction at each film thickness, hence the boundary friction.
The operating conditions have a major effect on the thickness of the film in the contact. Due to the fact that the conditions of scenario 2 are characterized by higher torque and speed, the film becomes thinner due to the higher load and thicker due to the higher speed. Consequently, asperities interactions in contact will change.
Finally, the contact mechanics is also affected by application of coating as presented in this work. This leads to a different contact footprint, hence the different apparent contact area and contact pressure, affecting the asperity and viscous frictions respectively.
The average effect of both coatings examined is summarized in
Table 8.
Finally, the difference achieved with the use of coatings for a bigger part of the RDE cycle is presented in
Figure 16. To be more precise, the results show the power loss reduction with the use of DLC coating as the cycle proceeds taking into account any gear shift as well as the constantly changing input torque and velocity.
Figure 16 showcases that the model developed is able to capture the effect of coating on transmission power losses at system level. Additionally, it is shown that the use of coatings can indeed reduce the total power losses of the transmission under various operating conditions, potentially reaching reduction up to 0.25%.