## 3 Results and Discussion
It is observed that some working points in the studies cycle fall in the hydrodynamic regime. Hydrodynamic condition corresponds to lightly loaded contacts. These points show the biggest difference between implicit and explicit models in Figures 8-10. Under higher loads, the working conditions approach PE and IE where the effect of film stiffness is diminished, and the implicit and explicit approached show a good agreement. To further investigate the results of Figure 12, the pressure and film thickness distributions of six points along a cycle are provided in Figure 13. These points are considered at points 1 to 6 on Figure 9 to show a variety of speed-load combinations. Each graph in Figure 13 shows pressure and film thickness distributions for uncoated and WC-C-coated samples with 4 \(\upmu\)m coating thickness. The results clearly show a variety of contact regimes from EHL, such as point 1 and 6, under high loads to the moderately deformed point 2. Under EHL conditions, the flattened film thickness as well as the secondary spike of the pressure distribution is apparent. It should be noted that the shape of pressure and film thickness distributions, as well as their values depend on both load and speed. Point 2, for example, resembles a near-zero velocity, leading to significantly lower film thickness. Figure 11: Speed of entertaining motion. Figure 12: Greenwood chart of working conditions in the cam-tappet contact. Figure 13: Pressure and film thickness distributions along a full cycle (uncoated:, WC-C coated: ). It is also clear that the application of a WC-C coating leads to an expanded contact area, which in turn supports a thicker film thickness. This effect is due to the lower modulus of elasticity of the coated surfaces, which agrees with the generic results in Figure 6. The expansion of the contact area and consequent increase in the film thickness value can be seen as a benefit of WC-C application, since it significantly affects the frictional and wear behaviour (the latter is not the subject of this study). This benefit is more pronounced under lightly loaded conditions such as points 2, 3, 4 and 5, which are away from the PE region on the Greenwood Chart. Figure 14a shows the pressure and film thickness distributions of the DLC-coated surfaces in comparison with the WC-C-coated cam-tappets. The effect of coating thickness is also analysed by comparing the results of 1 \(\upmu\)m coating thickness to those from 4 \(\upmu\)m coating thickness. It is seen that the results for DLC and WC-C, as well as the behaviour of different coating thicknesses, are similar. This is due to the negligible effect of the coating thickness in comparison to the ratio of modulus of elasticity, as shown in Figures 5 and 6. Similar values of modulus of elasticities from DLC and WC-C also yield similar pressure and film thickness distributions. The zoomed-in view in Figure 14b shows the minute level of variation from DLC to WC-C and between coating thickness values. Figure 15 is the variation of central film thickness during one cycle for 4 \(\upmu\)m thickness of coatings. It is revealed that the major effect of coatings is observed in the moderately  
Figure 14: Pressure and film thickness distributions of DLC and WC-C coatings with different coating thickness values. (**a**) the complete distribution, (**b**) the zoomed view. loaded region, as shown in Figures 13 and 14. It accounts for a maximum increase of 41%, mainly observed at the centre of the high-load section. The consequence of this variation in the film thickness will be on durability as well as frictional performance. The former is not the subject of this study; hence, the effect of coatings on friction will be further investigated. It is also revealed that the difference between DLC and WC-C on the central film thickness is minute, as can also be observed in Figure 14b. This will mean that any potential variation in friction between DLC and WC-C will be less related to the variation in the film thickness.