## 3 Results  
Following the development of the kinematic virtual model, Figure 10 and dynamic simulations were performed to determine whether the valve complied with the displacement law imposed by the cam [34]. Thus, it can be observed that the valve reached a maximum speed of 3 m/s and a maximum acceleration of 2620 m/s\({}^{2}\) for the considered maximum speed. It can be seen in the kinematic analysis that the valve followed exactly the profile of the cam. This is because neither the forces in the system nor the inertia of the parts are taken into account in this analysis. The following behaviour is clear from the comparison of kinematic analysis with dynamic analysis at low operating speeds: the dynamic behaviour of the system remains unchanged, and at high speeds due to the influence of rigidity and body mass displacement, speed and acceleration have different values than those required, which is due to inertial forces and shock loads [45]. So, the dynamic behaviour of the components of the valvetrain system are more important at high speeds [40]. However, due to the way in which the contacts between the parts were modelled and due to the errors that may occur in determining the cam profile, small variations of the valve acceleration were obtained in the area of its maximum opening for the considered maximum camshaft speed. These variations can be seen more clearly when analysing the shocks in the valve. Additionally, with the help of the virtual model it was possible to determine the values of the contact forces between the cam and the valve, respectively the valve and the valve or the valve and its seat. Thus, it can be seen that the force between the cam and the cleat is transmitted entirely to the valve, with the hydraulic cleat behaving like a pillow of oil of constant volume--more due to the way of defining contacts, approximation of surfaces with triangles, small variations of contact forces when opening and closing the valve, respectively (Figure 11). Figure 9: Spring of the valve: (**a**) defined in PDS, (**b**) free state, (**c**) prestressed, (**d**) stressed for maximum valve opening. The forces acting on the valve are influenced by the stiffness and the damping characteristics of the spring, with respective to the valve seat, but also by the geometry and the mass of the components. The type of lubrication and friction forces between the components in contact are other factors influencing these forces [32,46]. Additionally, contact between cam and tappet has a complex mechanism. This is due to variation in the type of lubrication during operation: elastohydrodynamic, mixed and hydrodynamic [47,48]. Linked to properties of this contact, it can also be said that during the cam rotation, the friction force between the cam and the tappet changes. So, when the cam acts on the tappet in the opening race we have friction by rolling, and when the top of the cam came into action we have slipping through sliding [47]  
Validation of the virtual model was achieved by comparing its dynamic accelerations with those measured experimentally on the test stand. It can be seen in Figures 12-14 that the difference between the two accelerations is below 5% and so the model can be considered valid. Figure 10: The kinematic behaviour of the valve at different speeds. Figure 11: Contact forces between cam and taper [N] for \(n_{AD}\) = 350 rpm. Figure 12: Valve acceleration for \(n_{AD}\) = 350 rpm. Figure 14: Valve acceleration for \(n_{AD}=1000\) rpm. Figure 13: Valve acceleration for \(n_{AD}=750\) rpm. the compression, extension and movement of it. This torque could not be evaluated with high accuracy because it was not established if it was transmitted to the upper seating surface and the valve retaining ring, or the valve guide and one at the bottom. One example of this limitation is revealed in Figures 12-14, where it can be observed that the bounce phenomenon of the valve upon its seat could not be reproduced, with values near 250 degrees of the crank angle.