## 3 Results and Discussion of the Research  
Figure 9 shows the graphs of function dependency \(V_{1}^{BA}\ =\ f\Big{(}\dot{\varphi}_{F},\varepsilon\Big{)}\), which demonstrates the characteristics of the influence level of the relative slippage \(\varepsilon\) in the main contact of the wheel with the rail due to the value \(V_{1}^{BA}\), when the wheel is rotating at a speed \(V_{W}\) = 20 m/s and with angles to attack \(\psi\) = 0.00 rad and \(\psi\) = 0.02 rad. Analyzing the graphs depicted in Figure 9 we can also confirm the insignificant influence of the level of the relative slip \(\varepsilon\) in the main contact on the value of the slip velocity \(V_{1}^{BA}\) in the flange contact of the railway wheel of the perspective constructive scheme. When we take into account the absence of strict restrictions on the value of the angular velocity of the movable flange in the wheel with the perspective wheel design, the stationary state of the considered mechanical system can be determined. We use the well-known principle of the minimum entropy of the system (the minimum energy dissipation). This principle states that if not a single state of the system is permissible, but a certain set of states consistent with conservation laws and constraints imposed on the system, then its state is realized, which corresponds to the minimum increase in the entropy of the system or, which is the same, the minimum energy dissipation. Therefore, we can consider, that the quasi-static state (steady state) of the investigated system (a wheel with a movable flange interacting with a rail) is its state, in which the energy dissipation in the flange contact is minimal [4]. When we want to assess the effectiveness of the perspective wheel design from the reducing the kinematic resistance to movement point of view, we have to determine how much the power of friction forces in the flange contact can be reduced using these wheel design. The value of the instantaneous power of the friction forces is usually represented as the scalar quantity of the friction force vector in the flange contact \(B_{1}\) and the vector of the corresponding instantaneous sliding velocity of the flange point \(B_{1}\) on the rail. When we take into account the fact that the friction force vector is directly opposite to the vector of the corresponding instantaneous velocity, i.e., \(\delta=\pi\) and \(\cos\pi=-1\), in our case, the magnitude of the power of friction forces in the flange contact when using the traditional constructive scheme \(P_{1}^{B}\) and the perspective constructive scheme of the wheel \(P_{1}^{B}\) can be determined, respectively, from the expressions (26), (27):  
\[P_{1}^{B}\ =\ \big{|}F_{1}^{B}\cdot V_{1}^{B}\big{|}, \tag{26}\]  
\[P_{1}^{B}/\ =\ \big{|}F_{1}^{B}/\cdot V_{1}^{BA}\big{|}, \tag{27}\]  
Some calculation results are shown in Figure 10, where graphs of the function dependencies \(V_{1}^{B}\ =\ f(\dot{\varphi}_{F})\) and \(V_{1}^{BA}\ =\ f(\dot{\varphi}_{F})\) at the velocity \(V_{W}=20\) m/s, \(F_{1}^{B}=12,500\) N, \(\varepsilon=0.01\) and \(\psi=0.015\) rad are depicted. There is noticeable decrease of the friction forces power dissipated in the flange contact of the perspective wheel design in comparison with the traditional wheel design for the given running conditions in the range of angular velocities of the flange \(39.8\) rad/s \(<\dot{\varphi}_{F}<42.5\) rad/s. Analyzing these dependencies graphs we identify, that when the perspective wheel design is applied, it is possible to reduce the friction forces power dissipated in the flange contact to 60% for a certain ratio of the angular velocities of the wheel tread surface and its flange for given running conditions.