# Reducing Oscillations in Suspension of Mine Monorail Track
## 3 Results  
Using the dependencies provided in the previous section, graphical dependencies are built \(W_{kv}=W_{kv}\,f(C_{e})\) for different combinations of dynamic parameters of the mono-rail. The dependence of the damping coefficient \(W_{kv}\) on the relation of the stiffness factors \(C_{e}=C_{2}/C_{1}\) is shown in Figure 3. As it is shown in this figure by \(\xi_{e}<1\), with the increase in \(C_{e}\), the damp coefficient multiply decreases and tends to take the value equal to 1, and by \(\xi_{e}>1\), it increases, taking the values less than 1 almost within the full range. In the first instance (Figure 3a), when \(\xi_{e}<1\) and \(C_{e}=1\), with the increase in the relation \(\mu_{e}=m_{2}/(m_{1}+m_{2})\) from 0.2 to 1.0, the value \(W_{kv}\) increases by a factor of 6, and in the second instance (Figure 3b), when \(\xi_{e}>1\), it decreases by a factor of 5. At that, the damping coefficient \(\mid W_{kv}\mid>4\) allows reducing the oscillation amplitude of the point where the suspension is fastened to the mine working support in the same proportion. At the same value of \(C_{e}\), the damping coefficient in the first instance is always greater than in the second one. At that, in the second instance (Figure 3b), the decrease in the amplitude does not occur in the full range of \(C_{e}\) variation, but only for the values:  
\[C_{e}<\ \frac{\mu_{e}(\xi_{e}^{2}-1+\mu_{e})}{2\xi_{e}^{2}(\xi_{e}^{2}-1)}. \tag{9}\]  
As it follows from this figure, a low efficiency of absorption is observed by \(\mu_{e}\leq 0.2\). Such value \(\mu_{e}\) occurs when the mass of the monorail suspension exceeds the mass of the rolling stock, which is quite uncommon in practice. The range of \(\mu_{e}\) variation from 0.50 to 0.99 is typical of the existing mine suspended monorail tracks. The higher values of this coefficient refer to the loaded stock and the lowest ones refer to the empty stock. Let us consider the influence of \(\mu_{e}\) and \(\xi_{e}\) on the damping coefficient \(W_{kv}\). The dependences \(W_{kv}=f(\mu_{e})\) and \(W_{kv}=f(\xi_{e})\), obtained by \(C_{e}=0.5\), are shown in Figure 4.  
The indicated value of \(C_{e}\) is characteristic of the relation when the stiffness factor of spring washers (elastic elements) is two times smaller than the stiffness factor of the monorail suspension, which can be implemented quite easily by means of the devices mentioned above in this chapter. The graph dependences of the functions shown in Figure 4a,c refer to the cases when natural frequency \(k_{e}\) is lower than the disturbing force frequency \(\omega\); therefore, \(\xi_{e}<1\), and in Figure 4c,d, \(k_{e}>\omega\) and \(\xi_{e}>1\). If natural frequency \(k_{e}\) is lower than the disturbing force frequency \(\omega\), then, with the increase of \(\mu_{e}\) from 0 to 1 (Figure 4a), the damping coefficient at first decreases and then, after it reaches its lowest value, increases. At that, the damping coefficient reaches its lowest values by \(\mu_{e}<0.5\). That is why, in this case, the efficiency of absorption is ensured when \(\mu_{e}\geq 0.5\). If \(k_{e}>\omega\), then with the increase of \(\mu_{e}\) from 0 to 1 (Figure 4b) the damping coefficient decreases within the full range. In this case, the efficiency of absorption is different for different values of \(\xi_{e}\). By \(\xi_{e}\leq 1.2\), the module of damping coefficient reaches 3.5 and more, and by \(\xi_{e}\geq 2.5\) it does not exceed 1 and the coefficient of \(\mu_{e}\) does not essentially affect the absorption efficiency. With the increase of \(\xi_{e}\) from 0 to 1 (Figure 4c), the damping coefficient increases with different intensity. Within the range of variation of \(\xi_{e}\) from 0.3 to 0.8, its influence on the absorption efficiency is insignificant. With the further increase, when \(\xi_{e}>1\) (Figure 4d), the module of damping coefficient decreases over a wide range, and by \(\xi_{e}\geq 1.2\), it tends to be the value of less than 1. To determine the suspension parameters of a monozial track, the following methods can be recommended.