# Reducing Oscillations in Suspension of Mine Monorail Track
## 4 Discussion  
Let us study the obtained dependences of the oscillation amplitudes \(A_{1}\) and \(A_{0}\) on the parameters of the suspension. In Figure 5a,b, graphs of the absolute values of the functions \(A_{1}=f(\xi_{\omega})\) and \(A_{0}=f(\xi_{\omega})\) are plotted for the following values of the coefficients: \(\mu_{e}=0.5\); \(\xi_{2}=0.6\). From Figure 5a, it can be seen that the curves \(A_{1}=f(\xi_{\omega})\) have two discontinuities and three branches. With an increase from \(\xi_{\omega}\) to \(\xi_{\omega 1}\), there is a significant increase in the amplitude \(A_{1}\), which, approaching the first discontinuity point of the function in the asymptote \(\xi_{\omega 1}\), tends to take on an infinitely large value. With a further increase from \(\xi_{\omega}\) to the asymptote \(\xi_{\omega 2}\), there is a decrease of \(A_{1}\) to a minimum, and then a repeated increase. At the same time, \(A_{1}\) again strives to take an infinitely large value, approaching the asymptote at the second discontinuity point of the function. After the second break of the function, the amplitudes decrease and tend to take on a zero value. A similar change in amplitude \(A_{1}\) occurs when the coefficient takes a value \(\mu_{e}\) from 0.5 to 0.9 (Figure 5c). If \(\mu_{e}\leq 0.8\), then at \(\xi_{\omega}\geq 3.5\) the amplitudes \(A_{1}\) are practically equal to zero. Calculations show that if \(\mu_{e}>0.8\), then the minimum amplitude values \(A_{1}\) are achieved at \(\xi_{\omega}\geq 6\). The nature of the change in amplitudes \(A_{0}\) from the ratio of frequencies \(\xi_{\omega}\) is shown in Figure 5b. It follows from this figure that the curve \(A_{0}=f(\xi_{\omega})\) has one discontinuity and two branches. If \(\xi_{v}=1\), then an increase \(\xi_{\omega}\) from 0 to 1 leads to a sharp increase in the amplitude \(A_{0}\), and when \(\xi_{\omega}=1\), then \(A_{0}\) tends to take on an infinitely large value. With afurther increase \(\xi_{\omega}\), this amplitude decreases, approaching unity. For other values \(\xi_{v}\), there is a similar increase and decrease in amplitudes \(A_{0}\), but they tend to reach their maximum when \(\xi_{v}=\xi_{\omega}\). Figure 5d shows the dependence of the absolute values of the depreciation coefficient \(W_{kv}\) on the frequency ratio \(\xi_{\omega}\). As mentioned earlier, the coefficient \(W_{kv}\) is the ratio of the amplitudes \(A_{0}\) and \(A_{1}\). It can be seen in this figure that effective depreciation is possible when \(W_{kv}>1\); therefore, it is advisable to choose the values of the function \(W_{kv}=f(\xi_{\omega})\) from the unshaded zone. It follows from the above that in order to decrease the oscillation amplitude of the suspension, it is reasonable to fix the monorail track by means of elastic and damping device (Figure 6). The conducted studies allowed us to develop the design of the suspension of the monorail track (patent RU2611660C1), the parameters of which were determined according to the method proposed above. The I-155 monorail manufactured by the company SMT SCHARF AG (Hamm, Germany) was adopted as the basic option. The elastic damping device consists of spring washers and plain washers located in the bushing and fixed by a lock ring. The bushings are connected to the bottom of the suspension, which is attached to the beams of the arch support by means of fastening bolts or clamps. At that, between the case and support profile, there are a damping insert made of elastic material and a metal compression limiter with a height equal to half the thickness of the insert in the undistorted state. The stiffness factor of spring washers is determined by the following dependence:  
\[C_{s2}=E_{n}F\frac{\delta}{4(t_{s}-h)(h+\delta)}, \tag{15}\]  
where \(E_{n}\)--elasticity modulus of the elastic material of which the insert is made; \(F\)--cross-section area of the insert; \(\delta\)--compression stroke of spring washers; \(t_{s}\)--thickness of the insert, the value of which is \(t_{s}\geq 25\); \(h\)--height of compression limiter.