## 4 Virtual Prototype Model Simulation Verification
### Virtual Simulation Analysis  
As depicted in Figure 18c, it is assumed that the misalignment of the rigid guides is generated on one side of the tank channel, with a height difference of 0.02 m. To observe the damping effect of the roller cage shoe on the mine lifting system, the changes in acceleration and displacement at the center of mass position of the hoisting vessel were selected for observation. The virtual prototype model, constructed using the data from Table 9, was employed to conduct vibration simulations of the lifting system under real working conditions. This process yielded response results for the traditional roller cage shoe under actual operational circumstances (Group 1). Following this, the damping and stiffness characteristics of the MRD-based roller cage shoe were incorporated, as illustrated in Figure 18b. For simplification purposes, two series springs were utilized to represent the MRD and the disc spring, respectively. It is worth noting that the output force-deformation relationship of the disc springs exhibits a nonlinear nature, which is defined using a spline curve approach in Equation (18). The damping force provided by the MRD at a current input value of 2 A is correlated with the velocity of the spring motion. By utilizing the structural parameters determined in the preceding chapter and substituting them into Equation (4), the relationship between the damping force and velocity is established. This is illustrated in Figure 19, where the damper's simplified spring is defined using a spline curve. Subsequently, a virtual prototype model featuring the new buffer cage shoe was generated and subjected to simulations to procure response data post-application of the new MRD-based roller cage shoe for damping purposes (Group 2). Figure 19: Sample curve of the MRD. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Numerical Value** & **Unit** \\ \hline Conveyance mass & 34,000 & kg \\ Lift height & 300 & m \\ The moment of inertia of the conveyance concerning the transverse direction & 208,000 & kg\(\cdot\)m\({}^{2}\) \\ The moment of inertia of the conveyance concerning the longitudinal direction & 33,100 & kg\(\cdot\)m\({}^{2}\) \\ The moment of inertia of the conveyance concerning the lateral direction & 234,000 & kg\(\cdot\)m\({}^{2}\) \\ The lateral direction spring stiffness & 2,250,000 & N/m \\ The lateral direction spring damping & 16,400 & N\(\cdot\)s/m \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Transverse vibration simulation parameters of a hoisting conveyance. As observed in Figure 20, in the hoisting system outfitted with the MRF roller cage shoe buffer, there is a more effective suppression of the vibration amplitude and the frequency of the transverse acceleration and displacement of the hoisting container compared to the utilization of the traditional cage shoe buffer. To provide a more intuitive analysis of the vibration suppression effect, the data concerning the transverse acceleration of the hoisting container were scrutinized. The root mean square (RMS) and maximum values of the acceleration values of the two response results were calculated through Equations (28) and (29), respectively, and the results are shown in Table 10.  
\[A_{RMS}=\left[\sum_{i=1}^{N}{(a_{i}-a_{0})^{2}/N}\right]^{\frac{1}{2}} \tag{29}\]  
\[A_{\text{max}}=Max\{a_{1},a_{2}\cdot\cdot\cdot,a_{N}\} \tag{30}\]  
where \(a_{i}\) is the transverse vibration acceleration of the hoisting container, \(a_{0}\) is the initial value of acceleration, and \(N\) is the number of data samples. The mean square value is a statistical measure used to measure the degree of dispersion of the values in a data set; the larger the mean square value, the greater the degree of dispersion of the data set, indicating that the data points are relative to the mean value of the greater degree of deviation.