## 3 Numerical Simulation of Drop Process of Single DOF System
### Drop Impact-Rubbings Behavior of Upper Unit Failure Model  
#### 3.1.1 Influence of Structural Parameters on Rotor Impact-Rubbing Behavior  
In the upper unit failure model, the maximum radial impact force of the rotor/stator collision varies with the structural parameters as shown in Figure 4.  
According to Figure 4, the maximum radial impact force decreased firstly and then increased with the increase of liquid film thickness, and decreased with the increase of plating thickness. The maximum value occurs in the combination of \(h_{0}\) is 30 \(\upmu\)m and \(l\) is 50 \(\upmu\)m. Therefore, take it as the typical example in order to analyze the operation rules as shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Variable** & **Size** \\ \hline \(i_{0}\) & Biasing circuit & 1 A \\ \(p_{s}\) & Supply pressure & 0.1 MPa \\ \(\beta\) & Throttling ratio & 2 \\ \(\mu\) & Dynamic viscosity & \(1.3\times 10^{-3}\) Pa-s \\ \(m\) & Mass of rotor & 4 kg \\ \(\mu_{0}\) & Permeability of air & \(4\pi\times 10^{-7}\) H/m \\ \(A_{e}\) & Area of supporting cavity & 416 mm\({}^{2}\) \\ \(A_{b}\) & Extrusion area & 56 mm\({}^{2}\) \\ \(h_{0}\) & Oil film thickness & 50 \(\upmu\)m \\ \(\theta\) & Angle & 22.5\({}^{\circ}\) \\ \(B\) & Flow coefficient & 0.71 \\ \(S\) & Area of pole & 1080 mm\({}^{2}\) \\ \(N\) & Turns per coil & 50 \\ \(Q\) & Load & 100 \\ \(k_{n}\) & Stator stiffness & \(3.5\times 10^{8}\) \\ \(l\) & Plating thickness & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Initial design parameters of MLDSB.  
Figure 4: Maximum radial impact force upper unit failure model.  
According to Figure 5, the upper unit failure occurs at \(t\) = 0.2 s, and the motion of rotor includes three stages: initial equilibrium, dropping, and collision.  
In initial equilibrium stage, the rotor is dropped from zero position and stays at \(-\)19.8 \(\upmu\)m stalely. The load is borne by electromagnetic force and hydrostatic force as shown in Stage 1.  
In dropping stage, the dropping speed of rotor decreases gradually. The current \(i_{My,1}\) of supporting unit 1 decreases to 0 A, and the current \(i_{My,2}\) of supporting unit 2 decreases, and then the electromagnetic force gradually approaches zero. The liquid resistance \(R_{h1}\) of supporting unit 1 remains the same basically, but the liquid resistance \(R_{h2}\) of supporting unit 2 rises rapidly due to the impact-rubbing damping effect of hydraulic oil. Therefore, the hydrostatic force increases rapidly first and then decreases slowly as shown in Stage 2.  
In collision stage, the rotor reaches a new equilibrium state. As the contact depth between rotor and stator increases, the impact force \(F_{n}\) increases gradually, and the external load of the rotor is balanced with electromagnetic force \(F_{My}\), hydrostatic force \(F_{Ly}\), and impact force \(F_{n}\). The current \(i_{My,2}\) of supporting unit 2 decreases to 0.5 A, and the residual electromagnetic force \(F_{My}\) is \(-\)37.4 N. The liquid resistance \(R_{h1}\) and the liquid resistance \(R_{h2}\) are 9.4 \(\times\) 10\({}^{9}\) N\(\cdot\)s/m and 2.3 \(\times\) 10\({}^{14}\) N\(\cdot\)s/m respectively. However, the latter is about 2.4 \(\times\) 10\({}^{4}\) times than the former, resulting in a tiny tremor after a collision between rotor and stator. And the hydrostatic force \(F_{Ly}\) gradually reduced and finally stabilized to about 67.7 N as shown in Stage 3.