# Study on the Effect Mechanism of MRD to Rotor System
## 3 Results Analysis  
### Mechanical Properties of MRD  
In this section, the mathematical model of MRD is calculated and the mechanical properties of it are analyzed. It is set that the rotor journal center performs a circular orbit at a constant radius of \(e_{B}\), and the line of the centers moves at a constant angular velocity \(\Omega\). The calculation parameters are given as \(e_{B}=6\times 10^{-4}\) m, \(\Omega=350\,\mathrm{rad/s}\), \(L=0.05\,\mathrm{m}\), \(R=0.075\,\mathrm{m}\), \(c=1\times 10^{-3}\,\mathrm{m}\), \(N=100\), \(\eta=0.3\,\mathrm{Pa}\cdot\mathrm{s}\), and \(\alpha_{\eta}=500\). Figure 5 shows the curve of the core volume of MRD varied with the applied current in the range of 0-1.5 A. It can be seen that when \(I=0\)-0.1 A, the core volume is sensitive to the change of  
Figure 4: Schematic diagram of the rotor supporting system. the current. With the increase of the current, the yield stress increases, which makes the core volume increase approximately linearly. When \(I>0.1\) A, the core volume changes slowly and starts to saturate. Figure 6 shows the positions of yield surface in MRD under several currents. When \(I=0.5\) A, the position of the yield surface moves significantly compared with that at \(I=0.03\) A, and the unyielding area is drastically enlarged. When \(I=1\) A and \(1.5\) A, the position of the yield surface moves slowly compared with that at \(I=0.5\) A. This phenomenon indicates that when the yield stress reaches a certain value, the position of the yield surface will be fixed at a certain position and not move anymore. In this case, the flow field is saturated with yield stress. Figure 7 shows the maximum film pressure and yield stress varied with the current in the range of 0-3 A. When \(I=0\)-0.4 A, the maximum film pressure approximately linearly increases with the increase of the current. After that, it increases slowly and reaches a peak at \(I=2\) A, then remains basically unchanged. The change trend of the maximum yield stress keeps consistent with that of the maximum film pressure. Compared with Figure 5, it can be found that the peak point of the core volume lags far  
Figure 5: Core volume of MRD varied with applied current. Figure 6: Positions of yield surface in MRD under several currents. (**a**) \(I=0.03\) A, (**b**) \(I=0.5\) A, (**c**) \(I=1\) A, (**d**) \(I=1.5\) A.  
behind that of the maximum film pressure. That is to say, when the core fulfills the clearance of MRD, the maximum film pressure still increases with the increase of the current until the yield stress of MRF reaches a peak. Figure 8 shows the pressure distribution in the middle plane of MRD under several currents. It can be seen that when \(I=0\) A, MRF is in a state of Newtonian fluid. The curve of film pressure is continuous and smooth. The maximum film pressure \(P_{\max}\) is 0.92 MPa. When \(I=0.5\) A, the curve of film pressure has mutations at the positions of film formation and fracture. Compared with \(I=0\) A, the film pressure increases significantly to 4.54 MPa and the increment is about 79.7%. In addition, the position of the maximum film pressure changes from 0.862 rad to 0.63 rad. When the current increases further to 2 A, the curve of film pressure is similar to that when \(I=0.5\) A, but the film pressure is further increased. The maximum film pressure \(P_{\max}\) at \(I=2\) A is 8.27 MPa. Compared with \(I=0.5\) A, the maximum film pressure increases by about 45.1%. When \(I=3\) A, the curve is basically consistent with that when \(I=2\) A, and the maximum film pressure remains unchanged. It can be seen from the above phenomena that the film pressure of MRD increases with the increase of the current and reaches saturation at a certain value of the current. The main reason is that with the increase of the current, the yield stress of MRF increases and the film becomes thinner, resulting in an increase of film pressure. When the two factors reach a peak, the film pressure reaches saturation.