# Study on the Effect Mechanism of MRD to Rotor System
## 3 Results Analysis
### The Effects of MRD on the Rotor System  
From the above analysis, it can be obtained that the current and eccentricity ratio have significant influences on the mechanical properties of MRD (e.g., core volume, oil film pressure, the equivalent stiffness and damping coefficients) which will affect the dynamic characteristics of the rotor system. In order to further discover the effect mechanism of MRD to a rotor system, MRD is introduced to a Jeffcott rotor, and a general coupling system model of MRD-bearing-rotor with supporting of squirrel cage is established. The numerical simulation is carried out, and the dynamic responses are analyzed. The calculation parameters of the rotor system are given as \(D_{s}=0.05\,\mathrm{m}\), \(D_{d}=0.4\) m, \(B_{d}=0.03\) m, \(L_{s}=0.6\) m, \(E=210\) Gpa, \(\
u=0.4\), \(\mu=0.9\), \(\rho=7850\) kg/m\({}^{3}\)\(k_{a}=1\times 10^{7}\) N/m and \(e=1.5\times 10^{-4}\) m. The parameters of the bearing are given as \(R_{i}=59.2\) mm, \(R_{o}=70.9\) mm, \(C_{b}=1.33\times 10^{10}\) N/m\({}^{3/2}\), \(m_{o}=0.23\) kg, \(r_{0}=3\times 10^{-5}\) m, \(N_{b}=8\), \(\alpha=0\) and \(c_{e}=400\) N \(\cdot\) s/m. Figure 12 shows the critical speed \(\omega_{c}\) and the vibration amplitude at this speed \(AP_{c}\) varied with the applied current in the range of 0-0.6 A. As can be seen from the figure, when \(I\) = 0-0.15 A, MRD has  
Figure 11: Equivalent stiffness and damping coefficients of MRD varied with the current. Figure 10: Equivalent stiffness and damping coefficients of MRD varied with eccentricity ratio. almost no influence on the critical speed, and the value of it is 500 rad/s. The reason may be that the supporting stiffness of the rotor system is equal to the series stiffness of the squirrel cage, bearing and MRD (as can be seen from Figure 4), and the stiffness of MRD in this current range is far less than the sum of the stiffness of the squirrel and bearing. When \(I\geq 0.15\) A, the stiffness of MRD reaches a certain level due to the increase of the yield stress of MRF, which has an influence on the critical speed of the rotor system. The higher the current, the larger the critical speed. When \(I=0.5\) A, MRD approaches quasi-rigid supporting, and the critical speed of the rotor system reaches the maximum value which is 690 rad/s. Compared with the critical speed at \(I=0\) A, the critical speed at \(I=0.5\) A increases by about 27.5%. When \(I\geq 0.5\) A, the critical speed remains relatively constant. It can also be seen from Figure 12 that MRD has a complex influence on the vibration amplitude of the rotor system at critical speed. When \(I=0\)-0.3 A, MRD mainly affects the vibration of the rotor system through its damping effect, which has a better suppression on \(AP_{c}\). The higher the current, the more obvious the damping effect. As shown in Figure 13, when \(I=0\) A and 0.3 A, there is an isolated point in the Poincare map, which indicates that the rotor system presents a stable 1T-periodic motion. But when \(I=0.3\) A, \(AP_{c}\) is 0.25 mm which is far less than 0.516 mm when \(I=0\) A. The decrement is about 51.6% and the size of the orbit is much smaller. After \(I=0.3\) A, with the increase of the current, the stiffness of MRD plays a major role, which weakens the damping effect of MRD and \(AP_{c}\) gradually increases. These phenomena are consistent with the experiment results of Figure 13 in Ref. [27]. The reason may be that the increase of MRD stiffness limits the oil film to be squeezed and the squeeze effect is the source of MRD damping. Comparing the dynamic responses in Figure 13, it can be found that \(AP_{c}\) at \(I=0.5\) A (0.31 mm) is larger than that at \(I=0.3\) A (0.25 mm). The increment is about 19.3%. The orbit size is larger and presents an unstable ellipse. In addition to the fundamental frequency, there appear irrational frequencies in the spectrogram and a closed loop in the Poincare map, which indicates that the rotor system takes nonlinearity and changes from 1T-periodic motion to quasi-periodic motion. The rotor system is unsteady.