## 5 Comparative Experimental Study
### Analysis of Experimental Results  
During the experiment, different currents were passed into the excitation coil of the MR drive and the braking torque of the magnetic powder brake was continuously adjusted. The relationship between the current and the torque transmitted by the MRF was derived from the value measured by the torque sensor.  
The Finite Element Analysis (FEA) results in Figure 7a were substituted into Equation (25), and the values obtained were \(r_{2}\) = 0.129 mm and \(r_{3}\) = 0.079 mm. The input disk speed \(\omega_{1}\) was 100 rad/s, the output disk speed \(\omega_{2}\) was 90 rad/s, the Herschel-Bulkley model coefficient \(m\) is 0.75, \(k\) was 0.085 Pa\(\cdot\)s\({}^{\rm m}\) and the thickness of the working gap \(h\) was 0.001 m. The relationship between the current passed into the excitation coil and the torque of the MR drive are shown in Figure 14.  
As can be observed from Figure 14, the MR torque can be divided into roughly two stages according to the rate of change of the transmitted torque.  
The transmission torque increased significantly with the current when the current was between 0.5 A and 1.5 A. When the current reached 0.5 A, the experimentally derived torque was 26.57 N\(\cdot\)m, and the theoretically calculated torque was 48.99 N\(\cdot\)m. The tested torque was 82.39 N\(\cdot\)m when the current was 1.0 A, and the theoretically calculated torque was 93.10 N\(\cdot\)m, with a transmission torque error of 11.50%.  
The current \(I\) was in the range of 1.5 A to 3.0 A in the second stage. At this time, the torque of the transmission device increased slowly with the current. When the current was 3.0A, the experimentally derived torque was 129.84 N\(\cdot\)m, and the theoretically calculated torque was 133.19 N\(\cdot\)m with a torque error of 2.52%.  
Figure 14: Relationship between current and torque.  
Figure 13: Internal structure of the MR transmission device.  
Due to problems such as the settling of the magnetic particles in the MRF [24], especially when the current is low, the magnetic force between magnetic particles decreased, the zero-field viscosity of the magnetorheological fluid and the shear yield stress under the action of the magnetic field decreased, the magnetorheological fluid performance was unstable, and the magnetic field distribution in the working gap was not uniform, resulting in a lower torque performance of the transmission than the calculated value.  
The torque sensor was installed between the output disc and the magnetic powder brake, and the braking torque of the magnetic powder brake was set to 125 N\(\cdot\)m. The input disc speed \(\omega_{1}\) was controlled by the inverter and stabilized at 100 rad/s. The relationship between the current of the coil \(I\) and the output disc speed \(\omega_{2}\) was determined according to the value taken by the speed-torque sensor and compared with the theoretical result of Equation (19).  
As can be observed from Figure 15, when the current increased to 2.3 A, the output disk started to rotate under the shear yield stress of the MRF, and it grew linearly with the increase of current, with the yield flow area of the MRF decreasing. Because of the fluctuation of the motor speed and additional friction during the experiment, there were some errors between the experimental and theoretical values, but the overall trend was consistent. The results indicate that the magnitude of the current significantly affects the angular velocity distribution of the flow of MRF in the working gap.