# Multiobjective Optimization Design for a MR Damper Based on EBFNN and MOPSO
## 5 Test performance of the Optimal MR Damper
### Experimental Analysis of Damping Performance  
Figure 16 shows the output damping force of the initial and optimal MR dampers with the input current of 1 A and sinusoidal displacement excitation with the same frequency of 0.25 Hz but with different amplitudes. The output damping forces of the initial and optimal MR dampers increase mildly with the increase in amplitude. With the varying amplitude from 2.5 mm to 10 mm, the maximum output damping force of the initial MR damper increases from 2696 N to 3403 N with the increase in amplitude. Meanwhile, the maximum output damping force of the optimal MR damper increases from 5681 N to 6933 N.  
Figure 14: Optimal MR damper (**a**) components; (**b**) prototype. Figure 15: Performance test rig of MR damper: 1. vibration excitation platform, 2. tested MR damper, 3. controlled computer, 4. DC power supply, 5. electrohydraulic servo controller [31]. The damping characteristics of the initial and optimal MR damper were discussed by fixing the input current and amplitude, but with varying frequency. Figures 17 and 18 show the output damping force of both the initial and optimal MR dampers at the input excitation current of 1 A, and the amplitude of 7.5 mm and 10 mm, respectively. The output damping forces of both dampers increase slowly with the increase in the exciting frequency. When the amplitude is 10 mm and the frequency is 1 Hz, the exciting speed is 0.0628 m/s, the maximum output damping force of the initial MR damper with the bended magnetic circuit and folded flow gap is 4739 N, and the maximum output damping force of the optimal damper is 6845 N.  
Figures 19 and 20 show the damping characteristics of the initial and optimal MR dampers with varying exciting currents under the sinusoidal displacement excitation with fixed amplitude of 7.5 mm and frequency of 0.25 Hz. The output damping forces of both the initial and optimal MR dampers increase with the increasing current. This is because that the magnetic flux density in the damping gap increases with the increasing current; thus, the magnetic flux density affects the yield stress and then increases the controllable damping force. The output damping force of the optimal MR damper is larger than that of the initial MR damper with the same current. In addition, as shown in Figure 20, the initial and optimal MR dampers exhibit the hysteresis loop characteristic at low piston velocities. Although the hysteresis loop characteristic is unable to be explained by the Bingham model, the effect on the optimization design stage of the MR damper is very insignificant. Figure 16: Damping force under different amplitudes: (**a**) initial; (**b**) optimal. Figure 17: Damping force with amplitude of 7.5 mm: (**a**) initial; (**b**) optimal. Figure 21a shows the damping force comparison of the simulation and experimental results of the initial MR damper. The damping force of the simulation is linear with the current, while the linear relationship between them in the experiment is not obvious. The maximum deviation between the test and simulation results is 446 N at a current of 0.25 A, which is within the acceptable range. Figure 19: Damping force versus displacement under different currents: (**a**) initial; (**b**) optimal. Figure 20: Damping force versus velocity under different currents: (**a**) initial; (**b**) optimal. Figure 21b compares the damping forces of the simulation and experimental results of the optimal MR damper. The experimental damping force is larger than the simulation damping force, which is due to the excessive interactive friction caused between the piston outer wall and cylinder. For better comparison, the experimental correction curve was generated by eliminating the friction factor from the field-off damping force of simulation. The experimental correction curve agrees well with the simulation curve. In addition, the dynamic range of the experimental correction of the optimal MR damper is consistent with the simulation results (Figure 13), and its value reaches 13.8 at the current of 1.5 A.