## 3 Results and Discussion  
### Rheological Properties of the HP-MRFs  
The correlation between shear stress and magnetic flux density in single-graded HP-MRFs is illustrated in Figure 4. This figure illustrates that at a magnetic flux density of 0.757 T, the shear yield strength of HP-MRF-1 is measured at 81.8 kPa, in contrast to the shear yield strength of HP-MRF-8, which is recorded at 45 kPa. As we progress from HP-MRF-1 to HP-MRF-8, there is a noticeable decrease in shear stress, suggesting that the volume of soft magnetic particles diminishes progressively with the reduction in particle size. Magnetic dipole and coupled field model theory [37, 38] suggests that the magnetic force between particles diminishes progressively, leading to a gradual reduction in shear stress. Simultaneously, as the magnetic induction intensity gradually increases, all HP-MRF samples approach magnetic saturation at 0.5 T. This suggests that when the mass fraction of soft magnetic particles remains constant, the size of the particles has minimal impact on the magnetic saturation of HP-MRFs. To evaluate the performance of double-graded HP-MRFs against single-graded HP-MRFs, the experimental results of HP-MRF-1, 4, and 10 were chosen for comparative analysis, as illustrated in Figure 5. Table 1 illustrates that the soft magnetic particles in HP-MRF-1 consist of unmilled CIPs, HP-MRF-4 contains CIPs that have undergone 24 h of ball milling, and HP-MRF-10 comprises a mixture of unmilled and 24 h ball-milled CIPs, with unmilled CIPs constituting 90% and 24 h ball-milled CIPs making up 10% of the soft magnetic particles. The shear yield strength of HP-MRF-10 is 99.6 kPa, exceeding that of HP-MRF-1 and HP-MRF-4 by 17.8 kPa and 31.3 kPa, respectively. Figure 3: Production and evaluation of the self-decoupling MR damper. (**a**) Structure and the magnetic circuit in the self-decoupling MR damper; (**b**) magnetic induction in the damping channel of the main piston; (**c**) experimental setup of the self-decoupling MR damper. Figure 6a illustrates the variation in particle sizes of the sub-micron particles across the HP-MRF-9, 10, and 11 samples, which were subjected to ball milling for durations of 12 h, 24 h, and 60 h, respectively. All other conditions remain the same. The shear yield strengths observed for the HP-MRF-9, HP-MRF-10, and HP-MRF-11 samples were recorded at 92.5 kPa, 99.6 kPa, and 74.1 kPa, respectively. The figure illustrates that HP-MRF-10, which underwent 24 h of ball milling with soft magnetic particles, exhibits the most favorable MR effect. In contrast, HP-MRF-11, subjected to 60 h of ball milling, demonstrates the least effective MR response, with its shear stress falling below that of the single-graded HP-MRF-1 that did not undergo ball milling. The particle size in HP-MRF-11 measures just 360 nm, indicating a further reduction in the average size of the particles. The shear stress displays a reduction. Consequently, the particle size of the sub-micron particles in the double-graded HP-MRFs should be optimized to significantly enhance their shear stress. Figure 4: The relationship between shear stress and magnetic flux density of single-graded HP-MRFs. Figure 5: The relationship between shear stress and magnetic flux density of single-graded and double graded HP-MRFs. Figure 6b illustrates that the sub-micron soft magnetic particles in the HP-MRF-10 and 12 samples exhibit identical particle sizes, as both had undergone ball milling for 24 h; however, their respective contents differ, being 10% and 8%, respectively. The shear yield strength of HP-MRF-12, containing a reduced amount of sub-micron soft magnetic particles, is measured at 97.5 kPa. Nonetheless, the content must not be excessively high, as an increase in content will lead to a further reduction in the average particle size, subsequently decreasing the shear stress. Consequently, in the double-graded HP-MRFs, the concentration of sub-micron particles must also be kept at a moderate level.