## 4 Conclusions  
This study involved the acquisition of CIPs with varying particle sizes through the ball milling method. Subsequently, a range of HP-MRF samples were prepared by dispersing both single-graded and double-graded CIPs into a compound consisting of a sol solution and methyl silicone oil. A rotational rheometer was employed to analyze the correlation between shear stress and magnetic flux density for the HP-MRF samples. Additionally, the previously developed self-decoupling MR damper was filled with HP-MRF, and the dynamic mechanical properties were evaluated under both small and large displacements. The findings are outlined as follows:  
1. In the case of HP-MRFs featuring single-graded CIPs, it is observed that the shear stress across all samples rises in conjunction with an increase in magnetic flux density. Additionally, the shear yield strength exhibits a decline from 81.8 kPa to 45 kPa as the particle size is progressively reduced. In the case of HP-MRFs featuring double-graded CIPs, the shear yield strength of HP-MRF-10 can reach 99.6 kPa. This suggests that an optimal combination of particle sizes effectively contributes to enhancing the shear yield strength of the HP-MRF.
2. The self-decoupling MR damper can achieve a maximum damping force of 281.5 kN at a small displacement of 5 mm, with an applied frequency of 2.5 Hz and an input current of 2.0 A. Additionally, the highest factor of adjustability of the damping force for the self-decoupling MR damper reaches 3.34 when the current ranges from \(-\)2.0 A to 2.0 A, with an applied frequency of 0.1 Hz. Furthermore, the self-decoupling MR damper exhibits a maximum damping force of 300 kN under a large displacement of 60 mm, which aligns with the measurement limit of the testing apparatus. The values of the calculated dynamic parameters, such as equivalent stiffness \(K_{\rm h}\) and yield force \(Q_{\rm d}\), can be enhanced by both the input current and the applied frequency.
3. Compared to the prior investigation of a self-decoupling MR damper utilizing a common MRF, the damping force may be increased by a maximum of 93.9 kN, and the adjustable range can also be enlarged. Furthermore, the computed dynamic parameters, including \(K_{\rm h}\) and the equivalent damping ratio \(h_{\rm eq}\), are improved, indicating the energy consumption capacity of the self-decoupling MR damper is enhanced with the HP-MRF.  
Methodology, F.G. and Z.M.; Formal analysis, F.G.; Investigation, F.G., H.C. and X.H.; Data curation, F.G.; Writing--original draft, F.G.; Writing--review & editing, F.G.; Supervision, Z.M. and X.L.; Project administration, C.D.; Funding acquisition, F.G., H.C., X.H., C.D., Z.M. and X.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Anhui Province University Research Project (2024 AH050128), Jiangsu Province Key R&D Project (Grant no. BE2022162), Nature Science Research Project of Anhui province (Grant no. 2308085 QD124), Housing Urban and Rural Construction Science and Technology Project of Anhui province (Grant no. 2023 YF061, and 2023-YY060), National College Students' innovation and en-trepreneurship training program (Grant no. 202310363113), Wuhu scientific and technological project (Grant no. 2024 kj025, 2023 yf088 and 2024 kj032), and the Research Start-up Fund Project of Ningbo University of Technology (Grant no. 2023 KQ031).  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.