## 5 Conclusions  
This article presents the design of a gradient magnet with a maximum absolute gradient value of 400 T\({}^{2}\)/m. The room-temperature aperture of the gradient magnet is 200 mm, and it achieves a central magnetic field of 10.78 T. Employing a magnetic-force coupling method grounded in generalized stretching, the preload parameters of gradient coils are optimized through orthogonal parameter scanning. The study conducts a comprehensive analysis and calculation of the stress distribution in the magnet coils and mandrel. Key conclusions include the following: the electromagnetic design parameters of the magnet meet the design requirements; the stress-strain values of gradient magnet coils are within the permissible limits of their respective materials; the maximum equivalent stress in the mandrel assembly part is 232 MPa, which is below the permissible material stress of 286 MPa at 4.2 K. The peak stress is observed in the middle and upper part of the connecting block in the middle of the mandrel. From the results, there are two points to pay attention to in the design of large gradient magnets. Firstly, due to the influence of the electromagnetic distribution characteristics of gradient magnets, stress concentration may occur at the connection points of mechanical structures. If necessary, the structure can be strengthened. Secondly, in the design of gradient magnets, adding a pre tensioning layer can effectively reduce the electromagnetic stress in the system.  
This article provides insights into magnet design optimization and stress-strain analysis methods in related fields. On a technical level, it can provide a reference for magnet design methods and stress calibration methods for researchers in the same field when designing similar high-gradient magnet structures. In terms of economic benefits, through finite element analysis, this design can save the costs in materials testing and stress testing or provide theoretical support. Meanwhile, the large-aperture high-field-strength gradient magnet designed in this study can generate considerable economic benefits in multiple fields such as life sciences, metal smelting, scientific research, semiconductors, and deep space exploration.  
Figure 12: (**a**) Equivalent force in coil mandrel; (**b**) equivalent forces in mandrel connecting block.  
**Author Contributions:** Conceptualization, Y.W. and P.G.; Data curation, Y.W.; Formal analysis, Y.W.; Funding acquisition, X.L. and H.H.; Investigation, Y.W.; Methodology, Y.W.; Project administration, P.G. and X.L.; Resources, X.L. and H.H.; Software, Y.W.; Supervision, P.G.; Validation, Y.W. and P.G.; Visualization, Y.W.; Writing--original draft, Y.W.; Writing--review and editing, Y.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Key R&D Program of China (Grant No. 2021 YFA1600201) and the National Natural Science Foundation of China, Grant No. 52207035.  
**Institutional Review Board Statement:** Not applicable.  
**Infrared Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available in the article. Further inquiries for the data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.