## 4 Conclusions  
This research introduces a HFAM which is composed of an RD and a CD. The HFAM supports a non-coaxial connection between the actuator and the load. A liquid replenishment device is incorporated to ensure timely replenishment of the liquid in the HFAM without disassembly. The dynamic model, based on the force balance method, was established in the Simulink, and the diaphragm forces were obtained by finite element simulations. Moreover, the experimental system was deployed to analyze the static and dynamic characteristics of the HFAM prototype. From this research, the conclusions could be obtained as follows:  
1. The experiments with different diaphragm displacements show that the forces of the diaphraggrams increase with the increase in the RD displacement and decrease with the increase in the CD displacement. There is hysteresis in the axial reciprocating motion of the diaphragm, and the hysteresis decreases with the increase in the CD displacement.
2. The trend of the FARs with displacement shows that when the displacements of the RD exceed 2 mm, the FARs increase with the increase in the RD displacement but decrease with the increase in the CD displacement. The maximum FAR of the HFAM in the research is 2.5. Based on the FARs of 1, 1.5, and 2, the fitting expressions of the critical curves were obtained, and the displacement ranges of the RD and CD under different FAR ranges were determined.
3. The experiments with different initial volumes show that when the displacements of the RD and the CD remain unchanged, the forces of the diaphraggrams increase with the increase in the initial volume. Furthermore, changing the initial volume does not affect the hysteresis of the diaphragms.
4. Dynamic experiments show that when the frequency is less than 1 Hz, the maximum magnitude deviation between the simulation and the experiment is 0.35 dB, and the maximum phase deviation is 3.04 degrees. When the frequency is greater than 1 Hz, the maximum magnitude deviation between the simulation and the experiment is 1.14 dB, and the maximum phase deviation is 21.96 degrees. The accuracy of the established dynamic model was verified, and the model is helpful to the practical application of the HFAM.
5. In subsequent research, factors such as temperature and pressure could be added to the model to further improve the accuracy of the model to adapt to different working conditions. And the influence of the diaphragm size parameters on the working effect of the HFAMs could be further studied. Based on the study results, the working effect of the HFAMs can be optimized by adjusting the diaphragms' sizes when facing different working conditions and requirements.  
Y.Y.: methodology, software, validation, formal analysis, investigation, data curation, and writing--original draft. T.G.: software, formal analysis, validation, data curation, and writing--review and editing. Z.Z.: conceptualization, formal analysis, resources, writing--review and editing, supervision, and funding acquisition. J.H.: supervision. D.N.: supervision. Y.G.: supervision. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (Grant Nos. 52175043 and UI908228), the Open Research Program of Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of Education of China (B202202), and the Fundamental Research Funds for the Central Universities (3132023513).  
**Institutional Review Board Statement:** Not applicable.  
**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 author.  
**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.