## 3 Experimental Research and Discussion
### Dynamic Characteristic
\begin{table}
\begin{tabular}{c c c c} \hline
**Definition** & **Parameter** & **Value** & **Unit** \\ \hline Force constant & \(K_{\text{f}}\) & \(24.55\) & N/A \\ Resistance & \(R\) & \(6.8\) & \(\Omega\) \\ Inductance & \(L\) & \(2.5\times 10^{-3}\) & H \\ Total mass of the RD end & \(m_{1}\) & \(0.17189\) & kg \\ Total mass of the CD end & \(m_{2}\) & \(0.13383\) & kg \\ Static friction force of the RD end & \(F_{\text{f1}}\) & \(2.5\) & N \\ Static friction force of the CD end & \(F_{\text{f2}}\) & \(0.2\) & N \\ RD elastic slope & \(k_{1}\) & \(2.182\) & N/mm \\ CD elastic slope & \(k_{2}\) & \(1.13\) & N/mm \\ Displacement proportional coefficient & \(k_{\text{p1}}\) & \(4.2829\) & - \\ Area proportional coefficient & \(k_{\text{p2}}\) & \(0.25\) & - \\ Viscous friction coefficient of the RD & \(c_{\text{v1}}\) & \(55\) & N-s/m \\ Viscous friction coefficient of the CD & \(c_{\text{v2}}\) & \(27\) & N-s/m \\ \hline \end{tabular}
\end{table} 
Table 6: Simulink simulation parameters. Figure 21: Dimensionless dynamic characteristics curves. (**a**) Dimensionless curves at \(0.1\) Hz; (**b**) dimensionless curves at \(1\) Hz; and (**c**) dimensionless curves at \(10\) Hz. The experimental magnitude ranges from 0.05 dB to \(-\)8.27 dB, and the phase ranges from \(-\)21.27 degrees to \(-\)62.28 degrees. The Simulink simulation magnitude ranges from 0 to \(-\)8.24 dB, and the phase ranges from \(-\)21.6 degrees to \(-\)80.28 degrees. When the frequency is less than 1 Hz, the maximum magnitude deviation between the simulation value and the experimental value 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 value and the experimental value is 1.14 dB, and the maximum phase deviation is 21.96 degrees. Therefore, in future dynamic experimental research, the Simulink model for the HFAM can be used to control the load movement. For example, spool movement can be controlled based on the Simulink model of the HFAM. It is worth noting that the research still has some limitations. At present, the HFAM is mainly suitable for working conditions at normal temperature and pressure and with small input force, such as amplifying the driving force of the electro-mechanical converter in the hydraulic control valve. However, when the HFAM is used in some extreme conditions, such as a very high input force resulting in a large deformation of the diaphragms or a large fluid pressure in the sleeve, the HFAM may have problems, such as diaphragm damage, and thus the failure of the amplification effect. In addition, in this research, it is assumed that the HFAM system is under a fixed temperature of 20 \({}^{\circ}\)C and a standard atmospheric pressure environment, and the influence of ambient temperature and air pressure on the working effect of the amplifier is not considered in the model. In actual working conditions, the change in temperature affects the physical property parameters of the diaphragms, for example, the hardness and elastic modulus of the diaphragms decrease with the increase in temperature, and then affect the elastic force generated by the diaphragms. The ambient pressure directly acts on the outer surfaces of the diaphragms, driving the diaphragms to produce elastic deformations and affecting the HFAM's amplification effect. 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. In addition, this research only deals with a HFAM with specific structure size and does not discuss the influence of RD and CD size parameters on the working effect of HFAMs. In the subsequent research, the influence of the diaphragm size parameters on the working effect of HFAMs could be studied through simulation and experiment methods. Figure 22: HFAM system Bode diagram.