## 3 Experimental Research and Discussion
### Dynamic Characteristic  
The static characteristics experiment found that friction force existed when the experimental system was running. Before the dynamic characteristic experiments, it was important to identify the friction parameters. The friction force experiment system was set up as shown in Figure 15b. The pilot shaft was replaced by the VCM2, and the coil actuator displacement of the VCM2 was measured by displacement sensor 2. The RD and the CD were removed, and shafts 1 and 2 remained free. There was no liquid in the sleeve chamber, and it was connected to the atmosphere. To simulate the static friction forces of the RD and the CD, under a sinusoidal signal with a frequency of 0.1 Hz, the displacement range of the VCM 1 was set from \(-\)1 mm to 1 mm, while that of the VCM 2 was set from \(-\)0.5 mm to 0.5 mm. In these conditions, the motion speeds of the diaphragms are very slow, and the friction forces acting on the diaphragms are regarded as the static friction forces. Specifically, the static friction forces of the RD and CD are obtained by averaging the data collected by the force sensor during the motions in one direction. The static friction forces of the RD and the CD were measured as 2.5 N and 0.2 N, respectively. Furthermore, the static friction forces were introduced into the Simulink model and simulation tests with sinusoidal voltage input of 1 Hz and 10 Hz were carried out. The displacements of the diaphragms in the simulation were compared with the experiments, and the viscous friction coefficients were manually adjusted to make the motion amplitudes of the simulations and experiments the same. The viscous friction coefficients of the RD and CD were obtained as 55 N\(\cdot\)s/m and 27 N\(\cdot\)s/m, respectively. A dynamic characteristics simulation was carried out based on the Simulink model in Section 2, and the simulation parameters are shown in Table 6.  
Figure 20: Different initial volume experiments. (**a**) RD mechanical characteristics. (**b**) CD mechanical characteristics. To validate the accuracy of the Simulink simulation, dynamic characteristics experiments were conducted. The dynamic experiment is shown in Figure 15c. The VCM coil actuator executed sinusoidal movement ranging from \(-1\) V to \(3\) V at frequencies of \(0.1\) Hz, \(0.3\) Hz, \(0.5\) Hz, \(0.7\) Hz, \(1\) Hz, \(3\) Hz, \(5\) Hz, \(7\) Hz, and \(10\) Hz with an inertial load. The displacement of the CD was measured and recorded as the system output. The sampling rate of the experimental points was \(10{,}000\) Hz. The frequency sweep method was employed for the Simulink simulation under identical working conditions. To compare the magnitude ratio and the phase difference between the voltage signals and the displacement signals, they were converted into dimensionless quantities. The magnitude at each frequency was converted to a ratio relative to the Simulink simulation magnitude at \(0.1\) Hz. Dimensionless dynamic characteristic curves with frequencies of \(0.1\) Hz, \(1\) Hz, and \(10\) Hz were selected, as shown in Figure 21.  
According to the dimensionless dynamic characteristic curves shown in Figure 21, the Bode diagram of the dynamic experiments and Simulink simulations in the frequency range from \(0.1\) Hz to \(10\) Hz were plotted, as shown in Figure 22.