# Study of High-Frequency Pulsating Flow Control Valves
## 4 Experimental Research  
In order to verify the performance of the high-frequency flow control valve, an experimental bench as shown in Figure 4 was built. The experimental bench mainly contains the constant differential pressure-reducing valve, sinusoidal flow valve, hydraulic cylinder, directional valve, speed sensor, and other devices. The oil selected was No. 46 hydraulic oil (Fluid temperature:40 \({}^{\circ}\)C; Density:850 g/m\({}^{3}\); Viscosity: 46 mm\({}^{2}\)/s). The output flow from the high-frequency flow control valve passes through the reversing valve into the hydraulic cylinder, causing the piston to move. On the other side of the hydraulic cylinder, flow exists through the reversing valve into the tank. A speed sensor, installed on one end of the piston rod, collect speed signals in the hydraulic cylinder. By multiplying these signals by the piston's effective area of action, the output flow of the high-frequency flow control valve is obtained. The parameters of the measured valve and the parameters of the hydraulic cylinder are shown in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Model Number** & **Parameters** \\ \hline Servo motor & 60 AST-M01930 & Maximum speed 3000 r/min \\  & & Rated torque 1.91 N\(\cdot\)m \\  & & Measuring range 0–0.1 m/s \\ Speed sensor & SD-150 & Accurate 0.1\%, Output voltage \\  & & 0–500 mV \\ Pressure sensors & NS-P-I-2A5-10 MPaG100 & Measuring range 0–10 MPa \\  & & Accurate 1\%, Output voltage 0–5 V \\ Hydraulic cylinder & & Piston diameter 172 mm, Piston rod \\  & & diameter 18 mm, Course 150 mm \\  & & 0–5 V to 0–5 V \\ Optoisolator & VDT-21 & 0–10 V to 0–10 V \\  & & 0–150 mV to 0–150 mV \\ Directional & 4 WMM10D10B & Maximum output flow rate \\  & & 100 L/min \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental bench instrument parameters. Figure 4: Laboratory bench. By controlling the speed of the servo motor in order to generate a sinusoidal flow rate of 0.1-25 Hz, the flow rate measured by the HPFCV can be calculated by picking the signal from the speed sensor. Figure 3 presents the sinusoidal flow rate obtained from the experiment and simulation at four different frequencies. As can be seen in Figure 5, in the low-frequency state at 1 Hz and 10 Hz, the HPFCV outputs a flow rate amplitude of about 24.5 L/min. Afterwards, as the frequency continues to rise, the amplitude of the resulting flow rate begins to gradually decay, and when the frequency reaches 25 Hz, the amplitude of the sinusoidal flow rate output from the sinusoidal flow control valve decays by about 33%. The amplitude-frequency characteristics of the HPFCV can be obtained according to Equation (17). \[L=20 lg\frac{A_{i}}{A_{0}} \tag{17}\]  
where, \(A_{i}\) is the flow amplitude at any frequency of the output of the HPFCV, and \(A_{0}\) is the flow amplitude at the fundamental frequency, which corresponds to 0.1 Hz in this paper. Figure 5: _Cont._  
At this point, the experimental Bode plot of the HPFCV shown in Figure 6 can be obtained. As can be seen from the figure, when the frequency reaches 23.5 Hz, the amplitude-frequency characteristic curve of the Bode plot decays to \(-3\) dB. At this time, the sinusoidal flow amplitude of the output of the HPFCV has been attenuated to less than 70% of the amplitude of the flow rate measured at the test frequency of 0.1 Hz. In addition, according to Figure 6, it can be seen that the experimental \(-3\) dB frequency is much smaller than the simulation results. It was assessed that this could be due to the fact that two longer rubber hoses were used for the oil to enter and exit the hydraulic cylinder, and these hoses would have a greater effect on the system. After that, the simulated Bode plots of the rubber hoses with a different Young's modulus were also obtained. From Figure 7, it can be seen that as the Young's modulus decreases, the frequency corresponding to \(-3\) dB also decreases; the Young's modulus corresponding to the rubber hose used in this experiment is around 60 MPa.