# Modeling and Multi-Objective Optimization Design of High-Speed on/off Valve System
## 5 Prototype and Experiment  
To validate the performance of the proposed HSV, a prototype was fabricated based on the computation results obtained from the AFSA algorithm. The prototype, denoted as HSV, is illustrated in Figure 13. As it is not feasible to directly measure the valve core opening, its movement can be observed by monitoring the input current to the solenoid coil and the flow rate. A test setup, as depicted in Figure 14, was devised specifically for this purpose. Since the flow channels from port P to port A and from port T to port A in the HSV are identical, it sufficed to test only one of them. The hydraulic pump was configured to generate an output pressure of 14 MPa, and this pressurized fluid was directed through the HSV before being measured by a flow meter. The flow meter provided a signal that was recorded by a data acquisition device, while the flowing hydraulic fluid subsequently entered the relief valve, which served to simulate the load. Following the relief valve, the fluid was channeled into the oil tank. The HSV was actuated by a step signal produced by a signal generator, with the current output from the flow transmitter and the pressure transmitter being captured by an oscilloscope. A step signal, lasting 50 ms and possessing a voltage of 12 V, was applied as an input to the HSV system, with the resulting current and flow data being recorded. Table 2 shows the model and parameters of the equipment used in the experiment, while Table 3 displays the initial and optimized dimensions of the valve. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Item** & **Model** & **Range** & **Remarks** \\ \hline Signal generator & OHR-B00 & 1–10 kHz (\(\pm\)100 Hz) & \\ Pump & - & 0–30 mPa & Max 50 L/min \\ Flow probe & KRACHT & 0–8 L/min & 25 \({}^{\circ}\)C \\  & TM8 TFC250S & 0–8 L/min & 25 \({}^{\circ}\)C \\ Pressure probe & AR-SS-S2J06 & 0.1–14.0 mPa & \\ Relief valve & DBET-6X/315G24K4 V & 0.1–31.5 mPa & Max 10 L/min \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design parameters to be determined. Figure 14: Schematic diagram of the hydraulic circuit in the experimental system. The experimental results depicted in Figure 14 provide insights into the displacement behavior of the ball valve through the analysis of recorded currents. When the step control signal was applied, the solenoid coil experienced inductance that impeded the increase in coil current. Insufficient input current prevented the armature from overcoming the pre-tightening force of the spring, resulting in an initial rise in current with no armature displacement. In the subsequent stage, the armature began to displace. The motion of the armature induced a back electromotive force due to the cutting of the magnetic flux lines, causing the driving current to decrease. However, the valve core quickly stopped and the driving current continued to rise until it reached its maximum value. Similarly, the closing process of the solenoid valve can be divided into two parts. After the control voltage rapidly dropped to zero, the armature could not move due to the interaction between coil eddy currents, inductance, and residual magnetic fields of the rotor. As the current decreased, the force generated could not continue to attract the armature. Under the action of the reset spring, the armature was pushed out until the maximum air gap was reached. The opening action of the valve core took about 3 ms, and the closing action took about 3 ms. The black dashed line in Figure 15 represents the BPNN's fitted output for the design parameter. By examining the flow output curve of the HSV, it becomes evident that, apart from a significant deviation at the initial movement of the valve and around its maximum opening, the predicted flow output and opening time of the HSV closely align with the experimental results. An analysis of the predicted current variation in the solenoid coil indicated that the BPNN exhibits some error in predicting the armature movement and the maintenance current; however, the overall trend remains consistent.