# Flow Analysis of a Novel, Three-Way Cartridge Flow Control Valve
## 5 Laboratory Test Bench and Experimental Results  
Figure 17 shows a diagram and an overall view of a test bench used for carrying out laboratory experiments. Through the supply system consisting of a variable displacement pump (1), a relief valve (2) and a filter (3), the input flow rate for the studied flow control valve (4) was generated. The pressure in the load line was set using the valve (8). Flow meters (5) and pressure transducers (6) were used to measure flow rates and pressures in all flow channels. The oil temperature in the tank was measured by a thermometer (7). Operational parameters of the measuring and data acquisition equipment, including the theoretical accuracies, are summarised in Table 5.  
The experiments carried out on the test stand allowed the actual _p_-_Q_ characteristics of the valve to be obtained. The procedure included the following steps: (a) installing a spring of appropriate stiffness, setting the initial tension to obtain a specific value of flow rate, (b) setting the minimum pressure in the load line, (c) switching on the power supply, (d) gradually increasing the load pressure to the maximum value by changing the relief valve setting and then (e) acquiring the measurement data with time step \(\Delta t=0.02\,\mathrm{s}\). In the first step, the flow control valve settings were adjusted to the required flow rate \(Q_{A}=10\,\mathrm{d}\mathrm{m}^{3}\,\mathrm{min}^{-1}\), while the load line pressure \(p_{A}\) was changed in the range of 2-30 MPa. The pump flow rate was set to \(Q_{0}=30\,\mathrm{d}\mathrm{m}^{3}\,\mathrm{min}^{-1}\), and the discharge channel \(B\) was not loaded. The obtained graphs of flow rate \(Q_{0}(t)\), \(Q_{A}(t)\) and load pressure \(p_{A}(t)\) are shown in Figure 18, while the uncertainties are summarised in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Mean Error** & **Mean \% Error** & **Max. Error** & **Std. Deviation** & **Std. Error** \\ \hline \(Q_{0}\) & 0.17 \(\mathrm{d}\mathrm{m}^{3}/\mathrm{min}\) & 1.58\% & 0.58 \(\mathrm{d}\mathrm{m}^{3}/\mathrm{min}\) & 0.38 \(\mathrm{d}\mathrm{m}^{3}/\mathrm{min}\) & 0.23 \(\mathrm{d}\mathrm{m}^{3}/\mathrm{min}\) \\ \(Q_{A}\) & 0.26 \(\mathrm{d}\mathrm{m}^{3}/\mathrm{min}\) & 2.59\% & 0.78 \(\mathrm{d}\mathrm{m}^{3}/\mathrm{min}\) & 0.60 \(\mathrm{d}\mathrm{m}^{3}/\mathrm{min}\) & 0.35 \(\mathrm{d}\mathrm{m}^{3}/\mathrm{min}\) \\ \(p_{A}\) & 0.24 \(\mathrm{MPa}\) & 2.15\% & 0.65 \(\mathrm{MPa}\) & 0.37 \(\mathrm{MPa}\) & 0.22 \(\mathrm{MPa}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Flow rate and pressure measurement uncertainty. Figure 17: Test bench: (a) scheme, (b) view; 1—pump; 2—safety relief valve; 3—filter; 4—flow control valve; 5—flow meter; 6—pressure transducer; 7—thermometer; 8—relief valve; 9—Data acquisition unit. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Pressure** & **Flow Rate** & **Temperature** & **DAQ Card** \\ \hline Name & Trafag NAT & KEM HM & Introl FH0 & Advantech 4704 \\ Range & 0–25 & 0.3–33 & 0–100 & 12 bit \\ Unit & MPa & \(\mathrm{d}\mathrm{m}^{3}\,\mathrm{min}^{-1}\) & \({}^{\circ}\)C & 8\(\times\)AI, 2\(\times\)AO \\ Accuracy & \(\pm\)0.2\% & \(\pm\)0.3\% & \(\pm\)0.5 \({}^{\circ}\)C & n.a. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Measuring and data acquisition equipment parameters. The approximated \(Q_{A}(p_{A})\) characteristic with the corresponding result from the Simulink model is shown in Figure 19.  
The valve response to a variable pump flow rate in the range \(Q_{0}=2-30\,\mathrm{d}\mathrm{m}^{3}\,\mathrm{min}^{-1}\) was tested in the second step. In this case, a constant load was also assumed in the load line \(Q_{A}=10\,\mathrm{d}\mathrm{m}^{3}\,\mathrm{min}^{-1}\). The obtained laboratory charts are shown in Figure 20, while a comparison of the approximated laboratory curve \(Q_{A}=f(Q_{0})\) and simulation results is shown in Figure 21.  
Figure 19: Comparison of the \(p\)-\(Q\) characteristic: solid—experimental curves, dashed—simulation results.