## 3 Experimental Validation  
Figure 8 depicts the test rig for the experimental campaign on a 40 cc/rev single crescent pump. It is worth noting that the layout of the test rig was in accordance with the hydraulic circuit displayed in Figure 4. As observed, the crescent pump was driven by a servo motor (0-2000 rpm), and its outlet pressure was built up by a throttle valve. The working medium of the pump was L-HM 46 mineral oil, and the oil temperature was maintained within (40 \(\pm\) 3) \({}^{\circ}\)C, consistent with the oil temperature in the simulation model. The test rig enabled measurements of the steady-state outlet flowrate via a gear type flowmeter and the outlet pressure ripples via a high frequency pressure sensor. Table 1 provides the main features of the flowmeter and the pressure sensor which have been calibrated before experiments, and Table 2 provides the main geometric parameters of the crescent pump. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensor** & **Type** & \multicolumn{2}{c}{**Main Feature**} \\ \hline Flowmeter & Kracht®, Germany, VCSF1 PV & scale: 1–250 L/min, 0.3\% accuracy (from measured value) \\ \hline Pressure sensor & Shuangqiao®, China, CYG140F & scale: 0–35 MPa, 0.5\% FS accuracy, 0.5\% nonlinearity, 100 KHz natural frequency \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main features of the flowmeter and the pressure sensor. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Notation** & **Value** & **Unit** \\ \hline Module of the gear & \(m\) & 3 & mm \\ Tooth numbers of the gear shaft and the ring gear & \(z_{1},z_{2}\) & \(13,19\) & – \\ Pressure angle of the gear & \(a_{0}\) & 22 & \({}^{\circ}\) \\ \hline Operating pressure angle of the gear pair & \(\kappa\) & 24.87 & \({}^{\circ}\) \\ Width of the gear & \(b\) & 55 & mm \\ Addendum and pitch radii of the gear shaft & \(r_{\text{al.}}\), \(r_{\text{p1}}\) & 23.43, 19.5 & mm \\ Addendum and pitch radii of the ring gear & \(r_{\text{al.}}\), \(r_{\text{p2}}\) & 26.95, 28.5 & mm \\ Radii of inner and outer borders of the floating plate & \(r_{\text{p1}}\), \(r_{\text{p2}}\) & 15.5, 38.25 & mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main geometric parameters of the crescent pump. Figure 8: Test rig for measuring the single crescent pump’s steady-state flowrate and outlet pressure ripples. Figure 9 depicts the comparison between the simulated and experimental results concerning the steady-state flow characteristics with respect to different operating conditions (500-2000 rpm, 5-20 MPa). As observed, there existed a linear relationship between the flowrate and the operating speed, and the outlet flowrate yielded roughly 40 L/min at 1000 rpm, in accordance with the pump's displacement (40 cc/rev). Furthermore, it was also observed that the outlet flowrate and the volumetric efficiency yielded a decrease as the outlet pressure increased (at a certain speed), which was expected since higher outlet pressure leads to greater internal leakage. A clear example can be given by the case of working at 500 rpm, where the volumetric efficiency drops from 0.98 at 5 MPa to 0.92 at 20 MPa. Moreover, it can be seen that a good agreement was found between the simulated and experimental results regarding the flowrate and the volumetric efficiency, noting that the accuracy of the flowmeter was within 0.3% (from measured value). Figure 10 depicts the comparison between the simulated and experimental results on the outlet pressure ripples for one shaft revolution with respect to different operating conditions (500 rpm, 5 MPa; 500 rpm, 20 MPa; 2000 rpm, 20 MPa). As observed, 13 outlet pressure ripples existed in a shaft revolution, which is believed to be due to the tooth number of the gear shaft (driving gear) which was 13. Apart from that, it was visible that the pressure ripples yielded greater amplitudes under the circumstance of low operating speed and high outlet pressure (500 rpm, 20 MPa).