## 4 Experimental Verification
### Experimental Results and Analysis  
For comparative analysis, as shown in Figure 12, three characteristic pressure conditions--7 MPa, 14 MPa, and 21 MPa--were selected. At the speed of 300 r/min, the difference between the simulated and experimental values of 7 MPa mechanical efficiency is 0.88%, the difference between the simulated and experimental values of 14 MPa mechanical efficiency is 1.18%, and the difference between the simulated and experimental values of 21 MPa mechanical efficiency is 5.11%. Mechanical efficiency demonstrates a declining trend across all pressure levels as rotational speed increases from 600 r/min to 3500 r/min. Notably, under 21 MPa conditions, mechanical efficiency paradoxically increases when rotational speed drops below 500 r/min. This phenomenon arises from amplified gear ring eccentricity under high pressure, which reduces the minimum oil film thickness between the gear ring and housing. Furthermore, diminished hydrodynamic lubrication effects at low speeds intensify friction at the gear ring housing interface, resulting in pronounced discrepancies between simulated and experimental mechanical efficiency values. As pressure increases, the discrepancy between simulation and experimental results gradually widens under low-speed conditions; while rising rotational speed enhances hydrodynamic lubrication effects in the oil film, reducing gear ring displacement and significantly improving mechanical efficiency. When operating at rotational speeds exceeding 600 r/min, the maximum discrepancy between simulated and experimental mechanical efficiency remained within 1.6% across all tested pressures, validating the accuracy of the mechanical loss model. Figure 12: Experimental validation of mechanical efficiency under all operating conditions. As evidenced by Figure 13, the experimental volumetric efficiency exhibits a characteristic \"steep initial increase followed by gradual growth\" trend when rotational speed rises from 300 r/min to 3500 r/min under varying pressures. A similar trend was observed for mechanical efficiency. At 300 r/min, the deviations between simulated and experimental volumetric efficiencies measured 0.83% at 7 MPa, 1.45% at 14 MPa, and 2.95% at 21 MPa. When the rotational speed is lower than 600 r/min, the simulation results of volumetric efficiency show significant discrepancies from the experimental results, and the greater the rotational speed, the larger the difference. This is due to the large eccentric movement of the gear ring under the speed operation condition, and the sealing clearance of the gear ring shell interface becomes larger, resulting in increased leakage. On the other hand, at low speed, the axial end face leakage direction of the gear ring is opposite to the speed direction, which also results in increased leakage. Higher rotational speeds enhanced hydrodynamic lubrication effects, reducing gear ring deflection and sealing clearance while improving sealing performance. At rotational speeds surpassing 600 r/min, the discrepancy between simulation outputs and empirical measurements was constrained within a 1% tolerance threshold under multi-stage pressure conditions of 7 MPa, 14 MPa, and 21 MPa, which systematically validated the predictive accuracy of the leakage dissipation model. Figure 14 shows the experimental total efficiency contour map of the internal gear pump under full operating conditions. The efficiency distribution reveals that two distinct low-efficiency zones predominantly exist: (1) a low-speed/high-pressure zone (0-800 r/min, 16-22 MPa) where efficiency drops to approximately 70-75%, primarily due to insufficient hydrodynamic film load capacity and weakened velocity sealing effects  
Figure 13: Experimental validation of volumetric efficiency under all operating conditions. resulting in volumetric losses; and (2) a high-speed/low-pressure zone (3200-4000 r/min, 7-10 MPa) where efficiency decreases to around 75-80%, mainly caused by increased frictional power consumption and degraded lubrication performance.