# Research on the High Speed of Piston Pumps Based on Rapid Erecting of Launch Vehicles
## 4 Results and Discussion  
### Flow Characteristics and Volumetric Efficiency of Piston Pumps  
To make the description easier, the following uses traditional flow to represent the flow of the axial piston pump using the traditional cylinder, and the improved flow represents the flow of the axial piston pump using the improved cylinder. Figure 9 shows that when the piston pump's rotational speed is less than 1500 rpm, there is no significant difference in flow rate and volumetric efficiency between the improved and traditional cylinder blocks. However, above 1500 rpm, the flow rate and volumetric efficiency of the piston pump increase greatly with the use of the improved cylinder block, and the maximum flow rate is increased from 1.765 kg/s to 2.295 kg/s. The maximum speed at which the volumetric efficiency remains above 90% is improved from 1500 rpm to 2100 rpm, greatly increasing the axial piston pump's rated speed. At 2000 rpm, 2500 rpm, 3000 rpm and 3500 rpm, the volumetric efficiency of the conventional block was 74.465%, 49.649%, 34.390% and 22.640%, respectively, which were improved by 23.219%, 54.958%, 64.024% and 78.405% with the improved block. The flow rate of the conventional cylinder was 1.753 kg/s, 1.472 kg/s, 1.222 kg/s and 0.935 kg/s at different speeds and improved by 24.073%, 54.823%, 63.993% and 79.251%, respectively. It can be found that when rotating at high speed, the volumetric efficiency and flow rate of the piston pump, although decreasing with increasing speed, increases with increasing speed after the improvement.  
The traditional flow pulsation equation is:  
\[\delta=\frac{Q_{\text{max}}-Q_{\text{min}}}{\frac{1}{2}(Q_{\text{max}}+Q_{ \text{min}})} \tag{17}\]  
where \(Q_{\text{max}}\) and \(Q_{\text{min}}\) are the maximum and minimum flow rates, respectively, and \(\delta\) is the flow pulsation. Equation (17), which is dependent solely on the maximum and minimum values for calculating the flow pulsation rate, is incapable of accurately characterising the flow pulsation properties. As a result, a new method of characterising flow pulsation  
Figure 8: Comparison of experimental and numerical simulation results.  
characteristics was proposed, in which the flow curve is discretised, and the mean squared difference is determined for each value using the expression:  
\[\delta_{1}=\frac{1}{n}\sum_{1}^{n}\left(Q_{\text{avg}}-Q_{i}\right)^{2} \tag{18}\]  
\[Q_{avg}=\frac{1}{n}(Q_{1}+Q_{2}+Q_{3}+\cdots+Q_{n}) \tag{19}\]  
The speed-pulsation curve is obtained by using the above pulsation calculation method and discretising the flow time history curve into 60 pieces (Figure 10). As the rotational speed increases, the flow pulsation also grows. At speeds below 1500 rpm, the flow pulsation of the enhanced cylinder is not noticeably different from that of the traditional cylinder. When the speed is more than 1500 rpm, the flow pulsation of the improved cylinder is significantly reduced. At 2000 rpm, the flow pulsation of the traditional block is 0.855, whereas that of the improved block is 0.090, a reduction of 89%. However, once the rotational speed is greater than 1500 rpm, the traditional flow becomes negative, which causes the hydraulic cylinder to vibrate more. After the cylinder body is improved, the negative flow will no longer emerge.  
Figure 10: Traditional and improved flow rate time travel curve at 2000 rpm and flow pulsation at different rotational speeds.  
Figure 9: Traditional and improved flow rate and volumetric efficiency at different rotational speeds.  
In conclusion, the volumetric efficiency of the piston pump is greatly increased, flow pulsation is reduced and the high speed of the axial piston pump is achieved by the use of improved cylinders at speeds exceeding 1500 rpm.