# Energy Regeneration Hydraulic System via a Relief Valve with Energy Regeneration Unit
## 5 Experimental Study and Discussion
### Results and Discussion
#### 5.2.2 Regeneration Efficiency  
One objective of the experiment is to determine how much energy can be stored by the HERU. As seen in Figure 12, the area between the pressure of the HA and inlet pressure of the PRV is the energy loss through the PRV. When combined with Figure 11, a higher pre-charge pressure results in a smaller area denoting the energy loss.  
The energy loss through PRV without HERU is given by  
\[E_{\mathrm{r}}=\int p_{1}Qdt \tag{16}\]  
where \(E_{\mathrm{r}}\) is the energy loss through PRV without HERU.  
The regenerated energy in HA can be obtained as  
\[E_{\mathrm{a}}=\frac{p_{\mathrm{a0}}V_{\mathrm{a0}}}{n-1}\left[\left(\frac{p_ {\mathrm{a2}}}{p_{\mathrm{a0}}}\right)^{\frac{n-1}{n}}-\left(\frac{p_{\mathrm{ a1}}}{p_{\mathrm{a0}}}\right)^{\frac{n-1}{n}}\right] \tag{17}\]  
where \(p_{0}\), \(p_{1}\), and \(p_{2}\) are the pre-charge pressure, minimum pressure, and maximum pressure of the HA, respectively; and \(V_{0}\) is the volume of the HA. The charging process is short and the compression of the gas can be considered as the adiabatic process. The gas index of the ideal gas \(n\) equals to 1.4.  
The regeneration efficiency of the HERU is calculated as:  
\[\eta_{\mathrm{r}}=\frac{E_{\mathrm{a}}}{E_{\mathrm{r}}} \tag{18}\]  
The energy loss and the regenerated energy by HA are listed in Table 1 when the pre-charge pressure is 6.7, 8.2 and 12.5 MPa, respectively. The target pressure of the HA is set to 20 MPa for the three conditions. It can be seen from Table 1 and Figure 10 that when the pre-charge pressure is 6.7 MPa, there is maximum energy loss through PRV without HERU and maximum regenerated energy in HERU. However, the lowest regeneration efficiency happens at this time, being only 61.2%. With an increase in the pre-charge pressure, the energy loss through PRV without HERU and the regenerated energy in HERU decrease, but there is an increase in regeneration efficiency. The reason is that the volume of the HA is the same in the test rig. When the pre-charge pressure of the HA is high, the time for regenerating the energy loss of the PRV via the HA is short, which is seen in Figure 10. As the inlet pressure and the flow rate of PRV are nearly the same, a higher pre-charge pressure results in less energy loss through PRV without HERU. Furthermore, when the pre-charge pressure is high, the outlet pressure of PRV is high. Following this, the pressure drop between the inlet and outlet reduces, which means that the regeneration efficiency will increase. The volume of the HA is chosen according to the installation space. In general, a larger volume means more energy that can be stored.  
Figure 14: Experimental results with different maximum pressures of HA. (**a**) Inlet pressure of PRV; (**b**) Inlet pressure vs. maximum pressure of HA.  
The choice of pre-charge pressure depends on the requirements. If the regeneration efficiency is the main consideration, a higher pre-charge pressure should be chosen. However, if there is need to regenerate as much energy as possible, a smaller pre-charge pressure should be chosen or multiple HA should be utilized.