## 4 Experiment and Results Analysis
### Potential Energy Regeneration Efficiency  
The potential energy recovery efficiency is defined as the percentage of the charged electric quantity of the battery and the potential energy of the load and door rack in one descending process, seen in Equation (7).  
\[\eta_{\rm s}=\frac{E_{\rm Q}}{E_{\rm dL}}\times 100\% \tag{7}\]  
where, \(\eta_{\rm s}\) is the regeneration efficiency of the potential energy of the system. \(E_{\rm Q}\) is the regenerated electric quantity of the lithium battery, J. \(E_{\rm dL}\) is the potential energy released by the descending of the door rack system and the load, J.  
The charged electric quantity of the lithium battery can be described as:  
\[E_{\rm Q}=-\int_{0}^{t}U_{\rm b}I_{\rm b}dt \tag{8}\]  
Figure 16: Speed curves of 2#HMG.  
Figure 15: Speed curves of 1#HMG.  
where, \(U_{\rm b}\) is the busbar voltage of the lithium battery, V. \(I_{\rm b}\) is the busbar current of the lithium battery, A. If \(I_{\rm b}\) is negative, it is generating. The generated electric energy by the motor when boom descending with a load can be calculated by Equation (9).  
\[E_{\rm dL}=M_{\rm e}gh \tag{9}\]  
\[M_{\rm e}=M+M_{\rm f}+M_{\rm fr}+\frac{1}{2}M_{\rm dr} \tag{10}\]  
where, \(M_{\rm e}\) is the effective mass of the load, forks, fork rack and inner door rack, kg. \(M\) is the load mass, kg. \(M_{\rm f}\) is the forks mass, kg. \(M_{\rm fr}\) is the mass of the fork rack, kg. \(M_{\rm dr}\) is the mass of the inner door rack, kg. \(h\) is the effective descending height, m. g is the gravitational acceleration, m/s\({}^{2}\).  
Seen from Equation (9), the regeneration efficiency of the potential energy is related to the load mass and the effective descending height. The effects of load mass, effective decreasing height and descending velocity on the regeneration efficiency of the potential energy were analyzed when the lifting cylinder descended.  
(1) Potential energy regeneration efficiency corresponding to a different load mass  
To study the influence of different load mass on the potential energy regeneration efficiency, using a single variable principle, the specific requirements were as follows. Before the test, the load was lifted to the same height. The load was descended to the same height with the same velocity no matter how heavy the load was. The busbar voltage and busbar current of the lithium battery were collected. The potential energy regeneration efficiency was calculated according to Equation (7) by the ratio of the charging quantity of the lithium battery and the released potential energy when the load and the door rack descending. The charging current and potential energy regeneration efficiency under 3 tons, 5 tons, 9 tons, 16 tons and 25 tons were discussed.  
In the test rig, the capacity of a lithium battery was 404 Ah, the rated voltage was around 540 V. Additionally, the recoverable energy when the load descending one time was small and the voltage rises caused by it was not obvious. Therefore, the voltage curve would not be discussed here. As shown in Figure 17, the generated current was not a steady-state value but fluctuated within a certain range when the load descending. The generated currents with loads of 3 tons, 5 tons, 9 tons, 16 tons and 25 tons were about -7.0 A, -9.2 A, -14.9 A, -25.7 A and -38.3 A, respectively. The effective value of the generated current was positively correlated with the load mass. That is, the larger the load mass is, the larger the generated current is and the faster the charging speed can achieve.  
At the same height and the same descending velocity, the energy loss of the system increased with the increase of the load mass seen from Figure 18. This is because with the increase of the load,  
Figure 17: Generating current under different loads.