Overﬂow Energy Loss Recovery System Based on Hydraulic Motor-Electric Generator

: Overﬂow loss is one of the main reasons for the inefﬁciency of the hydraulic system. Aiming at the overﬂow loss in the hydraulic system, an energy recovery system based on a hydraulic motor and generator is proposed. Further, a pressure monitoring and control strategy based on variable speed control for electric generator is adopted, which can control the pressure differential between the inlet and outlet of the proportional relief valve as a small value, and achieve the purpose of energy recovery by reducing the loss of the pressure differential between the inlet and outlet of the relief valve. Through establishing a simulation system model and test platform, the stability, step response characteristics and energy saving of the system are studied. The results show that the energy recovery unit at the outlet of the relief valve does not affect the normal operation of the relief valve, but also greatly reduces the pressure regulation deviation. Besides, the efﬁciency of overﬂow loss recovery system about is 67%.


Introduction
Hydraulic transmission has low energy efficiency. Taking the hydraulic excavator as an example, its energy utilization rate is only about 20%, and the efficiency of the hydraulic system is about 30% [1]. Therefore, the research on energy saving technology of the hydraulic system is of great significance [2].
The energy consumption of a hydraulic system mainly includes throttling loss and overflow loss [3]. Between of them, the overflow loss is mainly caused by the relief valve, which is used to limit the maximum working pressure of the system or to achieve constant pressure control. In the traditional system, the outlet of relief valve is connected to the oil tank. Since the pressure of the oil tank is approximately zero, the pressure drop at the inlet and outlet of the relief valve is the inlet pressure of the relief valve, while the pressure at the oil inlet is the target adjustment pressure of the user, which is set by the user and cannot be changed. The higher the overflow pressure level is, the greater the pressure loss at the valve outlet [4]. With the increasing pressure level of hydraulic system, the problem of overflow loss will be more prominent.
At present, a lot of research has been carried out to reduce the overflow loss at home and abroad. However, most of these studies are from the overall system aspect, reducing the flow through the relief valve by the flow matching between the pump and the load, such as volume control technology [5][6][7], variable frequency technology [8,9], and so on. However, there is still overflow in this technology.
Aiming at the problem of overflow loss, Lin et al. proposed an energy regeneration system through an accumulator to recover the energy of overflow loss. The accumulator was connected to the outlet of the relief valve to reduce the pressure difference between the inlet and outlet of the relief valve, reduce the overflow loss, and recover the overflow energy to the accumulator [10,11]. However, in this method, the accumulator cannot be When the proportional relief valve works, the pressure oil of the pilot oil circuit and the main oil circuit return to the port T together. In order to avoid the influence of the return oil back pressure on the pilot oil circuit, the pilot oil circuit can also be connected to the oil tank separately.
The working principle of the traditional proportional relief valve is given in Figure 2. The pressure difference loss at the relief valve port can be described as

Working Principle of Electric Energy Regeneration System for Relief Valve
The electric energy recovery system of proportional relief valve is shown in Figure 3. Generally, the pilot oil outlet of traditional proportional relief valve and the oil outlet of main valve core return to the oil tank together. When the oil outlet of the main valve core of the proportional relief valve is connected with the energy recovery unit, there is a certain pressure in the energy recovery unit, which makes the oil outlet pressure rise. In order to avoid the influence of the energy recovery unit on the pilot pressure, the pilot oil circuit must be connected to the oil tank separately. According to the schematic diagram shown in Figure 3, when the outlet pressure of the relief valve is higher, the differential pressure loss of relief valve is smaller. However, the excess energy generated by the pressure rise of the relief valve outlet can be recovered by energy regeneration system.

Performance Analysis
In order to study the electrical energy regeneration system of the relief valve, number analysis for relief valve is carried out to study the influence of back pressure on the relief valve. When establishing the mathematic model, the system is assumed that works in the ideal state, and (1) Only two hydraulic components (proportional overflow valve and back pressure valve) are considered. The system modeling is carried out by comparing the pilot stage and main stage of overflow valve; Because the main valve core outlet of the traditional proportional relief valve is connected to the oil tank. The tank pressure is basically 0 MPa. The pressure difference of the relief valve can be obtained as ∆p T = p 1 (2)

Working Principle of Electric Energy Regeneration System for Relief Valve
The electric energy recovery system of proportional relief valve is shown in Figure 3. Generally, the pilot oil outlet of traditional proportional relief valve and the oil outlet of main valve core return to the oil tank together. When the oil outlet of the main valve core of the proportional relief valve is connected with the energy recovery unit, there is a certain pressure in the energy recovery unit, which makes the oil outlet pressure rise. In order to avoid the influence of the energy recovery unit on the pilot pressure, the pilot oil circuit must be connected to the oil tank separately.

Working Principle of Electric Energy Regeneration System for Relief Valve
The electric energy recovery system of proportional relief valve is shown in Figure 3. Generally, the pilot oil outlet of traditional proportional relief valve and the oil outlet of main valve core return to the oil tank together. When the oil outlet of the main valve core of the proportional relief valve is connected with the energy recovery unit, there is a certain pressure in the energy recovery unit, which makes the oil outlet pressure rise. In order to avoid the influence of the energy recovery unit on the pilot pressure, the pilot oil circuit must be connected to the oil tank separately.  According to the schematic diagram shown in Figure 3, when the outlet pressure of the relief valve is higher, the differential pressure loss of relief valve is smaller. However, the excess energy generated by the pressure rise of the relief valve outlet can be recovered by energy regeneration system.

Performance Analysis
In order to study the electrical energy regeneration system of the relief valve, number analysis for relief valve is carried out to study the influence of back pressure on the relief valve. When establishing the mathematic model, the system is assumed that works in the ideal state, and (1) Only two hydraulic components (proportional overflow valve and back pressure valve) are considered. The system modeling is carried out by comparing the pilot stage and main stage of overflow valve; According to the schematic diagram shown in Figure 3, when the outlet pressure of the relief valve is higher, the differential pressure loss of relief valve is smaller. However, the excess energy generated by the pressure rise of the relief valve outlet can be recovered by energy regeneration system.

Performance Analysis
In order to study the electrical energy regeneration system of the relief valve, number analysis for relief valve is carried out to study the influence of back pressure on the relief valve. When establishing the mathematic model, the system is assumed that works in the ideal state, and (1) Only two hydraulic components (proportional overflow valve and back pressure valve) are considered. The system modeling is carried out by comparing the pilot stage and main stage of overflow valve; (2) The system is free of leakage; (3) The system oil tank pressure and return oil pressure are equal to zero; (4) The density of oil is constant; (5) The oil temperature and the volume modulus of elasticity of hydraulic oil are constant; and (6) The influence of oil pipeline is ignored.

Mathematical Model of Traditional Proportional Relief Valve
For the convenience of analysis, the structure schematic diagram of traditional relief valve can be simplified as shown in Figure 4.
(4) The density of oil is constant; (5) The oil temperature and the volume modulus of elasticity of hydraulic oil are constant; and (6) The influence of oil pipeline is ignored.

Mathematical Model of Traditional Proportional Relief Valve
For the convenience of analysis, the structure schematic diagram of traditional relief valve can be simplified as shown in Figure 4.
When the relief valve stops working, the main valve core and the pilot valve core are closed. The hydraulic oil from the pump reaches the front cavity 1 of the main valve core, enters the spring chamber 5 and the front chamber 6 of the pilot valve core through the pilot oil circuit and fixed damping hole R. when the hydraulic pressure acting on the pilot valve core is not enough to overcome the electromagnet output force, the pilot valve core 7 is closed, and the main valve core 2 is also closed. With the continuous oil supply of the hydraulic pump, the oil pressure rises. When the pilot valve core 7 is opened, the pilot oil will drain back to the oil tank separately. The oil in the pilot oil circuit flows, and the pressure drop in the spring chamber is less than the inlet pressure due to the pressure drop through the fixed damping hole R. At this time, the resultant force on the main valve core is shown in Equation (3). The resultant force is greater than zero, and the main valve core is opened and the main valve port overflows. . Simplified structure diagram of traditional proportional relief valve. 1-front chamber of main valve core, 2-main valve core, 3-fixed damping, 4-spring cavity, 5-return spring, 6front chamber of pilot valve core, 7-pilot valve core, 8-proportional electromagnet.
Dynamic force balance equation of pilot valve core can be described as When the relief valve stops working, the main valve core and the pilot valve core are closed. The hydraulic oil from the pump reaches the front cavity 1 of the main valve core, enters the spring chamber 5 and the front chamber 6 of the pilot valve core through the pilot oil circuit and fixed damping hole R. when the hydraulic pressure acting on the pilot valve core is not enough to overcome the electromagnet output force, the pilot valve core 7 is closed, and the main valve core 2 is also closed. With the continuous oil supply of the hydraulic pump, the oil pressure rises. When the pilot valve core 7 is opened, the pilot oil will drain back to the oil tank separately. The oil in the pilot oil circuit flows, and the pressure drop in the spring chamber is less than the inlet pressure due to the pressure drop through the fixed damping hole R. At this time, the resultant force on the main valve core is shown in Equation (3). The resultant force is greater than zero, and the main valve core is opened and the main valve port overflows. Dynamic force balance equation of pilot valve core can be described as Flow continuity equation of pilot valve port can be given as Dynamic force balance equation of main valve core can be expressed as Flow continuity equation of main valve port can be given as The Laplace transformation is taken for Equations (4)- (12). The transfer function can be deduced as For the convenience of simplification, the sign definition can be given as G 5 (s) = 1 In the steady-state working process of traditional proportional relief valve, the output force of electromagnet F EM (s) is the input signal, and the inlet pressure P 1 (s) is the output signal. The system is a constant flow system. The inlet flow Q 1 (s) is basically unchanged. The influence on the system is small. The interference term Q 1 (s) can be ignored. As shown in Figure 5, the block diagram of traditional proportional relief valve system can be obtained by combining each link of Equations (13)- (16).
In the steady-state working process of traditional proportional relief valve, the output force of electromagnet FEM(s) is the input signal, and the inlet pressure P1(s) is the output signal. The system is a constant flow system. The inlet flow Q1(s) is basically unchanged. The influence on the system is small. The interference term Q1(s) can be ignored. As shown in Figure 5, the block diagram of traditional proportional relief valve system can be obtained by combining each link of Equations (13)- (16).

Mathematical Model of Proportional Relief Valve with Energy Regeneration System
As shown in Figure 6, the internal structure of the proportional relief valve with an energy recovery unit is shown. Compared with the traditional proportional relief valve, the outlet is connected with the energy recovery unit, and the outlet pressure is not equal to zero.

Mathematical Model of Proportional Relief Valve with Energy Regeneration System
As shown in Figure 6, the internal structure of the proportional relief valve with an energy recovery unit is shown. Compared with the traditional proportional relief valve, the outlet is connected with the energy recovery unit, and the outlet pressure is not equal to zero.
Flow continuity equation of main valve port can be described as The Laplace transformation is taken for Equations (24)-(27). The transfer function can Dynamic force balance equation of main valve core can be expressed as Flow continuity equation of main valve port can be described as The Laplace transformation is taken for Equations (24)-(27). The transfer function can be deduced as In order to study the influence of outlet pressure P 2 (s) on the inlet pressure P 1 (s) of the relief valve in steady-state operation, the output force of electromagnet F EM (s) is the input signal. The inlet pressure P 1 (s) is the output signal. The outlet pressure P 2 (s) is the interference term. This paper mainly studies the influence of the outlet pressure P 2 (s) on the system stability, because the inlet flow Q 1 (s) is basically unchanged, the interference term Q 1 (s) may not be considered, and the system function block diagram is drawn, as shown in Figure 7. Flow continuity equation of main valve port can be described as The Laplace transformation is taken for Equations (24)-(27). The transfer function can be deduced as In order to study the influence of outlet pressure P2(s) on the inlet pressure P1(s) of the relief valve in steady-state operation, the output force of electromagnet FEM(s) is the input signal. The inlet pressure P1(s) is the output signal. The outlet pressure P2(s) is the interference term. This paper mainly studies the influence of the outlet pressure P2(s) on the system stability, because the inlet flow Q1(s) is basically unchanged, the interference term Q1(s) may not be considered, and the system function block diagram is drawn, as shown in Figure 7.  It can be seen from Figure 7 that when the outlet pressure of proportional relief valve is taken as interference, it is very complex to simplify the transfer function of the control system block diagram. For the convenience of follow-up research, the block diagram is transformed into a signal flow diagram and simplified. Figure 8 shows the signal flow diagram after the conversion of Figure 7.      Figure 9 shows the signal flow diagram after the conversion of Figure 5. It can be seen from Figures 8 and 9 that there are more back pressure interference items in the signal flow diagram of the traditional proportional relief valve after adding back pressure at the outlet of the proportional relief valve, and the other forward channels and feedback circuits are the same. Figure 9. Signal flow diagram of the traditional proportional relief valve control system.

Stability Analysis of Outlet Back Pressure System of Proportional Relief Valve
The closed-loop transfer functions from input variables FEM(s) and disturbances P2(s) to output variables P1(s) can be obtained by the Mason formula [23]. The Mason formula can be expressed as According to Figure 9, the transfer function of the electromagnet output force FEM(s) of the traditional proportional relief valve to the inlet pressure can be deduced as

Stability Analysis of Outlet Back Pressure System of Proportional Relief Valve
The closed-loop transfer functions from input variables F EM (s) and disturbances P 2 (s) to output variables P 1 (s) can be obtained by the Mason formula [23]. The Mason formula can be expressed as According to Figure 9, the transfer function of the electromagnet output force F EM (s) of the traditional proportional relief valve to the inlet pressure can be deduced as According to Figure 8, the interference P 2 (s) is input into the system from two different nodes. Therefore, the partial transfer functions M 2 (s) and M 3 (s) of the two-part transfer function P 2 (s) to the inlet pressure transfer function P 1 (s) can be obtained, respectively. The transfer function M 4 (s) of interference P 2 (s) to P 1 (s) is obtained by summation. By summing the transfer function M 4 (s) and M 1 (s), the total transfer function for the output inlet pressure P 1 (s) after adding the disturbance P 2 (s) can be obtained. P 2 (s) as input, M 2 (s) can be described as P 2 (s) as input, M 3 (s) can be described as After adding back pressure interference input P 2 (s), the total transfer function M 5 (s) of inlet pressure P 1 (s) output can be given as The closed-loop transfer function of the control system is obtained by introducing the actual values corresponding to the parameters in Equations (31)-(39), and the stability of the system is analyzed by the Routh criterion.

Control Strategy
The simplified working principle of the overflow energy regeneration system is given in Figure 10. In order to realize the recovery of overflow energy in the overflow process of the relief valve, the control flow chart of energy regeneration system for the relief valve is given in Figure 11.

Control Strategy
The simplified working principle of the overflow energy regeneration system is given in Figure 10. In order to realize the recovery of overflow energy in the overflow process of the relief valve, the control flow chart of energy regeneration system for the relief valve is given in Figure 11. During energy regeneration for the relief valve, the control framework can be given in Figure 12. The target pressure difference of the relief valve is taken as the input. The inlet and outlet pressure of the relief valve will be detected. Then, the pressure difference of the relief valve can be obtained as the feedback value of the energy recovery system. Through closed-loop feedback, PI control is used. On this basis, the differential pressure loss of the relief valve is reduced to realize the recovery of overflow energy.

Simulation Research
To study the influence of the energy regeneration system on the relief valve, simulation research is carried out. The system schematic diagram is given in Figure 13. The system consists of a hydraulic pump source, safety valve, proportional relief valve and energy regeneration system. The safety valve is used to limit the maximum working pressure of the system. The electric energy regeneration system is composed of the hydraulic motor and electric generator. The 2-3 direction valve is used to realize the switching between traditional overflow and energy regeneration.
The simulation model based on AMESim is built and given in Figure 14. The parameters of the system are given in Table 1. The pressure of inlet and outlet of relief valve can be detected through pressure sensors. Meanwhile, the flow rate through the hydraulic motor is indirectly detected by the electric generator.
The flow rate through the hydraulic motor can be described as During energy regeneration for the relief valve, the control framework can be given in Figure 12. The target pressure difference of the relief valve is taken as the input. The inlet and outlet pressure of the relief valve will be detected. Then, the pressure difference of the relief valve can be obtained as the feedback value of the energy recovery system. Through closed-loop feedback, PI control is used. On this basis, the differential pressure loss of the relief valve is reduced to realize the recovery of overflow energy. During energy regeneration for the relief valve, the control framework can be given in Figure 12. The target pressure difference of the relief valve is taken as the input. The inlet and outlet pressure of the relief valve will be detected. Then, the pressure difference of the relief valve can be obtained as the feedback value of the energy recovery system. Through closed-loop feedback, PI control is used. On this basis, the differential pressure loss of the relief valve is reduced to realize the recovery of overflow energy.

Simulation Research
To study the influence of the energy regeneration system on the relief valve, simulation research is carried out. The system schematic diagram is given in Figure 13. The system consists of a hydraulic pump source, safety valve, proportional relief valve and energy regeneration system. The safety valve is used to limit the maximum working pressure of the system. The electric energy regeneration system is composed of the hydraulic motor and electric generator. The 2-3 direction valve is used to realize the switching between traditional overflow and energy regeneration.
The simulation model based on AMESim is built and given in Figure 14. The parameters of the system are given in Table 1.

Simulation Research
To study the influence of the energy regeneration system on the relief valve, simulation research is carried out. The system schematic diagram is given in Figure 13. The system consists of a hydraulic pump source, safety valve, proportional relief valve and energy regeneration system. The safety valve is used to limit the maximum working pressure of the system. The electric energy regeneration system is composed of the hydraulic motor and electric generator. The 2-3 direction valve is used to realize the switching between traditional overflow and energy regeneration.   The feasibility of system differential pressure control is given in Figure 15. The simulation model based on AMESim is built and given in Figure 14. The parameters of the system are given in Table 1.   The feasibility of system differential pressure control is given in Figure 15.  The feasibility of system differential pressure control is given in Figure 15. At the beginning, the set pressure of the proportional relief valve is 15 MPa. At 3 s, the set pressure of this relief valve is adjusted to 18 MPa, and at 6 s, the set pressure of the relief valve is set to 15 MPa. By controlling the electric generator torque, the inlet pressure of the hydraulic motor can be controlled. At the beginning, the inlet pressure of the hydraulic motor is 12 MPa, and at 1.5, 3, 4.5 s, the inlet pressure of the hydraulic motor is adjusted 13, 16, 12, and 8 MPa, respectively. As can be seen, the pressure differences of the relief valve can be controlled through the energy regeneration system.
In order to study the control characteristics of the system, the pressure response of the system is simulated.
Under the condition of the overflow pressure of the proportional relief valve of 20 MPa and the flow of 100 L/min, the constant pressure control simulation of the outlet pressure is carried out. The pressure step response curve is given in Figure 16. As can be seen, for different target pressures of the relief valve outlet, the actual pressure can be realized within 80 ms.  To analyze the influence of system flow rate on system pressure control, the influence of system flow change on pressure is simulated.
The pressure change curve when the flow rate changes is given in Figure 17. As can be seen, when the flow rate changes through the proportional relief valve, the inlet pressure and outlet pressure of the relief valve fluctuate slightly, but maintain stability At the beginning, the set pressure of the proportional relief valve is 15 MPa. At 3 s, the set pressure of this relief valve is adjusted to 18 MPa, and at 6 s, the set pressure of the relief valve is set to 15 MPa. By controlling the electric generator torque, the inlet pressure of the hydraulic motor can be controlled. At the beginning, the inlet pressure of the hydraulic motor is 12 MPa, and at 1.5, 3, 4.5 s, the inlet pressure of the hydraulic motor is adjusted 13, 16, 12, and 8 MPa, respectively. As can be seen, the pressure differences of the relief valve can be controlled through the energy regeneration system.
In order to study the control characteristics of the system, the pressure response of the system is simulated.
Under the condition of the overflow pressure of the proportional relief valve of 20 MPa and the flow of 100 L/min, the constant pressure control simulation of the outlet pressure is carried out. The pressure step response curve is given in Figure 16. As can be seen, for different target pressures of the relief valve outlet, the actual pressure can be realized within 80 ms. At the beginning, the set pressure of the proportional relief valve is 15 MPa. At 3 s, the set pressure of this relief valve is adjusted to 18 MPa, and at 6 s, the set pressure of the relief valve is set to 15 MPa. By controlling the electric generator torque, the inlet pressure of the hydraulic motor can be controlled. At the beginning, the inlet pressure of the hydraulic motor is 12 MPa, and at 1.5, 3, 4.5 s, the inlet pressure of the hydraulic motor is adjusted 13, 16, 12, and 8 MPa, respectively. As can be seen, the pressure differences of the relief valve can be controlled through the energy regeneration system.
In order to study the control characteristics of the system, the pressure response of the system is simulated.
Under the condition of the overflow pressure of the proportional relief valve of 20 MPa and the flow of 100 L/min, the constant pressure control simulation of the outlet pressure is carried out. The pressure step response curve is given in Figure 16. As can be seen, for different target pressures of the relief valve outlet, the actual pressure can be realized within 80 ms.  To analyze the influence of system flow rate on system pressure control, the influence of system flow change on pressure is simulated.
The pressure change curve when the flow rate changes is given in Figure 17. As can be seen, when the flow rate changes through the proportional relief valve, the inlet pressure and outlet pressure of the relief valve fluctuate slightly, but maintain stability To analyze the influence of system flow rate on system pressure control, the influence of system flow change on pressure is simulated.
The pressure change curve when the flow rate changes is given in Figure 17. As can be seen, when the flow rate changes through the proportional relief valve, the inlet pressure and outlet pressure of the relief valve fluctuate slightly, but maintain stability quickly. The change curve of spool displacement, hydraulic motor speed and torque when the flow rate changes is given in Figure 18. As can be found, when the flow rate changes, the hydraulic motor speed also changes correspondingly to adapt to the change of flow rate. Since the target pressure does not change, the torque of the hydraulic motor remains unchanged. quickly. The change curve of spool displacement, hydraulic motor speed and torque when the flow rate changes is given in Figure 18. As can be found, when the flow rate changes, the hydraulic motor speed also changes correspondingly to adapt to the change of flow rate. Since the target pressure does not change, the torque of the hydraulic motor remains unchanged. Pressure, flow rate and main spool displacement curves of relief valve under traditional working mode and with energy regeneration are given in Figure 19. The outlet pressure of the proportional relief valve is 0 MPa from 0-0.5 s, and the relief valve works in the traditional overflow mode. At 0.5 s, the system performs energy recovery, and the outlet pressure of the relief valve is 15 MPa. At this time, the displacement of the main valve core increased immediately, from 0.04 to 0.072 cm; the pressure at the inlet of the overflow valve decreased from 22-21.5 MPa, while the system flow remained unchanged. Compared with the traditional working mode, the flow fluctuation of the system decreased and became more stable. This shows that the inlet pressure can be reduced and the pressure regulating deviation of the overflow valve can be reduced to a certain extent when the energy recovery unit is added. quickly. The change curve of spool displacement, hydraulic motor speed and torque when the flow rate changes is given in Figure 18. As can be found, when the flow rate changes, the hydraulic motor speed also changes correspondingly to adapt to the change of flow rate. Since the target pressure does not change, the torque of the hydraulic motor remains unchanged. Pressure, flow rate and main spool displacement curves of relief valve under traditional working mode and with energy regeneration are given in Figure 19. The outlet pressure of the proportional relief valve is 0 MPa from 0-0.5 s, and the relief valve works in the traditional overflow mode. At 0.5 s, the system performs energy recovery, and the outlet pressure of the relief valve is 15 MPa. At this time, the displacement of the main valve core increased immediately, from 0.04 to 0.072 cm; the pressure at the inlet of the overflow valve decreased from 22-21.5 MPa, while the system flow remained unchanged. Compared with the traditional working mode, the flow fluctuation of the system decreased and became more stable. This shows that the inlet pressure can be reduced and the pressure regulating deviation of the overflow valve can be reduced to a certain extent when the energy recovery unit is added. Pressure, flow rate and main spool displacement curves of relief valve under traditional working mode and with energy regeneration are given in Figure 19. The outlet pressure of the proportional relief valve is 0 MPa from 0-0.5 s, and the relief valve works in the traditional overflow mode. At 0.5 s, the system performs energy recovery, and the outlet pressure of the relief valve is 15 MPa. At this time, the displacement of the main valve core increased immediately, from 0.04 to 0.072 cm; the pressure at the inlet of the overflow valve decreased from 22-21.5 MPa, while the system flow remained unchanged. Compared with the traditional working mode, the flow fluctuation of the system decreased and became more stable. This shows that the inlet pressure can be reduced and the pressure regulating deviation of the overflow valve can be reduced to a certain extent when the energy recovery unit is added. Appl. Sci. 2021, 11 In order to further analyze the influence of the pressure regulating deviation of the relief valve in the energy regeneration system, the static characteristics of the relief valve are tested under different outlet pressures. The overflow pressure of the proportional relief valve is set as 21 MPa. The change of the inlet pressure of the relief valve is observed by increasing the system flow. The pressure regulation deviation characteristic curve is given in Figure 20 when the outlet pressure is 0, 15 and 18 MPa. The simulation results show that-with the increase of the outlet pressure, the pressure regulating deviation of the relief valve gradually decreases. Therefore, the pressure regulating deviation of the relief valve can be reduced and the pressure control precision of the relief valve can be improved by connecting the energy recovery unit at the outlet of the relief valve.

Experimental Research
Further experimental research is carried out as well. The schematic diagram of the test platform is given as Figure 13. The whole energy regeneration system is based on LabVIEW for control and data acquisition. Part of the experimental system is shown in Figure 21. In order to further analyze the influence of the pressure regulating deviation of the relief valve in the energy regeneration system, the static characteristics of the relief valve are tested under different outlet pressures. The overflow pressure of the proportional relief valve is set as 21 MPa. The change of the inlet pressure of the relief valve is observed by increasing the system flow. The pressure regulation deviation characteristic curve is given in Figure 20 when the outlet pressure is 0, 15 and 18 MPa. The simulation results show that-with the increase of the outlet pressure, the pressure regulating deviation of the relief valve gradually decreases. Therefore, the pressure regulating deviation of the relief valve can be reduced and the pressure control precision of the relief valve can be improved by connecting the energy recovery unit at the outlet of the relief valve. In order to further analyze the influence of the pressure regulating deviation of the relief valve in the energy regeneration system, the static characteristics of the relief valve are tested under different outlet pressures. The overflow pressure of the proportional relief valve is set as 21 MPa. The change of the inlet pressure of the relief valve is observed by increasing the system flow. The pressure regulation deviation characteristic curve is given in Figure 20 when the outlet pressure is 0, 15 and 18 MPa. The simulation results show that-with the increase of the outlet pressure, the pressure regulating deviation of the relief valve gradually decreases. Therefore, the pressure regulating deviation of the relief valve can be reduced and the pressure control precision of the relief valve can be improved by connecting the energy recovery unit at the outlet of the relief valve.

Experimental Research
Further experimental research is carried out as well. The schematic diagram of the test platform is given as Figure 13. The whole energy regeneration system is based on LabVIEW for control and data acquisition. Part of the experimental system is shown in Figure 21.

Experimental Research
Further experimental research is carried out as well. The schematic diagram of the test platform is given as Figure 13. The whole energy regeneration system is based on LabVIEW for control and data acquisition. Part of the experimental system is shown in Figure 21. l. Sci. 2021, 11 Figure 21. Overflow loss energy regeneration test platform.

Control Characteristics
In the differential pressure control test of energy regeneration system, the change of outlet pressure is observed by changing the pressure at the inlet of the proportional relief valve. The test results are shown in Figure 22. It can be seen that the outlet pressure changes with the inlet pressure, so that the valve port pressure difference is maintained at the target value. The experimental results are consistent with the simulation. The response curve of the control outlet pressure step change is given in Figure 23. When the target pressure step changes, the actual pressure can quickly follow the response. The response of outlet pressure under different pressure differences when the step change of the inlet pressure is controlled, which is given in Figure 24. Under different pressure difference, outlet pressure can respond quickly.

Control Characteristics
In the differential pressure control test of energy regeneration system, the change of outlet pressure is observed by changing the pressure at the inlet of the proportional relief valve. The test results are shown in Figure 22. It can be seen that the outlet pressure changes with the inlet pressure, so that the valve port pressure difference is maintained at the target value. The experimental results are consistent with the simulation.  Figure 21. Overflow loss energy regeneration test platform.

Control Characteristics
In the differential pressure control test of energy regeneration system, the change of outlet pressure is observed by changing the pressure at the inlet of the proportional relief valve. The test results are shown in Figure 22. It can be seen that the outlet pressure changes with the inlet pressure, so that the valve port pressure difference is maintained at the target value. The experimental results are consistent with the simulation. The response curve of the control outlet pressure step change is given in Figure 23. When the target pressure step changes, the actual pressure can quickly follow the response. The response of outlet pressure under different pressure differences when the step change of the inlet pressure is controlled, which is given in Figure 24. Under different pressure difference, outlet pressure can respond quickly. The response curve of the control outlet pressure step change is given in Figure 23. When the target pressure step changes, the actual pressure can quickly follow the response. The response of outlet pressure under different pressure differences when the step change of the inlet pressure is controlled, which is given in Figure 24. Under different pressure difference, outlet pressure can respond quickly. Appl. Sci. 2021, 11 Step change curve of the outlet pressure.  The pressure curve when the system flow changes is given in Figure 25. The inlet target pressure of the relief valve is 18.5 MPa, and the pressure difference of valve port is 4 MPa. When the flow rate changes, due to the influence of the pressure regulating characteristics of the relief valve, the inlet pressure of the relief valve slightly decreases, but it is basically not affected by the flow rate change. The pressure control of relief valve is tested under different outlet pressures, and the results are shown in Figure 26. When the outlet pressure of the relief valve is 0 MPa, the Step change curve of the outlet pressure. The pressure curve when the system flow changes is given in Figure 25. The inlet target pressure of the relief valve is 18.5 MPa, and the pressure difference of valve port is 4 MPa. When the flow rate changes, due to the influence of the pressure regulating characteristics of the relief valve, the inlet pressure of the relief valve slightly decreases, but it is basically not affected by the flow rate change. The pressure control of relief valve is tested under different outlet pressures, and the results are shown in Figure 26. When the outlet pressure of the relief valve is 0 MPa, the The pressure curve when the system flow changes is given in Figure 25. The inlet target pressure of the relief valve is 18.5 MPa, and the pressure difference of valve port is 4 MPa. When the flow rate changes, due to the influence of the pressure regulating characteristics of the relief valve, the inlet pressure of the relief valve slightly decreases, but it is basically not affected by the flow rate change. Step change curve of the outlet pressure. The pressure curve when the system flow changes is given in Figure 25. The inlet target pressure of the relief valve is 18.5 MPa, and the pressure difference of valve port is 4 MPa. When the flow rate changes, due to the influence of the pressure regulating characteristics of the relief valve, the inlet pressure of the relief valve slightly decreases, but it is basically not affected by the flow rate change. The pressure control of relief valve is tested under different outlet pressures, and the results are shown in Figure 26. When the outlet pressure of the relief valve is 0 MPa, the The pressure control of relief valve is tested under different outlet pressures, and the results are shown in Figure 26. When the outlet pressure of the relief valve is 0 MPa, the pressure regulating deviation of the relief valve is 10%. When the outlet pressure is 15 and 18 MPa, the pressure regulating deviation is 5% and 2.8%, respectively. The larger the outlet pressure is, the smaller the pressure regulation deviation of the relief valve is. Therefore, the energy recovery of the relief valve can improve the pressure control characteristics of the relief valve.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 19 of 25 pressure regulating deviation of the relief valve is 10%. When the outlet pressure is 15 and 18 MPa, the pressure regulating deviation is 5% and 2.8%, respectively. The larger the outlet pressure is, the smaller the pressure regulation deviation of the relief valve is. Therefore, the energy recovery of the relief valve can improve the pressure control characteristics of the relief valve.

Energy Saving Characteristics
The efficiency of the relief valve regeneration system can be described as The input energy of the relief valve can be given as The regenerated energy of battery can be described as

Energy Saving Characteristics
The efficiency of the relief valve regeneration system can be described as The input energy of the relief valve can be given as The regenerated energy of battery can be described as The input pressure and flow of relief valve under different pressure difference control are shown in the Figures 27 and 28. pressure regulating deviation of the relief valve is 10%. When the outlet pressure is 15 and 18 MPa, the pressure regulating deviation is 5% and 2.8%, respectively. The larger the outlet pressure is, the smaller the pressure regulation deviation of the relief valve is. Therefore, the energy recovery of the relief valve can improve the pressure control characteristics of the relief valve.

Energy Saving Characteristics
The efficiency of the relief valve regeneration system can be described as The input energy of the relief valve can be given as The regenerated energy of battery can be described as  As can be seen from Figures 27 and 28, the smaller the pressure difference, the smaller the energy consumption. Therefore, during the energy recovery of overflow loss, the pressure difference of relief valve port can be kept at the minimum value to ensure the operation of the relief valve through the control of valve port pressure difference, which can improve the energy saving of the system.

Energy Regeneration System Application in Throttle-Governing System
In order to analyze the practical engineering application of the overflow energy recovery system more effectively, the throttle-governing system with overflow energy regeneration system experimental platform is built and given in Figure 29. The partial physical diagram of the experimental system is given in Figure 30.  As can be seen from Figures 27 and 28, the smaller the pressure difference, the smaller the energy consumption. Therefore, during the energy recovery of overflow loss, the pressure difference of relief valve port can be kept at the minimum value to ensure the operation of the relief valve through the control of valve port pressure difference, which can improve the energy saving of the system.

Energy Regeneration System Application in Throttle-Governing System
In order to analyze the practical engineering application of the overflow energy recovery system more effectively, the throttle-governing system with overflow energy regeneration system experimental platform is built and given in Figure 29. The partial physical diagram of the experimental system is given in Figure 30. As can be seen from Figures 27 and 28, the smaller the pressure difference, the smaller the energy consumption. Therefore, during the energy recovery of overflow loss, the pressure difference of relief valve port can be kept at the minimum value to ensure the operation of the relief valve through the control of valve port pressure difference, which can improve the energy saving of the system.

Energy Regeneration System Application in Throttle-Governing System
In order to analyze the practical engineering application of the overflow energy recovery system more effectively, the throttle-governing system with overflow energy regeneration system experimental platform is built and given in Figure 29. The partial physical diagram of the experimental system is given in Figure 30.  For convenient comparison, the throttle-governing system without an overflow energy regeneration system is also implemented. The same control inputs are applied to these two systems. The displacement of the cylinder in these two systems is given in Figure 31. The inlet pressure of the relief valve is given in Figure 32. The overflow oil is given in Figure 33. As can be seen, the control performance of the cylinder and the relief valve are close.  For convenient comparison, the throttle-governing system without an overflow energy regeneration system is also implemented. The same control inputs are applied to these two systems. The displacement of the cylinder in these two systems is given in Figure 31. The inlet pressure of the relief valve is given in Figure 32. The overflow oil is given in Figure 33. As can be seen, the control performance of the cylinder and the relief valve are close. For convenient comparison, the throttle-governing system without an overflow energy regeneration system is also implemented. The same control inputs are applied to these two systems. The displacement of the cylinder in these two systems is given in Figure 31. The inlet pressure of the relief valve is given in Figure 32. The overflow oil is given in Figure 33. As can be seen, the control performance of the cylinder and the relief valve are close.   The power consumed in throttle-governing system without the energy regeneration system is given in Figure 34. The power consumed in the throttle-governing system with the energy regeneration system is given in Figure 35. As can be seen, the output power and overflow loss of the system basically remain unchanged, but with the increase of energy recovery, the loss power of the system decreases by 60%.   The power consumed in throttle-governing system without the energy regeneration system is given in Figure 34. The power consumed in the throttle-governing system with the energy regeneration system is given in Figure 35. As can be seen, the output power and overflow loss of the system basically remain unchanged, but with the increase of energy recovery, the loss power of the system decreases by 60%.  The power consumed in throttle-governing system without the energy regeneration system is given in Figure 34. The power consumed in the throttle-governing system with the energy regeneration system is given in Figure 35. As can be seen, the output power and overflow loss of the system basically remain unchanged, but with the increase of energy recovery, the loss power of the system decreases by 60%.  The power consumed in throttle-governing system without the energy regeneration system is given in Figure 34. The power consumed in the throttle-governing system with the energy regeneration system is given in Figure 35. As can be seen, the output power and overflow loss of the system basically remain unchanged, but with the increase of energy recovery, the loss power of the system decreases by 60%.

Conclusions
In this paper, an overflow energy loss recovery syst electric generator is studied. Furthermore, a pressure diff lief valve based on pressure compensation is adopted. T experimental research, the effectiveness of the system is the system has superior control characteristics. When the outlet pressure can respond quickly and achieve stability interference performance. After adding the energy recov characteristics of the relief valve are improved, and the the relief valve is reduced from 10% to 2.8%, and the press valve is improved. By reducing the pressure difference o energy can be recovered.
Author Contributions: Z.L. proposed the idea of relief energ structure and working mode. L.S. wrote the paper. All author lished version of the manuscript.

Funding:
The authors acknowledge the support of National N (51875218), Excellent Outstanding Youth Foundation of Fujian P Figure 35. Power consumed in the throttle-governing system with the energy regeneration system.

Conclusions
In this paper, an overflow energy loss recovery system based on a hydraulic motorelectric generator is studied. Furthermore, a pressure difference control method of the relief valve based on pressure compensation is adopted. Through simulation analysis and experimental research, the effectiveness of the system is verified. The results show that the system has superior control characteristics. When the overflow pressure changes, the outlet pressure can respond quickly and achieve stability, and the system has strong antiinterference performance. After adding the energy recovery unit, the pressure regulating characteristics of the relief valve are improved, and the pressure regulating deviation of the relief valve is reduced from 10% to 2.8%, and the pressure control accuracy of the relief valve is improved. By reducing the pressure difference of the relief valve, more overflow energy can be recovered.

Conflicts of Interest:
The authors declare no conflict of interest.