We built a simulation model to evaluate pump flow characteristics and performance of the single-shaft coaxial motor-pump assembly in electrohydrostatic actuators and investigate the overall efficiency in a wide set of working conditions of the motor-pump assembly experimentally.
An electrohydrostatic actuator (EHA) can be the most promising alternative compared with the traditional hydraulic servo actuators for its high power density, ease of maintenance, and reliability. As the core power unit that determines the performance and service life of the EHA, the motor-pump assembly should simultaneously possess a wide speed/pressure range and a high dynamic response.
This paper presents a method to test the performance of the motor-pump assembly through simulation and experimentation. The flow output characteristics were defined through simulation and analysis of the assembly at the beginning of the experiment, leading to the conclusion of whether the pump could meet the requirements of the EHA. A series of performance tests were conducted on the motor-pump assembly via a pump test bench in the speed range of 1,450-9,000 rpm and the pressure range of 1-30 MPa.
We tested the overall efficiency of the motor-pump assembly under various working conditions after confirming the consistency between the test results of the flow output characteristics with the simulation results. The results showed that the assembly has higher overall efficiency when working at 4,500-7,000 rpm under the pressure of 10-25 MPa and at 2,000-2,500 rpm under 5-15 MPa. Overall, this method can be utilized for determining in advance whether the motor-pump assembly meets the requirements of EHA. Moreover, this paper proposes a rapid test method of the motor-pump assembly in various working conditions, which could assist in predicting EHA performance.
Known as a typically integrated actuator with high power density, the EHA has broad prospects in areas such as aerospace, aviation, construction machinery, and robotics1,2. The EHA mainly consists of a servo motor, pump, cylinder, pressurized reservoir, valve block, mode control valves, module control valves, and sensors, constituting a highly integrated, pump-controlled, closed hydraulic system. The schematic diagram and physical model are shown in Figure 13,4,5,6,7. The motor-pump assembly is the core power and the control component, and it determines the static and dynamic performance of the EHA7.
The conventional motor-pump assembly consists of a separate motor and pump, whose shafts are connected by a shaft coupling8. This structure has significant negative effects on the performance and life of the EHA. First, both the motor and pump will bear a relatively large vibration due to the assembling accuracy, especially at high speed5. Vibration will not only affect the output characteristics of the pump but also accelerate the wear of the friction interfaces in the pump, leading to the failure of the motor-pump assembly9. Second, sealings must be set at the shaft ends of the pump, which cannot fundamentally prevent leakage. Meanwhile, the mechanical efficiency of the motor-pump assembly decreases with increasing friction resistance10. Third, the frequent reversing of the motor-pump assembly will accelerate the wear of the coupling and increase the possibility of fatigue fracture, reducing the system reliability of the EHA11,12.
Thus, a single-shaft coaxial motor-pump assembly within a shared housing was developed to avoid these shortcomings. The structure is shown in Figure 2. A no-coupling design is adopted in this component, which could simultaneously increase the dynamic performance and the lubricating status of the motor and pump. This single-shaft coaxial design ensures the alignment of the two rotors and improves dynamic balance under high-speed conditions. Moreover, shared housing fundamentally eliminates shaft end leakage.
Testing the output characteristics of the EHA motor-pump assembly is of great significance for the optimization and improvement of the EHA performance. However, there are relatively few studies on performance testing of the motor-pump assembly, especially for EHAs. Therefore, we conducted a testing method of combining simulation and experiments. This method is suitable for testing motor-pump assemblies with a wide range of operating conditions, especially EHA pumps.
There are two main challenges: the first is to build an accurate simulation model to analyze the output flow characteristics of the motor-pump and provide assistance for the optimal design of the motor-pump assembly. We have established a simulation model of the motor-pump assembly through hierarchical modeling and realized the simulation analysis of the output flow by changing different parameters. The second is the cavitation of the test element caused by high speed, which is the most important aspect that distinguishes it from ordinary pumps. Therefore, we focused more on the design of the oil supply system when designing the test system to realize the test under various working conditions.
In this protocol, a one-dimensional simulation model was established to simulate the pump flow characteristics initially, judging whether the pump flow characteristics meet the requirements of EHA. Then, the flow characteristics and the overall efficiency were experimentally tested on a dedicated test bench, obtaining the overall efficiency map that cannot be accurately simulated by simulation. Lastly, the pump flow characteristics were compared with the experimental results to verify the accuracy of the simulation results. Meanwhile, the overall efficiency map was obtained to evaluate the performance of the single-shaft coaxial motor-pump assembly.
1. Simulation of pump flow characteristics
2. Establishment of the experimental platform
3. Pump flow and overall efficiency test of the motor-pump assembly
The simulation result of the discharge flow (Figure 10A) indicated that the discharge flow decreased slightly with the increase in load pressure when the speed was constant. Furthermore, the output flow rate increased linearly with increasing speed when the pressure is constant, judging from the same belt width. To directly evaluate the performance of the motor-pump assembly under different working conditions, we plotted its volumetric efficiency diagram (Figure 11A). It showed that the pump volumetric efficiency was higher while the pressure and speed were relatively low. When the speed was 3,000 rpm, the maximum output pressure for volumetric efficiency of 95% was 5 MPa; when the speed was 8,000 rpm, this value rapidly rose to 23 MPa.
Figure 10B shows the experimental results of the discharge flow, which coincide well with the simulation. The slight difference between the experimental results and the simulation results is that when the speed is higher than 5,000 rpm, the output flow decreases first and then increases with the rising pressure. Figure 11B shows the volumetric efficiency of the experiment. The experimental results differ from the simulation results, especially when the motor-pump assembly works at high speed and low pressure. When the pressure drop is lower than 10 MPa, the volumetric efficiency decreases with the increase in rotational speed.
Figure 12 indicates the differences in volumetric efficiency and pump flow between the simulated and experimental results. It is shown in this figure that the simulation results of the pump flow are in good agreement with the experimental results. Further, the volume efficiency error is also kept within 10%. When the speed is higher than 4,000 rpm, the error can be controlled within 4%. Figure 13 shows the overall efficiency of the motor-pump assembly. When the motor-pump assembly works at the working conditions of low speed and high pressure or high speed and low pressure, its total efficiency is relatively low, especially at high speed and low pressure when its total efficiency drops to ~10%. When the pressure drop is in the range of 5 to 15 MPa, and the speed is 2,000-8,000 rpm, its total efficiency can reach up to 60%.
Figure 1: Structure and schematic diagram of the EHA. The upper picture of the model is the 3D model of the EHA, and the lower picture is the schematic diagram. Abbreviation: EHA = electrohydrostatic actuator. Please click here to view a larger version of this figure.
Figure 2: Structure of the single-shaft coaxial motor-pump assembly. This figure depicts the interior structure of a motor-pump assembly, which consists of housing, shaft, rotor, stator coil, encoder, rear end plate, swash plate, piston, cylinder block, and valve plate. Please click here to view a larger version of this figure.
Figure 3: Simulation model of a single piston. This figure shows the composition of a single-piston model, including a piston volume cavity model, a flow distribution model, and a slipper model. The function f(x,y) indicates the friction power loss of the swash plate/slipper interface, and the function f(x,y,z) indicates the viscous friction power loss of the piston/cylinder block interface. The numbers in this figure indicate the interfaces of the super component of the single piston simulation model. Abbreviations: PCI = Piston/Cylinder block interface; SSI = Swash plate/Slipper interface; P = pressure; V = velocity; µ = friction coefficient; Q = flow; A, B = ports of the motor-pump assembly; M = mass; F = force Please click here to view a larger version of this figure.
Figure 4: Simulation model of the motor-pump assembly. The motor-pump assembly model is mainly composed of 9 single-piston models with different phase angles, an ideal motor model, and a valve plate friction model. The function f(x,y) indicates the churning losses of the pump, the upper function f(x,y,z) indicates the volume power loss of the cylinder block/valve plate interface, and the lower one indicates the friction power loss of the cylinder block/valve plate interface. The numbers in this figure indicate the interfaces of the super component of the single-piston simulation model. Abbreviations: CVI = Cylinder block/ valve plate interface; P = pressure; V = velocity; µ = friction coefficient; Q = flow; A, B = ports of the motor-pump assembly; M = mass; F = force. Please click here to view a larger version of this figure.
Figure 5: Hydraulic schematic diagram of the experiments. This figure depicts the hydraulic scheme of the experiment. A bridge circuit composed of four check valves is used for switching the flow directions. Abbreviations: D = driver of the oil supply pump; P = pressure; T = temperature; I = sensor. Please click here to view a larger version of this figure.
Figure 6: Structural composition of the test bench. This photograph shows the composition of the test bench: the control panel, hydraulic system, oil cooler, and the test board. Please click here to view a larger version of this figure.
Figure 7: Installation of the motor-pump assembly. This photograph shows the installation state of the motor-pump assembly and the layout of the pressure and temperature sensors. Please click here to view a larger version of this figure.
Figure 8: Connection of the tooling. This photograph shows the connection of the motor-pump assembly and the test valve block with the tooling. Please click here to view a larger version of this figure.
Figure 9: Connection of the electrical interfaces. This photograph shows the connection of the motor-pump assembly, the driver, and the controller. Please click here to view a larger version of this figure.
Figure 10: Simulation and experimental results of the pump flow. (A) The contour line shows the simulated results of the pump flow. Results indicate a good liner characteristic of the discharge flow. (B) The contour line shows the experimental results of the pump flow. The experiment results are in line with the simulation results. Color bar indicates the pump flow. Please click here to view a larger version of this figure.
Figure 11: Simulation and experimental results of volumetric efficiency. (A) The contour line shows the simulated results of the volumetric efficiency. According to the simulation results, the volumetric efficiency of the motor-pump assembly is relatively high, except when the motor-pump assembly is working in a condition of high pressure and low speed. (B) The contour line shows the experimental results of the volumetric efficiency. The experimental results differ from the simulation results, especially at high-speed and low-pressure working conditions. Color bar indicates the % volumetric efficiency. Please click here to view a larger version of this figure.
Figure 12: Efficiency and pump flow of different speeds under the pressure drop of 15 MPa. The solid black line represents the volumetric efficiency experimental results, and the red line represents the simulation results. The volumetric efficiency increases with increasing speed, and the simulation results are closer to the experimental results when the speed is higher. The dashed black line represents the pump flow experimental results and the red line the simulation results. It can be seen from the figure that the simulation results almost coincide with the experimental results in the speed range of 3,500-9,000 rpm. Please click here to view a larger version of this figure.
Figure 13: Experimental results of the overall efficiency. The contour line shows the total efficiency of the motor-pump assembly. When the motor-pump assembly works in extreme conditions, the overall efficiency is relatively low. Color bar indicates the % overall efficiency. Please click here to view a larger version of this figure.
Parameter | Symbol | Unit | Value | ||
Distribution diameter of the cylinder block | df | mm | 29.3 | ||
Swash plate incline angle | β | ° | 9 | ||
Diameter of the piston | dz | mm | 7.5 | ||
Piston number | Z | – | 9 | ||
Length of piston ball head hole | lqt | mm | 7.3 | ||
Diameter of piston ball head hole | dqt | mm | 1 | ||
Invalid volume of plunger cavity | Vd | mm3 | 392.69 | ||
Oil film thickness of the piston/cylinder block interface | hp | μm | 3 | ||
Diameter of the slipper hole | ds | mm | 0.4 | ||
Length of the slipper hole | ls | mm | 1.5 | ||
Outer diameter of slipper seal belt | dsso | mm | 8.8 | ||
Inner diameter of slipper seal belt | dssi | mm | 6.3 | ||
Oil film thickness of the slipper/swash plate interface | hs | μm | 5 | ||
Inner diameter of valve plate inner seal belt | dci | mm | 12.05 | ||
Outter diameter of valve plate inner seal belt | Dci | mm | 13.15 | ||
Inner diameter of valve plate outter seal belt | dco | mm | 16.15 | ||
Outter diameter of valve plate outter seal belt | Dco | mm | 17.3 | ||
Oil film thickness of the cylinder block/ valve plate interface | hc | μm | 10 | ||
Diameter of the cylinder block | dc | mm | 41.7 | ||
Length of the cylinder block | lc | mm | 27.8 |
Table 1: Simulation parameters. This table lists the main parameters of the motor-pump assembly simulation model.
Critical speed (rpm) | Critical load Pressure difference for simulation (MPa) | Critical load Pressure difference for experimental test (MPa) | ||
1,450 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | ||
2,000 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | ||
3,500 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | ||
4,000 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | 0.4, 3, 6,9, 12, 15, 18, 21, 24, 27, 30 | ||
5,000 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27 | ||
6,500 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | 0.4, 3, 6, 9, 12, 15, 18, 21 | ||
8,000 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | 0.4, 3, 6, 9, 12, 15 | ||
9,500 | 0.4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 | 0.4, 3, 6, 9, 12 |
Table 2: Specific speed and pressure of the motor-pump assembly. This table lists the critical working points of the motor-pump assembly experiments.
When conducting these experimental steps, it is important to make sure that the pressure measuring points are close enough to the oil port of the pump, which would greatly influence the experimental results. In addition, pay attention to the pressure of the inlet port of the motor-pump assembly to ensure that no cavitation exists, especially at high-speed working conditions.
This method enables a dynamic adjustment of oil supply pressure, realizing an accurate simulation of different working conditions.
A limitation of this method is that the total efficiency of the motor-pump assembly cannot be accurately obtained by simulation. In the simulation model, the three main frictional surfaces of the pump are under full oil film lubrication, which means only viscous friction exists in the interface. However, the actual situation is that the state of oil film switches between full oil-film lubrication and boundary lubrication, which cannot be simulated by the simulation model. Therefore, we focus on using a simulation model to simulate the pump, which has the advantages of low cost and fast speed without being limited to the actual parameters of the prototype. Meanwhile, we make up for this limitation through experimental methods.
Another limitation is that the method does not simulate the thermal characteristics of the motor-pump assembly for EHA very well. As the EHA is a highly integrated system, the motor-pump assembly is tightly connected to the actuating cylinder and the pressurized reservoir, leading to a complex thermal situation. Thus, the method can only test the performance of the motor-pump assembly under a specific temperature condition, while the actual temperature variation range is wide.
The improved performance of the motor-pump assembly has played a crucial role in promoting the popularity of EHA. Based on the results reported in this paper, there is still room for improvement of the overall efficiency of the motor-pump assembly. Compared with the existing methods, motor-pump assembly characteristics can be investigated more efficiently under a wide range of working conditions by adopting this protocol. This method should lay a foundation for optimizing the motor-pump assembly and provide a strong guarantee for the rapid development of EHA. In addition, it is of great significance for testing the performance of the motor pump and thus realizing the positive design of the motor pump.
The authors have nothing to disclose.
This work was supported by Chinese Civil Aircraft Project [No. MJ-2017-S49] and China Postdoctoral Science Foundation [No.2021M700331].
AmeSim simulation platform | Siemens | Amesim 16 | |
DAQ card | Advantech | PCI1710 | |
Flowmeter | KRACHT | VC0.04E1RS, 0.02-4 L/min | |
Flowmeter | KRACHT | VC0.4E1RS, 0.2-40 L/min | |
Industrial Computer | Advantech | 610H | |
Oil supply motor | Siemens | 1TL0001-1BB23-3JA5 | |
Oil supply pump | Kangbaishi | P222RF01DT | |
OriginPro | OriginLab Corporation | OriginPro 2021 (64-bit) 9.8.0.200 | |
Pressure sensor | Feejoy | PI131G(0-5 MPA)F4MCAH5C | |
Proportional relief valve | Huade hydraulic | DBE10-30B/50YV | |
Proportional relief valve | Huade hydraulic | DBE10-30B/315YV | |
Spindle motor | HAOZHI | DGZX-18020 / 22A2-KFHWVJLS | Max speed: 18,000 rpm; Power: 22 kW |
Temperature sensor | Feejoy | TI-A42M1A180/30+F1 |