Flow characteristics of integrated motor-pump assembly with phosphate ester medium for aerospace electro-hydrostatic actuators

Jiangao ZHAO, Jian FU, Yuchen LI, Haitao QI, Yan WANG,Yongling FU

a The Laboratory of Aerospace Servo Actuation and Transmission, Beijing 100191, China

b Research Institute for Frontier Science, Beihang University, Beijing 100191, China

c School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

KEYWORDS

Abstract Motor-pump assembly is the core component of the Aerospace Electro-hydrostatic Actuator (EHA).Thus, the design of the motor pump can be very challenging under conditions of high speed and wide pressure range,especially in particular working mediums.Our ultimate goal is to pursue better flow characteristics under a wide range of working conditions.In this paper,we built a sub-model of the main friction interfaces and a model of single-shaft coaxial motor-pump assembly adopting the method of hierarchical modeling.The experimental investigation of the output characteristics was mainly carried out in a phosphate ester medium environment.Then,the flow characteristics were compared and analyzed with the simulation results.Results indicated that the flow characteristics of the motor-pump assembly could be accurately simulated by the model and quite severe in a low speed and high-pressure environment.

1.Introduction

The economic, safety and environmental demands of civil aircrafts promote the innovation of civil airliner flight control systems.1,2The adoption of Power-by-Wire (PbW) technology instead of the conventional Fly-by-Wire (FbW) is the primary means to satisfy the above requirements.3–5PbW technology uses electrical energy instead of traditional hydraulic energy to transmit power and thus eliminates the complex hydraulic lines throughout the airframe, decreasing the energy loss due to the throttling loss of transmission, reducing the weight of the flight control system and simultaneously avoiding the risk of leakage, as shown in Fig.1.

Fig.2 Configurations of EHA and motor-pump assembly.

Electro-hydrostatic actuator(EHA)is one of the main PbW actuators thanks to its high power density,good maintainability and high reliability.6–8It has been successfully applied on the primary flight control surfaces of typical civil aircraft such as A380 and A350.9,10EHA mainly consists of motor-pump assembly, cylinder, pressurized reservoir and valve block,and the position servo is realized by controlling the output flow of the motor-pump assembly.11Fig.2 depicts the main configurations of EHA and the detailed structure of the motor-pump assembly.As the core power and flow servo component,12motor-pump assembly determines the output performance of the EHA, which in turn faces severe challenges as follows: Firstly, the motor-pump assembly is required to have stable flow output characteristics and relatively high efficiency over a wide range of speed and pressure.Secondly, high dynamic response is needed to achieve position servo.Finally,since the working medium of civil aircraft is phosphate ester hydraulic oil according to the airworthiness requirements,each component of the motor-pump assembly must have good compatibility with the working medium.

To deal with the above challenges, we proposed a singleshaft coaxial integrated motor-pump assembly to replace the conventional structure of motor, pump and shaft coupling.

The challenges of wide working conditions mainly lie in the changing of the tribology characteristics in the main friction interfaces:13–16the cylinder block/valve plate interface,piston/-cylinder block interface and the slipper/swash plate interface.17,18These interfaces also assume the role of sealing,affecting the flow characteristics of the motor-pump assembly.To improve the friction and wear characteristics, the swash plate and valve plate are strengthened with TiAlN cermet coating, reducing mechanical friction losses and improving the wear resistance of the interfaces over a wide working condition.19Therefore, the flow characteristics of the motor-pump assembly could remain relatively stable in different working conditions.

In terms of improving dynamic response,the rotor adopts a slender tandem structure and the spindle adopts a hollow design to reduce rotational inertia.More importantly, the single-shaft coaxial structure eliminates the backlash of the conventional shaft coupling structure, improving the response accuracy significantly.Besides, since the motor and pump are in one housing, two shaft end seals are eliminated, decreasing the damping of the assembly.However, the co-housing design leads to turbulence in the internal flow field due to the wide rotational speed,20which changes the boundary conditions of the oil films in the main friction interfaces and therefore adversely affects the flow characteristics of the motor-pump assembly.

The special physicochemical properties of phosphate ester medium cannot be ignored for the motor-pump assembly.First, since its compatibility with varied materials differs greatly from that of conventional hydraulic medium,all materials in the housing must be chosen carefully, especially the adhesives and seals.Numerous compatibility tests were carried out to ensure the reliability of the motor-pump assembly.Second, the difference in the variation laws of fluid viscosity and density will have an impact on the flow characteristics of the assembly.21Besides, the rotor churning behavior in the housing may change, which will affect the boundary conditions.22Last, due to the differences in microstructure, the loadcarrying characteristics of the main friction interfaces change during the mixed and boundary lubrication conditions, which will likewise have an impact on the flow characteristics of the assembly.

The core objective of motor-pump assembly design for civil aircraft is to ensure a stable flow output in phosphate ester medium over a wide working condition.23Wang and Leaney proposed a hybrid pump-controlled system that combines the advantages of both valve-controlled and pump-controlled systems to achieve stable flow output and energy efficiency simultaneously.24But it can be realized only when the drive systems do not require fast response, which is not suitable for EHAs, due to the extremely high servo requirements.According to the above illustration, the main factors that determine the flow characteristics are the sealing performance of the three friction interfaces.Numerous studies have been carried out for the three main friction interfaces.25–28Wieczorek et al.29,30developed a simulation tool CASPAR (Calculation of swash plate type axial piston pump and motor) to investigate the behavior of the three friction interfaces,considering the effect of micro-motion on the sealing and flow characteristics of the pump.Chacon,31,32Li et al.33and Han et al.34adopts thermal elasto-hydrodynamic (TEHD) theory to study the oil film behavior of the friction interfaces.The methods above are all numerical-based, which can obtain the distribution of the fluid field accurately, but at the same time, their accuracy is greatly affected by the boundary conditions.The boundary conditions are changing rapidly in the motorpump assembly especially when it is operating at high frequency.Besides, solving numerical models requires high computational expense and simulation time.Therefore,the authors adopt an analytical method based on the fluid mechanics to develop the flow characteristics of the motor-pump assembly.

In this work, a model of the single-shaft coaxial integrated motor-pump assembly is established based on the analytical methods.Then, an experimental study of the motor-pump assembly is conducted to evaluate the accuracy of the model and reveal the flow characteristics in phosphate ester media under different working conditions.

2.System description and modeling

2.1.Working principle of the integrated motor-pump assembly

Fig.3 Cross sectional diagram of integrated motor-pump assembly.

The detailed diagram of the integrated motor-pump assembly is shown in Fig.3.Both of the motor rotor and pump core are connected in series with a single shaft in a shared housing,which is filled with phosphate ester medium.The motor rotor driven by electrical power rotates the shaft and cylinder block,and the pistons nested in the cylinder bores are forced to rotate simultaneously.Each slipper is articulated with a piston, sliding against the swash plate under the joint action of the retainer and piston.The presence of the swash plate inclination drives the reciprocation motion of each slipper-piston assembly relative to the corresponding cylinder bore.When the piston chamber volume expands, it is connected with the suction opening on the valve plate to receive low pressure medium,and vice versa,it is connected with the discharge opening to pump high pressure medium.The leakage of the three friction interfaces, i.e., the slipper/swash plate interface piston/cylinder block interface and the cylinder block/valve plate interface, is the core that affects the flow characteristics.

2.2.Modelling of the main friction interfaces

Using the method of hierarchical modeling,the analytical submodels of the three interfaces are established individually,focusing on the influence of the leakage behavior on the flow characteristics.On this basis, the simulation analysis model of the single-shaft coaxial motor-pump assembly is built, and the simulation analysis of the flow characteristics under different pressure and speed conditions is carried out.

2.2.1.Slipper/swash plate interface

The main function of the slipper/swash plate interface is to realize the suction and discharge of the hydraulic fluid.Fig.4 shows the position relationships of the slipper and piston at the outer dead center (ODC), inner dead center (IDC)and arbitrary point A, respectively.The trajectory of the piston is a circle of radius Rf, which is the reference radius of the cylinder block.Due to the existence of the inclination of the swash plate,the trajectory of the slipper is an ellipse,which can be expressed as:

The reciprocating motion principle of the piston yields:

In Eq.(2), the first term on the right is the piston relative motion due to the rotation of the slipper-piston assembly,and the second due to the rotation of the swash plate.

Based on the principle of Poiseuille flow,the leakage flow of the slipper/swash plate interface of this model yields:

The sub-model of the slipper/swash plate interface is built based on Eq.(2) and Eq.(3), shown in Fig.5.

2.2.2.Piston/cylinder block interface

The piston chamber formed by the piston, cylinder bore and valve plate is the smallest working unit of the flow output control unit.Select the control volume (CV) as shown in Fig.6, the pressure flow equation of the CV considering the oil compressibility and leakage can be expressed as:

Based on the principle of Poiseuille flow,the leakage flow of the piston/cylinder block interface of this model yields:

The sub-model of the piston/cylinder block interface is shown in Fig.7.

2.2.3.Cylinder block/valve plate interface

The cylinder block/valve plate interface is composed of the bottom surface of the cylinder block, the top surface of the valve plate, and the oil film between the surfaces.And the structure of the valve plate mainly consists of inner and outer sealing belts, flow distribution windows, triangular grooves and unloading groove, as shown in Fig.8.Since the length of the sealing belt and contact area are the largest among the three interfaces, the cylinder block/ valve plate interface determines the leakage flow of the motor-pump assembly to the maximum extent.The distribution curve is the core of the sub-model of the cylinder block/ valve plate interface, which will influence the output flow of the pump especially at high speed due to the effects of reverse flow and pressure pulsation.Besides, the error of the distribution curve will be amplified with the increase of the rotational speed.Since the motor-pump assembly switches the flow direction by changing the rotational direction, in order to ensure that the output characteristics of different directions are consistent, the valve plate adopts a symmetrical layout.Thus, only the flow model between 0–90 degrees needs to be built.The suction/discharge window is divided into 6 intervals according to the relative position of the kidney window in the cylinder block and the suction/discharge windows in the valve block.When calculating the minimum through-flow area, the clearance between the cylinder block/valve plate is not considered.

Fig.4 Motion analysis of slipper-piston assembly.

Fig.5 Sub-model of slipper/swash plate interface.

(1) 0 ≤φ < φ1.

When 0 ≤φ < φ1, the kidney window does not overlap with the suction/discharge window and the triangular groove,and the through-flow area S1=0.The angle of φ1is given by:

(2) φ1≤φ < φ2.

When φ1≤φ<φ2,the kidney window only intersects with the triangular slot, as shown in Fig.9.The through-flow area S2can be approximated as a 2-part composition, Saand Sb,respectively.The through-flow area S2yields:

The angle of φ2is given by:

OsB can be found by solving ΔOsOkB by the cosine theorem, and the magnitude yields:

The magnitude of OsE is related to the shaft rotation angle and is expressed as:

(3) φ2≤φ < φ3.

Fig.6 Control volume of piston/cylinder block interface.

Fig.7 Sub-model of piston/cylinder block interface.

Fig.8 Valve plate of motor-pump assembly.

When φ2≤φ<φ3,the kidney window intersects with both the triangular groove and the suction/discharge window, and its contour line intersects with the triangular groove,shown in Fig.10.And the algorithm of minimum through-flow area S3is the same as (2).

When φ = φ3, the intersection point of the contour line coincides with the tangent point of the triangular groove and the suction/discharge window.

The angle of φ3is:

Fig.9 Flow distribution diagram (φ1 ≤φ < φ2).

(4) φ3≤φ < φ4.

When φ3≤φ<φ4,the kidney window intersects with both the triangular groove and the suction/discharge window, and its contour line intersects with the semicircular surface of the suction/discharge window, shown in Fig.11.The throughflow area S4can be approximated as a 3-part composition,Sa, Sband Sc.The magnitudes of each area yields:

Fig.10 Flow distribution diagram (φ2 ≤φ < φ3).

In Eq.(13), OkG is the distance from the center of the kidney window Okto the line IH, which can be expressed by:

Combining Eq.(12)-Eq.(15), the through-flow area S4yields:

The upper bound of this interval is when Okand Ovare coincided, and the corresponding angle φ4is given by:

(5) φ4≤φ < φ5.

When φ4≤φ<φ5,the kidney window intersects with both the triangular groove and the suction/discharge window, as depicted in Fig.12.The through-flow area S5can be approximated as a 2-part composition, Saand Sb, respectively.The magnitudes of each area yields:

The through-flow area S5can be expressed as:

When φ = φ5, the intersection point of the contour line coincides with the tangent point of the triangular groove and the suction/discharge window.

Fig.12 Flow distribution diagram (φ4 ≤φ < φ5).

Fig.13 Flow distribution diagram (φ5 ≤φ < 90°).

Fig.14 Distribution curve of the suction/discharge window.

(6) φ5≤φ < 90°.

When φ5≤φ<90°,the kidney widow is completely overlaps with the suction/discharge window, as shown in Fig.13.The through-flow area S6is equal to the area of the kidney window.

According to the calculation above and principle of symmetry, the dimensionless flow distribution curve of the suction/discharge window can be obtained as shown in Fig.14.The suction window and discharge window in the valve plate are determined by the rotational direction of the motor-pump assembly, and the two windows have a phase difference of 180 degrees.

Based on the principle of Poiseuille flow,the leakage flow of the cylinder block/valve plate interface of this sub-model yields:

Based on the distribution curves and the leakage flow of the cylinder block/valve plate interface, the flow distribution submodel of a single piston is established, shown in Fig.15.

2.3.Modelling of the motor-pump assembly

2.3.1.Model of the pump core

The simulation model of the pump core for the motor-pump assembly can be obtained by association the sub-models of the three main interfaces, as shown in Fig.16.The main parameters of the pump core are listed in Table 1.

2.3.2.Model of the motor

The permanent magnet synchronous motor (PMSM) is adopted in the motor-pump assembly, which has the advantages of high power density and overload resistance.Its voltage and magnetic chain equations are expressed as:

Fig.15 Flow distribution sub-model of a single piston.

Fig.16 Model of the pump core.

Table 1 Main parameters of the pump core.

The electromagnetic power of a PMSM can be expressed as:

The balance equation of electromagnetic torque and mechanical torque yields:

Table 2 Main parameters of the PMSM.

Fig.17 Simulation model of motor-pump assembly.

Table 3 Physical and chemical properties (Hyjet-V).

The PMSM model is established based on the above equations,as shown in Fig.18.The main parameters of the PMSM are listed in Table 2.

2.3.3.Model of the motor-pump assembly

By connecting the mechanical interface of the PMSM and the pump core with the spline on the shaft, the simulation model of the motor-pump assembly is established, as shown in Fig.17.The medium of the motor-pump is phosphate ester hydraulic oil (Hyjet-V), whose basic properties are listed in Table 3.And the parameters of the fluid are set according to the Table 3.

Assume that the pressure of the suction port is stable and the flow is sufficient to avoid cavitation, and the pressure of the sharing housing is the same as the suction port pressure.Besides, an ideal relief valve is adopted for load simulation.The simulation platform is shown in Fig.19.And the environmental parameters are listed in Table 4.

Fig.19 Simulation platform of motor-pump assembly.

Table 4 Environmental parameters.

Table 5 Critical pressure drops and speed.

In order to analyze the distribution of the flow characteristics of the motor-pump assembly in a wide working condition,a series of critical points in its speed and pressure range are selected, listed in Table 5.

3.Experiments

3.1.Test bench

The experimental investigations of the flow characteristics were conducted on a phosphate ester medium test bench.The motor-pump assembly is tested in the experimental cabin,and the test data is transmitted and saved to the computer in the control panel through the sensors.The hydraulic system of the test bench realizes the oil supplement, load simulation and oil temperature control, whose principle is shown in Fig.20.The main structure of the test bench is shown in Fig.21.

3.2.Experimental procedure

The test motor-pump assembly is connected to a test valve block and fixed to the test platform, as shown in Fig.22.The temperature and pressure sensors are equipped on the test valve block to measure the temperature and pressure of the suction and discharge ports.In addition, the same sensors are equipped at the leakage port.

Fig.20 Hydraulic principle diagram of test bench.

Fig.21 Test bench with phosphate ester medium.

Before the experiments, the hydraulic system and motorpump assembly need to be preheated to maintain the oil temperature at 40°C according to Table 4,excluding the effects of temperature on the flow characteristics.At the same time, noload bi-directional operation of the motor-pump assembly is conducted,exhausting air from the motor-pump assembly,test valve block and the oil pipes.Finally,the method of inlet pressurization is adopted to avoid cavitation at high speed.By adjusting the oil supply pressure of the oil supply pump, the pressure of the pump inlet port is maintained at 1 MPa at each critical speed point.When the experimental environment is stable,the output flow is tested according to the critical points listed in Table 5.Due to the limitation of the motor power,the test for high speed and high pressure conditions were not conducted.

Fig.22 Installation of the motor-pump assembly.

Fig.23 Simulation results of flow characteristics under different pressures.

4.Results and discussion

4.1.Simulation results and analysis

The simulation results of the output flow when the motorpump assembly operates at low (3 MPa), medium (15 MPa)and high(27 MPa)pressures are shown in Fig.23(a).Simulation results have shown that the output flow rate of the motorpump assembly at a particular pressure drop possesses good linearity, indicating that the magnitude of the leakage is less sensitive to the rotational speed.At constant rotational speed,the output flow rate gradually decreases with the increase of the pressure drop.This decrease is mainly attributed to the increase in leakage due to the positive proportional relationship between the leakage flow and the pressure drop according to the principle of Poiseuille flow.

The variation law of volumetric efficiency of the motorpump assembly under different pressure conditions is shown in Fig.23 (b).When the pressure is constant, the volumetric efficiency increases with the increase of rotational speed, and the increase is more obvious at lower speeds.When the motor-pump assembly works at low pressure, its volumetric efficiency can be maintained above 95 % in the whole operating speed range.But as the pressure increases, the volumetric efficiency at low-speed conditions decreases significantly.Particularly,when the pressure increases to 27 MPa,the volumetric efficiency at 2000 r/min is only about 70 %.The reason is that the output flow rate of the motor-pump assembly increases with the increase in speed,and the change of leakage is not obvious due to the constant pressure,indicating that the output flow of the motor-pump assembly is more sensitive to the pressure drop.Besides, when the pressure increases, the change in volumetric efficiency with speed is more obvious,mainly because the leakage in the three interfaces increases with pressure.

To visualize the distribution of the output flow and volumetric efficiency over a wide working condition more intuitively, contour plots of the output flow characteristics are displayed in Fig.24.It can be seen in Fig.24 (a) that the iso-flow lines approximate as sloping straight lines, and the magnitude of the slope is related to the Poiseuille flow.Fig.24 (b) depicts that the volumetric efficiency is relatively low when the motor-pump assembly works in a low speed and high pressure condition.When the appropriate speed is less than 3500 r/min and the pressure drop is more than 18 MPa, the volumetric efficiency is reduced to less than 80 %.On the contrary, when the speed exceeds 5000 r/min or the pressure is less than 7 MPa, the volumetric efficiency can reach more than 90 %.In addition, the gradient of the volumetric efficiency along the horizontal and vertical axes can further illustrates that the volumetric efficiency is more sensitive to the pressure drop than to rotational speed.

Fig.24 Simulation results of output flow and volumetric efficiency distributions.

Fig.25 Experimental results of flow characteristics under different pressures.

4.2.Experimental validation and discussion

Fig.25 compares the experimental and simulation results of the output flow and volumetric efficiency under different pressures.As can be seen in the figure, the output flow rate coincides well with the simulation results at lower speeds.However, when the speed exceeds 5000 r/min, the deviation between the experimental and simulation increases with the augment of the speed.And this phenomenon gradually decreases with the increase of pressure.There are two main reasons for this phenomenon.

First,when the rotational speed is higher,the tilting motion of the cylinder block becomes more severe, which leading the oil film in the cylinder block/valve plate interface to change from parallel to wedge.Since the leakage flow is proportional to the cube of the oil film thickness due to the pressure-flow equation, the leakage volume increases significantly, which leads to the lower output flow.Second, the wedge-shaped oil film produced by tilting motion of the cylinder block enhances the strength of the dynamic pressure effect,thus increasing the load-carrying capacity of the oil film in the cylinder block/-valve plate interface.Consequently, the average oil film thickness is increased and therefore leading to an increase of the leakage flow rate.In addition, when the pressure increases,the phenomenon of increased leakage due to the rotational speed is diminished because of the enhanced hydrostatic effect.When the hydrostatic effect far exceeds the hydrodynamic effect, the above phenomenon is no longer obvious.Since the tilting motion of the cylinder block is not considered in the simulation model, the experimental output flow and volumetric efficiency at high speed are lower than the simulation values.

Fig.25 also shows that the experimental results of volumetric efficiency vary over a smaller range than the simulation results.When the pressure is less than 15 MPa,the volumetric efficiency can reach more than 92 % and up to 98 % in the whole speed range.The reason for this error should also lie in the modeling of the oil film.Experimental results indicates that the oil film in the interfaces is changing dynamically when operating at different points.When the speed is low,the actual oil film thickness is smaller, however in the simulation model the thickness of the oil film is uniform,which leads to the existence of the error.

In order to compare more intuitively the degree of agreement between the experimental and simulation results,the output flow and volumetric efficiency are drawn in the same coordinate system, as shown in Fig.26.It can be seen that the experimental and simulation results are in good agreement.

We introduced simulation accuracy a to show the error more intuitively between simulation and experiment, yields:

Fig.26 Comparison of simulation and experimental results.

Fig.27 Accuracy of the simulation.

The accuracy map is shown in Fig.27 When the motorpump assembly works at low speed and high pressure or high speed conditions, the accuracy is relatively low (about 94 %).Therefore, the simulation model can effectively evaluate the flow characteristics of the motor-pump assembly.

When the motor-pump work at low speed and high pressure or high speed conditions, the volumetric efficiency is significantly reduced, which is relatively large differences with the simulation results, the main reasons for the differences are as follows.First, the simulation model did not take into account the dynamic pressure effect generated by the wedgeshaped oil film due to the lateral force, which will have an impact on the leakage flow at high speed.Second, the friction pair of the cylinder block/valve plate interface works between the state of boundary lubrication and fluid lubrication due to the pulsation of the pump.It is difficult to accurately establish the simulation model when the interface is in the mixed friction state.Thus,there might be errors in this complex friction state,especially when the machine works at low speed and high pressure.Finally, the influence of the chemical properties might cause the error.The bearing characterizes of the oil film might related to the molecular structure of the medium, especially in the boundary lubrication state.The different chemical structure of the oil will affect the bearing capacity, leading to the changing of the output characteristics.Therefore, experimental means are the most direct,effective and accurate methods to analyze the flow characteristics of the motor-pump assembly.

Fig.28 Experimental results of output flow and volumetric efficiency distributions.

The contour plots of the output flow and volumetric efficiency are shown in Fig.28.The iso-flow lines in Fig.28 (a)obtains good linearity at low speed, and when the speed is increased, there are obvious bending, as shown in region A.The longitudinal height of region A increases with the increase of speed.It is because that the hydrodynamic effect is enhanced with the increase of the speed, and the hydrostatic effect of higher pressure is needed to balance the hydrodynamic effect.Fig.28 (b) indicates that the motor-pump assembly has the poorest output characteristics when operating at low speed and high pressure, followed by high speed and low pressure, and then the low speed and low pressure.At low speed and high pressure, due to the dominance of the throttling effect, the friction interfaces experience serious leakage due to the increased pressure drop under the influence of Poiseuille flow.The throttling effect is weakened along the arrow, as shown in region B.At high speed and low pressure, the oil film thickness increases with the hydrodynamic effect, leading to the increase in leakage.The hydrodynamic effect is weakened along the arrow, as shown in region C.

5.Conclusions

In this paper, a multidisciplinary model of the single-shaft coaxial motor-pump assembly is established,and then the simulation analysis and experimental investigation of the output flow characteristics in a phosphate ester medium are carried out, and the conclusions are as follows:

(1) The simulation model of the motor-pump assembly is constructed by establishing the sub-models of the slipper/swash plate interface,piston/cylinder block interface and cylinder block/valve plate interface.The flow characteristics of the motor-pump can be accurately obtained.

(2) The volumetric efficiency of the motor-pump assembly is highest at low speed and low pressure, and lowest at low speed and high pressure due to the Poiseuille flow in the three interfaces.

(3) When the motor-pump assembly is working at high speed and low pressure condition, more attention should be paid to the hydrodynamic effect on the output flow characteristics.

(4)Low speed and high pressure conditions have the greatest impact on the service life and performance of the motorpump assembly due to the severe lubrication status.Subsequently, the three main interfaces should be optimal designed especially for this working condition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the Chinese Civil Aircraft Project(No.MJ-2017-S49)and China Postdoctoral Science Foundation (No.2021M700331).