Unmanned aerial vehicle strike on a flat plate:Tests and numerical simulations

Jun LIU, Chi CHEN,b, Jingyu YU, Jin LI, Zhuguo ZHANG,Yfeng WANG, Yulong LI,*

aSchool of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

bAVIC (Chengdu) UAV System Co., Ltd, Chengdu 611731, China

cShanghai Aircraft Airworthiness Certification Center of CAAC, Shanghai 200335, China

dChina Aircraft Strength Research Institute, Xi’an 710065, China

KEYWORDSAir gun test;Dynamic response;Impact damage;LS-DYNA;UAV

AbstractThe incursion of Unmanned Aerial Vehicles(UAVs)into airports often occurs due to the popularity of drones, which may lead to a threat to aircraft flight safety.Therefore, estimating the dynamic impact load caused by drone strikes is essential.This paper proposes a test method with high precision and low cost involving launching of a UAV to impact a flat plate specimen by using an air gun.The test results of UAVs impacting flat plates at different impact velocities,such as the UAV damage deformation captured by a high-speed camera and strain vs time dynamic response curves of plates,were obtained and analysed.At the same time,a corresponding numerical simulation was carried out by using the explicit finite element software LS-DYNA.The predicted damage to the UAV and strain on the flat plate during the strike process were compared with the test results.The overall trend of the simulation results is in good agreement with the test results,at least for the first three milliseconds of the event.This shows that the numerical simulation model established in this paper is reasonable.The UAV numerical method established in the present paper can be used to carry out numerical simulations and evaluations of the collision safety of UAVs against large aircraft and high-value ground targets.The results show that the local deformation of the impacted target is uneven due to the distribution of concentrated mass components such as motors,battery,and camera.As the impact velocity of the UAV increases,all parts of the UAV are seriously damaged and basically in a fragmented state,and the battery is greatly deformed.The interaction between the UAV and the flat plate specimen is approximately 2.7 ms,and the UAV numerical simulation model established in this paper can well simulate the real UAV impact process.

1.Introduction

In recent years, with the increasing use of Unmanned Aerial Vehicles (UAVs) in many areas, UAVs striking aircraft structure,UAVs injuring people,UAV black flights leading to flight delays and other events have frequently occurred.The first alleged collision between a commercial airliner and a UAV occurred at Heathrow Airport on April 17, 2016.Although unconfirmed,this incident has drawn attention to the commercial airliner damage caused by a UAV.1-3On December 22,2018, a Brazilian Airlines civil aircraft collided with a UAV during flight, causing damage to the aircraft.4On September 4,2020,a 25 kg UAV of a Latvian company lost contact with the ground controller,which directly led to the closure of Riga International Airport.5In addition, safety accidents involving ground crowds and vehicles caused by UAV crashes are also worthy of attention.On May 18, 2017, a Chinese multirotor UAV fell out of control and crashed into a pedestrian, resulting in an eyeball being cut.6Research on the impact load and damage mechanism of UAVs has a certain reference value for the formulation of UAV safe flight airworthiness regulations.

Liu et al.7simulated the damage to engine fan blades caused by a drone (MAVIC Pro) impinging on a typical business engine (CFM56-5B) with the aid of the Finite Element Method (FEM).Both the collision position and posture were demonstrated to significantly affect the damage level of engine fan blades.More damage to fan blades could be detected for the 75 % collision position, and the complex collision posture would lead to much larger damage to the engine fan blades.Schroeder et al.8performed a parametric study based on statistically representative models for both the hobby and professional drone classifications.Using generalized drone models,systems incorporating wide-chord fan blade designs with both Carbon Fibre Reinforced Polymer (CFRP) and titanium fan blades were investigated.Through the analysis, the risk level posed by different classes of Unmanned Aircraft Systems(UASs) on the high-bypass commercial jet engine was quantitatively determined.This work complements an earlier part that focused on relating drone impact to the existing ingestion regulations.Lu et al.9studied the airborne collision safety between the windshield of transport aircraft and five light UAVs under various possible flight conditions.The collision simulation model of the drone and aircraft windshield was established in the PAM-CRASH software environment,which was used to simulate the dynamic response of and damage to the windshield after the impact of the drone and aircraft windshield under various conditions.Meng et al.10performed a ground collision test between a UAS and a commercial airliner horizontal stabilizer section to investigate the dynamic response of this primary operation component.Explicit dynamic code PAM-CRASHR was employed to simulate the collision process, followed by a series of simulations to assess the hazard of different collision scenarios.The results showed that a 3.4 kg drone impact at the airliner cruising speed can cause some damage to the horizontal stabilizer front spar,and the situation is more serious than a 3.6 kg bird strike.Rattanagraikanakorn et al.11investigated the differences in head and neck injuries subject to UAS collision with an often-used crash dummy and a human body.Multibody System (MBS)models have been used to simulate UAS impacts on validated models of the crash dummy and the human body.The findings confirm the moderate risks of head and neck injuries that have been reported.However, the neck load significantly differs between the crash dummy model and the human body model,and the human body model sustains larger head injury but smaller neck injury compared to the crash dummy model.Drumond et al.12carried out an impact simulation between a commercial aircraft wing fixed leading edge reinforced with a triangular structure and a UAV.Radi13researched the damage potential to manned aircraft from a mid-air collision with a small UAV.Scenarios of engine ingestion and impacts on the fuselage and cockpit windscreen were considered.The study provided velocity estimates above which penetration of the aircraft structure could be expected.Liu et al.14simulated the dynamic response in UAV airborne collisions with a manned aircraft engine.The damage severity level of the engine under UAV airborne collision was studied by considering different collision configurations, different collision positions and different flight phases.Both the damage to fan blades and the percentage of thrust loss were considered to reflect the influence of UAV airborne collisions on aircraft operation.Liu et al.15presented an FEM simulation method to analyse the performance of a commercial aircraft engine under collision with drones with weights of 250 g and 750 g.The damage levels of both the fan blades and compressor blades during the drone collision process were investigated.The result showed no apparent damage to the aircraft engine fan blades for the MAVIC MINI drone, while some damage could be detected for the engine fan blades under the impact of the MAVIC Pro drone.Beh et al.16focused on lightweight drone impact collisions on business jet engines.The fan blade was modelled based on the dimensions of the PW305 business jet engine.The UAV collision test with a lightweight drone was simulated at different blade span positions.The results showed that some material failure could occur at the leading edge of the fan blade, which was caused by the denser and heavier drone components.Other research organizations, such as the Federal Aviation Administration (FAA),17–22conducted studies to analyse the damage introduced into different areas of the aircraft structure for both commercial and business jet aircraft configurations.The research concluded that UAS impacts are likely to cause more damage than bird strikes for an equivalent initial kinetic energy.The European Union Aviation Safety Agency(EASA)23–24organizes or is present in working groups that discuss relevant or tangential topics,such as counter UAS approaches.

Although a large number of papers on UAV strike studies have been published,there is a shortage of test data in the open literature.The numerical simulation model of UAVs is not verified by experiments, which greatly reduces the reliability of UAV collision research conclusions.In view of this,this paper proposes a test method with high precision and low cost involving launching of a UAV to impact a plate specimen using an air gun.The test results of UAVs at different impact velocities provide a large amount of data for verifying the rationality of numerical simulations,such as the UAV damage deformation captured by a high-speed camera and strain vs time dynamic response curves of plates.At the same time, a numerical simulation model corresponding to the UAV strike test is established, and the test results are used to verify the rationality of the simulation results.

2.UAV strike test

The hazard assessment and method of UAVs impacting aircraft and high-value ground targets need to be verified by UAV strike tests.UAV strike test methods include the air gun method and rocket pulley method.The air gun method involves striking a static target specimen with a high-speed UAV.During the test, high-pressure gas is first input into the cylinder to the rated value, and then, the gas is quickly released.The air flow pushes the UAV out of the chamber at a high speed to strike the target specimen.The rocket pulley method involves suspending the UAV at a fixed position in space,installing the specimen on a pulley,and pushing the pulley with a rocket to make the specimen strike the suspended UAV.The rocket pulley test cost is very high, and the air gun method is generally used in UAV strike tests.The Taicang Research Institute of Northwest Polytechnical University took the lead in establishing China’s first UAV impact laboratory based on the air gun method in September 2021, and the UAV striking a flat plate test in the present paper was carried out in this laboratory.

2.1.Test principle

The schematic diagram of the principle for the UAV strike test is shown in Fig.1, which is mainly composed of a launch system, a target system and a measurement system.The launch system mainly includes an air compressor, a high-pressure chamber, switch equipment, a gun tube, and a stripper mechanism.The air compressor is the front-end pressure conveying equipment, which directly compresses the air into highpressure gas and transmits the gas to the high-pressure chamber.The high-pressure chamber is the back-end equipment of pressure transmission, equipped with an overflow safety valve and a pressure gauge.Through the displayed value of the pressure gauge and the UAV speed measured by the UAV speed measuring device, the corresponding relationship of pressure versus speed can be obtained and provided to the test technicians as a calibration curve.The high-pressure chamber is the power source for launching the UAV.The pressure in the chamber determines the speed of the UAV.

The UAV and its cartridge are preplaced in the gun barrel.After the chamber pressure reaches the predetermined value and is stable, the pressure valve is opened, and the highpressure gas is suddenly released to push the cartridge equipped with the UAV to slide along the gun tube and shoot at the target specimen fixed on the frame.At the front end of the gun tube, a stripper mechanism is fixedly connected to the muzzle,in which the diameter of the core hole is slightly smaller than the muzzle diameter, which plays the role of UAV shelling.The launch control device is mainly composed of a large-load high-speed solenoid valve and a control circuit.The test technician turns on the circuit switch, which drives the solenoid valve to quickly open the valve, thus generating high-pressure differential pressure in a very short time and pushing the cartridge equipped with the UAV to accelerate sliding along the gun tube and shoot at the target specimen.The device can provide a speed control accuracy for the UAV within 1000 km/h of less than 3 %.During the test,the UAV impact velocity and dynamic displacement and strain responses of the target specimen can be obtained through the measurement system.

2.2.Test equipment

Fig.1 Schematic diagram of the principle for UAV strike test.

The most important piece of equipment in the UAV strike test is the air cannon launch system.The system is mainly composed of a compressor, a high-pressure chamber, switch equipment,a gun tube and a stripper mechanism, as shown in Fig.2.Before the test,the cartridge with the UAV is placed in the gun tube.According to the empirical relationship between the pressure in the chamber and the launch speed,the pressure in the chamber can be calculated based on the required impact speed of the UAV.Then,the compressor is turned on,and the pressure gauge panel is observed.When the pressure on the gauge panel reaches a predetermined value and stabilizes, the pressure valve is opened to launch the UAV, which strikes the target specimen.

2.3.UAV projectile and target flat plate specimen

In the present paper, a Da Jiang Innovation (DJI) phantom 4 UAV with approximate dimensions of 290 mm × 290 mm ×190 mm was used to impact the flat plate.The UAV with a mass of 1.34 kg is packed into a cartridge made of plastic foam, and then, the UAV projectile is completed, as shown in Fig.3.The UAV projectile is placed in the gun tube for launching.Note that,due to the light weight and low strength of the propeller blade of the UAV,the dynamic response of the flat plate to this blade can be ignored.Therefore,to install the UAV into the cartridge of the existing size,the propeller of the UAV is not considered in the test in this paper.

Fig.4 shows the details of the target specimen and its clamping fixture.The impacted specimen is fixed by bolts to a clamping fixture connected to a heavy support attached to the concrete ground,and each of the rubbers between the specimen and clamping fixture is only 2.0 mm thick.The target specimen is a square flat plate made of 2024-T3 aluminum,which has dimensions of 1000 mm by 1000 mm and is 3.175 mm thick.

2.4.Data acquisition

2.4.1.UAV velocity

Fig.2 Equipment of gas gun launch system.

Fig.3 Process to make the UAV projectile.

Fig.4 Clamping fixture and target flat plate specimen.

A laser speedometer was used to measure the velocity of the UAV in the test.The error of the laser speedometer is less than 1 m/s.Accurately measuring the velocity of the UAV in tests is very important.Therefore,for insurance,a high-speed camera was used to capture the movement of the UAV before impacting the specimen.The shooting background was a pattern with grid.After the test, the velocity of the UAV can be approximately calculated according to the grid distance on the pattern and the high-speed camera shooting video.The two methods can confirm each other to ensure the accuracy of the UAV velocity.

2.4.2.High-speed cameras

A high-speed camera was used to record the interaction between the UAV and the flat plate during the process of the UAV strike test.At the same time, through high-speed video,the deformation of and damage to as well as failure of the UAV and plate can be observed, which are very important for the study of the numerical simulation model of the UAV.Two high-speed cameras were used in the test, as shown in Fig.5, with a resolution of 1024 × 512 and a frame rate of 100000 frames per second.Camera 1# captures the deformation of and damage to the UAV and the plate from the side during the test, and Camera 2# is used to assist in measuring the velocity of the UAV.The recorded results of the two high-speed cameras are all black and white images.

2.4.3.Strains

The strain measurement principle is that a strain gauge is connected to a super-dynamic strain instrument, and the output end of the super-dynamic strain instrument is connected to a transient recorder to obtain the variation relationship of the voltage signal related to the strain with the impact response time and then convert it into the final strain through the calibration relationship.The test specimens were instrumented with strain gauges in the impacted area to measure the local strains on the rear of the plate, as shown in Fig.6.The adhesion of the strain gauges on the back of the flat plate specimen is shown in Fig.6(a), and the locations of the measurement points are shown in Fig.6(b).The strain was measured at six points S1-S6.The distance between S1 and S2 as well as S4 and S5 is 100 mm,and the distance between S2 and S3 as well as S5 and S6 is 150 mm.

Fig.5 Layout of high-speed cameras.

Fig.6 Measurement of strain on target flat plate.

2.5.Test conditions

Strike tests involving the UAV with a mass of 1.34 kg were carried out on flat plate specimens in the present paper.The impact point is located at the centre of the plate.The predetermined impact speeds are 70 m/s, 120 m/s and 130 m/s.The impact velocity direction of all tests is perpendicular to the plane of the flat plate specimen.Table 1 shows 3 groups of test records under different test conditions.

2.6.Test results and discussion

The results of the laser speedometer and the high-speed camera were compared.The actual velocities of the UAV in the tests are 67.4 m/s, 122.1 m/s, and 133.2 m/s.The actual velocity of the UAV under each strike test condition is very close to the predetermined velocity, and the errors are only 3.7 %,1.8 %, and 2.5 %, respectively.

2.6.1.High-speed camera results

Through the video of the impact process taken by the highspeed camera, the interaction of, deformation of and damage to the UAV and the flat plate can be clearly observed.The moment of contact between the UAV and the flat plate is defined as 1.2 ms for 67.4 m/s, 0.4 ms for 122.1 m/s, and 0.3 ms for 133.2 m/s.Fig.7 shows the imaging results of the UAV striking the flat plate taken by the high-speed camera at 4 moments.The velocity is defined as v and the time as t.Under the three impact velocities, the impact attitude of the UAV is basically consistent with the expected attitude.First,two motors of the UAV impact the flat plate,resulting in largedeformation of and damage to the motors.After that,the fuselage shell,battery,camera,landing gear and other parts hit the flat plate, and these parts greatly deform and are damaged.After the final impact,all parts of the UAV are seriously damaged and basically in a fragmented state.For all three tests conducted, no damage to or failure of the plate was observed.

Table 1 Test matrix.

Fig.7 Typical photos of UAV damage and plate deformation during impact.

2.6.2.Dynamic strain response

Fig.8 Dynamic response curve of strain vs time history.

The strain vs time histories of the plate were recorded by the dynamic data acquisition system.As shown in Fig.8,for Test 1#, the deformation at the centre of the flat plate is relatively intense during the impact,and the strain gauge arranged at this position and its connecting wire are severely stretched and dragged during the measurement; hence, no effective data of strain gauges S1 and S4 are obtained.From the measurement positions, S2 and S5 are in symmetrical positions, and S3 and S6 are in symmetrical positions.The strain measurement results show that the difference between S3 and S6 is smaller than that between S2 and S5, indicating that farther from the flat plate impact area,the influence of the nonuniformity of the UAV mass distribution on the deformation at this position is smaller.S2 and S5 are in the impact area, and the local deformation in this area is closely related to the mass distribution of the UAV.Therefore, although S2 and S5 are in symmetrical positions, the strain results are quite different.The Test 2#results show that S1,S2,S4 and S5 in the impact area do not obtain effective data due to severe deformation.S3 and S6 are in symmetrical positions in the nonimpact area,and the nonuniformity of the UAV mass distribution has little effect on the deformation at these positions.Therefore,the difference between the S3 and S6 measurement results is small.For Test 3#, the impact velocity of the test is too large, and only valid data of strain gauge S5 are obtained,which can be used to verify the rationality of the subsequent numerical simulation method.

2.6.3.Damage to plate and UAV

Fig.9 shows the deformation morphology of the plate after impact.When the impact velocity is 67.4 m/s, the final plastic deformation of the flat plate is small, and small local pits appear on the flat plate.These pit locations on the flat plate should correspond to impact by a UAV motor.When the impact velocity increases to 122.1 m/s and 133.2 m/s, the final plastic deformation of the plate further increases,and local pits increase.When the impact velocity is 122.1 m/s, there are two obvious pits, and these pit locations should correspond to impact by two motors of the UAV.When the impact velocity is 133.2 m/s, there are three obvious pits, and these pit locations should correspond to impact by the battery and two motors of the UAV.During UAV impact, the local deformation of the impacted target is uneven due to the distribution of concentrated mass components such as motors, battery, and camera.

Fig.10 shows the damage morphology of the UAV after impact.When the impact velocity is small, the fuselage is broken into large blocks,the landing gear and fuselage shell of the UAV are less damaged, the battery is basically intact after impact,and there is no fire or smoke.With the impact velocity increasing to 122.1 m/s and 133.2 m/s, the UAV fuselage is broken into smaller fragments.The landing gear, fuselage shell, motors, camera and other components are seriously deformed and damaged, and the battery is greatly deformed after impact, resulting in fire and smoke.

3.Numerical simulation

By impact dynamics we mainly study the response of structure to dynamic loads.The loading process makes the structure produce significant acceleration, and the influence of inertial force caused by acceleration cannot be ignored.The basic assumptions of impact dynamics are the same as those of statics.Based on these assumptions, it can be known that in the basic equations of statics,except for the equilibrium equation,the geometric and physical equations can be directly applied to impact dynamics.

The detail of the governing equation with respect to numerical simulation of UAV is presented as follows:

Equations of motion

Geometric equations

Fig.9 Deformation of and damage to target flat plates.

Fig.10 Damage to UAV.

in whichσij,jrefers to stress,εijrefers to strain, uijrefers to displacement, q refers to density, and ¨u refers to acceleration.firefers to volume force.Combined with the boundary conditions, the numerical simulation method is used to solve the above equations to obtain the solution of UAV impact dynamics.The numerical solution of the above governing equations is based on the finite element method and the difference method,which are introduced in detail in most textbooks and will not be repeated here.

3.1.3D geometric model

The basic size of the DJI phantom 4 UAV with a quadcopter configuration is approximately 290 mm×290 mm×190 mm.As shown in Fig.11(a), this UAV adopts the classic quadcopter lift layout, a fixed landing gear, a battery arranged in the belly of the fuselage,a camera arranged under the fuselage,and a flight controller circuit board loaded inside the fuselage.The UAV is mainly composed of six parts: motors, battery,camera,fuselage shell,fuselage internal circuit board and landing gear.It is basically a shell structure except for the motors,battery and camera,which are composed of solid columns and solid blocks.

By combining laser scanning reverse modelling and mapping modelling of the UAV entity, a 3D geometric model of the UAV in this paper is obtained.First, laser scanning or mapping is carried out according to the geometric characteristics of the parts.The motors, battery, camera and fuselage shell are located outside the fuselage and have complex shapes.These parts are modelled by laser scanning reverse modelling.The internal circuit board and landing gear of the fuselage have regular shapes and are modelled by surveying and mapping.Then, modelling is carried out according to the laser scanning data or mapping data.Finally,the 3D digital models of all parts are assembled into a complete digital model of the whole UAV, as shown in Fig.11(b).

3.2.Mesh model

Most parts of the quadcopter UAV studied in the present paper are shell structures.The main geometric feature of this kind of shell part is that the size in one direction is 12 times larger than that in the other two directions.When this kind of structure is meshed, the middle surface of the geometric model is first extracted, and the quadrilateral shell element is used to mesh the middle surface.For other parts, hexahedral elements are mainly used for mesh generation.For parts with complex geometry, triangular elements and tetrahedral elements will inevitably appear in mesh generation.The mesh quality control method is used to control the number of triangular and tetrahedral elements to within 5%of the total number of elements.According to this meshing principle, the fuselage shell,fuselage internal circuit board,arm and landing gear of the UAV are divided into shell elements, and motor,battery and camera components are divided into solid elements.

Fig.11 UAV and geometric model.

Normally,the smaller the mesh size of the numerical model is, the more accurate the calculation results are.Considering the time cost of the actual calculation and that when the mesh size of the numerical model is reduced to a certain value, the calculation accuracy does not change with the mesh size,according to practical experience, the shell element size of the UAV finite element mesh model is finally determined to be approximately 5.5 mm,and the body element size is approximately 3.5 mm in the present paper.The mesh model of the UAV is shown in Fig.12.The total number of meshed elements is 95200,including 16660 shell elements and 78540 solid elements, accounting for 17.5 % and 82.5 %, respectively.

3.3.Constitutive model and parameters

The UAV is composed of a variety of materials,mainly including alloy, plastic, and compressible foam.Among the main components of the UAV,the structures of the fuselage,battery shell and camera stabilizer circuit board are simplified into polycarbonate (PC).The motor rotor, motor base, camera pan tilt housing and stabilizer arm are 6061-T6 aluminum alloy.The motor shaft, motor stator and magnet are 45 steel.In addition, the battery cell is compressible foam.The specific material distribution is shown in Fig.13.

The mechanical behaviour of the PC material in the UAV is characterized by an elastic–plastic constitutive model.The model parameters of PC were referenced from the research results of Dwivedi et al.25The material constitutive model parameters are shown in Table 2 where E refers to elastic modulus,v refers to Poisson’s ratio,σsrefers to yield strength,and εfrefers to failure strain.

The Johnson-Cook(J-C)constitutive model was selected to simulate the mechanical behaviour of 45 steel and 6061-T6.The J-C constitutive model considers the effects of strain strength,strain rate and temperature softening on the material.The stress triaxiality, strain rate and temperature are taken into account in J-C failure analysis.The mechanical behaviour of materials under large deformation can be simulated by the J-C constitutive model.26The expressions of the J-C constitutive model are:

Table 2 Constitutive model parameters of PC.

Fig.12 Mesh model of UAV.

Fig.13 Material composition of UAV.

Table 3 Constitutive model parameters of metal.

In these two equations, σ represents the effective stress, ε represents the effective plastic strain, ˙ε*represents the effective strain rate,T*represents the temperature change in the process of plastic deformation, Trand Tmare the reference temperature and melting temperature of materials respectively, and A, B, n, C and m are undetermined coefficients.The influence of temperature change on the material is not considered, and thus only A, B, n, and C are used.

The constitutive model parameters of 45 steel were obtained from the research results of Chen et al.27The constitutive model parameters of 6061-T6 were obtained from the relevant studies of Huang and Xu28and Robbins et al.29The J-C constitutive model parameters of these two kinds of materials are shown in Table 3.

The battery materials are based on the study of Xu and Sahraei et al.30–32An equivalent model is established.Its mechanical properties are simulated using a compressible foam material.The material performance parameters are shown in Table 4.

3.4.Calculation model

The UAV components are mainly connected by screws in the present paper.Therefore, the spot weld connection model is used to simulate the connection between the components.The corresponding nodes are selected on the mesh models oftwo screw-connected components, and a one-dimensional beam element is established to simulate the screw connection between the two components.This connection method is suitable for the connection of shell elements to shell elements,shell elements to body elements and body elements to body elements.In the whole UAV model, a total of 703 pairs of spot weld connection elements are established.

Table 4 Constitutive model parameters of compressible foam.

Fig.14 Calculation model.

Fig.15 Comparison of simulated UAV strike process with photos taken by a high-speed camera.

The target specimen is simulated by a rectangular flat plate with a size of 1000 mm×1000 mm×3.175 mm.The flat plate is divided into two-dimensional regular quadrilateral elements with a mesh size of 5 mm,and the total number of meshed shell elements is 40000.The plate is made of 2024-T3 aluminum material, and the constitutive model parameters are shown in Table 3.

Fig.16 Comparison of computed and measured strain vs time histories.

A surface-to-surface contact model is used to simulate the contact between the UAV and flat plate, and a single surface contact model is used to simulate the self-contact among various parts of the UAV.During the calculation, relevant settings are applied to eliminate the initial small penetration between parts.The viscous damping coefficient is set to 20 to reduce the numerical oscillation during the calculation.The four sides of the flat plate are fixed, the impact velocity direction of the UAV is perpendicular to the plate surface, and the impact velocity of the UAV is consistent with the test.The calculation model is established as shown in Fig.14.

4.Numerical simulation results and discussion

The computational run time in present paper is 3.5 h.The calculation judges the convergence according to the time step increment.When the time step increment is greater than a certain value,the calculation does not converge.Fig.15 shows the comparison between the numerical simulation results and test results of UAV damage at typical times during the interaction between the UAV and flat plate specimen at three strike velocities.The high-speed camera and numerical simulation of the three impact tests are timed starting from the moment when the UAV contacts the flat plate.Under the three strike velocities,the interaction time between the UAV and the flat plate is approximately 2.7 ms.The images taken by the high-speed camera show that at the initial moment of contact between the UAV and flat plate at the three strike velocities, the strike attitude of the UAV is not the ideal attitude shown in Fig.14 but has a small deflection.The slight change in UAV strike attitude will have a great influence on the deformation and damage results.Therefore, to bring the simulation results in good accordance with the test results during numerical simulation, the initial strike attitude of the UAV was minorly adjusted to keep consistent with the test.

When the UAV strikes at a low velocity of 67.4 m/s,the test results and numerical simulation results show that the flat plate specimen has obvious deformation but no breakdown.The UAV breaks into several large fragments,but the damage morphology of the battery shell, landing gear and other components is small, basically consistent with the original structure; in particular, the four motors have only slight deformation.The numerical simulation results are in good agreement with the experimental results.When the UAV strikes at high velocities of 122.1 m/s and 133.2 m/s, the test results and numerical simulation results show that the flat plate specimen has obvious deformation but no breakdown.The UAV breaks into numerous small pieces, including concentrated mass components such as the battery, motors and camera, which are broken.The numerical simulation results are in good agreement with the experimental results.

The UAV numerical simulation model established in this paper can well simulate the real UAV impact process.The UAV numerical method established in the present paper can be used to carry out numerical simulations and evaluations of the collision safety of UAVs against large aircraft and high-value ground targets.

The comparison between the calculation and test results of the flat plate strain response is shown in Fig.16.The effective strain data measured in the test are from S2,S3,S5 and S6 for Test 1#,S3 and S6 for Test 2#,and S5 for Test 3#.When collecting strain data, signal triggering to the end of collection takes 5 ms.The interaction between the UAV and the flat plate specimen is approximately 2.7 ms, so the strain–time history data can reflect the deformation of the flat plate specimen during the interaction between the UAV and the flat plate.The effective strain corresponding to the test position is extracted from the numerical simulation results of the UAV striking the plate and compared with the test results.The overall trend of the simulation results is in good agreement with the test results,at least for the first three milliseconds of the event.This shows that the numerical simulation model established in this paper is reasonable.

There is a relatively large error between the calculated strain and the test result after 3 ms.The reason is that after 3 milliseconds, the impact between the UAV and the flat plate basically ended.Then the strain response depends on the free swing of the plate.The numerical simulation does not consider the influence of the free swing damping of the plate.Therefore,the calculated results are higher than the experimental results.

5.Conclusions

In this study,experiments of UAV impact with a flat plate are conducted by using the air gun method at different strike velocities.The corresponding numerical simulation is carried out by using the explicit finite element software PAMCRASH.The predicted damage to the UAV and strain on the flat plate during the strike process are compared with the test results.The following conclusions can be drawn from this study:

(1)Instead of the expensive rocket pulley test method,first,an air gun was established to conduct the UAV strike test.The test results show that the actual velocity of the UAV under each strike test condition is very close to the predetermined velocity, and the impact attitude of the UAV is basically consistent with the expected attitude.This indicates that the air gun specially established for the UAV strike test is reasonable and reliable.

(2) The connecting wires of the strain gauge mostly arranged at the center position of the flat plate are severely stretched and dragged during the measurement, and only a small amount of effective strain data is obtained.The dynamic strain response indicated that the farther it is from the flat plate impact area, the smaller the influence of the nonuniformity of the UAV mass distribution on the deformation of the impact area is.

(3) The local deformation of the impacted target is uneven due to the distribution of concentrated mass components such as motors, battery, and camera.There are 3 obvious pits, and their locations should correspond to impact by the battery and two motors of the UAV.As the impact velocity of the UAV increases, all parts of the UAV are seriously damaged and basically in a fragmented state, and the battery is greatly deformed after impact, resulting in fire and smoke.

(4)The effective strain corresponding to the test position is extracted from the numerical simulation results of the UAV striking the plate and compared with the test results.The overall trend of the simulation results is in good agreement with the test results, and at least for the first three milliseconds of the event,the peak error between the calculated strain and the test result is within 10%.This shows that the numerical simulation model established in this paper is reasonable.

(5) The interaction between the UAV and the flat plate specimen is approximately 2.7 ms, and the UAV numerical simulation model established in this paper can well simulate the real UAV impact process.The UAV numerical method established in the present paper can be used to carry out numerical simulations and evaluations of the collision safety of UAVs against large aircraft and high-value ground targets.

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 supported by the Civil Aviation Security Capacity Building Fund and the Civil Aircraft 13th Five Year Pre-research Project (No.MJ-2018-F-18).