Temperature influences of the recoil characteristics for aluminum honeycomb buffer in the tether-net launcher

Wen-hui Shi ,Shui Yue ,* ,Chun-o Wu ,Zhou Liu ,Zhi Liu ,Bei-ei Zho ,Zhong-hu Du ,Gung-f Go

a School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

b Aerospace System Engineering Shanghai, Shanghai, 201109, China

c Xi'an North Qinghua Electromechancal Co., LTD, Xi'an, 710038, China

Keywords: Tether-net launcher Temperature Aluminum honeycomb buffer Interior ballistic responses Launch recoil characteristics

ABSTRACT Fluctuations in outer space's temperature would affect the spacecraft's regular operation.This paper aims to study the temperature influences of the aluminum honeycomb buffer in the tether-net launcher.Firstly,a buffer structure was designed to attenuate the pyroshock generated by the pyrotechnic device.Secondly,the mechanical properties of aluminum honeycomb at different temperatures were obtained through quasi-static compression experiments.Then,the internal ballistic responses of the launcher were gained by the closed bomb tests and the equivalent classical interior ballistic model.Finally,the recoil performance of the launcher with aluminum honeycomb buffer at different temperatures was studied.It is revealed that the aluminum honeycomb crushing force gradually decreases with the temperature increases.The peak pressure,burning rate coefficient and velocity increase while the peak time decreases with the temperature increase for the interior ballistics.For the launcher recoil responses,the average launch recoil decreases if the aluminum honeycomb doesn't enter the dense stage.The impact acceleration,projectile velocity and displacement increase as the temperature increase.The paper spotlights the temperature's influence on the recoil characteristics of the aluminum honeycomb buffer,which provides a new idea for buffering technology of pyrotechnic devices in a complex space environment.

1.Introduction

The number of space debris increases with the development of human space activities [1].Space debris poses a serious threat to spacecraft safety and affects the launching of new satellites [2,3].Therefore,Active Debris Removal (ADR) techniques have attracted increasing attention from significant space agencies and academic communities all around the world [4].One is the stiff connection capture using robotic arms or tentacles [5];the other is flexible connection capture using tether-net or flying gripper[6].The latter allows the capture from a long distance between the target and the chaser spacecraft [7].Compared with other capture mechanisms for ADR,such a tether-net system has a lighter weight,smaller volume and higher compatibility with an unknown target's shape and dynamic characteristic because of its flexibility.Besides,the tether-net system can perform the capture at a safe distance from the space target and does not need relative attitude control at a high cost [8],and the tether-net technique becomes a research hotspot [9].

Removing space debris using a tether-net system includes four phases: launch,contact,closing and pulling.The main launch methods of tether-net include spring ejection[10]and pyrotechnic launching [11].Pyrotechnic devices are widely used by the aerospace and defense industries [12].They provide high efficiency,high energy per unit weight,lighter weight,and controllable initiation and output energies [13,14].During the work of those pyrotechnic devices,a harsh mechanical environment known as pyroshock is inevitably induced by explosions with high frequency,short duration and high acceleration shock response,which could damage the nearby micro mechanism and hardware sensitive to high-frequency shock,and even cause disastrous flight accidents[15].Pyroshock rarely causes damage to structural members,and it can easily cause failures in electronic and optical components that are sensitive to high-frequency energy and failures in the relay and magnetic components that are sensitive to low frequency ranges from 2 to 4 kHz[16].Moening showed that 74% of the flight failures that occurred from 1963 to 1985 were highly suspected caused by pyroshock [17].Since 1960,the National Aeronautic and Space Administration (NASA) [18],European Space Agency (ESA) [19],Sandia National Laboratories (SNL) [20,21]and the United States Military (USM) [22]have performed many standards to guarantee the reliability of launching missions.The published kinds of literature on pyroshock have mainly focused on the modeling and experiments of different pyrotechnic devices and there are relatively few reports on pyroshock isolation [23,24].

Honeycomb structures are extensively applied to engineering and various industries such as aviation,aerospace,and transportation as load and thermal-resistance barriers,the core of sandwich structures,and impact energy-absorbing structures due to superior mechanical properties and considerable loadingbearing advantages impact [25,26].Aluminum honeycomb can absorb kinetic energy from impact and delay or attenuate stress waves in a typical explosion [27,28].The environment that spacecraft work in outer is terrible due to the external temperature being up and down,which will cause a great test to the regular operation of the spacecraft.With radiation from other stars,spacecraft in space absorbs heat,causing temperature fluctuations.The temperature change has a great relationship with the orbit of the spacecraft.It will also cause the thermal response of the spacecraft's internal structure,equipment,deformation,vibration and other consequences to affect its regular operation during the life period.Therefore,it is necessary to consider the change in space temperature when reducing the impact of the launch of a pyrotechnical device on the satellite platform through a buffer.

It innovatively introduced a buffer structure using an aluminum honeycomb to attenuate the pyroshock generated by the tether-net launcher in this paper.Firstly,the characteristics of aluminum honeycomb and gunpowder at different temperatures were obtained through experiments and simulations.Secondly,a recoil experiment was carried out to validate the numerical simulation.Finally,the temperature effects of the launcher with aluminum honeycomb buffer were analyzed.

This paper is organized as follows.In Section 2,the structure and working process of the aluminum honeycomb buffer is discussed.The quasi-static compression experiments and simulations of aluminum honeycomb at different temperatures and the theory of the crushable foam plasticity model are presented in Section 3.Closed bomb tests and internal ballistic properties at different temperatures are researched in Section 4.Recoil simulation,verification experiment and launch characteristics at different temperatures are discussed in Section 5,and the conclusions are provided in Section 6.

2.The structure and working process of the aluminum honeycomb buffer

A new buffer structure was designed in this paper,as is shown in Fig.1 and Table 1.It mainly includes a chamber,an aluminum honeycomb buffer and an igniter.The gunpowder is placed between the chamber and the chamber cover.An aluminum honeycomb buffer is put between the top plate and bottom plate,and the bottom plate is tied to the launch frame.There are six throughholes in the top plate,and a sleeve is installed on each throughhole.The sleeves are fixed on the bottom plate through threads to limit the movement direction of the top plate and aluminum honeycomb.

Fig.1.Buffer structure.

Table 1 The material for the main parts.

The igniter starts to work after receiving the signal.The igniter fires the gunpowder near the igniter.As the gunpowder continues to burn,a large amount of high-temperature and high-pressure gas will be produced,which works on the projectile bottoms to push them moving.The gas also acts on the chamber and chamber cover generating the recoil.The projectiles will be made forward with kinetic energy and reach a certain velocity as they leave the canister.The chamber and chamber cover move downward,causing the top plate to go below.The launch platform will be significantly impacted if the recoil force is too large.Therefore,it is necessary to design a buffer structure between the launch device and the platform for absorbing excess energy to ensure a safe launch.

The aluminum honeycomb begins to collapse when the downward movement of the top plate.The crushing deformation of the aluminum honeycomb absorbs the crushing force that exceeds the value of the aluminum honeycomb's steady-state collapse stage.Therefore,as the gunpowder continues to burn,the launch recoil force can be kept in a stable range,maximizing buffering and ensuring the launcher's and the platform's safety and reliability.

3.The experiment and simulation of aluminum honeycomb at different temperatures

In this section,the mechanical properties of aluminum honeycomb were obtained by quasi-static precompression tests at room temperature and complete crushing tests at different temperatures.The experimental results were used as input parameters of quasistatic simulation to verify the accuracy of the crushable foam plasticity model.

3.1. Quasi-static compression experiments of aluminum honeycomb

According to the mission requirements,the satellite platform will not be affected when the launch recoil is less than 21 kN.As shown in Fig.2,The specimen shape is cirque,with an outer diameter of 184 mm and an inner diameter of 148 mm;the crosssectional area is 8867 mm2.So the plane compression strength is 2.37 MPa.According to the“HB5443-1990 Specification for Durable Aluminium Honeycomb Core Materials for Sandwich Structures”,the aluminum foil material is 3003,with a foil thickness is 0.05 mm.The nominal length and density of aluminum honeycomb cells processed by aluminum foil are 2 mm and 105 kg/m3,respectively.

Fig.2.Dimension of aluminum honeycomb.

The quasi-static compression experiment using ETM series electromechanical universal testing machines was carried out to study the mechanical properties of aluminum honeycomb.The plate compressed the aluminum honeycomb at a 2 mm/min speed.The displacement-load curve acquired through quasi-static compression is shown in Fig.3(a).According to the result,the curve can be divided into four parts: A-B is the elastic stage.The elastic deformation of aluminum honeycomb occurs,and the relationship between displacement and load is linearly proportional.B-C is the dynamic buckling stage;C-D is the steady-state collapse stage,the aluminum honeycomb's primary energy absorption stage.As the displacement increases,the load almost remains unchanged.D-E is the dense stage,and the whole quasistatic compression process ends when the aluminum honeycomb enters the dense stage [29,30].

Fig.3.Displacement load curves: (a) Complete compression;(b) Precompression and complete compression.

The aluminum honeycomb is precompressed for 3 mm to maintain stable energy absorption during the compression energy absorption process,eliminating the B-C dynamic buckling stage,as shown in Fig.3(b).When the precompression aluminum honeycomb is compressed again,the displacement-load curve will be directly transferred from the elastic stage to the steady-state collapse stage,ensuring the stability of the energy absorption effect.

The quasi-static compression experiments were carried out at +40,+30,+20,+10,0,-10,-20 and -30°C to study the temperature effects of the aluminum honeycomb,with three aluminum honeycomb specimens at each temperature.Firstly,the twenty-four aluminum honeycomb specimens were precompressed at quasi-static room temperature(about+10°C),and then the aluminum honeycomb specimens were completely compressed at corresponding temperatures.The specimens were heated in an oven and cooled with liquid nitrogen.Experiment types of equipment are shown in Fig.4.

Fig.4.The types of experiment equipment at different temperatures: (a) High temperature;(b) Low temperature.

The quasi-static experiment results at different temperatures are shown in Fig.5.In the displacement-load curves,‘1′represents the precompression curve of 1#aluminum honeycomb specimen at room temperature,and‘1-1′represents the complete compression curve of 1# aluminum honeycomb specimen at the room temperature.It is clear that the curves of‘3-1′at+40°C,‘3-1′at-10°C and‘1-1′at-30°C are different from the others;the curves are short in the steady-state collapse stage.The reason is that the aluminum honeycomb specimens were squished during the experiments.When one side of the specimen enters the dense stage,the other side is still in the steady-state collapse stage,as shown in Fig.6.Therefore,the curves are invalid,and the data must be removed.

Fig.5.Aluminum honeycomb experiment results: (a) +40 °C;(b) +30 °C;(c) +20 °C;(d) +10 °C;(e) 0 °C;(f) -10 °C;(g) -20 °C;(h) -30 °C.

Fig.6.Invalid aluminum honeycomb specimen.

As is shown in Fig.6,taking +40°C.as an example.At room temperature,‘1′,‘2′and ‘3′are the precompression curves of aluminum honeycomb specimens.Each specimen was crushed by 3 mm to eliminate the dynamic buckling stage.‘1-1′,‘2-1′and‘3-1′are the complete compression curves of specimens at +40°C.By comparing the displacement-load curves of each specimen,it can be found that there is a longer displacement in the elastic stage after being precompressed.The reason is that when the aluminum honeycomb specimen is precompressed,the crushed side of the specimen is destroyed.When the specimen is crushed again,the damaged side continues to be crushed and destroyed.However,it doesn't need to go through the dynamic buckling stage,directly from the elastic stage to the steady-state collapse stage,and finally to the dense section to complete the collapse.

The statistical results of the tests are shown in Table 2.It can be seen that as the temperature increases,the crushing force of aluminum honeycomb specimens gradually decreases.Compared with room temperature,the average force reduces by 13.06% at +40°C and increases by 8.55% at -30°C.There are two main reasons:aluminum foil and organic adhesives.The yield strength of aluminum foil material decreases with the temperature increases.The J71 adhesive developed by Heilongjiang Petrochemical Research Institute is used to prepare aluminum honeycomb.After curing,the adhesive is resin material,softened at high and hardened at low temperatures [31].The common and consistent changes in the strength of aluminum foil and binder at different temperatures eventually change the strength of the honeycomb with temperature.

Table 2 Statistical table of experiment results.

3.2. The simulation of aluminum honeycomb quasi-static compression

3.2.1.The theory of the crushable foam plasticity model

ABAQUS's crushable foam plasticity model for analyzing crushable foams is typically used in energy absorption structures.Two phenomenological constitutive models are presented: the volumetric hardening and isotropic hardening models.Both models use a yield surface with an elliptical dependence of deviatory stress on pressure stress in the meridional plane [32].

The isotropic hardening model assumes symmetric behavior in tension and compression.The yield surface evolution is governed by an equivalent plastic strain,contributing to the volumetric and deviatory plastic strain.Therefore,the isotropic hardening model is adopted in this paper.

The isotropic hardening model was initially developed for metallic foams.The model assumes similar behaviors in tension and compression.The yield surface is an ellipse centered at the origin in thep-q stress plane and evolves in a self-similar manner governed by the equivalent plastic strain [32].

The yield surface for the isotropic hardening model is defined as

where α represents the shape of the yield ellipse in thep-q stress plane,and B defines the size of the yield strength in uniaxial compression.The yield surface is the Mises circle in the deviatory stress plane and an ellipse in the meridional plane,as depicted in Fig.7.

Fig.7.Yield surfaces and flow potential for the isotropic hardening model [32].

The parameter α can be calculated using the initial yield stress in uniaxial compressionand the initial yield stress in hydrostatic compression,as

The strength ratiokmust be in the range of 0 and 3.For many low-density foams,the initial yield surface is close to a circle in thep-qstress plane,which indicates that the value of α is approximately one.The special case ofk=0 corresponds to the Mises yield surface.

The flow potential for the isotropic hardening model is chosen as

where β represents the shape of the flow potential in the p-q stress plane and is related to the plastic Poisson's ratio vp,by

The plastic Poisson's ratio,which is the ratio of the transverse to the longitudinal plastic strain under uniaxial compression,should be defined by the user;and it must be in the range of -1 and 0.5.The upper limitvp=0.5 corresponds to an incompressible plastic flow[33].

The plastic flow is associative when the value of β is the same as that of α.In general,the plastic flow does not associate with allowing for the independent calibrations of the yield surface shape and the plastic Poisson's ratio.For many low-density foams,the plastic Poisson's ratio is nearly zero,corresponding to a value of β=2.12 [34].

When α and β are identical,the plastic flow is correlated.By default,the plastic flow is uncorrelated,allowing the yield surface.Furthermore,the plastic Poisson's ratio is calibrated independently of each other.Suppose only the value of plastic Poisson's ratio vpis obtained.In that case,the relevant plastic flow can be selected,and the compression yield stress ratio k can be calculated according to the plastic Poisson's ratio vp

A simple uniaxial compression test is sufficient to define the evolution of the yield surface.The hardening law defines the yield stress value in uniaxial compression as a function of the absolute value of the axial plastic strain.

The engineering strain-stress curve of the aluminum honeycomb can be obtained from the displacement-load curve obtained by the above axial compression experiment.The engineering strain εengand the engineering stress σengare defined as follows:

whereFis the tension or pressure exerted on a specimen at the moment,A0is the initial sectional area of the specimen,lis the instantaneous distance length after deformation,andl0is the initial length.Engineering strain and stress have positive and negative differences.

The cross-section area used for engineering stress is the cross in the state of no stress before experimental loading.However,in the actual loading process,axial deformation of materials is accompanied by transverse deformation,resulting in changes in the real cross-section during loading.True stress σtruerefers to the true stress during loading,which is derived from the force and true section

whereAtrueis the instantaneous cross-section area at a certain time during loading.

The true stress cannot be directly measured experimentally but is usually calculated by a series of assumptions.For most foam materials,the plastic Poisson's ratio is generally 0,and the transverse deformation is minimal in the compression process.It can usually be considered that the cross-section area of foam materials does not change during compression.Therefore,for foam materials,true stress is equal to engineering stress.The instantaneous lengthlof the specimen in the tensile process was differentiated,and the true strain increment dεtrueat a certain moment was obtained as follows:

The true strain can be obtained by integrating the above equation εtrue

Therefore,the relationship between the true strain and engineering strain can be obtained

The true stress-strain curves of aluminum honeycomb can be obtained by smoothing the true stress and strain data,and the main material properties of aluminum honeycomb is shown in Table 3.

Table 3 Material properties of aluminum honeycomb.

3.2.2.The simulation model

A simulation model was established according to the aluminum honeycomb quasi-static compression experiment,as shown in Fig.8.The plate and base deformation during the quasi-static compression process is minimal and can be ignored.So they are regarded as rigid bodies,and the aluminum honeycomb adopts the plastic crushable foam model.And the details of the finite element model are shown in Table 4.The base was fixed.The plate could only move down on theZ-axis at a certain speed of 100 mm/s.

Fig.8.Simulation model.

Table 4 Main parameters of the finite element model.

The displacement-load curves of the aluminum honeycomb in the simulation are shown in Fig.9.It can be seen that the displacement-load curves of the simulation and experiment are consistent.Different aluminum honeycomb crushing force peaks are distant in the same experimental conditions.Therefore,the simulation accuracy must be judged by the steady-state collapse part in the simulation and experiment displacement-load curves.In the steady-state collapse stage (displacement in 3-10 mm),the average value of the experiment collapse force is 20.044 kN.The average simulation value is 19.978 kN,and the error is 0.33% compared with the experiment.

Fig.9.Experiment and simulation displacement-load curves.

3.3. The simulation and test results

Simulation and test results of aluminum honeycomb specimens at different temperatures are shown in Fig.10,and the statistical data of the simulation and test results are shown in Table 5.At each temperature,the displacement-load curves of aluminum honeycomb specimens directly transition from the elastic stage to the steady-state collapse stage and finally to the dense section,showing the same trend.Through data statistics,the maximum and minimum error of the experiment and simulation crushing force at different temperatures is 0.46% and 0.02% in the steady-state,and the total average error is 0.255%,proving the correctness of the plastic crushing foam model and the quasi-static crushing simulation model.

Fig.10.Experimental and simulation results: (a) +40 °C;(b) +30 °C;(c) +20 °C;(d) +10 °C;(e) 0 °C;(f) -10 °C;(g) -20 °C;(h) -30 °C.

Table 5 Statistical table of test and simulation results.

4.The interior ballistic properties of the pyrotechnic device at different temperatures

In this section,the powder power and burning rate coefficient of gunpowder were obtained by closed bomb tests at different temperatures,which were used as the input parameters of the internal ballistic model to get the properties of the pyrotechnic device.

4.1. The closed bomb tests

In internal ballistic experiments,closed bomb devices are often used to study gunpowder's combustion and gas formation under constant volume conditions [35].Two critical data are obtained from the closed bomb test: peak pressure and peak time.The powder power and burning rate coefficient in the burning rate equation of gunpowder can be gained,which can be used for internal ballistic analysis.

In a closed bomb device,excluding heat loss,according to the first law of thermodynamics [36].

where dQis the change in heat energy into the working volume,dEis the change in energy in the gas,andpdWis the change in energy of work done by gas expansion.

Under the condition of constant volume,the volume of gunpowder is tiny,andpdWcan be ignored,then Eq.(13) can be changed into

During the combustion of gunpowder,the mass of gas ωg=ωψ increases.Therefore,the heat is increasing

where ω is the mass of gunpowder charge,ψ is the mass fraction of gunpowder burned off,ωgis the mass of charge in the gas phase of gunpowder combustion,and QWis the explosive heat of gunpowder.

Under the condition of constant volume,the gaseous inner energy is expressed as

Introduce specific heat ratiok=cp/cv,and consider the Mayer equation:

wherecpis the specific heat of gunpowder at constant pressure,cVis the specific heat of gunpowder at constant volume,Tis temperature,Ris the gas constant;α=1×10-3m3·kg-1is co-volume,pis pressure,and θ=k-1 is the thermal coefficient.Eqs.(15) and(20) can be obtained simultaneously

wheref=RT1is powder power.

When the mass combustion ratio of gunpowder is ψ,pψ=p,Wψ=W,

whereWψis the free volume of the chamber,andW0is the initial volume of the chamber.

Before the gunpowder burns,i.e.ψ=0,Wψ=W0-ω/δ;and when the gunpowder is finished burning,i.e.ψ=1,Wψ=W0-αω.According to Eq.(23),the maximum pressurepmmunder constant volume condition occurs at the moment when the gunpowder combustion ends,

Make the packing density Δ=ω/W0,

The closed bomb tests were carried out at+40,+10 and-30°C to study the gunpowder properties at different temperatures.And three tests were performed at each temperature to avoid the experiment's randomness.The structure of the closed bomb in this study is shown in Fig.11;one section of the cylinder is screwed into the igniter plug 2,which relies on an electric current to gunpowder 3,thus causing gunpowder 4 to burn.The pressure produced by gunpowder combustion and its time-varying law is recorded by the pressure sensor 5 screwed into the other end and various recording instruments.In this test,the chamber volume is 530 mL,and the mass of gunpowder 4 is 7.3 g.

Fig.11.Structure of closed bomb.

Fig.12.+40 °C: (a) 1#;(b) 2#;(c) 3#.

Fig.13.+10 °C: (a) 1#;(b) 2#;(c) 3#.

The internal ballistic equations under a constant volume state were established to obtain the two key parameters: gunpowder powder power and burning rate coefficient.The results of tests and simulations are shown in Figs.12-14.It can be seen from the pressure curves that the simulation results are in good agreement with the test results.The pressure curves at different temperatures increase from zero until it remains stable.In the constant volume,at the initial ignition stage,the chamber pressure rises gradually with the combustion of the gunpowder.When the gunpowder gas is filled with the container,the chamber pressure will remain stable with the gunpowder's continued combustion until the burst is completed.

To better match the pressure curves of the test and simulation,it is necessary to offset the simulated pressure curve in time to ensure the accuracy of the internal ballistic parameters.The initial chamber pressure doesn't affect the peak pressure and peak time,so the error is negligible.

The peak pressure,burning rate coefficient and powder power at different temperatures are shown in Table 6 according to the tests and the solution of the constant volume internal ballistic equation.And in the table,Pemrepresents the experiment peak chamber pressure,Psmrepresents the simulation peak chamber pressure andu1represents the burning rate coefficient.Compared with the experimental results,the maximum error of peak pressure simulation is 2.42%,and the minimum error is 0%,proving the accuracy of internal ballistic simulation at different temperatures under constant volume.

Table 6 Table of test and simulation results of closed explosive.

Eq.(26)can solve the powder powerf.Therefore,it can be seen that the powder power is only related to the peak pressurePmand the burning rate coefficientu1obtained through the test data optimization.Moreover,the peak pressurePmand the burning rate coefficientu1increase gradually with the temperature increase.The powder powerfrefers to the power of gunpowder per unit mass,so the higher the powder power,the higher the peak pressure.The burning rate coefficientu1represents the speed of combustion of gunpowder.The larger the burning rate coefficient,the faster the gunpowder combustion rate is and the shorter the peak pressure time.It can be seen from Figs.12-14 that the average time to peak pressure of gunpowder chamber pressure at+40°C is the shortest,which is about 2.28 ms,the time is about 3 ms at +10°C,and the longest time is approximately 3.40 ms at -30°C.

Figs.14.-30 °C: (a) 1#;(b) 2#;(c) 3#.

In conclusion,as the temperature increases,gunpowder's peak pressure and burning rate coefficient increase while the peak time decreases.

4.2. Internal ballistic properties at different temperatures

Studying the launcher's interior ballistic is necessary to obtain its recoil force.The six launch canisters share the same chamber.According to the parameter equivalence rule,the projectile's total mass is equivalent to the sum of the mass of six projectiles.The total cross-sectional area of the launch canister is equal to the sum of the cross-sectional area of six launch canisters.

Each projectile is symmetrically fixed in the launch canister by two copper pins with a diameter of 2.6 mm,and the shear strength of a copper pin is 300 MPa.Thus,the shear force of a single copper pin is 1600 N,and the total shear force of a single launch canister is 3200 N.The shear force can be converted into the projectile starting pressureP0=3.52 MPa.

The interior ballistic properties of the launcher can be acquired by the equivalent launch model adopting the classical internal ballistic equation,which is as follows [37,38]:

For the above internal ballistic equation,the main calculation parameters are shown in Table 7,and the results of the internal ballistic at +10°C are demonstrated in Fig.15.The duration of the chamber pressure of the launcher is 6.09 ms,and the maximum chamber pressurePmis 8.67 MPa.

Fig.15.Interior ballistics curves: (a) Chamber pressure curves;(b) Displacement and velocity curves.

When the pressure produced by gunpowder in the chamber doesn't meet the starting chamber pressure,the projectiles stay still,as is shown in stages A-C in Fig.15(a).In stage C-Pm,the projectiles move after the pressure exceeds the starting chamber pressure.The influence of the rate of gunpowder gas generation on chamber pressure is greater than that of the growth of space volume after projectile motion,and the pressure curve keeps rising.When these two influences reach balance,chamber pressure reaches the maximum.In stages Pm-D,with the continuous increase of the projectile velocity,the influence of the rise of the space volume after the projectile movement exceeds the effect of the gas generation rate,and the chamber pressure begins to decline.When the powder burns completely,the chamber pressure decreases with the increases in the velocity of the projectiles.

As described earlier,a single projectile is fixed by copper pins before firing,and only when the chamber pressure exceeds the shear strength of the copper pins (i.e.,the starting chamber pressure) does the projectile begins to move.Thus,the chamber pressure loaded on the projectile is divided into A-B-C and C-D.

As shown in Fig.15(b),the projectile's distance away from the launcher canister is 55 mm,and the projectile's velocity is 22.25 m/s.The displacement and velocity of the projectile are zero for about 2 ms at the beginning.The reason is that the chamber pressure has not reached the starting chamber pressure.When the pressure exceeds the starting chamber pressure,the projectile moves until it leaves the launch canister.

The interior ballistic curves at different temperatures are shown in Fig.16.It can be seen that the peak chamber pressure and the projectile launch velocity increase with the temperature increase,but the peak time and projectile flight time are reduced.The reason is that with the temperature increase,the peak pressure,burning rate coefficient and powder power of gunpowder increase.

Fig.16.Interior ballistics curves at different temperatures: (a) Chamber pressure curves;(b) Velocity curves;(c) Displacement curves.

5.The recoil simulation and experiment

In this section,based on the aluminum honeycomb and interior ballistic characteristics at different temperatures,the recoil model of the tether-net launcher was established,which was verified by the experiment,.and the recoil performance of the launcher at different temperatures was analyzed.

5.1. Recoil simulation and verification experiment

The dynamic launch model was built in ABAQUS/EXPLICIT.The launch frame is fixed,and because the rest of the parts have a more negligible effect on the launch recoil force,the aluminum honeycomb components are set to the rigid body to speed up the calculation.

In the quasi-static test,the initial height of the aluminum honeycomb specimen is 12 mm,the height after compression is 2 mm,and the loading speed is 2 mm/min,so the strain rate of the quasistatic test is 0.0028 s-1.In the launch recoil test,the initial height of the aluminum honeycomb is about 9 mm,the average height after compression is 5.133 mm,and the duration is about 6 ms,so the strain rate in the dynamic test is 71 s-1.

According to the law of conservation of energy and the principle of minimum energy,obtained quasi-static mean plastic collapse stress under the Tresca yield criterion [39].

where σ0is the yield stress of aluminum honeycomb material,tis aluminum honeycomb cell thickness,andlis cell length.

The cross-sectional area of the specimen is 8867 mm2,and the collapse force is 21 kN,so the plane compression strength σm=2.37 MPa.To incorporate the strain rate effect of materials into the Cowper-Symonds,the formula of dynamic compressive plateau stress can be written as

whereDandpare the strain rate material constants,for Al3003[40],D=24295.5 s-1,andp=1.094,the average height after compression is 5.133 mm,and the duration is about 6 ms,v=0.8555 m/s.

Meanwhile,a recoil experiment was designed to verify the accuracy of the launch recoil simulation.The experiment layout is shown in Fig.17.

The experiment and simulation process are shown in Fig.18.It can be seen that the experiment and simulation launch process are almost consistent.After the powder is ignited,there is a large amount of high-temperature and high-pressure gas.When the chamber pressure reaches the starting pressure,the copper pin is cut off,and the projectile moves along the launch canisters.After about 6 ms,the projectiles leave away from the launch canisters.The condition of the aluminum honeycomb before and after the experiment is shown in Fig.19.

Fig.18.Experiment and simulation process: (a) t=0 ms;(b) t=2 ms;(c) t=4 ms;(d) t=6 ms;(e) t=6.5 ms;(f) t=10 ms.

Fig.19.Aluminum honeycomb condition: (a) Before the experiment;(b) After the experiment.

The projectile's velocity is 21.75 m/s,measured by the experiment.As shown in Fig.20,the projectile's displacement in interior ballistic and simulation is 55 mm and 60.8 mm simultaneously.And the velocity of the projectile in interior ballistic and simulation is 22.25 m/s and 23.849 m/s.So the interior ballistic velocity and simulation velocity errors are 2.3% and 9.65% compared with the experiment.The main reason is that there is a sealing ring between the projectile and the canister in the experiment.The sealing ring and the launch canister will produce greater friction to hinder the projectile's movement,leading to the experiment speed being less than the calculation and simulation speed of the interior ballistic.Moreover,the projectiles have a different displacements simultaneously because of the velocity error.

The recoil curves of the experiment and simulation are shown in Fig.21.The peak recoil force of the experiment and simulation is 24.1328 kN and 18.962 kN.For the steady-state collapse stage(≥15 kN),the experiment and simulation average recoil forces are 19.552 kN and 18.66 kN.Compared with the experiment,the peak recoil error of the simulation is 21.4%,and the average recoil error is 4.56%.

Fig.21.Recoil force comparison curves of experiment and simulation.

As is shown in Fig.21,the recoil force curves of the experiment and simulation have little difference between the initial and end,mainly because the chamber pressure obtained by the interior ballistic model is the average chamber pressure,which has an inevitable error with the actual chamber pressure.

In the experiment,recoil force presented two trends in the steady-state collapse stage and the first was the downward oscillation in the first half and the upward oscillation in the second half.It was mainly because with the increase of chamber pressure,the recoil speed of the chamber began to increase,leading to the rise of aluminum honeycomb collapse force.Therefore,in the dynamic launch simulation,the recoil force remains constant in the steadystate collapse stage,which is different from the oscillation phenomenon in the experiment.But these differences accounted for only 4.56% of the average recoil,so they were considered reasonable.

In general,the simulation results match the experiment results in trends and magnitudes,validating the accuracy and reliability of the dynamic model.This provides a solid foundation for the following parameter analysis of deploying performance.

5.2. The launch characteristics at different temperatures

To explore the influence of different temperatures on the tethernet launcher's recoil force and emission characteristics,the launch dynamics simulation at +40,+10 and -30°C was set up.Fig.18 shows the launching characteristics at different temperatures,and Table 8 lists the critical parameters in the simulation results.

Table 8 Statistical table of simulation results.

The recoil curve can be divided into three stages for launch recoil: the rising stage,the stable stage,and the falling stage,respectively.In the increasing stage,+40°C firstly rises to the stable phase,and -30°C finally rises to the stable stage.As the temperature decreases,the burning rate and powder power decrease,resulting in a long time for chamber pressure to reach the honeycomb chamber pressure.In the stable stage,as shown in Table 8,the average force increases with the decrease in temperature,mainly because the aluminum honeycomb will soften at high and harden at low temperatures.

For maximum recoil,the biggest is at+40°C,and the temperatures are more significant than the other.The reason is mainly due to the enhanced performance of gunpowder at +40°C resulting in more impulse and the softening of aluminum honeycomb,leading to the aluminum honeycomb in the compression process quickly into the dense stage,making a secondary increase in recoil force.At the temperature of +10°C and -30°C,the aluminum honeycomb doesn't enter the dense stage,so the difference between the average and maximum recoil force at these two temperatures is small.And because of the relationship between powder power and aluminum honeycomb crushing force with temperature,the lower the temperature,the shorter the recoil stability stage duration.In conclusion,under the premise that aluminum honeycomb doesn't enter the dense phase during the launching process,the average recoil decreases with the temperature increase.

As for the impact acceleration,as shown in Fig.22(b) and Table 8,the maximum impact acceleration reaches 5651.9 g at +40°C,which is much higher than the other temperatures,mainly because the aluminum honeycomb enters the dense stage at this temperature and the recoil increases significantly.With the temperature decrease,the impulse produced by gunpowder decreases,and the crushing force of the aluminum honeycomb rises so that the aluminum honeycomb at the other two temperatures doesn't enter the dense stage,so the impact acceleration gradually decreases.To sum up,the impact acceleration produced by the tether-net launcher gradually increases with the temperature increase.

Fig.22.Launching characteristics at different temperatures: (a) Recoil force curves;(b) Acceleration curves;(c) Velocity curves;(d) Displacement curves.

As shown in Fig.22(c),the curve can be divided into the rising and stable stages for projectile launch velocity.In the rising phase,as the powder power and burning rate coefficient increase with the temperature increase,the time for chamber pressure to reach the starting chamber pressure becomes shorter.Hence,the projectile starts to move at +40°C firstly.As the powder continues to burn,the velocity of the projectile increases,and when it leaves the canister and keeps steady.As shown in Table 8,the projectile's speed fells by 2.12 m/s from the maximum to the final at +40°C.This is mainly because the aluminum honeycomb quickly reaches into the dense phase,increasing the chamber recoil displacement and velocity,leading to the projectile producing the opposite direction speed before it leaves the canister,which slows down the projectile velocity.At the other two temperatures,the aluminum honeycomb didn't enter the dense stage,so the maximum and final velocity of the projectile varied little.At the same time,it can also be seen that on the premise that the aluminum honeycomb doesn't enter the dense stage,the launch velocity of the projectiles increases with the temperature increases.

As for the projectile displacement curve,as shown in Fig.22(d),the projectile's displacement also decreased due to the projectile velocity decrease at +40°C,while the projectile displacement remained stable at the other two temperatures.If the aluminum honeycomb doesn't enter the dense stage,the projectile displacement will gradually increase with increasing temperature.

To sum up,with the temperature increases,the average launch recoil of the tether-net launcher decreases when the aluminum honeycomb doesn't enter the dense stage.However,the impact acceleration,projectile velocity and displacement will increase.

6.Conclusions

This paper designed a new buffer structure for the tether-net launcher to attenuate the large recoil force and impact.The characteristics of aluminum honeycomb and gunpowder at different temperatures were obtained through experiments and simulations.Based on the above data,the launching process was simulated with ABAQUS/EXPLICIT.In addition,the temperature effects on the tether-net launcher's recoil force and emission characteristics were analyzed.Some conclusions can be drawn as follows:

(1) As the temperature increases,the crushing force of the aluminum honeycomb gradually decreases.Compared with force at+10°C,the average force reduces by 13.06% at+40°C and increases by 8.55% at -30°C.

(2) Compared with responses at +10°C,when the temperature is +40°C,the average burning rate coefficient increase by 29.08%,the peak pressure increases by 6.9%,and the final velocity increase by 2.33%.When the temperature is-30°C,the average burning rate coefficient,the peak pressure and the final velocity decrease by 13.38%,6.44% and 2.43%,respectively.

(3) Under the assumption that the aluminum honeycomb does not enter the dense stage with increasing temperature,the average recoil force would decrease by 3.82% at +40°C and increase by 11.69% at -30°C compared with +10°C.With temperature increases,the impact acceleration,projectile velocity and displacement will increase.

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.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No.52102436);the Fundamental Research Funds for the Central Universities (Grant No.30920021109);Natural Science Foundation of Jiangsu Province(BK20200496);China Postdoctoral Science Foundation (Grant No.2020M681615);the project of Key Laboratory of Impact and Safety Engineering (Ningbo University),Ministry of Education (Grant No.CJ202107);and the State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and astronautics) (Grant No.MCMS-E-0221Y01).