Xin-yun Liu ,D-lin Wu ,Jin Hou

a Shijiazhuang Campus,Army Engineering University,Shijiazhuang,050003,China

b Naval University of Engineering,Wuhan,430000,China

Keywords: Naval gun Colloidal fluid damper Cartridge lock CFD MBD

ABSTRACT The test shell without projectile belt is widely used in the teaching,inspection and maintenance of modern automatic naval guns.In order to ensure the normal work of each mechanism,it is very important to design the buffer and limit of the test shell during the process of entering the bore.Taking a certain type of medium caliber naval gun as the research object,the design of colloidal fluid damper and cartridge lock was proposed to ensure the reliability of entering the bore and closing the breechblock.By combining the simulation methods of computational fluid dynamics(CFD)and multibody system dynamic(MBD),it was analyzed whether the structural design can meet the engineering requirements.The research results show that the colloidal fluid damper can dissipate a large amount of kinetic energy of the shell,and the cartridge lock can limit the rebound movement.The combination of the two ensures the smooth process of closing the breechblock.The research provides a design method for the process of the test shell entering the bore,and provides theoretical support for the feasibility of the method.

1.Introduction

Test shells are widely used in modern naval guns with high automation,and are also called bore shells or training shells.Test shells mainly replace live shells during teaching and demonstration,inspection and maintenance,research and experiment,and complete the movement process from the magazine to the bore of the barrel.When using live shell,the projectile belt will be stuck in the ri fling and dif ficult to take out.Compared with the live shell,the test shell has almost the same geometry,mass,center of mass,and moment of inertia,except that it has no projectile belt structure.

In order to ensure a high rate of fire and shorten the time of reloading,the ammunition loader of a certain medium caliber naval gun gives the shell a large kinetic energy.When a live shell enters the bore,the copper elastic belt contacts with the beginning of the ri fling,resulting in plastic deformation and friction.This will cause all the kinetic energy of the shell to be consumed and be tightly stuck in the barrel.When a test shell enters the bore,only part of the kinetic energy is consumed when the shell contacts the inner wall of the barrel and when the bottom edge of cartridge collides with the tail of the barrel.At this time,the shell will rebound,which may cause the failure to close the breechblock.Therefore,it becomes particularly important to design additional buffering and limiting structures to ensure the reliability of closing the breechblock.This article will analyze the effectiveness of the designed colloidal fluid damper and cartridge lock.

The core of the colloidal fluid damper is the internal viscoelastic material,which is generally a macromolecule silicon-oxygen organic polymer,with dual characteristics of elasticity and viscosity.This new functional material has excellent compressibility,chemical stability and damping viscosity due to its unique molecular helix structure and many molecular side groups[1].The earliest colloidal fluid damper in the world appeared in the 1960s.Until today,its performance and principle are still being studied by scholars.In recent years,the colloidal fluid damper has developed rapidly,and its application field has become wider and wider.Colloidal dampers have appeared in both civil and military applications,such as high-speed rail,automobiles,construction,and mechanical equipment,as well as armored vehicles,artillery,warships,aircraft,and radar equipment[2-4].

The differential colloidal fluid damper was designed to be installed in the test shell.The damper can convert a large amount of kinetic energy into heat energy and dissipate it.Cartridge lock is a structure used to block the shell and limit its rebound movement.It is designed to be installed behind the barrel,allowing the shells to pass forward and preventing backwards.Whether the combination of the two structures can achieve the expected effect of buffering and limiting is our research focus.

Due to the uniqueness of the application of the differential damper installed in the test shell,no relevant literature has been studied.For the colloidal fluid damper,early scholars used simplified mathematical models or empirical formulas to analyze and reduce the damping force to a function related to velocity.The damping force proposed by Pekcan[5]is a function of velocity.The damping force proposed by Terenzij[6]is a polynomial function of velocity.Meram[7]established Maxwell model,Kelvin model,Oscillation model of thermoplastic polyurethane elastomeric buffer,and compared with the experimental results.Wang Zhiqian[8]established a fractional Maxwell viscoelastic model for colloidal dampers,which can accurately simulate the start-up flow characteristics in the ori fice or gap.Ding Jianhua[9],Liu Hongliang[10],Xu Zhongsi[11,12],Tong Zhihui[13]and others analyzed the flow of fluid through gaps and holes,and proposed that the damping force is a function related to velocity,geometric parameters,and material parameters.On this basis,Qi Mengxiao[14]used AMESim hydraulic system simulation software to analyze the colloidal damper.Jia Jiuhong[15,16]and Wang Hongqin[17]analyzed the fluid in the gap based on the idea of differentiation,and also proposed a function relates to velocity.Ma Yanjin[18]established a velocity dependent function model for the colloidal damper,which was veri fied by experiments.Wang Donghua[19]used the uniform velocity compression experiment and the impact experiment to determine the undetermined coef ficient of the colloidal damper on the machine gun,and carried out dynamic simulation analysis in ADAMS.Chen Shuyun[20]used genetic algorithm and limited memory method to carry out parameter identi fication research on the velocity dependent functional model of colloidal damper.

However,the accuracy of these methods was limited after a large number of simpli fied models.With the development of computational fluid dynamics,using CFD method to analyze the colloidal fluid damper makes the results more accurate and intuitive.Tong Huan[21]established a fluid mesh model for colloidal dampers with holes and without gaps,and obtained velocity and pressure contour during compression and tension.Guo Qiang[22]and Ding Xingwu[23]also established a CFD model of a hole-type colloidal damper,compared the experimental and simulation curves of the damping force,and proved the feasibility of the numerical calculation method.Sun Jingya[24]established a laminar CFD model with"double rod and gap type"damper,and compared it with the experimental data of the drop hammer impact.Di Changchun[25]established a three dimensional fluid-solid coupling model of the colloid recoil device and veri fied it by firing experiments.Wael Elsaady[26]performed magnetic field and CFD simulation calculations on a magnetorheological damper,and the research methods and conclusions have certain reference value.

When the shell enters the bore,it involves multiple nonlinear contact forces,friction forces,and colloidal fluid damping forces.It is an extremely complex problem of the combination of multibody system dynamics(MBD)and computational fluid dynamics(CFD).By analyzing the action mechanism of the differential damper,the article calculated and obtained the movement laws of the test shell and the relevant mechanism of the naval gun.Based on the analysis and calculation of the simulation method,we finally predicted and evaluated whether this design can achieve the expected goal.

This study will innovatively propose a design that uses a colloidal damper and a cartridge lock to ensure that the test shell can smoothly enter the bore.For the first time,the CFD method will be used to accurately calculate the flow characteristics and mechanical properties of the differential colloidal fluid damper,and the MBD method will be used to accurately analyze and predict the force and motion of the relevant naval gun components.

2.Structural design

2.1.Differential colloidal fluid damper

Fig.1.Structure schematic diagram of the colloidal damper.

There are many types of colloidal fluid dampers,which can be divided into"double rod type"and"single rod type",and can also be divided into"gap type"and"hole type".Due to the short stroke and large capacity of the damper during the process of the shell entering the bore,the non-equal diameter double rod type was used.Compared with the single rod type,the design diameter is larger and the strength is higher.Compared with the equal diameter double rod type,it can store and release energy.The structural schematic diagram of the damper is shown in Fig.1,which is mainly composed of piston rod,piston,cylinder,limit block and colloidal fluid material.When the piston and piston rod move towards the compression direction,the space in the cylinder is reduced and the colloidal fluid is compressed.The elastic potential energy is stored,and at the same time,the colloidal fluid flows through the annular gap to generate a damping force.When the piston and piston rod move towards the recovery direction,the elastic potential energy is released,and the colloidal fluid flows through the annular gap in the opposite direction,continuing to dissipate energy.

The damper installed in the test shell is also called a differential colloidal damper.This is because in practice,both the piston rod and the cylinder are moving,and the relative motion between the two is the motion that enables the damper to work.The differential does not refer to the structure of damper,but to the purpose of damper.As shown in Fig.2,the differential colloidal damper is installed between the projectile and the cartridge,and is wrapped inside.The damper cylinder is fixed on the projectile by the limit structure and the stop screw,and the damper piston rod is fixed on the cartridge by the stop pin.The axial separation and combined movement between the projectile and the cartridge are the compression and recovery movement of the damper.The damper has a design with a certain initial pressure of colloidal fluid and a limit structure,which can ensure that the projectile and the cartridge are relatively stationary when there is no large external force in the axial direction.Table 1 shows geometric design dimensions of the colloidal damper.

Table 2 CFD model parameters.

Fig.2.Structural schematic diagram of the test shell.

Table 1 Geometric dimensions of the colloidal damper(mm).

The resistanceF（x’，v’）of the damper is a nonlinear function of the relative displacementx’and relative velocity v’between the projectile and the cartridge.During the process of transporting and pushing the shell,since the force between the projectile and the cartridge is less than the initial force of the damper,there is no relative movement between the two and the damper does not work.When the test shell enters the bore,the bottom edge of cartridge collides with the tail of barrel,and the cartridge velocity v2will drop to zero or even reverse,while the instantaneous velocity of the projectile v1will not change.Relative velocity and relative displacement will occur between the two,and the damper will start working.

Fig.3.Working schematic diagram of the cartridge lock.

2.2.Cartridge lock

Fig.4.Friction coef ficient.

The cartridge lock structure was designed behind the tail of barrel and also under the breechblock.Fig.3 is the working schematic diagram of the cartridge lock,which is mainly composed of stop lever,stop lever shaft,spring and base.The stop lever shaft is fixed on the base,and the stop lever can rotate around the stop lever shaft by a certain angle.The spring with preload can lift the stop lever to the maximum limit angle.When the test shell moves along the axial direction,only the bottom edge of cartridge can contact the upper surface of stop lever.When the test shell moves forward in inertia,the bottom edge of cartridge collides with the stop lever,causing it to be pressed down for a short time.Subsequently,the test shell bounces back,and the stop lever has returned to its original angle.The bottom surface of cartridge collides with the front side of stop lever,which limits the rebound distance of the test shell.The design principle of the cartridge lock is to only allow the test shell to pass in one direction.

3.Theory

3.1.Fluid governing equation

The CFD analysis of colloidal damper involves the fluid governing equation,and its principle is brie fly described.The colloidal fluid in the damper follows three basic physical laws:the law of mass conservation,the law of momentum conservation and the law of energy conservation.They correspond to three fluid governing equation,namely continuity equation,Navier-Stokes equation and energy equation[27].

Where,ρis the fluid density,Vis the fluid velocity vector,fbis the body force,pis the differential pressure,μis the dynamic viscosity,his the speci fic enthalpy,λis the heat conductivity coef ficient,φis the viscous dissipation term,Shis the source terms.

3.2.Mathematical model of colloidal fluid

The colloidal material is a viscoelastic fluid,and its composition is generally composed of macromolecule organic polymers.The typical material is silicone oil,which is a polyorganosiloxane with a chain structure of different degrees of polymerization.In mechanics,it shows both the viscosity of a liquid and the elasticity of a solid,and the viscosity is much larger than that of general fluid.In engineering,the mechanical properties of colloidal fluid materials are generally simpli fied as the Kelvin model,that is,the superposition of elastic model and viscous model.These two characteristics will be modeled separately in the CFD calculation.The following describes the principles of the compressible liquid elastic model and the non-Newtonian viscosity model.

Fig.5.Geometric model of the damper.

Fig.6.Mesh model of the damper.

3.2.1.Elastic model

The elasticity of a liquid is also called compressibility.As shown in Eq.(2),it is described by the simpli fied Tait compressible liquid state equation[28].The bulk modulus of elasticity is used to measure the compressibility of a liquid.The smaller the bulk modulus of elasticity,the easier the liquid is to be compressed.In engineering application,bulk modulus of elasticity is the inherent property of liquid,which is determined by the liquid itself.It is defined as the reciprocal of the relative change value of the liquid volume when the pressure of the liquid changes the unit size at a certain temperature,as shown in Eq.(3).

Where,n1is the liquid density exponent,Eis the bulk modulus,andE=E0+n1Δp,E0is the reference bulk modulus,ρis the liquid density,ρ0is the liquid reference density,pis the liquid pressure,Vis the liquid volume.

Fig.7.Velocity contour of uniform compression analysis.

3.2.2.Viscous model

Fluids can be divided into two categories according to the viscosity model:Newtonian fluids and non-Newtonian fluids.Newtonian fluid refers to a fluid that meets Newton’s internal friction law,and its viscosity value is constant.The viscosity value of non-Newtonian fluid is not constant with the change of shear force and shear rate.

The constitutive equation of viscosity for generalized non-Newtonian fluids can be described by the Ostwald de Waele empirical formula,which is a power-law model[29].The model considers viscosity to be a power function of shear rate,as shown in Eq.(4).

Fig.8.Hysteresis loop of uniform velocity compression.

Where,μis the dynamic viscosity,γis the shear rate,Kis the consistency coef ficient,n2is the rheological index.Whenn2=1,K=μ,the fluid is Newtonian fluid,whenn2>1,it means that the fluid has shear thickening behavior,and the fluid is dilatant fluid in non-Newtonian fluid,whenn2<1,indicating that the fluid has shear thinning behavior,and the fluid is pseudoplastic fluid in non-Newtonian fluid.Most industrial polymer fluids are pseudoplastic,and the rheological index is between 0.15 and 0.6.The colloidal fluid used in this damper is a pseudoplastic fluid.

3.3.Contact model

When the test shell enters the bore,contact and collision will occur between the projectile,the cartridge,the barrel,the breechblock,and the cartridge lock.In multi-body dynamics,the interaction force between components is very important,and it is generally decomposed into normal contact force and tangential friction force.The normal force model is based on Hertz contact theory,and the calculation of normal contact force is shown in Eq.(5).Where,kis the stiffness coef ficient,cis the damping coef ficient,δis the penetration,m1,m2andm3are the stiffness exponent,damping exponent,and indentation exponent,respectively.

The tangential force model is based on sliding friction theory,and the friction coef ficient is a function of the relative speed between the two surfaces,as shown in Fig.4.Where,vdis the dynamic threshold velocity,vsis the static threshold velocity,μdis the dynamic friction coef ficient,μsis the static friction coef ficient.

4.CFD modeling and analysis

4.1.Geometry and meshing

Before generating the CFD mesh,the geometric of the CAD model needs to be processed.The simpli fied differential colloidal fluid damper is shown in Fig.5.Extracted the geometry of the fluid domain between the piston rod,piston,and cylinder to generate a three-dimensional hexahedral structural mesh.In order to achieve the movement of the piston boundary,the cylindrical surface of the piston was used as the interface,and the merged mesh was generated by the Mesh Interface method.As shown in Fig.6,the total number of hexahedral structural mesh is about 1.4 million.

The CFD numerical simulation of the colloidal fluid damper was solved in ANSYS/Fluent.The turbulence model used thek-ε realizable model and the standard wall functions model.The fluid had an initial pressurep0to ensure the initial force of the damper.The maximum compression ratio of the liquid in the stroke is 1.2%,and the extremely low compression ratio makes the elastic constitutive relationship of this process approximately linear.The compressible liquid model and the viscosity model were set according to Eq.(2)and Eq.(4),respectively.Since the axial movement of the piston involves boundary movement and mesh reconstruction,in order to ensure the quality of the reconstructed mesh,the Layering dynamic mesh method was adopted.Some model parameters are shown in Table 2.

4.2.Uniform compression experiment and model verification

Before impact numerical calculation,it is very important and necessary to verify the established model.This paper veri fied by comparing the uniform velocity compression experiment and simulation data of the colloidal damper.The uniform velocity compression experiment of the colloidal damper was carried out on the CSS-55100 universal testing machine.The cylinder was fixed,and the piston rod was loaded and unloaded at a uniform velocity.The pressure and stroke sensors were used to collect the resistance and displacement data,and then the computer recorded and processed the resistance-displacement curve.

In the CFD model,the moving velocity of the mesh dynamic boundary was consistent with the experiment,and it was compressed and recovered at the same velocity.The fluid velocity and streamline distribution results obtained by numerical calculation are shown in Fig.7.The contour shows that the place with the highest fluid velocity is the piston annular gap.It can be seen from the distribution of streamlines that during the process of uniform compression and recovery,the flow is relatively stable without turbulence and belongs to laminar flow.In post-processing,the axial resultant force and displacement curve on the piston boundary were output.Comparing the experimental hysteresis loop and the simulated hysteresis loop,the results are shown in Fig.8.The results show that the simulation curve and the experimental data points are roughly consistent,and the error is within the allowable range.This shows that the model has certain accuracy and credibility,and can be used as the basis for further impact numerical calculation.

4.3.Impact numerical calculation

In order to obtain the mechanical properties of the damper in the process of entering the bore,it is necessary to carry out impact numerical calculation for the model.Unlike the active motion problem with known boundary conditions,the impact simulation cannot clearly know the state of the damper motion at each moment before calculation.This problem is called the passive motion problem.In the passive motion problem,the motion of the object will affect the motion of the fluid,and the motion of the fluid will in turn affect the motion of the object.This problem is also called the bidirectional coupling problem of fluid and solid[30].

Fig.9.Velocity contour of impact analysis.

The solution of this passive motion problem in CFD numerical calculation is to convert passive motion into active motion.First obtain the force and moment of the fluid to the object,then use the force and moment to calculate the acceleration and angular acceleration,and calculate the velocity,angular velocity,displacement and angular displacement by integration.Running this calculation at each time step can update the motion state of objects and fluids in real time.

The test shell was given kinetic energy by the ammunition loader and moved forward,and the velocity was 8 m/s when the bottomedge of cartridge collides with the rear surface of barrel.The relative velocity of projectile and cartridge,that is,the compression velocity of damper,can only reach 7.4 m/s.This will be calculated from the later multibody dynamics model.The designed damper requires that the buffer reaction force cannot be greater than 100 kNand the buffer stroke cannot be greater than 10 mm.The SIX DOF dynamic mesh model was used to simulate this fluid-solid bidirectional coupling problem.The load mass was set to the mass of the projectile 13.5 kg.The 3 rotational degrees of freedom and 2 translational degrees of freedom of the piston were limited,and only the translational movement along axial direction was allowed.The initial velocity of 7.4 m/s was given to the piston boundary,and the displacement of the boundary was limited between 0 mm and 10 mm.

Fig.9 shows the results of fluid velocity and streamline distribution during impact.Since the model is three-dimensional,some streamlines on the axisymmetric surface cannot be displayed continuously.The total time of the damper from the beginning of compression to the completion of recovery is about 7.7 ms,and the maximum compression stroke is 6.78 mm in 2.2 ms.The area with the highest fluid velocity is at the piston gap.During the compression process,with the compression of the damper,the maximum velocity of the fluid gradually decreases from 25 m/s to less than 1 m/s.During the recovery process,the maximumvelocity of the fluid remains stable in the range of 5 mm/s to 6 mm/s until the recovery is completed.The colloidal fluid has a large dynamic viscosity,which makes the streamline smooth and no large vortex appears.It is worth noting that from the contour diagram at 8 ms,although the piston has been reset at 7.7 ms,the colloidal fluid did not stop flowing,and the flow almost stopped until 10 ms.

Through the numerical calculation of impact,the resistancedisplacement hysteresis loopF（x’，v’）of the colloidal fluid damper can be obtained,as shown in Fig.10.During compression process,the resistance first increases and then decreases,and the maximum value reaches 83713 N.During the recovery process,the resistance gradually decreases to 0,and then increases in the reverse direction and remains constant.This is consistent with the design principle of colloidal dampers.

Fig.10.Hysteresis curve of impact analysis.

Fig.11.Elastic force-relative displacement curve.

Fig.12.Viscous force-relative velocity curve.

In order to substitute the mechanical performance parameters of the damper into the next dynamic calculation,the displacementresistance functionF（x’，v’）needs further data processing.The resistance was decomposed into the elastic componentFk（x’）and the viscous component forceFc（v’）of the colloidal fluid.Because the compression ratio is extremely small,the elastic component force can be approximately linear,that is,the liquid density exponent in Eq.(2)was 1.According to the constitutive relation expression(3)of the elastic model,substituting the geometric parameters and initial conditions of the damper,the speci fic expression(6)of the elastic component force was derived.Where,p0is the initial pressure of the colloidal fluid in the damper,S1is the thicker end area of the piston rod,S2is the thinner end area of the piston rod,andV0is the initial volume of the colloidal fluid in the damper.

Fig.13.Topological relationship of the dynamic model.

Fig.14.Multibody dynamics model.

The viscous component forceFc（v’）was obtained by solving the difference between the resistanceF（x’，v’）and the elastic component forceFk（x’）.Fig.11 and Fig.12 are the obtained elastic component force(colloidal fluid elastic force)-relative displacement curve and viscous component force(colloidal fluid damping force)-relative velocity curve,respectively.The positive direction of the abscissa represents the compression direction,and the negative direction represents the recovery direction.The curve shows that the viscous component force has hysteresis and nonlinearity.Although the relative velocity gradually decreases during compression,the viscous component force increases first and then decreases.This is because the velocity at the beginning of the impact is the fastest,and the compressibility occupies a dominant position.Most of the fluid has not yet produced a viscous component force through the piston gap,so the viscous component has a tendency to gradually increase.Then as the velocity decreases,the viscous component force gradually changes to a steady downward trend.However,this situation does not occur during the recovery process,and the viscous component force is positively correlated with the relative velocity.

Fig.16.Relative displacement of the damper.

5.MBD modeling and analysis

5.1.Topology and modeling

Before establishing the dynamic model of the test shell entering the bore,the topological relationship of the model must be established.After simpli fication and omission,only the mechanism related to the process of entering the bore in the naval gun system was retained.Fig.13 shows the topological relationship of the model,and the dynamic model is mainly composed of barrel,breech,breechblock,firing pin,control lever,cartridge extractor,equilibrator arm,reset joystick,reset connecting rod,breechblock joystick,breechblock damper,test shell and cartridge lock.The test shell is composed of projectile,cartridge,cylinder and piston rod,and the cartridge lock is composed of stop lever,stop lever shaft and base.Each part was connected with fixed joints(Fix),revolute joints(Rev),translational joints(Tra),spring force(Spr),contact force(Cont),function force(Force).The viscous component force of the damper obtained by CFD analysis was converted into a spline function force,and the elastic component force of the damper was converted into a linear spring force,and they were applied between the damper cylinder and the damper piston rod.

Fig.17.Relative velocity of the damper.

Finally,a multi-body dynamic model of test shell was established in RecurDyn,and its longitudinal section is shown in Fig.14.The starting time of simulation was the moment when the bottom edge of cartridge just enters the breech.At this time,the test shell velocity was 9166.6 mm/s,which was calculated in advance by the dynamic model including the communition conveyer system,the ammunition loader system,the swinging shell slot,etc.(The model and calculation for this part had been omitted).The breechblock had been lifted and hung on the cartridge extractor.The whole system was in static balance except the test shell,waiting for the shell to enter the bore.

5.2.Dynamic analysis

The model ran the dynamics calculation for 0.2 s,and Fig.15 shows the motion status of each mechanism at the important moment.At 31.8 ms,the test shell completely passes through the cartridge lock and the bottom edge of cartridge contacts the barrel.The cartridge extractor is rotated by the impact force,and the breechblock moves downwards under the action of the reset mechanism and gravity.After a collision,the stop lever rotates counterclockwise around the shaft and compresses the spring.At 34 ms,the bottom edge of cartridge is still close to barrel,the damper is compressed to the maximum,and the projectile and the cartridge are at a short standstill.At 45 ms,the recovered test shell moves in the opposite direction,and the bottom edge of cartridge collides again with the stop lever which have been restored to its original position,but the lever structure limits the backward movement displacement of the test shell.At 160 ms,the breechblock is tightly attached to the bottom edge of cartridge and completely closed.

Fig.16 and Fig.17 show the relative displacement and relative velocity of the obtained colloidal fluid damper.Under the impact velocity of 7.4 m/s,the maximum buffer displacement is about 6.78 mm,which is consistent with the CFD analysis results.Before the collision between the bottom edge of cartridge and the barrel,there is a slight fluctuation in the velocity of damper,which is caused by the bottom edge of cartridge impacting the stop lever.

In order to analyze the necessity of this design,four models with different designs were simulated and compared,including the model without colloidal damper and cartridge lock,only with colloidal damper,only with cartridge lock,and complete design.In the case of without the damper and the cartridge lock(Fig.18a),the rebound velocity of the test shell is very large.This causes the test shell to move below the breechblock before it falls.Eventually,the breechblock and the test shell collided and could not be closed.In the case of only with the damper(Fig.18b),although the rebound velocity is greatly reduced,it will still contact the underside of breechblock and affect the closing velocity of breechblock.In the case of only with the cartridge lock(Fig.18c),because the rebound velocity is too fast,the test shell has already passed the stop lever when it is not raised,and it cannot play a limiting role.Eventually,the breechblock could not be closed.

Fig.19 is the absolute velocity curve of the cartridge with and without the damper.Without the damper,the rebound velocity of the cartridge reached 2.6 m/s.That is,only by collision and friction,the rebound velocity of test shell can only be reduced to 32.5%before entering the bore,and 89.4%kinetic energy was lost.With the damper,the direction of the velocity changed several times after the cartridge collided with the bottom of the barrel,which was the result of the combined action of the barrel and the damper.After the damper was reset,the rebound velocity of the cartridge and the projectile was about 0.9 m/s,and the rebound velocity was reduced to 11.25%before entering the bore.The shell lost 98.7%of the kinetic energy in the whole impact process.

Fig.18.Model comparison.

6.Conclusion

Aiming at the feasibility of the test shell entering the bore designed for a certain type of naval gun,this paper proposed a simulation analysis method combining computational fluid dynamics and multibody system dynamics,and established the numerical model of colloidal damper and the dynamic model of entering the bore.Through calculation and analysis,some conclusions were obtained.

(1)The design scheme of differential colloidal fluid damper and cartridge lock can effectively buffer and limit the rebound movement of the test shell,and ensure the reliability of the action of closing the breechblock.This study provided a feasible reference scheme for the test shell entering the bore.

(2)The proposed simulation analysis method combining computational fluid dynamics(CFD)and multibody system dynamics(MBD)can accurately analyze and calculate various mechanical problems of the test shell with differential colloidal fluid damper.This study provided a reliable theoretical support for the design scheme.

(3)The CFD numerical analysis results show that when the colloidal fluid damper was impacted,its damping force curve did not change monotonously about the velocity.But as the compression velocity decreased,the damping force increased first and then decreased.During the compression process of the damper,the streamline was relatively stable,and no large vortex appeared.After the damper was restored,due to the elasticity of the colloidal fluid,the fluid will continue to pass through the gap of piston for a period of time before it stops.

Fig.19.Absolute velocity of the cartridge.

(4)This study only focused on the"gap type"colloidal damper,which had certain limitations.Further research can analyze and compare the dampers with different structural characteristics(such as"hole type"and"gap-hole type")and structural parameters(such as geometric and material).

Declaration of competing interest

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

Acknowledgments

This work was partially sponsored by Naval University of Engineering.