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1.Key Laboratory of Advanced Technology of Small and Medium?Sized UAV Ministry of Industry and Information Technology，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China；2.State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China；3.School of Aeronautic Engineering，Nanjing Vocational University of Industry Technology，Nanjing 210023，P.R.China；4.Key Laboratory of Fundamental Science for National Defense?Advanced Design Technology of Flight Vehicle，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China

Abstract: A new fluid bag buffer mechanism，which can provide large axial stiffness under the small displacement，is designed.The dynamic change laws of the mechanism stiffness and the internal pressure of the fluid bag are studied when it is subjected to impact load.According to the protection performance for the flexible joint and the pressure change in the fluid bag during the impact process，the sensitivity of the geometric parameters of the fluid bag to the axial stiffness is analyzed by using the orthogonal experimental method，and the optimal parameter combination of the geometric parameters of the fluid bag under impact is obtained，leading to the displacement of the inner shell reduce by 41.4%.The results show that the internal pressure of the fluid bag is a rising process of oscillation and fluctuation.The sensitivity of the geometric parameters of the fluid bag to the displacement of the inner shell from high to low is as follows：Height H，radius r，wall thickness t，chamfer A.The correlation between the geometric parameters of the fluid bag and its internal pressure is：H is negatively correlated with the internal pressure，while the r，t，and A are positively correlated with the internal pressure.

Key words：fluid bag buffer mechanism；flexible joint；axial stiffness characteristics；orthogonal experiment method；internal pressure of fluid bag

0 Introduction

With the continuous improvement of safety and reliability requirements of mechanical mechanism，different types of buffers are designed to prevent rig?id collision due to impact load，reduce vibration and noise，and improve the quality and life of mecha?nism.In this paper，a buffer which can withstand large impact load in a small displacement is studied.The fluid bag in the new buffer mechanism adopts nearly incompressible liquid，which can absorb a large amount of energy in small deformation and re?cover quickly.The flexible composite material is used in the contact part between the buffer fluid bag and the mechanism，which can fit the mechanism well under the impact load，so as to prevent the damage of the mechanism caused by stress concen?tration.

At present，there are few research on fluid bags with liquid as medium at home and abroad.However，the research on buffer airbags and air springs similar to buffer fluid bag is still deep.Simi?lar to the working principle of the fluid bag buffer，the buffer airbag and air spring charge gas into the flexible shell.Tutt et al.［1］introduced the test of a kind of space exploration vehicle’s falling impact on the ground，in which the buffer airbag was used for protection.Erin et al.［2］proposed a new modeling method for rubber airbags，which used linear spring，damper and hysteresis damper in parallel，and could approximately model the rubber airbag.Berg［3-4］adopted a new approximation method.When modeling the rubber airbag part of the air spring，the nonlinear characteristic model of the rub?ber airbag composed of linear elastic model，friction model and Maxwell model was used for modeling and analysis.Based on the theory of the elastic sup?port damping，Oda et al.［5］established the Nishimu?ra model.The new simulation model had a wider ap?plication range and could be used for simulation anal?ysis of air springs in wide frequency domain.Yuasa et al.［6］carried out simulation modeling and analysis on rubber airbags，studied its structure and mechani?cal characteristics，and optimized the design of air springs.Lee et al.［7-8］also simulated the diaphragm air spring，studied various mechanical properties of the rubber airbag，analyzed the influence of various factors on its mechanical characteristics，and studied the influence of initial filling pressure，cord and oth?er factors on the deformation of the air bag，as well as the mechanical characteristics of the air spring.Jeong et al.［9］used rebar，shell and Halpin tsal ele?ments to conduct finite element modeling of air springs，and studied the change of mechanical prop?erties of rubber airbags under the influence of differ?ent cord angles，and carried out experimental verifi?cation.Wong et al.［10］studied the mechanical charac?teristics of a new air spring，and studied the effects of various factors on its dynamic and static stiffness.Oman et al.［11］introduced the influence of piston geometric parameters of air springs on its load de?flection characteristics and fatigue life，considered two kinds of piston shapes，compared their load de?flection characteristics and fatigue life，predicted the fatigue life and the final failure time and global posi?tion of air springs，and compared the actual mea?sured results with the predicted results.Li et al.［12］proposed an improved finite element method，which could be used to solve the problem that the mechani?cal behavior of the air spring was controlled by the multi-directional thermodynamic process of the closed air.The results showed that the method was reliable and effective.Zhu et al.［13］established a gen?eralized analysis model to predict the amplitude and frequency dependent characteristics of the air spring，and established an accurate finite element simulation model of the air spring considering the thermodynamics of the pneumatic system of the bel?lows tank，the effective friction and viscoelastic damping of the bellows rubber.Heinrich et al.［14］compared the effects of two different cord setting methods on the local rubber matrix strain and stress of air springs，adopted a method that considered both the geometric shape of cord and the filament structure of cord，and analyzed the global model and sub model of cyclic symmetrical cross section includ?ing bellows.Li et al.［15］proposed and developed a hybrid vibration isolator composed of Maglev actua?tors and air springs.The performance of the hybrid isolator is experimented.The flexible gap protection technology and detachable mounting structure are used to improve the stability and adaptability of the hybrid vibration isolator in the marine environment.

To sum up，the research on air springs and buf?fer airbags at home and abroad mostly focuses on the influence of various materials and geometric pa?rameters of rubber airbags on the mechanism stiff?ness［16］.It is instructive to study the influence of geo?metric parameters of the buffer fluid bag on its me?chanical properties［17］.In this paper，taking a certain type of fluid bag buffer mechanism as the research object，the axial stiffness and internal pressure of the fluid bag in the working process are studied.Through the analysis and optimization of the buffer mechanism，the buffer performance of the buffer mechanism is improved and the safety of the fluid bag is enhanced.According to the change of axial stiffness and internal pressure of fluid bags during the impact process，the sensitivity of each geometric parameter of fluid bags to the change of axial stiff?ness is analyzed by the orthogonal experimental method，and the optimal parameter combination of each geometric parameter of fluid bags under impact is obtained.The safety performance and buffering performance of the fluid bag under the actual work?ing state are improved，which lays a foundation for the research of this new type of buffers.

1 Working Process Analysis of Flu?id Bag

1.1 Introduction of buffer mechanism of fluid bag

The buffer mechanism is mainly composed of two parts，one is the flexible joint，the other is the fluid bag.The mechanism is shown in Fig.1（a）.When the mechanism works，a large axial upward impact load is adopted at the bottom of the mecha?nism.

The flexible joint consists of a rubber layer and a metal layer，in which the metal plate and the rub?ber layer are bonded together.The material proper?ties of the flexible joint are as shown in Table 1.They should not have large axial static displace?ment；otherwise the flexible joint may fail and cause the mechanism failure.Therefore，it is necessary to use large stiffness buffer mechanism for axial protec?tion of the flexible joint.It is assumed that there is absolute adhesion between the elastic layer and the metal layer.The flexible joint is shown in Fig.1（b）.

Table 2 Material properties of model

Table 3 Mesh independence test

Fig.1 Fluid bag buffer mechanism

Table 1 Material properties of flexible joint

As shown in Fig.2（a），the fluid bag is a kind of conical ring flexible sealing container filled with approximately incompressible fluid.The real fluid bag is not connected in the ring direction，and the head end and tail end of the fluid bag have a closed ring，which is inserted with a hinge pin to lock the fluid bag in the mechanism［18-19］.The charging pipe is connected with the joint and the bottom of the flu?id bag to realize the charging of the fluid bag.The connector is connected to the liquid filling device at the same time.The pressure of the fluid bag can be adjusted to a predetermined value，and the fluid bag can be placed between the inner shell and the outer shell of the mechanism，which can greatly reduce the load transmitted to the flexible joint through the contact area between the inner shell and the outer shell.The simplified fluid bag model is shown in Fig.2（b）.

Fig.2 Fluid bag

1.2 Numerical method analysis of fluid bag

When the liquid reaches the static equilibrium state in the fluid bag，there is no tension and tangen?tial force between the liquid particles or between the liquid and the fluid bag，but there is only normal pressure，which is the hydrostatic pressure.In the fluid bag，the hydrostatic pressure has two impor?tant characteristics：Firstly，in the fluid bag，the ac?tion direction of the liquid pressure is vertical and points to the wall of the fluid bag.Secondly，when the liquid is still in the fluid bag，the hydrostatic pressure of any liquid particle is the same in all direc?tions.

The hydrostatic pressure acting on any point of the liquid in the fluid bag is the same in every direc?tion，which is independent of the normal direction of the pressure action surface，that is，independent of the shape of the fluid bag.Since the liquid in the flu?id bag is a continuous medium，its hydrostatic pres?sure is a continuous function related to the spatial co?ordinates.Therefore，it can be concluded that

A small parallelepiped is randomly selected from the liquid in the fluid bag.The sides of the six faces are dx，dy，and dz，respectively，and they are parallel to the three coordinate axes.Let the projec?tion of the unit mass force on the coordinate axis befx，fy，andfz.The components of the mass force inx，y，andzaxes areρfxdxdydz，ρfydxdydz，andρfzdxdydz，respectively，where the surface force is the hydrostatic pressure.Let the hydrostatic pres?sure at any point in the hexahedron bep，then the hydrostatic pressure at the center of the two surfaces parallel to thexaxis in the normal direction is divid?ed into

Because the hexahedron is a small hexahedron，the average hydrostatic pressure in the plane can be regarded as equal to the pressure at the central point.Therefore，the hydrostatic pressure of the flu?id on these two surfaces is

Since the sum of all the external force vectors acting on the hexahedron is 0，for thexaxis，it can be obtained that

After simplification，it can get the following re?sults

Similarly，the results can be obtained on theyandzaxes.Then，when the liquid in the fluid bag is in equilibrium，the differential equations are as fol?lows

According to the equation，when the liquid in the fluid bag is at rest，the change rate of the hydro?static pressure along any axis is equal to its unit mass force.

In the fluid bag，compared with the external force，the pressure change caused by the liquid mass force is negligible.Therefore，in Eq.（6），fx，fy，andfzcan be regarded as 0.Therefore，the follow?ing results are obtained

That is，the change rate of the hydrostatic pressure of the liquid in the fluid bag along any axis is 0.Combined with the second characteristic of the hy?drostatic pressure，it can be known that the pressure in the fluid bag is equal everywhere.

Finally，the finite element method is used to di?vide the fluid bag shell and liquid into fine meshes.Because the liquid pressure is equal everywhere，the pressure of each liquid unit is also the same，and the volume（density）of the liquid is related to tem?perature and pressure.Therefore，this paper will mesh a set of all liquid units，and set a reference point for this set，and assign the initial pressure and density of all liquid units on the reference point，so as to complete the real simulation of the fluid bag.

1.3 Establishment of finite element analysis model of fluid bag buffer mechanism

According to the structural characteristics of the fluid bag buffer mechanism，the mechanical anal?ysis model of the fluid bag buffer mechanism is es?tablished using ABAQUS.S4R mesh is used to de?fine the fluid bag，the inner shell and the outer shell.C3D8 mesh is used to define the flexible joint.It is assumed that the mass and temperature of the fluid in the bag remain unchanged during the process.The fluid chamber method is used to couple the liq?uid chamber and the fluid bag through the reference point.The fluid cavity method in ABAQUS can be used to calculate the liquid-structure interaction based on the surface defined fluid strength.When defining the fluid cavity，the properties of the filling in the fluid cavity can be defined by the reference point（RP），where the RP has coupling with the flu?id cavity.The real contact between the fluid bag and the inner shell and the outer shell is established with this method.Finally，the finite element model of the fluid bag buffer mechanism is completed，as shown in Fig.3.

Fig.3 Finite element model of mechanism

The filling material inside the fluid bag is wa?ter.The reason is that after the buffer task is com?pleted，the water in the fluid bag can be discharged to reduce the weight of the buffer mechanism.Set the properties of the water，the temperature is 20 ℃，and the density is 1.0e-06 kg/mm3.The material of the buffer mechanism is high strength steel.The fluid bag is made of composite materials.The relevant material properties are shown in Ta?ble 2.

In the actual working process of the fluid bag buffer mechanism，it will be subjected to strong im?pact load.Typical external input curve is shown in Fig.4（a）.The load is applied to the bottom of the mechanism in a short time，and then gradually de?creases.Therefore，the concentrated load is set to act on the bottom of the inner shell，and the load acts on the load coupling reference node in the mod?el，so that the load is distributed on the bottom sur?face of the inner shell，as shown in Fig.4（b）.The initial pressure of the fluid bag is 2.5 MPa，and the impact load on the bottom of the inner shell is 300 kN.Before the impact load，the fluid bag is pressurized to 2.5 MPa.Then，the inner shell is re?leased and the impact load is used.The impact load increases from 0 N to 300 kN in 0.1—0.5 s，and then decreases gradually.

Fig.4 Impact load case

Mesh independence test is an important task of finite element analysis（FEA）.The mesh indepen?dence test is analyzed.Considering the accuracy and time，10 mm mesh size is chosen，as shown in Ta?ble 3.

1.4 Simulation result analysis and experimen?tal verification

After the simulation model of the fluid bag buf?fer mechanism is established，the mechanical charac?teristics of the fluid bag buffer mechanism are ana?lyzed.The stress map of the fluid bag can be ob?tained，as shown in Fig.5.It can be seen from the figure that under the action of load，the inner shell moves upward along the axis，the fluid bag deforms with the axial displacement of the inner shell，and the stress map is evenly distributed in the circumfer?ential direction.On the surface of the fluid bag，the stress is concentrated in the lower part of the inner side of the fluid bag and the upper part of the outer side of the fluid bag.The maximum stress is located in the top part of the outside of the fluid bag.

Fig.5 Stress map of fluid bag when maximum load

The dynamic stress map within 0—1.1 s after the impact load is applied is shown in Fig.6.The re?sults show that during the dynamic deformation pro?cess，the stress map is evenly distributed in the cir?cumferential direction，and the stress is larger in the lower and upper parts of the fluid bag.During the loading process of impact load，the stress of the flu?id bag increases gradually and reaches the peak val?ue about 0.5 s，and then the stress on the fluid bag decreases.

Fig.6 Stress map of fluid bag dynamic process

Fig.7 is the stress curve of the element with the maximum stress value in the fluid bag from 0 s to 1.1 s.The results show that in the initial stage of 0—0.1 s，the process is the filling stage of the fluid bag.When the pressure of the fluid bag increases from 0 MPa to 2.5 MPa，the element stress will rap?idly increase to a fixed value；in the stage of 0.1—0.3 s，due to the existence of initial pressure of 2.5 MPa，the stress is in dynamic oscillation state at this stage with the increase of load，and the stress does not increase significantly；at the stage of 0.3—0.5 s，the stress of the element increases with the in?crease of load，at 0.5 s，the stress and load reach the maximum value at the same time；at the stage of 0.5—1.1 s，the load begins to decrease，and the stress of the element also begins to decrease；at 1.1 s，the load becomes half of the maximum value，and the stress value of the element returns to the same value as that of the oscillation stage.

Fig.7 Stress curve of maximum stress element

Fig.8 is the axial displacement map of the fluid bag.It can be seen that under the action of load，the inner shell moves upward along the axial direction，and the fluid bag deforms with the axial displace?ment of the inner shell，and the displacement map is evenly distributed in the circumferential direction.On the surface of the fluid bag，the position of the maximum absolute displacement is located in the blue part outside the fluid bag.The displacement at this position is due to the existence of the fluid bag initial filling pressure of 2.5 MPa.When the fluid bag is squeezed，the downward displacement oc?curs；at the same time，the positive axial displace?ment of the red part on the inner surface of the fluid bag is the largest，which is caused by the upward impact of the load.The minimum displacement is lo?cated at the green position of the top and bottom of the fluid bag，and the displacement at this position is almost zero，that is，there is no change in the dis?placement.It shows that the fluid bag has a strong resistance to deformation.

Fig.8 Axial displacement map of fluid bag with maximum load

As shown in Fig.9，it is the displacement curve of the inner shell from 0 s to 1.1 s，which represents the axial stiffness performance of the liquid bag.The results show that in the initial stage of 0—0.1 s，the pressure of the fluid bag increases from 0 MPa to 2.5 MPa，and the displacement of the in?ner shell oscillates around 0.5 mm；at the stage of 0.1—0.5 s，the load begins to be loaded.With the increase of load，the displacement of the inner shell gradually increases and reaches its maximum posi?tion；in the stage of 0.5—1.1 s，it can be seen from Fig.4 that with the decrease of load，the displace?ment of the inner shell begins to decrease and re?turns to the initial position.It can be seen that it has a great axial stiffness characteristic，the inner shell axial only changing about 1.6 mm，indicating that it has excellent buffering characteristics against large impact force.

Fig.9 Displacement curve of inner shell

Fig.10 is the experimental and simulation curves of the internal pressure of the fluid bag under the dynamic impact load.The experimental data are obtained from the experiment completed in the labo?ratory by Zhang et al.［20］Compared with the experi?mental data and simulation data，it can be seen that the initial filling pressure of the fluid bag is 2.5 MPa.At 0.1 s，the internal pressure of the fluid bag tends to oscillate and increase gradually，and the oscillation amplitude gradually decreases.At 0.5 s，the load reaches the maximum value，and the internal pressure of the fluid bag reaches the maxi?mum value，and then gradually decreases.It can be seen that the overall trend of the simulation result is close to the experimental result，and the agreement is good in the initial step-up stage.It proves the ac?curacy of the model.

Fig.10 Internal pressure curves of fluid bag during dynamic loading

2 Optimization of Geometric Pa?rameters for Axial Stiffness of Fluid Bag Buffer Mechanism

The displacement of the inner shell represents the axial stiffness of the new fluid bag buffer mecha?nism.Greater the axial stiffness，better the protec?tion of the flexible joint.It can be seen from the anal?ysis results in Section 1.4 that the inner shell is dis?placed after loading，and the internal pressure of the fluid bag increases correspondingly.In order to study the variation law of the inner shell displace?ment and the internal pressure of the fluid bag，the influence and sensitivity of the geometric parameters of the fluid bag on the displacement of the inner shell are analyzed by orthogonal experiments.

2.1 Orthogonal experiment design

Orthogonal experiment method is an experi?mental design method that uses orthogonal table to select representative combinations from all experi?mental combinations，and process and analyze these experimental data to obtain the most appropriate combination.

In this paper，the influence of geometry param?eters of the fluid bag on the displacement of the in?ner shell is studied.Through the analysis of the fluid bag structure and the previous engineering practice experience，we know that there are four main geo?metric design parameters of the fluid bag，which are the heightH，the radiusr，the chamferAand the shell thicknesstof the fluid bag，as shown in Fig.11 and Table 4.

Fig.11 Geometric parameters of fluid bag

Table 4 Initial geometric parameters of fluid bag

TakingH，r，Aandtas experimental factors，an orthogonal experimental design with 4 factors and 5 levels can be obtained，as shown in Table 5.

Table 5 Orthogonal experimental design of fluid bag

2.2 Orthogonal experiment result

According to the experimental scheme shown in Table 5，the total number of experiments with 4 factors and 5 levels is 54 groups，which is very large and cannot be tested one by one in production prac?tice and scientific research.However，with the method of orthogonal experimental method，only 25 groups of experiments are needed to obtain the opti?mal combination scheme.Secondary development of ABAQUS，which uses Python，is used to quick?ly modify the relevant parameters of the model.The results of mechanical analysis of the model are shown in Table 6.

According to the analysis results in Table 6，the mean，range and variance of experimental re?sults corresponding to each level of geometric pa?rameters of the fluid bag are calculated，and then the orthogonal experimental analysis table can be ob?tained，as shown in Table 7.

Table 6 Orthogonal experiment results of fluid bag

Table 7 Orthogonal experiment analysis of fluid bag

T1，T2，T3，T4andT5in the table represent the average displacement of the inner shell under each level of each factor.The influence of the horizontal variation of each factor on the axial stiffness is re?flected by the rangerunder each level of the same factor.The significant difference of the axial stiff?ness caused by the level change of each factor is evaluated by the varianceSunder each level of the same factor.The larger the rangerand varianceSare，the greater the influence of the horizontal varia?tion of the geometric parameter on the axial stiff?ness，the more significant and the higher the sensi?tivity.

According to Table 7，the results of range anal?ysis and variance analysis are consistent.The sensi?tivity of the geometric parameters of the fluid bag to the displacement of the inner shell from high to low is：H，r，t，andA.The influence curves of geomet?ric parameters of fluid bag are as shown in Fig.12.

Fig.12 Influence curves of geometric parameters of fluid bag

To sum up，the optimal scheme can be ob?tained，as shown in Table 8.

Table 8 Geometric parameters after optimization of flu?id bag

2.3 Analysis of optimized results

According to the above optimal parameters，the optimization model of the fluid bag buffer mech?anism is established.The same method is used to simulate the fluid bag，and the stress map of the optimized fluid bag is obtained，as shown in Figs.13—14.By comparing with the stress map be?fore optimization，it can be known that their com?mon characteristics are：The axial distribution is uni?form，and the stress changes smoothly in the dy?namic process.The difference between them is that the stress concentration area at the top disappears，the maximum stress position is located at the exter?nal chamfer of the bottom，and the stress of the whole bottom increases.

Fig.13 Stress map of fluid bag at maximum load after opti?mization

Fig.14 Stress map of dynamic process of optimized fluid bag

The optimized displacement map is shown in Fig.15.Compared with the displacement map be?fore optimization，it can be known that their com?mon characteristics is that the axial displacement dis?tribution in the whole deformation process is uni?form；their difference is that the axial displacement of the fluid bag is all vertical downward，and the po?sition of the maximum displacement is at the bottom of the fluid bag.

Fig.15 Axial displacement map of fluid bag at maximum load after optimization

Fig.16 is the inter shell displacement and inter?nal pressure curves of the fluid bag before and after optimization under the dynamic impact load.Com?paring the curves before and after optimization，it can be known that their common characteristics is：The internal pressure of the fluid bag shows an in?creasing trend of oscillation，and the amplitude of oscillation decreases with the increase of load.The displacement curve of the inner shell oscillates at a fixed value when the initial pressure is used.After the inter shell is subjected to impact load，the dis?placement curve begins to increase.At 0.5 s，the load value reaches the maximum value，and then the internal pressure of the fluid bag and the dis?placement of the inner shell reaches the maximum value，and then gradually decreases.Their differenc?es are as follows：The maximum pressure in the flu?id bag is reduced from 3.4 MPa to 3.0 MPa，and the pressure is reduced by 13.3%；the maximum dis?placement of the inner shell is reduced from 1.62 mm to 0.95 mm，and the displacement is re?duced by 41.4%.

Fig.16 Comparison of buffer performance curves before and after optimization

3 Influence of Geometric Parame?ters of Fluid Bag on Its Internal Pressure

The sensitivity ofr，t，AandHto the axial stiffness of the buffer mechanism is obtained by anal?ysis.At the same time，the geometric parameters al?so affect the internal pressure of the bag.Therefore，the internal pressure changes of the fluid bag under different working conditions are analyzed.

3.1 Influence of height on internal pressure of fluid bag

When the initial filling pressure is 1.5，2.5，and 3.5 MPa，respectively，and the load is 300 kN，the internal pressure of the fluid bag at different heights is calculated，as shown in Fig.17（a）.It can be seen from the figure that the internal pressure of the fluid bag decreases with the increase of height when the initial filling pressure is the same.When the initial filling pressure is different，the change trend of inter?nal pressure is basically the same at different heights，and the change curves are basically parallel.

Fig.17 Different initial filling pressure and load on internal pressure at different heights

When the initial filling pressure is 2.5 MPa and the loads are 100，300，and 500 kN，respectively，the internal pressure of the fluid bag at different heights is calculated，as shown in Fig.17（b）；it can be seen from the figure that the internal pressure of the fluid bag decreases with the increase of height when the load is the same.When the load is differ?ent，the change trend of the internal pressure at dif?ferent heights is basically the same.When the load is different，the change trend of internal pressure at different heights is basically the same.When the height is small，the difference is large，and when the height is large，the difference is small.There?fore，when the height of the fluid bag is large，the influence of load on internal pressure can be re?duced.The increase of the height of the fluid bag will increase the volume of the fluid bag，so the con?tact area between the liquid bag and the inner and outer shells will also increase.The increase of con?tact area leads to the increase of the overall stiffness of the mechanism.When the same load is added，the smaller the deformation of the mechanism，the smaller the internal pressure change of the fluid bag.

3.2 Influence of radius on internal pressure of fluid bag

When the initial filling pressure is 1.5，2.5，and 3.5 MPa，respectively，and the load is 300 kN，the internal pressure of the fluid bag at different radi?us is calculated，as shown in Fig.18（a）.It can be seen from the figure that when the initial filling pres?sure is the same，the internal pressure of the fluid bag increases with the increase of the radius.When the initial filling pressure is different，the change trend of internal pressure is basically the same at dif?ferent radii，and the change curves are basically par?allel.

When the initial filling pressure is 2.5 MPa and the loads are 100，300，and 500 kN，respectively，the internal pressure of the fluid bag at different radii is calculated，as shown in Fig.18（b）；it can be seen from the figure that when the load is the same，with the increase of the radius，the internal pressure force of the fluid bag increases.When the load is differ?ent，the change trend of internal pressure is basical?ly the same at different radii.The difference of the variation curve is smaller when the radius is small，and the difference is larger when the radius is larger.With the increase of the radius of the fluid bag，the volume of the fluid bag will also increase，which leads to the increase of the overall stiffness of the mechanism.Due to the obvious change of stiffness，there is an obvious difference in the change value of internal pressure.

Fig.18 Different initial filling pressure and load on internal pressure at different radii

3.3 Influence of shell thickness on internal pressure of fluid bag

When the initial filling pressure is 1.5，2.5，and 3.5 MPa，respectively，and the load is 300 kN，the internal pressure of the fluid bag under different shell thicknesses is calculated，as shown in Fig.19（a）；it can be seen from the figure that，with the increase of shell thickness，the internal pressure of the fluid bag increases first and then tends to be constant.When the initial filling pressure is differ?ent，the change trend of internal pressure is basical?ly the same with different shell thicknesses，and the change curves are basically parallel.

When the initial filling pressure is 2.5 MPa，and the loads are 100，300，and 500 kN，respective?ly，the internal pressure of the fluid bag under differ?ent shell thicknesses is calculated，as shown in Fig.19（b）；it can be seen from the figure that，with the increase of the shell thickness，the internal pres?sure force of the fluid bag first increases and then tends to be constant.When the load is different，the change trend of internal pressure at different shell thicknesses is basically the same.The difference of variation curves is smaller when the shell thickness is small，and the difference is larger when the shell thickness is larger.Therefore，when the shell thick?ness of the fluid bag is small，the influence of load on internal pressure can be reduced.

Fig.19 Different initial filling pressure and load on internal pressure at different shell thicknesses

3.4 Influence of chamfer on internal pressure of fluid bag

When the initial filling pressure is 1.5，2.5，and 3.5 MPa，respectively，and the load is 300 kN，the internal pressure of the fluid bag under different chamfers is calculated，as shown in Fig.20（a）；it can be seen from the figure that the internal pressure of the fluid bag increases slightly with the increase of the chamfer when the initial filling pressure is the same.When the initial filling pressure is different，the change trend of internal pressure in different chamfers is basically the same，and the change curves are basically parallel.

Fig.20 Different initial filling pressure and load on internal pressure at different chamfers

When the initial filling pressure is 2.5 MPa and the loads are 100，300，and 500 kN，respectively，the internal pressure of the fluid bag under different chamfer conditions is calculated，as shown in Fig.20（b）；it can be seen from the figure that when the load is the same，with the increase of the chamfer，the internal pressure of the fluid bag increases slight?ly.When the load is different，the change trend of internal pressure in different chamfers is basically the same.The difference of variation curves is small?er when the chamfer is small，and the difference is larger when the chamfer is larger.Therefore，when the chamfer of the fluid bag is small，the influence of load on internal pressure can be reduced.Howev?er，the chamfer of the fluid bag has little effect on the internal pressure overall，so the proper chamfer can be selected according to the actual situation.

To sum up，it can be seen from Figs.17—20 that ther，tandAare positively proportional to the internal pressure of the fluid bag；and theHis in?versely proportional to the internal pressure of the fluid bag.

4 Conclusions

The mechanical characteristics of the new fluid bag buffer mechanism is analyzed and optimized.The sensitivity of the four geometric parameters（r，t，AandH）of the fluid bag is studied by orthogonal experiment method；in order to reduce the displace?ment of the inner shell，which can enhance the pro?tection effect for the flexible joint，the structure of the buffer mechanism is optimized.Meanwhile，the relevant optimization parameters are obtained.Then，the influence of each parameter on the inter?nal pressure of the fluid bag is analyzed.Finally，the following conclusions can be drawn：

（1）When the fluid bag is impacted，its internal pressure is a rising process of oscillation and fluctua?tion，and when the impact load reaches the maxi?mum value，its internal pressure reaches the maxi?mum value at the same time.

（2）After optimization，the displacement of the inner shell is reduced by 41.4%，which enhances the protection for the flexible joint；the added value of the internal pressure of the fluid bag is reduced by 13.3%，which enhances the safety of the fluid bag.

（3）According to the results of the orthogonal experiment，the sensitivity of the geometric parame?ters of the fluid bag to the displacement of the inner shell from high to low is：H，r，t，A.

（4）Through the analysis，it can be known that the correlation between the geometric parameters of the fluid bag and its internal pressure is：Hhas a negative correlation with the internal pressure，whiler，t，andAare positively correlated with the internal pressure.